LECTURE-V
PRACTICE SESSION:
UNSTEADY COMPRESSIBLE FLOW-MODELLING
In this tutorial you will learn how to:
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Calculate a steady-state solution (using the coupled implicit solver) as an initial
condition for a transient flow prediction
Define an unsteady boundary condition using a user-defined function (UDF)
Calculate a transient solution using the second-order implicit unsteady
formulation and the coupled implicit solver
Create an animation of the unsteady flow using FLUENT's unsteady solution
animation feature
The geometry to be considered in this tutorial is shown in Figure. Flow through a simple
nozzle is simulated as a 2D planar model. The nozzle has an inlet height of 0.2 m, and the
nozzle contours have a sinusoidal shape that produces a 10% reduction in flow area. Due
to symmetry, only half of the nozzle is modeled.
Figure: Problem Specification
I have sent you a mail to your paws account. First save it to your H: drive and then start
this session further.
Use the 2D version of fluent.
Grid
1. Read in the mesh file nozzle.msh.
File
Read
Case...
2. Check the grid.
Grid
Check
FLUENT will perform various checks on the mesh and will report the progress in
the console window. Pay particular attention to the reported minimum volume.
Make sure this is a positive number.
3. Display the grid.
Display
Grid...
To make the view more realistic, you will need to mirror it across the centerline.
4. Mirror the view across the centerline.
Display
Views...
(a) Select symmetry under Mirror Planes.
(b) Click Apply.
The grid for the nozzle is shown in Figure
Figure: 2D Nozzle Mesh Display
Units
1. For convenience, define new units for pressure.
The pressure for this problem is specified in atm, which is not the default unit.
You will need to redefine the pressure unit as atm.
Define
Units...
(a) Select pressure under Quantities, and atm under Units.
Hint: Use the scroll bar to access pressure, which is not initially visible in the
list.
(b) Close the panel.
Models
1. Select the coupled implicit solver.
The coupled implicit solver is the solver of choice for compressible, transonic
flows.
Define
Models
Solver...
Note: Initially, you will solve for the steady flow through the nozzle. Later, after
obtaining the steady flow as a starting point, you will revisit this panel to enable
an unsteady calculation.
2. Enable the Spalart-Allmaras turbulence model.
Define
Models
Viscous...
The Spalart-Allmaras model is a relatively simple one-equation model that solves
a modeled transport equation for the kinematic eddy (turbulent) viscosity. This
embodies a class of one-equation models in which it is not necessary to calculate
a length scale related to the local shear layer thickness. The Spalart-Allmaras
model was designed specifically for aerospace applications involving wallbounded flows and has been shown to give good results for boundary layers
subjected to adverse pressure gradients.
Materials
1. Set the properties for air, the default fluid material.
Define
Materials...
(a) Select the ideal-gas law to compute Density.
Note: FLUENT will automatically enable solution of the energy equation when
the ideal gas law is used. You do not need to visit the Energy panel to turn it on.
(b) Retain the default values for all other properties.
Then click change/create button.
Operating Conditions
1. Set the operating pressure to 0 atm.
Define
Operating Conditions...
Here, the operating pressure is set to zero and boundary condition inputs for
pressure will be defined in terms of absolute pressures. Boundary condition inputs
should always be relative to the value used for operating pressure.
Boundary Conditions
Define
Boundary Conditions...
1. Set the conditions for the nozzle inlet ( inlet).
(a) Set the Gauge Total Pressure to 0.9 atm.
(b) Set the Supersonic/Initial Gauge Pressure to 0.7369 atm.
The inlet static pressure estimate is the mean pressure at the nozzle exit. This
value will be used during the solution initialization phase to provide a guess for
the nozzle velocity.
(c) In the Turbulence Specification Method drop-down list, select Turbulent
Viscosity Ratio.
(d) Set the Turbulent Viscosity Ratio to 1.
For low to moderate inlet turbulence, a viscosity ratio of 1 is recommended.
2. Set the conditions for the nozzle exit ( outlet).
(a) Set the Gauge Pressure to 0.7369 atm.
(b) In the Turbulence Specification Method drop-down list, select Turbulent
Viscosity Ratio.
(c) Accept the default value of 10 for Backflow Turbulent Viscosity Ratio.
If substantial backflow occurs at the outlet, you may need to adjust the backflow
values to levels close to the actual exit conditions.
Solution: Steady Flow
1. Initialize the solution.
Solve
Initialize
Initialize...
(a) Select inlet in the Compute From drop-down list.
(b) Click Init, and Close the panel.
2. Set the solution parameters.
Solve
Controls
Solution...
(a) Under Discretization, select Second Order Upwind for Turbulent
Viscosity.
Second-order discretization provides optimum accuracy.
3. Enable the plotting of residuals.
Solve
Monitors
Residual...
(a) Under Options, select Plot.
(b) Click OK.
4. Enable the plotting of mass flow rate at the flow exit.
Solve
Monitors
Surface...
(a) Increase the number of Surface Monitors to 1.
(b) Turn on the Plot and Write options for monitor-1.
Note: When the Write option is selected in the Surface Monitors panel, the mass
flow rate history will be written to a file. If you do not select the write option, the
history information will be lost when you exit FLUENT.
(c) Click on Define... to specify the surface monitor parameters in the Define
Surface Monitor panel.
i. Select Mass Flow Rate in the Report Type drop-down list.
ii. Select outlet in the Surfaces list.
iii.In the File Name field, enter the name noz_ss.out.
iv. Click on OK to define the monitor.
