work summery

Flow Field Measurements for a Cross Flow Tidal Turbine

Advisors:

M.L. Peterson, Professor of Mechanical Engineering

H. Xue, Professor of Marine Science

R.W. Kimball, Professor at Maine Maritime Academy

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By Matthew Cameron

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1. Tidal energy resource assessment ~ A step to understanding of the impacts of

turbines on flow and the potential size of this renewable energy resource

2. Power array density ~ A single high efficiency turbine might not yield

highest power array density

!." R#$#% P#&'% C()%)*$'%+,$+*, -.-

Figure !."#. Power coe/cients of wind rotors of di0erent designs ["]

Figure !."". Torque coe/cients of wind rotors of di0erent designs ["]

Eric Hue, “Wind Power”

Method:

Analyze a single wake from a cross flow turbine in a steady and uniform flow

Motivations!

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Test Turbine!

• Outer Support

• Drive Shaft

• Inner Beam

• Horizontal Load Cell

• Turbine Support Arm

• Shroud

• Vertical Load Cell

Dynamometer & Drive Train

Blade Profile NACA 63018

~76. mm

Cross Flow Turbine

~0.3 meter

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Turbine Coefficients

Test Matrix

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Turbine Force Coefficients!

!

Ci =Energy outEnergy in

B!

A!

The Acoustic Doppler Velocity Meter (ADV)!

!"#$!%&'()*%$+,-.$-/.$0-123,$#&3'1,$

./0!12'+32-$!4*+3-'%#2!

45 0*6/-3$)&$7&*(,$8-)*&$$

9$:-),8$/,,.,.$)&$;,$(,,.,.$*($-%&'()*%$2-8)*%3,($)&$1-*/)-*/$07<$=$4>$

?5 0-123,$<-),$@A$+B$

C5 #,3&%*)D$<-/6,$$$$E5EE4$)&$F$1(G4$9$H(,.$)I&$E5C1(G4$-/.$45E$1(G4$

A5 !%%'8-%*,($-8,$-$J'/%)*&/$&J$K,3&%*)D$8-/6,$-/.$(*6/-3$)&$/&*(,$8-)*&$

>5 L/),8/-3$.-)-$2&((,((*/6$9CG>$*/.*K*.'-3$2*/6($!$4$.-)-$2&*/)$

~1.1m

8m

0.55m

Water Surface

Z

X

0.156m

h3 h2

h1

h4

2.4m

0.761m

1.2m

Y

Sample Volume

Center Line

Experimental Setup!

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./0!5!6+%78'+&!'3%*#&

49+39%+6:!

$$$$$9$!"#$*($M&'/),.$)&$)N,$O3&&8$$$$

$$$$$9$P'8;*/,$&K,82-(($)N,$!"#$

$$$$$9$PN,$!"#$(-123,$K&3'1,$*($3&%-),.$&/$)N,$%,/),8$&J$)N,$$ )'8;*/,$-/.$)&I$)-/Q$*/$)N,$R$.*8,%)*&/$

$$$$$9$P'8;*/,$)8-K,3($4>$1,),8($-/.$!"#$*($3&%-),.$$ -228&S*1-),3D$*/$)N,$%,/),8$$

)+;'!0-3%-<$+;:!

$$$$$9$!"#T($(-123,$K&3'1,$N,*6N)$

$$$$$9$!"#T($#,3&%*)D$8-/6,$$$$$$9$U-88*-6,$.*8,%)*&/$

$$$$$9$V3-.,$2&(*)*&/$&8$P0<$$

Different Blade Positions Directly over ADV

Only for low solidity turbine (2 blade test) !

-# +# .#

Center Line !Of ADV#

C.L# C.L#

1#2%3'#45+,5+,--#

3. Repeatability of velocity measurements!

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Test Accuracy & Repeatability!

1. Combination of different velocity range! 2. Repeatability Of blade position at x = 0!

±3.5°!

One dot (") is one blade form one test!

1. Reynolds’ Time Averaging!! ~ Method of separating turbulent and steady flow!! ~ The results are need to determine 2 and 3 !

Wake Characteristics Objectives !

2. Turbulent Kinetic Energy (TKE)!! ~ Determines the amount of fluctuation !! ! ! energy per volume!!

UMeasured = U Mean + " U Fluctuation

!

U Mean = [u v w ]" U Fluctuation = [ " u " v " w ]

3. Reynolds’ Shear!! ! ~ Also know as turbulent shear!! ! ~ Depicts the amount of momentum transfer !! ! ! across a plane by turbulent motion!

!

TKE ="2( # u 2 + # v 2 + # w 2)

!

" turb =# u # v # v # w # w # u

$

%

& & &

'

(

) ) )

4. Energy Spectrum (Wavelet Transform)!! ! ~ Determines the magnitude of wide range of !! ! ! frequencies over a continues time period !

4#2%3'#45+,5+,--#!

WL = URaw(t)" #( f ,t)Time$

Frequency$

!

