Modeling a Composition PDF Transport

8/2/2019 Modeling a Composition PDF Transport

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Chapter 18. Modeling a Composition PDF Transport

Problem

FLUENT provides a composition PDF transport model for modeling finite-rate chemistryin turbulent flames. Information about this model is presented in the following sections:

• Section 18.1: Overview and Limitations

• Section 18.2: Composition PDF Transport Theory

• Section 18.3: Steps for Using the Composition PDF Transport Model

18.1 Overview and Limitations

The composition PDF transport model, like the EDC model (see Section 14.1.1: TheEddy-Dissipation-Concept (EDC) Model), should be used when you are interested insimulating finite-rate chemical kinetic effects in turbulent reacting flows. With an ap-propriate chemical mechanism, kinetically-controlled species such as CO and NOx, aswell as flame extinction and ignition, can be predicted. PDF transport simulations arecomputationally expensive, and it is recommended that you start your modeling withsmall grids, and preferably in 2D.

A limitation that applies to the composition PDF transport model is that you must usethe pressure-based solver. The composition PDF transport model is not available witheither of the density-based solvers.

18.2 Composition PDF Transport Theory

Turbulent combustion is governed by the reacting Navier-Stokes equations. While thisequation set is accurate, its direct solution (where all turbulent scales are resolved) is fartoo expensive for practical turbulent flows. In Chapter 14: Modeling Species Transportand Finite-Rate Chemistry, the species equations are Reynolds-averaged, which leads to

unknown terms for the turbulent scalar flux and the mean reaction rate. The turbulentscalar flux is modeled by gradient diffusion, treating turbulent convection as enhanceddiffusion. The mean reaction rate is modeled by the finite-rate, eddy-dissipation, orEDC models. Since the reaction rate is invariably highly non-linear, modeling the meanreaction rate in a turbulent flow is difficult and prone to error.

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Modeling a Composition PDF Transport Problem

An alternative to Reynolds-averaging the species and energy equations is to derive atransport equation for their single-point, joint probability density function (PDF). ThisPDF, denoted by P , can be considered to be proportional to the fraction of the time thatthe fluid spends at each species and temperature state. P has N + 1 dimensions for theN species and temperature spaces. From the PDF, any thermochemical moment (e.g.,mean or RMS temperature, mean reaction rate) can be calculated. The compositionPDF transport equation is derived from the Navier-Stokes equations as [ 288]:

∂

∂t(ρP ) +

∂

∂xi(ρuiP ) +

∂

∂ψk(ρS kP ) = −

∂

∂xi

ρu

i |ψP

+∂

∂ψk

ρ

1

ρ

∂J i,k∂xi

ψ

P

(18.2-1)

where

P = Favre joint PDF of compositionρ = mean fluid density

ui = Favre mean fluid velocity vectorS k = reaction rate for species kψ = composition space vectoru

i = fluid velocity fluctuation vectorJ i,k = molecular diffusion flux vector

The notation of . . . denotes expectations, and A|B is the conditional probability of event A, given the event B occurs.

In Equation 18.2-1, the terms on the left-hand side are closed, while those on the right-hand side are not and require modeling. The first term on the left-hand side is theunsteady rate of change of the PDF, the second term is the change of the PDF due to

convection by the mean velocity field, and the third term is the change due to chemicalreactions. The principal strength of the PDF transport approach is that the highly-non-linear reaction term is completely closed and requires no modeling. The two terms onthe right-hand side represent the PDF change due to scalar convection by turbulence(turbulent scalar flux), and molecular mixing/diffusion, respectively.

The turbulent scalar flux term is unclosed, and is modeled in FLUENT by the gradient-diffusion assumption

−∂

∂xiρu

i |ψP =∂

∂xi

µt

ρSct

∂P

∂xi (18.2-2)

where µt is the turbulent viscosity and Sct is the turbulent Schmidt number. A turbulencemodel, as described in Chapter 12: Modeling Turbulence, is required for composition PDFtransport simulations, and this determines µt.

