- •Why CFD is Important for Modeling
- •How the CFD Module Helps Improve Your Modeling
- •Model Builder Options for Physics Feature Node Settings Windows
- •Where Do I Access the Documentation and Model Library?
- •Typographical Conventions
- •Quick Start Guide
- •Modeling Strategy
- •Geometrical Complexities
- •Material Properties
- •Defining the Physics
- •Meshing
- •The Choice of Solver and Solver Settings
- •Coupling to Other Physics Interfaces
- •Adding a Chemical Species Transport Interface
- •Equation
- •Discretization
- •Transport Feature
- •Migration in Electric Field
- •Reactions
- •Reactions
- •Initial Values
- •Initial Values
- •Boundary Conditions for the Transport of Concentrated Species Interface
- •Mass Fraction
- •Mass Fraction
- •Flux
- •Inflow
- •Inflow
- •No Flux
- •Outflow
- •Flux Discontinuity
- •Flux Discontinuity
- •Symmetry
- •Open Boundary
- •Physical Model
- •Transport Properties
- •Model Inputs
- •Fluid Properties
- •Diffusion
- •Migration in Electric Field
- •Diffusion
- •Model Inputs
- •Density
- •Diffusion
- •Porous Matrix Properties
- •Porous Matrix Properties
- •Initial Values
- •Initial Values
- •Domain Features for the Reacting Flow, Concentrated Species Interface
- •Boundary Conditions for the Reacting Flow, Concentrated Species Interface
- •Reacting Boundary
- •Inward Flux
- •Physical Model
- •Transport Properties
- •Fluid Properties
- •Migration in Electric Field
- •Porous Matrix Properties
- •Initial Values
- •Domain Features for the Reacting Flow, Diluted Species Interface
- •Boundary Conditions for the Reacting Flow, Diluted Species Interface
- •Pair and Point Conditions for the Reacting Flow, Diluted Species Interface
- •Multicomponent Mass Transport
- •Multicomponent Diffusion: Mixture-Average Approximation
- •Multispecies Diffusion: Fick’s Law Approximation
- •Multicomponent Thermal Diffusion
- •References for the Transport of Concentrated Species Interface
- •Domain Equations
- •Combined Boundary Conditions
- •Effective Mass Transport Parameters in Porous Media
- •Selecting the Right Interface
- •The Single-Phase Flow Interface Options
- •Laminar Flow
- •Coupling to Other Physics Interfaces
- •The Laminar Flow Interface
- •Discretization
- •The Creeping Flow Interface
- •Discretization
- •Fluid Properties
- •Fluid Properties
- •Mixing Length Limit
- •Volume Force
- •Volume Force
- •Initial Values
- •Initial Values
- •The Turbulent Flow, Spalart-Allmaras Interface
- •The Rotating Machinery, Laminar Flow Interface
- •Rotating Domain
- •Rotating Domain
- •Initial Values
- •Initial Values
- •Rotating Wall
- •Wall
- •Boundary Condition
- •Interior Wall
- •Boundary Condition
- •Inlet
- •Boundary Condition
- •Velocity
- •Pressure, No Viscous Stress
- •Normal Stress
- •Outlet
- •Boundary Condition
- •Pressure
- •Laminar Outflow
- •No Viscous Stress
- •Vacuum Pump
- •Symmetry
- •Open Boundary
- •Boundary Stress
- •Boundary Condition
- •Periodic Flow Condition
- •Flow Continuity
- •Pressure Point Constraint
- •Non-Newtonian Flow—The Power Law and the Carreau Model
- •Theory for the Pressure, No Viscous Stress Boundary Condition
- •Theory for the Laminar Inflow Condition
- •Theory for the Laminar Outflow Condition
- •Theory for the Slip Velocity Wall Boundary Condition
- •Theory for the Vacuum Pump Outlet Condition
- •Theory for the No Viscous Stress Condition
- •Theory for the Mass Flow Inlet Condition
- •Turbulence Modeling
- •Eddy Viscosity
- •Wall Functions
- •Initial Values
- •Wall Distance
- •Inlet Values for the Turbulence Length Scale and Intensity
- •Initial Values
- •The Spalart-Allmaras Turbulence Model
- •Inlet Values for the Turbulence Length Scale and Intensity
- •Pseudo Time Stepping for Turbulent Flow Models
- •References for the Single-Phase Flow, Turbulent Flow Interfaces
- •Selecting the Right Interface
- •Coupling to Other Physics Interfaces
- •Discretization
- •Fluid-Film Properties
- •Initial Values
- •Initial Values
- •Inlet
- •Outlet
- •Wall
- •Symmetry
- •Discretization
- •Initial Values
- •Initial Values
- •Fluid-Film Properties
- •Border
- •Inlet
- •Outlet
- •Conditions for Film Damping
- •The Reynolds Equation
- •Structural Loads
- •Gas Outflow Conditions
- •Rarefaction and Slip Effects
- •Geometry Orientations
- •References for the Thin-Film Flow Interfaces
- •Selecting the Right Interface
- •The Multiphase Flow Interface Options
- •The Relationship Between the Interfaces
- •Bubbly Flow
- •Coupling to Other Physics Interfaces
- •The Laminar Two-Phase Flow, Level Set Interface
- •Discretization
- •The Laminar Two-Phase Flow, Phase Field Interface
- •Domain Level Settings for the Level Set and Phase Field Interfaces
- •Fluid Properties
- •Mixing Length Limit
- •Initial Values
- •Initial Values
- •Volume Force
- •Volume Force
- •Gravity
- •Boundary Conditions for the Level Set and Phase Field Interfaces
- •Wall
- •Boundary Condition
