express introductory training in ansys fluent · lecture theme: the problem ... • unsteady,...

© 2012 ANSYS, Inc. September 19, 2013 1 Release 14.5

PRACE Autumn School 2013 - Industry Oriented HPC Simulations, September 21-27,

University of Ljubljana, Faculty of Mechanical Engineering, Ljubljana, Slovenia

Express Introductory Training in ANSYS Fluent

Lecture 3

Turbulence Modeling, Heat Transfer & Transient Calculations

Dimitrios Sofialidis

Technical Manager, SimTec Ltd.

Mechanical Engineer, PhD


14.5 Release

Introduction to ANSYS Fluent

Lecture 3. Turbulence Modeling, Heat Transfer & Transient Calculations


Introduction

Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary

Lecture Theme: The problem definition for all CFD simulations includes boundary conditions,

cell zone conditions and material properties. The accuracy of the simulation results depends on defining these properly.

Learning Aims: You will learn:

• How to define material properties. • The different boundary condition types in FLUENT and how to use them. • How to define cell zone conditions in FLUENT including solid zones and

porous media. • How to specify well–posed boundary conditions.

Learning Objectives: You will know how to perform these essential steps in setting up a CFD

analysis.

Part 1. Turbulence Modeling


Lecture Theme:

The majority of engineering flows are turbulent. Successfully simulating such flows requires understanding a few basic concepts of turbulence theory and modeling. This allows one to make the best choice from the available turbulence models and near –wall options for any given problem.


•Basic turbulent flow and turbulence modeling theory . •Turbulence models and near–wall options available in Fluent. •How to choose an appropriate turbulence model for a given problem. •How to specify turbulence boundary conditions at inlets.

Learning Objectives:

You will understand the challenges inherent in turbulent flow simulation and be able to identify the most suitable model and near–wall treatment for a given problem.

Introduction

Introduction Theory Models Near–Wall Treatments Inlet BCs Summary


• Flows can be classified as either :

Laminar (Low Reynolds Number)

Transition (Increasing Reynolds Number)

Turbulent (Higher Reynolds Number)

Observation by Osborne Reynolds [1]



Observation by Osborne Reynolds [2]

• The Reynolds number is the criterion used to determine whether the flow is laminar or turbulent.

• The Reynolds number is based on the length scale of the flow:

• Transition to turbulence varies depending on the type of flow:

• External flow:

• Along a surface : ReX > 500000

• Around on obstacle : ReL > 20000

• Internal flow: : ReD > 2300

. .ReL

U L

etc. ,d d, x,L hyd



• A turbulent flow contains a wide range of turbulent eddy sizes.

• Turbulent flow characteristics:

• Unsteady, three–dimensional, irregular, stochastic motion in which transported

quantities (mass, momentum, scalar species) fluctuate in time and space.

• Enhanced mixing of these quantities results from the fluctuations.

• Unpredictability in detail.

• Large scale coherent structures are different in each flow, whereas small

eddies are more universal.

Turbulent Flow Structures [1]

Small

structures

Large

structures



Turbulent Flow Structures [2]

• Energy is transferred from larger eddies to smaller eddies.

(Kolmogorov Cascade).

• Large scale contains most of the energy.

• In the smallest eddies, turbulent energy is converted to internal energy by viscous dissipation.

Energy Cascade Richardson (1922), Kolmogorov (1941)



Backward Facing Step

Instantaneous velocity contours.

Time–averaged velocity contours.

• As engineers, in most cases we do not actually need to see an exact snapshot of the velocity at a particular instant.

• Instead for most problems, knowing the time–averaged velocity (and intensity of the turbulent fluctuations) is all we need to know. This gives us a useful way to approach modelling turbulence.



• If we recorded the velocity at a particular point in the real (turbulent) fluid flow, the instantaneous velocity (U) would look like this:

Time–average of velocity.

Velo

city

U Instantaneous velocity.

U

u Fluctuating velocity.

• At any point in time:

• The time–average of the fluctuating velocity must be zero:

• BUT, the RMS of u' is not necessarily zero:

• Note you will hear reference to the turbulence energy, k. This is the sum of the three normal fluctuating velocity components: .

uUU

0u

0u 2

222 wvu

2

1k

Time

Mean and Instantaneous Velocities


u


Overview of Computational Approaches

• Different approaches to make turbulence computationally tractable.

DNS

(Direct Numerical Simulation)

• Numerically solving the full unsteady Navier–Stokes equations.

• Resolves the whole spectrum of scales.

• No modeling is required.

• But the cost is too prohibitive!

Not practical for industrial flows!

• Solves the spatially averaged N–S equations.

• Large eddies are directly resolved, but eddies smaller than the mesh are modeled.

