1 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential 16.0 Release Lecture 7: Phase Change Modeling Multiphase Modeling using ANSYS Fluent
1 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
16.0 Release
Lecture 7:
Phase Change Modeling
Multiphase Modeling using
ANSYS Fluent
2 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Outline
• Conservation Equations
• Phase Change Models
– Cavitation
– Evaporation - Condensation model
– Wet steam model
3 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Thermal:
• Driven by temperature differences
Applications:
– Condensation
– Evaporation
– Boiling
• Pool Boiling
• Wall Boiling
Mechanical:
• Driven by pressure differences
Applications:
• Cavitation
• Flashing
Phase Change Phenomena
Phase Change Mechanisms
4 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Phase Change Mechanisms
http://www.physicalgeography.net/fundamentals/6c.html
5 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
qqtqqq
n
p
qpqpqqqqqqqqq
qqqmp
t,vm,lif
1
FFFuRτguuu
n
p
pqqqq
qqm
t 1
u
qppqpq K uuR
transient convection pressure shear
interphaseforces
exchange
interphase mass
exchange
body external, lift, andvirtual mass forces
Volume fraction for the qth phase
Solids pressure term is included for granular model.
Phase Change!!
Model Conservation Equations (Eulerian)
• Continuity:
• Momentum for qth phase:
• The inter-phase exchange forces are expressed as :
• Energy equation for the qth phase can be similarly formulated
6 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Mixture Model Conservation Equations
• Solves one equation for continuity of mixture
• Solves one equation for the momentum of the mixture
• Solves for the transport of volume fraction of each secondary phase
r
k
r
kk
n
k
km
T
mmmmmm uuFguupuu
t
u
1
eff
0
mm
m ut
).().()( r
pppmpppp uut
Phase Change sources added
+ Source
7 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
secm
kg
312 iiS Am
Mass flux vectorkg/(m2 sec)
Interfacial areadensity, 1/m
Phase 1Phase 2
Interface
12S
Mass Transfer
• Interfacial mass transfer
– Mass transfer rate per unit of volume – source terms in phase mass conservation equation
8 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Phase Change Models
• Cavitation
• Wall Boiling *
• Evaporation - Condensation
• Wet Steam
• Population balance Model *
* Detailed in separate training lectures
9 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Mass Transfer
• Mass transfer defined through phase interaction panel
• Mass transfer models available with mixture and Eulerian multiphase model
– Cavitation
– Evaporation - Condensation
– User defined mass transfer
– Boiling
– Heterogeneous Reactions
– Nucleation and growth in population balance models
10 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
• Latent heat is accounted forwhen mass transfer isprescribed through standardmeans
• Latent heat is calculated from standard state enthalpy of species/phase participating inmass exchange
• Material type must be fluid
• Be aware of values of standard state enthalpy – only enthalpy difference matters. For example, vapor enthalpy must be larger than liquid enthalpy.
Mass Transfer
11 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
16.0 Release
Cavitation
12 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Cavitation Models
• Cavitation occurs in many engineering devices
• A liquid at constant temperature can be subjected to a decreasing pressure, which may fall below the saturated vapour pressure
• The liquid also contains non-condensable gases (dissolved or ingested)
– Hydrofoils, Propellers, Inducers, Nozzles, Biomedical, …
• Need for cavitation models which account for
– N-phase flows with multiphase species transport
– Effects of slip velocities between the liquid and gas phases
– Thermal effects and compressibility of both liquid and gas phases
13 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Cavitation Characteristics & Numerical Challenges
• Physical Challenges
– Phase Change (bubble generation & collapse)
– Large density ratio of liquid to vapor (e.g. water 300K, the ratio is 4e+4)
– Strong dependence of geometry and flow conditions
– In cavitating zones, static pressure remains a constant (= saturation pressure)
– Turbulence effects
– Thermal influence
• Numerical challenges:
– Handle the large liquid-to-vapor density ratios
– Deal with cavitation mass transfer and possibly heat transfer
– Phasic transitions within the domain (vapor flooding, liquid/vapor regimes)
14 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Cavitation Modeling
• Cavitation zones are prevalently noted in fuel injectors, fluid pumps, valves, sharp edged orifices etc.
• Cavitation is an undesirable because it can cause:
– Significant degradation in performance, as manifested by reduced mass flow rates, lower head rise in pumps, load asymmetry, vibration and noise.