- •Initial Interface
- •The Turbulent Flow, Two-Phase Flow, Level Set Interface
- •The Turbulent Two-Phase Flow, Phase Field Interface
- •Wall Distance Interface and the Distance Equation
- •Level Set and Phase Field Equations
- •Conservative and Non-Conservative Formulations
- •Phase Initialization
- •Numerical Stabilization
- •References for the Level Set and Phase Field Interfaces
- •Stabilization
- •Discretization
- •Level Set Model
- •Initial Values
- •Initial Values
- •Boundary Conditions for the Level Set Function
- •Inlet
- •Initial Interface
- •No Flow
- •Outlet
- •Symmetry
- •Discretization
- •Initial Values
- •Initial Values
- •Phase Field Model
- •Boundary Conditions for the Phase Field Function
- •Initial Interface
- •Inlet
- •Wetted Wall
- •Wetted Wall
- •Outlet
- •The Level Set Method
- •Conservative and Non-Conservative Form
- •Initializing the Level Set Function
- •Variables For Geometric Properties of the Interface
- •Reference for the Level Set Interface
- •About the Phase Field Method
- •The Equations for the Phase Field Method
- •Conservative and Non-Conservative Forms
- •Additional Sources of Free Energy
- •Variables and Expressions
- •Reference For the Phase Field Interface
- •The Laminar Bubbly Flow Interface
- •Reference Pressure
- •Discretization
- •The Turbulent Bubbly Flow Interface
- •Reference Pressure
- •Discretization
- •Fluid Properties
- •Slip Model
- •Initial Values
- •Initial Values
- •Volume Force
- •Volume Force
- •Gravity
- •Gravity
- •Mass Transfer
- •Mass Transfer
- •Boundary Conditions for the Bubbly Flow Interfaces
- •Wall
- •Liquid Boundary Condition
- •Gas Boundary Condition
- •Inlet
- •Liquid Boundary Condition
- •Gas Boundary Condition
- •Outlet
- •Liquid Boundary Condition
- •Gas Boundary Condition
- •Symmetry
- •Gas Boundary Conditions Equations
- •The Mixture Model, Laminar Flow Interface
- •Stabilization
- •Discretization
- •The Mixture Model, Turbulent Flow Interface
- •Stabilization
- •Mixture Properties
- •Mass Transfer
- •Mass Transfer
- •Initial Values
- •Initial Values
- •Volume Force
- •Volume Force
- •Gravity
- •Gravity
- •Boundary Conditions for the Mixture Model Interfaces
- •Wall
- •Mixture Boundary Condition
- •Dispersed Phase Boundary Condition
- •Inlet
- •Mixture Boundary Condition
- •Dispersed Phase Boundary Condition
- •Outlet
- •Mixture Boundary Condition
- •Symmetry
- •The Bubbly Flow Equations
- •Turbulence Modeling in Bubbly Flow Applications
- •References for the Bubbly Flow Interfaces
- •The Mixture Model Equations
- •Dispersed Phase Boundary Conditions Equations
- •Turbulence Modeling in Mixture Models
- •Slip Velocity Models
- •References for the Mixture Model Interfaces
- •Dispersed Phase
- •Discretization
- •Domain Conditions for the Euler-Euler Model, Laminar Flow Interface
- •Phase Properties
- •Solid Viscosity Model
- •Drag Model
- •Solid Pressure Model
- •Initial Values
- •Boundary, Point, and Pair Conditions for the Euler-Euler Model, Laminar Flow Interface
- •Wall
- •Dispersed Phase Boundary Condition
- •Inlet
- •Two-Phase Inlet Type
- •Continuous Phase
- •Dispersed Phase
- •Outlet
- •Mixture Boundary Condition
- •The Euler-Euler Model Equations
- •References for the Euler-Euler Model, Laminar Flow Interface
- •Selecting the Right Interface
- •The Porous Media Flow Interface Options
- •Coupling to Other Physics Interfaces
- •Discretization
- •Fluid and Matrix Properties
- •Mass Source
- •Mass Source
- •Initial Values
- •Initial Values
- •Boundary Conditions for the Darcy’s Law Interface
- •Pressure
- •Pressure
- •Mass Flux
- •Mass Flux
- •Inflow Boundary
- •Inflow Boundary
- •Symmetry
- •No Flow
- •Discretization
- •Fluid and Matrix Properties
- •Volume Force
- •Volume Force
- •Forchheimer Drag
- •Forchheimer Drag
- •Initial Values
- •Initial Values
- •Mass Source
- •Boundary Conditions for the Brinkman Equations Interface
- •Discretization
- •Fluid Properties
- •Porous Matrix Properties
- •Porous Matrix Properties
- •Forchheimer Drag
- •Forchheimer Drag
- •Volume Force
- •Volume Force
- •Initial Values
- •Initial Values
- •Boundary Conditions for the Free and Porous Media Flow Interface
- •Microfluidic Wall Conditions
- •Boundary Condition
- •Discretization
- •Domain, Boundary, and Pair Conditions for the Two-Phase Darcy’s Law Interface
- •Fluid and Matrix Properties
- •Initial Values
- •Initial Values
- •No Flux
- •Pressure and Saturation
- •Pressure and Saturation
- •Mass Flux
- •Inflow Boundary
- •Inflow Boundary
- •Outflow
- •Pressure
- •Darcy’s Law—Equation Formulation
- •About the Brinkman Equations
- •Brinkman Equations Theory
- •References for the Brinkman Equations Interface
- •Reference for the Free and Porous Media Flow Interface
- •Darcy’s Law—Equation Formulation
- •The High Mach Number Flow, Laminar Flow Interface
- •Surface-to-Surface Radiation
- •Discretization
- •Initial Values
- •Initial Values