• Less expensive than DNS, but the amount of computational resources and efforts are still too large for most practical applications.

• Solve time–averaged Navier–Stokes equations.

• All turbulent length scales are modeled in RANS.

• Various different models are available.

• This is the most widely used approach for industrial flows.

LES

(Large Eddy Simulation)

RANS

(Reynolds Averaged Navier–Stokes Simulation)



RANS Modeling: Averaging

• Thus, the instantaneous Navier–Stokes equations may be rewritten as Reynolds–Averaged equations (RANS):

• The Reynolds stresses are additional unknowns introduced by the averaging procedure, hence they must be modeled (related to the averaged flow quantities) in order to close the system of governing equations.

jiij uuR

j

ij

j

i

jik

ik

i

x

R

x

u

xx

p

x

uu

t

u

(Reynolds stress tensor)

2

2

2

' ' ' ' '

' ' ' ' '

' ' ' ' '

xx xy xz

yx yy yz

zx zy zz

u u v u w

u v v v w

u w v w w

τ jiij uuR

Symmetric tensor 6 unknowns …



• The Reynolds Stress tensor must be solved.

• The RANS models can be closed in two ways:

• Note: All turbulence models contain empiricism.

• Equations cannot be derived from fundamental principles.

• Some calibrating to observed solutions and 'intelligent guessing' is contained in the models.

Eddy Viscosity Models

• Boussinesq hypothesis Reynolds stresses are modeled using an eddy (or turbulent) viscosity, μT.

• The hypothesis is reasonable for simple turbulent

shear flows: boundary layers, round jets, mixing layers, channel flows, etc.

ijij

k

k

i

j

j

ijiij k

x

u

x

u

x

uuuR

3

2

3

2TT

RANS Modeling: The Closure Problem

Reynolds–Stress Models (RSM)

• Rij is directly solved via transport equations (modeling is still required for many terms in the

transport equations).

• RSM is more advantageous in complex 3D

turbulent flows with large streamline curvature and swirl,

• but the model is more complex, computationally intensive, more difficult to converge than eddy viscosity models.

jiij uuR

ijijTijijijjikk

ji DFPuuux

uut



Turbulence Models Available in Fluent

RANS based models

One–Equation Model

Spalart–Allmaras

Two–Equation Models

Standard k–ε

RNG k–ε

Realizable k–ε*

Standard k–ω

SST k–ω*

Reynolds Stress Model

k–kl–ω Transition Model

SST Transition Model

Detached Eddy Simulation

Large Eddy Simulation

Increase in Computational Cost Per Iteration

* Recommended choice for standard cases.



Two–Equation Models

• Two transport equations are solved, giving two independent scales for calculating t. – Virtually all use the transport equation for the turbulent kinetic energy, k.

– Several transport variables have been proposed, based on dimensional arguments, and used for second equation. The eddy viscosity t is then formulated from the two transport variables.

• Kolmogorov, w: t k / w, l k

1/2 / w, k / w

– w is specific dissipation rate.

– Defined in terms of large eddy scales that define supply rate of k.

• Chou, : t k2 / , l k3/2 /

• Rotta, l: t k1/2l, k3/2 / l

ijijt

jkj

SSSskeSPPx

k

xDt

Dk2)(; 2t

production dissipation



RANS:EVM: Standard k–ε (SKE) Model

• The Standard k–ε model (SKE) is the most widely–used engineering turbulence model for industrial applications.

– Model parameters are calibrated by using data from a number of benchmark experiments such as pipe flow, flat plate, etc.

– Robust and reasonably accurate for a wide range of applications. – Contains submodels for compressibility, buoyancy, combustion, etc.

• Known limitations of the SKE model: – Performs poorly for flows with larger pressure gradient, strong separation, high

swirling component and large streamline curvature.

– Inaccurate prediction of the spreading rate of round jets. – Production of k is excessive (unphysical) in regions with large strain rate (for example,

near a stagnation point), resulting in very inaccurate model predictions.



RANS:EVM: Realizable k–epsilon

• Realizable k–ε (RKE) model (Shih):

– Dissipation rate (ε) equation is derived from the mean–square vorticity fluctuation, which is fundamentally different from the SKE.

– Several realizability conditions are enforced for Reynolds stresses.

– Benefits: • Accurately predicts the spreading rate of both planar and round jets.

• Also likely to provide superior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and recirculation.

OFTEN PREFERRED TO STANDARD k–ε



RANS: EVM: Spalart–Allmaras (S–A) Model

• Spalart–Allmaras is a low–cost RANS model solving a single transport equation for a modified eddy viscosity.

• Designed specifically for aerospace applications involving wall–bounded flows . – Has been shown to give good results for boundary layers subjected to adverse

pressure gradients.

