UConn AIAA Lecture Series: Rotating Detonation Engines | Dr. Craig Nordeen 10/01/20 

Good question. Don't know. But I can use Feynman's procedure and guess. Sounds (!) like a research proposal. I assume by "solid state" you mean "no moving parts." First, it is a very noisy high energy environment. The frequency spectrum is broad band with lots of harmonics and sideband. Some non-harmonics have been observed. All of that is typical of non-linear systems. The primary non-linearity is the shock and can be thought of as a step impulse. Second, any desired behavior will have to be matched to the injected acoustic energy. Assuming a standalone engine, the energy has to come from somewhere, and so would be a loss to the system. Unless the resulting behavior causes an entropy decrease and performance increase to pay for it. But maybe that question is getting ahead of things. Thirdly, we (collective RDE community) probably don't understand enough of the fine details of the wave to know what needs modifying. The base thermodynamic cycle is pretty close to the ZND model. That models the detonation as a pure planar sandwich of shock, induction, combustion, and thermal choke. Using that model with some modifications gets a reasonable estimate of performance. Of the order of a 10% error. A realistic detonation is much more complicated, dynamic and three dimensional. This raises the question, just what behavior would we be after? I would turn the question around and ask what behavior could piezo sound probe and uncover? That is, could you use it to find specific resonances that might be susceptible to manipulation? 4. Flush mounted piezo pressure sensors are known to have short lives in the RDE environment. They are fragile relative to the shocks. Current work on pressure sensors hide the piezo in a recess or have a buffer tube of some configuration to filter the incoming signal before it hits the diaphragm. So a piezo sound source would have to be pretty robust. That might create a large stiff piezo which undoubtably change its response and frequencies. A real design challenge. Maybe the source can be isolated somehow like the pressure sensors.

like a high intensity echo canceling of unwanted modes at high frequencies.

As a dampener or an amplifier? Because yeah. But is it useful? Who knows. Maybe as a frequency drift correction mechanism but it’s gonna have serious considerations for heat and life cycles since most of them are too fragile

The average pressure can be as high as you want it, depending on the supply pressure…plus whatever pressure gain is created by the detonation. The pressure within the detonation can be 30X (or more) of the upstream pressure. But it is a small region and passes by the individual injectors very quickly. No, injector pressures do not have to be higher than the max detonation pressure. They do have to be somewhat higher than the fill region of unburned gas that rotates just ahead of the detonation. There is a pressure drop from the plenum to this region. The exact magnitude is a topic of much research and very dependent on the specific design. The lines do not generally require check valves. Maybe for safety reasons. There is a momentary back flow that must be accounted for and is also a topic of research. The back flow is driven by the passing shock wave. Any check valve would have to contend with that. Not a good environment for a mechanically moving part. The environment is very dynamic and complex in spite of a very simple geometry.

You have enough questions for a good paper. Maybe a thesis. I may have to do this by parts. I have a paper in progress at the moment that needs to be finished. It is not a coincidence. It is the conservation of energy. The peak enthalpy appears to be greater than the added heat of combustion. A related question was put to me as, "where does all this extra energy come from?" There is no violation and there is no extra energy. As you note, there must be energy to power the shock. But the rise in shock total enthalpy is greater than the drop in enthalpy from the CJ condition. (Skip to method #2 to see how to do this.) Also note this must be done with total or stagnation enthalpy. There is a transfer of work similar to that of a turbine powering a compressor. Instead of a shaft, the energy transfer is the same you would find in a rocket or gas turbine. It is a momentum exchange.There are three ways to do the energy accounting. The method of rothalpy transfers the problem to the rotating frame of reference and the sum of energies is quite easy. There is no total gain of rothalpy across the shock and the remaining rise of rothalpy is the heat of combustion, which brings the total rothalpy to the same total enthalpy as a CP process. The problem is much simplified in the rotating frame. After the detonation combustion is completed (ideally) the expansion of useful work can begin. The final rothalpy before useful expansion is the same energy as the constant pressure. The difference in determining the useful work is due to the (ideally) less entropy generated by the detonation, because of the curvature of the constant ambient pressure line that is the end of that expansion. It is the reduced entropy and increased useful work that has created all the interest in detonation engines. The accounting in the fixed laboratory frame is more complicated and the source of the confusion. Here the shock compression enthalpy must be paid for by a comparable expansion. There are two expansions that together power the shock. One expansion is almost invisible. The second is the expansion from the CJ stagnation point to the same enthalpy as the CP process, but with less entropy. The second expansion occurs during combustion. This expansion is more obvious on a P-V diagram of the ZND model. Combustion occurs on a Rayleigh line with a negative slope. As the combustion proceeds down the Rayleigh line, temperature increases, but pressure drops and specific volume increases…an expansion. This can be accounted for on the h-s diagram by substituting an equivalent process consisting of a constant pressure line starting at the end of the shock stagnation line. Add the heat of combustion to find the end. It should end with the same entropy as the CJ point. Taking the expansion down to the same CJ stagnation point completes the excercise. The excess enthalpy of the hypothetical CP combustion is the expansion work required to power the shock plus the additional expansion starting at the CJ condition. The third method requires an integration along the process to account for the energies. Tom Kaemming used this approach in his work. I will think some more about your remaining questions. But I will note that there are deviations from the ideal process. One such deviation accounts for the streamlines ending at unexpected points. There is an expansion in the fill zone that causes each streamline to follow a unique path that is due to starting at different initial conditions. There is a gradient of all properties across the front of the detonation that causes the different paths. There is a more complex story just in the injection and fill process than I wish to recount here. I hope this helps. More later.

