Pulse Detonation Propulsion

The objective of theoretical, computational and experimental studies outlined in this lecture note was to evaluate the design principles and propulsion performance of prospective air-breathing engines operating on pulse detonations of realistic hydrocarbon fuels with a realistic technique of detonation initiation via deflagration-to-detonation transition (DDT). 1.0 INTRODUCTION Activities in the field of pulse detonation propulsion are currently focused on investigations and practical development of propulsion engines operating on propagating detonations in a pulse mode. The concept of pulse detonation engine (PDE) is attractive for both subsonic and supersonic flight with PDE as a main propulsion unit or as an afterburner in turbojet or turbofan propulsion system. In particular, PDE-based propulsion is attractive for flight Mach number up to about 3–4. Within this range of Mach number, solid rocket motors are known to be very efficient in terms of simplicity and high-speed capability, but they have a limited powered range. Turbojet and turbofan engines, due to their high specific impulse, provide longer range and heavier payloads, but at flight Mach number exceeding 2–3 they are getting too expensive. Ramjets and ducted rockets designed for flight Mach number up to 4 require solid rocket boosters to accelerate them to the ramjet take over speed, which increases the complexity and volume of a propulsion system. Combined-cycle engines, such as turborockets or turboramjets, are also very complex and expensive for similar applications. In a PDE, detonation is initiated in a tube that serves as the combustor. The detonation wave rapidly traverses the chamber resulting in a nearly constant-volume heat addition process that produces a high pressure in the combustor and provides the thrust. The operation of PDE at high detonation-initiation frequency (about 100 Hz) can produce a near-constant thrust. In general, the near-constant volume operational cycle of PDE provides a higher thermodynamic efficiency as compared to the conventional constant-pressure (Brayton) cycle used in gas turbines and ramjets. The advantages of PDE for airbreathing propulsion are simplicity and easy scaling, reduced fuel consumption, and intrinsic capability of operation from zero approach stream velocity to high supersonic flight speeds. In order to use propagating detonations for propulsion and realize the PDE advantages mentioned above, a number of challenging fundamental and engineering problems has yet to be solved. These problems deal basically with low-cost achievement and control of successive detonations in a propulsion device. To ensure rapid development of a detonation wave within a short cycle time, one needs to apply: • Efficient liquid fuel injection and air supply systems to provide fast and nearly homogeneous mixing of the components in the detonation chamber; • Low-energy source for detonation initiation to provide fast and reliable detonation onset; • Cooling technique for rapid, preferably recuperative, heat removal from the walls of detonation chamber to ensure stable operation and avoid premature ignition of fuel–air mixture leading to detonation failure; Pulse Detonation Propulsion 4 2 RTO-EN-AVT-185 • Geometry of the combustion chamber to promote detonation initiation and propagation at lowest possible pressure loss and to ensure high operation frequency; and • Control methodology that allows for adaptive, active control of the operation process to ensure optimal performance at variable flight conditions, while maintaining margin of stability. In addition to the fundamental issues dealing with the processes in the detonation chamber, there are other issues such as: • Efficient integration of PDE with inlets and nozzles to provide high performance; • Durability of the propulsion system; and • Noise and vibration. The lecture note is organized in such a way that the reader first gets acquainted with the thermodynamic grounds for detonation-based propulsion (Section 2), followed by the principles of practical implementation of the detonation-based thermodynamic cycle in Section 3. As the main focus of this lecture is the utilization of PDE for propulsion, various performance parameters of PDEs (e.g., specific impulse, thrust, etc.) are discussed in Section 4 for the idealized PDE configuration with direct detonation initiation. The main operational constraints of PDEs are discussed in Section 5. Section 6 is dedicated to the numerical simulation of the operation process in a more realistic PDE configuration with DDT rather than direct detonation initiation. For the numerical simulation of DDT, a coupled Flame Tracking – Particle (FTP) method combined with the look-up tables of