cfx12 08 transient

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April 28, 2009Inventory #002598

Chapter 8

Transient Simulations

Introduction to CFX




Training ManualMotivation• Nearly all flows in nature are transient!

– Steady-state assumption is possible if we:• Ignore unsteady fluctuations• Employ ensemble/time-averaging to remove unsteadiness (this is what is done

in modeling turbulence)

• In CFD, steady-state methods are preferred– Lower computational cost– Easier to postprocess and analyze

• Many applications require resolution of transient 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




Training ManualOrigins of Transient Flow

• 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

Kelvin-Helmholtz Cloud Instability Rotor-Stator Interaction in an Axial Compressor




Training ManualTransient CFD Analysis

• 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• Etc.

• 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 – fast Fourier transform (FFT)




Training Manual

20

Timestep = 2 s

Initial Time = 0 s

Total Time = 20 s

Coefficient Loops = 5

2 4 6 8 10 12 14 16 18

Time (seconds)

5 coefficient Loops

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

• At each time point we must iterate to the solution

How to Solve a Transient Case




Training Manual

• Similar setup to steady state• The general workflow is

1. Set the Analysis Type to Transient

2. Specify the transient time duration to solve and the time step size

3. Set up physical models and boundary conditions as usual

– Boundary conditions may change with time

4. Prescribe initial conditions

– Best to use a physically realistic initial condition, such as a steady

solution

5. Assign solver settings

6. Configure transient results files, transient statistics, monitors points

7. Run the solver

How to Solve a Transient Case




Training Manual1. Analysis Type

• Edit Analysis Type in the Outline tree and set the option to Transient




Training Manual

• Set the Time Duration– This controls when the simulation will end

• Options are:– Total Time

• When restarting this time carriers over

– Time Per Run• Ignores any time completed in previous runs

– Maximum Number of Timesteps • The number of timesteps to perform, including

any completed in previous runs

– Number of Timesteps per Run• For this run only. Ignores previously

completed timesteps

2. Time Duration and Time Step




Training Manual2. Time Duration and Time Step

• Set the Time Step size– This controls the spacing in time between

the solutions points

• Options are:– Timesteps / Timesteps for the Run

• Various formats accepted, e.g.• 0.001• 0.001, 0.002, 0.002, 0.003• 5*0.001, 10*0.05, 20*0.06

– Adaptive• Timestep size will change dynamically within

specified limits depending on specified convergence criteria or Courant number





• The Time Step size is an important parameter in transient simulations– It must be small enough to resolve time-dependent features …

True solution

Time

Variable ofinterest

t

Time

Variable ofinterest

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





– … 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 timestep 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 timestep

– Typical values are 2 – 10, but in some cases higher values are acceptable– The average and maximum Courant number is reported in the Solver out

file each timestep

• A smaller timestep will typically improve convergence

SizeElement

VelocityNumber Courant

t




Training Manual

• If required, boundary conditions can be functions of time instead of constant values

– Velocities, Mass flows, pressure conditions, temperatures, etc. can all be expressed as functions

– In CEL expressions use “t” or “Time”– Can read in time varying experimental data through User FORTRAN

3. Boundary Conditions




Training Manual

• Physically realistic initial conditions should be used

– A converged steady state solution is often used as the starting point

• If a transient simulation is started from an approximate initial guess the initial transient will not be accurate

– The first few timesteps 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

2 4 6 8 10 12 14 16

Time (seconds)

4. Initialization

Res

idua

ls




Training Manual

• The transient scheme defines the numerical algorithm for the transient term

• Two implicit time-stepping schemes are available:

– First Order Backward Euler (more stable)– Second Order Backward Euler (more

accurate)

• The default Second Order Backward Euler scheme is generally recommended for most transient runs

• Timestep Initialisation controls the way the previous timestep is used as the starting point for the next timestep

– Can use the last solution “as is”– Or the solver can extrapolate the previous

solution to try to provide a better starting point

• Not recommended at high Courant numbers– Automatic (default) switches between the two

depending on the Courant number

5. Solver Control




Training Manual

• The Min. and Max. Coeff. Loops set limits on the number of iterations to use within each timestep

• Should aim to converge each timestep within about 3 – 5 loops

– Complex physics may need more loops

• If convergence is not achieved in the maximum number of loops, it is generally better to reduce the timestep size rather than increase the number of loops

– The solution will proceed to the next timestep regardless of whether the convergence criteria was met

– Important to monitor the solution

5. Solver Control




Training Manual

• Transient Results– By default only a final res file is written

• No information about the transient solution

– Need to define Transient Results under Output Control

• Transient Results Option– Standard

• Like a full results file• Can take up a lot of disk space

– Smallest• Writes the smallest file which can still be

used for a restart (still quiet large)

– Selected Variables• Pick only the variables of interest to give

smaller files

• Output Frequency– Controls how often results are written

6. Output Control




Training Manual

• Transient Statistics– Used to generate running statistics for

solution variables

• Arithmetic Average, RMS, Minimum, Maximum, Standard Deviation and Full (everything) are available options

• Pick the variables of interest

• Start and Stop Iteration List defines when to begin and end collecting the statistics

6. Output Control




Training Manual6. Output Control

• Monitor Points are generally used as in steady-state simulations

• Monitor Coefficient Loop Convergence creates monitor history for each iteration within a timestep

– Useful to see if quantities of interest are converging within a timestep

– By default only the monitor values from the end of the timestep are displayed

• Tip: Monitoring an expression will create a transient history chart in the Solver Manager. This can be easier than creating the chart from transient results files after-the-fact, and it doesn’t require transient results files to be written




Training Manual

• Output differs from steady state in that each time step now contains coefficient loop output

• Courant number information shown at the start of each timestep

• Make sure convergence has been achieved by the end of the timestep by monitoring the RMS and MAX residual plots

7. Solver Output

cfx12 08 transient

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