2 edition of **Hypersonic similarity solutions for airfoils supporting exponential shock waves** found in the catalog.

Hypersonic similarity solutions for airfoils supporting exponential shock waves

Julian D. Cole

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Published
**1968** by Rand Corporation in Santa Monica, Calif .

Written in English

- Aerofoils.,
- Shock waves.,
- Aerodynamics, Hypersonic.

**Edition Notes**

Statement | [by] J.D. Cole and J. Aroesty. |

Series | Rand Corporation. Research memorandum -- RM-5724, Research memorandum (Rand Corporation) -- RM-5724. |

Contributions | Aroesty, J. |

The Physical Object | |
---|---|

Pagination | 44 p. |

Number of Pages | 44 |

ID Numbers | |

Open Library | OL18747381M |

A revised edition to applied gas dynamics with exclusive coverage on jets and additional sets of problems and examples The revised and updated second edition of Applied Gas Dynamics offers an authoritative guide to the science of gas dynamics. Written by a noted expert on the topic, the text contains a comprehensive review of the topic; from a definition of the subject, to the three essential. aerodynamics: Creation of Shock Waves Enter your search terms: Above speeds of Mach.7 the air flowing over the wing accelerates above the speed of sound, causing a shock wave (also known as a sonic boom) as the airplane compresses air molecules .

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A study of airfoil optimization, using the equations of hypersonic gas dynamics to explore the "Newtonian chine strip" theory that airfoil concavity enhances the lift-to-drag ratio for a fixed drag penalty.

The flow behind concave and convex exponential shock waves is investigated, and the corresponding airfoil surfaces are by: 5. Cole and J. Aroesty, Hypersonic similarity sol- utions for airfoils supporting exponential shock waves.

A1AA MS, (). Hui, A solution for hypersonic flow past slender bodies. Fluid Mech. 48, (). Hui and H. Hemdan, Higher order simi- larity solutions for hypersonic flow past by: 1. A solution to the hypersonic small disturbance equations is obtained for a class of two-dimensional bodies supporting logarithmic shock waves by reducing the partial differential equation to an.

This book presents a basic study of the behaviour of compressible gases, including gas dynamic equations, isentropic flow, isothermal flow, and shock waves. Hypersonic similarity solutions for. 3. Interaction of Disturbances with a Shock Wave 4.

Flows Past Wedgelike Bodies and Slender Airfoils at Large Angles of Attack 5. Approximate Method Using Shock and Simple Wave Relations (Shock-Expansion Method) 6. Generalization to Flows Past Bodies of Revolution Chapter V Effect of Slight Leading Edge Blunting on Hypersonic Flows Past Bodies Edition: 1.

We gratefully acknowledge support from the Simons Foundation and member institutions. > math > arXiv Hypersonic Similarity for the Two Dimensional Steady Potential Flow with Large Data. Authors: Jie Kuang, the shock solution structures (after scaling) are consistent, when the Mach number of the flow is sufficiently.

Further, Hui [7] found another similarity solution for two-dimensional flow, with a logarithmic shock wave. Both Cole and Arosety and Hui's solution, like that of Sedov, assumed infinite freestream Mach number, M~.'t To show the effect of finite values of M~, Hui and Hemdan[8] perturbed the two sol- utions [6,7] and reduced the perturbation.

American Institute of Aeronautics and Astronautics Sunrise Valley Drive, Suite Reston, VA Similarity solutions for oscillating pointed-nose slender axisymmetric bodies—part ii: curved bodies Acta Astronautica, Vol.

49, No. 11 Analytical Model of Unsteady Shock Motion on Hypersonic Forebodies. John J. Bertin, United States Air Force Academy. Russell M. Cummings. © | Pearson | Available | Pearson | Available. A self-similar model for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving Hypersonic similarity solutions for airfoils supporting exponential shock waves book time according to an exponential law in an ideal gas in the presence of azimuthal magnetic field and variable density is discussed in a rotating atmosphere.

The ambient medium is assumed to possess radial, axial and. A method based on the use of the two-approximation theory developed in [1, 2] is proposed for the computation of hypersonic flow past a conical wing with a Mach-type shock configuration.

