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  1. 1. 8-1 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Chapter 8 Transient Simulations Introduction to CFX
  2. 2. Transient Simulations 8-2 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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
  3. 3. Transient Simulations 8-3 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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
  4. 4. Transient Simulations 8-4 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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)
  5. 5. Transient Simulations 8-5 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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
  6. 6. Transient Simulations 8-6 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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 1. Prescribe initial conditions Best to use a physically realistic initial condition, such as a steady solution 1. Assign solver settings 2. Configure transient results files, transient statistics, monitors points 3. Run the solver How to Solve a Transient Case
  7. 7. Transient Simulations 8-7 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual1. Analysis Type Edit Analysis Type in the Outline tree and set the option to Transient
  8. 8. Transient Simulations 8-8 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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
  9. 9. Transient Simulations 8-9 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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
  10. 10. Transient Simulations 8-10 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual2. Time Duration and Time Step 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 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
  11. 11. Transient Simulations 8-11 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual2. Time Duration and Time Step 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 Velocity NumberCourant t =
  12. 12. Transient Simulations 8-12 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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
  13. 13. Transient Simulations 8-13 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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 Residuals
  14. 14. Transient Simulations 8-14 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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
  15. 15. Transient Simulations 8-15 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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
  16. 16. Transient Simulations 8-16 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 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
  17. 17. Transient Simulations 8-17 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual Transient Statistics Used to generate running statistics for solution variables Arithmetic Average, RMS, Mini