– Used mainly for aerospace and turbomachinery applications.

• Limitations: – The model was designed for wall bounded flows and flows with mild separation

and recirculation.

– No claim is made regarding its applicability to all types of complex engineering flows.


• In k–w models, the transport equation for the turbulent dissipation rate, , is replaced with an equation for the specific dissipation rate, w.

– The turbulent kinetic energy transport equation is still solved. – See Appendix for details of w equation.

• k–w models have gained popularity in recent years mainly because:

– Much better performance than k– models for boundary layer flows. • For separation, transition, low –Re effects, and impingement, k–w models are more

accurate than k– models.

– Accurate and robust for a wide range of boundary layer flows with pressure gradient.

• Two variations of the k–w model are available in Fluent. – Standard k–w model (Wilcox, 1998). – SST k–w model (Menter).

k–omega Models



• Shear Stress Transport (SST) Model. – The SST model is an hybrid two–equation model that combines the advantages of

both k– and k–w models.

• k–w model performs much better than k– models for boundary layer flows.

• Wilcox’ original k–w model is overly sensitive to the freestream value (BC) of w, while k– model is not prone to such problem.

– The k–e and k–w models are blended such that the SST model functions like the k–ω close to the wall and the k–ε model in the freestream.

SST is a good compromise between k– and k–w models

SST Model

Wall

k–

k–w



RANS: Other Models in Fluent

• RNG k– model. – Model constants are derived from renormalization group (RNG) theory instead of

empiricism.

– Advantages over the standard k– model are very similar to those of the RKE model.

• Reynolds Stress model (RSM). – Instead of using eddy viscosity to close the RANS equations, RSM solves transport

equations for the individual Reynolds stresses.

• 7 additional equations in 3D, compared to 2 additional equations with EVM.

– More computationally expensive than EVM and generally difficult to converge. • As a result, RSM is used primarily in flows where eddy viscosity models are

known to fail.

• These are mainly flows where strong swirl is the predominant flow feature, for instance a cyclone (see Appendix).


• The Structure of Near–Wall Flows.

Turbulence Near a Wall [1]



• Near to a wall, the velocity changes rapidly.

• If we plot the same graph again, where: – Log scale axes are used.

– The velocity is made dimensionless, from U/U ( ,, is friction velocity)

– The wall distance vector is made dimensionless.

• Then we arrive at the graph on the next page. The shape of this is generally the same for all flows:


Velo

city,

U

Distance from Wall, y



• By scaling the variables near the wall the velocity profile data takes on a predictable (universal) form (transitioning from linear to logarithmic behavior).

• Since near wall conditions are often predictable, functions can be used to determine the near wall profiles rather than using a fine mesh to actually resolve the profile.

– These functions are called wall functions.

Linear

Logarithmic

Scaling the non–dimensional

velocity and non–dimensional

distance from the wall results in a

predictable boundary layer profile

for a wide range of flows.




Choice of Wall Modeling Strategy.

• In the near–wall region, the solution gradients are very high, but accurate calculations in the near–wall region are paramount to the success of the simulation.

The choice is between:

Resolving the Viscous Sublayer.

– First grid cell needs to be at about y+ = 1. – This will add significantly to the mesh count. – Use a low–Reynolds number turbulence model (like k–omega) . – Generally speaking, if the forces on the wall are key to your simulation (aerodynamic drag,

turbomachinery blade performance) this is the approach you will take.

Using a Wall Function.

– First grid cell needs to be 30


• In some situations, such as boundary layer separation, logarithmic–based wall functions do not correctly predict the boundary layer profile.

• In these cases logarithmic–based wall functions should not be used.

• Instead, directly resolving the boundary layer can provide accurate results.

Wall functions applicable. Wall functions not applicable.

Limitations of Wall Functions

Non–Equilibrium Wall Functions have been developed

in Fluent to address this situation but they are very

empirical. A more rigorous approach is recommended if

affordable.



• Standard Wall Functions. – The Standard Wall Function options

is designed for high Re attached flows.

– The near–wall region is not resolved. – Near–wall mesh is relatively coarse.

• Non–Equilibrium Wall Functions. – For better prediction of adverse pressure gradient flows and

separation.

– Near–wall mesh is relatively coarse.

• Enhanced Wall Treatment* – Used for low–Re flows or flows with complex near–wall phenomena.

– Generally requires a very fine near–wall mesh capable of resolving the near–wall region.

– Can also handle coarse near–wall mesh.

• User–Defined Wall Functions. – Can host user specific solutions.

Choosing a Near Wall Treatment

* Recommended choice for standard cases.



Inlet Boundary Conditions

• When turbulent flow enters a domain at inlets or outlets (backflow), boundary conditions for k, ε, ω and/or must be specified, depending on which turbulence model has been selected.

