Sign-up for free online course on ANSYS simulations!Authors: Lara Backer, Cornell University - taken in part from MAE 7340 Analysis of Turbulent Flows and Dr. S. Pope
Problem Specification
1. Pre-Analysis & Start-Up
2. Laminar Setup and Solution
3. Laminar Results
4. Turbulent Setup and Solution
5. Turbulent Results
6. Verification & Validation
Exercises
Comments
Turbulent Jet Setup and Solution
Background
The k-ε model solves the RANS - Reynolds Averaged Navier Stokes model, which solves time-averaged Navier Stokes equations.Two additional equations for the turbulent kinetic energy k, and the turbulent dissipation ε, account for the turbulent properties, using the turbulent viscosity to calculate the additional Reynolds stress terms that emerge when time averaging the Navier Stokes equations. It is one of the more widely used models, particularly for flows with small pressure gradients.
The following empirical formulas are useful in defining this model. I is the turbulent intensity,
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is the hydraulic diameter, and d is the jet diameter.
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$$
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= {0.16Re^{-1/8}}
$$
,
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=
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$$
,
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$$
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=
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$$
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$$
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= {C_\mu^
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k^
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$$
,
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$$
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=
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$$
Setup
Use the same case and data files as you downloaded in the Laminar setup for the geometry and mesh.
Now, set up the k-ε model for turbulence. In Solution Setup-Models, double click the previous "Viscous-Laminar" option to open the dialogue. Select the "k-epsilon (2eqn)" model for turbulence. Leave the model constants the same as defined in the dialogue below; these values have been refined to constraints of the model and are typically not varied. Press OK. Note that wall functions are not required for this case as they were in the turbulent pipe flow solution, as there are no wall boundary viscous effects to account for.
In the Materials dialogue. change the viscosity for a higher Reynolds number:
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$$
The inlet jet velocity will remain at 1m/s; the inlet diameter is still 0.01m from the geometry (ignoring the larger diameter with 0m/s velocity inflow), so enter the viscosity for air as ν = 1E-7. Select Change/Create and then Close.
The k-ε terms must be specified on all boundaries. Go to Solution Setup - Boundary Conditions and edit both Farfield and Inlet boundaries. Select "Intensity and Hydraulic Diameter" as the turbulence specification method. At Inlet 1, from the specified Reynolds number and above equations, the intensity should be I=0.037942, and the hydraulic diameter should be 0.01m (twice the measured inlet height).
The other Inlet and both Farfield boundaries should have turbulent kinetic energy and dissipation rates set to zero, because there is no inlet velocity or turbulence associated with them. Press OK for all boundaries to save the inputs.
To initialize the solution, go to Solution Initialization. Select "Inlet 1" to initialize the domain, and press "Initialize".
Go to Monitors and edit the residual monitors. Note that both k and ε both have residual criteria; change it to 1E-06 for both.
Now go to Run Calculation. Run the solution until it all residuals appear to reach a steady state value. This should take a bit more than 5000 iterations, and you should end up with a residuals plot somewhat like this:
