Lecture 7: Phase Change Modeling

1 © 2015 ANSYS, Inc. December 15, 2015 ANSYS Confidential

16.0 Release

Lecture 7:

Phase Change Modeling

Multiphase Modeling using

ANSYS Fluent


Outline

• Conservation Equations

• Phase Change Models

– Cavitation

– Evaporation - Condensation model

– Wet steam model


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


Phase Change Mechanisms

http://www.physicalgeography.net/fundamentals/6c.html


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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


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

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Mass Transfer

• Interfacial mass transfer

– Mass transfer rate per unit of volume – source terms in phase mass conservation equation


Phase Change Models

• Cavitation

• Wall Boiling *

• Evaporation - Condensation

• Wet Steam

• Population balance Model *

* Detailed in separate training lectures


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


• 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


16.0 Release

Cavitation


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


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)


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.


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)

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Mass transfer due to growth and collapse of vapor bubbles


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

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Singhal’s Full Cavitation model

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Variable properties

Turbulence effects on saturation pressure


Zwart’s & Schnerr’s Cavitation Model

Variable 𝑷𝒔𝒂𝒕


Zwart’s and Schnerr’s Cavitation Models

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Zwart-Gerber-Belamri Model Schnerr-Sauer Model


Turbulence Effects

• When using the cavitation model, you can include the effect of turbulence on the threshold cavitation pressure:


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


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.


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


Steady-State Cavitating Flow in a Sharp-Edged 2D-Axisymmetric Orifice

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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)

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Sharp-Edged 2D-Axisymmetric – convergence and results

Schnerr-Sauer Model Zwart-Gerber-Belamri Model

Total pressure Vapor volume fraction


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


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


Cavitating Flow in a Centrifugal Pump (II)

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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.


16.0 Release

Evaporation - Condensation model


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


• 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


Evaporation and Condensation Models

Single Resistance

No Interfacial

HTLee Model

Two Resistance

Interfacial Heat

Transfer

Thermal Phase

Change Model


• 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

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Accommodation coefficient Latent Heat

𝑻𝒗 > 𝑻𝒔𝒂𝒕

𝑻𝒗 < 𝑻𝒔𝒂𝒕


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


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

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• 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


• 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


• 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


Problem Description And Mesh Details

Pressure inletPin=555 kPaTin=420 K

Pressure outletPout=378 kPa

Adiabatic wall

2D Axisymmetric

Quadrilateral Mesh


Results Using Evaporation-Condensation Model

Pressure Volume Fraction

Temperature


16.0 Release

Wet steam model


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


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


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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


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


Nucleation Rate (Log10)

Liquid Mass Fraction

Pressure Profile Comparison

Wet Steam Example – deLaval Nozzle


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


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

Documents

Lecture 7: Phase Change Modeling