scholarly journals Numerical solutions for transonic flow

1949 ◽  
Vol 196 (1044) ◽  
pp. 32-36 ◽  
Keyword(s):  
Mach Number ◽  
Exact Solutions ◽  
Compressible Fluid ◽  
Transonic Flow ◽  
Numerical Solutions ◽  
Free Stream ◽  
Two Dimensional ◽  
Transverse Axis ◽  
Two Dimensional Flow ◽  
Free Stream Mach Number

In a previous paper (Cherry 1947), the author has established a family of exact solutions for steady two-dimensional flow of a compressible fluid past a cylinder; the final formulae are given in theorem 6, equations (5.17) to (5.21). These formulae have now been evaluated (taking γ = 1.405) for the value T 1 = 0.05, corresponding to a free-stream Mach number of 0.510, and the streamlines are shown in figure 1. The cylindrical obstacle has a thickness ratio 0.93, but is markedly different from an ellipse, being almost exactly circular over its up- and downstream quadrants. The Mach number a t the ends of its transverse axis is 1.39. The flow is everywhere regular, but a small increase in the free-stream Mach number would be critical; a shock-line would begin to appear near the points on the surface where the tangent is inclined at about 25 or 30° to the direction of the free-stream.

A note on turbulent shear-layer reattachment downstream of a backward-facing step in confined supersonic two-dimensional flow

1971 ◽  
Vol 46 (2) ◽  
pp. 293-297 ◽  
Author(s):  
T. Mukerjee ◽  
A. Farshi ◽  
B. W. Martin
Keyword(s):  
Free Stream ◽  
Supersonic Jet ◽  
Surface Flow ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Flow Measurements ◽  
Turbulent Shear Layer ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Free Stream Mach Number

The reattachment of a supersonic jet with a turbulent separating boundary layer abruptly expanding into a two-dimensional parallel diffuser has been experimentally investigated using a surface-flow technique. The reattachment criterion proposed by Mukerjee & Martin (1969) for axisymmetric confined and unconfined flows is found to correlate equally well similar two-dimensional flow measurements in terms of the free-stream Mach number after separation.

scholarly journals Two-dimensional compressible viscous flow around a circular cylinder

2015 ◽  
Vol 785 ◽  
pp. 349-371 ◽  
Author(s):  
Daniel Canuto ◽  
Kunihiko Taira
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Mach Number ◽  
Critical Reynolds Number ◽  
Free Stream ◽  
Critical Value ◽  
Dominant Frequency ◽  
Two Dimensional ◽  
Free Stream Mach Number ◽  
Compressibility Effects

Direct numerical simulation is performed to study compressible viscous flow around a circular cylinder. The present study considers two-dimensional shock-free continuum flow by varying the Reynolds number between 20 and 100 and the free-stream Mach number between 0 and 0.5. The results indicate that compressibility effects elongate the near wake for cases above and below the critical Reynolds number for two-dimensional flow under shedding. The wake elongation becomes more pronounced as the Reynolds number approaches this critical value. Moreover, we determine the growth rate and frequency of linear instability for cases above the critical Reynolds number. From the analysis, it is observed that the frequency of the Bénard–von Kármán vortex street in the time-periodic fully saturated flow increases from the dominant unstable frequency found from the linear stability analysis as the Reynolds number increases from its critical value, even for the low range of Reynolds numbers considered. We also find that the compressibility effects reduce the growth rate and dominant frequency in the linear growth stage. Semi-empirical functional relationships for the growth rate and the dominant frequency in linearized flow around the cylinder in terms of the Reynolds number and free-stream Mach number are presented.

scholarly journals Flow of a compressible fluid about a cylinder

1947 ◽  
Vol 192 (1028) ◽  
pp. 45-79 ◽  
Keyword(s):  
Exact Solutions ◽  
Perfect Fluid ◽  
Compressible Fluid ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
The Family ◽  
Two Dimensional Flow ◽  
Infinite Set

In this paper, a family of exact* solutions is found for the two-dimensional flow of a compressible perfect fluid about a cylinder. The present work is restricted to the case where the circulation is zero and the speed at large distances from the cylinder is subsonic; but there is no restriction that the speed near the cylinder be subsonic. In a later paper I hope to remove these restrictions, which are not essential to the theory. The family of solutions involves an infinite set of constants, upon the values of which depends the shape of the cylinder; but the question of so disposing these constants as to suit a prescribed shape is not here entered upon.