– Physical damage to a device (due to bubble impact on surfaces – Cavitation Erosion) which can ultimately affect structural integrity.
15 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Transport Equations
• In Cavitation, the liquid-vapor mass transfer (evaporation and condensation) is governed by the vapor transport equation
• Estimation of the rate of vapour production is based on the asymptotic growth rate of Rayleigh-Plesset equation
– Zwart et al. Model
– Schnerr and Sauer Model
– Singhal Model (Mixture model only)
cevv
v RRvt
)(
Mass transfer due to growth and collapse of vapor bubbles
16 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Cavitation Modeling
• System consists of liquid and vapor phase
• All models are based on Rayleigh-Plesset equation describing growth of single vapor bubble in a fluid
• Non-condensable gases accounted within Singhal’s model (mass fraction of these gases = constant)
• Fluid property for working material can be constant or function of Temperature / user-defined
l
B
l
l PP
Rdt
dR
Rdt
dR
dt
RdR
24
2
32
2
2
Pressure difference between bubble inside and exterior
Bubble growth (dR/dt) approximated using first order effects!
17 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Singhal’s Full Cavitation model
vPP
vPP
l
vvl
gv
vap
PPkFRe
3
20.1,1max
l
vvl
vcond
PPkFRc
3
2,1max
kPP satv 39.02
1
cevv
v RRVt
).(
)(
𝐹𝑣𝑎𝑝= 0.02, 𝐹𝑐𝑜𝑛𝑑= 0.01
/solve/set/expert Singhal et al. model [no] yes
Variable properties
Turbulence effects on saturation pressure
18 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Zwart’s & Schnerr’s Cavitation Model
Variable 𝑷𝒔𝒂𝒕
19 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Zwart’s and Schnerr’s Cavitation Models
vPP
vPP
01.0
50
105
10
4
6
cond
vap
nuc
B
F
F
m
vPP
vPP
1310
1
4
3
1
B
)3
41/(
3
4 33
BB
cevv
v RRVt
).(
)(
l
v
B
vvnuc
vape
PPFR
)(
3
2)1(3
l
v
B
vvcondc
PPFR
)(
3
23
l
v
B
lv
e
PPR
)(
3
23)1(
l
v
B
lv
c
PPR
)(
3
23)1(
Zwart-Gerber-Belamri Model Schnerr-Sauer Model
20 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Turbulence Effects
• When using the cavitation model, you can include the effect of turbulence on the threshold cavitation pressure:
21 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Guidelines for Model Usage
• Zwart et al. or Schnerr et al. models are highly recommended due to quick convergence behavior and accuracy
• If non-condensable gases present, only Singhal’s model can take it into account
• SIMPLE/SIMPLEC/PISO & Coupled solvers can be used with any cavitation models. For rotating equipment, Coupled Solvers are recommended
• Pressure Schemes: PRESTO! (highly recommended), body-force weighted, second order
22 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Tips and Tricks
• For Zwart’s and Schnerr’s model– Keep under-relaxation for vapor to 0.5 or higher
– Keep Density and Vaporization mass to 1.0
– If coupled solver is used consider reducing the courant number to 20-50 for complicated scenarios
• For Singhal’s model – Momentum relaxation from 0.05-0.4
– Pressure relaxation: 0.2 – 0.4
– Vaporization mass: 0.1 – 1.0
• When using the cavitation model, you can model the temperature-dependence of the vaporization pressure as a first-order Taylor approximation about the free-stream value. This can help with numerical stability in cases with small temperature deviations.
23 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Limitation of Cavitation Models
• None of the cavitation models can be used with the explicit VOF option because the surface tracking schemes are incompatible with the interpenetrating continua assumption of the cavitation models.
• They can only be used for a single cavitation process
• The Singhal et al. model requires the primary phase to be a liquid and the secondary phase to be a vapour
• Singhal’s model is only compatible with the multiphase mixture model. However, it is not compatible with the LES turbulence model
• The Zwart-Gerber-Belamri and Schnerr and Sauer models do not take the effect of no condensable gases into account by default
24 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Steady-State Cavitating Flow in a Sharp-Edged 2D-Axisymmetric Orifice
L
dD
• D/d=2.88 and L/d=5• Exit pressure of Pout= 0.95 bar• Inlet total pressure is ranging from 1.9 to 4000 bars and that corresponding to Cavitation number from
1.96274 to 1.00023.