The Normal Shock Wave Oblique and Curved Shocks Mach Number Independence Principle Real-Fluid Effects II. Small-Disturbance Theory Introduction and Basic Equations Hypersonic Similitude Unified Supersonic-Hypersonic Similitude Strip Theory Examples of Small-Disturbance Solutions Similar Solutions Experimental studies of hypersonic shock-wave boundary-layer interactions Two classes of shock-wave boundary-layer interactions were studied experimentally in a shock tunnel in which a low Reynolds number, turbulent flow at Mach 8 was developed on a cold, flat test surface.

The two classes of interactions were: (1) a swept interaction generated by a wedge ('fin') mounted. A computer algorithm has been developed to determine the bluntbody flow fields supporting symmetric parabolic and paraboloidal shock waves at infinite free stream Mach number.

Solutions are expressed in an analytic form as high‐order power series, in the coordinate normal to the shock, whose coefficients can be determined exactly. McGraw-Hill Book Company, New York. ISBN Albert A.

Merrill (–) Instructor in Aeronautics, –, – First Instructor in Aeronautics at Caltech. Inthe Boston Aeronautical Society was formed with Merrill, William H.

Pickering, and James Means forming the executive committee. Inhe learned. The Similarity Law for Nonsteady Hypersonic Flows and Requirements for the Dynamical Similarity of Related Bodies in Free Flight, NACA TN No.

() Google Scholar Lighthill, M.J.: Higher Approximations in General Theory of High Speed Aerodynamics. Hypersonic Aerodynamics Introduction Hypersonic vehicles are commonplace. There are many more of them than the supersonic aircraft discussed in the last chapter.

Applications include missiles, launch vehicles and entry bodies. A huge effort has been made developing hypersonic aerodynamics methods and configurations. The self-similar solution for adiabatic flow headed by a magnetogasdynamic cylindrical shock wave in a rotating non-ideal gas is obtained by Vishwakarma et al.

Sedov () (see Rao and Ramana ) indicated that a limiting case of a self-similar flow-field with a power-law shock is the flow-field formed with an exponential shock. However, as the Mach number increases to hypersonic speeds, the shock wave approaches the surface of the body.

Thus, as the ow velocity changes direction after crossing the shock, the ow appears to be de ected by the body similar to Newtonian ow theory. Transonic Flow Past Unswept Airfoils Wave Drag Reduction by Design Airfoil Contour Wave Drag Approaches Supercritical Airfoil Sections Swept Wings at Transonic Speeds Wing—Body Interactions and the “Area Rule” Second-Order Area-Rule Considerations Forward Swept.

Southwest Research Institute engineers are advancing what researchers know about hypersonic flight. A new study presented at the Joint Army-Navy-NASA-Air Force (JANNAF) Propulsion Meeting describes a series of tests conducted at SwRI’s San Antonio headquarters that elucidate the conditions a future aircraft may experience traveling faster than 10 times the speed of sound.

X was the only manned aircraft to fly at low hypersonic speeds, i.e. at Mach 6. During its re-entry, space shuttle also acquires such speeds.

The distance between shock wave, generated by a hypersonic aircraft and the aircraft is smaller than in case of supersonic aircraft. If the specific - heat ratio isthe weak -shock solu- tion reduces to Newtonian theory, while the strong-shock solution yields a pressure coefficient of 2 consistent with the normal -shock solution.

Simple relations are shown (fig. 9) for "the pressure coefficient and shock-wave angle for detachment for any specific - heat ratio.

At high hypersonic speeds, the molecules break apart producing an electrically charged plasma around the aircraft. Large variations in air density and pressure occur because of shock waves, and expansions.

The only manned aircraft to fly in the low hypersonic regime were the X and the Space Shuttle during re-entry. Hypersonic vehicle design is a complicated and ongoing process. As a conventional rule of thumb, hypersonic flow can be defined as flow above Mach 5.

However, this number is not set in stone, and only refers to an approximate Mach number where certain physical flow phenomena become important such as strong shock waves, thin shock.

Hypersonic Airfoil with Power Law Shock Waves. A, Wagner* CNLS & C-3, B25S Los Alamos, N,M. S Introduction.

paper the flow field over a class of two-dimensiorml lifting slwfnrrs the viewpoint of inviscid, hypersonic slnall-(listurl)nll.{’ theory (HSDT). It is WCIIknown that a flow field in which the shock.