- •Shared Interface Features
- •Fluid
- •Dynamic Viscosity
- •Inlet
- •Outlet
- •Consistent Inlet and Outlet Conditions
- •Pseudo Time Stepping for High Mach Number Flow Models
- •References for the High Mach Number Flow Interfaces
- •Selecting the Right Interface
- •The Non-Isothermal Flow Interface Options
- •Coupling to Other Physics Interfaces
- •The Non-Isothermal Flow, Laminar Flow Interface
- •Discretization
- •The Conjugate Heat Transfer, Laminar Flow Interface
- •The Turbulent Flow, Spalart-Allmaras Interface
- •Fluid
- •Dynamic Viscosity
- •Wall
- •Boundary Condition
- •Initial Values
- •Pressure Work
- •Viscous Heating
- •Dynamic Viscosity
- •Turbulent Non-Isothermal Flow Theory
- •References for the Non-Isothermal Flow and Conjugate Heat Transfer Interfaces
- •Selecting the Right Interface
- •The Heat Transfer Interface Options
- •Conjugate Heat Transfer, Laminar Flow
- •Conjugate Heat Transfer, Turbulent Flow
- •Coupling to Other Physics Interfaces
- •Accessing the Heat Transfer Interfaces via the Model Wizard
- •Discretization
- •Heat Transfer in Solids
- •Translational Motion
- •Translational Motion
- •Pressure Work
- •Heat Transfer in Fluids
- •Viscous Heating
- •Dynamic Viscosity
- •Heat Source
- •Heat Source
- •Initial Values
- •Initial Values
- •Boundary Conditions for the Heat Transfer Interfaces
- •Temperature
- •Temperature
- •Thermal Insulation
- •Outflow
- •Symmetry
- •Heat Flux
- •Heat Flux
- •Inflow Heat Flux
- •Inflow Heat Flux
- •Open Boundary
- •Periodic Heat Condition
- •Surface-to-Ambient Radiation
- •Boundary Heat Source
- •Boundary Heat Source
- •Heat Continuity
- •Pair Thin Thermally Resistive Layer
- •Pair Thin Thermally Resistive Layer
- •Thin Thermally Resistive Layer
- •Thin Thermally Resistive Layer
- •Line Heat Source
- •Line Heat Source
- •Point Heat Source
- •Convective Cooling
- •Out-of-Plane Convective Cooling
- •Upside Heat Flux
- •Out-of-Plane Radiation
- •Upside Parameters
- •Out-of-Plane Heat Flux
- •Domain Selection
- •Upside Inward Heat Flux
- •Change Thickness
- •Change Thickness
- •Porous Matrix
- •Heat Transfer in Fluids
- •Thermal Dispersion
- •Dispersivities
- •Heat Source
- •Equation Formulation
- •Activating Out-of-Plane Heat Transfer and Thickness
Thermal Dispersion
Right-click the Porous Matrix node to add the Thermal Dispersion feature. This adds an extra term ·kd T to the right-hand side of Equation 13-9 and specify the values of the longitudinal and transverse dispersivities.
D O M A I N S E L E C T I O N
From the Selection list, choose the domains to activate the thermal dispersion.
D I S P E R S I V I T I E S
The Dispersivities group adds these fields:
Longitudinal Dispersivity
Specify the Longitudinal dispersivity lo (SI unit: m).
Transverse Dispersivity
Specify the Transverse dispersivity tr (SI unit: m).
The feature node defines the tensor of dispersive thermal conductivity
kijd = LCp LDij
where Dij is the dispersion tensor
ukul
Dij = ijkl-----------
u
and ijkl is the fourth order dispersivity tensor
–
ijkl = tr ij kl + ----lo-------------tr-- ik jl + il jk
2
Heat Source
Add one or more Heat Source nodes. The heat source describes heat generation within the domain. Express heating and cooling with positive and negative values, respectively.
D O M A I N S E L E C T I O N
From the Selection list, choose the domains to add the heat source.
438 | C H A P T E R 1 3 : H E A T T R A N S F E R B R A N C H
H E A T S O U R C E
Select either the General source or Linear source button:
If General source is selected, heat sources from electrochemical current distribution interfaces will be listed in the pull-down menu. Choose the appropriate one, or choose User defined and enter a value for Q (SI unit: W/m3). The default is 0.
If Linear source (Q=qs·T) is selected, enter the Production/absorption coefficient, qs
(SI unit: W/(m3·K)).
The advantage in writing the source in this form is that it can be stabilized by the streamline diffusion. The theory covers qs that is independent of
the temperature, but some stability can be gained as long as qs is only
Tip
weakly dependent on the temperature.
• Stabilization Techniques in the COMSOL Multiphysics Reference
Guide
See Also
T H E H E A T T R A N S F E R I N P O R O U S M E D I A I N T E R F A C E | 439
O u t - o f - P l a n e H e a t T r a n s f e r T h e o r y
When the object to model in COMSOL Multiphysics is thin or slender enough along one of its geometry dimensions, there is usually only a small variation in temperature along the object’s thickness or cross section. For such objects, it is efficient to reduce the model geometry to 2D or even 1D and use the out-of-plane heat transfer mechanism. Figure 13-2 shows examples of likely situations where this type of geometry reduction can be applied.
q
qup
qdown
Figure 13-2: Geometry reduction from 3D to 1D (top) and from 3D to 2D (bottom).
