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Multiphase Flow Modeling Pep Pepi Maksi aksim movic ovic May 20, 2005 St. John’s Conference Center, Plymouth, MI
Welcome Fluent Inc.’s Lunch’N’Learn Seminar Series Topical seminars on leading edge CFD applications Held frequently
Aeroacousti coustics cs Modeling Modeling – March 18, 2005 2005 Aeroa Flo FloWiz Wizard ard – Apr Aprilil 22, 22, 2005 2005
Unsteady dy Flow Flow Modeling Modeling – April 29, 2005 2005 Unstea Multiphase phase Model Modeling ing – May 20, 20, 2005 2005 Multi Purpose Inform the FLUENT community about the subject
Discuss basics, physics, theory, modeling techniques techniques
Tools available in FLUENT to model the subject
Examples
Agenda Overview of Multiphase Flow Modeling Boiling Cavitation Defogging VOF Evaporation Water Ingestion Sprays Summary
Physics, Physics, Numerics Numerics and Case Studies Studies
Agenda Overview of Multiphase Flow Modeling Boiling Cavitation Defogging VOF Evaporation Water Ingestion Sprays Summary
Why Model Multiphase Flows? There are numerous examples of Multiphase Flow problems relevant to Automotive Industry:
Powertrain Engine Piston Cooling
Tank Filling
Boiling in Cooling Jacket
Fuel Sloshing
Cavitation in Water Pump
Fuel Vapor Emissions
Fuel Injector Lubrication
Fuel System
HVAC System
Transmission System Clutch Performance
External Flows
Two-Phase Heat Exchangers
Tire Splashing / Hydroplaning
Oil Separation
Rain Water Management
Cabin Flows Window Deicing Window Defogging
Windshield Wiper Performance
Manufacturing Process Spray Painting Casting
Multiphase Flow Modeling Objectives
Typical modeling objectives: Evaluate component / system performance Understand the dynamics of flow behavior free surface location of phase change contact and interaction between phases
Compute velocity and pressure fields Compute heat-transfer-related values of interest
Definitions
A phase is a class of matter with a definable boundary and a particular dynamic response to the surrounding flow/potential field. Phases are generally identified by solid, liquid or gaseous states of matter but can also refer to other forms e.g. particles of different size.
Species are substances of different chemical composition.
Multiphase flow is simultaneous flow of:
Materials with different states or phases (i.e. gas, liquid or solid).
Materials with different chemical properties but in the same state or phase (i.e. liquid-liquid, such as, oil-water)
In contrast, multicomponent/multi-species flow refers to a “mixture” formulation where components are mixed at molecular level and velocity and temperature are the same for all components gas phase = air + fuel vapors (two species) liquid phase (one species)
Phase Change
Phase change can be defined as departure from an equilibrium state, moving into another equilibrium state, across the two-phase equilibrium curves
Different paths may represent different phase change phenomena vaporization of a liquid by isobaric heating is boiling vaporization of a liquid by adiabatic expansion is cavitation
p [Pa]
L S
V T [K]
Multiphase Flow Regimes
Bubbly flow/ Droplet flow/ Particle-laden flow = Discrete secondary phase structures (bubbles, droplets, solid particles) in a continuous primary phase
Slug flow = Large bubbles in a continuous liquid
Annular flow = Continuous liquid along walls, gas in core
Stratified / Free-surface flow = Immiscible fluids separated by a clearly-defined interface
Jet flow = thin liquid core surrounded by bulk gas phase
Film flow = thin liquid layer flowing along wall boundaries
Bubbly flow / Droplet flow / Particle-laden flow
Annular flow
Jet flow
Slug flow
Free-surface flow
Film flow
Flow Regimes Example • Vertical gas-liquid flow
CFD Modeling Requirements
User must know a priori the characteristics of the flow: Flow regime, e.g., bubbly flow , slug flow, annular flow, etc. Only model one flow regime at a time Predicting the transition from one regime to another possible only if the
flow regimes can be predicted by the same model
Slug and annular flow predicted by the VOF model
Laminar or turbulent Dilute or dense Secondary phase diameter for drag considerations
Modeling Approaches There are two approaches for the numerical calculation of multiphase flows: Euler-Lagrange approach
Fluid phase, treated as a continuum, is solved via Navier-Stokes equations while dispersed phase solved by tracking particles/ bubbles/ droplets through calculated flow field. A fundamental assumption: the dispersed second phase occupies a low volume fraction. (High mass loading acceptable). In FLUENT, Lagrangian Discrete Phase Model.
Practical for α ≤ 10%
α i
≡
lim
δ V
δ V1
V i (cell )
δ V
δ V → 0
α (cell ) ≡
δ V i
V (cell )
∑
2
Euler-Euler approach
Phases treated mathematically as interpenetrating continua.
Since the volume of a phase cannot be occupied by other phases, the concept of “ phasic volume fraction, ” is introduced: assumed to be continuous functions of space and time with their sum equal to 1.
Solve set of conservation equations for each phase.
In FLUENT, three different Euler-Euler models available:
Volume of Fluid (VOF) model
Mixture model
Eulerian model
δ V
FLUENT Modeling Approaches
The discrete phase model is used for modeling particles/bubbles/droplets dispersed in continuous phase
The mixture model is designed for two or more phases (fluid or particulate)
The phases are treated as interpenetrating continua. Solves for the mixture momentum equation and prescribes relative velocities to describe the dispersed phases. Applications: bubbly, droplet, particle-laden flows with α ≥10%
The Eulerian model is the most complex of the multiphase models in FLUENT.
Solve transport equations for the continuous phase + discrete second phase in a Lagrangian frame of reference Computes the trajectories of the discrete phase at specified intervals during the fluid phase calculation, as well as heat and mass transfer to/from them ( spray, combustion). Can include coupling between the phases (i.e. impact on both the discrete phase trajectories and the continuous phase flow). Applications: bubbly, droplet, particle-laden flows with α ≤ 10%
Solves a set of momentum and continuity equations for each phase. Coupling is achieved through the pressure and interphase exchange coefficients. Applications: particle suspension.
The VOF model is surface-tracking technique designed for two or more immiscible fluids where the position of the interface between the fluids is of interest
Solves single set of momentum equations shared by the fluids + volume fraction of each fluid in each computational cell Applications: free-surface / stratified flows, filling, sloshing.