(d) Click on OK in the Surface Monitors panel to enable the monitor.
5. Save the case file ( noz_ss.cas).
File
Write
Case...
6. Start the calculation by requesting 800 iterations.
Solve
Iterate...
The solution will converge after about 600 iterations. However, the residual
history plot is only one indication of solution convergence. Notice that the mass
flow rate has not reached a constant value. To remedy this, you will reduce the
convergence criterion for the continuity equation and iterate until the mass flow
rate reaches a constant value.
7. Reduce the convergence criterion for the continuity equation.
Solve
Monitors
Residual...
(a) Set the Convergence Criterion for continuity to 1e-04.
(b) Click OK.
Note: To obtain better convergence of the mass flow rate, only the convergence
tolerance for the continuity equation is adjusted. In general, the convergence
behavior of the continuity equation is a good indicator of the overall convergence
of the solution.
8. Request 500 more iterations.
Solve
Iterate...
After about 400 iterations (1000 total), the mass flow rate has leveled off and the
solution has converged. The mass flow rate history is shown in Figure
Figure: Mass Flow Rate History
9. Save the data file ( noz_ss.dat).
File
Write
Data...
10. Check the mass flux balance.
Report
Fluxes...
(a) Keep the default Mass Flow Rate option.
(b) Select inlet and outlet in the Boundaries list.
(c) Click Compute.
The net mass imbalance should be a small fraction (say, 0.5%) of the
total flux through the system. If a significant imbalance occurs, you should
decrease your residual tolerances by at least an order of magnitude and
continue iterating.
11. Display the steady-flow velocity vectors.
Display
Vectors...
(a) Select arrow in the Style drop-down list.
(b) Change the Scale to 10.
(c) Click Display.
The steady flow prediction shows the expected form, with peak velocity of about
326 m/s through the nozzle.
Figure: Velocity Vectors (Steady Flow)
12. Display the steady flow contours of static pressure (Figure).
Display
Contours...
(a) Under Options, select Filled.
(b) Click Display.
The steady flow prediction shows the expected pressure distribution, with low
pressure near the nozzle throat.
Figure: Contours of Static Pressure (Steady Flow)
Enable Time Dependence and Set Unsteady Conditions
In this step you will define a transient flow by specifying an unsteady pressure
condition for the nozzle.
1. Enable a time-dependent flow calculation.
Define
Models
Solver...
(a) Under Time, select Unsteady.
(b) Under Unsteady Formulation, select 2nd-Order Implicit.
Implicit (dual) time-stepping allows you to set the physical time step used for the
transient flow prediction (while FLUENT continues to determine the time step
used for inner iterations based on a Courant condition). Here, second-order
implicit time-stepping is enabled: this provides higher accuracy in time than the
first-order option.
2. Define the unsteady condition for the nozzle exit ( outlet).
The pressure at the outlet is defined as a wave-shaped profile , and is described
by the following equation:
(1)
where
= circular frequency of unsteady pressure (rad/s)
= mean exit pressure (atm)
In this case,
rad/s, and
0.7369 atm.
Note: To input the value of Equation 1 in the correct units, the function pexit.c
has been multiplied by a factor of 101325 to convert from the chosen pressure
unit (atm) to the SI unit required by FLUENT (Pa). This will not affect the
displayed results
(a) Read in the user-defined function.
Define
User-Defined
Functions
Interpreted...
i. Enter pexit.c as the Source File Name.
ii. Click Compile.
The user-defined function has already been defined, but it needs to be compiled
within FLUENT before it can be used in the solver.
iii. Close the Interpreted UDFs panel.
(b) Set the unsteady boundary conditions at the exit.
i. Select udf unsteady_pressure (the user-defined function) in the Gauge
Pressure drop-down list.
Solution: Unsteady Flow
1. Set the time step parameters.
The selection of the time step is critical for accurate time-dependent flow
predictions. Using a time step of
seconds, 50 time steps are
required for one pressure cycle. The pressure cycle begins and ends with the
initial pressure at the nozzle exit.
Solve
Iterate...
(a) Set the Time Step Size to 7.1857e-05 s.
(b) Set the Number of Time Steps to 300.
(c) Set the Max Iterations per Time Step to 30.
(d) Click Apply.
2. Modify the plotting of the mass flow rate at the nozzle exit.
Because each time step requires 30 iterations, a smoother plot will be generated
by plotting at every time step.
Solve
Monitors
Surface...
(a) For monitor-1, select Time Step in the drop-down list under Every.
(b) Click Define... to modify the surface monitor parameters.
i. In the Define Surface Monitor panel, change the File Name to noz_uns.out.
ii. In the X Axis drop-down list, select Time Step.
iii. Click OK.
(c) Click OK in the Surface Monitors panel.
3. Save the transient solution case file ( noz_uns.cas).
File
Write
Case...
4. Start the transient calculation.
Solve
Iterate...
Calculation of 300 time steps will require significant CPU resources. Instead of
calculating, you can read the data file saved after the iterations have been
completed:
noz_uns.dat
(The data file is available in the same directory where you found the mesh and UDF
files.)
By requesting 300 time steps, you are asking FLUENT to compute six
pressure cycles.
Figure: Mass Flow Rate History (Unsteady Flow)
5. Save the transient solution data file ( noz_uns.dat).
File
Write
Data...
In this tutorial, you modeled the transient flow of air through a nozzle. You learned how
to generate a steady-state solution as an initial condition for the unsteady case, and how
to set solution parameters for implicit time-stepping.