[aero_peace]

Dear all,

I am having difficulty modeling a single shot detonation in a tube. Below are the details of the setup.

Mesh:
-5 cm by 1.25 cm (small domain for grid convergence study)
-Cell size = 10e-6 m
-Level 3 adaptive mesh refinement

Problem Setup:
-Solver: Density based - 2d inviscid Euler equation

-Species Model: Finite Rate Laminar with 18-step mechanism for stoichiometric H2/O2 combustion with species H2, O2, OH, O, H, H2O, HO2, and H2O2. The Arrhenius parameters, third body efficiencies, and Troe parameters are taken from Petersen E. L., and Hanson, R. K., "Reduced Kinetics Mechanism for Ram Accelerated Combustion"-Journal of Propulsion and Power.

-Boundary Conditions: A thrust wall, tube wall, pressure outlet, and symmetry

-Solution Method: Explicit spatial formulation, AUSM flux type, second order upwind, and I have tried both explicit and first order implicit transient formulation.

-Initial Condition: The tube is filled with stoichiometric H2/O2 at 1 atm and 298 K. A region of high temperature (3500 K) and pressure (30 atm) is patched at the thrust wall to initiate shock induced detonation. Note, that the species concentration in this region correspond to post detonation equilibrium as predicted from NASA CEA.

I have tried many different approaches regarding the time step size ranging from 1e-8~1e-11 with either the implicit or explicit transient formulation. I have had no luck in creating a CJ detonation. Regarding my residuals, the species converge to about 1.0e-6, however the continuity, energy and velocities hang around 1. I don't know if this is due to an ill posed solution strategy, initial condition, or other. I have a hunch that the Arrhenius parameters are too stiff for fluent to handle, but cannot confirm this. Any support and assistance would be greatly appreciated.

-Future Work: I am going to attempt a very simplified 2-step kinetic mechanism for stoichiometric H2/air by Rogers, R. C., Chinitz, W., "Using a Global Hydrogen-Air Combustion Model in Turbulent Reacting Flows". I believe initiating a detonation in H2/air is computationally less expensive as the induction length for H2/air is approximately 0.22 mm compared to H2/O2 being .039 mm. Hence, since it desired to have at least 10 points in the induction zone behind the detonation.

I will let everyone know my results of the H2/Air solution, however any help regarding the H2/O2 would be greatly appreciated.

-Peace

[aero_peace]

After changing the problem setup to hydrogen air, I was able to get the solutions to converge. However, they do not converge to the Chapman-Jouguet values. The reason is because it appears that the reaction zone detaches from the shock front. I have read many papers regarding this issue and the main reason is due to over resolving the reaction zone with excessive cells. However, I have tried resolving the reaction zone from 0 to 50 cells and I receive the same behavior. Any help would be greatly appreciated.

-Peace

[JMDag2004]

Hello James, I hope you are having a great Thanksgiving holiday! If you have a second, I had a question about your set up. I am attempting to simulate a Ejector-Augmented Pulse detonation rocket. A set up in which the PDR is housed within an ejector duct, thus exhausting into a secondary flow stream. The ejector is preceded by a 15 degree wedge, consequently the secondary flow stream has the flow characteristics of flow passing over the wedge. The secondary flow stream is air, while the combustion within the PDR is and H2/O2 combustion reaction. I'm using a non-equilibrium reversible Arrhenius reaction consisting of a two reaction chemistry model. I would like to set up the simulation such that the PDR cavity is initially filled with a stoichiometric H2/O2 mixture and I am having trouble doing this. I'm fairly certain I need to use a setfields.dict file but not entirely sure. I would be very grateful if you would be willing to share your method for setting up your simulation. I am very new to OpenFOAM, actually I am very new to CFD in general, however, I view CFD as an incredibly useful career tool. I'm working as hard as I can to assimilate information and seeking advice from someone well versed in the practice certainly facilitates my goal. Again, if you have time and would like to see my setup, I would be more than willing to share them. I chose not to include them yet for the sake of brevity. Thank you!