The characteristics of the orifice flow are the discharge coefficient
and the cavitation number:
where and (contraction coefficient)
L
)(2 00 bl
actual
ideal
actuald
PPA
m
m
mC
b
v
PP
PP
0
0
cd CC 62.0cC
25 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Sharp-Edged 2D-Axisymmetric – convergence and results
Schnerr-Sauer Model Zwart-Gerber-Belamri Model
Total pressure Vapor volume fraction
26 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Fuel injector example
Convergence history
Wall Static Pressure Contours (Pa)
Vapor Volume Fractions on the Injector Surface
Mass flow rate with cavitation = 0.01287 kg/s
Mass flow rate from non-cavitating flow =0.015 kg/sec
14% of mass reduction due to cavitation
27 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Cavitating Flow in a Centrifugal Pump (I)
TFA Centrifugal Pump Geometry Computational Grid (284,955 hex cells)
• Single rotating reference with rotational speed = 2160 rpm.
• Steady-state simulations over 1/5 of the pump (72-degree sector)
• Realizable turbulence model
• Flow conditions:
inlet : fixed velocity with volumetric flow-rate of 210m3/hr
exit : pressure outlet with Pb=600 kPa – 350 kPa
fluid : water with Pv = 2620 Pa
k
28 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Cavitating Flow in a Centrifugal Pump (II)
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.5 1.0 1.5
Cavitation number
Hea
d ri
se c
oeff
icie
nt
Hofmann et al [20]
CFD
Head rise coefficient variation with cavitation numberat design flow-rate for the TFA pump
Surface Vapor Volume Fraction: Pb = 350 kPa.
Impeller surface pressure: Pb = 350 kPa.Impeller Surface Pressure: Pb = 600 kPa.
29 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
16.0 Release
Evaporation - Condensation model
30 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Evaporation - Condensation processes
• Evaporation is the transformation of a substance from liquid to vapor resulting from energy addition
• Condensation is the transformation of a substance from vapor to liquid resulting from energy removal from the vapor phase
• In condensation processes, the vapor temperature is at or below the saturation temperature
• Condensation occurs in various modes :– Droplet formation in vapor
– Liquid droplet formation on a cooled surface
– Liquid film condensation on a cooled surface
31 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
• This model is available with the mixture, VOF and Eulerian multiphase models
• For the Eulerian framework
– Lee Model
– Thermal Phase Change
• For the VOF and Mixture
– Lee Model
Evaporation-Condensation Modeling
Model selection will influence the setup of heat and mass exchange among the phases
32 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Evaporation and Condensation Models
Single Resistance
No Interfacial
HTLee Model
Two Resistance
Interfacial Heat
Transfer
Thermal Phase
Change Model
33 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
• The Lee model is a mechanistic model with a physical basis
• It is available in the mixture, VOF and the Eulerian multiphase models
– Allows specification of a single overall interfacial heat transfer coefficient between phase
• 𝜆𝑐 is a tunable coefficient and may be interpreted as relation time or frequency
– It can be approximated via the Hertz-Knudsen equation
LEE Model
lvvlvv
v mmvt
)(
sat
satvvvclv
sat
satlllcvl
T
TTm
T
TTm
gl
l
sat
c LRT
M
d
2
6
Accommodation coefficient Latent Heat
𝑻𝒗 > 𝑻𝒔𝒂𝒕
𝑻𝒗 < 𝑻𝒔𝒂𝒕
34 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Lee Model Setup
• Positive mass transfer rate is defined as being from liquid to vapor
• Saturation temperature can be provided as function of pressure
• If saturation temperature is a function of other variable such as volume fraction, pressure and other solutions, a User-Defined-Functions (UDFs) may be necessary to define the entire phase change mechanism
35 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Thermal Phase Change Model
• Mass transfer rate based on overall heat balance across interface
• There is no calibration required for the mass transfer coefficients as there is in the Lee model
• It is generally recommended that you use the two-resistance heat transfer method when simulating evaporation-condensation using Thermal Phase Change Model
lv
vSativlSatillv
h
TTAhTTAhm
lv
vllv
h
QQm
36 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
• Recommended for modelling evaporation and condensation processes using Thermal Phase Change Model
• Allows specification of separate Heat transfer models for each phase directly
• Allows for zero resistance condition to be imposed on the dispersed phase
Two Resistance Model
37 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
• Specify Latent Heat as Standard State Formation Enthalpy– Standard state enthalpy of vapor = latent heat @Saturation
properties (in j/kg-mol units)
– Standard state enthalpy of liquid = 0
– Same molecular weight for liquid and vapor
– Reference temperature = Saturation Temperature