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Since single-point PDFs are described, information about neighboring points is missingand all gradient terms, such as molecular mixing, are unclosed and must be modeled. Themixing model is critical because combustion occurs at the smallest molecular scales whenreactants and heat diffuse together. Modeling mixing in PDF methods is not straightfor-ward, and is the weakest link in the PDF transport approach. See Section 18.2.3: ParticleMixing for a description of the mixing models.

18.2.1 Solution of the PDF Transport Equation

The PDF has N + 1 dimensions and the solution of its transport equation by conven-tional finite-difference or finite-volume schemes is not tractable. Instead, a Monte Carlomethod is used, which is ideal for high-dimensional equations since the computationalcost increases just linearly with the number of dimensions. The disadvantage is thatstatistical errors are introduced, and these must be carefully controlled.

To solve the modeled PDF transport equation, an analogy is made with a stochasticdifferential equation (SDE) which has identical solutions. The Monte Carlo algorithminvolves notional particles which move randomly through physical space due to particleconvection, and also through composition space due to molecular mixing and reaction.The particles have mass and, on average, the sum of the particle masses in a cell equalsthe cell mass (cell density times cell volume). Since practical grids have large changes incell volumes, the particle masses are adjusted so that the number of particles in a cell iscontrolled to be approximately constant and uniform.

The processes of convection, diffusion, and reaction are treated in fractional steps asdescribed below. For information on the fractional step method, refer to [46].

18.2.2 Particle Convection

A spatially second-order-accurate Lagrangian method is used in FLUENT, consisting of two steps. At the first convection step, particles are advanced to a new position

x1/2i = x0

i +1

2u0i ∆t (18.2-3)

where

xi = particle position vectorui = Favre mean fluid-velocity vector at the particle position

∆t = particle time stepFor unsteady flows, the particle time step is the physical time step. For steady-stateflows, local time steps are calculated for each cell as

∆t = min(∆tconv, ∆tdiff , ∆tmix) (18.2-4)


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where

∆tconv = convection number × ∆x / (cell fluid velocity)∆tdiff = diffusion number × (∆x)2 / (cell turbulent diffusivity)∆tmix = mixing number × turbulent time scale∆x = characteristic cell length = volume1/D where D is the problem dimension

After the first convection step, all other sub-processes, including diffusion and reactionare treated. Finally, the second convection step is calculated as

x1i = x

1/2i + ∆t

u1/2i −

1

2u0i +

1

ρSct

∂µt

∂xi+ ξi

2µt

ρ∆tSct

(18.2-5)

where

ρ = mean cell fluid densityui = mean fluid-velocity vector at the particle positionµt = turbulent viscosity

Sct = turbulent Schmidt numberξi = standardized normal random vector

18.2.3 Particle Mixing

Molecular mixing of species and heat must be modeled and is usually the source of thelargest modeling error in the PDF transport approach. FLUENT provides three modelsfor molecular diffusion: the Modified Curl model [161, 263], the IEM model (which issometimes called the LSME model) [83] and the EMST model [358].

The Modified Curl ModelFor the Modified Curl model, a few particle pairs are selected at random from all theparticles in a cell, and their individual compositions are moved toward their mean com-position. For the special case of equal particle mass, the number of particle pairs selectedis calculated as

N pair =1.5C φN ∆t

τ t(18.2-6)

where

N = total number of particles in the cellC φ = mixing constant (default = 2)τ t = turbulent time scale (for the k- model this is k/)

The algorithm in [263] is used for the general case of variable particle mass.


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For each particle pair, a uniform random number ξ is selected and each particle’s com-position φ is moved toward the pair’s mean composition by a factor proportional to ξ:

φ1i = (1 − ξ)φ0

i + ξ(φ0

i mi + φ0 jm j)

(mi + m j)

φ1 j = (1 − ξ)φ0

j + ξ(φ0

i mi + φ0 jm j)

(mi + m j)(18.2-7)

where φi and φ j are the composition vectors of particles i and j, and mi and m j are themasses of particles i and j.

