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Conical nozzle flow of a viscous compressible gas with energy extraction

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Summary

A study is made of source type diabatic (nonadiabatic) flow of a viscous, heat conducting perfect gas in a conical nozzle. For such a flow a class of exact solutions to the Navier-Stokes equations is possible provided the transport properties vary as the n-th power of the absolute temperature. It is found that for a given wall angle, wall temperature, and internal heat source (sink) strength, solutions of this type are possible only for certain combinations of centerline Mach number, Reynolds number, ratio of specific heats, and Prandtl number. Some examples of calculated velocity and temperature profiles are presented for the special case where the viscosity and thermal conductivity vary as the square root of the absolute temperature.

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Abbreviations

a, b, c, d, e :

constant exponents

C f :

skin friction coefficient

c p :

specific heat at constant pressure

E :

energy flux in the radial direction

f :

dimensionless velocity

F :

velocity ratio

g :

dimensionless temperature

G :

temperature ratio

h :

dimensionless pressure

k :

thermal conductivity

l :

dimensionless heat source (sink) strength

m :

dimensionless density

M :

Mach number

p :

pressure

Pr :

Prandtl number

LEIGH :

heat source (sink) parameter

r :

radial distance

Re :

Reynolds number

R :

gas constant

T :

temperature

u :

radial component of velocity

γ :

ratio of specific heats

θ :

angular coordinate

μ :

viscosity coefficient

ρ :

density

c:

centerline condition

O:

reference condition

s:

stagnation or total condition

w:

wall conditions

References

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Authors and Affiliations

  1. Dept. of Mechanical and Aerospace Eng., North Carolina State University, Raleigh, N.C., USA

    James C. Williams III

Authors
  1. James C. Williams III
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Williams, J.C. Conical nozzle flow of a viscous compressible gas with energy extraction. Appl. Sci. Res. 19, 285–301 (1968). https://doi.org/10.1007/BF00383928

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  • DOI: https://doi.org/10.1007/BF00383928

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