• Four methods for directly or indirectly specifying turbulence parameters: 1) Explicitly input k, ε, ω, or Reynolds stress components (this is the only method that

allows for profile definition). • Note by default, the Fluent GUI enters k=1 [m²/s²] and =1 [m²/s³]. These values

MUST be changed, they are unlikely to be correct for your simulation.

2) Turbulence intensity and length scale. • Length scale is related to size of large eddies that contain most of energy.

– For boundary layer flows: l 0.4δ99. – For flows downstream of grid: l opening size.

3) Turbulence intensity and hydraulic diameter (primarily for internal flows). 4) Turbulence intensity and viscosity ratio (primarily for external flows). The default setting is turbulent intensity=5% and turbulent viscosity ratio=10. This

should be reasonable for many flows if more precise information not available.


'j

'iuu


Inlet Turbulence Conditions

• If you have absolutely no idea of the turbulence levels in your simulation, you could use following values of turbulence intensities and viscosity ratios:

– Usual turbulence intensity ranges from 1% to 5%.

– The default turbulence intensity value of 0.037 (that is, 3.7%) is sufficient for nominal turbulence through a circular inlet, and is a good estimate in the absence of experimental data.

– For external flows, turbulent viscosity ratio of 1÷10 is typically a good value. – For internal flows, turbulent viscosity ratio of 10÷100 it typically a good value.

• For fully developed pipe flow at Re=50,000, the turbulent viscosity ratio is around 100.



RANS Turbulence Model Usage

Model Behavior and Usage

Spalart–Allmaras Economical for large meshes. Performs poorly for 3D flows, free shear flows, flows with strong separation. Suitable for mildly complex (quasi–2D) external/internal flows and boundary layer flows

under pressure gradient (e.g. airfoils, wings, airplane fuselages, missiles, ship hulls).

Standard k–ε Robust. Widely used despite the known limitations of the model. Performs poorly for complex flows involving severe pressure gradient, separation, strong streamline curvature. Suitable for initial

iterations, initial screening of alternative designs, and parametric studies.

Realizable k–ε* Suitable for complex shear flows involving rapid strain, moderate swirl, vortices, and locally transitional flows (e.g. boundary layer separation, massive separation, and vortex shedding behind bluff bodies, stall

in wide–angle diffusers, room ventilation).

RNG k–ε Offers largely the same benefits and has similar applications as Realizable. Possibly harder to converge than Realizable.

Standard k–ω Superior performance for wall–bounded boundary layer, free shear, and low Reynolds number flows. Suitable for complex boundary layer flows under adverse pressure gradient and separation (external

aerodynamics and turbomachinery). Can be used for transitional flows (though tends to predict early

transition). Separation is typically predicted to be excessive and early.

SST k–ω* Offers similar benefits as standard k–ω. Dependency on wall distance makes this less suitable for free shear flows.

RSM Physically the most sound RANS model. Avoids isotropic eddy viscosity assumption. More CPU time and memory required. Tougher to converge due to close coupling of equations. Suitable for complex

3D flows with strong streamline curvature, strong swirl/rotation (e.g. curved duct, rotating flow

passages, swirl combustors with very large inlet swirl, cyclones).

* Recommended choice for standard cases


RANS Turbulence Model Descriptions

Model Description

Spalart –

Allmaras

A single transport equation model solving directly for a modified turbulent viscosity. Designed specifically

for aerospace applications involving wall–bounded flows on a fine near–wall mesh. Fluent’s implementation

allows the use of coarser meshes. Option to include strain rate in k production term improves predictions of

vortical flows.

Standard k–ε The baseline two–transport–equation model solving for k and ε. This is the default k–ε model. Coefficients are empirically derived; valid for fully turbulent flows only. Options to account for viscous heating,

buoyancy, and compressibility are shared with other k–ε models.

RNG k–ε A variant of the standard k–ε model. Equations and coefficients are analytically derived. Significant changes in the ε equation improves the ability to model highly strained flows. Additional options aid in predicting

swirling and low Reynolds number flows.

Realizable k–ε A variant of the standard k–ε model. Its "realizability" stems from changes that allow certain mathematical constraints to be obeyed which ultimately improves the performance of this model.

Standard k–ω A two–transport–equation model solving for k and ω, the specific dissipation rate (ε / k) based on Wilcox (1998). This is the default k–ω model. Demonstrates superior performance for wall–bounded and low

Reynolds number flows. Shows potential for predicting transition. Options account for transitional, free

shear, and compressible flows.

SST k–ω A variant of the standard k–ω model. Combines the original Wilcox model for use near walls and the standard k–ε model away from walls using a blending function. Also limits turbulent viscosity to guarantee

that τT ~ k. The transition and shearing options are borrowed from standard k–ω. No option to include

compressibility.

