Hypersonic weak-interaction solutions for flow past a very slender axisymmetric body

1969 ◽  
Vol 38 (3) ◽  
pp. 547-564 ◽  
Author(s):  
Arthur K. Cross ◽  
William B. Bush
Keyword(s):  
Weak Interaction ◽  
Free Stream ◽  
Axisymmetric Body ◽  
Absolute Temperature ◽  
The Body ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Order Unity ◽  
Specific Heats ◽  
Viscous Heat

The Navier–Stokes hypersonic weak-interaction theory is presented for the flow of a viscous, heat-conducting, compressible fluid past a very slender axisymmetric body, when the ratio of the radius of the body to the radial thickness of the viscous region, produced and supported by the body, is much less than unity. The fluid is assumed to be a perfect gas having constant specific heats, a constant Prandtl number of order unity, and viscosity coefficients varying as a power of the absolute temperature. Solutions are studied for the free-stream Mach number, the free-stream Reynolds number based on the axial length of the body, and the reciprocal of the weak-interaction parameter much greater than unity.It is shown that, for the viscosity-temperature exponent ω less than 1, seven distinct layers span the region between the shock wave and the body, which is of arbitrary shape. The leading approximations for the behaviour of the flow in these seven layers are analyzed, and the restrictions imposed on the theory are obtained.

Hypersonic weak-interaction similarity solutions for flow past a flat plate

1967 ◽  
Vol 29 (2) ◽  
pp. 349-359 ◽  
Author(s):  
William B. Bush ◽  
Arthur K. Cross
Keyword(s):  
Flat Plate ◽  
Weak Interaction ◽  
Free Stream ◽  
Stokes Equations ◽  
Viscosity Coefficient ◽  
Similarity Solutions ◽  
Absolute Temperature ◽  
Heat Conducting ◽  
Order Unity ◽  
Specific Heats

The hypersonic weak-interaction regime for the flow of a viscous, heat-conducting compressible fluid past a flat plate is analysed using the Navier-Stokes equations as a basis. The fluid is assumed to be a perfect gas having constant specific heats, a constant Prandtl number, σ, of order unity, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied for the free-stream Mach number,M, the free-stream Reynolds number (based on the plate length),RL, and the reciprocal of the weak-interaction parameter, (ξ*)−1= [Fscr ](M,RL, ω, σ), greater than order unity.By means of matched asymptotic expansions, it is shown that, for (1 − ω) > 0, the zone between the shock wave and the plate is composed of four distinct regions for which similarity exists. The behaviour of the flow in these four regions is analysed.

scholarly journals On the viscous hypersonic blunt body problem

1964 ◽  
Vol 20 (3) ◽  
pp. 353-367 ◽  
Author(s):  
William B. Bush
Keyword(s):  
Blunt Body ◽  
Free Stream ◽  
Stokes Equations ◽  
Viscosity Coefficient ◽  
Absolute Temperature ◽  
The Body ◽  
Navier Stokes ◽  
Nose Radius ◽  
Navier Stokes Equations ◽  
Specific Heats

The viscous hypersonic flow past an axisymmetric blunt body is analysed based upon the Navier-Stokes equations. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number, P, whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach number, M, and the free-stream Reynolds number based on the body nose radius, R, go to infinity, and ε = (γ − 1)/(γ + 1), where γ is the ratio of the specific heats, and δ = 1/(γ − 1) M2 go to zero.

Hypersonic strong-interaction similarity solutions for flow past a flat plate

1966 ◽  
Vol 25 (1) ◽  
pp. 51-64 ◽  
Author(s):  
William B. Bush
Keyword(s):  
Flat Plate ◽  
Strong Interaction ◽  
Free Stream ◽  
Stokes Equations ◽  
Viscosity Coefficient ◽  
Similarity Solutions ◽  
Absolute Temperature ◽  
Heat Conducting ◽  
Specific Heats ◽  
Plate Length

The hypersonic strong-interaction regime for the flow of a viscous, heat-conducting compressible fluid past a flat plate is analysed using the Navier–Stokes equations as a basis. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number σ, whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach numberM, the free-stream Reynolds number based on the plate lengthRL, and the interaction parameterx= {(γM2)2+ω/RL}½, go to infinity.Through the use of asymptotic expansions and matching, it is shown that, for (1−ω) > 0, three distinct layers for which similarity exists make up the region between the shock wave and the plate. The behaviour of the flow in these three layers is analysed.

scholarly journals NUMERICAL CALCULATION OF CONVECTIVE FLOW OF GAS AT CIRCULAR-TYPE SCHEME OF HEATING

2015 ◽  
pp. 87-93
Author(s):  
E. M. Sorokina ◽  
A. G. Obukhov
Keyword(s):  
Convective Flow ◽  
Stokes Equations ◽  
Complete System ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Boundary Condi Tions ◽  
Navier Stokes Equations ◽  
Viscous Heat ◽  
Condi Tions

To investigate the convective flows of polytropic gas a complete system of Navier - Stokes equations is consid-ered. As the initial and boundary conditions the specific ratios are offered. The proposed initial and boundary condi-tions realization is carried out at construction of the numerical solution of the complete system of Navier - Stokes equations for modeling the unsteady state three-dimensional convection flows of the compressible viscous heat-conducting gas in the isolated cubic area. Three components of the velocity vector are calculated for the initial stage of the convective flow. It is shown that the velocity components are complex and depend essentially on the heating shape, height and time.

On the formation of weak plane shock waves by impulsive motion of a piston

1966 ◽  
Vol 25 (4) ◽  
pp. 705-718 ◽  
Author(s):  
John P. Moran ◽  
S. F. Shen
Keyword(s):  
Large Time ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Plane Shock ◽  
Heat Conducting ◽  
Piston Problem ◽  
Navier Stokes Equations ◽  
Viscous Heat ◽  
Equation Boundary ◽  
Weak Plane

The piston problem for a viscous heat-conducting gas is studied under the assumption that the piston Mach number ε is small. The linearized Navier–Stokes equations are found to be valid up to times of the order of ε−2mean free times after the piston is set in motion, while at large times the solution is governed by Burgers's equation. Boundary conditions for the large-time solution are supplied by the matching principle of the method of inner and outer expansions, which is also used to construct a composite solution valid both for small and for large times.

scholarly journals Decay rate of generalized solutions for equations of a viscous heat-conducting gas

2021 ◽  
Author(s):  
Zhilei Liang
Keyword(s):  
Large Time ◽  
Stokes Equations ◽  
Large Time Behavior ◽  
Ideal Gas ◽  
Generalized Solutions ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Time Behavior ◽  
Navier Stokes Equations ◽  
Viscous Heat

The large time behavior is considered for the solutions of the Navier-Stokes equations for one-dimensional viscous polytropic ideal gas in unbounded domains. Using the local anti-derivatives functions technique, we obtain the power type decay estimates for the generalized solutions as time goes to infinity

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