References
FLUENT 6.2 Documentation Chapter 22: Introduction to Modeling Multiphase Flows Chapter 23: Discrete Phase Models Chapter 24: General Multiphase Models 24.2 Volume of Fluid (VOF) Model 24.3 Mixture Model 24.4 Eulerian Model 24.6.4 Mass Transfer through Cavitation
Agenda
Overview of Multiphase Flow Modeling Boiling Physics Numerics Case Studies
Cavitation Defogging VOF Evaporation Water Ingestion Sprays Summary
Boiling
Process of substance transformation from liquid into vapor by heat addition
Heat added through a solid boundary
p [Pa]
Temperature is maintained higher than saturation
L
superheat = Twall-Tsat
V
S
Controlled Heat Flux is supplied
On this solid surface
Nuclei (vapor bubbles) develop in surface cavities
Vapor bubbles grow through micro-evaporation
Upon growing above certain size, bubbles detach and migrate in the bulk flow
Eventually, a film of vapor covers the solid surface
T [K]
Classes of Boiling Problems
For heated surfaces submerged in a liquid where there is no motion except that induced by the boiling itself, the process is called pool boiling.
Flow driven by buoyancy forces acting on the bubbles
When liquid is forced over a heated surface and it boils, the process is called forced convection boiling.
Flow dominated by convection
Saturation boiling occurs on surfaces immersed in a liquid which is at the saturation temperature.
Subcooled boiling occurs when the average liquid temperature stays below the saturation value, producing local boiling at the wall with subsequent condensation of the vapor as it departs the wall and moves into the colder bulk of the fluid.
Pool Boiling
Pool boiling Curve and Heat transfer Regimes: Single Phase Natural Convection regime Onset of Boiling regime Nucleate Boiling regime Unstable Film regime Stable Film regime
q” Critical Heat Flux
Film Minimum Heat Flux Nucleate Transition Nat. Conv.
Τw−Τs
Convective Boiling
Two-phase flow regimes and associated boiling regimes: Single-Phase Liquid – Forced
Convection Bubbly Flow - Subcooled
Nucleate Boiling Plug / Slug / Churn Flow –
Saturated Nucleate Boiling Annular Flow – Film evaporation Mist Flow – Droplet evaporation Single-Phase Vapor – Dryout
Subcooled Boiling UDF
In FLUENT 6.2, boiling is implemented through a UDF
The UDF is based on RPI subcooled boiling model
RPI Model: Model scope Basic equations Setup example Validation examples
RPI Model The model was developed at Rensselaer Polytechnic Institute
and is commonly called RPI model of subcooled boiling The model itself is a framework within Euler model The model has an open architecture – it allows arbitrary correlations
for key boiling physical quantities to be inserted. That is why it may be called a framework rather than model It includes at least two phases: liquid (primary or continuous phase)
and vapor bubbles (secondary or discrete phase) It prescribes rate of mass and heat transfer between liquid and
vapor bubbles
RPI Model Scope
Physics Subcooled boiling occurs when wall and thin liquid boundary layer
have temperature higher than saturation temperature at local pressure, i.e., are superheated
d bw
Departing bubble
Heated wall Tw Thin superheated layer
Bubble nucleating site
Tsat Tbulk
RPI Model Scope
The model This model is not plug and play like
κ-ε model of turbulence,
for example. In many cases it may fail and requires certain customization. However, key elements of the model are universal. The following is the scope of the model Developed and validated for forced convection subcooled
nucleate boiling, i.e., below Critical Heat Flux (CHF or Boiling crisis). This means that this model cannot adequately describe CHF itself.
RPI Model Scope
The model Boiling curve example – wall heat flux vs wall superheat Tw-Tsat
FLUENT
Model valid CHF & Film boiling
Model not valid
Wall superheat, Twall-Tsat
RPI Model Scope
The model The model framework can be extended to include: Pool boiling (as long as bulk liquid is not superheated) Laminar regime Different turbulence models ( κ-ε,
κ-ω, RSM) as long as
turbulent kinetic energy is part of the model However, these boiling regimes have not been validated to
our knowledge Validation was done mainly for boiling in turbulent upward
flows in vertical channels (pipe, annulus) with heated walls
Basic Equations
Conservation equations for phase q (Euler model) Mass: n r ∂ (α q ρ q ) + ∇ ⋅ (α q ρ q vq ) = ∑ m& pq ∂t p =1
Evaporation/condensation rate
Momentum: n r r r r r ∂ (α q ρ q vq ) + ∇ ⋅ (α q ρ q vq vq ) = −α q ∇ p + ∇ ⋅ τ q + α q ρ q g q + ∑ ( R pq + m& pq vr pq ) ∂t p =1
r
r
r
+ α q ρ q ( F q + F lift ,q + F vm,q ) Turb. Diffusion force and modified Lift force
Terms prescribed by RPI model
Basic Equations
Conservation equations for phase q (Euler model) Energy n r r r ∂ ∂ p (α q ρ q hq ) + ∇ ⋅ (α q ρ q vq hq ) = −α q + τ q : ∇vq − ∇qq + S q + ∑ (Q pq + m& pq h pq ) ∂t ∂t p =1
Energy exchange + Latent heat Mixture k-e model with bubble induced terms
µ r ∂ ( ρ m k ) + ∇ ⋅ ( ρ m vm k ) = −∇ ⋅ t ,m ∇k + Gk ,m − ρ m ε + S k ∂t Pr k
optional