On solutions of the compressible laminar boundary-layer equations and their behaviour near separation

1977 ◽  
Vol 80 (2) ◽  
pp. 279-292 ◽  
Author(s):  
T. Davies ◽  
G. Walker
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mach Number ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Free Stream ◽  
Suction Velocity ◽  
Boundary Layer Equations ◽  
Free Stream Mach Number

A numerical solution of the two-dimensional compressible laminar boundary-layer equations up to the point of separation is presented. For a particular mainstream velocity distribution it is necessary to specify the surface temperature (or the heat flux across the surface), the suction velocity, the free-stream Mach number and the viscosity-temperature relationship for a solution to be generated. The effect upon the position of separation of a hot or cold wall and of varying the free-stream Mach number is given special emphasis. The variations of the skin friction, heat transfer and various boundary-layer thicknesses for compressible flow past a circular cylinder and for flow with a linearly retarded mainstream were found. The behaviour of the solutions close to separation is investigated. Known functions which model the skin friction and heat transfer are introduced and are used to match the numerical solutions with the Buckmaster (1970) expansions.

Spin-up from rest of a compressible fluid in a rapidly rotating cylinder

1992 ◽  
Vol 237 ◽  
pp. 413-434 ◽  
Author(s):  
Jae Min Hyun ◽  
Jun Sang Park
Keyword(s):  
Mach Number ◽  
Compressible Fluid ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Axial Direction ◽  
Ekman Layer ◽  
Infinite Cylinder ◽  
Full Time ◽  
Viscous Effects ◽  
Initial State

Spin-up flows of a compressible gas in a finite, closed cylinder from an initial state of rest are studied, The flow is characterized by small reference Ekman numbers, and the peripheral Mach number is O(1). Comprehensive numerical solutions have been obtained for the full, time-dependent compressible Navier-Stokes equations. The details of the flow, temperature, and density evolution are described. In the early phase of spin-up, owing to the thermoacoustic disturbances caused by the compressible Rayleigh effect, the flows are oscillatory, and this oscillatory behaviour is pronounced at higher Mach numbers. The principal dynamical role of the Ekman layer is dominant over moderate times of orders of the homogeneous spin-up timescales. Owing to the density stratification in the radial direction, the Ekman layer is thicker in the central region of the interior. The interior azimuthal flows are mainly uniform in the axial direction. As the Mach number increases, the rate of spin-up in the interior becomes slower, and the propagating shear front is more diffusive. Explicit comparisons with the results for an infinite cylinder are made to ascertain the contributions of the endwall disks. In contrast to the usual incompressible spin-up from rest, the viscous effects are relatively more important for the case of a compressible fluid.

Direct numerical simulation of flow past a transversely rotating sphere up to a Reynolds number of 300 in compressible flow

2018 ◽  
Vol 857 ◽  
pp. 878-906 ◽  
Author(s):  
T. Nagata ◽  
T. Nonomura ◽  
S. Takahashi ◽  
Y. Mizuno ◽  
K. Fukuda
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Drag Coefficient ◽  
Rotation Rate ◽  
Free Stream ◽  
Rotating Sphere ◽  
Free Stream Mach Number ◽  
Low Reynolds

In this study, direct numerical simulation of the flow around a rotating sphere at high Mach and low Reynolds numbers is conducted to investigate the effects of rotation rate and Mach number upon aerodynamic force coefficients and wake structures. The simulation is carried out by solving the three-dimensional compressible Navier–Stokes equations. A free-stream Reynolds number (based on the free-stream velocity, density and viscosity coefficient and the diameter of the sphere) is set to be between 100 and 300, the free-stream Mach number is set to be between 0.2 and 2.0, and the dimensionless rotation rate defined by the ratio of the free-stream and surface velocities above the equator is set between 0.0 and 1.0. Thus, we have clarified the following points: (1) as free-stream Mach number increased, the increment of the lift coefficient due to rotation was reduced; (2) under subsonic conditions, the drag coefficient increased with increase of the rotation rate, whereas under supersonic conditions, the increment of the drag coefficient was reduced with increasing Mach number; and (3) the mode of the wake structure becomes low-Reynolds-number-like as the Mach number is increased.

scholarly journals Звуковой удар от тонкого тела и локальных областей нагрева сверхзвукового набегающего потока

2021 ◽  
Vol 91 (4) ◽  
pp. 558
Author(s):  
А.В. Потапкин ◽  
Д.Ю. Москвичев
Keyword(s):  
Mach Number ◽  
Supersonic Flow ◽  
Free Stream ◽  
Local Heating ◽  
Air Flow ◽  
Sonic Boom ◽  
Incoming Flow ◽  
Combined Method ◽  
Cold Flow ◽  
Free Stream Mach Number

The problem of a sonic boom generated by a slender body and local regions of supersonic flow heating is solved numerically. The free-stream Mach number of the air flow is 2. The calculations are performed by a combined method of phantom bodies. The results show that local heating of the incoming flow can ensure sonic boom mitigation. The sonic boom level depends on the number of local regions of incoming flow heating. One region of flow heating can reduce the sonic boom by 20% as compared to the sonic boom level in the cold flow. Moreover, consecutive heating of the incoming flow in two regions provides sonic boom reduction by more than 30%.

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