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THE earlier classical treatises on aerodynamics concerned themselves with the properties of incompressible fluids. The theory developed on this basis gave an excellent theoretical background to the aeronautical engineer and made possible a scientific approach to the problems of aircraft flight. With the steady increase of aircraft speed, however, it soon became evident that the theory would have to be extended to take compressibility into account. One important result, brought out by Glauert's analysis, was the modification of the flow pattern with increasing Mach number. A more striking divergence of compressible from incompressible flow, first encountered at near sonic speeds, is the occurrence of shock waves. A shock wave, in the specialized aeronautical sense, is a pressure impulse travelling through the flow causing a sudden transition from supersonic to subsonic speeds (normal to the wave front) with an attendant increase in pressure and temperature. A brief statement of this sort, however, is of little or no value in giving an idea of the physical nature of the phenomenon. A considerable amount of attention is now focused on the repercussions of shock waves on aeroplane design. It is far easier to understand these design trends if one has a good grasp of the fundamentals underlying the problem. This article sets out to give a brief survey of these fundamentals. It is not easy also to give a complete physical picture of a shock wave but at least a discussion of their formation, propagation, etc. goes a long way towards clarifying one's ideas.

The purpose of this paper is to conduct an experimental investigation on the shock cell structure of jets emanating from a four-lobed corrugated nozzle using Schlieren imaging technique.

The Schlieren images were captured for seven different nozzle pressure ratios (NPR = 2, 3, 4, 5, 6, 7 and 8) and compared with the shock cell structure of a round nozzle with an identical exit area. The variation in the length of the shock cell, width of boundary interaction between adjacent shock cells, maximum width of first shock cell, Mach disk position and diameter for different NPR was measured from the Schlieren images and analysed.

A three-layer shock net observed in the jet emanating from the four-lobed corrugated nozzle is a novel concept in the field of under-expanded jet flows. A shock net represents interconnected layers of shock cells developed because of the interaction between the core and peripheral shock waves in a jet emanating from a corrugated lobed nozzle. Also, the pattern of shock net is different while taking Schlieren images across the groove and lobe sections. Thus, the shock net emerging from a corrugated lobed nozzle varies azimuthally and primarily depends on the nozzle exit cross section. The length of the shock cell, width of boundary interaction between adjacent shock cells, maximum width of first cell, Mach disk position and diameter were found to exhibit increasing trend with NPR.

A novel concept of interconnected layers of shock waves defined as “shock net” developed from a single jet emanating from a four-lobed corrugated nozzle was observed.

The purpose of this paper is to perform a computational fluid dynamics (CFD) simulation that is able to reveal what is happening for the shock wave generated by high speed flow test facility and to develop deeper understanding of all parameters which affect the shock wave velocity profile and pressure and temperature histories inside the facility.

Two dimensional time accurate Euler solver for shock tube applications was developed to simulate the flow process inside the shock tube. To ensure the ability of the CFD code to capture shocks, rarefaction waves and contact discontinuity and to produce the correct pressure, temperature, density and speed profiles, the code has been validated using two verification approaches. First, the code results have been compared to the Sod's tube problem (exact solution). Second, the code solution is compared with selected experimental measurements for a certain diaphragm pressure ratio.

Results presented in this paper show that after diaphragm rapture and when the shock did not reflect yet, the flow is symmetry and uniform in y‐direction. As the shock wave reflects from the tube end it will move to the left and interact with the discontinuity surface and the flow no longer symmetry. Results also show that two‐dimensional modeling of the high speed flow test facility is an effective way to obtain facility performance data. Although this paper focused on UNITEN's facility, the CFD code is generic and may be applied to other facilities. The present code showed good capability to provide the x‐t diagram successfully. From this diagram one can determine the useful duration (for this case it is about 10 ms), which is quite comparable compared to other facilities. It can be concluded, based on the agreement with the analytical results, that the numerical formulation for the inviscid part of the solver is valid.

This paper performs a CFD simulation that is able to reveal the shock wave behavior at high speed flow test facility.

The purpose of this paper is to carry out a comprehensive study of compressible flow over double wedge and biconvex airfoils using computational fluid dynamics (CFD) and three analytical models including shock and expansion wave theory, Busemann's second‐order linearized approximation and characteristic method (CHM).

Flow over double‐wedge and biconvex airfoils was investigated by the CFD technique using the Spalart‐Allmaras turbulence model for computation of the Reynolds stresses. Flow was considered compressible, two dimensional and steady. The no slip condition was applied at walls and the Sutherland law was used to calculate molecular viscosity as a function of static temperature. First‐order upwind discretization scheme was used for the convection terms. Finite‐volume method was used for the entire solution domain meshed by quadratic computational cells. Busemann's theory, shock and expansion wave technique and CHM were the analytical methods used in this work.

Static pressure, static temperature and aerodynamic coefficients of the airfoils were calculated at various angles of attack. In addition, aerodynamic coefficients of the double‐wedge airfoil were obtained at various free stream Mach numbers and thickness ratios of the airfoil. Static pressure and aerodynamic coefficients obtained from the analytical and numerical methods were in excellent agreement with average error of 1.62 percent. Variation of the static pressure normal to the walls was negligible in the numerical simulation as well as the analytical solutions. Analytical static temperature far from the walls was consistent with the numerical values with average error of 3.40 percent. However, it was not comparable to the numerical temperature at the solid walls. Therefore, analytical solutions give accurate prediction of the static pressure and the aerodynamic coefficients, however, for the static temperature; they are only reliable far from the solid surfaces. Accuracy of the analytical aerodynamic coefficients is because of accurate prediction of the static pressure which is not considerably influenced by the boundary layer. Discrepancies between analytical and numerical temperatures near the walls are because of dependency of temperature on the boundary layer and viscous heating. Low‐speed flow near walls causes transformation of the kinetic energy of the free stream into enthalpy that leads to high temperature on the solid walls; which is neglected in the analytical solutions.