µ t ,m ε r ∂ ( ρ mε ) + ∇ ⋅ ( ρ m vmε ) = −∇ ⋅ ∇ε + (C ε 1Gk ,m − C ε 2 ρ m ε ) + S ε ∂t Pr ε k Terms prescribed by RPI model
Basic Equations
Rate of mass exchange from liquid to vapor per unit of volume is given by n
∑ m&
qp
= m& lv = hlv (T l − T s ) Ai / L + q E ′′ Aw / ( L + C pl max(T s − T l ,0))
p =1
First term on RHS describes evaporation (condensation) occurring at bubble surface after it departed wall
Second term is vapor generation rate at superheated wall
Basic Equations Volume Swarm of rising vapor bubbles. Vapor inside is at saturation temperature
d
V
Interface area N p A p
Area density Surrounding liquid at temperatures Tl
A N V 6α = α ≡ p p = α p = V V p V V p d
N p A p V p
Evaporation rate = [hlv (T l − T s ) / L ]⋅ Ai
Rate of mass exchange between phases is given as product of mass flux per unit of interfacial area and interface area per unit of volume (interfacial area density)
Basic Equations
Rate of vapor generation at superheated wall comes from heat flux partition model which is a cornerstone of the model
Total wall heat flux is split into three components: Single phase convective heat flux is applied to wall area not
covered by nucleation site Quenching heat flux is applied to wall area covered by nucleation
sites. It is due to transient refilling at bubble departure site Evaporation heat flux which is a source of bubbles
q ′w′
= ql ′′ + qQ′′ + q E ′′
Basic Equations
The wall surface is subdivided into portion covered by nucleating bubbles Ω and portion covered by fluid 1 − Ω
Convective heat flux is expressed as
q l ′′ = hlw ⋅ (T w
− T l cell ) ⋅ (1 − Ω )
hlw single phase heat transfer coefficient is derived from either
log law if flow is logarithmic or Fourier law if flow is laminar (hence formal compatibility with laminar flow)
Ω
is calculated from nucleation site density departure diameter d wv
π d wv2 Ω = min ⋅ n,1.0 4
n
and bubble
Basic Equations
Quenching heat flux is given by
qQ′′
= 2π −0.5 Ω( f κ l ρ l C pl )0.5 (T w − T l cell ) quenching heat transfer coeff
Notice that it has the same form as single phase flux – heat transfer coefficient multiplied by temperature difference
Bubble departure frequency is given by
4 g ∆ ρ f = 3d bw ρ l
Basic Equations
Bubble departure diameter is given by correlation
d vw a
=
−5
= 2.42 ⋅ 10 ⋅ p
(T w − T s )
ρ s C psκ s
2 ρ v
π
b=
1 2(1 − ρ v / ρ l )
0.709
−0.5
⋅ a ⋅ (bθ )
θ = max(U l / 0.61, 1.0 )
MAX (T s − T l ),
(0.0065 ρl C pl U l ) q′w′
Bubble departure diameter is most important model variable because evaporation heat flux is
′′ q E
=
π 6
3 d vw fnρ v L
′′ ∝ d vw2.5 q E
Setup Example
Example of upward flow of water in pipe with heated wall 2m
P=45 atm Water, 900 kg/(m2sec) Tin=Tsat-60K
2 ′ ′ qw = 570 kW / m
C TD
=1
D=15.4 mm
gravity
Setup Example
Start 2ddp version, compile UDF and read in the mesh
Set Euler model with 2 phases and define materials. Pay attention to standard enthalpy because it defines all important latent heat.
Notice that standard enthalpy is given in J/kmole while in UDF it is J/kg.
Setup Example
In definition of phases assign bubble diameter to UDF
In all inlet/outlet BC temperature of vapor must be set to saturation
In all fluid zones vapor T v must be set to T sat – this is assumption of the model
In all inlet BCL: Tl must be below Tsat
In all outlet BC: back flow Tl must be
set to Tsat
Setup Example
In all fluid zones sources for all momentum equations of all phases must be set for turbulent diffusion force
User-Defined Functions Hooks ADJUST – gradient of VOF HEAT_FLUX – wall heat balance
Validation Examples
The model had been validated for 5 published experiments:
Boiling liquid
exp-1
exp-2
exp-3
exp-4
exp-5
water
water
R-113
R-113
R-113
Geometry
Vertical pipe with heated walls, 2D
System pressure, bar
45
BRW core channel geometry with vertical heated rods, 3D 50
Inner wall heat flux, MW/m2
0.57
Fluid mass velocity/Re, kg/m2/sec Mean liquid subcooling at test
Vertical annulus with internal wall heated, 2D
Vertical annulus with internal wall heated, 2D
Vertical annulus with internal wall heated, 2D
2.69
2.69
2.69
0.522
0.094
0.116
0.126
900/104,210
1163/294,500
785/34,300
785/34,300
785/34,300
60
4.5
30.3
30.3
30.3
Stainless steel
Stainless steel
Stainless steel
Stainless steel
Stainless steel
section inlet, 0C Wall material
Validation Examples
Wall super heat Tw-Tsat for exp-1. Notice how single phase calculation overpredicts superheat.
Validation Examples
Axial vapor content development vs axial distance for exp-1. Onset of significant boiling is well predicted.
0.45 0.4 0.35 0.3
exp-1
n o i t c 0.25 a r f
cal
0.2 d i o V 0.15 0.1 0.05 0 0
0.5
1
Position, m
1.5
2
Validation Examples
Axial bulk liquid temperature development for exp-1. Notice how boiling model improves comparison with experiment vs single flow solution. 0 -10
cal s.p. cal
g -20 n i l o o -30 c b u s -40 k l u B -50
exp-1
-60 -70 0
0.5
1
Position, m
1.5
2
Validation Examples
Grid and vapor VOF prediction for exp-2
Side rods Water-vapor mixture
Central rod rod
Subcooled water
Validation Examples
Comparison for vapor content from X-ray attenuation measurement (very inaccurate) for exp-2.