The reduced geometry does not include all the boundaries of the original 3D geometry. For example, the reduced geometry does not represent the upside and downside surfaces of the plate in Figure 13-2 as boundaries. Instead, heat transfer through these boundaries appears as sources or sinks in the thickness-integrated version of the heat equation used when out-of-plane heat transfer is active.
Equation Formulation
When out-of-plane heat transfer is enabled, the equation for heat transfer in solids, Equation 13-1 is replaced by
d |
C |
T |
– d |
k T = d |
Q |
(13-7) |
------ |
||||||
z |
|
p t |
z |
z |
|
|
where dz is the thickness of the domain in the out-of-plane direction. The equation for heat transfer in fluids, Equation 13-3, is replaced by
440 | C H A P T E R 1 3 : H E A T T R A N S F E R B R A N C H
C |
|
d |
T |
|
= d |
k T + d |
Q |
(13-8) |
p |
------ |
+ u T |
||||||
|
|
z t |
|
z |
z |
|
|
The Pressure Work attribute on Solids and Fluids and the Viscous Heating attribute on Fluids are not available when out-of-plane heat transfer is activated.
|
Heat Source features that are added to a model with out-of-plane heat |
|
transfer enabled are multiplied by the thickness, dz. Boundary conditions |
Note |
are also adjusted. |
|
|
Activating Out-of-Plane Heat Transfer and Thickness
Using a 1D or 2D model, activate the features for out-of-plane heat transfer and the thickness property by clicking the main Heat Transfer feature and selecting the
Out-of-plane heat transfer check box under Physical Model.
O U T - O F - P L A N E H E A T TR A N S F E R T H E O R Y | 441
T h e o r y f o r t h e H e a t T r a n s f e r i n P o r o u s M e d i a I n t e r f a c e
The Heat Transfer in Porous Media Interface uses the following version of the heat equation as the mathematical model for heat transfer in porous media:
C |
|
T |
+ C |
|
u T = k |
|
T + Q |
(13-9) |
------ |
p |
eq |
||||||
|
p |
eq t |
|
|
|
|
with the following material properties:
•is the fluid density.
•Cp is the fluid heat capacity at constant pressure.
•( Cp)eq is the equivalent volumetric heat capacity at constant pressure.
•keq is the equivalent thermal conductivity (a scalar or a tensor if the thermal conductivities are anisotropic).
•u is the fluid velocity field, either an analytic expression or a velocity field from a fluid-flow interface. u is interpreted as the Darcy velocity, that is, the volume flow
rate per unit cross-sectional area. The average linear velocity, the velocity within the pores, is calculated as uL u L, where L is the fluid’s volume fraction, or equivalently the porosity.
•Q is the heat source (or sink). Add one or several heat sources as separate features.
The equivalent conductivity of the solid-fluid system, keq, is related to the conductivity of the solid kp and to the conductive of the fluid, k by
keq = pkp + Lk
The equivalent volumetric heat capacity of the solid-fluid system is calculated by
Cp eq = p pCp p + L Cp
Here p denotes the solid material’s volume fraction, which is related to the volume fraction of the liquid L (or porosity) by
L + p = 1
For a steady-state problem the temperature does not change with time, and the first term in the left-hand side of Equation 13-9 disappears.
442 | C H A P T E R 1 3 : H E A T T R A N S F E R B R A N C H
14
G l o s s a r y
This Glossary of Terms contains application-specific terms used in the CFD Module software and documentation. For finite element modeling terms, mathematical terms, and geometry and CAD terms, see the glossary in the COMSOL Multiphysics User’s Guide. For references to more information about a term, see the index.
443
G l o s s a r y o f T e r m s
anisotropy Variation of a transport property in different directions in a material. Is often obtained from homogenization of regular structures, for example, monolithic structures in tubular reactors.
Boussinesq approximation A method to treat buoyancy where the density variation is only taken into account in the buoyancy term.
Brinkman equations Extension of Darcy’s law in order to include the transport of momentum through shear in porous media flow.
boundary layer Region in a fluid close to a solid surface. This region is characterized by large gradients in velocity and other properties. In turbulent flow it is often treated with approximative methods, because of the difficulty to geometrically resolve the large gradients.
bubbly flow Flow with gas bubbles dispersed in a liquid.
conjugate heat transfer heat transfer that takes place in both a solid and a fluid.
crosswind diffusion numerical method to reduce oscillations near sharp gradients
Darcy’s law Equation that gives the velocity vector as proportional to the pressure gradient. Often used to describe flow in porous media.
Euler flow flow of an inviscid fluid. Often used as approximation for high speed compressible flows.
Euler-Euler model fA two-phase flow model that treats both phases as being continuous.
Fick’s law The first law relates the concentration gradients to the diffusive flux of a solute infinitely diluted in a solvent. The second law introduces the first law into a differential material balance for the solute.
fluid-structure interaction (FSI) When a flow affects the deformation of a solid object
and vice versa.
444 | C H A P T E R 1 4 : G L O S S A R Y
fully developed laminar flow Laminar flow along a channel or pipe that only has velocity components in the main direction of the flow. The velocity profile perpendicular to the flow does not change downstream in the flow.