RSM Reynolds stresses are solved directly using transport equations, avoiding isotropic viscosity assumption of other models. Use for highly swirling flows. Quadratic pressure–strain option improves performance for

many basic shear flows.


Summary – Turbulence Modeling Guidelines

• Successful turbulence modeling requires engineering judgment of: – Flow physics. – Computer resources available. – Project requirements.

• Accuracy.

• Turnaround time.

– Choice of Near–wall treatment.

• Modeling procedure 1. Calculate characteristic Reynolds number and determine whether flow is turbulent. 2. If the flow is in the transition (from laminar to turbulent) range, consider the use of one

of the turbulence transition models (not covered in this training).

3. Estimate wall–adjacent cell centroid y+ before generating the mesh. 4. Prepare your mesh to use wall functions except for low–Re flows and/or flows with

complex near–wall physics (non–equilibrium boundary layers).

5. Begin with RKE (Realizable k–ε) and change to S–A, RNG, SKW, or SST if needed. Check the tables on previous slides as a guide for your choice.

6. Use RSM for highly swirling, 3–D, rotating flows. 7. Remember that there is no single, superior turbulence model for all flows!



Introduction








analysis.

Part 2. Heat Transfer


Lecture Theme:

Heat transfer has broad applications across all industries. All modes of heat transfer (conduction, convection – forced and natural, radiation, phase change) can be modeled in Fluent and solution data can be used as input for one–way thermal FSI simulations.


•How to treat conduction, convection (forced and natural) and radiation in Fluent.

•How to set wall thermal boundary conditions. •How to export solution data for use in a thermal stress analysis (one–way

FSI).


You will be familiar with Fluent’s heat transfer modeling capabilities and be able to set up and solve problems involving all modes of heat transfer.

Introduction

Intro. Energy Equation Wall BCs Applications 1–way Thermal FSI Summary


Heat Transfer Modeling in Fluent

• All modes of heat transfer can be taken into account in the CFD simulation:

– Conduction. – Convection (forced and natural). – Fluid–solid conjugate heat transfer. – Radiation. – Interphase energy source (phase change). – Viscous dissipation. – Species diffusion.



• To model heat transfer, the energy equation must be activated.

"Define>Models>Energy"=ON.

Enabling Heat Transfer



Energy Equation – Introduction

• Energy transport equation:

– Energy E per unit mass is defined as:

– Pressure work and kinetic energy are always accounted for with compressible flows or when using the density–based solvers. For the pressure–based solver, they are omitted and can be added through a text command:

– The TUI command define/models/energy? will give more options when enabling the energy equation.

Conduction Species

Diffusion

Viscous

Dissipation

Convection Unsteady Enthalpy

Source/Sink



Governing Equation : Convection

• As a fluid moves, it carries heat with it this is called convection. – Thus, heat transfer can be tightly coupled to the fluid flow solution. – Energy + Fluid flow equations activated means Convection is computed.

Tbody

T

ThTThq body )(

average heat transfer coefficient (W/m2–K) h

q

• Additionally:

• The rate of heat transfer is strongly dependent of fluid velocity.

• Fluid properties may vary significantly with temperature (e.g., air).

• At walls, heat transfer coefficient is computed by the turbulent thermal wall functions.



Governing Equation: Conduction

• Conduction heat transfer is governed by Fourier’s Law.

• Fourier’s law states that the heat transfer rate is directly proportional to the gradient of temperature.

• Mathematically,

• The constant of proportionality is the thermal conductivity (k). – k may be a function of temperature, space, etc.

– for isotropic materials, k is a constant value.

– for anisotropic materials, k is a matrix.

Thermal conductivity

Tkq conduction



Governing Equation: Viscous Dissipation

• Energy source due to viscous dissipation:

– Also called viscous heating. • Often negligible, especially in

incompressible flow.

– Important when viscous shear in fluid is large (e.g., lubrication) and/or in high–velocity, compressible flows.

– Important when Brinkman number approaches or exceeds unity:

Tk

UBr e

2



Thermal Wall Boundary Conditions • Six thermal conditions at Walls:

– Heat Flux. – Temperature. – Convection – simulates an external convection environment which is not modeled (user–

prescribed heat transfer coefficient).

– Radiation – simulates an external radiation environment which is not

modeled (user–prescribed external

emissivity and radiation temperature).

– Mixed – Combination of Convection and Radiation boundary conditions.

– Via System Coupling – Can be used when Fluent is coupled with another system in Workbench using System Couplings.

)( wextextconv TThq

)( 44 wextrad TTq

)()( 44 wextwextextmixed TTTThq



Conjugate Heat Transfer (CHT)

• At Fluid/Solid or Fluid/Fluid interface, a wall/wall_shadow is created automatically by Fluent while reading the mesh file.

