getting started with two-phase flow systems

Two-Phase Flows Library rev11Romain Bonnet – Product Developer

Two-Phase Flows Library

2 copyright LMS International - 2013

Two-Phase Flows

Getting started with Two-Phase Flow systems


Main features Composed of elementary components used to model the physics of two-phase flows,

Used to monitor phase change occurrences,

Used to model energy transport,

Definition of the two-phases flow library (TPF)

Two phases flow calculations Computation of pressure losses, temperature levels, mass flow rates and enthalpy flowrates,

Computation of gas mass fraction evolution in the systems,

Thermal calculations Based on a lumped transient heat transfer approach,

Modeling of internal convective heat transfer (single phase or convective boiling orcondensation),

Computation of external flow convective heat transfer (moist air),


Main features The different states of the fluid modeled are:

Superheated gas or subcooled liquid (single phase) Saturated gas or saturated liquid Supercritical Two-phases

Variables displayed are total quantities,

Main assumptions Gravity in pipes is not accounted for so far,

Dealing with internal and external flows:

Main features and main assumptions

Internal flow External flow

Any refrigerant in TPF_FP01 (R134a, CO2, H20, etc)

Moist air

1D with homogeneous flow (no slip between the phases, homogeneous

temperature in the volume)

0D (no pressure loss calculation)


Classical manipulated variables:

Name Variable Unit

T Temperature °C

P (state variable) Pressure barA

ρ (state variable) Density kg/m**3

v Specific volume m**3/kg

x Gas mass fraction null

h Specific enthalpy kJ/kg

s Specific entropy kJ/kg/K

Cp Specific heat at constant pressure

kJ/kg/K

∆T Superheat (> 0) or subcooling (< 0)

°C

δp (p-pcrit) barA

μ Dynamic viscosity kg/m/s

λ Thermal conductivity W/m/K

σ Surface tension N/m

Dealing with fluid properties


Icon categories: Fluid properties

Transformers

Boundary conditions and sources

Sensors

Regular pressure drop components

Singular pressure drop components

Adiabatic capacitive elements

Convective heat exchange elements

Mechanical transformers

Moist air components

Components of the two-phases flow library

Connecting components together

Bond graph

Efforts variables: P [barA] and [kg/m**3] (states)

Flux variables: dm [kg/s] and dmh [W]

Special TPF variable: tpfnull: index of internal structure (c code) so that resistive elements can have access to all fluid properties within adjacent capacitive elements without having to recompute them. Ie special feature to enhance CPU time.

Link with other libraries: SIG (Signal), TH (Thermal)


(R) (C-R)(~C) (~C)


3 equations of states available in Imagine.Lab:

MBWR formulation (R134a, CO2…):

Helmholtz formulation (water, R245fa…):

ECS formulation (1234yf, R236ea, R236fa…):

232

20

19

1

ργ

i

cbi

i

cbi eTρaTρaTrρP iiii

Fluid properties: a piece of theory

n

k

cdt

k

RR

kkk en

RT

Aa

1

00 ,, TaTRTA


Tutorial 1:

Using these components, determine the state of R134a fluid under 3 barA and 5 degCconditions.

Use appropriate transformer component and sensor to display the same state usinganother system.

(tip on necessary icons: tpf_tr_pt_to_ph, tpf_ph_modulated_source, tpf_generic_sensor_extra)

Model refrigerant thermodynamics

and transport properties

Compute the state of a fluid at specified

conditions (fluid property calculator)

Determining the state of fluid with two thermodynamic variables


NIST database

Determining the state of fluid with two thermodynamic variables

Tutorial 1: Results


Main equations to keep in mind:

Maxwell criterion used to calculate the fluid saturation curve:

Gas mass fraction expression:

lgsat

vl

vgvvPdvP

lg

l

vv

vvx

Fluid properties: a piece of theory

P

Psat

liquid

A

C

K

B Gas

D

Isothermal T

isothermal TK

supercritical

v Vlsat Vgsat

1

2


Important and useful information about transformers

Name Single phase (liquid or vapor

Supercritical Two-phases and saturated

X X

X

X

X

X X X

X X X


Tutorial 2:

Display Mollier Diagram (P-h) of R600a fluid. To do this, use appropriate transformercomponents and vary the pressure between relevant values.

Use two additional systems to display the critical isothermal curve and another isothermalcurve (@40 degC)

(tips: use a logarithmic scalefor the pressure axis;remember plotting X-Y axis;saturation is easily defined byx=0 and/or x=1)

Getting familiar with typical two-phases flow diagrams


Tutorial 2: Results

Getting familiar with typical two-phases flow diagrams


Tutorial 3:

Study the temperatures, pressures and gas mass fraction within two closed volumes (1Leach) exchanging heat with each other using an aluminum conductance characterized by0.2m shape factor.