• Calculation strategy– Use coupled solver with low Courant numbers
– Lower the explicit relaxation factors
– for pressure and momentum to 0.5
– Ensure reverse flow volume fraction
– properly defined at outlet boundaries
Evaporation-Condensation Model – Tips & Tricks
38 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
• Tuning evaporation and condensation frequency– Compare the numerical results with experimental results
– Use simple calculation to estimate evaporation
• Evaporation expected = (Htotal – Hsensible)/Latent Heat
– Adjust evaporation/condensation frequencies (0.001 – 100)
• In Evaporation-Condensation Model, departure from saturation determines the rate of mass transfer– (Tcell - Tsat) is the driving force
– For mass transfer to happen, Tcell > or < Tsat
• Increasing these frequencies– Predict the mixture temperature closer to saturation
temperature
Evaporation-Condensation Model – Tips & Tricks
39 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Problem Description And Mesh Details
Pressure inletPin=555 kPaTin=420 K
Pressure outletPout=378 kPa
Adiabatic wall
2D Axisymmetric
Quadrilateral Mesh
40 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Results Using Evaporation-Condensation Model
Pressure Volume Fraction
Temperature
41 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
16.0 Release
Wet steam model
42 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Wet Steam Model
• During the rapid expansion of steam, a condensation process will take place shortly after the state path crosses the vapor-saturation line.
• The expansion process causes the superheated dry steam to first sub cool and then nucleate to form two phase mixture
• The formation of liquid-droplets in a homogeneous non-equilibrium condensation process, is based on the classical non-isothermal nucleation theory
• Assumptions
– The velocity slip between the droplets and gaseous-phase is negligible.
– The interactions between droplets are neglected.
– Mass fraction of the condensed phase is small (<0.2), so the volume of the condensed phase is negligible
43 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Wet Steam Model
• Two additional transport equations are solved for
– Mass fraction of the condensed liquid phase
– Number density of the droplets per unit volume
• Mass generation rate is given by the sum of mass increase due to nucleation (the formation of critically sized droplets) and also due to growth/demise of these droplets.
• Nucleation rate is described by the steady-state classical homogeneous nucleation theory and corrected for non-isothermal effects
• The droplet growth is based on average representative mean radii
• The droplet is assumed to be spherical
• The droplet is surrounded by infinite vapor space. The heat capacity of the fine droplet is negligible compared with the latent heat released in condensation
44 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Ivt
vt
v
1
TTCRTh
P
dt
dr
eM
qI
op
llv
TK
r
ml
vc b
2
1
2
2
1
3
4
3
22
Nucleation rate
Droplet radius (growth rate)
Mixture density
Mass Fraction Transport
Number density Transport
Droplet temperature
Non-Equilibrium Condensation Process
Load Material by Text Command: Define/models/multiphase/wet-steam/compile-user-defined-wetsteam-functions
Wet Steam Model
45 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Limitations of Wet-Steam Model
• The wet steam model is available for the density based solvers only
• Pressure inlet, mass-flow inlet, and pressure outlet are the only inflow and outflow boundary conditions available
• The access to material panel is restricted because the fluid mixture properties are determined from the built in steam property function or user-defined wet steam property function
• Therefore, if solid properties need to be set and adjusted, then it must be done in the Create/Edit Materials dialog box before activating the wet steam model
46 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Nucleation Rate (Log10)
Liquid Mass Fraction
Pressure Profile Comparison
Wet Steam Example – deLaval Nozzle
47 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Solution Strategies for Wet-Steam Model
• Adjust temperature limits, minimum of 273 K
• Make sure maximum wetness factor is not beyond 0.2 since the present model assumes low wetness factor
• With wetness factor, β > 0.1, solution becomes less stable
• For wet-steam models, solve flow solution initially without condensation and once proper solution is achieved, switch on condensation
• Switching off condensation can be done by deselecting Wetsteam equations in the solution control panel
48 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential
Summary
• Multiple phase change mechanisms (pressure / temperature change)
• Mass transfer models activated through multiphase panel
• Be aware of values of standard state enthalpy
• Cavitation: use of Presto! pressure scheme
• Evaporation-Condensation model: adjust model constants
• Wet Steam model: Use Pressure or mass-flow for inlets, specify pressure atoutlet Density based solver