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Fluid Dynamics

, Volume 1, Issue 5, pp 73–76 | Cite as

Laminar boundary layer in an equilibrium dissociated gas for arbitrary external velocity distribution

  • N. V. Krivtsova
Article
  • 19 Downloads

Abstract

The development of machine computing technology permits calculating the boundary layer by direct numerical integration of the corresponding system of partial differential equations [1, 2]. In order to derive general conclusions concerning the boundary layer with a pressure gradient we must perform the integration for each concrete form of velocity specification at the outer edge of the boundary layer.

The method of calculating the boundary layer used in the present study [3], based on the solution of a universal (independent of the specification of the velocity at the outer edge of the boundary layer) system of equations, permits the clarification of several general relationships.

Keywords

Differential Equation Boundary Layer Partial Differential Equation Pressure Gradient Velocity Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notation

x, y

longitudinal and transverse coordinates

s, ξ

longitudinal and transverse coordinates in the plane of the transformed variables

u

longitudinal velocity component

r

radius of the body of revolution

ψ

stream function

P

Prandtl number

L

Lewis Number

N

Nusselt number

ρ,μ, λ

density, dynamic viscosity, and thermal conductivity

cp

gas specific heat at constant pressure

υ

kinematic viscosity

h

enthalpy

h1

enthalpy in the external flow

T

temperature

Φ

reduced stream function

h∘

dimensionless enthalpy

g

dimensionless total enthalpy

B

normalizing constant

ϰ

local compressibility parameter

Δ*, Δ**

displacement thickness and momentum thickness in the plane of the new variables

δ*, δ**

displacement thickness and momentum thickness in the physical plane

f

form parameter

f

form parameter at the separation point

f+

form parameter at the “frontal point”

M

Mach number

ζ

“reduced” friction

ζ*

“reduced” thermal flux

Cf

local friction coefficient

The subscript

w

applies to values of the parameters at the wall

e

applies to the outer edge of the boundary layer

0

applies to the initial section of the layer

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References

  1. 1.
    I. Yu. Brailovskaya and L. A. Chudov, “Solution of boundary layer equations by a difference method”, collection: Computational Methods and Programming [in Russian], Izd. Mosk. un-ta, no. 1, 1962.Google Scholar
  2. 2.
    V. M. Paskonov, “Standard program for solving boundary layer problems”, collection: Numerical Methods in Gasdynamics [in Russian], Izd. Mosk. un-ta, no. 2, 1963.Google Scholar
  3. 3.
    L. G. Loitsyanskii, “Universal equations and parametric approximations in laminar boundary layer theory”, PMM, vol. 29, no. 1, 1965.Google Scholar
  4. 4.
    N. V. Krivtsova, “A Parametric method of solving laminar boundary layer equations with longitudinal pressure gradient in an equilibrium dissociated gas”, Inzh.-fiz. zh. [Journal of Engineering Physics], vol. 10, no. 2, 1966.Google Scholar
  5. .5.
    L. G. Loitsyanskii, The Laminar Boundary Layer [in Russian], Fizmatgiz, 1962.Google Scholar
  6. 6.
    L. M. Simuni and N. M. Terent'ev, “Numerical solution of the equations of “single-parameter” boundary layer theory”, Tr. Leningr. politekhn. in-ta, Tekhnicheskaya gidromekhanika, no. 248, 1965.Google Scholar
  7. 7.
    S. K. Godunov and V. S. Ryaben'kii, Introduction to the Theory of Difference Schemes [in Russian], Fizmatgiz, 1962.Google Scholar
  8. 8.
    W. D. Hayes and R. F. Probstein, Hypersonic Flow Theory [Russian translation], Izd. inostr. lit., 1959.Google Scholar

Copyright information

© The Faraday Press, Inc. 1966

Authors and Affiliations

  • N. V. Krivtsova
    • 1
  1. 1.Leningrad

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