study on impact of turbine location on hydrodynamics in...

Research ArticleStudy on Impact of Turbine Location on Hydrodynamics inTidal Farm

Hongqiang Zhang 1 Daming Li 1 Yanqing Li1 Ting Yang2 Shan Luo1

Shunfa Tian1 and Shilong Bu1

1State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University Tianjin 300072 China2Tianjin Port amp Channel Engineering Co Ltd Tianjin 300457 China

Correspondence should be addressed to Daming Li lidamingtjueducn

Received 30 March 2018 Accepted 15 November 2018 Published 9 January 2019

Academic Editor Luisa Di Paola

Copyright copy 2019 Hongqiang Zhang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This work aims at investigating the impact of different tidal turbine locations on hydrodynamics in near-field and far-field flowthus three- and two-dimensional (3- amp 2-D) models were exploited in combination and applied in a case study of Putuo-HuluIslandsrsquo tidal farm We present a method for the simplification of tidal turbine which based on the energy equation determinesturbinersquos equivalent roughness by calculating resistance loss in flow passage A 3-D turbine model of near-field flow in the frame ofComputational Fluid Dynamics was constructed and the flow velocity distributions in 7 combinations of ldquoimpeller rotating speed- inflow velocityrdquo were simulated Also a 2-D tidal model of far-field flow was established and Finite Element Method was adoptedto solve the 2-D shallow water circulation equations thus the impact of tidal turbine could be simulated by utilizing differentlocationrsquos compositive roughnessThe results show that the impact of turbine location on hydrodynamics is depending on the opendegree of sea area channel trend and bathymetric and geographic features and that the farther distance from the turbine the lessimpact on the flow field Overall the impact of turbine location on far-field flow is not significant and the flow velocity varies below8 relative to the velocity prior to turbine installation

1 Introduction

Tidal current power is a green and renewable energy and theprospect of its development is considerable Many countrieswith abundant marine resources are promoting the researchon tidal current power generation technology and buildingup test field of tidal current generation

In near-field hydrodynamic study of tidal turbine BetzrsquoLaw and Blade Element Momentum (BEM) theory wereadopted to generalize the turbine Bai et al [1] calculatedthe eddy effect of the tidal turbine by Computational FluidDynamics (CFD) method based on Betzrsquo Law OrsquoDoherty etal [2] simulated the effect of tidal turbine on hydrodynamiccharacteristics of flow field under different arrangementmodes

In far-field hydrodynamic study of tidal turbine momen-tum method was used to generalize tidal turbine that is toadd resistance loss item of turbine to the dynamic control

equation Couch and Bryden [3] added the bottom frictioncoefficient to a one-dimensional (1-D) model to simulate theeffects of tidal turbine Bluden and Bahaj [4 5] added thebottom friction coefficient in the model and utilized it tosimulate the array of tidal turbine the results showed that theeffect of array on initial flow rate is about 5 to 10 Brydenand Couch [6] established a 1-D model to study the potentialimpact of tidal current development on the local tidal currentfield under steady conditions Karsten et al [7] constructed atwo-dimensional (2-D) model to study the tidal current fieldof Fendi Bay by increasing the bottom friction Myers andBahaj [8] replaced turbines with perforated discs and studiesshowed that the test method is feasible Georgenes et al[9] investigated the relationship between tidal distortion andsalinity by utilizing classical methods of comparison of threecross-channel circulation characteristics Gaurav and Tate[10] applied the adaptive hydraulics numerical code to studytidal propagation in Lower Columbia River estuary Jeyar et

HindawiDiscrete Dynamics in Nature and SocietyVolume 2019 Article ID 7983907 21 pageshttpsdoiorg10115520197983907

2 Discrete Dynamics in Nature and Society

al investigated the hydrodynamic impacts of whole lagoondue to tidal waves using a 2-D depth-averaged hydrodynamicmodel based on the shallow water equations Gillibrand et al[11] adopted a three-dimensional (3-D) hydrodynamicmodelto consider the potential effects of energy extraction by anarray of tidal turbines on ambient near-bed velocity field andlocal bed shear stress Yamamoto et al [12] exploited ANSYSto select the best shape of oscillator in order to efficientlyharness the tidal flow energy in a cost-efficient manner

Although the study of tidal current power started late inChina the scientists also made some new breakthroughs inthe research and development of energy-harvesting deviceand the study of flow field also has a lot of achievementsFor example Xin et al [13] predicted the hydrodynamiccharacteristics of double rotor turbines arranged in seriesAn [14] made the 3-D steady-state numerical simulation ofthe horizontal axis turbine by CFD method and mutualeffect rule between devices under different arrangementconditions was obtained Yuan [15] utilized a perforated discto simulate the tidal turbine by increasing drag coefficientto replace device group Hou [16] exploited Finite VolumeCommunity Ocean Model to simulate the effect of tidalturbine on 2-Dhydrodynamic environment Li [17] usedCFDmethod to study reasonable arrangement distance of the arrayof horizontal axis tidal turbine Ma [18] established blademodel according to BEM drawing on the experience of windenergy generation and applied CFD method in studying thehydrodynamic characteristics of the impellers under differentworking conditions Ding et al [19] found local surge currentvelocity in each depth with a magnitude of the same order asastronomic tidal currents

At home and abroad studies on the effect of tidalturbine on hydrodynamic characteristics of large-scale far-fields which are combined with the integrated simulationof near-field hydrodynamic characteristics of turbine arefew especially in the aspects of turbine simplification andbottom friction determination But in the previous stud-ies generalized bottom frictions were fixed values and didnot change with the variation of flow velocity Due tothe large subjectivity of the existing research methods andthe poor adaptability of the simplification method underdifferent working conditions the research methods couldbe developed in the direction of ldquonear-field amp far-fieldrdquointegrated simulation Therefore in order to clarify theeffect on flow field because of turbine installation and thenrationally arrange the berthages of tidal turbine in test fieldldquoPutuo-Hulu Islands Tidal Power Demonstration Projectrdquoin Zhoushan City China was regarded as the study objectFirstly we constructed a 3-D turbine model of near-fieldflow in the frame of CFD and simulated the flow velocitydistributions in 7 combinations of ldquoimpeller rotating speed -inflow velocityrdquo Next we presented a simplification methodof tidal turbine based on the energy equation to determineturbinersquos equivalent roughness by calculating resistance lossin flow passage Then we established a 2-D tidal model offar-field flow and applied Finite Element Method (FEM) insolving the 2-D shallow water circulation equations Finallythe impact of tidal location on hydrodynamics could be sim-ulated by utilizing different locationrsquos compositive roughness

Figure 1 Geographical location of tidal farm

We combined 3-D turbine model and 2-D tidal model andsimulated and analyzed the impact of turbine location onnear-field and far-field hydrodynamics in tidal farm

2 Study Area

21 Tidal Farm Introduction The site of project is locatedin the channel between Putuo Island and Hulu Island inZhoushan City China and the geographical location of thetidal farm is shown in Figure 1 The channel is about 66 kmlong and 16 km wide and the water depth is about 20mto 80m (1985 National Elevation Benchmark) The offshoretopography on both sides of channel is steeper and the centralsite is relatively flat

Putuo Island and Hulu Island lie in a sea area whereislands are numerous and water depth changes complexlyIn the sea area the tidal current is characterized by theirregular semidiurnal tide the fluctuation of tidal current isobviously affected by topography and shallow sea effect isobvious Velocity of tidal current between islands is relativelylarge the mainly flow pattern is reciprocating flow andthe direction is roughly parallel to the channel Meanwhilethe direction of tidal current is basically consistent withthe tidal wave propagation [20] In the channel the tidalcurrent is reciprocating flow along NW-SE direction thevertical average velocity is about 067ms to 081ms andthe maximum velocity of tidal current on surface is 229msThe channel is a sub-rich area of tidal current resources andunder the cover of Hulu Island the extreme sea conditions ofopen sea have little effect on channel

22 Tidal Turbine Location Based on the compositive anal-ysis of the bathymetric data engineering geology and tidalcurrent resource conditions in this sea area combining withthe existingmeasured data it is proposed to set themeasuringpoints B1 to B5 as the berthages of the tidal turbine The tidalturbine location in tidal farm is shown in Figure 2 The whiteparts in Figure 2 represent the islands or land (ie correspondto Putuo Island and Hulu Island in Figure 1) and the restrepresents the sea area Figure 2 is an enlarged view of thered frame of Figure 1

Discrete Dynamics in Nature and Society 3

(km)

(km)

Bathymetry (m)Above 0-8 - 0-16 - -8-24 - -16-32 - -24-40 - -32

-48 - -40-56 - -48-64 - -56Below -64Undefined Value

N

W

S

E

Figure 2 Tidal turbine location

3 Methodology

31 Establishment of 3-D Near-Field Hydrodynamic Model

311 Turbine Model and Grids Generation There are twodifferent carrier forms of tidal turbine with horizontal axisvariable pitch and double impellers One is for column typewith single pile that is the structure is supported by a singlepile and the impeller can be up and down according to thework needs The other is for floating the unit is supportedby the floating platform and the entire device is fixed byfour anchor chains Both the two carrier forms are doubleimpellers with a rotary diameter (1198630) of 163m and theequivalent diameter (119863119864 = radic21198630) [21] of an impeller is about23m

The role of the carrier is ignored in the 3- and 2-D numer-ical simulation and only the effect of the double impellerson the flow field is considered The rotation direction of theimpellers is opposite the spacing between impellers is 3mand the hub diameter is 01 1198630 Then the 3-D modelingsoftware is used to simplify and establish the model of doubleimpellers The turbine model is shown in Figure 3

According to the calculation needs a cylinder flow fieldis designed as shown in Figure 4(a) The length of the flowfield is 300m (X direction) the diameter is 100m (Y andZ direction) the longitudinal axis is parallel to the inflowdirection and the center of the double impellers is locatedin the longitudinal axis which is away from the upstreaminlet 60m and 240m from the downstream outlet This 3-D region is divided by unstructured tetrahedral mesh inwhich the green parts represent the rotating domains of

(m)X

Y

Z

Figure 3 3-D turbine model

impellers and other parts are the nonrotating domains asshown in Figure 4(b) The grids of rotating domains wherethe impellers are located are refined and the grids far awayfrom the impellers are sparse The maximum grid size on thesurface of the impellers (ie nearby the walls) is 002m themaximum grid size of the rotating domains is 01m and themaximum grid size of the nonrotating domains is 06m Andthen a total of 3489648 grids are generated

The density of grids in the range of 240m from rotatingdomain to nonrotating domain in the cylinder flow fielddecreases gradually and the maximum size of the gridsincreases from 01m to 06m Moreover there is no too largeor too small size mutation All these conform to the require-ments of renormalization group (RNG) k-120576 turbulencemodelfor the calculating grids In the simulation of Fluent thecalculation equations of RNG k-120576 turbulence model are asfollows120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894) = 120597120597119909119895 (120572119896120583119890119891119891 120597119896120597119909119895) + 119866119896 + 119866119887

minus 120588120576 minus 119884119872 + 119878119896(1)

120597120597119905 (120588120576) + 120597120597119909119894 (120588120576119906119894) = 120597120597119909119895 (120572120576120583119890119891119891 120597120576120597119909119895)+ 1198621120576 120576119896 (119866119896 + 1198623120576119866119887)minus 11986221205761205881205762119896 minus 119877120576 + 119878120576

(2)

where 119896 is turbulence kinetic energy 120576 is energy dissipatingrate 119909119894 is spatial scale 119906119894 is flow velocity 120572119896 and 120572120576 arethe Prandtl numbersrsquo reciprocals of effective turbulent of 119896and 120576 respectively 120583119890119891119891 is viscosity of effective vortex 119866119896is turbulence kinetic energy generated by average velocitygradient119866119887 is turbulence kinetic energy generated by flotage119884119872 is influence of turbulent pulsation expansion on overalldissipating rate and 119878119896 and 119878120576 are user-defined source items

This paper selects 3 points which are away from theimpeller surface 50m 100m and 150m on the axis ofimpeller in Condition 1 (inflow velocity is 1843ms) and thethree points are recorded as Point 1 2 and 3 respectivelyThechanges of velocity of the 3 points under different numbers ofgrids are shown in Figure 5


inlet

60m240m

outlet100m

XYZ

(a) (b)

Figure 4 Computational domain and grids (a) schematic of computational domain and (b) 3-D grids

Point 1Point 2Point 3

00

04

08

12

16

Velo

city

(ms

)

1 2 3 40Grid Numbers (million)

Figure 5 Variations in velocity with grid numbers

From Figure 5 it is known that when the grid numberis greater than 3 million the variations of velocity of the3 points are very small with the increase of grid numberthus indicating that the grid number has little effect onthe simulation results Therefore when the grid number ishigher than 3 million the simulation results almost do notchange with the variations of the grid number and results areundoubtedly convergent So the grid density has little effecton the simulation results that is the grid number is almostindependent of the simulation results