The IEM Model

For the Interaction by Exchange with the Mean (IEM) model, the composition of all

particles in a cell are moved a small distance toward the mean composition:

φ1 = φ0 −

1 − e−0.5C φ/τ t

φ0 − φ̃

(18.2-8)

where φ0 is the composition before mixing, φ1 is the composition after mixing and φ̃ isthe Favre mean-composition vector at the particle’s location.

The EMST Model

Physically, mixing occurs between fluid particles that are adjacent to each other. The

Modified Curl and IEM mixing models take no account of this localness, which can be asource of error. The Euclidean Minimum Spanning Tree (EMST) model mixes particlepairs that are close to each other in composition space. Since scalar fields are locallysmooth, particles that are close in composition space are likely to be close in physicalspace. The particle pairing is determined by a Euclidean Minimum Spanning Tree, whichis the minimum length of the set of edges connecting one particle to at least one otherparticle. The EMST mixing model is more accurate than the Modified Curl and IEMmixing models, but incurs a slightly greater computationally expensive. Details on theEMST model can be found in [358].

Liquid Reactions

Reactions in liquids often occur at low turbulence levels (small Re), among reactantswith low diffusivities (large Sc). For such flows, the mixing constant default of C φ = 2overestimates the mixing rate. The Liquid Micro-Mixing option interpolates C φ frommodel turbulence [291] and scalar [111] spectra.


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18.2.4 Particle Reaction

The particle composition vector is represented as

φ = (Y 1, Y 2, . . . , Y N , T , p) (18.2-9)

where Y k is the kth species mass fraction, T is the temperature and p the pressure.

For the reaction fractional step, the reaction source term is integrated as

φ1 = φ0 + ∆t

0Sdt (18.2-10)

where S is the chemical source term. Most realistic chemical mechanisms consist of tensof species and hundreds of reactions. Typically, reaction does not occur until an ignitiontemperature is reached, but then proceeds very quickly until reactants are consumed.Hence, some reactions have very fast time scales, on the order of 10−10 s, while others

have much slower time scales, on the order of 1 s. This time-scale disparity resultsin numerical stiffness, which means that extensive computational work is required tointegrate the chemical source term in Equation 18.2-10. In FLUENT, the reaction step(i.e., the calculation of φ1) can be performed either by Direct Integration or by In-SituAdaptive Tabulation (ISAT), as described in the following paragraphs.

A typical steady-state PDF transport simulation in FLUENT may have 50000 cells, with20 particles per cell, and require 1000 iterations to converge. Hence, at least 109 stiff ODE integrations are required. Since each integration typically takes tens or hundredsof milliseconds, on average, the direct integration of the chemistry is extremely CPU-demanding.

For a given reaction mechanism, Equation 18.2-10 may be considered as a mapping.With an initial composition vector φ0, the final state φ1 depends only on φ0 and themapping time ∆t. In theory, if a table could be built before the simulation, covering allrealizable φ0 states and time steps, the integrations could be avoided by table look-ups.In practice, this a priori tabulation is not feasible since a full table in N + 3 dimensions(N species, temperature, pressure and time-step) is required. To illustrate this, considera structured table with M points in each dimension. The required table size is M N +3,and for a conservative estimate of M = 10 discretization points and N = 7 species, thetable would contain 1010 entries.

On closer examination, the full storage of the entire realizable space is very wastefulbecause most regions are never accessed. For example, it would be unrealistic to find acomposition of Y OH = 1 and T = 300K in a real combustor. In fact, for steady-state, 3Dlaminar simulations, the chemistry can be parameterized by the spatial position vector.Thus, mappings must lie on a three dimensional manifold within the N + 3 dimensionalcomposition space. It is, hence, sufficient to tabulate only this accessed region of thecomposition space.





The accessed region, however, depends on the particular chemical mechanism, moleculartransport properties, flow geometry, and boundary conditions. For this reason, the ac-cessed region is not known before the simulation and the table cannot be preprocessed.Instead, the table must be built during the simulation, and this is referred to as in-situ tabulation.

