On the characterization of fields of diabatic flow

Hicks, Bruce L.

doi:10.1090/qam/27662

Cited by 12 publications

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“…An inverse method which differed from that of Starr's was presented by Hicks [22] where the introduction of a potential function allowed the retention of some control over the heat sources. This inverse method consisted of calculating the flow properties from prior knowledge of a flow pattern satisfying a governing potential equation.…”

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“…This inverse method consisted of calculating the flow properties from prior knowledge of a flow pattern satisfying a governing potential equation. To investigate specific questions arising as a result of an earlier paper [23] where the governing equations were expressed alternately in terms of velocity, Mach, and Crocco vectors, Hicks [22] utilized an initially arbitrary vector N, parallel to the velocity vector. A wide variety of diabatic irrotational N flows (rotational velocity vector) was suggested in discussions of the choice of two arbitrary functions which were defined to give the "form" and "character" of the irrotational flows.…”

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“…It was demonstrated that the governing potential equation for these diabatic flows could remain of fixed type (elliptic for example) for all values of the local Mach number. Later [14], a linearization transformation due to Dimsdale was presented. The linearization transformation was completed [24,25], and the results were used to calculate exactly some simple diabatic flow fields not previously considered.…”

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“…An advantage of Hicks' inverse method [22], where the governing equations were expressed in terms of an irrotational vector parallel to the velocity vector, is that the velocity field is allowed to have restricted rotationality.…”

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Characterization and calculation of steady, compressible, diabatic flow fields

Chenoweth¹

1964

Quart. Appl. Math.

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Several physical and chemical phenomena invalidate the assumption of adiabatic flow in many compressible flow problems. When such processes are included in the mathematical model, the difficulties of calculation usually mask the important non-adiabatic nature of the flow. Hence, the effects of the variation of total temperature along the streamlines is often studied without direct reference to the mechanisms responsible for this behavior. These inviscid, non-conducting, steady flows with energy addition by heat sources are termed "diabatic" and correspond to heating processes which are thermodynamically reversible. The results from diabatic flow studies provide the basic insight into heat addition effects which is necessary before investigating more complicated problems where such phenomena as viscosity, conduction, diffusion, changes in gas composition, and electromagnetic effects are considered. Some fluid dynamics problems related to combustion processes and involving changes in total temperature were first formulated correctly in the independent work of Chapman [1] and Jouguet [2] at the early part of this century. In a later paper, with application to meteorology, Kiebel [3] gave a complete classification of viscous, compressible flow with energy addition into thirteen dynamically permissible categories. In spite of the early recognition of the importance of heating effects, the discipline of diabatic flow has essentially been developed since 1944. Only a few representative papers and those which are necessary to place this work in proper perspective with respect to past investigations will be discussed here, but a more complete summary of the existing literature on diabatic flow can be found elsewhere [4]. Compressible flow textbooks usually present only the fundamentals of one-dimensional "simple-heating", although Tsien [5] and Krzywoblocki [6] present discussions of some of the more general aspects of diabatic flow. Most of the basic ideas about the effects of heat addition on the flow properties, the behavior of the streamlines at the sonic condition, and the phenomenon of thermal choking were obtained from the early one-dimensional studies [7, 8, 9, 10]. It was established [11, 12, 13, 14] that the effects of localized heat sources are much like those of fluid sources. Such ideas led to the patent *

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Characterization and calculation of steady, compressible, diabatic flow fields

Chenoweth¹

1964

Quart. Appl. Math.

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“…The hot-wire bridge was found to need no compensation for time lag in the frequency range of 0-200 cps and could be used without any amplifiers. (2) MEASUREMENT OF DOWNWASH IN A KARMAN VORTEX STREET As a first application of the zig-zag hot wire, it was used to measure average streamwise flux of lateral momentum in the wake behind a cylinder.…”

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An Exact Calculation of Some Steady, Diabatic, Two-Dimensional Fields of Compressible Flow

Hicks

1960

Journal of the Aerospace Sciences

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HOT WIRE SCHEMATIC N where the (rotational) velocity vector V = N[g(N)RT} lh ; R and T are the gas constant and the absolute temperature, respectively; N = | N |; and the scalar g(N) is a function of N only. 1 We describe the rate of heat addition by a coefficientwhere Q is the heat added to the flow per unit mass and time, and q$ is, at the outset, an unknown function of position. We further characterize the types of flows considered here by a series of three restrictions. Restriction 1. The partial differential equation satisfied by 4> N is of the elliptic type with determinant identically equal to one. Then, g(N) = 2(1 -N 2 )~1.In this case, an exact transformation on the dependent variable cf> N -*• i, suggested by Dr. Bernard Dimsdale, 2 leads to the linear differential equation

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Fundamental Equations of the Dynamics of a Compressible Inviscid, Non-Heat-Conducting and Radiating Fluid
Pai¹,
Luo²
1991
Theoretical and Computational Dynamics of a Compressible Flow
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On the characterization of fields of diabatic flow

Cited by 12 publications

References 4 publications

Characterization and calculation of steady, compressible, diabatic flow fields

Characterization and calculation of steady, compressible, diabatic flow fields

An Exact Calculation of Some Steady, Diabatic, Two-Dimensional Fields of Compressible Flow

Fundamental Equations of the Dynamics of a Compressible Inviscid, Non-Heat-Conducting and Radiating Fluid

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