0.5 0.45 0.4 0.35 n o 0.3 i t c a r 0.25 f d i 0.2 o V
0.15 0.1 0.05 0 0
0.2
0.4
0.6
0.8
Axial distance, m
1
1.2
1.4
Validation Examples
Comparison for vapor radial profiles for exp-3,4,5. Experiments differ in heat flux, lowest for exp-3 and highest for exp-5
Heated wall
Vapor VOF
Radial position
Validation Examples
Comparison for liquid temperature radial profile for exp-3,4,5. Experiments differ in heat flux, lowest for exp-3 and highest for exp-5
Heated wall
Liquid T
Radial position
Validation Examples
Automotive cooling jackets with applied heat flux
Subcooled water
Validation examples
Automotive cooling jackets with applied heat flux
gravity
Outlet
Subcooled water, Tsub=40C
Heat flux
Validation examples
Wall superheat Tw-Tsat for two cases: nominal and 10 times larger heat fluxes
Tw-Tsat, nominal
Tw-Tsat, 10*nominal
Validation examples
Vapor volume fraction for two cases: nominal and 10 times larger heat fluxes
Hot spots with high vapor content
VOF, nominal
VOF, 10*nominal
Conclusions
RPI turbulence model can mechanistically predict all aspects of nucleate subcooled boiling
It is validated for turbulent forced convection
It is formally expandable for
Laminar convection (flow is small channels)
Pool boiling
One must not overestimate its power
Cannot predict superheated boiling
Cannot describe CHF, but can point out where CHF may happen
Work is underway to “marry” RPI model with Population Balance model
Agenda
Overview of Multiphase Flow Modeling Boiling Cavitation Physics Numerics Case Studies Fuel Injector Fuel Pump Gerotor Pump Bearing Propeller
Defogging VOF Evaporation Water Ingestion Sprays Summary
What is Cavitation?
Cavitation is the process of generation of vapor bubbles in a liquid due to a local reduction in pressure below the vapor pressure of the liquid at a given temperature.
Cavitation = nucleation which occurs for P < Pvapor
Boiling = nucleation which occurs for T > Tsaturated
From a basic physical point of view, cavitation and boiling are similar processes.
Types of cavitation:
Bubble
Sheet
Cloud
Vortex
Shear flow
Relevance
Cavitating flows occur in many engineering fluid devices. Auto industry: pumps (water, oil, fuel), fuel injectors, valves (butterfly, spool, power steering), orifices (gasket holes), pipe bends, shock absorbers, clutches, bearings…
Presence of cavitating vapor bubbles can cause:
Reduced performance due to alteration of flow passages when significant amount of vapor is generated (“thrust breakdown”, surging instabilities)
Structural damages (~ wall erosion) due to collapse of vapor bubbles
Vibration and Noise due to pressure pulsations
Characteristics of Cavitating Flows
Two-way phase change (bubble generation & collapse)
Large density ratio of liquid to vapor e.g. for water at room temperature, the ratio is ~ 10 4
In cavitating zones, static pressure remains constant (~ Psat)
Turbulence effects
Thermal effects
Air releasing from liquid / gas injection
Strong dependence on geometry and flow conditions
Modeling Challenges
Numerical simulation of cavitating flows poses unique challenges, both in modeling of the physics and in developing a robust numerical methodology:
Physical Model: ideally, must be able to capture all the characteristics of cavitating flows
Numerical Algorithm: must be able to handle large density ratios prevent the static pressure from a large negative value in
the cavitating region, which a single-phase solution usually gives
Cavitation Model in Fluent 6.2
Based on so-called “full cavitation model” developed by Singhal et al (2001).
Implemented under Fluent Mixture model.
The Basic Cavitation Model, accounts for all “first-order effects”:
Phase change
Bubble dynamics (formation and collapse)
Turbulent pressure fluctuations
Non-condensable gases (dissolved gases, aeration)
Slip velocities between phases
Thermal effects (Psat, Surf. tension)
Compressibility of both liquid and gas phases
In addition, the model can be Extended for multiphase (N-phase) flows, or flows with multiphase species transport
New to Fluent 6.2: Can specify
Can model
vapor pressure as function of temperature !
mixture of liquid and vapor entering the domain
boundaries! Improved robustness of numerical model:
Allows for more aggressive URFs
Solution process less sensitive to initial conditions
Extended Cavitation Model for multiphase (N-phase) or multiphase
species flows.
Assumptions and Limitations of the 6.2 Cavitation Model
The basic model can be used for flows that involve two phases only (liquid and its vapor), and a certain fraction of separately modeled noncondensable gases.
Can be solved for flows that involve two phases only.
Mass fraction of non-condensable gases is constant value, known a priori .
Cannot account for non-condensable gas release or injection.
The primary phase must be liquid, the secondary phase must be vapor.
Assumes interpenetrating continuum between the phases.
Cannot be used with VOF model.
Cavitation Model in Fluent 6.2
The fluid assumed to consist of liquid, vapor and non-condensable gases.
Solve:
Continuity, momentum, momentum, turbulence (and energy, if necessary) equations for the mixture
Transport equation for mass fraction of vapor, f v:
r ∂ ( ρ f v ) + ∇ ⋅ ( ρ V v f v ) = ∇ ⋅ (γ ∇ f v ) + Re − Rc ∂t where ρ – mixtu mixture re densit density, y,
r
velocity of of the vapor vapor phase, phase, V v – velocity γ − turbulent diffusion coefficient, Re – rate of vapor vapor generatio generation n (evaporati (evaporation), on), Rc – rate rate of condens condensati ation. on.
Slip velocities between liquid and gaseous phases (optional).
Cavitation Model in Fluent 6.2 (cont)
The phase change rates derived from the simplified Rayleigh-Plesset equation:
pb − p 4ν l & 2σ ℜb + = − ℜ − ρ ℜ b ρ ℜ 2 Dt Dt 2 l b l 0 b 0 0 D 2ℜb
where where
3 Dℜ b
2
bubble radius radius,, σ – surfa surface ce ten tensi sion on ℜb - bubble
and assumptions that pb=psat and bubble size limited by Re
Rc
=
C e
=
V ch
C c
σ
ρ l ρ v
V ch σ
ρ l ρ v
2 p sat − p 3
ρ l
ρ l
~
σ V
2
:
(1 − f )
2 p − p sat 3
ℜb
for p < psat f for p > psat
where Vch – charact characteri eristi stic c velocit velocity y ~ k 1/2, Ce and Cc Cc empiric empirical al constan constants. ts.
