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

http://cfd.solvcon.net/pub/styu/jcp2002.pdf

A space-time conservation element and solution element method for solving the two- and three-dimensional unsteady euler equations using quadrilateral and hexahedral meshes

A modular approach to the study of system performance and thermodynamic cycle efficiency of airbreathing pulse detonation engines (PDEs) is described. Each module represents a specific component of the engine, and its dynamic behavior is formulated using conservation laws in either one or two spatial dimensions. A framework is established for assessing quantitatively the influence of all known processes on engine dynamics. Various loss mechanisms limiting the PDE performance are identified. As a specific example, a supersonic PDE for high-altitude applications is studied comprehensively. The effects of chamber configuration and operating sequence on the engine propulsive efficiency are examined. The results demonstrate the existence of an optimum cycle frequency and valve close-up time for achieving maximum performance in terms of thrust and specific impulse. Furthermore, a choked convergent-divergent nozzle is required to render the PDE competitive with other airbreathing propulsion systems, such as gas-turbine and ramjet engines.

System Performance and Thermodynamic Cycle Analysis of Airbreathing Pulse Detonation Engines

http://web2.utc.edu/~bfc365/welcome_files/aiaa.2006.0109.pdf

Implicit solution of the unsteady Euler equations for high-order accurate discontinuous Galerkin discretizations

In this paper, the spacetime conservation element and solution element (CESE) method is applied to threedimensional magnetohydrodynamics (MHD) equations in Cartesian coordinates for solar wind plasma, with the purpose of modeling the steady state solar atmospheric study. To illustrate this newly developed scheme we have studied two examples: (1) two-dimensional coronal dynamical structure with multipole magneticfields and (2) threedimensional coronal dynamical structure, using measuredsolar surface magnetic fields and the empirical values of the plasma properties on the solar surface as the initial conditions for the set of MHD equations and then the relaxationmethod toachieve aq uasiYsteadystate.From these examples we have shown that the newlydeveloped modified spacetime CESE scheme possesses the ability to model the Sun-Earth environment and other astrophysical flows. Subject headingg methods: numerical — MHD — solar wind

https://www.spaceweather.ac.cn/group/articles/2007/70115_web.pdf

A Novel Numerical Implementation for Solar Wind Modeling by the Modified Conservation Element/Solution Element Method

In this paper, we report an extension of the Space-Time Conservation Element and Solution Element (CE/SE) Method for solving the Navier-Stokes equations. Numerical algorithms for both structured and unstructured meshes are developed. To calculate the viscous flux terms, a ‘midpoint rule’ is used. In the setting of space-time flux conservation, a new and unified boundary-condition treatment for solid wall is introduced. The Navier Stokes solvers retain all favorable features of the original CE/SE method for the Euler equations, including high fidelity resolution of unsteady flows, easy implementation of nonreflective boundary conditions, and simplicity of computational logic. In addition, numerical results show that the present Navier-Stokes solvers can be used for high-speed flows as well as low-Mach-number flows without preconditioning. The present Navier Stokes solvers are efficient, accurate, and very robust for flows at all speeds.

/pdf/the-ce-se-method-for-navier-stokes-equations-using-pvrsoxlhhn.pdf

The CE/SE Method for Navier-Stokes Equations Using Unstructured Meshes for Flows at All Speeds

In this paper, we report a variation of Chang’s SpaceTime Conservation Element and Solution Element CE/SE Method for structured mesh. The algorithm of the present modified CE/SE method is even simpler than the original CE/SE method. Nevertheless, all advantageous features of the original CE/SE method have been retained, including a unified treatment of space and time, accurate calculation of the space-time flux, high-fidelity resolution of unsteady flow motions, and full compliance with the physics of initial valued problems. The present modified method is also extended to solve Navier Stokes equations. To calculate the viscous flux terms, a ‘midpoint rule’ is used. In the setting of space-time flux conservation, two boundary-condition treatments for solid wall are introduced. Numerical results show that the present Navier Stokes solver can be used for high-speed flows as well as low-Mach-number flows without preconditioning. Results of several standard flow problems show that the present method is efficient and accurate.

/pdf/a-modified-space-time-conservation-element-and-solution-4keti0p7zm.pdf

A Modified Space-Time Conservation Element and Solution Element Method for Euler and Navier-Stokes Equations

In this paper, we report the calculations of low-Mach-number viscous flows without preconditioning by the space-time CE/SE method It is shown that the CE/SE method can sustain highly resolved solution for long-term calculations with large numbers of time steps Several numerical examples are calculated to demonstrate the efficiency and accuracy of the CE/SE method in calculating low-speed flows

/pdf/calculations-of-low-mach-number-viscous-flows-without-4rpqrbbv07.pdf

Calculations of Low-Mach-Number Viscous Flows without Preconditioning by the Space-Time CE/SE Method

This paper reports preliminary numerical results of plume dynamics for a pulse detonation engine (PDE). The space-time CE/SE method was used to solve the two-dimensional and axisymmetric Euler equations in conjunction with one chemical species equation in a time-accurate manner. Chemical reactions are simulated by a one-step, irreversible, finite rate model. The stiff source term in the species equation is treated by a point-wise implicit method based on a space-time volumetric integration of the source term over each CE. Numerical results show complex vortex/shock interactions in the vicinity of the thruster exit. Away from the PDE tube, spherical expansion of sound waves is evident. Although a much finer mesh will be needed to further resolve the relevant flow physics, the present results provide an encouraging first step toward the analysis of this challenging computational aeroacoustics problem.

Zeng-Chan Zhang

Papers

A space-time conservation element and solution element method for solving the two- and three-dimensional unsteady euler equations using quadrilateral and hexahedral meshes

The CE/SE Method for Navier-Stokes Equations Using Unstructured Meshes for Flows at All Speeds

A Modified Space-Time Conservation Element and Solution Element Method for Euler and Navier-Stokes Equations

Calculations of Low-Mach-Number Viscous Flows without Preconditioning by the Space-Time CE/SE Method

Direct Calculations of Plume Dynamics of a Pulse Detonation Engine by the CE/SE Method