​@@craignordeen8245 Thank you so much for taking the time to write that all out. I understand much better now why the point of useful work is constrained by the enthalpy of the CP process/heat release of the combustion reaction. This seems to suggest that regardless of where the detonation falls on the Hugoniot (above or below the CJ) as long as some pre-compression occurs prior to the actual combustion (meaning there is some level of shock combustion coupling putting you on the supersonic/high mass flow regime of the Hugoniot) you’ll get lower entropy and therefore some benefit over the CP process. This to me is useful because it is an argument for not constraining RDE designs to those that will produce near CJ condition behavior. As long as there is a shock wave involved you’re improving efficiency assuming the same heat release. Also, the function of the rothalpy approach is much clearer. I know the PDE and RDE cycles are very similar, so if you get good results using rothalpy in an RDE, does that mean you could use it for PDE analysis? Or does the lack of a rotational component force the math to become essentially method 2 and/or 3?

@@CAVU101 Yes you can use it for the PDE. The 2 things to realize that the turbomachinery equation (h_t=U*V +h_I ) is an equation of relative motion (not just rotation) and that the U*V is a vector dot product. It becomes a rotational problem when it is expressed in cylindrical coordinates. Or U=omega*Radius. An interesting thing is when you do that and if you consider only the rotational axis: U*V becomes omega*R*V_theta. The term R*V_theta is the specific angular momentum and is conserved…if you integrate or mass average around the chamber. So in the PDE, the U*V term become just U_x*V_x, where the y & z components are assumed to be zero. Where U_x is the wave speed down the tube. V_x is the particle velocity. In the wake of the detonation, V_x is called, by some, the "following velocity." If you substitute the vector equation V=W+U into the turbo equation to introduce the W relative velocity, you get h_W=U^2/2 + h_I. where h_W=h+W^2/2 or total enthalpy in the moving frame. A working assumption is that flow is steady in the moving frame. So for any point in the moving frame all those terms are constant or conserved. The substitution is best done using vector algebra. If acceleration is involved, the equations can become much more complex. For the RDE, some have invoked the coriolis force to explain some things. There is some very obvious acceleration in a detonation. To date, I am not aware of any identifiable effect of the coriolis force. So far, the engineering rule of "close enough" to steady flow works pretty well and coriolis must be a negligible thing. But beware and aware of assumptions. They can lead you astray. There may yet be an effect. As an exercise, you might try to work out how the above scheme is related to the equations here. en.wikipedia.org/wiki/Fictitious_force

I am unaware of any harmonic noise issues anywhere in the RDE that require necessary attention. Can you be more specific? If you mean across the thermal gradient in a chamber wall by the passing wave, the heat flux quickly becomes an average temperature some microns below the surface. Any harmonics in that layer are beyond detection. There are enough issues keeping the thermocouples from melting. The problems of the heat transfer include material limits, cooling and shock spalling. If you mean across the detonation itself, there certainly is enough noise, but does not appear to cause any difficulties, except in our understanding of the dynamics. A harmonic noise implies a sonic phenomena, perhaps what might be found in the combustion instability of a deflagration combustor. The rotating detonation is supersonic and often of the order of Mach 4. So any sonic phenomena get quickly over run by the detonation. Many numerical simulations use the inviscid Euler equations rather than the more complete Navier-Stokes which models diffusion mechanism like heat transfer and viscous flow. The cost of computational modeling motivates the use of the simpler Euler models. The diffusion mechanisms in N-S models are usually not a serious concern for the basic modeling because the diffusion processes are limited by sonic velocities. The detonation is much faster than those mechanisms. A FFT of pressure probe data typically exhibits a primary frequency with many high frequency harmonics of decreasing amplitude. This is typical of non-sinusoidal wave shapes. A saw-tooth wave creates a similar form. Along with the harmonics there exists a considerable noise background which is typical of non-linear systems. Non-harmonic frequencies of unknown origins have also been seen. Much of the noise certainly comes from the transverse waves. But our knowledge of the detonation structure is incomplete. There is no consensus on the mechanisms of the detonation cell structure. Rather than a harmonic phenomena, it is more closely driven by the reflection of transverse shocks off boundary conditions. The detonation is highly non-linear and non-linear theories and tools are required. One current hot research topic is the creation mechanisms of multiple detonation waves. Hope this helps.

Depends. But probably it does not depend on the number of waves. I assume you mean a torque applied to the chamber by the wave. A reduced order model indicates zero torque because of the conservation of angular momentum. Recent research shows there may be a small amount of residual torque for a symmetrical chamber with no inlet swirl and a flush exit. Any torque would be transmitted through viscous boundary layer forces. However, there is evidence of torque that is applied to aerospike type nozzles. There appears to be no agreement on the existence or source of the torque. Perhaps from the reacting torque being applied to the surrounding ambient air.

@@craignordeen8245 can you suggest some books or paper where I get learned about there basic concept and designing? For reference I'm a mechanical graduate!!

@@manishkumawat3939 Welcome to the field. For starters, I would get "The Detonation Phenomenon" by John H.S. Lee. It covers the detonation in general. It does not cover the propulsion aspects. Many, but not all, combustion texts have some basics on detonation. There are some texts now appearing on rotating detonation, but I have not read them yet. The field is moving fast enough to outstrip any current book. Especially about injection methods. Even for the basic cycle, there is no commonly excepted thermodynamic model. Nor are there a commonly accepted area rules. My own dissertation is a bit dated by now, it does have a reference list with papers that are still relevant. opencommons.uconn.edu/dissertations/277/ The biggest collection of papers and the most active community is through AIAA. AIAA has a searchable database arc.aiaa.org. There are some survey papers occasionally that attempt to summarize the field. It does sound like we need a deep comprehensive survey and a list of the most influential papers.

@@craignordeen8245 thanks Mr Craig!!