2 edition of **Similarity solution for transonic flow past a cone** found in the catalog.

Similarity solution for transonic flow past a cone

Yung-chung Shen

- 210 Want to read
- 15 Currently reading

Published
**1956**
by California Institute of Technology in Pasadena
.

Written in English

- Aerodynamics, Transonic.,
- Cone.

**Edition Notes**

Statement | by Yung-chung Shen. |

Series | GALCIT report |

Classifications | |
---|---|

LC Classifications | TL571 .S48 1956 |

The Physical Object | |

Pagination | 45 leaves : |

Number of Pages | 45 |

ID Numbers | |

Open Library | OL4473512M |

LC Control Number | 79300769 |

Lubard, S.C., Helliwell, W.S.: Calculation of the flow on a cone at high angle of attack. AIAA J. 12, – (). Also AIAA Paper 75– ADS CrossRef zbMATH Google Scholar. [7] Chen G-Q, Chen J, Feldman M. Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations. Interfaces Free Bound, , in press. Interfaces Free Bound, , in press.

High mach numbers. Hypersonic similarity Chapter Transonic flow Introduction Definition of the transonic range Transonic flow past wedge sections Transonic flow past a cone Transonic flow past smooth two-dimensional shapes. The question of shock-free flow The hodograph transformation of the equations. The two-dimensional transonic potential flow equation, when solved in discrete form for steady flow over an airfoil, has been found to yield more than one solution in certain bands of angle of attack and Mach number. The most striking ex- ample of this is the appearance of nonsymmetric solutions with large positive or negative lift, for.

A survey is given of transonic small disturbance theory. Basic equations, shock relations, similarity laves, lift and drag integrals are derived., The airfoil boundary value problem is formulated. Finite difference methods and computational algorithms are described. Results are compared with other calculation methods and experiments. We use our own and third-party cookies to enable you to navigate around our Site, use its features and engage on social media, and to allow us to perform analytics, remember your preferences, provide services that you have requested and produce content and advertisements tailored to your interests, both on our Site as well as others.

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For an upstream supersonic flow past a straight-sided cone in R 3 whose vertex angle is less than the critical angle, a transonic (supersonic-subsonic) shock-front attached to the cone vertex can be formed in the flow.

In this paper we analyze the stability of transonic shock-fronts in three-dimensional steady potential flow past a perturbed by: 7. The theoretical problem of transonic flow past finite cones is discussed briefly and an approximate solution of the axially symmetric transonic equations, valid for a semi-infinite cone, is presented.

INTRODUCTION Transonic flow past certain two-dimensional bodies has been the subject of several recent papers and the phenomena are well by: A self-similar transonic shock in three-dimensional steady flow past a straight-sided cone Apple curve and shock polar for the self-similar solutions Stability of transonic shock-front solutions.

Similarity solution for transonic flow past a cone. By Yung-chung Shen. Abstract. By applying a transonic expansion procedure to a conical flow field, a system of approximate transonic equations, boundary conditions, and shock relations is derived.

A similarity law for the pressure coefficient on the surface of slender cones is established Author: Yung-chung Shen. [16] Xu, G. and Yin, H., Global transonic conic shock wave for the symmetrically perturbed supersonic flow past a cone, J.

Differential Equations (), – [17] Xu, G. and Yin, H., Global multidimensional transonic conic shock wave for the perturbed supersonic flow past a cone, SIAM J. Math. by: 5. This is a transonic flow case for which experimental results are available in the literature to compare [7].At inflow Mach number of and angle of attack of degrees, the adapted meshes and Mach number contours for levels 2 and 3 are shown in Figure 3, along with the initial mesh increased sharpness of the shock regions is evident from the results.

We establish boundary gradient estimates for a solution for selfsimilar transonic potential flow on the subsonic region. The gradient estimates enable us to verify the ellipticity of the solution in the region. We consider both convex and general domains. We provide the sufficient conditions to show that the flow becomes transonic.