This paper is useful for researchers in the area of external compressible flows. This work is original.

In this paper, we examine the concept of “vulnerability” within the context of income mobility of the poor. We test for the dynamics of vulnerable households in the UK using waves 1–12 of the British Household Panel Survey and find that, of three different types of risks that we test for, household-specific shocks and economy-wide aggregate shocks have the greatest impact on consumption, in comparison to shocks to the income stream.

A novel numerical formulation of the two‐phase macroscopic balance equations governing the flow field in incompressible porous media is presented. The numerical model makes use of the weighted average flux method and total variation diminishing flux limiting techniques, and results in a second‐order accurate scheme. A shock tube study was carried out to examine the interaction of a normal shock wave with a thin layer of porous, incompressible cellular ceramic foam. Particular attention was paid to the transmitted and reflected flow fields. The numerical model was used to simulate the experimental test cases, and their results compared with a view to validate the numerical model. A phenomenological model is proposed to explain the behaviour of the transmitted flow field.

Underwater shock wave loading has been implemented on various metals, foods and wood. The main goal of this study is to investigate the performance of unbleached jute fiber in terms of underwater shock wave loading and fiber surface parameters. The input short wave loading is varied by shock pressure. The underwater shock wave is generated by the explosion of a detonating fuse in the water tank. The process of bubble generation and expansion inside the water results in the formation of shock waves. After shock loading, jute fiber is taken for physico - mechanical and physico-chemical testing, such as those for breaking strength, elongation, moisture content, wicking, permeability, etc. The effects on jute fiber exposed by the underwater shock waves are also demonstrated by a scanning electron microscope (SEM). The maximum effect is observed at 100 MPa. Jute fiber treated by underwater shock waves shows improved moisture content and dye permeability than that of untreated jute fiber.

AN account is given or the principle of a three‐dimensional shadowgraph recorder, its exemplification in the laboratory and its application to models in open and closed jets. Details are given of photographical, mechanical and graphical methods of reconstruction of the form of the shock wave from the records obtained, including correction for refraction due to thick glass walls of tunnels.

The purpose of this paper is to quantify the relative importance of the multiphase model for the simulation of a gas bubble impacted by a normal shock wave in water. Both the free-field case and the collapse near a wall are investigated. Simulations are performed on both two- and three-dimensional configurations. The main phenomena involved in the bubble collapse are illustrated. A focus on the maximum pressure reached during the collapse is proposed.

Simulations are performed using an inviscid compressible homogeneous solver based on different systems of equations. It consists in solving different mixture or phasic conservation laws and a transport-equation for the gas volume fraction. Three-dimensional configurations are considered for which an efficient massively parallel strategy was developed. The code is based on a finite volume discretization for which numerical fluxes are computed with a Harten, Lax, Van Leer, Contact (HLLC) scheme.

The comparison of three multiphase models is proposed. It is shown that a simple four-equation model is well-suited to simulate such strong shock-bubble interaction. The three-dimensional collapse near a wall is investigated. It is shown that the intensity of pressure peaks on the wall is drastically increased (more than 200 per cent) in comparison with the cylindrical case.

The study of bubble collapse is a key point to understand the physical mechanism involved in cavitation erosion. The bubble collapse close to the wall has been addressed as the fundamental mechanism producing damage. Its general behavior is characterized by the formation of a water jet that penetrates through the bubble and the generation of a blast wave during the induced collapse. Both the jet and the blast wave are possible damaging mechanisms. However, the high-speed dynamics, the small spatio-temporal scales and the complicated physics involved in these processes make any theoretical and experimental approach a challenge.

Cavitation erosion is a major problem for hydraulic and marine applications. It is a limiting point for the conception and design of such components.

Such a comparison of multiphase models in the case of a strong shock-induced bubble collapse is clearly original. Usually models are tested separately leading to a large dispersion of results. Moreover, simulations of a three-dimensional bubble collapse are scarce in the literature using such fine grids.

This paper aims to describe a proposal for an innovative method of normal shock wave–turbulent boundary layer interaction (SBLI) and shock-induced separation control.

The concept is based on the introduction of a tangentially moving wall upstream of the shock wave and in the interaction region. The SBLI control mechanism may be implemented as a closed belt floating on an air cushion, sliding over two cylinders and forming the outer skin of the suction side of the airfoil. The presented exploratory numerical study is conducted with SPARC solver (steady 2D RANS). The effect of the moving wall is presented for the NACA 0012 airfoil operating in transonic conditions.

To assess the accuracy of obtained solutions, validation of the computational model is demonstrated against the experimental data of Harris, Ladson & Hill and Mineck & Hartwich (NASA Langley). The comparison is conducted not only for the reference (impermeable) but also for the perforated (permeable) surface NACA 0012 airfoils. Subsequent numerical analysis of SBLI control by moving wall confirms that for the selected velocity ratios, the method is able to improve the shock-upstream boundary layer and counteract flow separation, significantly increasing the airfoil aerodynamic performance.

The moving wall concept as a means of normal shock wave–turbulent boundary layer interaction and shock-induced separation control has been investigated in detail for the first time. The study quantified the necessary operational requirements of such a system and practicable aerodynamic efficiency gains and simultaneously revealed the considerable potential of this promising idea, stimulating a new direction for future investigations regarding SBLI control.