Hagen-Poiseuille equation See Poiseuille’s law.
heterogeneous reaction Reaction that takes place at the interface between two phases.
homogeneous reaction Reaction that takes place in the bulk of a solution.
k- turbulence model A two-equation RANS model that solves for the turbulence kinetic energy, k, and the dissipation of turbulence kinetic energy, . Utilizes wall functions to describe the flow close to solid walls.
k- turbulence model A two-equation RANS model that solves for the turbulent kinetic energy, k, and the specific dissipation rate, . Utilizes wall functions to describe the flow close to solid walls.
law of the wall See wall function.
low-Reynolds k- turbulence model Two-equation RANS model that solves for the turbulence kinetic energy, k, and the dissipation of turbulence kinetic energy, . Includes damping functions to be able to describe regions with low Reynolds numbers, for example close to solid walls.
Mach number Dimensionless number equal to the flow velocity over the speed of sound. Compressible effects because of the flow speed can be neglected for Mach number less than 0.3.
multiphase flow Flow with more than one phase.
Navier-Stokes equations Equations for the momentum balances coupled to the equation of continuity for a Newtonian incompressible fluid.
Newtonian fluid A fluid where the stress is proportional to the rate of strain. Many common fluids such as water and air are Newtonian.
non-Newtonian fluid A fluid where the stress is not proportional to the rate of strain. Blood and suspensions of polymers are example of non-Newtonian fluids.
G L O S S A R Y O F TE R M S | 445
Poiseuille’s law Equation that relates the mass rate of flow in a tube as proportional to the pressure difference per unit length and to the fourth power of the tube radius. The law is valid for fully developed laminar flow.
pressure work describes the reversible part of the fact that work can be turned into heat and heat into work.
RANS Reynolds-averaged Navier-Stokes; implying that a time averaging of the velocity fluctuations in turbulent flow has been performed. The Reynolds’ stresses obtained by this averaging have to be expressed with an additional set of equations. Turbulence models like the k- and Spalart-Allmaras models belong to this class.
Reynolds number A dimensionless number that describes the relative importance between inertia and viscous effects. Flow at high Reynolds number have a tendency to undergo transition to turbulence.
A one-equation turbulence model that solves for the undamped turbulent kinematic viscosity, T .
streamline-diffusion stabilization A numerical technique for stabilization of the numeric solution to a convection-dominated PDE by artificially adding upwinding in the direction of the streamlines.
thin-film flow Flow in very thin regions where the flow can be assumed to always have a fully developed profile.
viscous heating The fact that the viscous friction in a fluid irreversibly converts work to heat.
wall function Semi-empirical expression for the anisotropic flow close to a solid surface used in turbulence models.
446 | C H A P T E R 1 4 : G L O S S A R Y
I n d e x
1D and 2D models
out-of-plane heat transfer 410, 440
Aadded mass force 302 advanced settings 20
AKN model 154
BBasset force 302 border (node) 171 boundary conditions
Brinkman equations interface 325 bubbly flow interfaces 250
Darcy’s law interface 316 dispersed phase 281
Euler-Euler model, laminar flow interface 294
heat transfer interfaces 419
high mach number flow interface 354 level set interface 220
mixture model interface 268 phase field interface 226 single-phase flow interfaces 107 transport of concentrated species
interface 54
two phase flow interfaces 200 two-phase Darcy’s law interface 334
boundary heat source (node) 425 boundary stress (node) 129
Brinkman equations interface 320 theory 341
bubble number density 276 bubbly flow, laminar 238
CCarreau model 135, 387 cell Reynolds number 123
CFL number 366
CFL number, pseudo time stepping, and
91
change thickness (node) 433 channel base 174
conjugate heat transfer laminar flow interface 379
turbulent flow interfaces 381, 383–384 conjugate heat transfer interface
theory 393
consistent stabilization settings 21 constraint settings 22
contacting COMSOL 23
continuity equation, Darcy’s law 340 continuity equation, multiphase flow 281 convection and diffusion (node) 51 convection, diffusion, and migration
(node) 51
convective cooling (node) 428 creeping flow 90, 192 creeping flow interface 92
theory 134
Ddamping, film 174
Darcy velocity 318, 340
Darcy’s law interface 313 theory 340
dense flows 302 diffusion (node) 51, 64 diffusion models 48 dilute flows 303
dimensionless distance to cell center variable 155
discretization settings 20 dispersed liquid droplets 301 dispersed phase particles 299 dispersed phase viscosity 301 dispersed solid particles 301 dispersivities, porous media 438 dissipation, turbulent 276
I N D E X | 447
documentation, finding 22 domain conditions
Euler-Euler model, laminar flow interface 290
high mach number flow interface 354 laminar, two-phase flow interfaces 195 two-phase Darcy’s law interface 334
drag force 302
drag law, Hadamard-Rybczynski 245, 283
Eeddy viscosity 145
elastic contribution to entropy 413 emailing COMSOL 23
Eötvös number 245 equation view 20
