The supersonic flow of compressible fluid through axially symmetric tubes of uniform and varying section

1950 ◽  
Vol 200 (1063) ◽  
pp. 511-523
Keyword(s):  
Supersonic Flow ◽  
Velocity Field ◽  
Power Series ◽  
Wide Class ◽  
Compressible Fluid ◽  
Inviscid Fluid ◽  
Nozzle Wall ◽  
Axially Symmetric ◽  
Rates Of Change ◽  
Rotational Flows

The paper considers potentials representing the supersonic flow of a compressible, inviscid fluid in axially symmetric tubes or diffusers. General formulae are given to determine the linearized flows completely when the inlet distributions of velocity are known, in cases where the slope of the nozzle wall is continuous, and where there are no discontinuities in the velocity field or in the rates of change of velocity. Particular reference is made to the flows resulting from velocity distributions which are initially parabolic. Formulae are given to enable the computer to tabulate a very wide class of axisymmetric flows, mention being made of the propagation of other profiles which are non-parabolic. A further method is given for extending the field by use of power series approximation. A discussion of rotational flows in divergent diffusers will be given in a later paper.

Analysis of Lift Augmentation of Vertical Solid Jets in Proximity of the Ground

1965 ◽  
Vol 32 (2) ◽  
pp. 263-270 ◽  
Author(s):  
M. J. Cohen
Keyword(s):  
Potential Flow ◽  
Control Parameter ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Nozzle Wall ◽  
Wall Angle ◽  
Subsonic Jet ◽  
Flow Techniques

An analysis of the lift augmentation properties of a vertical solid two-dimensional subsonic jet due to the presence of the ground is presented. The jet efflux is assumed to behave as an ideal, inviscid fluid, and familiar potential flow techniques are used to solve the resultant problems. The factors controlling the phenomenon are height from the ground, nozzle wall angle, and compressibility. The results in the form of curves of lift augmentation against height from ground show that, whereas the effects of compressibility are very small, the effect of nozzle wall angle is important and can be a useful design-control parameter.

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.

scholarly journals Large Deflection Analysis of Axially Symmetric Deformation of Prestressed Circular Membranes under Uniform Lateral Loads

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1343
Author(s):  
Xue Li ◽  
Jun-Yi Sun ◽  
Zhi-Hang Zhao ◽  
Xiao-Ting He
Keyword(s):  
Power Series ◽  
Initial Stress ◽  
Axisymmetric Deformation ◽  
Radial Coordinate ◽  
Axially Symmetric ◽  
Computational Accuracy ◽  
Power Series Method ◽  
Deflection Analysis ◽  
Membrane Problem ◽  
Geometric Equation

In this study, the problem of axisymmetric deformation of peripherally fixed and uniformly laterally loaded circular membranes with arbitrary initial stress is solved analytically. This problem could be called the generalized Föppl–Hencky membrane problem as the case where the initial stress in the membrane is equal to zero is the well-known Föppl–Hencky membrane problem. The problem can be mathematically modeled only in terms of radial coordinate owing to its axial symmetry, and in the present work, it is reformulated by considering an arbitrary initial stress (tensile, compressive, or zero) and by simultaneously improving the out-of-plane equilibrium equation and geometric equation, while the formulation was previously considered to fail to improve the geometric equation. The power-series method is used to solve the reformulated boundary value problem, and a new and more refined analytic solution of the problem is presented. This solution is actually observed to be able to regress into the well-known Hencky solution of zero initial stress, allowing the considered initial stress to be zero. Moreover, the numerical example conducted shows that the obtained power-series solutions for stress and deflection converge very well, and have higher computational accuracy in comparison with the existing solutions.

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