Since thin shock layers are so common in hypersonic flight, designers must be careful to prevent the shock wave from one component of the aircraft from adversely interfering with another component.

In addition, a hypersonic vehicle will likely utilize some kind of ramjet or scramjet engine. Finally we look at the role, which shock waves play in hypersonic airbreathing propulsion and in aerothermodynamic airframe/propulsion integration of CAV’s [9].

It is recalled that the flight-speed range of turbojet engines is up to Ыж = 3 to 4, that of ramjet engines 3 ^ M^ 6, and of scramjet engines 6 ^ M^ The inviscid hypersonic aerodynamic characteristics of circularly blunt- wedge airfoils are derived from numerical solutions.

Hy-personic wedge theory based on explicit oblique-shock equations is shown to provide rapid estimates of the pressures over both sharp and blunt airfoils. The effects of varying. History. The first manufactured object to achieve hypersonic flight was the two-stage Bumper rocket, consisting of a WAC Corporal second stage set on top of a V-2 first stage.

In Februaryat White Sands, the rocket reached a speed of 8, km/h (5, mph), or approximately Mach The vehicle, however, burned on atmospheric re-entry, and only charred remnants were found. 8 Unsteady wave motion; acoustic, finite and shock wave propagation. Propagation and reflection of shock and expansion waves.

9 Midterm Exam (GFS – Ma – pm) Shock-tubes and shock-tunnels. Potential flow and linearized potential theory. 5 Week 11 10 Transonic flow; small perturbation theory and similarity parameter.

Overview. In real life supersonic flow applications, normal shocks as the ones studied in Chapter 3 appear in very specific situations only.

The situation will rather be that a complex shock pattern built up of combinations of oblique shocks, expansion waves and slip lines will be formed. Hypersonic Shock Relations in Terms of the Hypersonic Similarity Parameter Edit The parameter group K = M 1 θ has been found to be a "hypersonic similarity parameter." The term similarity means that a group (in this case K) can be found that reduces the independent variables of a problem, that is, the number of independent variables of a.

"Hypersonic speed is defined as faster than five times the speed of sound or greater than Mach 5. When something is flying that fast, the air will chemically decompose around the craft," said SwRI. The structure of hypersonic shock waves using Navier-Stokes These modiﬁcations are shown to be stable and produce physic al solutions to the shock problem of a qual-ity broadly similar to those from the family of extended hydrodynamic models that includes the Burnett It is of some concern, however, that shock solutions are nonphysical.

EXPERIMENTAL STUDY OF THE SHOCK WAVE DUE TO A BLUNT LEADING EDGE IN THE HYPERSONIC MERGED- FLOW REGIME By Roger M. Winebarger Langley Research Center SUMMARY An experimental investigation of low-density flow over two-dimensional blunt bodies has been conducted in the Langley 1-foot (meter) hypersonic arc tunnel.

Hypersonic Aerodynamics Index Here is a list of all the topics available from the NASA's Guide to Hypersonics web site. These pages are intended principally for undergraduates who are studying hypersonic and high supersonic flows.

hypersonic technology, a hypersonic cruise missile technical development program in support of a hypersonic cruise missile acquisition program, and sustained procurement of the missile to ensure a sufficient inventory is maintained.

Growing Importance of Hypersonic Flight. Several different methods exist to reach hypersonic flight. With increasing strength of interaction, the separation shock moves upstream of its initial position at the base of the incident shock.

Interestingly, there are strong visual similarities between shock-wave-laminar and shock-wave-turbulent boundary layer interactions at high hypersonic.

In a hypersonic flow, the viscous boundary layer interacts with the shock and entropy layer and the kinetic energy of the flow is dissipated by the effect of friction within the boundary layer.

Due to these viscous effects, the flow is no longer irrotational. Note that the linear theory is not applicable if the flow is considered hypersonic.Shock Wave - Free download as Powerpoint Presentation .ppt), PDF File .pdf), Text File .txt) or view presentation slides online.

Materi Aerodinamika.boundary layer is blown away from the wall as a free shear layer. Self-similar solutions are obtained for the thin layer of blown gas adjacent to the surface, for the thin viscous shear layer, and for the outer inviscid-flow region between the shear layer and the shock wave.

Pressures obtained in the strong- .