Simple Formulae for Supersonic Flow past a Cone

1975 ◽  
Vol 26 (1) ◽  
pp. 11-19 ◽  
Author(s):  
W H Hui
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Surface Pressure ◽  
Simple Formula ◽  
Pressure Coefficient ◽  
Circular Cone ◽  
Number Range ◽  
Thin Shock Layer ◽  
Cone Vertex

SummaryThe problem of the supersonic flow with attached shock wave past a circular cone at zero angles of attack is treated, using the thin-shock-layer expansion. The solution is calculated to the fourth approximation. A simple formula is then derived for the surface pressure coefficient by the application of the parameter-straining technique and it is shown to be very accurate for the whole Mach number range for which the shock remains attached to the cone vertex.

Higher-Order Solutions for Unsteady Hypersonic and Supersonic Flow

1974 ◽  
Vol 25 (1) ◽  
pp. 59-68 ◽  
Author(s):  
W H Hui ◽  
J Hamilton
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Power Series ◽  
Unsteady Flow ◽  
The Body ◽  
Wedge Flow ◽  
First Order ◽  
Order Solution ◽  
Method Of Solution

SummaryThe problem of unsteady hypersonic and supersonic flow with attached shock wave past wedge-like bodies is studied, using as a basis the assumption that the unsteady flow is a small perturbation from a steady uniform wedge flow. It is formulated in the most general case and applicable for any motion or deformation of the body. A method of solution to the perturbation equations is given by expanding the flow quantities in power series in M−2, M being the Mach number of the steady wedge flow. It is shown how solutions of successive orders in the series may be calculated. In particular, the second-order solution is given and shown to give improvements uniformly over the first-order solution.

XXVII.—The Rotational Field behind a Bow Shock Wave in Axially Symmetric Flow using Relaxation Methods

1952 ◽  
Vol 63 (4) ◽  
pp. 371-380
Author(s):  
A. R. Mitchell ◽  
Francis McCall
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Bow Shock ◽  
Axially Symmetric ◽  
Relaxation Methods ◽  
Bow Shock Wave ◽  
Constant Vorticity ◽  
Complete Field ◽  
Rotational Field

SynopsisThe relaxation technique of R. V. Southwell is developed to evaluate mixed subsonic-supersonic flow regions with axial symmetry, changes of entropy being taken into account. In the problem of a parallel supersonic flow of Mach number I·8 impinging on a blunt-nosed axially symmetric obstacle, the new technique is used to determine the complete field downstream of the bow shock wave formed. Lines of constant vorticity and Mach number are shown in the field, and where possible a comparison is made with the corresponding 2-dimensional problem.

Iterative Solutions of the Equations Jor Plane Oblique Shock Waves

1959 ◽  
Vol 63 (587) ◽  
pp. 669-672 ◽  
Author(s):  
A. R. Collar
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Free Stream ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Two Dimensional ◽  
Iterative Solutions ◽  
Flow Through ◽  
Image Position

If a plane oblique shock wave, inclined to the free stream at the angle ε, is produced in two-dimensional supersonic flow of Mach number M by (for example) a wedge which deflects the flow through an angle δ, the equation connecting these quantities may be writtenIn this form, δ is given explicitly when M, ε are fixed. Similarly, we may obtain M explicitly when ε, δ are fixed; equation (1) may be written (see, for example, Liepmann and Puckett, Equation 4.27)

The perturbed region behind a diffracting shock wave

1967 ◽  
Vol 29 (4) ◽  
pp. 705-719 ◽  
Author(s):  
B. W. Skews
Keyword(s):  
Shock Wave ◽  
Experimental Study ◽  
Mach Number ◽  
Shock Waves ◽  
Contact Surface ◽  
Fair Agreement ◽  
Number Range ◽  
Corner Angle ◽  
Theoretical Predictions

The results of an experimental study of the diffraction of shock waves on plane-walled convex corners are given for a Mach number range from 1·0 to 5·0. The behaviour of the disturbances produced in the region perturbed by the corner are discussed. It is shown that the position of the slipstream and tail of the Prandtl-Meyer fan, and the velocities of the contact surface and second shock become independent of corner angle for angles greater than 75°. Comparisons with theoretical predictions of Jones, Martin & Thornhill (1951) and Parks (1952) are included. In most cases fair agreement is obtained.

scholarly journals High subsonic flow of an organic vapor past a circular cylinder

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Felix Reinker ◽  
Robert Wagner ◽  
Leander Hake ◽  
Stefan aus der Wiesche
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Wind Tunnel ◽  
Circular Cylinder ◽  
Drag Coefficient ◽  
Surface Pressure ◽  
Subsonic Flow ◽  
Ideal Gas ◽  
Organic Vapor ◽  
Surface Pressure Distribution