FLUENT employs ISAT [289] to dynamically tabulate the chemistry mappings and accel-erate the time to solution. ISAT (In-Situ Adaptive Tabulation) is a method to tabulatethe accessed composition space region “on the fly” (in-situ) with error control (adaptivetabulation). When ISAT is used correctly, accelerations of two to three orders of mag-nitude are typical. However, it is important to understand how ISAT works to use itoptimally.

18.2.5 The ISAT Algorithm

ISAT is a powerful tool that enables realistic chemistry to be incorporated in multi-dimensional flow simulations by accelerating the chemistry calculations. Typical speed-ups of 100-fold are common. This power is apparent if one considers that with a 100-foldspeed-up, a simulation that would take three months without ISAT can be run in oneday.

At the start of a FLUENT simulation using ISAT, the ISAT table is empty. For the firstreaction step, Equation 18.2-10 is integrated with a stiff ODE solver. This is called DirectIntegration (DI). The first table entry is created and consists of:

• the initial composition φ0

• the mapping φ1

• the mapping gradient matrix A = ∂φ1/∂φ0

• a hyper-ellipsoid of accuracy

The next reaction mapping is calculated as follows: The initial composition vector forthis particle is denoted φ0

q, where the subscript q denotes a query . The existing table(consisting of one entry at this stage) is queried by interpolating the new mapping as

φ1q = φ1 + A(φ0

q − φ0) (18.2-11)

The mapping gradient is hence used to linearly interpolate the table when queried. Theellipsoid of accuracy (EOA) is the elliptical space around the table point φ0 where thelinear approximation to the mapping is accurate to the specified tolerance, tol.


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If the query point φ1q is within the EOA, then the linear interpolation by Equation 18.2-11

is sufficiently accurate, and the mapping is retrieved . Otherwise, a direct integration (DI)is performed and the mapping error = |B(φ1

DI − φ1q)| is calculated (here, B is a scaling

matrix). If this error is smaller than the specified error tolerance ( < tol), then theoriginal interpolation φ1

q is accurate and the EOA is grown so as to include φ0q. If not, a

new table entry is added .

Table entries are stored as leaves in a binary tree. When a new table entry is added ,the original leaf becomes a node with two leaves—the original leaf and the new entry.A cutting hyper-plane is created at the new node, so that the two leaves are on eitherside of this cutting plane. A composition vector φ0

q will hence lie on either side of thishyper-plane.

The ISAT algorithm is summarized as follows:

1. The ISAT table is queried for every composition vector during the reaction step.

2. For each query φ0q the table is traversed to identify a leaf whose composition φ0 isclose to φ0

q.

3. If the query composition φ0q lies within the EOA of the leaf, then the mapping φ1

q

is retrieved using interpolation by Equation 18.2-11. Otherwise, Direct Integration(DI) is performed and the error between the DI and the linear interpolation ismeasured.

4. If the error is less than the tolerance, then the ellipsoid of accuracy is grown andthe DI result is returned. Otherwise, a new table entry is added .

At the start of the simulation, most operations are adds and grows. Later, as more of the composition space is tabulated, retrieves become frequent. Since adds and grows arevery slow whereas retrieves are relatively quick, initial FLUENT iterations are slow butaccelerate as the table is built.




18.3 Steps for Using the Composition PDF Transport Model


The procedure for setting up and solving a composition PDF transport problem is out-lined below, and then described in detail. Remember that only steps that are pertinentto composition PDF transport modeling are shown here. For information about inputsrelated to other models that you are using in conjunction with the composition PDF

transport model, see the appropriate sections for those models.

1. Read a CHEMKIN-formatted gas-phase mechanism file and the associated thermo-dynamic data file in the CHEMKIN Mechanism panel (see Section 14.1.9: Importinga Volumetric Kinetic Mechanism in CHEMKIN Format).