laminar flame velocities and fuel oxidation kinetics has been developed and implemented. The method proved to be very efficient in terms of CPU requirement and has been successfully tested for several two-dimensional (2D) configurations with flame acceleration in smooth-walled channels of different length, in channels with regular obstacles, and in complex-geometry channels with orifice plates (Subsection 6.1). The results of numerical simulation of DDT in the stoichiometric propane – air mixture filling a PDE channel with regular obstacles and convergent-divergent nozzle are presented in Subsection 6.2. Thrust performances of the idealized and DDT-based propane-fueled PDEs are compared in Subsection 6.3 for the zero flight speed conditions. Section 7 presents the results of calculations of the operation process and thrust performance for the PDE under Mach 3.0 flight conditions. Finally, the operation principles and thrust performances of liquid-fueled research PDEs developed and tested at the Semenov Institute of Chemical Physics (SICP) are discussed in Section 8. The experimental data substantiate the possibility of obtaining DDT in air mixtures of practical fuels (aviation kerosene) with short run-up distances and times and with very low ignition energies. 2.0 THERMODYNAMIC GROUNDS FOR DETONATION-BASED PROPULSION Zel’dovich [1] has shown that detonative combustion is thermodynamically more efficient than constantvolume and constant-pressure combustion. This can be seen from Fig. 1 that is the pressure ) ( p – specific volume ) (v diagram. Consider as an example the combustion of stoichiometric propane – air mixture: C3H8 + 5O2 + 18.8N2 = 3CO2 + 4H2O + 18.8N2 Assume that the initial thermodynamic state of the reactive mixture corresponds to point O in pressure – specific volume diagram of Fig. 1, i.e., 0 0 , v v p p = = . The thick solid curve is the reactive mixture Hugoniot. Detonative combustion corresponds to the jump from point O to shock Hugoniot (not shown) Pulse Detonation Propulsion RTO-EN-AVT-185 4 3 followed by transition to point D – Chapman–Jouguet (CJ) point – along the Reyleigh line (OD is a piece of that Reyleigh line). At point D, the entropy of combustion products is known to attain a minimum and the corresponding Poisson adiabat is tangent to the reactive Hugoniot. If one assumes that after expansion the combustion products attain the initial pressure 0 p , then isentropic expansion from point D proceeds along dotted curve ' DD towards point ' D . In case of constant-volume combustion, the thermodynamic state of the mixture varies along vertical line OE. Further isentropic expansion proceeds along curve ' EE that terminates at point ' E . Finally, constant-pressure combustion results in variation of the thermodynamic state along line ' OG with point ' G representing the final thermodynamic state. Note that points D, E, and ' G are located at the same reactive Hugoniot. Clearly, the entropy rise during detonative combustion is minimal, i.e., O G O E O D S S S S S S − < − < − ′ ′ ′ (1) Figure 1: Thermodynamic cycles with constant-pressure, constant-volume, and detonative combustion (no precompression). From now on, the constant-pressure, constant-volume, and detonative combustion cycles will be referred to as Brayton, Humphrey, and PDE cycles. The efficiency of thermodynamic cycles O ' ODD , O ' OEE , and O ' OG can be readily estimated. At point O, the total specific enthalpy of the reactive mixture is q h H + = 0 0 , where 0 h is the specific thermal enthalpy, and q is the heat effect of combustion. The enthalpy of the combustion products is h H = . The work W performed in the cycles is determined as q h h H H W W W a e + − = − = − = 0 0 , where e W is the expansion work and ) ( 0 0 v v p Wa − = is the work against ambient pressure. The thermal efficiency is defined as q H H q W − = = 0 χ (2) Assume that the gas obeys the ideal gas law with constant specific heats. The heat effect of combustion reaction for the stoichiometric propane – air mixture is taken equal to = q 19760 cal/mol (mix). Initial Pulse Detonation Propulsion 4 4 RTO-EN-AVT-185 temperature is taken equal to 300 0 = T K. The initial mixture properties, such as specific heats at constant pressure 0 p c and at constant volume 0 v c are taken as 78 . 8 0 = p c cal/mol/K and 79 . 6 0 = v c cal/mol/K, so that the specific heat ratio is 293 . 1 / 0 0 0 = = v p c c γ . The corresponding mean properties of combustion products irrespectively of the combustion mode are taken, respectively, as 40 . 10 = p c cal/mol/K and 42 . 8 = v c cal/mol/K, so that 235 . 1 / = = v p c c γ . Figure 1 discussed above is plotted for these values of governing parameters. The reactive Hugoniot in Fig. 1 satisfies the following equation: