By L I Sedov London: Cleaver-Hume Press Ltd Pp xvi + 363 Price 105s This is really two separate books within the same pair of covers First of all Chapters 1-3, some 145 pages, are devoted to the discussion of similarity and dimensional, methods and their application to a variety of problems in mechanics and fluid mechanics

http://iopscience.iop.org/article/10.1088/0031-9112/11/6/008/pdf

Similarity and Dimensional Methods in Mechanics

Pulse detonation engines (PDEs) are currently attracting considerable research and development attention because they promise performance improvements over existing airbreathing propulsion devices. Because of their inherently unsteady behavior, it has been difficult to conveniently classify and evaluate them relative to their steady-state counterparts. Consequently, most PDE studies employ unsteady gasdynamic calculations to determine the instantaneous pressures and forces acting on the surfaces of the device and integrate them over a cycle to determine thrust performance. A classical, closed thermodynamic cycle analysis of the PDE that is independent of time is presented. The most important result is the thermal efficiency of the PDE cycle, or the fraction of the heating value of the fuel that is converted to work that can be used to produce thrust. The cycle thermal efficiency is then used to find all of the traditional propulsion performance measures. The benefits of this approach are 1) that the fundamental processes incorporated in PDEs are clarified; 2) that direct, quantitative comparisons with other cycles (e.g., Brayton or Humphrey) are easily made; 3) that the influence of the entire ranges of the main parameters that influence PDE performance are easily explored; 4) that the ideal or upper limit of PDE performance capability is quantitatively established; and 5) that this analysis provides a basic building block for more complex PDE cycles. A comparison of cycle performance is made for ideal and real PDE, Brayton, and Humphrey cycles, utilizing realistic component loss models. The results show that the real PDE cycle has better performance than the real Brayton cycle only for flight Mach numbers less than about 3, or cycle static temperature ratios less than about 3. For flight Mach numbers greater than 3, the real Brayton cycle has better performance, and the real Humphrey cycle is an overoptimistic (and unnecessary) surrogate for the real PDE cycle.

Thermodynamic Cycle Analysis of Pulse Detonation Engines

Introduction I Nprinciple,detonationsare an extremelyef cientmeans of combustinga fuel-oxidizermixture and releasing its chemical energy content. During the past 60 years or so, there have been numerous researcheffortsat harnessingthepotentialof detonationsfor propulsion applications.1 There is a renewed interest lately on intermittent or pulsed detonations engines. Eidelman et al. and Eidelman and Grossmann3 have reviewed some of the initial research as well as work done in the late 1980s on pulse detonation engines (PDEs). The basic theory, design concepts, and the work in the early 1990s related to pulse detonationengines have been discussedby Bussing and Pappas.4 The focus of a more recent review5 is on performance estimates fromvarious experimental, theoreticaland computational studies. More recently, work related to nozzles for PDEs has been discussed. Other reviews7i9 discussing the objectives and accomplishments of various programs are also available.The objective of this paper is to update the previousreviews, focusingon themore recent developmentsin the researchon PDEs. The review is restricted toworkopenlyavailablein the literaturebut includesongoingefforts around the world. Currently, there are several programs sponsored by Of ce of Naval Research (ONR), U.S. Air Force, NASA, Defense Advanced Research Projects Agency, and other agencies in the United States as well as several parallel efforts in Belarus, Canada, France, Japan, Russia, Sweden, and other countries.The results from some of these programs are just beginning to be published.A summary of recent progress and the various organizationsand people involved in PDE research in Japan has been presented.9 Reports of the basic PDE research sponsoredby ONR are available in the proceedingsof a recurringannualmeeting(forexample, seeRef. 10).Recentwork conducted outside the United States has been reported at international meetings on detonations such as those held in Seattle11 (for more information, see http://www.engr.washington.edu/epp/icders/) and Moscow.12 Although an attempt is made to cover a broad range of the reported research, the shear volume of papers presented with PDEs in the title make it impractical to be exhaustive. Rather than providing a chronologicalreport, an attempt is made here to discuss the recent progress in terms of broad topic areas. The key issues that need to be resolved have been addressed in a number of papers (e.g., Refs. 13 and 14). The speci c order in which to discuss the various topics was determined by considering the schematic of an idealized, laboratory pulse detonation engine shown in Fig. 1. This idealizedengine is representativeof the device

Recent Developments in the Research on Pulse Detonation Engines

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Fundamentals Of Engineering Thermodynamics

We review recent progress in gaseous detonation experiment, modeling, and simulation. We focus on the propagating detonation wave as a fundamental combustion process. The picture that is emerging is that although all propagating detonations are unstable, there is a wide range of behavior with one extreme being nearly laminar but unsteady periodic flow and the other chaotic instability with highly turbulent flow. We discuss the implications of this for detonation propagation and dynamic behavior such as diffraction, initiation, and quenching or failure.

https://shepherd.caltech.edu/EDL/publications/reprints/proci_1374.pdf

Detonation in gases

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.

/pdf/analytical-model-for-the-impulse-of-single-cycle-pulse-2ol2i7xxaq.pdf

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

Direct impulse measurements were carried out by using a ballistic pendulum arrangement for detonations
and deflagrations in a tube closed at one end. Three tubes of different lengths and inner diameters were tested
with stoichiometric propane– and ethylene–oxygen–nitrogen mixtures. Results were obtained as a function of
initial pressure and percent diluent. The experimental results were compared to predictions from an analytical
model and generally agreed to within 15% (Wintenberger, E., Austin, J., Cooper, M., Jackson, S., and Shepherd,
J. E., “Analytical Model for the Impulse of a Single-Cycle Pulse Detonation Engine, AIAA Paper 2001–3811,
July 2001). The effect of internal obstacles on the transition from deflagration to detonation was studied. Three
different extensions were tested to investigate the effect of exit conditions on the ballistic impulse for stoichiometric
ethylene–oxygen–nitrogen mixtures as a function of initial pressure and percent diluent.

/pdf/direct-experimental-impulse-measurements-for-detonations-and-x20q8v3h9o.pdf

Direct Experimental Impulse Measurements for Detonations and Deflagrations

http://ronney.usc.edu/AME514/Lecture12/Shephard.AIAA.2001.PDE.model.pdf

An analytical model for the impulse of a single-cycle pulse detonation engine

Experiments were conducted to characterize the detonation phase-velocity dependence on charge thickness for two-dimensional detonation in condensed-phase explosive slabs of PBX 9501, PBX 9502 and ANFO. In combination with previous diameter-effect measurements from a cylindrical rate-stick geometry, these data permit examination of the relative scaling of detonation phase velocity between axisymmetric and two-dimensional detonation. We find that the ratio of cylinder radius ( ) to slab thickness ( ) at each detonation phase velocity ( ) is such that . The variation in the scaling is investigated with two detonation shock dynamics (DSD) models: a lower-order model relates the normal detonation velocity to local shock curvature, while a higher-order model includes the effect of front acceleration and transverse flow. The experimentally observed ( ) scaling behaviour for PBX 9501 and PBX 9502 is captured by the lower-order DSD theory, revealing that the variation in the scale factor is due to a difference in the slab and axisymmetric components of the curvature along the shock in the cylindrical geometry. The higher-order DSD theory is required to capture the observed ( ) scaling behaviour for ANFO. An asymptotic analysis of the lower-order DSD formulation describes the geometric scaling of the detonation phase velocity between the cylinder and slab geometries as the detonation phase velocity approaches the Chapman–Jouguet value.

Scaling of detonation velocity in cylinder and slab geometries for ideal, insensitive and non-ideal explosives

A device capable of creating a collapsing toroidal detonation wave front has been designed and constructed. The goal is to generate pressures and temperatures at the focal region of the collapsing detonation wave that will be sufficient to initiate detonations in insensitive fuel-air mixtures inside of a detonation tube without blocking the flow path and causing associated losses in propulsive efficiency. This toroidal initiator uses a single spark and an array of small-diameter channels to generate and merge many detonation waves to create a single detonation wave with a toroidal front. The development process of the initiator system is described. Steps investigated involve detonation propagation through small tubes, development of a planar initiator capable of initiating a planar detonation wave from a single weak spark, and design and testing of the toroidal initiator. Results presented include the temporal history of pressure at locations near the focus of the collapsing torus and images of the front luminosity. The symmetry of the implosion and practical considerations related to repetitive operation are discussed.

Scott I. Jackson

Papers

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

Direct Experimental Impulse Measurements for Detonations and Deflagrations

An analytical model for the impulse of a single-cycle pulse detonation engine

Scaling of detonation velocity in cylinder and slab geometries for ideal, insensitive and non-ideal explosives

Initiation Systems for Pulse Detonation Engines