File −→ Import −→CHEMKIN Mechanism...

i If your chemical mechanism is not in CHEMKIN format, you will have toenter the mechanism into FLUENT as described in Section 14.1.2: Overview

of User Inputs for Modeling Species Transport and Reactions.2. Enable a turbulence model.

Define −→ Models −→Viscous...

3. Enable the Composition PDF Transport model and set the related parameters.

Define −→ Models −→ Species −→Transport & Reaction...

4. Check the material properties in the Materials panel and the reaction parametersin the Reactions panel. The default settings should be sufficient.

Define −→Materials...

5. Set the operating conditions and boundary conditions.

Define −→Operating Conditions...

Define −→Boundary Conditions...

6. Check the solver settings.

Solve −→ Controls −→Solution...

The default settings should be sufficient, although it is recommended to change thediscretization to second-order once the solution has converged.

7. Initialize the solution. You may need to patch a high-temperature region to ignitethe flame.

Solve −→ Initialize −→Initialize...

Solve −→ Initialize −→Patch...


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8. Run the solution.

Solve −→Iterate...

9. Solve the problem and perform postprocessing.

i A good initial condition can reduce the solution time substantially. It isrecommended to start from an existing solution calculated using the EDCmodel, non-premixed combustion model, or partially premixed combus-tion model. See Chapters 14, 15, and 17 for further information on suchsimulations.

This procedure is demonstrated in the PDF transport tutorial, which is available at theFluent User Services Center (www.fluentusers.com).

18.3.1 Enabling the Composition PDF Transport Model

To enable the composition PDF transport model, select Composition PDF Transport inthe Species Model panel (Figure 18.3.1).

Define −→ Models −→Species...

Figure 18.3.1: The Species Model Panel for Composition PDF Transport

When you turn on Composition PDF Transport, the panel will expand to show the relevantinputs.


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18.3.2 Setting Integration Parameters

Under Reactions in the Species Model panel, enable Volumetric. Click on the Integration

Parameters button to open the Integration Parameters panel (Figure 18.3.2).

Figure 18.3.2: The Integration Parameters Panel

The stiff ODE integrator has two error tolerances—the Absolute Error Tolerance and theRelative Error Tolerance under ODE Parameters—that are set to default values of 10−8

and 10−9 respectively. These should be sufficient for most applications, although thesetolerances may need to be decreased for some cases such as ignition. For problems inwhich the accuracy of the chemistry integrations is crucial, it may be useful to testthe accuracy of the error tolerances in simple zero-dimensional and one-dimensional testsimulations with parameters comparable to those in the full simulation.





ISAT Parameters

If you have selected ISAT under Integration Method, you will then be able to set additionalISAT parameters.

The numerical error in the ISAT table is controlled by the ISAT Error Tolerance under

Integration Parameters. It may help to increase this during the initial transient solution. Alarger error tolerance implies larger EOAs, greater error, but smaller tables and quickerrun times. The default ISAT Error Tolerance of 0.001 may be sufficiently accurate fortemperature and certain major species, but will most likely need to be decreased to getaccurate minor species and pollutant predictions.

i After your simulation is converged, you should always decrease the ISAT

Error Tolerance and perform further iterations until the species that youare interested in are unchanged.

The Max. Storage is the maximum RAM used by the ISAT table, and has a default value

is 100 MB. It is recommended that you set this parameter to a large fraction of theavailable memory on your computer.

You can also specify the Number of Trees and the Verbosity. The Number of Trees isthe number of sub-tables within the ISAT table. For simulations with a large numberof species, ISAT efficiency may be improved by increasing the number of trees fromthe default value of 1. The value of Verbosity allows you to monitor ISAT performancein different levels of detail. See Section 18.3.8: Monitoring ISAT for details about thisparameter.

To purge the ISAT table, click on Clear ISAT Table. See Section 18.3.9: Using ISATEfficiently for more details about using ISAT efficiently.

18.3.3 Enabling KINetics from Reaction Design

For the Composition PDF Transport model, enabling the KINetics from Reaction Design

option will allow you to use reaction rates from Reaction Design’s KINetics module,instead of the default FLUENT reaction rates. FLUENT’s ISAT algorithm is employedto integrate these rates. Please refer to the KINetics for Fluent manual [3] from Reac-tion Design for details on the chemistry formulation options. For more information, orto obtain a license to the Fluent/KINetics module, please contact Reaction Design [email protected] or +1 858-550-1920, or go to http://www.reactiondesign.com


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18.3.4 Enabling Liquid Micro-Mixing

For cases where reactions in liquids occur at low turbulence levels, among reactants withlow diffusivities, a default value of C φ = 2 may not be desirable, as it over-estimates themixing rate. Therefore, enabling the Liquid Micro-Mixing option results in interpolationof C φ from turbulence models and scalar spectra, as noted in Section 18.2.3: Liquid

Reactions.

18.3.5 Selecting the Particle Mixing Model

In the Species Model panel, select Modified Curl, IEM, or EMST under Mixing Model andspecify the value of the Mixing Constant (C φ in Equation 18.2-6). For more informationabout particle diffusion, see Section 18.2.3: Particle Mixing.

18.3.6 Defining the Solution Parameters

After you have defined the rest of the problem, you will need to specify solution param-eters that are specific to the composition PDF transport model in the Solution Controls

panel (Figure 18.3.3).

Solve −→ Controls −→Solution...

Under PDF Transport Parameters, you can specify the following:

Particles Per Cell sets the number of PDF particles per cell. Higher values of thisparameter will reduce statistical error, but increase computational time.

Local Time Stepping toggles the calculation of local time steps. If this option is dis-

abled, then you will need to specify the Time Step directly (see Equation 18.2-4).

If Local Time Stepping is enabled, then you can specify the following parameters:

Convection # specifies the particle convection number (see ∆tconv in Equation 18.2-4).

Diffusion # specifies the particle diffusion number (see ∆tdiff in Equation 18.2-4).

Mixing # specifies the particle mixing number (see ∆tmix in Equation 18.2-4).





Figure 18.3.3: The Solution Controls Panel for Composition PDF Transport





18.3.7 Monitoring the Solution

At low speeds, combustion couples to the fluid flow through density. The Monte CarloPDF transport algorithm has random fluctuations in the density field, which in turncauses fluctuations in the flow field. For steady-state flows, statistical fluctuationsare decreased by averaging over a number of previous iterations in the Iterate panel

(Figure 18.3.4).

Figure 18.3.4: The Iterate Panel for Composition PDF Transport

Averaging reduces statistical fluctuations and stabilizes the solution. However, FLUENToften indicates convergence of the flow field before the composition fields (temperaturesand species) are converged. You should lower the default convergence criteria in theResidual Monitors panel, and always check that the Total Heat Transfer Rate in the Flux

Reports panel is balanced. It is also recommended that you monitor temperature/specieson outlet boundaries and ensure that these are steady.

By default FLUENT performs one finite-volume iteration and then one PDF transportparticle step. This should be optimal for most cases; however, control is provided toperform multiple finite-volume iterations (Number of FV Sub-Iterations) and multiplePDF transport particle steps (Number of PDF Sub-Iterations).





By increasing the Iterations in Time Average, fluctuations are smoothed out and residualslevel off at smaller values. However, the composition PDF method requires a largernumber of iterations to reach steady-state. It is recommended that you use the defaultof 50 Iterations in Time Average until the steady-state solution is obtained. Then, togradually decrease the residuals, increase the Iterations in Time Average by setting a Time

Average Increment to a value from 0 to 1 (the value 0.2 is recommended). Subsequentiterations will increase the Iterations in Time Average by the Time Average Increment.