Cavitation Model in Fluent 6.2 (cont)
Turbulence-induced pressure fluctuations accounted for via
pv
=
1
( p sat + pturb ),
0.39 ρ k
=
2 Effects of Non-condensable gases accounted for via ρ
=
α v ρ v
+
where α is volume fraction
pturb
α l ρ l α i
+ =
α g ρ g f
ρ i ρ
, α l
+
α v
+
α g
The final phase rate expressions are: for p < pv
for p > pv
Re
=
C e
R c
=
C c
k σ
ρ l ρ v
k σ
ρ l ρ v
2 pv 3
−
p
ρ l
(1 − f v − f g )
2 p
−
3
ρ l
p v
f v
=
1
Fluent 6.2 Cavitation Model GUI
Define > Models > Multiphase…
Define > Phases…
Vaporization Pressure: Property of the liquid at given temperature. Default value is for water at ambient temp. Absolute pressure ( not gauge value)! Liquid Surface Tension: Property of the liquid at given temperature Non Condensable Gas: Mass fraction of dissolved gases; input value
Tips for Using the Cavitation Model
Preferable to solve without slip velocity.
Non-Condensable Gases:
Slip velocities can be turned on if the problem suggests that there is significant slip between phases
Avoid zero values for mass fraction of non-condensable gases
Limits for Dependent Variables:
Set the upper limit for pressure to a reasonable value Fluent defaults to 5*10 6Pa (~ 50 atm)
Recommended Pressure discretization schemes:
PRESTO Body Force Weighted
Double Precission Solver:
Due to large density ratio between phases
Case Study: Fuel Injector
Cavitating fuel injector modeled in FLUENT 6.2
Inlet pressure: 2400 bar Outlet pressure: 0 bar
Transient flow simulation Movement of the plunger modeled with Dynamic Mesh
Pure layering (without nonconformal interface)
Cavitation model Turbulent flow:
operating pressure: 1 bar
Reliazable k-epsilon with std. wall function
Discretization schemes:
second order in space first order in time
Mesh motion
Case Study: Fuel Injector
Contours of volume fraction of cavitation zones
Case Study: Fuel Injector
Contours of pressure
Case Study: Fuel Injector •
Contours of pressure (auto range)
Case Study: Fuel Injector
Contours of velocity magnitude
Case Study: Gerotor Pump
Cavitating gerotor pump analyzed in FLUENT 6.2
Working fluid: oil
10 outer, 9 inner gears
3000 rpm for inner rotor
Hybrid mesh of ~730k cells:
Hexes in the rotor
Tets elsewhere
Dynamic Mesh model
Turbulent flow
Standard k-epsilon
Cavitation enabled
Case Study: Gerotor Pump
Vapor volume fraction contours:
Case Study: Fuel Pump
Fluent 6.2 used for analyzing performance of the cavitating fuel pump over a range of operating conditions:
Pressure rise across the pump fixed Inlet and outlet pressures vary
Compared pump flow rates computed in Fluent with lab data Geometry:
Rotor
Pressure Outlet
Purge (pressure outlet)
Case Study: Fuel Pump
Pure tetrahedral mesh of 680,000 cells
Non-conformal interface between rotating and stationary fluid
Mesh:
Case Study: Fuel Pump Physical Models, Solver Settings
FLUENT 6.2, Double precision, Segregated solver
MRF (Multiple reference Frame) Model
Steady state solution
Flow: incompressible, isothermal
RNG k-e turbulence model, standard wall function
Cavitation model
Primary phase = liquid fuel
Secondary phase = fuel vapor
Vapor pressure ~ 50 kPa
Case Study: Fuel Pump
Results: Formation of cavitation bubbles
120.0
100.0
] 80.0 % [ e t a R w60.0 o l F t e l t u O40.0
20.0
exp. Fluent 6.2 0.0 -60.0
-50.0
-40.0
-30.0
Inlet Pressure [kPa]
-20.0
-10.0
0.0
Case Study: Journal Bearing Problem Description:
Journal bearings are used for high radial loads, low to high speeds Engine cranks Milling systems Compressors Gear boxes, etc
Fluent used to study cavitation inside a journal bearing
Force information can also be obtained easily.
Case Study: Journal Bearing Setup:
Operating conditions simulated: Oil enters at the top and exits at two side pipes and also at the bearing gaps Bearing rotates at 3000 rpm Minimum gap thickness of 10 microns
Models used: Multiphase Cavitation Sliding mesh Porous media for downstream resistances
Case Study: Journal Bearing Mesh:
Gap meshed with hex cells of high aspect ratio (up to 50)
Four layers of cells across the gap
Total number of cells: 190k
Solution:
It took five complete cycles before achieving periodic solution
Case Study: Journal Bearing
Results:
Low pressure is predicted at the correct location:
Cavitation is predicted at the expected location:
Case Study: Journal Bearing Results:
Contours of Absolute of Absolute Pressure: Pressure:
Force can be obtained from pressure integration
Contours of Vapor of Vapor Volume Fraction: Fraction:
Cavitation occurs downstream of the lowest thickness
Case Study: Propeller Cavitation
Cavitation of marine propellers is highly undesirable
degrades propeller performance (thrust breakdown), erodes blades, causes noise and ship hull vibrations
…but, for heavily-loaded modern propellers unavoidable.