Ergun packed bed expression 303
Ettehadieh solid pressure model 304
Euler-Euler equations bubbly flow theory 274
Euler-Euler model theory 299 implementing 304
mixture model theory 279
Euler-Euler model, laminar flow interface
288 theory 299
exit length 124 expanding sections 20
FFavre average 146, 395
Fick’s law approximation diffusion 75
Fick’s law diffusion model 49, 53 flow continuity (node) 133
fluid (node)
high mach number flow interfaces 355 non-isothermal flow/conjugate heat
transfer interfaces 385 fluid and matrix properties (node)
Brinkman equations interface 322
Darcy’s law interface 314 fluid flow
approaches to analysis 32
Brinkman equations theory 341
Darcy’s law theory 340 laminar bubbly flow theory 274 mixture model theory 279 rotating machinery theory 160 selecting interfaces 374 thin-film theory 174
turbulent flow theory 143 two-phase flow level set and phase
field theory 211 fluid properties 33 fluid properties (node)
bubbly flow interface 243
free and porous media flow interface
328
single-phase, laminar flow interface 94 two-phase flow interfaces 196
fluid-film properties (node) lubrication shell interface 165 thin-film flow interfaces 170
fluids and matrix properties (node) 335 fluid-solid mixtures 300
flux (node) 56
flux discontinuity (node) 58
Forchheimer drag (node) Brinkman equations interface 324
free and porous media flow interface
330
free and porous media flow interface 326 theory 344
Ggas boundary conditions 256 general stress (boundary stress
condition) 130 geometry, simplifying 33 geometry, working with 22
Gidaspow and Ettehadieh solid pressure model 304
448 | I N D E X
Gidaspow models 303–304 |
theory 362 |
|
Ginzburg-Landau equation 233 |
hybrid outlet 365 |
|
gravity (node) |
implementing, Euler-Euler equations 304 |
|
I |
||
bubbly flow interface 248 |
inconsistent stabilization settings 21 |
|
mixture model flow interface 267 |
||
inflow (node) 56 |
||
two-phase flow interfaces 199 |
||
inflow boundary (node) 318 |
||
|
||
H Hadamard-Rybczynski drag law 245, 283, |
inflow heat flux (node) 423 |
|
303 |
initial interface (node) |
|
heat continuity (node) 425 |
level set interface 221 |
|
heat flux (node) 422 |
phase field interface 226 |
|
heat source (node) |
two-phase flow interfaces 204 |
|
heat transfer in porous media interface |
initial values (node) |
|
438 |
Brinkman equations interface 324 |
|
heat transfer interface 418 |
bubbly flow interface 246 |
|
heat sources |
Darcy’s law interface 316 |
|
defining as total power 418, 425 |
Euler-Euler model, laminar flow |
|
line and point 427 |
interface 293 |
|
heat transfer coefficients |
free and porous media flow interface |
|
out-of-plane heat transfer interfaces |
331 |
|
431 |
heat transfer interface 419 |
|
heat transfer in fluids (node) 414 |
level set interface 220 |
|
extended features 436 |
lubrication shell interface 166 |
|
heat transfer in porous media interface |
mixture model flow interface 266 |
|
434 |
non-isothermal flow/conjugate heat |
|
theory 442 |
transfer interfaces 353, 390 |
|
heat transfer in solids (node) 411 |
phase field interface 224 |
|
heat transfer interfaces 407 |
reacting flow, concentrated species |
|
selecting 374 |
interface 65 |
|
Henry’s law 249 |
reacting flow, diluted species interface |
|
hide button 20 |
70 |
|
high Mach number flow, laminar flow |
single-phase, laminar flow interface 97 |
|
interface 349 |
thin film flow interfaces 170 |
|
theory 362 |
transport of concentrated species |
|
high Mach number flow, turbulent flow, |
interface 54 |
|
k-e interface 351 |
two-phase Darcy’s law interface 336 |
|
theory 362 |
two-phase flow interfaces 199 |
|
high Mach number flow, turbulent flow, |
initializing functions 230 |
|
Spalart-Allmaras interface 353 |
inlet (boundary stress condition) 131 |
I N D E X | 449
inlet (node)
bubbly flow interface 252
Euler-Euler model, laminar flow interface 295
high Mach number flow interfaces 358 level set interface 221
lubrication shell interface 167 mixture model flow interface 270 phase field interface 226 single-phase flow interfaces 114 thin-film flow interfaces 172
Interior wall (node)
single-phase flow, turbulent flow interfaces 113
interior wall (node) 113
Internet resources 22
interphase momentum transfer 302 intrinsic volume averages 341
KKays-Crawford models 397 k-epsilon turbulence model theory, bubbly flow 276
theory, mixture models 282 theory, single-phase flow 147 knowledge base, COMSOL 23
Knudsen number 178
Krieger type model 302
Krieger type viscosity model 264
Llaminar bubbly flow interface 238
theory 274 laminar flow
conjugate heat transfer interface 379 mixture model interface 257 non-isothermal flow interface 376 rotating machinery, fluid flow interface
103
laminar flow interface 88 turbulence model 89 turbulent flow k-epsilon 98
turbulent flow, low re k-epsilon 100 laminar inflow (inlet boundary condition)
117
laminar outflow (outlet boundary condition) 124
laminar two-phase flow level set interface 191 phase field interface 194
leaking wall, wall boundary condition 111 level set functions, initializing 230
level set interface 218 theory 228
level set model (node) 219 lift force 302
line heat source (node) 427 liquid boundary conditions 251 local CFL number 91, 158, 366 low Reynolds number
k-epsilon turbulence theory 154 neglect inertial term 377