18.3.8 Monitoring ISAT

You can monitor ISAT performance by setting the Verbosity in the Integration Parameters

panel. For a Verbosity of 1 or 2, FLUENT writes the following information periodically toa file named isat stats.dat:

• total number of queries

• total number of queries resulting in retrieves

• total number of queries resulting in grows

• total number of queries resulting in adds

• total number of queries resulting in direct integrations

• cumulative CPU seconds in ISAT

• cumulative CPU seconds outside ISAT

• cumulative wall-clock time in seconds (i.e., total CPU time in ISAT plus total CPUtime out of ISAT plus CPU idle time)

The ISAT Verbosity option of 2 is for expert users who are familiar with ISATAB v3.0 [290].FLUENT writes out the following files for Verbosity = 2:

• tablename stats.out, as described above

• tablename ODE accuracy.out reports the accuracy of the ODE integrations. Forevery new ISAT table entry, if the maximum absolute error in temperature orspecies is greater than any previous error, a line is written to this file. This line

consists of the total number of ODE integrations performed up to this time, themaximum absolute species error, the absolute temperature error, the initial tem-perature and the time step.

• tablename ODE diagnostic.out prints diagnostics from the ODE solver

• tablename ODE warning.out prints warnings from the ODE solver


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Initially, the table name is equal by default to the current case name, and is changed asthe table is written or read.

In parallel, each processor builds its own ISAT table. If Verbosity is enabled in parallel,each compute node writes out the Verbosity file(s) with the node ID number appendedto the file name.

18.3.9 Using ISAT Efficiently

Efficient use of ISAT requires thoughtful control. What follows are some detailed recom-mendations concerning the achievement of this goal.

i The numerical error in the ISAT table is controlled by the ISAT Error Tol-

erance, which has a default value of 0.001. This value is relatively large,which allows faster convergence times. However, once the solution has con-verged, it is important to reduce this ISAT Error Tolerance and re-converge.This process should be repeated until the species that you are interestedin modeling are unchanged. Note that as the error tolerance is decreased,the memory and time requirements to build the ISAT table will increasesubstantially. There is a large performance penalty in specifying an errortolerance smaller than is needed to achieve acceptable accuracy, and theerror tolerance should be decreased gradually and judiciously.

i Once the ISAT table is full, all queries that cannot be retrieved are directlyintegrated. Since retrieves are much quicker than direct integrations, largerISAT tables are faster. Hence, you should set the ISAT Max. Storage to alarge fraction of the available memory on your computer.

During the initial iterations, before a steady-state solution is attained, transient com-position states occur that are not present in the steady-state solution. For example,you might patch a high temperature region in a cold fuel-air mixing zone to ignite theflame, whereas the converged solution never has hot reactants without products. Sinceall states that are realized in the simulation are tabulated in ISAT, these initial mappingsare wasteful of memory, and can degrade ISAT performance. If the table fills the allo-cated memory and contains entries from an initial transient that are no longer accessed,it may be beneficial to purge the ISAT table. This is achieved by either clearing it in theIntegration Parameters panel, or saving your case and data files, exiting FLUENT, thenrestarting FLUENT and reading in the case and data.

The optimum ISAT table is achieved when a new table is started from the convergedFLUENT solution. If you are simulating a range of parametric cases where the flamechanges gradually, it is likely beneficial to create such an optimum table for the firstcase, and then save it.

File −→ Write −→ISAT Table...





Subsequent runs can start from this table by reading it into memory.

File −→ Read −→ISAT Table...

See Section 18.3.10: Reading and Writing ISAT Tables in Parallel for information aboutreading and writing ISAT tables in parallel.

ISAT efficiency may be increased by employing multiple tables (also called trees). In-creasing the number of trees has the effect of decreasing the table size and hence thetime needed to build the table, but increasing the retrieve time. Hence, for long simu-lations with simple chemistry, a small number of tables may be optimal. On the otherhand, for short simulations with complex chemistry, computers with limited memory, orsimulations with a small ISAT error tolerance, a large number of trees is likely optimalsince most of the CPU time is spent building the table.

From experience, ISAT performs very well on premixed turbulent flames, where therange of composition states are smaller than in non-premixed flames. ISAT performancedegrades in flames with large time-scales, where more work is required in the ODE

integrator.

