1. Numerical Model of a PDRE
Michael Hoyt

2. The Pulse Detonation Rocket Engine
What is it?
Rocket engine where the combustion process involves a detonation wave
Uses shock wave to generate high pressures

3. Purpose Attempting to simulate a single pulse detonation wave
Based upon the process set by C. I. Morris who emphasize the importance of nozzle selection for the PDRE
Also compared with steady state rocket engine in terms of performance

4. System Model Constant volume reactor governs the timestep
Plug flow reactor governs the spacestep

5. Governing Equations Stoichiometric reaction of kerosene in oxygen
Model the products as a whole instead of carbon dioxide and water

6. Governing Equations Quasi 1-D Euler equations
Assumes adiabatic, no viscosity, ideal conditions

7. Governing Equations

8. Other Equations

9. Chemistry Model
Assume global chemistry model

10. Numerical Model Solved in split form
Timestep splitting approach by Strang[2].

11. Numerical Model
Uses ghost cells as the means to evaluate the conditions in each timestep and spacestep
Similar to the finite elements on a solid model
Allows for proper boundary conditions to be applied

12. Initial and Boundary conditions
Initial conditions
Basic state initial conditions, nothing all that special
Example T(x,0) = T0
Boundary conditions
Reflective boundary conditions to simulate walls
Method of characteristics to model exit flow boundary conditions, determined by interior flow

13. Expected Results
Mach number contour plot (space-time diagram)[1]

14. Quick Comparison
Taken from Morris[1].

15. References
[1]Morris, C. I., “Numerical Modeling of Single-Pulse Gasdynamics and Performance of Pulse Detonation Rocket Engines,” Journal of Propulsion and Power, Vol. 21, No. 3, 2005, pp
[2]Strang, G., “On the Construction and Comparison of Difference Schemes,” SIAM Journal on Numerical Analysis, Vol. 5, No. 3, 1968, pp

16. Questions?