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Shaikh Amaanur Rahman

Department of Aerospace Engineering

21AE30025

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Motivation

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Motivation

Using a MATLAB code to solve for the Chapman Jouguet point, a thermodynamic cycle based on Fickett-Jacobs cycle, following ZND detonation theory was constructed. The performance of the FJ cycle was compared with the Brayton cycle, with different compression ratios, and a standard heat release(H2-O2 stoichiometric mixture heat).

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Cycle Analysis with varying Compression Ratio

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Thermodynamic Cycle Analysis of RDE (FJ vs Brayton)

Cycle Analysis with varying Heat Release Value

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Thermodynamic Cycle Analysis of RDE (FJ vs Brayton)

Specific Impulse values

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Since the cycle analysis was done for a unit mass flow, it can be said that the thrust value would actually turn out to be the specific impulse. The exit velocity was calculated by assuming perfect expansion from the Chapman-Jouguet point. More accurate thrust calculations need to be made.

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Pressure History Model

The cycle analysis done until now assumed that the detonation products immediately expand into the turbine. However, that is not the case. To model the turbine inlet conditions, we take a pressure history on the injection face, as proposed by Shepherd[2].

The pressure history model obtains a close analytical representation of the pressure experienced by the injector face. The pressure trace for a typical fuel-air mixture is similar to as shown in Fig. 4.

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Fig. 4. Pressure traces obtained from a numerical solution for a detonation in an RDE. a) Stoichiometric C2H4-air mixture b) Stoichiometric C2H4-O2 mixture

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Pressure History Model

The pressure can be fitted using a decay term, which depends on the distance in the x-direction(along the circumference) and the combustion products. However, according to Sichel and Foster[3], the decay function is found to be mostly independent of the gas composition.

Using the above, average pressure can be calculated, giving us a better estimate of the turbine inlet conditions. Since the expansion wave behind the shock wave can be considered isentropic, we can form a similar decay model for the temperature.

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Pressure History Model

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Detonation initiation experiment

  1. Previous work: Rama tried with a coupled inductor circuit. Sudden discharge was achieved with the help of a MOSFET. Suggested using an HFSSTC(High-Freq Solid State Tesla Coil).
  2. Some works suggest using a simpler capacitor discharge circuit. Energy deposited can be estimated using integration of (i2r).dt. JHS Lee seems to have some work on direct detonation initiation. He has pointed out that 1/4th of energy estimated by the discharge works in initiating the detonation.
  3. Energy deposited can be more accurately measured using oscillator measurement.
  4. Multiple sources suggest using a higher initial pressure to reduce the energy requirements.
  5. Link: http://www.icders.org/ICDERS2009/abstracts/ICDERS2009-0157.pdf

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Literature Review

Thermodynamics of an RDE(Craig)

Mode-Locked Detonations(Kutz)

Deals with thermodynamics, and resolution of the flow field within RDE, using a reduced order model

Deals with the wave nature of the principle detonation wave

Principle energy conservation is a conservation of rothalpy(enthalpy in rotating frame)

Principle energy conservation involves energy balance between gain depletion, gain recovery and dissipation

Deals with injector non-ideality using isentropic expansion in the injector nozzle, sensitive to pressure downstream(in the RDE)

Injector flow is modeled as an exponential activation function.

More quantitative

Qualitative analysis. Needs to be scaled correctly to simulate any actual variable involved

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References

[1] Thermodynamics of a Rotating Detonation Engine, Nordeen�[2] Analytical Models for the Thrust of a Rotating Detonation Engine, Shepherd