Summary
A numerical analysis has been performed to investigate turbulent compressible flow over a hemisphere-cylinder body at zero incidence in the Mach number range of 0.8–2.0. The numerical code solves the Navier-Stokes equations using finite volume technique in conjunction with multistage Runge-Kutta time-stepping method. Comparisons have been made with the available experimental data such as shadowgraph pictures, shock stand-off distance, shock position and surface pressure distribution. They are found in good agreement. A separated flow on the hemisphere-cylinder junction is noticed between Mach numbers 0.8 and 0.9. It is observed from the velocity vector plots that the flow appears to become parallel to the body in the vicinity of the stagnation point of the hemisphere at supersonic Mach number.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- C P :
-
pressure coefficient
- C P :
-
specific heat at constant pressure
- e :
-
total energy per unit mass
- F, G, H :
-
flux vectors
- i, j :
-
unit vectors in (x, r) directions
- M:
-
Mach number
- n :
-
unit normal vector
- Pr:
-
Prandtl number
- Q :
-
flux tensor
- q :
-
heat flux vector
- R :
-
cylinder radius
- T :
-
temperature
- t :
-
time
- u, v :
-
velocity components in (x, r) directions
- W :
-
vector of conserved variables
- x, r :
-
coordinate directions
- Δ:
-
shock stand-off distance
- γ:
-
ratio of specific heats
- μ:
-
viscosity
- ϱ:
-
density
- σ:
-
stress tensor
- t :
-
turbulent
- w :
-
wall
- ∞:
-
freestream condition
References
Hsieh, T.: Flow field study about a hemispherical cylinder in transonic and low supersonic Mach number range. AIAA paper 75-83 (1975).
Hsieh, T.: Hemisphere-cylinder in transonic flow,M ∞=0.7–1.0. AIAA J.13, 1411–1413 (1975).
Baldwin, B. S., Lomax, H.: Thin layer approximation and algebraic model for separated turbulent flow. AIAA paper 78-257 (1978).
Jamesons, A., Schmidt, W., Turkel, E.: Numerical solution of Euler equations by finite volume methods using Runge-Kutta time stepping schemes. AIAA paper 81-1259 (1981).
Shang, J. S.: Numerical simulation of wing-fuselage interference. AIAA paper 81-0048 (1981).
Doerffer, P., Zierep, J.: An experimental investigation of the Reynolds number effect on a normal shock wave-turbulent boundary layer interaction on a curved wall. Acta Mech.73, 77–73 (1988).
Ramm, H. J.: Fluid dynamics for the study of transonic flow, pp. 152–154. New York: Oxford University Press 1990.
Frank, W., Zierep, J.: Schallnahe Überschallströmung um rotationssymmetrische Körper. Acta Mech.19, 277–287 (1974).
Stilp, A.: Strömungsuntersuchungen an Kugeln mit transonischen und supersonischen Geschwindigkeiten in Luft und Frigen-Luftgemischen. Bericht Nr. 10.65, Eckerstrasse 4, Germany (1965).
Van Dyke, M. D., Gordon, H. D.: Supersonic flow past a family of blunt-axisymmetric bodies. NASA TR-R 1 (1959).
Heberle, J. W., Wood, G. P., Gooderum, P. B.: Data on shape and location of detached shock waves on cones and spheres. NACA TN 2000 (1958).
Holder, D. W., Chinneck, A.: The flow past elliptic-nosed cylinder and bodies of revolution in supersonic air stream. Aeronaut. Q.4, 317–340 (1954).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mehta, R.C. Numerical investigation of viscous flow over a hemisphere-cylinder. Acta Mechanica 128, 49–58 (1998). https://doi.org/10.1007/BF01463159
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01463159