312 Relationship between Impellerrsquos Rotating Speed andInflow Velocity Since the turbine model in this paper isconstructed by imitating the shape of SeaGen impeller of tidalturbine its radius 119903 = 8m rated flow velocity V119903 = 225msand rated revolving speed of turbine 119899119903 = 143 radminFrom those we could obtain that the rated angular speed120596119903 = 2120587119899119903 = 15 rads and the design tip speed ratio 120582 =119903120596119903V119903 = 53 Therefore the design tip speed ratio of impeller120582 is taken as 53 to establish the corresponding relationshipbetween the impellerrsquos rotating speed and the inflow velocityas shown in Table 1

313 Solver Setting The CFD software Fluent is applied innumerical simulation and the specific setting of the CFDsolver is as follows

(1) Select the 3-D single-precision solver(2) Select the pressure-based correction method andselect the steady state for the time type(3) Select RNG k-120576 turbulence model and MultipleReference Frame (MRF) model(4)The inflow velocity of the velocity-inlet is V119894 becausethe outlet velocity or pressure cannot be known before theproblem is solved Free outflow is used at the outlet boundarythe side wall is a stationary wall and the impellers aremovingwalls(5) 1000 iterations each time step

32 Turbine Simplification For the flow passage where theturbine is located the flux of any flow section of this flowpassage is equal when it is assumed that there is no flow cross-ing According to the continuity equation the acreage of flowsections of the downstream flow passage will be greater thanthe upstream because the flow velocity of the downstream ofthe turbine will decrease as shown in Figure 6

The turbine causes partial energy loss of the water flow itcan be expressed by the frictional resistance loss ℎ119891 betweenflow sections along upstream to downstream of the flowpassage and the corresponding equivalent roughness 119899119864 isobtained then the roughness 119899 can be obtained by combiningthe original natural roughness 1198990 of the grid so as torealize the simplification of the effect of the turbine on thehydrodynamic force that is the local roughness correctionmethod

The cross section of the impeller is taken as the referenceplane two flow sections are taken in the upstream L1 anddownstream L2 respectively and the water body surroundedby the two flow sections and the side wall of the flow tubeis studied It is assumed that the average flow velocity of theflow section 1-1 at a certain time is V1 the pressure is 1199011 andthe average flow velocity of the flow section 2-2 is V2 thepressure is 1199012 The energy equation of the constant pipe flowof incompressible fluid is established as shown in (3) andonly the resistance loss along the path is considered In (3)1205721 = 1205722 = 1 and 1199111 = 1199112 = 0 because the central axis isregarded as the datum plane

1199111 + 1199011120588119892 + 1205721V212119892 = 1199112 + 1199012120588119892 + 1205722V

222119892 + ℎ1198911minus2 (3)


Table1Re

lationshipbetweenim

pellerrsquos

rotatin

gspeedandinflo

wvelocity

Inflo

wVe

locity

(ms)

Parameter

sIm

pelle

rRotatin

gPo

sition

perS

econ

dRe

latio

nshi

pSchematicbetw

een

Impelle

rrsquosRo

tatin

gSp

eedAng

ular

Speedan

dIn

flowVe

locity

Ang

ular

Speed

(rad

s)

Rotatin

gSp

eed

(rm

in)

00

05

10

15

20

25

30

Inflow Velocity (ms)

48

1216

200

Rota

ting

Spee

d (r

min

)

00

05

10

15

20

25

30


04

08

12

16

20

00

Ang

ular

Spe

ed (r

ads

)

0614

04

382

0921

06

573

1229

08

764

1536

1095

5

1843

121146

2150

141337

2457

161528


p1v1

1

1

p2v2

2

2

L1

L2

L

Figure 6 Flow passage parameters

And then (3) can be written as (4)

ℎ1198911minus2 = 1199011 minus 1199012120588119892 + V21 minus V222119892 (4)

According to Darcy Formula ℎ1198911minus2 can be expressed as

ℎ1198911minus2 = 120582 1198714119877 V212119892 (5)

The approximate relationship between the resistancecoefficient (120582) and the Chezy Coefficient (119862) is shown as

120582 = 81198921198622 (6)

The relationship between 119862 and 119899119864 is obtained by theManning Formula as shown in the following

119862 = 111989911986411987716 (7)

The equivalent roughness (119899119864) of tidal current powergeneration equipment is obtained by synthesizing (3) to (7)as shown in

119899119864 = radic ℎ1198911minus211987743119871V21 = radic(1199011 minus 1199012120588119892 + V21 minus V222119892 ) 11987743119871V21 (8)

The wall shear stress formula is shown as

120591 = 120588119892119877119869 = 120588119892 V21198622 = 1205881198921198992V211987716 (9)

The shear stress 120591 of the seabed is considered to becomposed of two parts One is the equivalent shear stress Δ120591produced by turbinersquos layout the corresponding equivalentroughness is 119899119864 and the flow velocity is V2 The other one isthe shear stress of the sea itself 1205910 when the flow velocity is V2and the corresponding roughness of seabed is 1198990 According

to the superposition principle the shear stress of the seabedcan be expressed as

120591 = 1205910 + Δ120591 = 120588119892119877119869 = 12058811989211989920V2211987716 + 1205881198921198992119864V2211987716 = 120588119892119899

2V2211987716 (10)

The compositive roughness of the turbine after it is placedis as shown in

119899 = radic11989920 + 1198992119864 (11)

33 Establishment of 2-D Far-Field Hydrodynamic Model

331 Finite Element Discretization of Governing EquationThe 3-D N-S equation is integrated along the depth direction(Z direction) to obtain the 2-D shallow water circulationequation which is used as the governing equation Mean-while the role of wind is ignored as shown in the following

120597z120597119905 + 120597 (119906ℎ)120597119909 + 120597 (Vℎ)120597119910 = 0 (12)

120597119906120597119905 + 119906120597119906120597119909 + V120597119906120597119910 + 119892120597119911120597119909 = minus119892radic1199062 + V21198622ℎ 119906 + 119891V +119872119909 (13)

120597V120597119905 + 119906 120597V120597119909 + V120597V120597119910 + 119892120597119911120597119910 = minus119892radic1199062 + V21198622ℎ V minus 119891119906 +119872119910 (14)

where119872119909 = 119860119867(12059721199061205971199092 + 12059721199061205971199102)119872119910 = 119860119867(1205972V1205971199092 +1205972V1205971199102) are vortex viscosity terms 119860119867 is vortex viscositycoefficient and its value ranges from 04 to 08 119911 is tidelevel ℎ is water depth 119911 = ℎ + 1199110 1199110 is bottom elevation119905 is time 119906 and V are components of velocity in 119909 and 119910direction respectively 119862 is Chezy coefficient 119891 is Coriolisforce coefficient and 119892 is gravitational acceleration

In this paper FEM is used to discretize the 2-D shallowwater circulation equationThe computational area is dividedby the uniform triangle grids the number of unstructuredgrids is119872 and the number of nodes is119873 In addition120593119899 (119899 =1 2 119873) is set as the basis function of the solution functionof the finite element equation and 120593119890119901 is set as the shapefunction of local units Then the solution of the governingequation can be expressed as

119906 (119905 119909 119910) = 119873sum119899=1

119906119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119906119890119903)V (119905 119909 119910) = 119873sum

119899=1

V119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)V119890119903)119911 (119905 119909 119910) = 119873sum

119899=1

119911119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119911119890119903)(15)

where the part after the first equal sign is the solution functionunder the condition that the grid nodes are arranged byordinal number in the whole coordinate the part after thesecond equal sign is the solution function under the condition


that the grids are arranged by ordinal number in the localcoordinate The solution of arbitrary units in (15) is given by

119906119890 (119905 119909 119910) = 3sum119903=1

120593119890119901(119903) (119909 119910) 119906119890119903 (119905)V119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) V119890119903 (119905)119911119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) 119911119890119903 (119905)(16)

Equation (16) is substituted into (12) to (14) ℎ119890(119909 119910 119905) =119911119890(119909 119910 119905) minus 1199110(119909 119910) then continuity Equation (17) andmotion Equation (18) of triangle grids are obtained byGalerkin method

intΩ

[[3sum119903=1

120593119890119901(119903) 120597119911119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895) 3sum119903=1

120593119890119901(119903)ℎ119890119903+ ( 3sum119895=1

120597120593119890119901(119895)120597119909 ℎ119890119895) 3sum119903=1

120593119890119901(119903)119906119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 V119890119895)sdot 3sum119903=1

120593119890119901(119903)ℎ119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 ℎ119890119895) 3sum119903=1

120593119890119901(119903)V119890119903]]120593119890119902(119896)119889Ω

= 0 (119896 = 1 2 3)

(17)

intΩ

[[[[3sum119903=1

120593119890119901(119903) 120597119906119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895)( 3sum119903=1

120593119890119901(119903)119906119890119903)

+ ( 3sum119895=1

120597120593119890119901(119895)120597119910 119906119890119895)( 3sum119903=1

120593119890119901(119903)V119890119903) + 119892 3sum119903=1

120597120593119890119901(119903)120597119909 119911119890119903+ 119892sdot radic(sum3119895=1 120593119890119901(119895)119906119890119895)

2 + (sum3119895=1 120593119890119901(119895)V119890119895)2sum3119895=1 1198882119895 120593119890119901(119895)ℎ119890119895 ( 3sum119903=1

120593119890119901(119903)119906119890119903)

minus 3sum119903=1

119891119903120593119890119901(119903)V119890119903]]]]120593119890119902(119896)119889ΩΩ = 0 (119896 = 1 2 3)

(18)

119860119903119896 = intΩ120593119890119901(119903)120593119890119902(119896)dΩ 119861119903119896 = sum3119895=1(119906119890119895(120597120593119890119901(119895)120597119909) +

V119890119895(120597120593119890119901(119895)120597119910))119860119903119896 119862119903119896 = sum3119895=1(ℎ119890119895(120597120593119890119901(119895)120597119909))119860119903119896 119863119903119896 =1199041199061198983119895=1(ℎ119890119895(120597120593119890119901(119895)120597119910))119860119903119896 are substituted into Equation(17) and 119864119903119896 = sum3119895=1(119906119890119895(120597120593119890119901(119895)120597119909))119860119903119896 1198641015840119903119896 =sum3119895=1(V119890119895(120597120593119890119901(119895)120597119909))119860119903119896 119865119903119896 = sum3119895=1(119906119890119895(120597120593119890119901(119895)120597119910))119860119903119896 1198651015840119903119896 =sum3119895=1(V119890119895(120597120593119890119901(119895)120597119910))119860119903119896 119867119903119896 = 119892int

Ω(120597120593119890119901(119903)120597119909)120593119890119902(119896)dΩ1198671015840119903119896 = 119892int

Ω(120597120593119890119901(119903)120597119910)120593119890119902(119896)dΩ 119869119903119896 = int

Ω119891119903120593119890119901(119903)120593119890119902(119896)dΩ

119868119903119896 = 119892intΩ120593119890119901(119903)120593119890119902(119896)(radic(sum3119895=1 120593119890119901(119895)119906119890119895)2 + (sum3119895=1 120593119890119901(119895)V119890119895)2sum3119895=1 1198882119895 120593119890119901(119895)ℎ119890119895)dΩ are substituted into Equation (18) Then

finite element equation of element matrix Equation (19) isobtained by changing the order of integration summation

A z + Bh + Cu + Dv = 0Au + Eu + Fv +Hz + Iu minus Jv = 0

Av + E1015840u + F1015840v +H1015840z + Iv + Ju = 0(19)

where z = 120597119911112059711990512059711991121205971199051205971199113120597119905

119890 u = 120597119906112059711990512059711990621205971199051205971199063120597119905

119890 v = 120597V1120597119905120597V2120597119905120597V3120597119905

119890 z = 119911111991121199113119890

h = ℎ1ℎ2ℎ3

119890 u = 119906111990621199063119890 v = V1

V2V3119890 A = [ 11986011 11986012 1198601311986021 11986022 11986023

11986031 11986032 11986033] 119861 119862

119863 119864 119865119867 119868 119869 1198641015840 11986510158401198671015840 are similar to 119860 and they are 3 times 3matrixes which correspond to the elements corresponding tothe unit

After the unit partition is determined the number ofthe local unit nodes in whole coordinate is determined toform thewholematrix (increase the subscript119879 to represent)Moreover the time differential is discretized by the forwarddifference and the moment to be sought is expressed bythe superscript 119905 + Δ119905 and the remainder is 119905 Then (20) isobtained

A119879z119905+Δ119905 = A119879z

119905 minus Δ119905 (B119879h119905 + C119879u119905 + D119879v119905)A119879u119905+Δ119905

= A119879u119905 minus Δ119905 [H119879z119905 + (E119879 + I119879) u119905 + (F119879 minus J119879) v119905]

A119879v119905+Δ119905

= A119879v119905

minus Δ119905 [H1015840119879z119905 + (E1015840119879 + J119879) u119905 + (F1015840119879 + I119879) v119905]

(20)

