The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

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

Development of aerospace airframes and propulsion systems depends on the accurate simulation of these components in their normal operating environment. Measurement of velocity fields is of critical importance in these aerodynamic studies in order to both verify the external flow field and also to determine the performance of these components/systems in the flow field. Quantitative flow field measurements were initially obtained in aerodynamic studies using Pitot static probes, which were suitable for measuring the time-average or low frequency response flow field properties at a single point in the flow.1 Hot wire anemometry proved to be a significant improvement over pitot probes by providing high frequency response velocity measurements.1 Adding more wires enabled multi-component flow measurements. By their design, hot wires are very fragile and easily damaged by foreign objects or particles in the flow. While able to provide continuous records of flow fluctuations, hot wire anemometers only perform reliably in low turbulence flows. Similar to pitot probes, hot wire anemometers were invasive and disturbed the flow field under study. The first non-invasive point velocity measurement technique was Laser Doppler Velocimetry (LDV), which used a crossed pair of laser beams to measure the velocity of seed particles entrained in the flow.1

Digital Particle Image Velocimetry

Chemiluminescence imaging of an optically accessible non-premixed rotating detonation engine

Rotating detonation combustors and their similarities to rocket instabilities

A numerical model has been developed that is capable of predicting the performance of a wave-rotor (pressure exchanger) of specified geometry over a wide range of operating conditions. The model can account for the major loss mechanisms of leakage from the tube ends, fluid viscosity, heat transfer to the tube walls, finite tube opening time, shock waves, and nonuniform port flows. It is a one-dimensional flow model that follows a single tube as it rotates past the various stationary ports. Since the model is relatively simple (i.e., one dimensional), it uses little computer time. This makes it suitable for design as well as analytical purposes. This article will present a brief description of the model and then discuss a comparison between the model predictions and several wave-rotor experiments.

Comparison Between Numerically Modeled and Experimentally Measured Wave-Rotor Loss Mechanisms

An experimental investigation is described in which thrust augmentation and mass entrainment were measured for a variety of simple cylindrical ejectors driven by a gasoline-fueled pulsejet. The ejectors were of varying length, diameter, and inlet radius. Measurements were also taken to determine the effect on performance of the distance between pulsejet exit and ejector inlet. Limited tests were also conducted to determine the effect of driver cross-sectional shape. Optimal values were found for all three ejector parameters with respect to thrust augmentation. This was not the case with mass entrainment, which increased monotonically with ejector diameter. Thus, it was found that thrust augmentation is not necessarily directly related to mass entrainment, as is often supposed for ejectors. Peak thrust augmentation values of 1.8 were obtained. Peak mass entrainment values of 30 times the driver mass flow were also observed. Details of the experimental setup and results are presented. Preliminary analysis of the results indicates that the enhanced performance obtained with an unsteady jet (primary source) over comparably sized ejectors driven with steady jets is due primarily to the structure of the starting vortex-type flow associated with the former.

/pdf/unsteady-ejector-performance-an-experimental-investigation-18phbv7lcb.pdf

Unsteady Ejector Performance:An Experimental Investigation Using a Pulsejet Driver

A two-dimensional, computational fluid dynamic (CFD) simulation of a semi-idealized rotating detonation engine (RDE) is described. The simulation operates in the detonation frame of reference and utilizes a relatively coarse grid such that only the essential primary flow field structure is captured. This construction yields rapidly converging, steady solutions. Results from the simulation are compared to those from a more complex and refined code, and found to be in reasonable agreement. The performance impacts of several RDE design parameters are then examined. Finally, for a particular RDE configuration, it is found that direct performance comparison can be made with a straight-tube pulse detonation engine (PDE). Results show that they are essentially equivalent.

/pdf/numerical-analysis-of-a-rotating-detonation-engine-in-the-5abtrgtfsk.pdf

Numerical Analysis of a Rotating Detonation Engine in the Relative Reference Frame

Wave rotor optimization for gas turbine engine topping cycles

The detonation structure, pressure gain, and thrust production in a rotating detonation engine (RDE) are studied using a combination of experimental and numerical approaches. High frequency time-dependent and low frequency time-averaged static pressure and thrust measurements are acquired for a range of operating conditions and geometry configurations. Acoustic coupling between the detonation channel and air plenum is important for low air mass flow rates and large air injection slots based on analyses of the pressure measurements in the time and frequency domains. The static pressure increases across the air inlet by up to approximately 15% when utilizing a large air injection slot. The pressure increase across the air inlet demonstrates encouraging progress towards realizing pressure gain combustion in RDEs with corresponding challenges associated with isolating the inlet plenums. The time-dependent pressure measurements acquired using a semi-infinite tube arrangement and time-averaged pressure measurements acquired using a capillary tube attenuated arrangement agree to within 30% depending upon location. Quantification of the similarities and differences between the two techniques represents important progress towards acquiring quantitative time-dependent pressure measurements in the challenging environment presented by RDEs. Twodimensional simulations of the RDE capture the essential features of the flow field such as the detonation wave height and angle, trailing edge oblique shock wave, shear layer between the freshly and previously detonated products, and deflagration between the fuel fill region and expansion region containing detonated products. The presence of air purging from the plenum to the channel behind the detonation wave is suggested by the comparison of measured and simulated channel pressure distributions. The pressure, thrust, and wave speed measurements provide benchmark data that are useful for evaluating low and high fidelity simulations of RDEs and improving fundamental understanding of the critical design parameters that influence RDE operation and performance.

Daniel E. Paxson

Papers

Comparison Between Numerically Modeled and Experimentally Measured Wave-Rotor Loss Mechanisms

Unsteady Ejector Performance:An Experimental Investigation Using a Pulsejet Driver

Numerical Analysis of a Rotating Detonation Engine in the Relative Reference Frame

Wave rotor optimization for gas turbine engine topping cycles

Experimental and Numerical Evaluation of Pressure Gain Combustion in a Rotating Detonation Engine