Study of cavitating flow around a four-bladed marine propeller MP 017 in open water conditions
FLUENT results benchmarked against experimentally measured values for thrust (KT) and torque (KQ) coeffs. over a range of J = V a / nD advance ratios (J):
K T = K Q
=
Thrust ρ l n 2 D 4
Thrust ρ l n 2 D 5
Case Study: Propeller Cavitation FLUENT pressure contours overlaid with cavity shape for J = 0.2, = 2.0
Thrust breakdown: J=0.2 0.4 Q
K × 0 1 d0.3 n a T
K
Experiment (Univ. of Tokyo): J = 0.2,
= 2.0
K T (Present) 10×K Q (Present) K T (Data) 10×K Q (Data)
0.2 1
2
σ
3
Cavitation number : σ = p − pv 0.5 ρ l v 2
4
Case Study: Propeller Cavitation
The results of benchmark study are in good agreement with experiment for
inception location and cavity shape
global quantities such as thrust and torque
thrust breakdown trend
Agenda
Motivation and Goals Boiling Cavitation Defogging Physics Numerics Case Study
VOF Evaporation Water Ingestion Sprays Summary
Definitions
Defogging = Removing the fog layer through evaporation
Fog = Condensed water forming a film on a wall boundary
Dry Air = Air without any Water Vapor
Moist Air = Gaseous mixture of Dry Air and Water Vapor
Absolute Humidity = Density of Water Vapor = Mass of Water Vapor per unit volume
Specific Humidity = Water Vapor mass fraction = Mass of Water Vapor per unit mass of Moist Air
Relative Humidity = Ratio of partial pressure of Water Vapor to saturation pressure at local temperature Water saturation curve = pressure as a function of temperature at
saturation conditions
Defogging Example Initial Fog Layer = 10 µm 20 seconds of simulation
Defogging Implementation
Defogging Module (DFM) for FLUENT 6.2 is a combination of User Defined Function (UDF) and Scheme Function which add to the standard functionalities of FLUENT
Evaporation of water film from specified walls
Condensation of water vapors on specified walls
Ease of Use
DFM has Graphical User Interface (GUI)
There is a version for batch mode runs
DFM can be used in parallel simulations
DFM comes with a Step-by-Step user procedure
Special Requirements
FLUENT Case using DFM must be setup in an interactive GUI session
Defogging UDF can run only as Compiled UDF
It can be run in batch mode afterwards
DFM UDF cannot be Interpreted
Batch mode scripts need to port files to the scratch directory
Scheme file for batch mode run
Model Assumptions 1. Evaporation / condensation of water is happening only on user specified walls between a fluid zone and a solid zone 2. Fog film is fully contained by the first layer of cells adjacent to the specified walls 3. Water Vapor, Dry Air, and Moist Air are gases obeying Dalton’s Law 4. Evaporation / condensation mass transfer rates are determined only by the gradient of Water Vapor mass fraction in the cells containing the fog film 5. Water Vapor is at saturation conditions at the interface between the fog film and moist air 6. Inflow / outflow mass flow rates of Moist Air are much larger than the mass transfer through evaporation / condensation
Model Assumptions (cont) 7. Thermal resistance and thermal inertia of the fog film are neglected 8. Radiation heat transfer effects of the fog film are neglected 9. Surface tension effects on the fog film are neglected 10. Gravity effects on the fog film are neglected 11. The fog film is stationary 12. The fog film has no effect on the Moist Air flow 13. The inlet relative humidity is constant in time 1 14. Diffusion coefficient of water vapor in moist air is known as a function of local pressure and temperature 2 1
Can be modified if UDF source code is modified – additional work and desired transient profile / law for relative humidity of the air entering the cabin is needed 2
A different relation can be used if UDF source code is modified – additional work and desired diffusion coefficient expression / tabled values are needed
Meshing Requirements
Must have solid cell zones adjacent to the defogging walls
Defogging walls must have shadows
Y+ < 5 on the walls defogging walls
Height of the cells adjacent to defogging walls greater than twice the fog layer thickness at any time
Conformal mesh (no hanging node adaptions or non-conformal interfaces) on the defogging walls
Non-conformal interfaces in other parts of the mesh are OK, but the grid can be partitioned only in serial solver
Hexcore meshing of the cabin is OK
Strictly observe the maximum cell skewness guideline: less than 0.95
Smooth variation of cell sizes and prism heights
At least one layer of Hexahedral or Prisms in the fluid adjacent to the specified walls
Model Validity for Cabin Flows
Fog layer range
0.5 µ m < δ FOG
< 200 µ m
Speed along the windshield
U ≈ 4 K5 m/s
Reynolds number (L ~ 0.5 - 1.5 m) Re L
=
ρ UL µ
≈ 170,000
Turbulent Boundary Layer thickness δ TBL
≅
0 .37 ⋅ L ⋅ Re L
≈
0 .017 m
= 17 , 000 µ m
Model Validity for Cabin Flows
Y+ requirement sets an upper bound on y 1 (first cell height) y +
≡
uτ y1 υ
≅ 0.19 ⋅
y1 L
⋅ Re L0.9 < 5
Stationary fog layer model sets a lower bound on y 1 y1 ≥ 2δ FOG
Substitute the lower limiting value into y+ requirement, a maximum value for the speed will be obtained 1.111
L Re L < 17.6 δ FOG
Examples verifying model validity: L = 1 m
δ
= 20 µ m
144 4 4 2 FOG 44 4 4 3 ⇓
U < 42 m/s
L = 1 m
δ
= 50 µ m
144 4 4 2 FOG 44 4 4 3 ⇓
U < 15 m/s
L = 1 m
δ
= 150 µ m
FOG 144 4 4 2 44 4 4 3
⇓
U < 5 m/s
Fluent Models Needed
Solve for Energy
Solve for Two Non-Reacting Species Dry Air Water Vapor
Viscous Model Laminar Turbulent k-ε models (Realizable / RNG preferred for accurate solution)
Use only Enhanced Wall Treatment for the near-wall modeling
k-ω Standard model with Transitional Flows option ON preferred
Defogging Example
Agenda
Motivation and Goals
Boiling
Defogging
Cavitation
VOF + DM FLUENT 6.2 Update Case Studies Piston Cooling Crank Case Fuel Tank
Evaporation
Water Ingestion
Sprays
Summary
VOF Model
The VOF model is surface-tracking technique designed for solving flow of two or more immiscible fluids where the position of the interface between the fluids is of interest
Solves single set of momentum equations shared by the fluids + volume fraction of each fluid in each computational cell
For numerics, check out FLUENT 6.2 Documentation
Chapter 24.2: Volume of Fluid (VOF) Model
VOF update for FLUENT 6.2 Let’s look at few examples where VOF was combined
with Dynamic Mesh (DM) for advanced multiphase flow modeling …
FLUENT 6.2 Enhancements
VOF model enhancements: enhancements Modified High Resolution Interface Capture (HRIC) scheme
More efficient (i.e. faster) front tracking
Very efficient for Steady-State and Transient problems where getting faster to final interface shape is more important than accurate interface shape history
Speed Increase by a factor of 100 versus Geo-Reconstruct! » Fuel Injector » Hydroplaning » Sealing Problems
Better resolution than QUICK or Second Order, but more diffuse than GeoReconstruct
Enable Implicit or Euler Explicit
HRIC Case Study: Swirl Fuel Injector
First Order
QUICK
Second Order
HRIC
Interface Capture Using Implicit VOF Velocity Vectors Colored by Volume Fraction
FLUENT 6.2 Enhancements
VOF model enhancements: enhancements Modified High Resolution Interface Capture (HRIC) scheme More efficient (i.e. faster) front tracking Very efficient for Steady-State and Transient problems where getting faster to final interface shape is more important than accurate interface shape history Speed Increase by a factor of 100 versus Geo-Reconstruct » Fuel Injector » Hydroplaning » Sealing Problems Better resolution than QUICK or Second Order, but more diffuse than
Geo-Reconstruct
Transient 6.2 solver efficiency improvements: Non-Iterative Time-Advancement (NITA) schemes Fractional-step method PISO
NITA Case Study: VOF Tank Sloshing
Automotive fuel tank with baffles
Tank ¼ full
Horizontal acceleration of 9.81 m/s2 applied for 1 second
Hybrid mesh: hex elements in the pipes, tets elsewhere
Geo-reconstruct scheme
∆t=2.5 ms for most of the simulation (400 time steps for 1s real time)
How do run time and accuracy stack up in FLUENT 6.2?
