Walter G. Vincenti

Effect of thermal radiation on the propagation of plane acoustic waves

A study is made of the propagation of acoustic waves in a semi-infinite expanse of radiating gas on one side of an infinite, plane, radiating wall. A solution is found, in particular, for the case of sinusoidal oscillations in both position and temperature of the wall. The solution is based on a single linear integro-differential equation that plays the same role here as does the classical wave equation in equilibrium acoustic theory. The solution is applicable throughout the range from a completely transparent to a completely opaque gas and from very low to very high temperatures. The solution appears, in general, as the sum of two types of travelling waves: (1) an essentially classical sound-wave, but with a slightly altered speed and a small amount of damping and (2) a radiation-induced wave whose speed and damping may be either large or small, depending on the temperature and absorptivity of the gas. Since the waves are coupled, both types will usually be present together, even in the special cases of pure motion or pure temperature variation of the wall.

INVISCID RADIATING FLOW OVER A BLUNT BODY

Abstract : The effect of thermal radiation is investigated for the axisymmetric flow over the blunt body associated with a given paraboloidal shock wave. Radiative transfer is treated by means of the differential approximation, which applies to multidimensional flow and is valid throughout the entire range of temperature and optical thickness. The gas is assumed to be perfect and optically grey, and molecular-transport processes are neglected. A semi-analytical solution for the flow and radiation fields is obtained by the method of series truncation. Results are presented, in the strong-shock approximation, for various values of the appropriate dimensionless variables. In general, radiation is found to have significant influence on temperature and density, moderate effect on velocity, and little effect on pressure. The stand-off distance between the shock wave and the body is found to decrease significantly with increasing radiation; the body shape is less affected. The results show correct physical behavior throughout the flow field for all values of optical thickness. The detailed flow quantities exhibit a number of features of multidimensional radiating flow. They also provide a check on the special assumptions made in other, more approximate treatments. Similarities between radiating flow and nonequilibrium reactive flow over blunt bodies are apparent. (Author)

A substitute-kernel approximation for radiative transfer in a nongrey gas near equilibrium, with application to radiative acoustics

Abstract The equations for radiative transfer in plane-parallel geometries are studied for a nongrey gas near equilibrium. Local thermodynamic equilibrium is assumed in the molecular processes. On the supposition that deviations from a reference state of radiative equilibrium are small, the equation of radiative transfer is linearized. This allows the required integrations over space and spectral frequency to be carried out independently. In analogy to the grey-gas procedures, a nongrey substitute-kernel (or exponential) approximation is then made for certain frequency-integrated transmission functions that occur in the expressions for the heat fluxes. This leads to a purely differential equation for the net radiative flux. The spectral properties appear in the formulation in two functions, which are introduced by the approximation and which depend on the reference state of the gas. These functions are found by analytical matching procedures, which define linearized Planck- and Rosseland-like mean absorption coefficients that are physically meaningful for a general nongrey gas. For use in radiative acoustics, the differential equation for the heat flux is coupled with the linearized equations of gas dynamics. The resulting nongrey equations have the same mathematical structure as the grey equations, which are now contained as a special case. The results of existing grey-gas solutions can therefore be reinterpreted in terms of a nongrey gas by an appropriate normalization.

Engineering Knowledge, Type of Design, and Level of Hierarchy: Further Thoughts About What Engineers Know…

This article comes at a point in my work that is both advantageous and awkward. The awkwardness comes from the fact that I have recently published a book under the title What Engineers Know and How They Know It (hence the allusion in the title of the present piece). 1 This book contains most of what I think I know about what engineers know, and what I offer here will not be essentially new. The advantages arise because, like most authors, I have been having second thoughts about what I have written and about ideas I think I see more clearly now. I shall attempt here to repackage and summarize those ideas in a way that — I hope — will make more explicit the historiographic and epistemological structure behind them. This structure did not appear so clearly when I was occupied with the nuts and bolts of the work. A diagram has also occurred to me that embodies some of the key ideas in an easily remembered and suggestive form. I will present and discuss it in the concluding part of this material.

Criteria for acoustic instability in a gas with ambient vibrational and radiative nonequilibrium

When acoustic waves propagate in a gas, nonequilibrium phenomena can manifest themselves in either (or both) the ambient and perturbed states of the gas. To study the relatively unexamined effects of ambient nonequilibrium, the present paper uses a macroscopic, gas‐dynamic approach to investigate the influence of such nonequilibrium, primarily as regards vibration and secondarily as regards associated radiation. In situations where the vibrational temperature exceeds the translational temperature, ambient vibrational nonequilibrium, from whatever source, is shown to cause instability (i.e., wave amplification) provided the vibrational relaxation time is a descreasing function of temperature (or increases at less than a specified rate) and the degree of ambient nonequilibrium is sufficiently high. Ambient radiative nonequilibrium will cause instability, in cases where the external‐source temperature exceeds the gas temperature, provided the absorption coefficient is an increasing function of temperature an...