18.3.10 Reading and Writing ISAT Tables in Parallel

When FLUENT is run in parallel, each partition builds its own ISAT table and does notexchange information with ISAT tables on other compute nodes. You can save the ISATtables on all compute nodes:

File −→ Write −→ISAT Table...

Each compute node writes out its ISAT table to the specified file name, with the node IDnumber appended to the file name. For example, a specified file name of my name on a

two compute node run will write two files called my name-0.isat and my name-1.isat.

Subsequent runs can start from existing ISAT tables by reading them into memory.

File −→ Read −→ISAT Table...

Files can be read in two ways:

• Parallel nodes can read in corresponding ISAT tables saved from a previous parallelsimulation. The appended node ID should be removed from the input file name.For the above example, the file name my name should be specified in the Select File

dialog box. You should never read ISAT tables generated from a parallel simulationwith a different number of parallel nodes.

• All nodes can read one unique ISAT table. You might use this approach if youhave a large table from a serial simulation. FLUENT first checks to see if the exactfilename that you specified exists, and if it does, all nodes will read this one file.





18.3.11 Running Unsteady Composition PDF Transport Simulations

For unsteady composition PDF transport simulations, a fractional step scheme is em-ployed where the PDF particles are advanced over the time step, and then the flowis advanced over the time step. Unlike steady-state simulations, composition statisticsare not averaged over iterations, and to reduce statistical error you should increase the

number of particles per cell in the Solution Monitors panel.

For low speed flows, the thermochemistry couples to the flow through density. Statisticalerrors in the calculation of density may cause convergence difficulties between time stepiterations. If you experience this, increase the number of PDF particles per cell, ordecrease the density under-relaxation.

18.3.12 Running Compressible Composition PDF Transport Simulations

Compressibility is included when ideal-gas is selected as the density method in theMaterials panel. For such flows, particle internal energy is increased by p∆v over the

time step ∆t, where p is the cell pressure and ∆v is the change in the particle specificvolume over the time step.

18.3.13 Running Composition PDF Transport Simulations with Conjugate Heat

Transfer

When solid zones are present in the simulation, FLUENT solves the energy equation inthe turbulent flow zones by the Monte Carlo particle method, and the energy equationin the solid zones by the finite-volume method.

18.3.14 Postprocessing for Composition PDF Transport Calculations

Reporting Options

FLUENT provides several reporting options for composition PDF transport calculations.You can generate graphical plots or alphanumeric reports of the following items:

• Static Temperature

• Mean Static Temperature

• RMS Static Temperature

• Mass fraction of species-n

• Mean species-n Mass Fraction

• RMS species-n Mass Fraction





The instantaneous temperature in a cell is calculated as

T instant =

N ci=1 T pm pN ci=1 m p

(18.3-1)

whereT instant = instantaneous cell temperature at the present iterationN c = number of particles in the cellT p = particle temperaturem p = particle mass

Mean and root-mean-square (RMS) temperatures are calculated in FLUENT by averag-ing instantaneous temperatures over a user-specified number of previous iterations (seeSection 18.3.7: Monitoring the Solution).

Note that for steady-state simulations, instantaneous temperatures and species representa Monte Carlo realization and are as such unphysical. Mean and RMS quantities aremuch more useful.

Particle Tracking Options

When you have enabled the composition PDF transport model, you can display thetrajectories of the PDF particles using the Particle Tracks panel (Figure 18.3.5).

Display −→Particle Tracks...

Select the Track PDF Transport Particles option to enable PDF particle tracking. To speedup the plotting process, you can specify a value n for Skip, which will plot only every

nth particle. For details about setting other parameters in the Particle Tracks panel, seeSection 22.16.1: Displaying of Trajectories.

When you have finished setting parameters, click Display to display the particle trajecto-ries in the graphics window.


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Figure 18.3.5: The Particle Tracks Panel for Tracking PDF Particles


Modeling a Composition PDF Transport

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