– By default energy is balanced automatically on the two sides of the walls.

– Possibility to uncouple and to specify different thermal conditions on each side.

Coolant Flow Past Heated Rods

Grid

Velocity Vectors

Temperature Contours



Convection

• Convection heat transfer results from fluid motion. – Heat transfer rate can be closely coupled to the fluid flow solution. – The rate of heat transfer is always strongly dependent on fluid velocity and

fluid properties (uncoupled equations – can solve energy after flow solution).

– Fluid properties may vary significantly with temperature (coupled equations).

• There are three types of convection. – Natural convection: fluid moves due to buoyancy effects. – Boiling convection: body is hot enough to cause fluid phase change. – Forced convection: flow is induced by some external means.

Flow and heat transfer past a heated block.

Example: When cold air flows past a warm body, it draws away warm air near the body and replaces it with cold air.



Tcold

Heat Transfer Coefficient

• In general, h is not constant but is usually a function of temperature gradient.

• There are three types of convection. – Natural Convection – Fluid moves due to

buoyancy effects.

– Forced Convection – Flow is induced by some external means.

– Boiling Convection – Body is hot enough to cause fluid phase change.

3/14/1 , ThTh

)( Tfh

2Th

Typical

values of h

(W/m2·K)

4 – 4,000

10 – 75,000

300 – 900,000

hotT

hotT

hotT

Tcold

Tcold

(Laminar) (Turbulent)


Natural Convection: Gravity–Reference Density

• Momentum equation along the direction of gravity (z in this case).

• In Fluent, a variable change is done for the pressure field as soon as gravity is enabled.

– Hydrostatic reference pressure head and operating pressure are removed from pressure field.

• Momentum equation becomes.

where P' is the static gauge pressure used by Fluent for boundary conditions and post–processing.

• This pressure transformation avoids round off error and simplifies the setup of pressure boundary conditions.

g

z

PWW

t

W0

2

U

g

z

PWW

t

W abs

2U

zgPPP operatingabs 0



Radiation

• Radiative heat transfer is a mode of energy transfer where the energy is transported via electromagnetic waves.

• Thermal radiation covers the portion of the electromagnetic spectrum from 0.1 to 100 m.

• For semi–transparent bodies (e.g., glass, combustion product gases), radiation is a volumetric phenomenon since emissions can escape from within bodies.

• For opaque bodies, radiation is essentially a surface phenomena since nearly all internal emissions are absorbed within the body.

Headlight

Glass furnace Solar load (HVAC)

Visible

Ultraviolet

X rays

-5 -4 -3 -2 -1 0 1 2 3 4 5

rays

Thermal Radiation

Infrared

Microwaves

log10 (Wavelength), m



When to Include Radiation?

• Radiation effects should be accounted for if:

is of the same order or magnitude than the convective and conductive heat transfer rates. This is usually true at high temperatures but can also be true at lower temperatures, depending on the application.

• Estimate the magnitude of conduction or convection heat transfer in the system as:

• Compare qrad with qconv.

Stefan–Boltzmann constant

5.6704×10–8 W/(m2·K4)

4min4maxrad TTq

bulkwall TThqconv



Optical Thickness and Radiation Modeling

• The optical thickness should be determined before choosing a radiation model.

• a Absorption Coefficient (m–1) (Note: ≠Absorptivity of a Surface).

• L Mean beam length (m) (a typical distance between 2 opposing walls).

• Optically thin means that the fluid is transparent to the radiation at wavelengths where the heat transfer occurs.

– The radiation only interacts with the boundaries of the domain.

• Optically thick/dense means that the fluid absorbs and re–emits the radiation.

Optical Thickness (a+s)L a= absorption coefficient.

s=scattering coefficient (often=0).

L= mean beam length.



• The radiation model selected must be appropriate for the optical thickness of the system being simulated.

• In terms of accuracy, DO and DTRM are most accurate. – S2S is accurate for optical thickness = 0.

Choosing a Radiation Model

Available Model Optical

Thickness

Surface to surface model (S2S) 0

Solar load model 0 (except window panes)

Rosseland > 5

P–1 > 1

Discrete ordinates model (DO) All

Discrete Transfer Method (DTRM) All



Additional Factors in Radiation Modeling

• Additional guidelines for radiation model selection:

– Scattering. • Scattering is accounted for only with

P1 and DO.

– Particulate effects. • P1 and DOM account for radiation

exchange between gas and

particulates.

– Localized heat sources. • S2S is the best.

• DTRM/DOM with a sufficiently large

number of rays/ ordinates is most

appropriate for domain with

absorbing media. Intro. Energy Equation Wall BCs Applications 1–way Thermal FSI Summary


Phase Change

• Heat released or absorbed when matter changes state.