AbstractA circular cylinder was tested in the cross-flow of an organic vapor (Novec™ 649) and of air over the subsonic (M < 0.4) and high subsonic (0.4 < M < 0.8) speed range in a continuously running pressurized closed-loop wind tunnel test facility. Time-averaged pressure measurements gave information on surface pressure distributions, and the corresponding drag and base pressure drag coefficients were obtained. Due to the charging of the wind tunnel, different values of the compressibility factor (0.876 < Z < 0.999) could be achieved for the organic vapor flow. This enabled in combination with the results for air an assessment of the impact of non-ideal gas dynamics on the form drag of a cylinder in the considered highly subsonic flow regime. The new experimental data were compared with available literature results. Changes in surface pressure distribution at higher subsonic velocities were identified and discussed. It was found that non-ideal gas effects did not strongly affect the overall drag. The variation of drag coefficient over the Mach number range was comparable with literature data for ideal-gas compressible flow, including shock-less and intermittent shock wave, and permanent shock wave flows regimes. At Mach 0.4, the flow of Novec™ 649 was in the shock-less regime and exhibited a pronounced dependency on the Reynolds number. An increase in drag was observed at Mach 0.6 which was attributed to the commencement of vortex shedding. Non-ideal thermodynamics only affected the flow locally and a reduction of the critical pressure coefficient in the high subsonic flow regime was observed in the surface pressure distribution. However, this mechanism did not alter significantly the overall drag behavior. Graphic abstract Drag coefficient CD against Re for several Mach numbers M and comparison with available literature results obtained for air (colored symbols indicate different Mach number clusters)

scholarly journals Hysteresis in Supersonic Flow Past a Plane Cascade of Cylindrical Rods

2021 ◽  
Vol 56 (6) ◽  
pp. 886-896
Author(s):  
S. V. Guvernyuk ◽  
F. A. Maksimov
Keyword(s):  
Mach Number ◽  
Supersonic Flow ◽  
Stokes Equations ◽  
Aerodynamic Drag ◽  
Flow Regimes ◽  
Wake Flow ◽  
Computational Technique ◽  
Infinite Plane ◽  
Continuous Increase ◽  
Number Range

Abstract— The results of numerical simulation of the interaction of supersonic flow with a permeable screen in form of an infinite plane cascade (lattice) of circular cylinders are given. The interaction regime in which the shocks ahead of the cylinders are localized on the scale of the cascade step is considered. The multi-block computational technique in which the viscous boundary layers are resolved by means of local grids using the Navier–Stokes equations, while the effects of inteferrence between the shock-wave structures in supersonic wake are described within the framework of Euler’s equations. The action of shock waves induced by the neighboring elements of lattice to the near-wake region behind the intermediate elements can ambiguously affect the aerodynamic lattice performance as well as generate time-dependent phenomena in the wake. The flow regimes are classified depending on continuous increase and decrease in the free-stream supersonic air flow in the Mach number range from 2.4 to 4.2 with reference to the lattice of the 80% permeability. The sources of the hysteresis behavior of the lattice aerodynamic drag with respect to the Mach number and the mechanisms of the onset of self-oscillating wake flow regimes are discussed.

scholarly journals Экспериментальное исследование нового способа уменьшения волнового сопротивления профиля при трансзвуковых скоростях

2020 ◽  
Vol 46 (12) ◽  
pp. 34
Author(s):  
М.А. Брутян ◽  
А.В. Волков ◽  
А.В. Потапчик
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Wave Drag ◽  
New Method ◽  
Optical Studies ◽  
Supercritical Airfoil ◽  
Aerodynamic Loads ◽  
Compression Waves ◽  
Supersonic Zone

A new method is proposed for wave drag reducing of a supercritical airfoil at transonic speeds, which is associated with the organization of a microwave section in a local supersonic zone on the upper surface. Simultaneously with optical studies, aerodynamic loads acting on a model were obtained. It is experimentally established that the proposed approach leads to the formation of a system of weak compression waves, to consecutive deceleration of the supersonic flow, to decrease of the Mach number in front of the shock wave, and, as a consequence, to weakening of its intensity and to reducing of the airfoil wave drag

Super-Alfvénic supersonic flow over a cone in aligned fields

1972 ◽  
Vol 52 (1) ◽  
pp. 17-31 ◽  
Author(s):  
Lee A. Bertram ◽  
Y. M. Lynn
Keyword(s):  
Shock Wave ◽  
Supersonic Flow ◽  
Flow Field ◽  
Surface Pressure ◽  
Magnetic Induction ◽  
Closed Form Solution ◽  
Form Solution ◽  
Apex Angle ◽  
Induction Vector ◽  
Pressure Coefficients

Super-Alfvénic supersonic aligned magnetogasdynamic flow over a cone of finite semi-apex angle, with an attached fast shock wave, is solved numerically. We obtain ‘almond curves’ in the plane of magnetic induction vector variation, analogous to Busemann's ‘apple curves’ for supersonic cone flows, to describe the flow field near the cone. Total surface pressure coefficients, current and vorticity distributions are presented. A closed-form solution of the flow is obtained when a switch-on shock occurs.

scholarly journals Возникновение усилий на клине при взаимодействии скользящего разряда со сверхзвуковым потоком

2021 ◽  
Vol 47 (9) ◽  
pp. 33
Author(s):  
В.М. Бочарников ◽  
В.В. Голуб ◽  
А.С. Савельев
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Mach Number ◽  
Supersonic Flow ◽  
Wind Tunnel ◽  
Static Pressure ◽  
Discharge Energy ◽  
Pulse Heat ◽  
The Impact ◽  
Sliding Discharge

It was investigated generation of forces on the wedge during the interaction of a sliding discharge in the supersonic flow. Sliding discharge was generated in a supersonic atmospheric-vacuum wind tunnel with a flow Mach number M = 2, Reynolds number of about 106, and static pressure in the flow p = 0.15 bar. It was found that the impact of the discharge is not limited by the appearance of a shock wave, and also significantly changes the properties of the flow around the wedge due to pulse heat generation. As the discharge energy increases, the force from its impact on the wedge also increases. Force produced by the sliding discharge in the supersonic flow is several times greater than in the quiescent air regardless of its pressure: 0.15 bar or 1 bar.

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