THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Some Preliminary Thoughts * Part I: Inviscid Hypersonic Flow * Hypersonic Shock and Expansion-Wave Relations * Local Surface Inclination Methods * Hypersonic Inviscid Flowfields: Approximate Methods * Hypersonic Inviscid Flowfields: Exact Methods * Part II: Viscous Hypersonic Flow * Viscous Flow: Basic Aspects, Boundary Layer Results, and Aerodynamic Heating * Hypersonic Viscous Interactions * Computational Fluid Dynamic Solutions of Hypersonic Viscous Flows * Part III: High-Temperature Gas Dynamics * High-Temperature Gas Dynamics: Some Introductory Considerations * Some Aspects of the Thermodynamics of Chemically Reacting Gases (Classical Physical Chemistry) * Elements of Statistical Thermodynamics * Elements of Kinetic Theory * Chemical Vibrational Nonequilibrium * Inviscid High-Temperature Equilibrium Flows * Inviscid High-Temperature Nonequilibrium Flows * Kinetic Theory Revisited: Transport Properties in High-Temperature Gases * Viscous High-Temperature Flows * Introduction to Radiative Gas Dynamics.

Hypersonic and high temperature gas dynamics

A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in two dimensions and shows that if the local ' mesh Reynolds number ', based on the size of the mesh used in the solution, exceeds a certain fixed value, the numerical solution will not converge.

On the Navier-Stokes equations

Rayleigh scattering is a powerful diagnostic tool for the study of gases and is particularly useful for aiding in the understanding of complex flow fields and combustion phenomena. Although the mechanism associated with the scattering, induced electric dipole radiation, is conceptually straightforward, the features of the scattering are complex because of the anisotropy of molecules, collective scattering from many molecules and inelastic scattering associated with rotational and vibrational transitions. These effects cause the scattered signal to be depolarized and to have spectral features that reflect the pressure, temperature and internal energy states of the gas. The very small scattering cross section makes molecular Rayleigh scattering particularly susceptible to background interference. Scattering from very small particles also falls into the Rayleigh range and may dominate the scattering from molecules if the particle density is high. This particle scattering can be used to enhance flow visualization and velocity measurements, or it may be removed by spectral filtering. New approaches to spectral filtering are now being applied to both Rayleigh molecular scattering and Rayleigh particle scattering to extract quantitative information about complex gas flow fields. This paper outlines the classical properties of Rayleigh scattering and reviews some of the new advances in flow field imaging that have been achieved using the new filter approaches.

https://iopscience.iop.org/article/10.1088/0957-0233/12/5/201/pdf

Laser Rayleigh scattering

Recent interest in supersonic combustion (scramjets) and noise reduction for the high speed civil transport (HSCT) plane prompted renewed research in supersonic mixing processes and means to control them. The scramjet propulsion concept requires rapid mixing between fuel and air in order to minimize the size of the combustor and affect the performance of the entire vehicle system. Also, accelerated mixing of exhaust plumes with coflowing air has been shown to lead to jet noise reduction. Other examples of technological applications requiring control of mixing in compressible flows include thrust augmenting ejectors, thrust vector control, metal deposition, and gas dynamic lasers. The technological challenge of mixing enhancement in compressible flows stems from the inherently low growth rates of supersonic shear layers. Many mixing augmentation methods employed efficiently in sub­ sonic flows failed to work at elevated Mach numbers, and some were inefficient because they were utilized outside their effective range. Never-

Mixing enhancement in supersonic free shear flows

A current research effort is underway at the NASA Langley Research Center to achieve a detailed understanding of important phenomena present when a supersonic flow undergoes chemical reaction. A computer program has been developed to study the details of such flows. The program has been constructed to consider the multicomponent diffusion and convection of important species, the finite-rate reaction of these species, and the resulting interaction between the fluid mechanics and chemistry. Code results from the analysis of a spatially developing and reacting mixing layer are presented, and conclusions are drawn regarding the structure of the evolving layer and its associated flame.