• There are many different forms of phase change. – Condensation. – Evaporation. – Boiling. – Melting/Solidification.

• Multiphase models and/or UDFs are needed to properly model these phenomena.

Tracks from evaporating liquid pentane droplets and temperature contours for pentane combustion with the non–premixed combustion model.

Contours of vapor volume fraction for boiling in a nuclear fuel assembly calculated with the Eulerian multiphase model.



Summary

• After activating heat transfer, you must provide: – Thermal conditions at walls and flow boundaries. – Fluid properties for energy equation.

• Available heat transfer modeling options include: – Species diffusion heat source. – Combustion heat source. – Conjugate heat transfer. – Natural convection. – Radiation. – Periodic heat transfer.

• Double precision solver usually needed to balance accurately the heat transfer rate inside the domain.



Introduction








analysis.

Part 3. Transient Calculations


Lecture Theme:

Performing a transient calculation is in some ways similar to performing a steady state calculation, but there are additional considerations. More data is generated and extra inputs are required. This lecture will explain these inputs and describe transient data post–processing.


•How to set up and run transient calculations in Fluent. •How to choose the appropriate time step size for your calculation. •How to post–process transient data and make animations.


Transient flow calculations are becoming increasingly common due to advances in High Performance Computing (HPC) and reductions in hardware costs. You will understand what transient calculations involve and be able to perform them with confidence.

Introduction

Introduction Unsteady Flow Time Step Setup Post–Processing Summary


Motivation

• Nearly all flows in nature are unsteady! – Steady–state assumption is possible if we:

• Ignore unsteady fluctuations.

• Employ ensemble/time–averaging to remove unsteadiness. – This is what is done in modeling RANS turbulence.

• In CFD, steady–state methods are preferred. – Lower computational cost. – Easier to post–process and analyze.

• Many applications require resolution of unsteady flow: – Aerodynamics (aircraft, land vehicles, etc.) – vortex shedding. – Rotating Machinery – rotor/stator interaction, stall, surge. – Multiphase Flows – free surfaces, bubble dynamics. – Deforming Domains – in–cylinder combustion, store separation. – Unsteady Heat Transfer – transient heating and cooling. – Many more …



Origins of Unsteady Flow

Kelvin–Helmholtz Cloud Instability.

• Natural unsteadiness. – Unsteady flow due to growth of instabilities within the fluid or a non–equilibrium

initial fluid state. – Examples: natural convection flows, turbulent eddies of all scales, fluid waves (gravity

waves, shock waves). • Forced unsteadiness.

– Time–dependent boundary conditions, source terms drive the unsteady flow field. – Examples: pulsing flow in a nozzle, rotor–stator interaction in a turbine stage.

Rotor–Stator Interaction in an Axial Compressor.



Unsteady CFD Analysis [1]

• Simulate a transient flow field over a specified time period. – Solution may approach:

• Steady–state solution: Flow variables stop changing with time.

• Time–periodic solution: Flow variables fluctuate with repeating pattern.

– Your goal may also be simply to analyze the flow over a prescribed time interval. • Free surface flows.

• Moving shock waves.

• …

• Extract quantities of interest. – Natural frequencies (e.g. Strouhal Number). – Time–averaged and/or RMS values. – Time–related parameters (e.g. time required to cool a hot solid, residence time

of a pollutant).

– Spectral data – Fourier Transform (FT).



Unsteady CFD Analysis [2]

• Transient simulations are solved by computing a solution for many discrete points in time.

• At each time point we must iterate & converge to the solution.

Time step size = 2 [s]

Initial Time = 0 [s]

Total Time = 20 [s]

Number of time steps = 10

20 2 4 6 8 10 12 14 16 18

Time (seconds) Several iterations per time step.


Resid

ual


Convergence Behavior

• Residual plots for transient simulations are not always indicative of a converged solution.

• You should select the time step size such that the residuals reduce by around three orders of magnitude within one time step. – This will ensure accurate resolution of transient behavior. – For smaller time steps, residuals may only drop by 1–2 orders of magnitude – look for a

monotonic decrease throughout the time step.

• A residual plot for a simple transient calculation is shown here.



Selecting the Transient Time Step Size [1]

• The time step size is an important parameter in transient simulations. – t must be small enough to resolve time–dependent features …

True solution.

Time

Variable of

interest.

t

Time

Variable of

interest.

t

Time step too large to resolve transient changes. – Note the solution points generally will not lie on the true

solution because the true behaviour has not been resolved.

A smaller time step can

resolve the true solution. – At least, 10–20 t per period.




• … and it must be small enough to maintain solver stability.