Equation (20) can be rewritten as (21) by using massconcentration method diagonalizing 3 times 3 matrix startingfrom unit matrix replacing matrix 119860119879 at time 119905 + Δ119905 bydiagonal matrix 1198600 and then solving 119906119905+Δ119905 and V119905+Δ119905 of theequation and finally 119906119905+Δ119905 and V119905+Δ119905 are substituted into theequation z119905+Δ119905

A0u119905+Δ119905


A0v119905+Δ119905

= A119879v119905

minus Δ119905 [H1015840119879z119905 + (E1015840119879 + J119879) u119905 + (F1015840119879 + I119879) v119905]A0z119905+Δ119905 = A119879z

119905 minus Δ119905 (B119879h119905 + C119879u119905+Δ119905 + D119879v119905+Δ119905)

(21)

332 Grids Generation and Submarine Topography Thestudy area mainly includes the northeastern coast of Putuo


N

W

S

E

(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)

Figure 7 Grids generation of tidal model

(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)

Bathymetry (m)Above 0

-6 - 0

-24 - -18-30 - -24

-18 - -12-12 - -6

-36 - -30-42 - -36-48 - -42-54 - -48-60 - -54-66 - -60-72 - -66-78 - -72-84 - -78

Below -84Undefined

N

W

S

E

Figure 8 Submarine elevation contour

Island and Hulu Island the quadrilateral open sea facing theEast China Sea The study area is about 10 km from west toeast about 8 km from south to north covering about 74 km2The unstructured grids are used to divide the computationalarea in the model and the density of the grids increasesgradually from the open sea area to the island coastlineFinally the number of unstructured gridsrsquo nodes is 7970and the number of unstructured grids is 15264 The gridsgeneration of tidal model is shown in Figure 7 According tothe data the contour map of submarine elevation is obtainedthrough the transformation of coordinate and datum planethe interpolation of grid nodes and a series of processing asshown in Figure 8

Comparing Figures 7 and 8 it could be found that thetopography near the open boundary is relatively flat and thesimulation of tidal wave is more stable Therefore increasingthe grid size and reducing the resolution is reasonable but alsocan improve the model calculation efficiency Increasing thedensity of the grid at the waterway and the island coast canimprove the accuracy of the operation and fully reflect thesubmarine topography

8162013 000

8172013 000

8182013 000

8192013 000

8202013 000

8212013 000

8222013 000

8232013 000

8242013 000

8252013 000

Time (h)Calculated ResultsMeasured Data

minus25minus2

minus15minus1

minus050

051

152

25

Tida

l Lev

el (m

)

Figure 9 Validation of tidal level

The type of the open boundary of the model is the tideboundary that is the water level process of each grid node ofthe determined boundary is given along the open boundaryThe water level process is obtained by harmonic analysismethod and it is predicted by the global ocean tide model[22] and eight tidal constituents M2 S2 N2 K2 K1 O1 P1Q1 are taken into account

333 Validation of 2-DModel Themarine hydrological datais obtained by the Second Institute of Oceanography of theState Oceanic Administration in August 2013 such as tideand tidal wave The observation period was 1000 on August16th 2013 to 1700 on August 17th 2013 (small tide) 1400on August 19th to 1500 on August 19th (middle tide) and1000 on August 23th to 1100 on August 24th (spring tide) Inaddition the temporary tide level station of Hulu Island alsoprovided the hourly tide level data from August 5th 2013 toSeptember 4th 2013Themeasuring pointsrsquo location is shownin Figure 2 in which 0 is Hulu Island tide test point B1 to B5are the test points for the flow velocity and flow direction oftidal farm

Tidal model is validated by a long series pattern and themodel is calculated from 300 on August 16th 2013 to 1400on August 24th which lasted 204 hours The measured dataof the tidal level at the temporary test points on the westernshore ofHulu Island are comparedwith the calculated resultsas shown in Figure 9

By contrast the calculated results are in good agreementwith the measured results the phase of the calculated resultsare consistentwith themeasured results and the relative errorof the tidal height is less than 10 which indicates that themodel is satisfactory for the verification of tide level andcan simulate the change of tide level in the sea area moreaccurately Taking the middle tide process for example thevalidation results of flow velocity and flow direction of eachmeasuring point are shown in Figure 10

On the whole the variation trend of flow velocity andflow direction of measuring points is basically the same asmeasured value From the point of time corresponding toflow peak and the change of flow direction the two are alsorelatively close Relative error between the simulated valueand the calculated value of flow velocity is less than 10 and


Calculated ResultsMeasured Data

0

40

80

120

160

Veloci

ty in

B1

(cms

)

19 24 5 10 1514Time (h)

(a)


060

120180240300360

14 19 24 5 10 15Time (h)D

irec

tion

in B

1 (∘

)

(b)


0

40

80

120

160

Veloci

ty in

B2

(cms

)

19 24 5 10 1514

Time (h)

(c)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(d)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B3

(cms

)

(e)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(f)


0

40

80

120

160

Veloci

ty in

B4

(cms

)

19 24 5 10 1514

Time (h)

(g)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514Time (h)

(h)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B5

(cms

)

(i)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(j)Figure 10 Validation of flow velocity and direction (a) (c) (e) (g) and (i) are validation results of flow velocity (b) (d) (f) (h) and (j) arevalidation results of flow direction


the error can be controlled within 18 in addition to somespecial moments

From the foregoing the velocity distribution of the tidalfarm in the computational area is reasonable the calculatedresults of flow velocity and flow direction are consistent withthe measured data and the variation trend is also similarwhich shows that themathematical model of the tidal currentis basically reliable and can be used in the hydrodynamicstudy of the tidal farm

4 Results and Discussions

41 3-D Near-Field Hydrodynamic Characteristics Based onCFD results velocity distributions in center plane of doubleimpellers in each combination are shown in Table 2 Becausebladersquos diameter is larger linear velocity near blade is muchgreater than velocity of inflow and other flow field In orderto reflect effect of impellers on near-field flow and comparesimilarities and differences between flow fields better areawith large flow velocity near blade will be ignored and areawith velocity distributions from 0 to 114 V119894 is emphasizedwhen drawing contours

Flow velocity profiles of each V119894 - 120596119894 combinationhave some common features which are manifested inthe upstream downstream and inner and outer sides ofimpellers respectively As for the upstream of impellersthe upstream inflow is blocked because of the installationand operation of turbine which is shown as a flow velocitydeceleration zone which is convex to inflow in the upstreamof impeller in flow velocity profiles After the flow runningthrough the impellers the flow velocity decreased signif-icantly because of energy loss and a strip of wake flowwith the length of about 240m (about 10 119863119864) is formeddownstreamof each impellerThewake of impellers graduallycloses together in the downstream and merges into oneThe width of the wake narrows along the forward directionof X-axis and disappears gradually in the distance Thegradient distribution of the change of flow velocity in thestrip of wake flow is not well-distributed and the closer thevelocity of the impeller is the more severe the loss is Onthe outside at downstream of the impellers due to turbinersquoslayout and the widening of the strip of wake flow the waterarea on both sides decreases and the flow velocity increasesslightly (relative to the inflow velocity) Similarly there willbe a ldquoseparation zonerdquo on the inside at downstream of theimpellers where the flow velocity is larger than the wakeflow

With different V119894 - 120596119894 combinations the flow velocitydistributions are different The greater the inflow velocity isthe faster the impellers rotate and the greater the hindrancefunction of the impellers on the upstream is As for thelength of the strip of wake flow the green contours are takenas an example the larger the impellersrsquo angular speed thelonger the length of the green strip of wake flow and thenthe position where the strip of wake flow narrows obviouslymoves downstream which results in the length of the areawhere the flow velocity increased (dark red) in the outside ofthe double impellers is longer in theXdirection and the spaceon both sides of the wake is gradually filled in the Y direction

RoughnessTrend Line

05 10 15 20 25 30 00 Inflow Velocity (ms)

027

028

029

030

031

Com

preh

ensiv

e Rou

ghne

ss

1minus1

2minus2

3minus3

4minus4

5minus5

6minus6

7minus7

Figure 11 Relationship between inflow velocity and compositiveroughness

The flow velocity of the wake at the impeller axis inthese 7 combinations has been restored to 969 941940 911 912 883 and 883 of their inflow velocityrespectively In this paper we take the investigation of Yang asa criterion to determine whether the computational range isnormal enough that is when the flow velocity is restored to80 sim 90 of the inlet velocity it is determined that it meetsthe energy generation efficiency and the work needs [23]Thevelocity of the wake can be restored to more than 80 of theinflow velocity so the computational range of the 3-D modelis sufficient

42 Turbine Simplification Results Equivalent roughness iscalculated according to (8) then compositive roughness isobtained from (11) by combining with natural roughness oftidal farm which is 0025 the results shown in Table 3

Figure 11 is drawn according to the correspondence ofeach combination in which the blue points represent thecalculated results of compositive roughness and the blackline represents the trend line which is obtained by regressionof scatter points The function is expressed as

119899 = 001899 sdot ln (V) + 028441 (22)

Compositive roughness of turbine increases logarithmi-cally with the increasing of inflow velocity

Equation (22) is applied to that the impellerrsquos rotatingspeed is changed according to the design tip speed ratio 120582119903=53 with the flow velocity changing and the equivalent rough-ness is calculated by the method mentioned above Equation(22) can be used for the calculation of 2-D tidal currentfield but should be used according to the actual situationBased on the ldquoroughness increment - compositive roughnessrdquorelationship expressed by (11) and the ldquocompositive roughness- inflow velocityrdquo relationship expressed by (22) the ldquobridgerdquowhich connects 3-D model and 2-D model is constructedThus the local roughness correction that is the ldquoroughnessincrement - compositive roughnessrdquo relationship is obtained


Table 2 Velocity distributions on impellersrsquo center planes in different combinations

V119894 minus 120596119894 Combinations Flow Velocity Contours on Impellersrsquo Center Planes

A

InflowVelocity V1 0614 070

0 ms m

Y

XZ

minus

minus

(ms)

AngularSpeed 1205961 04(rads)

B

InflowVelocity V2 0921

0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327

40 41 42 43Radius 100mRadius 200mRadius 300m

44 45 46 47(km)

Figure 12 Exploratory circumference schematic

through the 3-D model to simulate the resistance loss (ieCFD simulation results of ℎ119891) from upstream to downstreamand the resistance loss is converted into equivalent roughnessof the turbine by (8) Through regression of the simulatedresults the ldquocompositive roughness - inflow velocityrdquo rela-tionship is obtained and substituted into the grids whereturbines are located for calculationThe roughness is changedwith the velocity in the 2-D flow field which reflects the effectof the turbine on the flow field thus the connection of 3-Dmodel and 2-D model can be achieved

43 2-D Far-Field Hydrodynamic Characteristics In thispaper 5 different installation locations of the tidal turbineare considered and the comparison of the flow field beforeand after the installation is simulated in the process of springtide under the 5 conditions Taking the center of the doubleimpeller as the center of the circle the radius 100m 200mand 300m is taken as the exploratory circumference to countand compare the changes of flow field Take the B4 berthageas an example and the exploratory circumference as shownin Figure 12

Difference of flow velocity is the velocity after installationminus the velocity before installation at the same time andmaximum difference of flow velocity represents maximumvalue of deceleration in flow velocity at a certain timeDistribution of maximum difference of flow velocity nearturbine was shown in Figure 13 To reflect deceleration effectof device better Figure 13 only makes the contour lines ofmaximumdifference of flow velocity in range from -0015msto -005ms Since maximum difference of flow velocity doesnot appear to be the same at all times area enclosed bycontour lines is an extreme case which means that maximalaffecting range of the turbine on flow field at any time will notexceed area shown in Figure 13

It can be seen from Figure 13 that turbine location at bothend andmiddle of channel has a certain effect on surroundingflow field and a certain range of velocity deceleration zoneswhich are ldquo8-shapedrdquo areas appears in facing flow side and

reverse flow side of turbine and flow velocity on two sidesof turbine increases slightly In the process of spring tidedifference of flowvelocity in near flowfield has largest changeand affecting area is biggestwhenB4berthage is installedwithturbine B3 berthage is next to B4 berthage B5 berthage isfollowed byB3 berthage B1 berthage is second to B5 berthageand B2 berthage is smallest B4 and B3 berthage are in narrowsection of channel and B2 berthage is located in open sectionof channel This indicates that the effect of installation ofturbine on flow field in narrow sea area is relatively largerand the effect of installation of turbine on flow field in opensea area is relatively smaller In addition water depth of B2berthage is largest in the 5 berthages but the effect on the flowfield is the smallest Affecting range of B4 and B3 berthage inchannel onflowfield is substantially consistentwithwaterwaydirection indicating that the effect of installation of turbineon flow field is also related to water depth topography andchannel direction