"( f ,t) =

!

" turb >> "Lam

Wake Analysis!

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Raw ADV Velocity Data!

Rotation Matrix!

4<=+>'%9+:!

$$$$9$P&$.,),81*/,$)N,$<,D/&3.($U&12&/,/)($WXY$Z[$

$$$$9$:*)N$X$-/.$Z$)N,$I-Q,$%N-8-%),8*()*%($%-/$;,$28,.*%),.$

?@@+>';:!

~ low pass filter effect on !

~ The cut off frequency for the filter was shown to be 10Hz

:*/.&I$(*B,$'(,.$\$?>

Free Stream

Laminar Flow

! = Vc ú " 0

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Introduce Turbine & Surface Elevation Change

Power side

Return side

Effect on Surface Elevation

Influence: strong

1. Blockage effect

(ATurbine/Atank = 0.09)

2. Inflow Speed

3. Turbine height

4. Solidity

5. TSR

weak

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Surface Elevation Change

Low Solidity Turbine (2 Blades) High Solidity Turbine (4 Blades)

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Surface Elevation Change for Low Solidity Turbine

~Fast Fourier transform of surface elevation equal to blade frequency

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Flow Field Visualization

Vector Field

U

u

w

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Notes: ~ Four blade high solidity turbine (0.32) ~ TSR 1.4 (on design) ~ Random blade position - Blade position is a minor effect on flow field

~ One Vector is the mean of four data points

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Flow Field of Rotating Turbine Notes: ~ Two blades low solidity turbine (.16) ~ Three different blade position

~ One Vector is the mean of three data points

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Flow Field of Rotating Turbine

Flow Recovery

Laminar Flow

! = Vc U` " 0

X/D

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Flow Recovery using Reynolds !

1 0 1 2 3 4 5 6

1

0

1

u Mean for Position 1

Non Dimensional Distance (x/D)

Non

Dim

ensi

onal

Dis

tanc

e (x

/D)

& Ve

loci

ty (u

/Vc)

1 0 1 2 3 4 5 6

1

0

1

u’for Position 1


Non

Dim

ensi

onal

Dis

tanc

e (x

/D)

& Ve

loci

ty (u

/Vc)

1 0 1 2 3 4 5 6

1

0

1



1 0 1 2 3 4 5 6

1

0

1

u’for Position 3


1 0 1 2 3 4 5 6

1

0

1



1 0 1 2 3 4 5 6

1

0

1

u’for Position 2


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Low Solidity Turbine with Three Different Blade Positions

1 0 1 2 3 4 5 6

1

0

1



Non

Dim

ensi

onal

Dis

tanc

e (x

/D)

& V

eloc

ity (u

/Vc)

1 0 1 2 3 4 5 6

1

0

1

u’for Position 1


Non

Dim

ensi

onal

Dis

tanc

e (x

/D)

& V

eloc

ity (u

/Vc)

1 0 1 2 3 4 5 6

1

0

1



1 0 1 2 3 4 5 6

1

0

1

u’for Position 3


1 0 1 2 3 4 5 6

1

0

1



1 0 1 2 3 4 5 6

1

0

1

u’for Position 2


High Solidity Turbine

Region of Entrained Flow

Characteristics

!

u v w

"

#

$ $ $

%

&

' ' ' (

000

"

#

$ $ $

%

&

' ' '

u'v 'w'

"

#

$ $ $

%

&

' ' ' )

000

"

#

$ $ $

%

&

' ' '

L.E. Myers, (2010) !"#$%&'()*##+,-+# ++#

1 0 1 2 3 4 5 6

1

0

1

u Mean


Non

Dim

ensi

onal

Dis

tanc

e(z/

D) &

Vel

ocity

(U/V

c)

1 0 1 2 3 4 5 6

1

0

1

u Mean


Non

Dim

ensi

onal

Dis

tanc

e(z/

D) &

Vel

ocity

(U/V

c)

Off Design (TSR 0.9) Off Design (TSR 1.9)

1 0 1 2 3 4 5 61.75

1.25

0.75

0.25

0.25

0.75

1.25u Mean


Non

Dim

ensi

onal

Dis

tanc

e(z/

D)

& Ve

loci

ty(U

/Vc)

On Design (TSR 1.4)

u Mean for High Solidity & Different TSR

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1 0 1 2 3 4 5 6

1

0

1


Non

Dim

ensi

onal

Dis

tanc

e (z

/D)

& Ve

loci

ty (u

/Vc)

1 0 1 2 3 4 5 6

1

0

1


1 0 1 2 3 4 5 6

1

0

1



u Mean for Low Solidity & Different Blade Position

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Flow Bypass for High Solidity Turbine (0.32)

TSR Bypass Fraction

Power Side Return Side Total

0.9 0.033 0.013 0.05

1.4 (On design) 0.033 0.100 0.13

1.9 0.223 0.152 0.38

Results:#

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!