lubrication shell interface 164 theory 174
lumped curves
outlet boundary condition, vacuum pump 125
outlet boundary condition, vacuum pump theory 139
M Mach number
pressure work, and 391 mass balance 299
mass conservation, level set equations
214
mass flow, theory 141
mass flux (node)
Darcy’s law interface 317
mass flux (node)_ two-phase Darcy’s law
interface 338
mass fraction (node) 55
450 | I N D E X
mass source (node)
Brinkman equations interface 324
Darcy’s law interface 316 mass transfer (node)
bubbly flow interface 249 mixture model flow interface 265
mass transport 73 mathematics, moving interfaces
level set 218 phase field 223 theory 228, 232
mean effective thermal conductivity 412 meshing 34
microfluidic wall conditions (node) 331 mixture model interface
slip model 258
mixture model, laminar flow interface
257
theory 279
mixture model, turbulent flow interface
260
theory 279
mixture properties (node) 262 mixture viscosity 263 mixture-averaged diffusion 74
mixture-averaged diffusion model 48, 52 model builder settings 20
Model Library examples Euler-Euler outlet condition 297 heat transfer in fluids 414
heat transfer in solids 411
high mach number flow turbulent interface 353
inlet (laminar flow) 116 laminar flow interface 88
laminar two-phase flow, level set interface 191
laminar two-phase flow, phase field
interface 194
lubrication shell interface 164 mixture model, laminar flow interface
257
non-isothermal flow interface 376, 379 outlet (laminar flow) 116
single-phase flow, rotating machinery interface 103
thermodynamics 412
turbulent bubbly flow interface 241 turbulent flow, k-epsilon interface 98
modeling strategy, physics 32 momentum balance equations 300 moving interfaces 228, 232
moving wall (wall functions), boundary condition 113
moving wall, wall boundary condition
110, 114
moving wetted wall (boundary condition) 204
MPH-files 23 multiphase flow
laminar bubbly flow theory 274 level set and phase field flow theory
211
level set theory 228 mixture model theory 279 phase field theory 232
NNavier-Stokes equations 211
Neumann condition 151
Newtonian model 135 no flow (node)
Darcy’s law interface 319 level set interface 221
no flux (node) 337
transport of concentrated species interface 57
no slip, interior wall boundary condition
I N D E X | 451
113
no slip, wall boundary condition 109 no viscous stress (outlet boundary
condition) 124 non-conservative formulations 214 non-isothermal flow interface
laminar flow 376 theory 393
turbulent flow 381, 383–384 non-Newtonian fluids 84 non-Newtonian power law and Carreau
model 387
normal stress (boundary condition) 117 normal stress, normal flow (boundary
stress condition) 130
O open boundary (boundary stress condition) 131
open boundary (node) heat transfer 424
single-phase flow interfaces 127 transport of concentrated species
interface 59 outflow (node)
heat transfer interfaces 421 transport of concentrated species
interface 58
two-phase Darcy’s law interface 339 outlet (boundary stress condition) 131 outlet (node)
bubbly flow interface 254
Euler-Euler model, laminar flow interface 297
high Mach number flow interfaces 360 level set interface 221
lubrication shell interface 167 mixture model flow interface 271 phase field interface 227 single-phase flow interfaces 121
thin-film flow interfaces 172 out-of-plane convective cooling (node)
430
out-of-plane heat flux (node) 432 out-of-plane heat transfer
change thickness 433 general theory 440
shallow channel approximation 378 out-of-plane radiation (node) 431 override and contribution settings 20
Ppair selection 21
pair thin thermally resistive layer (node)
425
periodic flow condition (node) 132 periodic heat condition (node) 424 phase field interface 223
theory 232
phase field model (node) 225 phase properties (node) 291
physics interface settings windows 20 point heat source (node) 427 pointwise mass flux, theory 141 porous matrix (node) 435
porous matrix properties (node) 329 reacting flow, concentrated species
interface 64
porous media and subsurface flow Brinkman equations interface 320
Darcy’s law interface 313
free and porous media flow interface
326
theory, Brinkman equations 341 theory, Darcy’s law 340
theory, free and porous media flow
344
power law, non-Newtonian 387
power law, single-phase flow theory 135
Prandtl number 371, 397
452 | I N D E X
pressure (node) 317
pressure (outlet boundary condition)
123
pressure and saturation (node) 337 pressure point constraint (node) 133 pressure work (node)
heat transfer interfaces 413 non-isothermal flow/conjugate heat
transfer interfaces 391 pressure, no viscous stress (inlet and
outlet boundary conditions) 116 pseudo time stepping
advanced settings 91
high mach number flow theory 366 turbulent flow theory 158
pseudoplastic fluids 135
Rradiation, out-of-plane 431
RANS
mixture model interface 261 rotating machinery interface 104 theory, single-phase flow 144
rarefaction 178
ratio of specific heats 415 reacting boundary (node) 66
reacting flow, concentrated species interface 61
theory 78
reacting flow, diluted species interface 67 theory 80
reactions (node) 53
relative flow rate, theory 179
Reynolds equation 176–177
Reynolds number
extended Kays-Crawford 398 low, turbulence theory 154 slip velocity models 284 turbulent flow theory 143
Reynolds stress tensor 145, 148
Reynolds-averaged Navier-Stokes. See
RANS.