Hourly changing process of extreme value of decelerationand relative difference of flow velocity in different exploratorycircumference with radius of 100m 200m and 300m arerespectively shown in Figures 14 15 and 16 Wherein max-imum of deceleration represents maximum value of decreaseof flow velocity at every point on circumference at a certaintime definition of minimum of deceleration is just theopposite The relative difference of flow velocity representsthe ratio of the maximum of deceleration to the maximumof flow velocity before the installation of the turbine

As can be seen from these figures the extremal curvesof deceleration at each berthage show a certain periodicitywhich is the result of the periodicity of the tidal currentThe curves of B2 berthage are special and the curve patternsof other berthages are similar Most of the decelerationminimum curves of all circumferences are located abovethe horizontal axis and most of the deceleration maximumcurves are below the horizontal axis This shows that there isa certain degree of deceleration and growth of flow velocityappearing near the turbine which is also consistent with theresults of the 3-D near-field simulation The peak value ofthe deceleration maximum curves of each turbine generallydecreases with the increase of the circumferential radiuswhich means that the farther away from the turbine thesmaller the effect of the turbine on the flow field From thecurves of relative difference of flow velocity the effect of theturbine on the far-field of flow field is smaller as a wholeand the maximum change in flow velocity does not exceed8 of the flow velocity before the installation of the turbineThe degree of deceleration and growth of all berthages werecompared as shown in Table 4

As can be seen from Table 4 the results of comparisonof the deceleration degree (B4gt B3gt B1gt B5gt B2) areapproximately the same as the comparison of the maximumvalue distribution of the flow velocity difference (B4gt B3gtB5gt B1gt B2) For the growth degree B4 berthage changesgreatly There is no growth in its 100m range but the degreeof growth near 300m is the largest In order to better reflectthe specific changes in the affected area the change of theextremum of flow velocity difference is formed by differentlocation under the spring tide as shown in Table 5


Table 4 Comparison of deceleration and growth degree

Circumferential Radius Comparison of Deceleration Degree Comparison of Growth Degree100 m B4gt B3gt B1gt B5gt B2 B3gt B2gt B1gt B5gt B4200 m B4gt B3gt B1gt B5gt B2 B3gt B2gt B1gt B4gt B5300 m B4gt B3gt B1gt B5gt B2 B4gt B2gt B3gt B1gt B5

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)

Figure 13 Distribution of maximum difference of flow velocity in (a) B1 location (b) B2 location (c) B3 location (d) B4 location and (e) B5location


0 4 8 12 16 20 24

Time (h)

Deceleration MaximumDeceleration Minimum

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(j)Figure 14 Variations in flow velocity of circumferencewith radius of 100m (a) and (b) represent B1 location (c) and (d) represent B2 location(e) and (f) represent B3 location (g) and (h) represent B4 location and (i) and (j) represent B5 location

0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(f)Figure 15 Continued



0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()

(j)Figure 15 Variations in flow velocity of circumference with radius of 200m (a) and (b) represent B1 location (c) and (d) represent B2location (e) and (f) represent B3 location (g) and (h) represent B4 location and (i) and (j) represent B5 location


0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(d)Figure 16 Continued



0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)

Figure 16 Variations in flow velocity of circumference with radius of 300m (a) and (b) represent B1 location (c) and (d) represent B2location (e) and (f) represent B3 location (g) and (h) represent B4 location and (i) and (j) represent B5 location

It can be seen from Table 5 that B4 location has thelargest effect on the flow field and the affected area is alsothe most extensive and B2 location has the least effect onthe flow field The deceleration maximum of B1 B3 B4 andB5 decreases with the increase of radius the change of B2location is smaller and there is fluctuation around the radiusof 300mThe growth maximum of B2 and B3 decreases withthe increase of radius and the growth changes of B1 B4 andB5 are smaller and the fluctuation also appears This showsthat when the degree of deceleration and growth of flowvelocity is greater the value of deceleration and growth will

decrease with the increase of radius When the decelerationand growth of velocity are less than 001ms the value ofdeceleration and growth will only fluctuate and there is noobvious law

To sum up for the installation of tidal turbine in tidalfarm the following conclusions can be obtained by combin-ing the consideration of the bathymetric data and the tidalresource in the engineering sea area(1) Compared to other berthages the effect of test pointB4 on the flow field is the largest after turbinersquos layout thispoint can be considered to avoid in the layout of berthages


Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714


(2) Tidal current power resources of B1 B3 and B5 testpoints are more abundant the degree of effect after turbinersquoslayout is also within the acceptable range(3) Combining the offshore distance of each point testpoints B1 and B3 are the ideal layout points for the fiveberthages through synthetical consideration

5 Conclusion

(1) 3-D CFD simulation results show that the tidal turbinehas a certain degree of hindrance to the upstream inflowand the faster the rotating speed of the impellers the moreobvious the hindrance After water flow through the turbineflow velocity decreases significantly and a strip of wake flowwith the length of about 240m (about 10 119863119864) is formeddownstream of impellers The distribution of variation gra-dient of flow velocity in the strip of wake flow is not well-distributed and the closer the velocity of the impeller isthe more severe the loss is The wake flow of the doubleimpellers is gradually approaching downstream converginginto one then narrowing and disappearing in the distanceFlow velocity of inner and outer flow downstream the doubleimpellers is greater than the inflow velocity because the flowsection is narrowing(2)The tidal level which is simulated by 2-D tidal modelis in good agreement with the measured values the flowvelocity distribution of the tidal farm is reasonable thecalculated values of the flow velocity and the flow directionare consistent with the measured values and the variationtrend is consistent which indicated that the mathematicalmodel of the tidal current is reliable and can be usedto simulate the flow field of the channel of Putuo-HuluIslands(3)The simulation results of the 2-D tidal mathematicalmodel show that turbinersquos installation at both ends and themiddle of the channel has a certain effect on the surroundingflowfield a certain range of velocity deceleration zoneswhichare ldquo8-shapedrdquo areas appears in the facing flow side andreverse flow side of the turbine and the flow velocity on twosides of the turbine increases slightly The water area at bothends of the channel is wide and affected little by the turbineThe area where the flow velocity is affected is larger in themiddle of the channel because of the superimposed effect ofthe narrowed area and the turbine The size of the affectedarea is also related to the inflow velocity and the topographymeanwhile the reciprocating flow of the tidal current is oneof the reasons for the expansion of the affected area(4) From the statistical results of the relative velocitydifference the effect of the turbine on the flow velocity of far-field is relatively smaller The effect of turbine on the far-fieldof flow field is smaller as a whole the maximum change inflow velocity does not exceed 8 of the flow velocity beforethe installation of the turbine(5)Compared to other berthages the effect of B4 berthageon the flow field is the largest after turbinersquos layout this pointcan be considered to avoid Tidal current power resources ofB1 B3 B5 berthages are more abundant the degree of effectafter turbinersquos installation is also within the acceptable rangeCombining the offshore distance of each berthage B1 and B3

berthages are the ideal location for the five berthages throughsynthetical consideration

Data Availability

The data supporting this article is confidential TianjinUniversity requires that these data cannot be released

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Hongqiang Zhang assisted in setting up the two modelsprocessed and analyzed the data and drafted the manuscriptDaming Li established the conceptual framework of thispaper and set up the two models Yanqing Li and TingYang assisted in setting up the two models and revised themanuscript Shan Luo Shunfa Tian and Shilong Bu assistedin processing the data and revised themanuscript All authorsprovided completion in their field

Acknowledgments

This research was financially supported by the NationalNatural Science Foundation of China (Grant No 51079095)and the Science Fund for Creative Research Groups ofthe National Natural Science Foundation of China (GrantNo 51021004) This work was supported by the State KeyLaboratory of Hydraulic Engineering Simulation and Safetyof Tianjin University

References

[1] L Bai R Spence and G Dudziak ldquoInvestigation of theInfluence of Array Arrangement and Spacing on Tidal EnergyConverter (TEC) Performance Using a 3D CFDModelrdquo in Pro-ceedings of the 8th EuropeanWave and Tidal Energy Conferencepp 654ndash660 Uppsala Sweden 2009

[2] D M ODoherty J A Mason C Morris et al ldquoInteraction ofMarine Turbines in Close Proximityrdquo in Proceedings of the 9thEuropean Wave and Tidal Energy Conference pp 5ndash9 2011

[3] S Couch and I Bryden ldquoThe Impact of Energy Extraction onTidal Flow Developmentrdquo in Proceedings of the 3rd IMar ESTInternational Conference on Marine Renewable Energy 2004

[4] L S Blunden and A S Bahaj ldquoInitial evaluation of tidal streamenergy resources at Portland Bill UKrdquo Journal of RenewableEnergy vol 31 no 2 pp 121ndash132 2006

[5] L Blunden and A Bahaj ldquoEffects of Tidal Energy Extraction atPortlandBillrdquo inProceedings of EuropeanWave andTidal EnergyConference pp 11ndash14 2007

[6] I G Bryden and S J Couch ldquoHow much energy can beextracted from moving water with a free surface A questionof importance in the field of tidal current energyrdquo Journal ofRenewable Energy vol 32 no 11 pp 1961ndash1966 2007

[7] R H Karsten J M McMillan M J Lickley and R D HaynesldquoAssessment of tidal current energy in the Minas Passage Bayof Fundyrdquo Proceedings of the Institution ofMechanical Engineers


Part A Journal of Power and Energy vol 222 no 5 pp 493ndash5072008

[8] L E Myers and A S Bahaj ldquoAn experimental investigationsimulating flow effects in first generationmarine current energyconverter arraysrdquo Journal of Renewable Energy vol 37 no 1 pp28ndash36 2012

[9] G H Cavalcante D A Feary and B Kjerfve ldquoEffects of TidalRange Variability and Local Morphology on HydrodynamicBehavior and Salinity Structure in the Caete River EstuaryNorth Brazilrdquo International Journal of Oceanography vol 2013Article ID 315328 10 pages 2013

[10] G Savant and T O McAlpin ldquoTidal hydrodynamics in thelower columbia river estuary through depth averaged adaptivehydraulics modelingrdquo Journal of Engineering (United States)vol 2014 2014

[11] P A Gillibrand R A Walters and J McIlvenny ldquoNumericalsimulations of the effects of a tidal turbine array on near-bedvelocity and local bed shear stressrdquo Energies vol 9 no 10 2016

[12] I Yamamoto G Rong Y Shimomoto and M Lawn ldquoNumer-ical simulation of an oscillatory-type tidal current poweredgenerator based on robotic fish technologyrdquo Applied Sciencesvol 7 no 10 p 1070 2017

[13] X-P Xin X-M Shao J Deng and W Li ldquoHydrodynamic per-formance prediction of marine current turbine with dual rotorin tandem arrangementrdquo Zhejiang Daxue Xuebao (GongxueBan)Journal of Zhejiang University (Engineering Science) vol45 no 7 pp 1227ndash1231 2011

[14] B An Numerical Analysis of the Wake and Interaction EffectAnalysis for Tidal Arrays in the Tidal FarmMasterrsquosThesis [Mscthesis] China Ocean University 2012

[15] J Yuan Numerical Simulation on Hydrodynamic Response toTidal Current Energy Extraction [Msc thesis] Zhejiang Univer-sity 2012 (Chinese)

[16] F Hou The Analysis of Tidal Energy in Zhoushan Island Basedon FVCOM [Msc thesis] China Ocean University 2012

[17] L Li Research on Effect of Turbines Array on Flow Field in TidalFarm [Msc thesis] China Ocean University 2013

[18] D Ma Simulation Research of Hydrodynamic Characteristicsof Tidal Turbine with Horizontal Axis [Masterrsquos thesis] XianUniversity of Technology 2013

[19] Y Ding and L Ding ldquoA Numerical Simulation of ExtratropicalStorm Surge and Hydrodynamic Response in the Bohai SeardquoDiscrete Dynamics in Nature and Society vol 2014 Article ID282085 8 pages 2014

[20] L Xu Planning Research of Anchorage in Zhoushan Port [Mscthesis] Shanghai Maritime University 2005

[21] ldquoAssessment of Tidal Energy Resourcerdquo httpwwwemecorgUkassessment-of-tidal-energy-resourceResource

[22] O B Andersen ldquoGlobal ocean tides from ERS 1 andTOPEXPOSEIDON altimetryrdquo Journal of GeophysicalResearch Atmospheres vol 100 no C12 p 25249 1995

[23] C J Yang and A D Hoang ldquoA Study on Effect of Longitudinaland Lateral Spaces in Tidal Farm by CFXrdquo in Proceedings ofAsian Wave and Tidal Conference 2012

Hindawiwwwhindawicom Volume 2018

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International Journal of Mathematics and Mathematical Sciences


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Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


al investigated the hydrodynamic impacts of whole lagoondue to tidal waves using a 2-D depth-averaged hydrodynamicmodel based on the shallow water equations Gillibrand et al[11] adopted a three-dimensional (3-D) hydrodynamicmodelto consider the potential effects of energy extraction by anarray of tidal turbines on ambient near-bed velocity field andlocal bed shear stress Yamamoto et al [12] exploited ANSYSto select the best shape of oscillator in order to efficientlyharness the tidal flow energy in a cost-efficient manner