– The quantity of interest may be changing very slowly (e.g. temperature in a solid), but you may not be able to use a large time step if other quantities (e.g. velocity) have smaller timescales.

• The Courant Number is often used to estimate a time step:

– This gives the number of mesh elements the fluid passes through in one time step.

– Typical values are 1÷10, but in some cases higher values are acceptable.

Size Cell Typical

velocityflow sticCharacteriNumber Courant

t



• Tips & Tricks for the estimation of the time step:

• Usual Case:

– Restrictive but safe for convergence with L=cell characteristic size, V=characteristic velocity.

• Turbomachinery:

• Natural Convection:

• Conduction in solids:

• A smaller time step will typically improve convergence.


L = Characteristic length V = Characteristic velocity

V.

3

1

Lt

Velocity Rotational

Blades ofNumber .

10

1 t

1/2T.L) .(g.

Lt

Cp

Lt

.

2



Transient Flow Modeling Workflow • Similar set–up as steady–state simulation, then:

1. Enable the unsteady solver.

2. Set up physical models and boundary conditions as usual. • Transient boundary conditions are possible – you can use either a UDF or profile to

accomplish this.

3. Prescribe initial conditions, according to the type of transient flow: • Time History : Cannot be any guess; must be what is the situation at time t=0 [s].

• Steady–State or Cyclic: Best to use a physically realistic initial condition, such as a steady solution.

4. Assign solver settings and configure solution monitors.

5. Configure animations and data output/sampling options.

6. Select time step size and max iterations per time step.

7. Prescribe the number of time steps.

8. Run the calculations (Iterate).



Enabling the Transient Solver • To enable the unsteady solver, select the Transient button on the General

problem setup form.



Set Up Time Step Size


• Set the time step size. – This controls the spacing in time

between the solution points.

• Options are:

– Number of time steps.

– Maximum number of iterations per time step.


Non–Iterative Time Advancement


• Non–iterative Time Advancement (NITA) is available for faster computation time (not always guaranteed).

– NITA runs about 2x to 10x as fast as ITA scheme.

• Limitations: Available with pressure–based solvers only.

• NITA schemes are not available for multiphase (except VOF), reacting flows, radiation models, porous media, fan models, etc.

• Consult the Appendix and Fluent Documentation for additional details.


Unsteady Flow Modeling Options


• Adaptive Time Stepping. – Automatically adjusts time–step size

based on local truncation error analysis.

– Customization possible via UDF.

• Extrapolate Variables. – Speed up the transient solution by reducing required sub–

iteration.

• Using Taylor series expansion solution will be extrapolated to the next time level to improve the predicted initial value.

• Data Sampling for Time Statistics. – Particularly useful for LES turbulence calculations.


• Physically realistic initial conditions should be used. – A converged steady state solution is often used as the

starting point (for cyclic or steady–state flows).

• If a transient simulation is started from an approximate initial guess, the initial transient will not be accurate. – The first few time steps may not converge.

– A smaller time step may be needed initially to maintain solver stability.

– For cyclic behavior the first few cycles can be ignored until a repeatable pattern is obtained.

Initialization

2 4 6 8 10 12 14 16

Time (seconds)

Resid

uals



Tips for Success in Transient Flow Modeling

• With Pressure–based Solvers, use PISO scheme for Pressure–Velocity Coupling: this scheme provides faster convergence for unsteady flows than the standard SIMPLE approach.

• Select the number of iterations per time step to be around 20. – It is better (faster) to reduce the time step size than to do too many iterations per time

step.

• Remember that accurate initial conditions are as important as boundary conditions for unsteady problems.

– Initial condition should always be physically realistic!

• To iterate without advancing in time, specify zero time steps. – This will instruct the solver to converge the current time step only.



Unsteady Flow Modeling – Animations [1]

• You must set up any animations BEFORE performing iterations. – Animation frames are written/stored on–the–fly during calculations.



CFD–Post: Fourier Transform

• FT can be applied to signals to extract frequency data.

Original Signal.

FT of Signal Showing

Dominant Frequency.



Summary

• No matter what solver is being used. – The time step size will be determined by the minimum of:

• The value at which the solution will converge.

• The value needed to resolve mean flow physical time scales (e.g. vortex shedding frequency given by Strouhal number) and/or turbulent eddies (Courant number 1).

– The solution must converge at every time step. • Non–convergence within the very first steps may be acceptable when there is

a non–physical initial condition.

• If the solution is not converging, it is almost always more efficient to reduce the time step size.

– Solution monitors are an important tool for ensuring the solution is correct. • Watch out for physically unrealistic behavior of monitored variables.

– Second order temporal discretization is almost always preferred.


express introductory training in ansys fluent · lecture theme: the problem ... • unsteady,...

Documents