Theoretical Investigation of the Influence of Viscous Friction on a Plane Wave of Finite Mplitude in a Compressible Fluid

Owczarek, J. A.

doi:10.1093/qjmam/9.2.143

Cited by 6 publications

(4 citation statements)

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“…Although equation ( 5) is not, in general, amenable to direct integration, several analyses have been given, e.g. Jenny (1950) and Owczarek (1956), in which the heat transfer rate is prescribed independently of the local flow conditions. Skinner (1967) was the first to give a comprehensive analysis of the equation, using the method of characteristics, in which the quasi-steady heat transfer rate is related to the friction coefficient as described above.…”

Section: Analysis Of the Expansion Wave Be Written Asmentioning

confidence: 99%

The influence of wall heat transfer on the expansion following a C-J detonation wave

Edwards

Brown

Hooper

et al. 1970

J. Phys. D: Appl. Phys.

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Numerous investigations have shown that the wave velocity of a self-sustaining detonation is less than the ideal Chapman-Jouguet (C-J) value and that the deficit increases with decreasing tube diameter. Moreover, in small diameter tubes, the pressure gradient in the expansion behind the wavefront is steeper than that predicted by isentropic relations. Estimates of these deviations from ideality by the nozzle model of Fay, based on a viscous boundary-layer displacement, only partly account for the observed values.Numerical integration by Skinner of the non-steady equations of motion of the burned gases, assuming the Reynolds' analogy to hold between friction and heat transfer, shows that a growing region behind the front becomes time-steady as the wave recedes from its plane of origin. This prediction is confirmed in the present work by gas velocity measurements. An approximate solution of the non-steady equation is derived that is valid near the front and which allows a simple criterion to be stated for the attainment of a steady profile.Wall heat transfer measurements are described using platinum resistance gauges coated with silicon monoxide to suppress the effect of ionization. Transfer rate measurements near the wavefront of oxy-hydrogen waves agree well with the calculations of Sichel and David for the situation obtaining near the C-J plane. The value of the friction coefficient derived from the heat transfer data is used to compute the pressure and gas velocity profiles; these profiles are found to be in satisfactory accord with the observational values.

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Section: Analysis Of the Expansion Wave Be Written Asmentioning

confidence: 99%

The influence of wall heat transfer on the expansion following a C-J detonation wave

Edwards

Brown

Hooper

et al. 1970

J. Phys. D: Appl. Phys.

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“…The damping of individual finiteamplitude waves has been investigated experimentally for non-reflecting systems by Owczarek (1956). This work is not applicable to the present problem, however, owing to the absence of reflection and to the high harmonic content of the shock wave ¥~THEMATICAL ANALYSIS employed.…”

Section: The Acoustic Damping Coerficientmentioning

confidence: 99%

“…(7) and (8) T ,.., _ Eo = 0 T P (10) (11) (12) (13) The non-linear term u·1u\ , in Eq. (7) has been linearized by replacing it with the first term of -its Fourie~ series representat)lon, (0.85~) u = a. u, where u is the amplitude of the velocity oscillation.…”

Section: Linearization Of Equationsmentioning

confidence: 99%

Pulsating Gas Flow in Pipes Part I--Damping Coefficients

Converse¹,

Pigford²

1961

Proceedings of Fall Meeting of the Society of Petroleum Engineers of AIME

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“…(7) and (8) T ,.., _ Eo = 0 T P (10) (11) (12) (13) The non-linear term u·1u\ , in Eq. (7) and (8) T ,.., _ Eo = 0 T P (10) (11) (12) (13) The non-linear term u·1u\ , in Eq.…”

Section: Linearization Of Equationsmentioning

confidence: 99%

Pulsating Gas Flow In Pipes Part I -- Damping Coefficients

Converse

Pigford

1961

Fall Meeting of the Society of Petroleum Engineers of AIME

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Publication Rights Reserved This paper is to be presented at the 36th Annual Fall Meeting of the Society of Petroleum Engineers of AIME in Dallas October 8–11, 1961, and is considered the property of the Society of Petroleum Engineers. Permission to publish is hereby restricted to an abstract of not more than 300 words, with no illustrations, unless the paper is specifically released to the press by the Editor of JOURNAL OF PETROLEUM TECHNOLOGY or the Executive Secretary. Such abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in JOURNAL OF PETROLEUM TECHNOLOGY or SOCIETY OF PETROLEUM ENGINEERS JOURNAL is granted on request, providing proper credit is given that publication and the original presentation of the paper. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and considered for publication in one of the two SPE magazines with the paper. Introduction Pulsating flow of a gas in a piping system closely resembles sound transmission. As a result acoustic theory has been used in the design of such systems, e.g. Isakoff (1955), Chilton and Handby (1952), and Murphy (1945). There are, however, two principal differences:the amplitudes of the oscillations in a compressor piping system are likely to be much greater than those in acoustic systems, andthere is a time-average flow of gas through the piping system. This paper is concerned only with the effects resulting from the high (or finite) amplitude oscillations, however. The presence of the finite-amplitude pulsations has two effects: first, the flow regime becomes at least partially turbulent rather than laminar; and, second, the dependent variables, such as pressure, density, velocity, and temperature, can not always be considered to be related to each other in a linear manner. Hence, the waveform of the resulting pulsation can be quite different from that of the impressed disturbance. This paper is thus divided into two parts. Part I deals with wave damping; the studies of waveform change are reported in Part II. THEORY OF PULSATION DAMPING Definition of the Damping Coefficient As is shown below, the linearized solution to the differential equations which represent the gas oscillations, is of the form (1) where the symbol "Re" means the real part of what follows. (Other nomenclature used is listed at the end of the paper.) The damping coefficient, , is of particular interest because as the real part of the exponential dependence on distance, it sets the rate of decay of a wave as it progresses down the pipe; if wave reflection occurs at the open or closed end of a pipe, sets the amplitude of the standing wave. The principal aim of Part I of this paper is to find a way of predicting from fluid mechanical principles. The Acoustic Damping Coefficient Consider transmission of sound in a tube, the wave length being much greater than the tube's radius. The fluid motion is damped, primarily owing to heat and momentum exchange with the pipe wall. Kirchhoff (1868) developed the expression for the damping factor which results from the consideration of these effects in the limit of small amplitude. It was given by Rayleigh (1945) and by Weston (1953). (2) It is important to note that, according to the above expression, is dependent on the frequency, , but is independent of the wave amplitude. Damping of Waves of Finite Amplitude Lebmann (1934) and Fredericksen (1954) have previously measured damping coefficients for finite amplitude waves. They found to be much greater than indicated by Eq. (2).

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Theoretical Investigation of the Influence of Viscous Friction on a Plane Wave of Finite Mplitude in a Compressible Fluid

Cited by 6 publications

References 0 publications

The influence of wall heat transfer on the expansion following a C-J detonation wave

The influence of wall heat transfer on the expansion following a C-J detonation wave

Pulsating Gas Flow in Pipes Part I--Damping Coefficients

Pulsating Gas Flow In Pipes Part I -- Damping Coefficients

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