Although the study of tidal current power started late inChina the scientists also made some new breakthroughs inthe research and development of energy-harvesting deviceand the study of flow field also has a lot of achievementsFor example Xin et al [13] predicted the hydrodynamiccharacteristics of double rotor turbines arranged in seriesAn [14] made the 3-D steady-state numerical simulation ofthe horizontal axis turbine by CFD method and mutualeffect rule between devices under different arrangementconditions was obtained Yuan [15] utilized a perforated discto simulate the tidal turbine by increasing drag coefficientto replace device group Hou [16] exploited Finite VolumeCommunity Ocean Model to simulate the effect of tidalturbine on 2-Dhydrodynamic environment Li [17] usedCFDmethod to study reasonable arrangement distance of the arrayof horizontal axis tidal turbine Ma [18] established blademodel according to BEM drawing on the experience of windenergy generation and applied CFD method in studying thehydrodynamic characteristics of the impellers under differentworking conditions Ding et al [19] found local surge currentvelocity in each depth with a magnitude of the same order asastronomic tidal currents

At home and abroad studies on the effect of tidalturbine on hydrodynamic characteristics of large-scale far-fields which are combined with the integrated simulationof near-field hydrodynamic characteristics of turbine arefew especially in the aspects of turbine simplification andbottom friction determination But in the previous stud-ies generalized bottom frictions were fixed values and didnot change with the variation of flow velocity Due tothe large subjectivity of the existing research methods andthe poor adaptability of the simplification method underdifferent working conditions the research methods couldbe developed in the direction of ldquonear-field amp far-fieldrdquointegrated simulation Therefore in order to clarify theeffect on flow field because of turbine installation and thenrationally arrange the berthages of tidal turbine in test fieldldquoPutuo-Hulu Islands Tidal Power Demonstration Projectrdquoin Zhoushan City China was regarded as the study objectFirstly we constructed a 3-D turbine model of near-fieldflow in the frame of CFD and simulated the flow velocitydistributions in 7 combinations of ldquoimpeller rotating speed -inflow velocityrdquo Next we presented a simplification methodof tidal turbine based on the energy equation to determineturbinersquos equivalent roughness by calculating resistance lossin flow passage Then we established a 2-D tidal model offar-field flow and applied Finite Element Method (FEM) insolving the 2-D shallow water circulation equations Finallythe impact of tidal location on hydrodynamics could be sim-ulated by utilizing different locationrsquos compositive roughness

Figure 1 Geographical location of tidal farm

We combined 3-D turbine model and 2-D tidal model andsimulated and analyzed the impact of turbine location onnear-field and far-field hydrodynamics in tidal farm

2 Study Area

21 Tidal Farm Introduction The site of project is locatedin the channel between Putuo Island and Hulu Island inZhoushan City China and the geographical location of thetidal farm is shown in Figure 1 The channel is about 66 kmlong and 16 km wide and the water depth is about 20mto 80m (1985 National Elevation Benchmark) The offshoretopography on both sides of channel is steeper and the centralsite is relatively flat

Putuo Island and Hulu Island lie in a sea area whereislands are numerous and water depth changes complexlyIn the sea area the tidal current is characterized by theirregular semidiurnal tide the fluctuation of tidal current isobviously affected by topography and shallow sea effect isobvious Velocity of tidal current between islands is relativelylarge the mainly flow pattern is reciprocating flow andthe direction is roughly parallel to the channel Meanwhilethe direction of tidal current is basically consistent withthe tidal wave propagation [20] In the channel the tidalcurrent is reciprocating flow along NW-SE direction thevertical average velocity is about 067ms to 081ms andthe maximum velocity of tidal current on surface is 229msThe channel is a sub-rich area of tidal current resources andunder the cover of Hulu Island the extreme sea conditions ofopen sea have little effect on channel

22 Tidal Turbine Location Based on the compositive anal-ysis of the bathymetric data engineering geology and tidalcurrent resource conditions in this sea area combining withthe existingmeasured data it is proposed to set themeasuringpoints B1 to B5 as the berthages of the tidal turbine The tidalturbine location in tidal farm is shown in Figure 2 The whiteparts in Figure 2 represent the islands or land (ie correspondto Putuo Island and Hulu Island in Figure 1) and the restrepresents the sea area Figure 2 is an enlarged view of thered frame of Figure 1


(km)

(km)



N

W

S

E


3 Methodology





(m)X

Y

Z




minus 120588120576 minus 119884119872 + 119878119896(1)

120597120597119905 (120588120576) + 120597120597119909119894 (120588120576119906119894) = 120597120597119909119895 (120572120576120583119890119891119891 120597120576120597119909119895)+ 1198621120576 120576119896 (119866119896 + 1198623120576119866119887)minus 11986221205761205881205762119896 minus 119877120576 + 119878120576

(2)




inlet

60m240m

outlet100m

XYZ

(a) (b)



00

04

08

12

16

Velo

city

(ms

)










1199111 + 1199011120588119892 + 1205721V212119892 = 1199112 + 1199012120588119892 + 1205722V

222119892 + ℎ1198911minus2 (3)


Table1Re

lationshipbetweenim

pellerrsquos

rotatin

gspeedandinflo

wvelocity

Inflo

wVe

locity

(ms)

Parameter

sIm

pelle

rRotatin

gPo

sition

perS

econ

dRe

latio

nshi

pSchematicbetw

een

Impelle

rrsquosRo

tatin

gSp

eedAng

ular

Speedan

dIn

flowVe

locity

Ang

ular

Speed

(rad

s)

Rotatin

gSp

eed

(rm

in)

00

05

10

15

20

25

30


48

1216

200

Rota

ting

Spee

d (r

min

)

00

05

10

15

20

25

30


04

08

12

16

20

00

Ang

ular

Spe

ed (r

ads

)

0614

04

382

0921

06

573

1229

08

764

1536

1095

5

1843

121146

2150

141337

2457

161528


p1v1

1

1

p2v2

2

2

L1

L2

L





ℎ1198911minus2 = 120582 1198714119877 V212119892 (5)


120582 = 81198921198622 (6)


119862 = 111989911986411987716 (7)




120591 = 120588119892119877119869 = 120588119892 V21198622 = 1205881198921198992V211987716 (9)



120591 = 1205910 + Δ120591 = 120588119892119877119869 = 12058811989211989920V2211987716 + 1205881198921198992119864V2211987716 = 120588119892119899

2V2211987716 (10)


119899 = radic11989920 + 1198992119864 (11)



120597z120597119905 + 120597 (119906ℎ)120597119909 + 120597 (Vℎ)120597119910 = 0 (12)

120597119906120597119905 + 119906120597119906120597119909 + V120597119906120597119910 + 119892120597119911120597119909 = minus119892radic1199062 + V21198622ℎ 119906 + 119891V +119872119909 (13)




119906 (119905 119909 119910) = 119873sum119899=1

119906119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119906119890119903)V (119905 119909 119910) = 119873sum

119899=1

V119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)V119890119903)119911 (119905 119909 119910) = 119873sum

119899=1

119911119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119911119890119903)(15)




119906119890 (119905 119909 119910) = 3sum119903=1

120593119890119901(119903) (119909 119910) 119906119890119903 (119905)V119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) V119890119903 (119905)119911119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) 119911119890119903 (119905)(16)


intΩ

[[3sum119903=1

120593119890119901(119903) 120597119911119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895) 3sum119903=1

120593119890119901(119903)ℎ119890119903+ ( 3sum119895=1

120597120593119890119901(119895)120597119909 ℎ119890119895) 3sum119903=1

120593119890119901(119903)119906119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 V119890119895)sdot 3sum119903=1

120593119890119901(119903)ℎ119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 ℎ119890119895) 3sum119903=1

120593119890119901(119903)V119890119903]]120593119890119902(119896)119889Ω

= 0 (119896 = 1 2 3)

(17)

intΩ

[[[[3sum119903=1

120593119890119901(119903) 120597119906119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895)( 3sum119903=1

120593119890119901(119903)119906119890119903)

+ ( 3sum119895=1

120597120593119890119901(119895)120597119910 119906119890119895)( 3sum119903=1

120593119890119901(119903)V119890119903) + 119892 3sum119903=1

120597120593119890119901(119903)120597119909 119911119890119903+ 119892sdot radic(sum3119895=1 120593119890119901(119895)119906119890119895)

2 + (sum3119895=1 120593119890119901(119895)V119890119895)2sum3119895=1 1198882119895 120593119890119901(119895)ℎ119890119895 ( 3sum119903=1

120593119890119901(119903)119906119890119903)

minus 3sum119903=1

119891119903120593119890119901(119903)V119890119903]]]]120593119890119902(119896)119889ΩΩ = 0 (119896 = 1 2 3)

(18)

119860119903119896 = intΩ120593119890119901(119903)120593119890119902(119896)dΩ 119861119903119896 = sum3119895=1(119906119890119895(120597120593119890119901(119895)120597119909) +


Ω(120597120593119890119901(119903)120597119909)120593119890119902(119896)dΩ1198671015840119903119896 = 119892int

Ω(120597120593119890119901(119903)120597119910)120593119890119902(119896)dΩ 119869119903119896 = int

Ω119891119903120593119890119901(119903)120593119890119902(119896)dΩ




Av + E1015840u + F1015840v +H1015840z + Iv + Ju = 0(19)

where z = 120597119911112059711990512059711991121205971199051205971199113120597119905

119890 u = 120597119906112059711990512059711990621205971199051205971199063120597119905

119890 v = 120597V1120597119905120597V2120597119905120597V3120597119905

119890 z = 119911111991121199113119890

h = ℎ1ℎ2ℎ3

119890 u = 119906111990621199063119890 v = V1

V2V3119890 A = [ 11986011 11986012 1198601311986021 11986022 11986023

11986031 11986032 11986033] 119861 119862



A119879z119905+Δ119905 = A119879z



A119879v119905+Δ119905

= A119879v119905

minus Δ119905 [H1015840119879z119905 + (E1015840119879 + J119879) u119905 + (F1015840119879 + I119879) v119905]

(20)


A0u119905+Δ119905


A0v119905+Δ119905

= A119879v119905


119905 minus Δ119905 (B119879h119905 + C119879u119905+Δ119905 + D119879v119905+Δ119905)

(21)



N

W

S

E

(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


-6 - 0

-24 - -18-30 - -24

-18 - -12-12 - -6

-36 - -30-42 - -36-48 - -42-54 - -48-60 - -54-66 - -60-72 - -66-78 - -72-84 - -78

Below -84Undefined

N

W

S

E




8162013 000

8172013 000

8182013 000

8192013 000

8202013 000

8212013 000

8222013 000

8232013 000

8242013 000

8252013 000


minus25minus2

minus15minus1

minus050

051

152

25

Tida

l Lev

el (m

)









0

40

80

120

160

Veloci

ty in

B1

(cms

)

19 24 5 10 1514Time (h)

(a)


060

120180240300360

14 19 24 5 10 15Time (h)D

irec

tion

in B

1 (∘

)

(b)


0

40

80

120

160

Veloci

ty in

B2

(cms

)

19 24 5 10 1514

Time (h)

(c)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(d)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B3

(cms

)

(e)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(f)


0

40

80

120

160

Veloci

ty in

B4

(cms

)

19 24 5 10 1514

Time (h)

(g)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514Time (h)

(h)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B5

(cms

)

(i)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)









RoughnessTrend Line


027

028

029

030

031

Com

preh

ensiv

e Rou

ghne

ss

1minus1

2minus2

3minus3

4minus4

5minus5

6minus6

7minus7





119899 = 001899 sdot ln (V) + 028441 (22)






A


0 ms m

Y

XZ

minus

minus

(ms)


B


0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018









(km)

(km)



N

W

S

E


3 Methodology





(m)X

Y

Z




minus 120588120576 minus 119884119872 + 119878119896(1)

120597120597119905 (120588120576) + 120597120597119909119894 (120588120576119906119894) = 120597120597119909119895 (120572120576120583119890119891119891 120597120576120597119909119895)+ 1198621120576 120576119896 (119866119896 + 1198623120576119866119887)minus 11986221205761205881205762119896 minus 119877120576 + 119878120576

(2)




inlet

60m240m

outlet100m

XYZ

(a) (b)



00

04

08

12

16

Velo

city

(ms

)










1199111 + 1199011120588119892 + 1205721V212119892 = 1199112 + 1199012120588119892 + 1205722V

222119892 + ℎ1198911minus2 (3)


Table1Re

lationshipbetweenim

pellerrsquos

rotatin

gspeedandinflo

wvelocity

Inflo

wVe

locity

(ms)

Parameter

sIm

pelle

rRotatin

gPo

sition

perS

econ

dRe

latio

nshi

pSchematicbetw

een

Impelle

rrsquosRo

tatin

gSp

eedAng

ular

Speedan

dIn

flowVe

locity

Ang

ular

Speed

(rad

s)

Rotatin

gSp

eed

(rm

in)

