Fluent - Benard Convection

Introduction and Instructions:

This learning module contains abbreviated instructions for solving the free convection problem between two parallel horizontal plates, with the bottom wall hotter than the top wall. The CFD program, Fluent, is used as the solver. The solution illustrates the Benard instability.

Set up the Fluent model:

  1. Start Fluent in its 2-D mode (enter "fluent 2d &") and read in the grid you just created with Gambit.
  2. Turn on heat transfer: Define-Models-Energy, check Enable Energy. OK.
  3. Turn on gravity in the negative y-direction: Define-Operating Conditions. Turn on Gravity. Enter "-9.81" (m/s2) in the Y text box.
  4. Notice the default operating temperature under Boussinesq Parameters. Set this temperature to 60 oC (333.16 K), which will be the temperature of the lower wall. It is tempting to specify an operating density here too, but the help panels say that it is not necessary to specify operating density when using the Boussinesq approximation. OK.

Define the fluid as liquid water with the Boussinesq approximation:

  1. The default fluid is air, which must be changed to water. In the main Fluent window, Define-Materials-Database. Select water-liquid from the Fluid Materials drop down list. Copy. Close.
  2. Now turn on the Boussinesq model: In the Materials window, make sure water-liquid is selected from the Fluid Materials drop down list. In the section of this window called Properties, open the drop down list for Density. Change from constant (the default) to boussinesq.
  3. For some reason (I think this is a bug in Fluent), the default reference density becomes zero. Change this to the appropriate reference density for water at 60 oC. (Look up this density in a thermodynamics textbook.)
  4. Similarly, scroll down through the other fluid properties, and enter the appropriate values at our reference temperature. (I'd suggest looking in the tables of a thermodynamics book.) Note that Fluent does not automatically update these properties at our specified reference temperature, so these must be changed by hand.
  5. Note especially the Thermal Expansion Coefficient (called beta in Fluent, but called alpha in Kundu's book). For some reason (I think this is another bug in Fluent), the default thermal expansion coefficient is zero. Change it to 5.29E-4 1/K, which is the coefficient of thermal expansion for water at 60 oC. Change/Create.
  6. Write down the property values as listed in the Materials window for liquid water, since some of these will be necessary to calculate Rayleigh number, etc.
  7. Finally, Close the Materials window. Caution: This has added liquid water (with Boussinesq) into the list of fluids available as boundary conditions, but has not actually changed the fluid from air to water. This must be done when specifying the boundary conditions.

Define the boundary conditions:

  1. Now the boundary conditions need to be specified. Define-Boundary Conditions. Select fluid. Set . Choose water-liquid from the list of Material Names. OK.
  2. Now choose the lower wall. Set. Change Thermal Conditions to Temperature, and enter the desired temperature of the lower wall, which is the reference temperature in this problem, i.e. 333.16 K. OK.
  3. Similarly, define the (cooler) temperature of the upper wall, according to your desired Rayleigh number.
  4. Now Close the Boundary Conditions window.

Initialize and iterate:

  1. To initialize the solution, Solve-Initialize-Initialize. The default initial value of pressure is okay, but I recommend a small value for the initial velocity field (something like 0.001 m/s in the y direction), just to give the flow some initial "kick" to help set up the instability. Also, set the temperature everywhere to some kind of average between the lower and upper limits. Init and Close.
  2. Set the convergence criteria for the continuity residual to about 1.E-06, as described in previous learning modules.
  3. Reduce the under-relaxation values to about half of their default values, as described in previous learning modules.
  4. In addition, the discretization method recommended for natural convection flows is PRESTO!. (This can be changed by Solve-Controls-Solution.)
  5. It is strongly recommended that you save your case and data files at this point, in case anything goes wrong.
  6. Iterate towards a solution. If having difficulty converging, try this: Turn off the flow equations first, and just solve for the heat transfer. (Solve-Controls-Solution, and turn off the Flow equations.) This should converge very quickly to the basic state (steady state pure conduction through the fluid). Then turn the Flow equations back on and iterate some more. You may not be able to converge completely to residuals lower than 10-6. Grid adaption helps a little, but may not be necessary for this problem. Use your judgement.
  7. Benard cells, if they appear, should be readily visible by displaying velocity vectors.
  8. After the solution has converged, make a hardcopy plot of the velocity vectors, colored by velocity magnitude, if there are clear Benard cells. It is desirable here to zoom in to a couple cells so that the flow pattern is clear. Follow the directions given in previous learning modules if you don't remember how to generate hardcopies. Be sure to add your name and the Rayleigh number to the plot title.
  9. Generate a plot of the streamlines over the entire computational domain if there are Benard cells: Display-Contours. Choose contours of Velocity and choose Stream Function. Display. Generate a hardcopy of the streamline pattern (make sure the entire domain is visible). This plot will be necessary for measuring the wavelength of the Benard cells.

Save your calculations, repeat for another Rayleigh number, and exit Fluent:

  1. In the main Fluent window, save your calculations.
  2. Repeat the calculations for the other Rayleigh number (all you need to change is the temperature of the upper wall). I would suggest re-initializing the flow field. Make hardcopy plots as described above, but be sure to change the Rayleigh number on the plot title. Save these calculations as different file names if you have enough disk space available.
  3. Exit Fluent: File-Exit.