A detailed numerical model of a supersonic reacting mixing layer

An absorption filter planar Doppler velocimeter has been constructed and tested on a pressure-matched sonic jet and an overexpanded supersonic jet (A/design = 1-9). The current system can acquire single-velocity-component single-shot planar images (15-ns exposures) at 30 Hz. A unique aspect of the system is the use of a single camera and lens, made possible by the application of an image splitter system. This development reduces the expense and experimental complexity of the technique. The most extensive of the three data sets taken comprises 1100 centerline planes of instantaneous velocity acquired in the overexpanded supersonic jet. Mean and rms velocity fields are presented for this data set; a mean centerline and a mean transverse profile are extracted and compared with profiles from a computational fluid dynamics solution generated using the LARCK computer code employing a k-e turbulence model.

Application of absorption filter planar Doppler velocimetry to sonic and supersonic jets

Two assumed probability density functions (pdfs) are employed for computing the effect of temperature fluctuations on chemical reaction. The pdfs assumed for this purpose are the Gaussian and the beta densities of the first kind. The pdfs are first used in a parametric study to determine the influence of temperature fluctuations on the mean reaction-rate coefficients. Results indicate that temperature fluctuations significantly affect the magnitude of the mean reaction-rate coefficients of some reactions depending on the mean temperature and the intensity of the fluctuations. The pdfs are then tested on a high-speed turbulent reacting mixing layer. Results clearly show a decrease in the ignition delay time due to increases in the magnitude of most of the mean reaction rate coefficients.

Modeling turbulent/chemistry interactions using assumed pdf methods

At flight speeds, the residence time for atmospheric air ingested into a scramjet inlet and exiting from the engine nozzle is on the order of a millisecond. Therefore, fuel injected into the air must efficiently mix within tens of microseconds and react to release its energy in the combustor. The overall combustion process should be mixing controlled to provide a stable operating environment; in reality, however, combustion in the upstream portion of the combustor, particularly at higher Mach numbers, is kinetically controlled where ignition delay times are on the same order as the fluid scale. Both mixing and combustion time scales must be considered in a detailed study of mixing and reaction in a scramjet to understand the flow processes and to ultimately achieve a successful design. Although the geometric configuration of a scramjet is relatively simple compared to a turbomachinery design, the flow physics associated with the simultaneous injection of fuel from multiple injector configurations, and the mixing and combustion of that fuel downstream of the injectors is still quite complex. For this reason, many researchers have considered the more tractable problem of a spatially developing, primarily supersonic, chemically reacting mixing layer or jet that relaxes only the complexities introduced by engine geometry. All of the difficulties introduced by the fluid mechanics, combustion chemistry, and interactions between these phenomena can be retained in the reacting mixing layer, making it an ideal problem for the detailed study of supersonic reacting flow in a scramjet. With a good understanding of the physics of the scramjet internal flowfield, the designer can then return to the actual scramjet geometry with this knowledge and apply engineering design tools that more properly account for the complex physics. This approach will guide the discussion in the remainder of this section.

/pdf/fuel-air-mixing-and-combustion-in-scramjets-bv65ir26s9.pdf

Fuel-Air Mixing and Combustion in Scramjets

Research has been conducted for a number of years at the NASA Langley Research Center to develop a supersonic combustion ramjet (scramjet) capable of propelling a vehicle at hypersonic speeds in the atmosphere or beyond. Recently, that research has been directed toward the optimization of the scramjet combustor, and in particular the efficiency of fuel-air mixing and reaction in the engine. This paper describes a numerical study of fuel-air mixing and reaction in a supersonic combustor, and discusses the analysis of a technique that was used to enhance the mixing processes and overall combustion efficiency in the flow. Based on the results of that study, conclusions are drawn regarding the applicability of the technique to enhance mixing in a scramjet combustor.

J. P. Drummond

Papers

A detailed numerical model of a supersonic reacting mixing layer

Application of absorption filter planar Doppler velocimetry to sonic and supersonic jets

Modeling turbulent/chemistry interactions using assumed pdf methods

Fuel-Air Mixing and Combustion in Scramjets

Mixing Enhancement in a Supersonic Combustor