Lecture 11
Transient Flows
14. 0 Release
Introduction to ANSYS
CFX
1 © 2011 ANSYS, Inc. January 16, 2012 Release 14.0
Introduction
" 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
" Learning Aims  you will learn:
 How to set up and run transient calculations
 How to choose the appropriate time step size for your calculation
 How to post process transient data and make animations
" Learning Objectives:
 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
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Outline
" Motivation
" Setup
" Time step estimation
" Output
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Motivation
" 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
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Origins 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
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Transient 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)
Introduction Motivation Setup Time Steps Output
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How to Solve a Transient Case
" Transient simulations are solved by
Timestep = 2 s
computing a solution for many
Initial Time = 0 s
discrete points in time
Total Time = 20 s
" At each time point we must iterate
Coefficient Loops = 5
to the solution
5 coefficient
12
8
2 4 6 10 14 16 18 20
Loops
Time (seconds)
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How to Solve a Transient Case
" Similar setup to steady state
" The general workflow is:
 Set the Analysis Type to Transient
 Specify the transient time duration to solve and the time step size
 Set up physical models and boundary conditions as usual
" Boundary conditions may change with time
 Prescribe initial conditions
" Best to use a physically realistic initial condition, such as a steady solution
 Assign solver settings
 Configure transient results files, transient statistics, monitor points
 Run the solver
Introduction Motivation Setup Time Steps Output
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Analysis Type
" Edit  Analysis Type in the Outline tree and set the Option to  Transient
Introduction Motivation Setup Time Steps Output
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Time Duration and Time Step
" Set the Time Duration
 This controls when the simulation will end
" Options are:
 Total Time
" When restarting, this time carries 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
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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
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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
Time step too large to resolve transient
True solution
changes. Note the solution points generally
will not lie on the true solution because the
true behaviour has not been resolved.
Variable of
interest
Dðt
Time
Variable of
A smaller time step can
interest
resolve the true solution
Dðt
Time
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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:
Velocity´ð Dðt
Courant Number =ð
Element Size
 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
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Boundary Conditions
" 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
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Initialization
" 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 early
timesteps 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
6
8 12
2 4 10 14 16
pattern is obtained
Time (seconds)
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Residuals
Solver Control
" 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
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Solver Control
" The Min. and Max. Coeff. Loops set limits on
the number of iteratins 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
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Output Control
" Transient Results
 By default only a final res file is written
" No information about the transient solution
 Need to define the 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 quite large)
 Selected Variables
" Pick only the variables of interest to give
smaller files
" Output Frequency
 Controls how often results are written
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Output Control
" 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
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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
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Solver Output
" Output differs from steady
state in that each time step
now contains coefficient loop
output onitor Points are
generally used as in steady
state simulations
" 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
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