Parameters and inputs: Initial pressure: 3 barA for volume 1 and 4 barA for the other Initial gas mass fraction: 0.5 for each Fluid R134a

(tips: see THCD2 in the Thermal library for heat exchange by conduction using shape factor)

Conservation laws / volumes


Tutorial 3: Results



Tutorial 3: Results (other)



Method 1: using the components thermodynamic state

Each capacitive elements have to be initialized independently.

Initializing the state variables

Method 2: using the temperature and charge initialization facility

All capacitive elements are initialized at the same thermodynamical state which is defined by the initial temperature and the initial density resulting from the specified charge of fluid (AMESim automatically computes the volume of all capacitive elements that are present on the sketch).


Regular pressure losses

Singular pressure losses

Particular components

Pressure losses components

Tutorial 4:

Sketch

Parameters and inputs: Pressure: 3.2 barA Gas mass fraction from 1 to 0 (or 0 to 1) in 10 s

Display mass flow rate evolution as a function of gas mass fraction. Comments.


Predefined pressure losses


Tutorial 4: Results

Predefined pressure losses


Imposed heat flux:

Heat flux calculated in the component (internal convection)

Heat transfer


Tutorial 5:

Sketch and parameters

Initial pressure everywhere: 3 barA Initial specific enthalpy: 250 kJ/kg Volume: 2L Orifice: 10 mm

Display and compare classical variables in the volumes. Comments.

Imposed heat flux


Tutorial 5: Results

Imposed heat flux


Tutorial 6: Sketch

Parameters and inputs: Temperature source at 60 degC for condensation, 5 degC for boiling. Pipe: length = 0.1 m, diam = 100 mm.

Display heat transfer coefficients (in boiling and condensation conditions). Comments.

Internal predefined convective heat exchanges


Tutorial 6: Results

Two-phases flow enhances heat exchanges.

(note: high value of hconv even though single phase correlation at t=0 because of very high unrealistic dm ( high Re high

hconv). This is a "problem" of initialization, not a glitch in the equations).

Internal predefined convective heat exchanges


Water vapor has to be accounted for in the calculation of external heat transfer (has animportant influence (condensation))

Tutorial 7: Display moist air diagram

Moist air properties


Tutorial 8: Modeling a parallel flow condenser pass

R134a refrigerant flow exchanging with moistair flow through aluminum tubes and fins. R134a: 0.005 kg/s @ +10 degC (superheat)and 12.7 barA. Moist air: 2 kg/s @ 40 degC, 1 barA and40% relative humidity Discretization along the width of the heatexchanger in 5 parts.

External heat transfer (with Moist air)

10.51.5

30

2

Internal flow per tube:- Cross sectional area: 26.88 mm²- Hydraulic diameter: 1.816 mm

4 tubes

Total mass = 0.571 kg

…(50 fins)

600

128

= (

30+

2)*4


Tutorial 8: Parameters


External flow- Total frontal area = 600*128 = 76800 mm²- Cross sectional area = 4*50*30*10.5 = 63000 mm² Ratio = 0.820- Total wet perimeter = 4*50*(2*(10.5+30)) = 16200 mm Convective exchange area = 16200*20 = 324000 mm²

rfa (relative finned area, see help for definition) = 74.1 %.cdim (characteristic length of the heat exchange) = 20 mm

10.51.5

30

2…

(50 fins)

600

128

= (

30+

2)*4


Tutorial 8: Sketch


or


Tutorial 8: Results


or


AMESim Remember not to connect small resistances (large diameters) to small volumes (forinstance small pipe length).

TPF Keep the model as simple as possible on first modeling. Complexity often leads to poorCPU times.

Beware of initialization state. Try setting consistent values to help the solver at simulationstarting.

Bold lines on sensor or nodes indicate the closerC (capacitive) element

Tips and tricks

cr

f = 1/(r.c) >> 1 solver will decrease its time step CPU time will increase


About closed loops: build and run the system one step at a time. Each time the simulationruns right, add a new component.

Tips and tricks


Use aliases for generic TPF sensors so that the setting of the nodes of thethermodynamic plot is easier.

Tips and tricks


You can modify a thermodynamic plot after itis created:

Tips and tricks

Two-Phase Flows Library rev11Romain Bonnet – Product Developer

Thank you

getting started with two-phase flow systems

Documents