Feasibility of Detonation Driven, Linear Electric Power Generation 
Introduction 
The pulsed detonation engine (PDE) has been developed over several decades due to the promise it has for efficient propulsion. A PDE can also be used for power generation and may be more efficient than a deflagrationbased power turbine under certain conditions. One must consider if the unique properties of the detonation wave can be utilized for highly efficient power generation. This research topic is aimed at determining the feasibility of operating a generator that uses the force created by the wave by converting it into to mechanical energy. Converting the force of pulsed detonations into work may be accomplished with a resonant system consisting of a free piston and linear generator. Highly efficient hybrid systems using both the heat and the force produced from the detonation wave are envisioned.



Approach 
Initial research on this topic was sponsored by the Norwegian company Neo Power Technology. A free piston between sets of springs was attached to a linear detonation tube in order to study the basic interaction with common gaseous fuels. A singleshot generator was also built in a manner similar to the example resonance system above. These results were then used to develop and validate a model for a PDE linear power generator.



The images above show the interaction test facility and free piston. The springs on each side were precompressed with rigid plates.
A second setup was later constructed which could generate electricity. 

Detonation Wave/Free Piston Interaction 
The interaction tests measured the detonation tube pressure, piston movement, and forces. The reflected detonation wave pressure history appears as an impulse function compared to the longer time in which the piston oscillates. However, both the pressure and the mass of the detonated gas mixture make contributions to the piston movement. Specific impulse was measured while varying the H2–O2 equivalence ratio over a series of tests that showed the fuellean, heavier initial mixture had superior performance. The energy transferred from the wave was studied for different spring stiffness values and piston masses. Although the energy transferred was far from optimal, enough information was collected to understand how to optimize the system.






Generator Model 
A model was developed in order to understand the maximum efficiency which can be obtained. The example resonance system can be modeled with the following differential equation system where subscripts 1 and 2 are associated with the piston and slider masses, respectively.


These equations were linearized and solved using a MATLAB environment. The most difficult modeling aspect was the determination of the boundary conditions. Using the Friedlander equation for the pressure decay behind a detonation wave, the boundary conditions were formulated and validated with the H2–O2 experimental results.


To model a PDEdriven system that is operating with resonance conditions, a continuous F(t) function is required. A Fourier series expansion of the Friedlander equation was developed to model the PDE with variable operating frequency and overpressure duration. The graph below shows that many expansion terms were required for accuracy.




Modeling Results 
Mass and spring stiffness ratios μ = m1/m2 and κ = k1/k2 were used for parametric studies. Damping ratios ζ1 and ζ2 are also specified. The figures below show an arbitrary system operating at resonance where the piston amplitude is 1 cm to limit mechanical wear. The phase portrait shows that high gain values can be reached quickly and the generator mass movement is sinusoidal.



Optimal performance occurs when the mass and spring ratios are equivalent. The ratios must be at least 100 to reach maximum gain. Such trends occur whether the piston is heavy or light. The graphs below were generated for a PDE that can be built with available technology. Optimization of this system must be conducted when a practical estimation of the generator mass is available.




Conclusions 
 It is possible to harness the detonation waves for linear power generation in a resonating system by using a PDE operating at a practical frequency.
 Since hydrocarbon fuels have higher detonation pressures and mass, their performance is actually higher than hydrogen at stoichiometric conditions. Most optimization strategies for gasdriven generators can be reversed for high PDE linear generator performance.
 Constant area detonation tubes connected to a piston do not have high enough efficiency to be used by themselves, but high efficiency can be reached if the hot exhaust gas are collected and used. A patent disclosure has been filed for concepts related to nozzle design, exhaust gas management, and hybrid generator design.


Sponsors 


Publications 
 E.M. Braun, E. Baydar, F.K. Lu. Modeling of a detonation driven, linear electric generator facility. 28th International Symposium on Shock Waves, Paper 2667, July 17–22, 2011, Manchester, England.
 E.M. Braun, F.K. Lu. Methods and processes for linear power generation from a combustion source. Disclosure, UTA Ref. No. #1130, 2011.
 E.M. Braun, F.K. Lu, M.S. Sagov, D.R. Wilson, P. Grubyi. Proofofprinciple detonation driven, linear electric generator facility. 8th Annual International Energy Conversion Engineering Conference, AIAA paper 20106767, July 25–28, 2010, Nashville, Tennessee.