rotating machinery
fluid flow interface, theory 160 laminar flow interface 104 turbulent flow interface 104
SSchiller-Naumann model 303
Schiller-Naumann slip model 283
Schmidt number 283 selecting
conjugate heat transfer interfaces 374 heat transfer interfaces 402, 407
high mach number flow interfaces 348 multiphase flow interfaces 184 non-isothermal flow interfaces 370,
374
porous media and subsurface flow interfaces 308
single-phase flow interfaces 82 shallow channel approximation 378 shear rate magnitude variables 94 shear thickening fluids 135
show button 20 single-phase flow
rotating machinery 160
rotating machinery, turbulent 104 turbulent flow theory 143
single-phase flow interface boundary conditions 107 creeping flow 92 laminar flow 88
rotating machinery, laminar 103 theory 160
turbulent flow low re k-e 100 slide-film damping 174
sliding wall (wall functions), boundary condition 112
sliding wall, wall boundary condition 110
I N D E X | 453
slip effects 178 slip model
bubbly flow interface 244
Hadamard-Rybczynski 245, 283 mixture model interface 258
Schiller-Naumann 283 theory, Reynolds number 284
slip velocity, wall boundary condition 111 theory 137
slip, wall boundary condition 109, 114 solid pressure and particle interaction
303
Soret effect 76
Spalart-Allmaras turbulence model 101 squeezed-film damping 174 stabilization settings 21
standard flow rate, theory 142 static pressure curves 125
Stokes equations 92
Stokes flow. see Creeping Flow interface strain-rate tensors 417
superficial volume averages, porous media 342
supersonic inlet 365 supersonic outlet 366
surface-to-ambient radiation (node) 424
Sutherland’s law 357 swirl flow theory 148 symmetry (node)
Darcy’s law interface 319 heat transfer interfaces 422 level set interface 222 lubrication shell interface 168 mixture model interfaces 272
single-phase flow interfaces 126 transport of concentrated species
interface 59
T tangential momentum accommodation
coefficient. see TMAC technical support, COMSOL 23 temperature (node) 420 tensors
Reynolds stress 148 strain-rate 417
viscous stress theory 134 theory
Brinkman equations interface 341 conjugate heat transfer interface 393 creeping flow interface 134
Darcy’s law interface 340
Euler-Euler model, laminar flow interface 299
free and porous media flow interface
344
heat transfer in porous media interface
442
high Mach number flow interfaces 362 laminar bubbly flow interface 274 level set interface 228
mixture model interfaces 279 non-isothermal flow interface 393 out-of-plane heat transfer 440 phase field interface 232
reacting flow, concentrated species 78 reacting flow, diluted species 80 rotating machinery, fluid flow interface
160
thin-film flow interface 174 transport of concentrated species
interface 73
turbulent flow k-e interface 143 turbulent flow low re k-e interface 143 two-phase flow level set and phase
field interfaces 211
thermal conductivity, mean effective 412 thermal creep, wall boundary condition
454 | I N D E X
112
thermal diffusion 76
thermal dispersion (node) 438 thermal insulation (node) 421
thin thermally resistive layer (node) 426 thin-film flow interface 169
lubrication shell 164 theory 174
TMAC
microfluidic wall conditions 332 thin film flow theory 179
total heat flux 423 total power 418, 425
traction boundary conditions 129 translational motion (node) 413 transport mechanisms 50 transport of concentrated species
interface 47 theory 73
transport properties (node)
reacting flow, concentrated species interface 63
reacting flow, diluted species interface
69
turbulence models k-epsilon 147, 276, 282 single-phase flow 89
Spalart-Allmaras 101, 156 turbulent bubbly flow interface 240 turbulent compressible flow 146 turbulent conjugate heat transfer
interfaces theory 395
turbulent dissipation rate, multiphase flow 276
turbulent flow k-e interface non-isothermal flow interface 381 single-phase flow 98
theory 143
turbulent flow k-omega interface 100 turbulent flow low re k-e interface 100,
381
theory 143
turbulent flow Spalart-Allmaras interface
383
turbulent kinetic energy theory k-epsilon model 147
laminar bubbly flow interface 276 mixture model interface 282
RANS 147
turbulent length scale 157
turbulent non-isothermal flow interfaces theory 395
turbulent Prandtl number 397 turbulent two-phase flow, level set
interface 206
turbulent two-phase flow, phase field interface 208
two-fluid Euler-Euler model bubbly flow theory 274 mixture model interfaces 279
two-phase Darcy’s law interface 333 two-phase flow
level set and phase field interfaces, theory 211
typographical conventions 24
U undamped turbulent kinematic viscosity
156
user community, COMSOL 23
V vacuum pump (outlet boundary conditions) 125
variables
dimensionless distance to cell center
155
shear rate magnitude 94 velocity (inlet and outlet boundary
I N D E X | 455
conditions) 116
velocity of moving wall, wall boundary condition 111
viscous drag, coefficient 245 viscous heating (node)
heat transfer interfaces 417 non-isothermal flow/conjugate heat
transfer interfaces 391
viscous slip, wall boundary condition 111 viscous stress tensors, theory 134 volume averages 341
volume force (node)
Brinkman equations interface 323 bubbly flow interface 248
free and porous media flow interface
330
mixture model flow interface 267 single-phase, laminar flow interface 96 two-phase flow interfaces 199
W wall (node)
bubbly flow interface 251
Euler-Euler model, laminar flow interface 294
lubrication shell interface 168 mixture model flow interface 269 non-isothermal flow/conjugate heat
transfer interfaces 389 single-phase flow, laminar flow
interfaces 108, 113 single-phase flow, turbulent flow
interfaces 108
two-phase flow interfaces 201
wall distance initialization study step 154 wall functions, turbulent flow 150
wall functions, wall boundary condition
112
weak constraint settings 22 web sites, COMSOL 23
well posedness 362
Wen and Yu fluidized state expression
302
wetted wall (boundary condition) 202 wetted wall (node) 227
Z zero shear rate viscosity 135
456 | I N D E X