Euler ﬂow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed. Introduction and main results If there is a uniform supersonic ﬂow (ρ 0,0,0,q 0,P 0)whichcomesfrom minus inﬁnity, and the ﬂow hits the circular cone x2 1.

Summary and application of the similarity laws High mach numbers. Hypersonic similarity Chapter Transonic flow Introduction Definition of the transonic range Transonic flow past wedge sections Transonic flow past a cone Transonic flow past smooth two-dimensional shapes.

The question of shock-free flow You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

() The uniqueness of transonic shocks in supersonic flow past a 2-D wedge. Journal of Mathematical Analysis and Applications() The problem for the supersonic plane flow past a curved wedge.

The problem of subsonic, transonic, and supersonic separation flow of water past a circular cone of finite length is solved. The water is assumed to be an ideal compressible fluid. A steady flow picture is obtained in a process of stabilization with respect to the time by means of a two-dimensional finite-difference scheme [1].

The dependence of the drag coefficient on the Mach number of the. The transonic and hypersonic similarity parameters for conical flow may be obtained from those for the wedge flow.

At high Mach numbers, a Newtonian approximation can be extracted. For A′(r) ≠ 0, the existence of global solutions for the transonic nozzle flow problem was obtained in Liu [] by first incorporating the steady-state building blocks into the random choice method [], provided that the initial data have small total variation and are bounded away from both sonic and vacuum states.

On this web page, we show a method for determining the supersonic flow past a cone. The method was first developed by G.I. Taylor and J.W. Maccoll in The derivation of the differential equation shown on the slide is fairly complicated.

The method assumes that the supersonic flow along a cone is simplified because of symmetry considerations. Supersonic Flow Past Blunt Bodies Nozzle and Jet Flows Subsonic Flow Past a Convex Corner Disturbance/Subsonic Region Interaction Existence of steady-state solutions Self-similar Solutions Basic Concepts Cone in Incompressible Flow Transonic Problems Cone in Supersonic Flow Conical Flows Cone at Incidence Delta Wing in a Supersonic Flow.

MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction has been studied by Ibrahim et al. [15]. Roy et al.

[16] have obtained Non-similar solution of an unsteady mixed convection flow over a vertical cone in the presence of surface mass transfer.

The effect of combined viscous. Antony Jameson, Numerical calculation of transonic flow past a swept wing by a finite volume method, Computing Methods in Applied Sciences and Engineering.

Calculation of Transonic Potential Flow Past Three-Dimensional Configurations Computational Study of the Asymptotic Flow Structure of a High-Aspect-Ratio Swept Wing in Transonic Flow Some Remarks on the Numerical Solution of Tricomi-Type Equations. A free boundary value problem of Euler system arising in supersonic flow past a curved cone Chen, Shuxing, Tohoku Mathematical Journal, ; On a global supersonic-sonic patch characterized by 2-D steady full Euler equations Hu, Yanbo and Li, Jiequan, Advances in Differential Equations, ; Instability of marginally stable streamwise varying shear flow to long rossby waves Hodyss, Daniel.

7. Transonic Aerodynamics of Airfoils and Wings Introduction Transonic flow occurs when there is mixed sub- and supersonic local flow in the same flowfield (typically with freestream Mach numbers from M = or to ). Usually the supersonic region of the flow is terminated by a shock wave, allowing the flow to slow down to subsonic."Experimental results are presented for transonic flow post cone-cylinder, axially symmetric bodies.

The drag coefficient and surface Mach number are studied as the free-stream Mach number is varied and, wherever possible, the experimental results are compared with theoretical predictions. Interferometric results for several typical flow configurations are shown and an example of shock-free.transonic shock.

New ideas are to needed dealthiswith problem. Some results on Steady Supersonic Flow past a cone Forthe circular cone,[13]in Courant-Friedrichgave the solutionsby making use the shock of polarand the apple curves, 5. Due to their results, there are two solutionsthe forcone withan openingangleless thana criticalvalue.