˙ V = wdA"

˙ V FB =˙ V Bypass

˙ V Re f

=wdx"

2# r# Vc

Flow Bypass for High Solidity Turbine (0.32)

Results:#

Free Spin 2.25 Prediction 0.65 to 0.75

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!

˙ V = wdA"

˙ V FB =˙ V Bypass

˙ V Re f

=wdx"

2# r# Vc

TSR Bypass Fraction

Total

Flow Bypass for Low Solidity Turbine (0.16)

Results:#

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TSR Blade Position

Bypass Fraction

Power Side

Return Side Total

2.25

1 ~0.032 ~0.052 ~0.08

2 ~0.043 ~0.091 ~0.13

3 ~0.045 ~0.068 ~0.11

Propagation of Turbulent Energy

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Turbulent Kinetic Energy for High Solidity Turbine (Vc=1.0ms-1)

!"#$%&'()*##+,-+# +4#1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.5

1

0.5

0

0.5

1

1.5

Turbulent Kinetic Energy


Non

Dime

nsio

nal

Dist

ance

(z/D

)&

Ener

gy p

er M

ass(

m2/

s2)

1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.5

1

0.5

0

0.5

1

1.5



Non

Dimensional Distance(z/D)

& Energy per Mass(m2/ s2)

1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.5

1

0.5

0

0.5

1

1.5



Non

Dime

nsio

nal

Dist

ance

(z/D

)&

Ener

gy p

er M

ass(

m2/

s2)

Reynolds Stress (u`w`) for High Solidity Turbine at (Vc=1.0ms-1)

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1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.5

1

0.5

0

0.5

1

1.5

Reynolds Shear


Non

Dime

nsio

nal

Dist

ance

(z/D

) &

She

ar(T

au/R

ho/V

c2)

1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.5

1

0.5

0

0.5

1

1.5

Reynolds Shear


Non


& Shear(Tau/Rho/Vc2)

1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.5

1

0.5

0

0.5

1

1.5

Reynolds Shear


Non


& Shear(Tau/Rho/Vc2)

Turbulent Kinetic Energy for Low Solidity Turbine at Vc=0.8ms-1

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Reynolds Stress (u`w`) for Low Solidity Turbine at Vc=0.8ms-1

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Energy Spectrum

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Energy Spectrum

Energy Spectrum For High Solidity Turbine (Vc=1.0ms-1)

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Energy Spectrum for Low Solidity Turbine (Vc=0.8ms-1)

The Flow Field

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Relation Turbulent Energy between Flow Bypass & Flow Recovery

How does turbulence diffusion compared to flow recovery & entrained flow?

X/D TKE " 0

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Reynolds Decomposition for High Solidity Turbine

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A#'+!

! BC!D#$$-*;+!#@!'8+!E+-2!+2'3-%2+&!F$#6!-'!B!'#!G!!

! ! &%-E+'+3;!&#62!;'+-E!@3#E!!H!0>!'#!IJ+3#!

! GC!)8+!F$K>'K-'%#2!9+$#>%'(!+L8%<%'!-!;K&&+2!<K%$&!K*!-2&!!!

! ! -<3K*'!+2&!#9+3!'8+!;-E+!;*->+!-;!'8+!E+-2!F$#6!>#$$-*;+! ! !

Reynolds Decomposition For Low Solidity Turbine

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Lessons Learned

)8+!M-9+$+'!8-;!8%78+3!*#'+2'%-$!-;!-2!-2-$(;%;!'##$!

!!!!!!I!)K3<K$+2'!N%2+'%>!?2+37(!

! ! !

!! !

! BC!.!M-9+$+'!@#3!+->8!KO!9O!-2&!6!6#K$&!(%+$&!+L->'!PK-2'%'%+;!#@!'8+!,+(2#$&;!"'3+;;!

2. Achieving the highest Nyquist frequency possible with hardware

3. Resolve a wide spectrum of vortices

!

WL = U(t)" e2# "i( t$ to ) f dfdt%%

!

TKE " WL( f ,t)df#

!

WLu = u(t)" #(t, f )dfdt$$WLv = v(t)" #(t, f )dfdt$$WLw = w(t)" #(t, f )dfdt$$

!

RS "WLu#WLwWLv#WLwWLv#WLu

!"#$%&'()*##+,-+# /+#

Lessons Learned

)8+!M-9+$+'!8-;!8%78+3!*#'+2'%-$!-;!-2!-2-$(;%;!!'##$!

!!!!!!I!Q3+$%E%2-3(!6-9+$+'!%2'+73-'%#2!3+;K$';!(%+$&%27!)K3<K$+2'!N%2+'%>!?2+37(!

! ! !

!! !

!"#$%&'()*##+,-+# /.#

University Of Maine

MTPI

Huijie Xue

Mick Peterson

Rich Kimball

Acknowledgments

Geoff deBree

Raul Urbina

Tom McKay

ORPC, Jarlath McEntee

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Questions

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?

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