A Gas‐Dynamic Model for Coupled Vibrational and Radiative Nonequilibrium in CO2—with Application to the Spectrophone

Macroscopic equations are formulated for the nonequilibrium interaction of vibrational and radiative rate processes in CO2. A model for CO2 is used that assumes that the energy levels of each vibrational mode are evenly spaced and that each mode can be assigned a vibrational temperature. The bending and symmetric‐stretching modes are, however, taken to be in mutual equilibrium so that they have the same vibrational temperature. Collisional rate equations for the V—T and V—V processes are derived on a phenomenological basis. The resulting phenomenological coefficients are interpreted, with the help of basic knowledge of the microscopic physics, in terms of characteristic relaxation times and parameters measuring the relative amounts of energy exchanged by the various modes during V—V transitions. Radiative transfer equations are developed for the three strongest infrared bands, located in the spectrum at 15, 4.3, and 2.7 μ, by appropriately summing a previously derived microscopic transfer equation. It is ...

Radiation‐Driven Acoustic Waves in a Confined Gas

Preliminary to a projected experimental program, the linearized theory of radiative gas dynamics is applied to the problem of the standing acoustic waves produced inside a closed cylindrical tube by a sinusoidal input of radiation at one end of the tube. The gas in the tube is taken to be perfect, optically grey, and in local thermodynamic equilibrium; the radiative transfer is treated on the basis of the differential approximation. The results of dimensionless, parametric calculations are analyzed in terms of the two types of simultaneous harmonic acoustic waves present in the theory: (1) the modified classical wave and (2) the radiation‐induced wave. For temperatures and pressures attainable in the laboratory, the results show a marked resonance effect from tuning of the tube length with respect to the wavelength of the modified classical wave. The resonance condition exhibits equal levels of pressure and velocity response with marked spatial variation in both quantities. In certain situations the off‐r...

Boundaries, Contingencies and Rigor Thoughts on Mathematics Prompted by a Case Study in Transonic Aerodynamics

A case study in the history of transonic aerodynamics, circa 1950, is used as a basis for reflecting on the character of the distinction between pure and applied mathematics, including the mathematics used by engineers. The case study is set against an historical background of disciplinary confrontation led by such eminent representatives of mathematics and aerodynamics as Garrett Birkhoff and Theodore von Kármán. The successful attempt to construct an adequate account of the aerodynamics of the transonic realm highlighted some sharp differences in the procedures and preferences of mathematical practitioners operating in different fields. The existence and general character of these differences is already widely acknowledged but the task of exploring them from a sociological standpoint still requires much work. The nature of the disciplinary distinctions between different areas of mathematics is examined using Barnes’ theory of (idealized) natural-and social-kind terms (so-called N-and S-predicates). Although the ultimate status of the disciplinary boundaries turns out, uncontroversially, to be ‘conventional’, the attempt to make out and exhibit the conventionality in detail proves to be a non-trivial exercise. It transpires that a thorough study of the issues turns on deep questions about the nature of mathematical rigor and a process that might be called ‘the exploitation of contingency’. These points are illustrated in detail by reference to the technical work of the area (in which one of the authors was an active participant).

Variation--selection in the innovation of the retractable airplane landing gear: the Northrop 'anomaly'

Abstract In the early 1930s, when the retractable landing gear was appearing in airplane design (in retrospect, seemingly inevitably), a series of trim, high-performance craft from the innovative designer John Northrop continued to exhibit a carefully streamlined fixed undercarriage. This, at first sight anomalous, episode, viewed in the context of its time, proves in fact typical of the variation-selection learning process normal in engineering. The results are relevant to evolutionary theories of techno-economic change, with particular regard to how new technologies arise and replace (or do not replace) old technologies.

The Scope for Social Impact in Engineering Outcomes: A Diagrammatic Aid to Analysis

This Note presents ideas, and a resulting diagram, for use in analysis of social impact in the outcomes of engineering design. The diagram shows the degree of technical constraint in a design problem as a function of the independent variables type of design (radical to normal) and level of hierarchy within a systematic device (upper to lower). It is argued that technical constraint is greatest in normal design at the lower levels of hierarchy. On the (plausible) assumption that scope for social impact tends to decrease as technical constraint increases, these ideas have implications for the social study of technology.