The CFLOW solver is a solver for simulation of compressible flows based on an explicit time-marching finite-volume-method (FVM) approach for which you can find a thorough description in the lectures on time-marching methods (Lectures 13 and 14). In order to be able to solve the tasks, you will have to make changes to the solver settings in accordance with the task description such as tube geometry, number of cells, number of time steps, boundary conditions, and initial flow properties. In order for the solver to run in a stable manner, you will also need to make changes to the solver numerics settings in some of the cases. In cases with steep gradients or discontinuities, extra damping will be needed. The extra damping is activated in the Numerics section. Pressure damping is used for shocks and density damping is for cases with steep temperature gradients.

Note that for compressible flows, the CFL-number is defined as:

where \(\Delta t\) is the time step size, \(c\) is the speed of sound, \(u\) is the fluid velocity, and \(\Delta x\) is the local cell size. Since the solver uses explicit time marching, it is important that the CFL-number is below unity, otherwise the computation may diverge. You can find more details on the numerics of compressible flow solvers in the lecture notes on time-marching methods.

Detailed description of the solver settings and solver functionality can be found in the solver manual.

Computational Domain

The figure below shows a schematic representation of the computational domain in CFLOW. Note that the solver is of finite-volume-method (FVM) type, which means that it solves for cell averages of flow properties.

Convergence

The convergence history is visualized in the solver log. Depending on task, the number of iterations needed in order to reach convergence will vary. In case the solver is not converged when the specified number of iterations are completed, increase the number of iterations and restart the solver.

Postprocessing

CFLOW will produce graphs of \(\rho\), \(u\), \(p\), \(T\), \(M\), \(p_o\), and \(T_o\) for each obtained solution. Study the graphs and make sure that you can explain what you see.

Export

When done with one of the tasks below, save the CFLOW state to a JavaScript data base file (JSON) using the export functionality. The file can later be used to restore the solver state and should be submitted in Canvas along with the report.

For each of the tasks, report the following:

1. Analytical solution
   • you may include photos/scans of hand-written calculations if you want
2. CFLOW solver settings
   • you only need to report solver settings if you have used something else than the recommended settings for the task
3. Solver convergence
   • residual plot (found under convergence in the cflow solver)
   • Do you consider the solution to be converged enough? Justify your answer
   • Where there any problems getting the solver to converge for this specific case. If so, speculate on the cause for this behavior.
4. Results
   • Flow field plots (for example Mach number, temperature, pressure and/or any of the other available flow field variables if you find something that is particularly interesting) - flow field plots are found under postprocessing in the cflow solver
   • Comment on what you see (are there any specific flow features that can be observed in the results)
5. Discussion
   • Are there any significant deviations from the analytical solution? If so, what is the reason for the deviations? (it might be difficult to answer exactly but a speculation will do)
   • Are there any indications of numerical errors in the solution?
     • wiggles in flow field data
     • changes in total temperature for cases that should be adiabatic
     • changes in total pressure for cases that should be isentropic
     • other indications of numerical errors