Stagnation Hugoniot Analysis for Steady Combustion Waves in Propulsion Systems

The combustion mode in a steady-flow propulsion system has a strong influence on the overall efficiency of the system. To evaluate the relative merits of different modes, we propose that it is most appropriate to keep the upstream stagnation state fixed and the wave stationary within the combustor. Because of the variable wave speed and upstream stagnation state, the conventional Hugoniot analysis of combustion waves is inappropriate for this purpose. To remedy this situation, we propose a new formulation of the analysis of stationary combustion waves for a fixed initial stagnation state, which we call the stagnation Hugoniot. For a given stagnation enthalpy, we find that stationary detonation waves generate a higher entropy rise than deflagration waves. The combustion process generating the lowest entropy increment is found to be constant-pressure combustion. These results clearly demonstrate that the minimum entropy property of detonations derived from the conventional Hugoniot analysis does not imply superior performance in all propulsion systems. This finding reconciles previous analysis of flowpath performance analysis of detonation-based ramjets with the thermodynamic cycle analysis of detonation-based propulsion systems. We conclude that the thermodynamic analysis of propulsion systems based on stationary detonation waves must be formulated differently than for propagating waves, and the two situations lead to very different results

Analytical Model for the Impulse of Single-Cycle Pulse Detonation Tube

An analytical model for the impulse of a single-cycle pulse detonation tube has been developed and validated against experimental data. The model is based on the pressure history at the thrust surface of the detonation tube. The pressure history is modeled by a constant pressure portion, followed by a decay due to gas expansion out of the tube. The duration and amplitude of the constant pressure portion is determined by analyzing the gasdynamics of the self-similar flow behind a steadily moving detonation wave within the tube. The gas expansion process is modeled using dimensional analysis and empirical observations. The model predictions are validated against direct experimental measurements in terms of impulse per unit volume, specific impulse, and thrust. Comparisons are given with estimates of the specific impulse based on numerical simulations. Impulse per unit volume and specific impulse calculations are carried out for a wide range of fuel–oxygen–nitrogen mixtures (including aviation fuels) of varying initial pressure, equivalence ratio, and nitrogen dilution. The effect of the initial temperature is also investigated. The trends observed are explained using a simple scaling analysis showing the dependency of the impulse on initial conditions and energy release in the mixture

Thermodynamic Cycle Analysis for Propagating Detonations

Propagating detonations have recently been the focus of extensive work based on their use in pulse detonation engines [1]. The entropy minimum associated with Chapman–Jouguet (CJ) detonations [2] and its potential implications on the thermal efficiency of these systems [3] has been one of the main motivations for these efforts. The notion of applying thermodynamic cycles to detonation was considered first by Zel’dovich [4], who concluded that the efficiency of the detonation cycle is slightly larger than that of a cycle using constant-volume combustion. More recently, Heiser and Pratt [3] conducted a thermodynamic analysis of the detonation cycle for a perfect gas using a one-γ model of detonations. Other studies have used constant-volume combustion as a surrogate for the detonation process [5]. This work presents two main contributions. First, we present an alternative physical model for the detonation cycle handling propagating detonations in a purely thermodynamic fashion. The Fickett–Jacobs (FJ) cycle is a conceptual thermodynamic cycle that can be used to compute an upper bound to the amount of mechanical work that can be obtained from detonating a given mass of explosive. Second, we present computations of the cycle thermal efficiency for a number of fuel-oxygen and fuel-air mixtures using equilibrium chemistry, and we discuss the strong influence of dissociation reactions on the results

Small Scale Detonation Studies: Direct impulse measurements for detonations and deflagrations

This report is an account of research carried out from January to June 2000 on the feasibility of detonation initiation and impulse generation for small-scale pulse detonation engines. The initial work was focussed on the direct measurement of impulse using the ballistic pendulum technique for single detonations initiated in a tube with one end open to the atmosphere through a thin diaphragm. Three tubes were used: (1) 38-mm diameter by 1.5 m long. (2) 75-mm diameter by 0.6 m long. (3) 75-mm diameter by 1 m long. At the closed end of the tube, combustion was initiated by a low energy, less than 50 mJ, capacitor discharge system. A fast flame or detonation was created by transition to detonation. The effect of spirals and orifice plates was examined on propane- and ethylene-oxygen-nitrogen mixtures with varying initial pressure, equivalence ratio, and dilution amounts. A simple model for the impulse in prompt detonations was developed and calibrated. The results of our experiments were compared with this model