00

05

10

15

20

25

30


48

1216

200

Rota

ting

Spee

d (r

min

)

00

05

10

15

20

25

30


04

08

12

16

20

00

Ang

ular

Spe

ed (r

ads

)

0614

04

382

0921

06

573

1229

08

764

1536

1095

5

1843

121146

2150

141337

2457

161528


p1v1

1

1

p2v2

2

2

L1

L2

L





ℎ1198911minus2 = 120582 1198714119877 V212119892 (5)


120582 = 81198921198622 (6)


119862 = 111989911986411987716 (7)




120591 = 120588119892119877119869 = 120588119892 V21198622 = 1205881198921198992V211987716 (9)



120591 = 1205910 + Δ120591 = 120588119892119877119869 = 12058811989211989920V2211987716 + 1205881198921198992119864V2211987716 = 120588119892119899

2V2211987716 (10)


119899 = radic11989920 + 1198992119864 (11)



120597z120597119905 + 120597 (119906ℎ)120597119909 + 120597 (Vℎ)120597119910 = 0 (12)

120597119906120597119905 + 119906120597119906120597119909 + V120597119906120597119910 + 119892120597119911120597119909 = minus119892radic1199062 + V21198622ℎ 119906 + 119891V +119872119909 (13)




119906 (119905 119909 119910) = 119873sum119899=1

119906119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119906119890119903)V (119905 119909 119910) = 119873sum

119899=1

V119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)V119890119903)119911 (119905 119909 119910) = 119873sum

119899=1

119911119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119911119890119903)(15)




119906119890 (119905 119909 119910) = 3sum119903=1

120593119890119901(119903) (119909 119910) 119906119890119903 (119905)V119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) V119890119903 (119905)119911119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) 119911119890119903 (119905)(16)


intΩ

[[3sum119903=1

120593119890119901(119903) 120597119911119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895) 3sum119903=1

120593119890119901(119903)ℎ119890119903+ ( 3sum119895=1

120597120593119890119901(119895)120597119909 ℎ119890119895) 3sum119903=1

120593119890119901(119903)119906119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 V119890119895)sdot 3sum119903=1

120593119890119901(119903)ℎ119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 ℎ119890119895) 3sum119903=1

120593119890119901(119903)V119890119903]]120593119890119902(119896)119889Ω

= 0 (119896 = 1 2 3)

(17)

intΩ

[[[[3sum119903=1

120593119890119901(119903) 120597119906119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895)( 3sum119903=1

120593119890119901(119903)119906119890119903)

+ ( 3sum119895=1

120597120593119890119901(119895)120597119910 119906119890119895)( 3sum119903=1

120593119890119901(119903)V119890119903) + 119892 3sum119903=1

120597120593119890119901(119903)120597119909 119911119890119903+ 119892sdot radic(sum3119895=1 120593119890119901(119895)119906119890119895)

2 + (sum3119895=1 120593119890119901(119895)V119890119895)2sum3119895=1 1198882119895 120593119890119901(119895)ℎ119890119895 ( 3sum119903=1

120593119890119901(119903)119906119890119903)

minus 3sum119903=1

119891119903120593119890119901(119903)V119890119903]]]]120593119890119902(119896)119889ΩΩ = 0 (119896 = 1 2 3)

(18)

119860119903119896 = intΩ120593119890119901(119903)120593119890119902(119896)dΩ 119861119903119896 = sum3119895=1(119906119890119895(120597120593119890119901(119895)120597119909) +


Ω(120597120593119890119901(119903)120597119909)120593119890119902(119896)dΩ1198671015840119903119896 = 119892int

Ω(120597120593119890119901(119903)120597119910)120593119890119902(119896)dΩ 119869119903119896 = int

Ω119891119903120593119890119901(119903)120593119890119902(119896)dΩ




Av + E1015840u + F1015840v +H1015840z + Iv + Ju = 0(19)

where z = 120597119911112059711990512059711991121205971199051205971199113120597119905

119890 u = 120597119906112059711990512059711990621205971199051205971199063120597119905

119890 v = 120597V1120597119905120597V2120597119905120597V3120597119905

119890 z = 119911111991121199113119890

h = ℎ1ℎ2ℎ3

119890 u = 119906111990621199063119890 v = V1

V2V3119890 A = [ 11986011 11986012 1198601311986021 11986022 11986023

11986031 11986032 11986033] 119861 119862



A119879z119905+Δ119905 = A119879z



A119879v119905+Δ119905

= A119879v119905

minus Δ119905 [H1015840119879z119905 + (E1015840119879 + J119879) u119905 + (F1015840119879 + I119879) v119905]

(20)


A0u119905+Δ119905


A0v119905+Δ119905

= A119879v119905


119905 minus Δ119905 (B119879h119905 + C119879u119905+Δ119905 + D119879v119905+Δ119905)

(21)



N

W

S

E

(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


-6 - 0

-24 - -18-30 - -24

-18 - -12-12 - -6

-36 - -30-42 - -36-48 - -42-54 - -48-60 - -54-66 - -60-72 - -66-78 - -72-84 - -78

Below -84Undefined

N

W

S

E




8162013 000

8172013 000

8182013 000

8192013 000

8202013 000

8212013 000

8222013 000

8232013 000

8242013 000

8252013 000


minus25minus2

minus15minus1

minus050

051

152

25

Tida

l Lev

el (m

)









0

40

80

120

160

Veloci

ty in

B1

(cms

)

19 24 5 10 1514Time (h)

(a)


060

120180240300360

14 19 24 5 10 15Time (h)D

irec

tion

in B

1 (∘

)

(b)


0

40

80

120

160

Veloci

ty in

B2

(cms

)

19 24 5 10 1514

Time (h)

(c)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(d)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B3

(cms

)

(e)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(f)


0

40

80

120

160

Veloci

ty in

B4

(cms

)

19 24 5 10 1514

Time (h)

(g)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514Time (h)

(h)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B5

(cms

)

(i)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)









RoughnessTrend Line


027

028

029

030

031

Com

preh

ensiv

e Rou

ghne

ss

1minus1

2minus2

3minus3

4minus4

5minus5

6minus6

7minus7





119899 = 001899 sdot ln (V) + 028441 (22)






A


0 ms m

Y

XZ

minus

minus

(ms)


B


0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018









inlet

60m240m

outlet100m

XYZ

(a) (b)



00

04

08

12

16

Velo

city

(ms

)










1199111 + 1199011120588119892 + 1205721V212119892 = 1199112 + 1199012120588119892 + 1205722V

222119892 + ℎ1198911minus2 (3)


Table1Re

lationshipbetweenim

pellerrsquos

rotatin

gspeedandinflo

wvelocity

Inflo

wVe

locity

(ms)

Parameter

sIm

pelle

rRotatin

gPo

sition

perS

econ

dRe

latio

nshi

pSchematicbetw

een

Impelle

rrsquosRo

tatin

gSp

eedAng

ular

Speedan

dIn

flowVe

locity

Ang

ular

Speed

(rad

s)

Rotatin

gSp

eed

(rm

in)

00

05

10

15

20

25

30


48

1216

200

Rota

ting

Spee

d (r

min

)

00

05

10

15

20

25

30


04

08

12

16

20

00

Ang

ular

Spe

ed (r

ads

)

0614

04

382

0921

06

573

1229

08

764

1536

1095

5

1843

121146

2150

141337

2457

161528


p1v1

1

1

p2v2

2

2

L1

L2

L





ℎ1198911minus2 = 120582 1198714119877 V212119892 (5)


120582 = 81198921198622 (6)


119862 = 111989911986411987716 (7)




120591 = 120588119892119877119869 = 120588119892 V21198622 = 1205881198921198992V211987716 (9)



120591 = 1205910 + Δ120591 = 120588119892119877119869 = 12058811989211989920V2211987716 + 1205881198921198992119864V2211987716 = 120588119892119899

2V2211987716 (10)


119899 = radic11989920 + 1198992119864 (11)



120597z120597119905 + 120597 (119906ℎ)120597119909 + 120597 (Vℎ)120597119910 = 0 (12)

120597119906120597119905 + 119906120597119906120597119909 + V120597119906120597119910 + 119892120597119911120597119909 = minus119892radic1199062 + V21198622ℎ 119906 + 119891V +119872119909 (13)




119906 (119905 119909 119910) = 119873sum119899=1

119906119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119906119890119903)V (119905 119909 119910) = 119873sum

119899=1

V119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)V119890119903)119911 (119905 119909 119910) = 119873sum

119899=1

119911119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119911119890119903)(15)




119906119890 (119905 119909 119910) = 3sum119903=1

120593119890119901(119903) (119909 119910) 119906119890119903 (119905)V119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) V119890119903 (119905)119911119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) 119911119890119903 (119905)(16)


intΩ

[[3sum119903=1

120593119890119901(119903) 120597119911119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895) 3sum119903=1

120593119890119901(119903)ℎ119890119903+ ( 3sum119895=1

120597120593119890119901(119895)120597119909 ℎ119890119895) 3sum119903=1

120593119890119901(119903)119906119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 V119890119895)sdot 3sum119903=1

120593119890119901(119903)ℎ119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 ℎ119890119895) 3sum119903=1

120593119890119901(119903)V119890119903]]120593119890119902(119896)119889Ω

= 0 (119896 = 1 2 3)

(17)

intΩ

[[[[3sum119903=1

120593119890119901(119903) 120597119906119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895)( 3sum119903=1

120593119890119901(119903)119906119890119903)

+ ( 3sum119895=1

120597120593119890119901(119895)120597119910 119906119890119895)( 3sum119903=1

120593119890119901(119903)V119890119903) + 119892 3sum119903=1

120597120593119890119901(119903)120597119909 119911119890119903+ 119892sdot radic(sum3119895=1 120593119890119901(119895)119906119890119895)

2 + (sum3119895=1 120593119890119901(119895)V119890119895)2sum3119895=1 1198882119895 120593119890119901(119895)ℎ119890119895 ( 3sum119903=1

120593119890119901(119903)119906119890119903)

minus 3sum119903=1

119891119903120593119890119901(119903)V119890119903]]]]120593119890119902(119896)119889ΩΩ = 0 (119896 = 1 2 3)

(18)

119860119903119896 = intΩ120593119890119901(119903)120593119890119902(119896)dΩ 119861119903119896 = sum3119895=1(119906119890119895(120597120593119890119901(119895)120597119909) +


Ω(120597120593119890119901(119903)120597119909)120593119890119902(119896)dΩ1198671015840119903119896 = 119892int

Ω(120597120593119890119901(119903)120597119910)120593119890119902(119896)dΩ 119869119903119896 = int

Ω119891119903120593119890119901(119903)120593119890119902(119896)dΩ




Av + E1015840u + F1015840v +H1015840z + Iv + Ju = 0(19)

where z = 120597119911112059711990512059711991121205971199051205971199113120597119905

119890 u = 120597119906112059711990512059711990621205971199051205971199063120597119905

119890 v = 120597V1120597119905120597V2120597119905120597V3120597119905

119890 z = 119911111991121199113119890

h = ℎ1ℎ2ℎ3

119890 u = 119906111990621199063119890 v = V1

V2V3119890 A = [ 11986011 11986012 1198601311986021 11986022 11986023

11986031 11986032 11986033] 119861 119862



A119879z119905+Δ119905 = A119879z



A119879v119905+Δ119905

= A119879v119905

minus Δ119905 [H1015840119879z119905 + (E1015840119879 + J119879) u119905 + (F1015840119879 + I119879) v119905]

(20)


A0u119905+Δ119905


A0v119905+Δ119905

= A119879v119905


119905 minus Δ119905 (B119879h119905 + C119879u119905+Δ119905 + D119879v119905+Δ119905)

(21)



N

W

S

E

(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


-6 - 0

-24 - -18-30 - -24

-18 - -12-12 - -6

-36 - -30-42 - -36-48 - -42-54 - -48-60 - -54-66 - -60-72 - -66-78 - -72-84 - -78

Below -84Undefined

N

W

S

E




8162013 000

8172013 000

8182013 000

8192013 000

8202013 000

8212013 000

8222013 000

8232013 000

8242013 000

8252013 000


minus25minus2

minus15minus1

minus050

051

152

25

Tida

l Lev

el (m

)









0

40

80

120

160

Veloci

ty in

B1

(cms

)

19 24 5 10 1514Time (h)

(a)


060

120180240300360

14 19 24 5 10 15Time (h)D

irec

tion

in B

1 (∘

)

(b)


0

40

80

120

160

Veloci

ty in

B2

(cms

)

19 24 5 10 1514

Time (h)

(c)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(d)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B3

(cms

)

(e)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(f)


0

40

80

120

160

Veloci

ty in

B4

(cms

)

19 24 5 10 1514

Time (h)

(g)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514Time (h)

(h)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B5

(cms

)

(i)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)









RoughnessTrend Line


027

028

029

030

031

Com

preh

ensiv

e Rou

ghne

ss

1minus1

2minus2

3minus3

4minus4

5minus5

6minus6

7minus7





119899 = 001899 sdot ln (V) + 028441 (22)






A


0 ms m

Y

XZ

minus

minus

(ms)


B


0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018









Table1Re

lationshipbetweenim

pellerrsquos

rotatin

gspeedandinflo

wvelocity

Inflo

wVe

locity

(ms)

Parameter

sIm

pelle

rRotatin

gPo

sition

perS

econ

dRe

latio

nshi

pSchematicbetw

een

Impelle

rrsquosRo

tatin

gSp

eedAng

ular

Speedan

dIn

flowVe

locity

Ang

ular

Speed

(rad

s)

Rotatin

gSp

eed

(rm

in)

00

05

10

15

20

25

30


48

1216

200

Rota

ting

Spee

d (r

min

)

00

05

10

15

20

25

30


04

08

12

16

20

00

Ang

ular

Spe

ed (r

ads

)

0614

04

382

0921

06

573

1229

08

764

1536

1095

5

1843

121146

2150

141337

2457

161528


p1v1

1

1

p2v2

2

2

L1

L2

L





ℎ1198911minus2 = 120582 1198714119877 V212119892 (5)


120582 = 81198921198622 (6)


119862 = 111989911986411987716 (7)




120591 = 120588119892119877119869 = 120588119892 V21198622 = 1205881198921198992V211987716 (9)



120591 = 1205910 + Δ120591 = 120588119892119877119869 = 12058811989211989920V2211987716 + 1205881198921198992119864V2211987716 = 120588119892119899

2V2211987716 (10)


119899 = radic11989920 + 1198992119864 (11)



120597z120597119905 + 120597 (119906ℎ)120597119909 + 120597 (Vℎ)120597119910 = 0 (12)

120597119906120597119905 + 119906120597119906120597119909 + V120597119906120597119910 + 119892120597119911120597119909 = minus119892radic1199062 + V21198622ℎ 119906 + 119891V +119872119909 (13)




119906 (119905 119909 119910) = 119873sum119899=1

119906119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119906119890119903)V (119905 119909 119910) = 119873sum

119899=1

V119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)V119890119903)119911 (119905 119909 119910) = 119873sum

119899=1

119911119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119911119890119903)(15)




119906119890 (119905 119909 119910) = 3sum119903=1

120593119890119901(119903) (119909 119910) 119906119890119903 (119905)V119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) V119890119903 (119905)119911119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) 119911119890119903 (119905)(16)


intΩ

[[3sum119903=1

120593119890119901(119903) 120597119911119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895) 3sum119903=1

120593119890119901(119903)ℎ119890119903+ ( 3sum119895=1

120597120593119890119901(119895)120597119909 ℎ119890119895) 3sum119903=1

120593119890119901(119903)119906119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 V119890119895)sdot 3sum119903=1

120593119890119901(119903)ℎ119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 ℎ119890119895) 3sum119903=1

120593119890119901(119903)V119890119903]]120593119890119902(119896)119889Ω

= 0 (119896 = 1 2 3)

(17)

intΩ

[[[[3sum119903=1

120593119890119901(119903) 120597119906119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895)( 3sum119903=1

120593119890119901(119903)119906119890119903)

+ ( 3sum119895=1

120597120593119890119901(119895)120597119910 119906119890119895)( 3sum119903=1

120593119890119901(119903)V119890119903) + 119892 3sum119903=1

120597120593119890119901(119903)120597119909 119911119890119903+ 119892sdot radic(sum3119895=1 120593119890119901(119895)119906119890119895)

2 + (sum3119895=1 120593119890119901(119895)V119890119895)2sum3119895=1 1198882119895 120593119890119901(119895)ℎ119890119895 ( 3sum119903=1

120593119890119901(119903)119906119890119903)

minus 3sum119903=1

119891119903120593119890119901(119903)V119890119903]]]]120593119890119902(119896)119889ΩΩ = 0 (119896 = 1 2 3)

(18)

119860119903119896 = intΩ120593119890119901(119903)120593119890119902(119896)dΩ 119861119903119896 = sum3119895=1(119906119890119895(120597120593119890119901(119895)120597119909) +


Ω(120597120593119890119901(119903)120597119909)120593119890119902(119896)dΩ1198671015840119903119896 = 119892int

Ω(120597120593119890119901(119903)120597119910)120593119890119902(119896)dΩ 119869119903119896 = int

Ω119891119903120593119890119901(119903)120593119890119902(119896)dΩ




Av + E1015840u + F1015840v +H1015840z + Iv + Ju = 0(19)

where z = 120597119911112059711990512059711991121205971199051205971199113120597119905

119890 u = 120597119906112059711990512059711990621205971199051205971199063120597119905

119890 v = 120597V1120597119905120597V2120597119905120597V3120597119905

119890 z = 119911111991121199113119890

h = ℎ1ℎ2ℎ3

119890 u = 119906111990621199063119890 v = V1

V2V3119890 A = [ 11986011 11986012 1198601311986021 11986022 11986023

11986031 11986032 11986033] 119861 119862



A119879z119905+Δ119905 = A119879z



A119879v119905+Δ119905

= A119879v119905

minus Δ119905 [H1015840119879z119905 + (E1015840119879 + J119879) u119905 + (F1015840119879 + I119879) v119905]

(20)


A0u119905+Δ119905


A0v119905+Δ119905

= A119879v119905


119905 minus Δ119905 (B119879h119905 + C119879u119905+Δ119905 + D119879v119905+Δ119905)

(21)



N

W

S

E

(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


-6 - 0

-24 - -18-30 - -24

-18 - -12-12 - -6

-36 - -30-42 - -36-48 - -42-54 - -48-60 - -54-66 - -60-72 - -66-78 - -72-84 - -78

Below -84Undefined

N

W

S

E




8162013 000

8172013 000

8182013 000

8192013 000

8202013 000

8212013 000

8222013 000

8232013 000

8242013 000

8252013 000


minus25minus2

minus15minus1

minus050

051

152

25

Tida

l Lev

el (m

)









0

40

80

120

160

Veloci

ty in

B1

(cms

)

19 24 5 10 1514Time (h)

(a)


060

120180240300360

14 19 24 5 10 15Time (h)D

irec

tion

in B

1 (∘

)

(b)


0

40

80

120

160

Veloci

ty in

B2

(cms

)

19 24 5 10 1514

Time (h)

(c)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(d)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B3

(cms

)

(e)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(f)


0

40

80

120

160

Veloci

ty in

B4

(cms

)

19 24 5 10 1514

Time (h)

(g)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514Time (h)

(h)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B5

(cms

)

(i)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)









RoughnessTrend Line


027

028

029

030

031

Com

preh

ensiv

e Rou

ghne

ss

1minus1

2minus2

3minus3

4minus4

5minus5

6minus6

7minus7





119899 = 001899 sdot ln (V) + 028441 (22)






A


0 ms m

Y

XZ

minus

minus

(ms)


B


0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018









p1v1

1

1

p2v2

2

2

L1

L2

L





ℎ1198911minus2 = 120582 1198714119877 V212119892 (5)


120582 = 81198921198622 (6)


119862 = 111989911986411987716 (7)




120591 = 120588119892119877119869 = 120588119892 V21198622 = 1205881198921198992V211987716 (9)



120591 = 1205910 + Δ120591 = 120588119892119877119869 = 12058811989211989920V2211987716 + 1205881198921198992119864V2211987716 = 120588119892119899

2V2211987716 (10)


119899 = radic11989920 + 1198992119864 (11)



120597z120597119905 + 120597 (119906ℎ)120597119909 + 120597 (Vℎ)120597119910 = 0 (12)

120597119906120597119905 + 119906120597119906120597119909 + V120597119906120597119910 + 119892120597119911120597119909 = minus119892radic1199062 + V21198622ℎ 119906 + 119891V +119872119909 (13)




119906 (119905 119909 119910) = 119873sum119899=1

119906119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119906119890119903)V (119905 119909 119910) = 119873sum

119899=1

V119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)V119890119903)119911 (119905 119909 119910) = 119873sum

119899=1

119911119899 (119905) 120593119899 (119909 119910) = 119872sum119890=1

( 3sum119903=1

120593119890119901(119903)119911119890119903)(15)




119906119890 (119905 119909 119910) = 3sum119903=1

120593119890119901(119903) (119909 119910) 119906119890119903 (119905)V119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) V119890119903 (119905)119911119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) 119911119890119903 (119905)(16)


intΩ

[[3sum119903=1

120593119890119901(119903) 120597119911119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895) 3sum119903=1

120593119890119901(119903)ℎ119890119903+ ( 3sum119895=1

120597120593119890119901(119895)120597119909 ℎ119890119895) 3sum119903=1

120593119890119901(119903)119906119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 V119890119895)sdot 3sum119903=1

120593119890119901(119903)ℎ119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 ℎ119890119895) 3sum119903=1

120593119890119901(119903)V119890119903]]120593119890119902(119896)119889Ω

= 0 (119896 = 1 2 3)

(17)

intΩ

[[[[3sum119903=1

120593119890119901(119903) 120597119906119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895)( 3sum119903=1

120593119890119901(119903)119906119890119903)

+ ( 3sum119895=1

120597120593119890119901(119895)120597119910 119906119890119895)( 3sum119903=1

120593119890119901(119903)V119890119903) + 119892 3sum119903=1

120597120593119890119901(119903)120597119909 119911119890119903+ 119892sdot radic(sum3119895=1 120593119890119901(119895)119906119890119895)

2 + (sum3119895=1 120593119890119901(119895)V119890119895)2sum3119895=1 1198882119895 120593119890119901(119895)ℎ119890119895 ( 3sum119903=1

120593119890119901(119903)119906119890119903)

minus 3sum119903=1

119891119903120593119890119901(119903)V119890119903]]]]120593119890119902(119896)119889ΩΩ = 0 (119896 = 1 2 3)

(18)

119860119903119896 = intΩ120593119890119901(119903)120593119890119902(119896)dΩ 119861119903119896 = sum3119895=1(119906119890119895(120597120593119890119901(119895)120597119909) +


Ω(120597120593119890119901(119903)120597119909)120593119890119902(119896)dΩ1198671015840119903119896 = 119892int

Ω(120597120593119890119901(119903)120597119910)120593119890119902(119896)dΩ 119869119903119896 = int

Ω119891119903120593119890119901(119903)120593119890119902(119896)dΩ




Av + E1015840u + F1015840v +H1015840z + Iv + Ju = 0(19)

where z = 120597119911112059711990512059711991121205971199051205971199113120597119905

119890 u = 120597119906112059711990512059711990621205971199051205971199063120597119905

119890 v = 120597V1120597119905120597V2120597119905120597V3120597119905

119890 z = 119911111991121199113119890

h = ℎ1ℎ2ℎ3

119890 u = 119906111990621199063119890 v = V1

V2V3119890 A = [ 11986011 11986012 1198601311986021 11986022 11986023

11986031 11986032 11986033] 119861 119862



A119879z119905+Δ119905 = A119879z



A119879v119905+Δ119905

= A119879v119905

minus Δ119905 [H1015840119879z119905 + (E1015840119879 + J119879) u119905 + (F1015840119879 + I119879) v119905]

(20)


A0u119905+Δ119905


A0v119905+Δ119905

= A119879v119905


119905 minus Δ119905 (B119879h119905 + C119879u119905+Δ119905 + D119879v119905+Δ119905)

(21)



N

W

S

E

(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


-6 - 0

-24 - -18-30 - -24

-18 - -12-12 - -6

-36 - -30-42 - -36-48 - -42-54 - -48-60 - -54-66 - -60-72 - -66-78 - -72-84 - -78

Below -84Undefined

N

W

S

E




8162013 000

8172013 000

8182013 000

8192013 000

8202013 000

8212013 000

8222013 000

8232013 000

8242013 000

8252013 000


minus25minus2

minus15minus1

minus050

051

152

25

Tida

l Lev

el (m

)









0

40

80

120

160

Veloci

ty in

B1

(cms

)

19 24 5 10 1514Time (h)

(a)


060

120180240300360

14 19 24 5 10 15Time (h)D

irec

tion

in B

1 (∘

)

(b)


0

40

80

120

160

Veloci

ty in

B2

(cms

)

19 24 5 10 1514

Time (h)

(c)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(d)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B3

(cms

)

(e)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(f)


0

40

80

120

160

Veloci

ty in

B4

(cms

)

19 24 5 10 1514

Time (h)

(g)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514Time (h)

(h)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B5

(cms

)

(i)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)









RoughnessTrend Line


027

028

029

030

031

Com

preh

ensiv

e Rou

ghne

ss

1minus1

2minus2

3minus3

4minus4

5minus5

6minus6

7minus7





119899 = 001899 sdot ln (V) + 028441 (22)






A


0 ms m

Y

XZ

minus

minus

(ms)


B


0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018










119906119890 (119905 119909 119910) = 3sum119903=1

120593119890119901(119903) (119909 119910) 119906119890119903 (119905)V119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) V119890119903 (119905)119911119890 (119905 119909 119910) = 3sum

119903=1

120593119890119901(119903) (119909 119910) 119911119890119903 (119905)(16)


intΩ

[[3sum119903=1

120593119890119901(119903) 120597119911119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895) 3sum119903=1

120593119890119901(119903)ℎ119890119903+ ( 3sum119895=1

120597120593119890119901(119895)120597119909 ℎ119890119895) 3sum119903=1

120593119890119901(119903)119906119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 V119890119895)sdot 3sum119903=1

120593119890119901(119903)ℎ119890119903 + ( 3sum119895=1

120597120593119890119901(119895)120597119910 ℎ119890119895) 3sum119903=1

120593119890119901(119903)V119890119903]]120593119890119902(119896)119889Ω

= 0 (119896 = 1 2 3)

(17)

intΩ

[[[[3sum119903=1

120593119890119901(119903) 120597119906119890119903120597119905 + (3sum119895=1

120597120593119890119901(119895)120597119909 119906119890119895)( 3sum119903=1

120593119890119901(119903)119906119890119903)

+ ( 3sum119895=1

120597120593119890119901(119895)120597119910 119906119890119895)( 3sum119903=1

120593119890119901(119903)V119890119903) + 119892 3sum119903=1

120597120593119890119901(119903)120597119909 119911119890119903+ 119892sdot radic(sum3119895=1 120593119890119901(119895)119906119890119895)

2 + (sum3119895=1 120593119890119901(119895)V119890119895)2sum3119895=1 1198882119895 120593119890119901(119895)ℎ119890119895 ( 3sum119903=1

120593119890119901(119903)119906119890119903)

minus 3sum119903=1

119891119903120593119890119901(119903)V119890119903]]]]120593119890119902(119896)119889ΩΩ = 0 (119896 = 1 2 3)

(18)

119860119903119896 = intΩ120593119890119901(119903)120593119890119902(119896)dΩ 119861119903119896 = sum3119895=1(119906119890119895(120597120593119890119901(119895)120597119909) +


Ω(120597120593119890119901(119903)120597119909)120593119890119902(119896)dΩ1198671015840119903119896 = 119892int

Ω(120597120593119890119901(119903)120597119910)120593119890119902(119896)dΩ 119869119903119896 = int

Ω119891119903120593119890119901(119903)120593119890119902(119896)dΩ




Av + E1015840u + F1015840v +H1015840z + Iv + Ju = 0(19)

where z = 120597119911112059711990512059711991121205971199051205971199113120597119905

119890 u = 120597119906112059711990512059711990621205971199051205971199063120597119905

119890 v = 120597V1120597119905120597V2120597119905120597V3120597119905

119890 z = 119911111991121199113119890

h = ℎ1ℎ2ℎ3

119890 u = 119906111990621199063119890 v = V1

V2V3119890 A = [ 11986011 11986012 1198601311986021 11986022 11986023

11986031 11986032 11986033] 119861 119862



A119879z119905+Δ119905 = A119879z



A119879v119905+Δ119905

= A119879v119905

minus Δ119905 [H1015840119879z119905 + (E1015840119879 + J119879) u119905 + (F1015840119879 + I119879) v119905]

(20)


A0u119905+Δ119905


A0v119905+Δ119905

= A119879v119905


119905 minus Δ119905 (B119879h119905 + C119879u119905+Δ119905 + D119879v119905+Δ119905)

(21)



N

W

S

E

(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


-6 - 0

-24 - -18-30 - -24

-18 - -12-12 - -6

-36 - -30-42 - -36-48 - -42-54 - -48-60 - -54-66 - -60-72 - -66-78 - -72-84 - -78

Below -84Undefined

N

W

S

E




8162013 000

8172013 000

8182013 000

8192013 000

8202013 000

8212013 000

8222013 000

8232013 000

8242013 000

8252013 000


minus25minus2

minus15minus1

minus050

051

152

25

Tida

l Lev

el (m

)









0

40

80

120

160

Veloci

ty in

B1

(cms

)

19 24 5 10 1514Time (h)

(a)


060

120180240300360

14 19 24 5 10 15Time (h)D

irec

tion

in B

1 (∘

)

(b)


0

40

80

120

160

Veloci

ty in

B2

(cms

)

19 24 5 10 1514

Time (h)

(c)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(d)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B3

(cms

)

(e)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(f)


0

40

80

120

160

Veloci

ty in

B4

(cms

)

19 24 5 10 1514

Time (h)

(g)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514Time (h)

(h)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B5

(cms

)

(i)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)









RoughnessTrend Line


027

028

029

030

031

Com

preh

ensiv

e Rou

ghne

ss

1minus1

2minus2

3minus3

4minus4

5minus5

6minus6

7minus7





119899 = 001899 sdot ln (V) + 028441 (22)






A


0 ms m

Y

XZ

minus

minus

(ms)


B


0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018









N

W

S

E

(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


(km)

320

321

322

323

324

325

326

327

40 42 44 46 48 50(km)


-6 - 0

-24 - -18-30 - -24

-18 - -12-12 - -6

-36 - -30-42 - -36-48 - -42-54 - -48-60 - -54-66 - -60-72 - -66-78 - -72-84 - -78

Below -84Undefined

N

W

S

E




8162013 000

8172013 000

8182013 000

8192013 000

8202013 000

8212013 000

8222013 000

8232013 000

8242013 000

8252013 000


minus25minus2

minus15minus1

minus050

051

152

25

Tida

l Lev

el (m

)









0

40

80

120

160

Veloci

ty in

B1

(cms

)

19 24 5 10 1514Time (h)

(a)


060

120180240300360

14 19 24 5 10 15Time (h)D

irec

tion

in B

1 (∘

)

(b)


0

40

80

120

160

Veloci

ty in

B2

(cms

)

19 24 5 10 1514

Time (h)

(c)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(d)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B3

(cms

)

(e)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(f)


0

40

80

120

160

Veloci

ty in

B4

(cms

)

19 24 5 10 1514

Time (h)

(g)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514Time (h)

(h)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B5

(cms

)

(i)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)









RoughnessTrend Line


027

028

029

030

031

Com

preh

ensiv

e Rou

ghne

ss

1minus1

2minus2

3minus3

4minus4

5minus5

6minus6

7minus7





119899 = 001899 sdot ln (V) + 028441 (22)






A


0 ms m

Y

XZ

minus

minus

(ms)


B


0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018










0

40

80

120

160

Veloci

ty in

B1

(cms

)

19 24 5 10 1514Time (h)

(a)


060

120180240300360

14 19 24 5 10 15Time (h)D

irec

tion

in B

1 (∘

)

(b)


0

40

80

120

160

Veloci

ty in

B2

(cms

)

19 24 5 10 1514

Time (h)

(c)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(d)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B3

(cms

)

(e)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)

(f)


0

40

80

120

160

Veloci

ty in

B4

(cms

)

19 24 5 10 1514

Time (h)

(g)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514Time (h)

(h)


19 24 5 10 1514

Time (h)0

40

80

120

160

Veloci

ty in

B5

(cms

)

(i)


060

120180240300360

Dir

ectio

n in

B

(∘)

19 24 5 10 1514

Time (h)









RoughnessTrend Line


027

028

029

030

031

Com

preh

ensiv

e Rou

ghne

ss

1minus1

2minus2

3minus3

4minus4

5minus5

6minus6

7minus7





119899 = 001899 sdot ln (V) + 028441 (22)






A


0 ms m

Y

XZ

minus

minus

(ms)


B


0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018















RoughnessTrend Line


027

028

029

030

031

Com

preh

ensiv

e Rou

ghne

ss

1minus1

2minus2

3minus3

4minus4

5minus5

6minus6

7minus7





119899 = 001899 sdot ln (V) + 028441 (22)






A


0 ms m

Y

XZ

minus

minus

(ms)


B


0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018











A


0 ms m

Y

XZ

minus

minus

(ms)


B


0 ms

105

m

Y

XZ

minus

minus

(ms)


C


0 ms

140

m

Y

XZ

minus

minus

(ms)


D


0 ms

175

m

Y

XZ

minus

minus

(ms)


E


0 ms

210

m

Y

XZ

minus

minus

(ms)


F


0 ms

245

m

Y

XZ

minus

minus

(ms)


G


0 ms

280

m

Y

XZ

minus

minus

(ms)



Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018









Table3Simulated

results

indifferent

combinatio

ns

Com

binatio

nsPressure

p 1(Pa)

Pressure

p 2(Pa)

Energy

Lossh f

ResistanceC

oefficient120582

ChezyCoefficientC

Equivalent

Roug

hness119899 119864

Com

positiveR

ough

ness119899

No

V120596

(ms)

(rads)

10614

04

101097

101079

0015

1598

7005

0274

0275

20921

06

100777

100737

0036

1687

6817

0282

0283

312

2908

100301

100228

006

817

606674

0288

0289

415

3610

9966

499551

0109

1809

6583

0292

0293

518

4312

98854

98693

0160

1848

6514

0295

0296

6215

1497836

97616

0222

1887

644

50298

0299

72457

1696593

96304

0296

1923

6385

0301

0302


NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018









NW

S

E

(km)

321

322

323

324

325

326

327


44 45 46 47(km)













(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018











(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(a)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(b)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(c)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(d)

(km)

(km)

NW E

S

(ms)-0015

-0020

-0025

-0030

-0035

-0040

-0045

-0050B Location

(e)



0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018









0 4 8 12 16 20 24

Time (h)


minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)

0 4 8 12 16 20 24Time (h)


minus0004

0000

0004

0008

0012

0016

0020

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

01

02

03

04

Flow

Vel

ocity

()

(d)

0 4 8 12 16 20 24

Time (h)


minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

1

2

3

4

5

Flow

Vel

ocity

()

(f)

0 4 8 12 16 20 24

Time (h)


minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

0

2

4

6

8

Flow

Vel

ocity

()

(h)

Figure 14 Continued


0 4 8 12 16 20 24

Time (h)


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minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


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minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018









0 4 8 12 16 20 24

Time (h)


minus0020

minus0016

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(i)

0 4 8 12 16 20 24

Rela

tive D

iffer

ence

of

Time (h)

00

04

08

12

16

Flow

Vel

ocity

()


0 4 8 12 16 20 24

Time (h)


minus0024

minus0016

minus0008

0000

0008

Diff

erence

of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

20

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24Time (h)

minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

000

006

012

018

024

Flow

Vel

ocity

()

(d)


0 4 8 12 16 20 24

Time (h)

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()




0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018










0 4 8 12 16 20 24

Time (h)

minus0012

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(g)


0 4 8 12 16 20 24

Time (h)

minus010

minus008

minus006

minus004

minus002

000

002

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

0

2

4

6

8

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

10

Flow

Vel

ocity

()



0 4 8 12 16 20 24

Time (h)

minus0018

minus0012

minus0006

0000

0006

Diff

eren

ce of F

low

Vel

ocity

(ms

)

(a)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

04

08

12

16

Flow

Vel

ocity

()

(b)


0 4 8 12 16 20 24

Time (h)minus0004

0000

0004

0008

0012

Diff

erence

of F

low

Vel

ocity

(ms

)

(c)

Rela

tive D

iffer

ence

of

00

01

02

03

Flow

Vel

ocity

()

4 8 12 16 20 240Time (h)




0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018










0 4 8 12 16 20 24

Time (h)

minus0008

minus0004

0000

0004

Diff

erence

of F

low

Vel

ocity

(ms

)

(e)


0 4 8 12 16 20 24

Time (h)

minus003

minus002

minus001

000

001

Diff

erence

of F

low

Vel

ocity

(ms

)

(f)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

Flow

Vel

ocity

()

(g)


0 4 8 12 16 20 24

Time (h)

minus006

minus004

minus002

000

002

004

Diff

erence

of F

low

Vel

ocity

(ms

)

(h)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

0

1

2

3

4

Flow

Vel

ocity

()

(i)

Rela

tive D

iffer

ence

of

4 8 12 16 20 240Time (h)

00

02

04

06

08

Flow

Vel

ocity

()

(j)






Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018









Table5Ex

tremum

offlo

wvelocityvaria

tion

Locatio

nRa

dius

100m

Radius

200m

Radius

300m

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

Deceleration

Growth

RelativeD

ifference

(ms)

(ms)

()

(ms)

(ms)

()

(ms)

(ms)

()

B1-0023

000

617

58-0022

0007

1754

-0016

000

613

91B2

-0001

0017

0419

-0001

0011

0226

-0003

000

90281

B3-0064

0034

4754

-0043

0024

3354

-0034

0007

3147

B4-0091

0002

7461

-0088

001

6877

-0053

0024

3947

B5-0019

0002

1503

-0012

0003

0953

-0009

0003

0714



5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018










5 Conclusion



Data Availability






Acknowledgments


References

































Journal of












Journal of







Volume 2018






Volume 2018

































Journal of












Journal of







Volume 2018






Volume 2018








study on impact of turbine location on hydrodynamics in...

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