NITA Case Study: VOF Tank Sloshing (2) NITA vs. ITA: Run Time FLUENT 6.1 ITERATIVE PISO CPU=29,591
FLUENT 6.2 ITERATIVE PISO CPU=15,794
FLUENT 6.2 NITA – Fractional Step CPU=4,043
FLUENT 6.2 NITA – PISO CPU=3,450
Case Study: VOF Tank Sloshing (3)
NITA vs. ITA: Accuracy
Recommendations for FLUENT 6.2 VOF with NITA Body Force Weighted scheme for Pressure (not PRESTO! ) NITA-PISO (not Fractional Step Method, because it may require
a smaller time time-step for stability) Pressure under-relaxation factor of 0.7
(Solve>Controls>Solution NITA panel)
Case Study: Piston Cooling
Oil jet impinging on the engine piston underside
VOF model + DM model
Case Study: Piston Gallery Cooling
Heat transfer in diesel engine piston gallery of interest:
Increase in diesel engine power requirements demands effective thermal management of the engine piston
Piston temperature controlled by injecting oil into piston gallery
FLUENT 6.2
VOF model + DM model + conj. HT
Animation of oil motion within piston gallery for different CA:
Air-oil interface colored by local surface temperature of gallery walls
Courtesy of Federal Mogul
Case Study: Crank Case
Simplified automotive crank case geometry
Rotating assembly sweeps through oil causing windage
FLUENT 6.2 VOF model + DM model
Modeling Fuel Tank Sloshing
Show an alternative to traditional tank sloshing modeling approach … In general, the need with this class of problem is to resolve the dynamics of fuel free surface for given fuel tank geometry under various vehicle driving conditions
The fuel pickup tube should not be exposed to air
without baffles
with baffles
Traditional Modeling Method
Use of relative reference frame attached to the tank As the reference frame is not an inertial frame, need to add body force term to the momentum equation. Body force is modeled by changing gravitational force through a Scheme file. Disadvantages: Need to specify tank acceleration as opposed to tank motion. Post-processing in relative reference frame less intuitive.
A sample Scheme file for tank sloshing:
;; The tank motion is : v = max_vel*sin(omega*t) ;; The acceleration of the tank is : a = max_vel*omega*cos(omega*t) ;; The gravity acceleration is : gx = max_vel*omega*cos(omega*t) ;; ;; How to use the scheme; ;; 1) Set up tank sloshing problem ;; 2) Turn on gravity (Define>Operating Conditions) ;; 3) Load the scheme (File>Read>Scheme) ;; 4) Specify in Solve>Execute a command with (accelerate) ;; so that the gx will be updated every time step ;; ;; User input part of the scheme ;; (define omega 5) (define max_vel 0.25) ;; ;; Do not change the following part without consulting with your support ……
Alternative Modeling Method
Dynamic Mesh (DM) can be employed to study tank sloshing
The tank is moving in an absolute reference frame. (No need for addition of body force term.) Solid body motion is assigned to all cells and boundary faces. (No special requirement on mesh type). Specify tank velocity via UDF, as opposed to tank acceleration.
Both methods yield same solution.
A sample udf used for tank sloshing with DM method:
# include "udf.h" # include "dynamesh_tools.h" static real omega=5; static real max_vel=0.25; DEFINE_CG_MOTION(tank, dt, cg_vel, cg_omega, time, dtime) { NV_S(cg_vel, =, 0); cg_vel[0] = max_vel*sin(omega*time); }
Case Study: Tank Sloshing
Test case
Box (20cm x 10cm x 10cm) half filled with water
2,000 hex cells used for both runs
Tank has a sinusoidal motion
Traditional method g x = −ω × V × cos(ω × t )
DM method
v = V × sin (ω × t )
Traditional method
DM method
Case Study: Tank Sloshing
Both modeling approaches yield qualitatively and quantitatively the same solution.
The run time for both cases are similar (no extra cost for DM method).
300
) a P ( e r u s s e r P d e g a r e v A
250 200 150 100
DM method
50
Tradi tional method
0 -50 -100 -150 0
50
100
150
200
250
300
350
Time Step
Averaged pressure on a line in x direction passing point (0, 0, -4cm)
Agenda
Motivation and Goals
Boiling
Defogging
Cavitation
VOF
Evaporation Physics Numerics Case Study: Filler pipe
Water Ingestion
Sprays
Summary
Evaporation
Evaporation is a process of substance transformation from liquid into vapor at continuous liquid-vapor interface
Vapors diffuse and convect within another gas
Classes of Evaporation Problems:
Film Evaporation Adjacent to a solid surface Shape of the liquid-vapor interface doesn’t change Flow in the liquid layer is neglected
Evaporation at free surfaces Shape of the interface changes significantly, affecting the mass
transfer rates
Evaporation equations
Temperature condition at interface
T liq
≥ T sat ( pv ,interf )
Heat Flux balance at the interface & lv′′ Llv m
p [Pa]
= − q′′ interface
S
L triple point
V
Mass Flux balance at the interface & lv′′ m
′′ ′′ = m& diffusion + m& convection
′′ & diffusion m
= − ρ v Dv − g ∇Y v interface
Transport equations in the bulk liquid and gas-vapor phases
Closure for the model
Saturation condition at the interface
p v,interface
= p sat (T l,interface )
T [K]
Free Surface Evaporation UDF
Free Surface Evaporation in FLUENT 6.2 implemented through User-Defined Function
UDF used in conjunction with VOF and multi-species model
The evaporation process is modeled as mass transfer across the interfacial surface between liquid fuel and a fuel vapor/air mixture.
Mass transfer rate across the interface assumed to scale with the difference between the mass fraction of vapor at the surface and its equilibrium value at saturation.
The equilibrium mass fraction is computed from the saturation pressure of the fuel mixture.
The saturation pressure is fluid property and a function of temperature.
Mass fraction of gasoline vapors in the flow field around nozzle
Evaporation
Filling, fuel liquid only:
Filling, with evaporation:
Animations courtesy of TI Automotive Group
Agenda
Motivation and Goals
Boiling
Defogging
Cavitation
VOF
Evaporation
Water Ingestion
Sprays
Summary
BMW Z4 Air Intake
Standard shielded air intake replaced with a ram air scoop.
The upgrade provides the engine with a greater volume of air at higher velocity, enabling the engine to produce additional power for faster acceleration.
The air scoop, mounted behind the front grill and in front of the radiator, is designed with groves to collect rainwater before the air enters the air box.
Courtesy of Dinan Engineering
Problem Description
When the scoop was originally designed, it was noticed that during heavy rain the water was entering the air-mass meters and damaging the sensors.
Performed a series of CFD analyses of the scoop to determine the ability of the groves to remove rainwater from the incoming air.
Courtesy of Dinan Engineering
Original Geometry
Modeling Approach The following FLUENT models were used: Volume of Fluid (VOF) model in FLUENT •
tracks the motion of two or more fluids (in this case, air and water), as well as the interface between them.
Transient, 3D simulations Turbulent Isothermal User-Defined Function (UDF) for the inlet boundary condition to
account for the raindrops entering the system. •
The raindrops are simulated as spheres entering the system at equally spaced points. The time interval between drops entering the system was chosen to give the required water inflow.
Original Design Results The simulation showed a problem:
A significant amount of water enters the air box when the car moves at high speed, through heavy rain
The inertial forces in the curved air scoop large; the scoop quickly fills with air/water mixture
…but, the gravitational force not strong enough to divert the water down and out of the scoop
In addition, the opening on the bottom too small, water collects faster than it drains out
Courtesy of Dinan Engineering
Contours of volume fraction of liquid
New Design
Instead of inlet with grooves and a water outlet at the bottom, the new design has water exit on the outer sidewall of the scoop.
Courtesy of Dinan Engineering
New Design Results
The new design with the side exit has been found to perform much better than the original one.
For large inertial forces, most of the water hits the back wall of the scoop and exits, leaving less water to pass into the air box.
In addition, the new design is much simpler and less expensive to manufacture.
Courtesy of Dinan Engineering
Agenda
Motivation and Goals
Boiling
Defogging
Cavitation
VOF
Evaporation
Water Ingestion
Sprays Wall-Film Wall-Jet
Summary
Spray Models in FLUENT Implemented under Discrete Phase Model (part of standard FLUENT software)
Atomizer models
Droplet (spray) breakup
Plain-orifice atomizer
TAB
Pressure-swirl atomizer
Wave
Flat-fan atomizer
Air/blast atomizer
Effervescent atomizer
Predict initial spray characteristics based on global atomizer parameters such as nozzle type, orifice diameter, liquid flow rate…
Droplet collision
O’Rourke
Drag laws
Spherical
Non-spherical
Stokes-Cunningham
High Mach number
Dynamic-Drag
Detailed information available in FLUENT 6.2 Documentation Chapter 23: Discrete Phase Models
Spray Model GUI in FLUENT 6.2 Define > Models > Discrete Phase…
Wall-Film Model
New to FLUENT 6.2
Improvement to spray modeling capabilities: allows modeling of the build-up of thin liquid film on walls. important for in-cylinder combustion simulations, for example
Particles impinge on a surface and form a thin film: Impinging Fuel Droplet
Flow separation and Sheet Breakup
Splashing Convective Heat Transfer
Evaporation Shear Force Film Thickness
Fuel Film Wall
Conduction Ref. Stanton Int. J. of Heat & Mass Transfer (1998)
Wall-Film Model (cont)
Impingement regimes are based on the impact energy and wall temperature : Splash
E
Spread
Impinging Fuel Droplet
Rebound
Stick
Impinging Fuel Droplet
α
Tw
α
Spread – Particles join the film and move outwards from the point of impingement
Impinging Fuel Droplet
Stick – Particles join the film
α
α β
Rebound – Particles bounce off of the wall
Impinging Fuel Droplet
β ψ
Splash – more complex physics
Wall-Film Model Applicability
Useful for:
Spray Colored by Particle Velocity
SI engines port fuel injected GDI engines
Diesel engines
Example: port fuel injected
gasoline engine
Wall Film Height (mm)
Wall-Film Model Assumptions
The film layer is thin
less than 500 microns
The simulation is transient
Available with unsteady particle tracking only
Heat transfer from the wall to the film takes place by conduction
Film particles in direct contact with the wall surface
Film temperature never exceeds boiling temperature
To model a spray impacting a very hot wall, the wall-jet model may be more appropriate:
Assumption in the wall-jet impingement model is that there is a vapor layer underneath the drops which keeps them from making direct contact with the boundary surface.
This may be a more accurate assumption for in-cylinder diesel computations at typical operating conditions
Wall-Film GUI in FLUENT 6.2
wall-jet wall-film
Example: KIVA SI engine
Fuel droplets injected to the ports at 35m/s using solid cone injector. Droplet break-up process simulated with TAB break-up model. Formation of a thin fuel film on the valve simulated with wall film model. Evaporation occurs at the droplet surface and wall film. The fuel vapor mixes with turbulent air.
Models used:
Solid-cone injector
TAB break-up model
Wall film
DM for piston and valve motion
Standard k-e turbulence model
Mesh size: 150K
Wall-Film Example: KIVA SI Engine
Wall-Jet Model
3-D in-cylinder test case – 2000 rpm, solid cone spray, 6 hole diesel injector, Wave breakup, O’Rourke collision Contours of temperature on an iso-surface of F=4.0
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