Unsteady drag on a sphere by shock wave loading

The dynamic drag coefficient of a sphere by shock wave loading is investigated numerically and experimentally. The diameter of the sphere is varied from 8 m to 80 mm in numerical simulation. The axisymmetric Navier-Stokes equations are solved on a fine grid, and the grid convergence of the drag coefficient is achieved. The numerical result is validated by comparing the experimental data of a 80 mm sphere, measured by the accelerometer in a vertical shock tube. It is found that the sphere experiences in the early interaction one order higher drag than in the steady state. A transient negative drag, mainly resulting from the focusing of shock wave on the rear side of the sphere, is observed only for high Reynolds number flows, and the drag becomes positive because of increased skin friction for low Reynolds number flows.Received: 10 March 2004, Accepted: 24 May 2004, Published online: 20 August 2004[/PUBLISHED]M. Sun: Send offprints requests to     

Explicit algebraic Reynolds stress model for shock-dominated flows

Shock waves drastically alter the nature of Reynolds stresses in a turbulent flow, and conventional turbulence models cannot reproduce this effect. In the present study, we employ explicit algebraic Reynolds stress model (EARSM) to predict the Reynolds stress anisotropy generated by a shockwave. The model by Wallin and Johansson (2000) is used as the baseline model. It is found to over-predict the post-shock Reynolds stresses in canonical shock turbulence interaction. The budget of the transport equation of Reynolds stresses computed using linear interaction analysis shows that the unsteady shock distortion mechanism and the pressure–velocity correlations are important. We propose improvement to the baseline model using linear interaction analysis results and redistribute the turbulent kinetic energy between the principle Reynolds stresses. The new model matches DNS data for the amplification of Reynolds stresses across the shock and their post-shock evolution, for a range of Mach numbers. It is applied to oblique shock/boundary-layer interaction at Mach 5. Significant improvements are observed in predicting surface pressure and skin friction coefficient, with respect to experimental measurements.     

A shock tube research facility for high-resolution measurements of compressible turbulence

A new shock tube facility with a 30.5 cm (1 ft) inside diameter is currently in operation that allows for high-spatial-resolution measurements of compressible turbulence. Small scales of turbulence behave very differently from large scales when they interact with shock or expansion waves. Highly resolved measurements can provide new information on the interaction at small scales. Another notable characteristic of the present facility is the ability to control the flow velocity behind the reflected shock through the porosity of the reflecting wall. Tests showed good flow quality with sufficiently long observation times. Measurements of piecewise average skin friction over short segments of the tube indicated strong viscous effects very close to the diaphragm where the shock is developing. The skin friction and the shock propagation speed virtually remained constant inside the working section of the shock tube in all investigated flow cases, even in low Mach number cases where viscous effects are stronger. The experimental results are compared with numerical simulations, including the effects of the reflecting porous wall and viscous effects.     

Spherical shock wave reflection from a surface with a heated gas layer

The two-dimensional axisymmetric problem of the interaction between smallscale spherical shock waves initiated by a laser explosion and an absolutely rigid surface in the presence of a layer of hot gas is numerically investigated. A number of effects previously observed in physical and numerical experiments [5–8] are confirmed, in particular: the distortion of the reflected shock front and its acceleration on passage through the hot central zone of the laser explosion (lens effect), the strong deformation of this zone, and the formation of a precursor on the surface ahead of the shock wave interacting with the thermal layer. In addition, certain new anomalous effects are revealed: the formation of a pair of suspended shocks — one on the periphery of the hot central zone upon interaction with the reflected shock wave and the other behind the Mach stem in the triple point zone, etc.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 141–147, July–August, 1989.     

Computation of Gas–Dynamic Parameters and Heat Transfer in Supersonic Turbulent Separated Flows near Backward–Facing Steps

Computation results of plane turbulent flows in the vicinity of backward–facing steps with leeward–face angles = 8, 25, and 45° for Mach numbers M_infin = 3 and 4 are presented. The averaged Navier—Stokes equations supplemented by the Wilcox model of turbulence are used as a mathematical model. The boundary–layer equations were also used for the case of an attached flow ( = 8°). The computed and experimental distributions of surface pressure and skin friction, the velocity and pressure fields, and the heat–transfer coefficients are compared.     

Numerical Simulation of a Supersonic Flow with Transverse Injection of Jets

A plane supersonic flow with symmetric perpendicular injection of jets through slots in the walls is numerically simulated with the use of Navier–Stokes equations. The effect of the jet pressure ratio and Mach number on the flow structure is considered. The angle of inclination of the shock wave and the separationregion length are found as functions of the jet pressure ratio. The influence of the jet pressure ratio on the increase in the lift force arising owing to interaction of the flow with the injected jet is found.     

Problem of a piston in a plastic medium with cultivation

The article discusses the self-similar problem of the motion of a spherical piston in a medium with dry friction and the differential connection between the first invariant of the stress tensor and the second invariant of the tensor of the deformation rates. For the case of flow with a shock wave, the method of a stationary wave is used to obtain the required relationships at a strong discontinuity. It is disclosed that the velocity of the piston, as well as the relationship between the cultivation coefficients and the dry friction, are determined by the smoothness of the friction.Translated from Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, 86–93, September–October, 1974.     

Biomechanical effects of shock waves onEscherichia coli and λphage DNA

Escherichia coli (recombinant cells) and phage DNA in suspension liquid were exposed to pressure pulses of about 20s duration and amplitude of up to 14 MPa. These pulses were generated by a diaphragmless shock tube. The destruction of cells was monitored by the assay of phenylalanine dehydrogenase leaking from the recombinant cells and was found to increase remarkably at the peak pressure of higher than 12 MPa. A probability relation for the cell destruction expressed as a function of pressure was proposed. It is most likely that there exists a threshold pressure for the cell destruction. Fragmentation effects of shock waves on phage DNA were analyzed by electrophoresis. They were enhanced by increasing the shock wave strength and the number of shots. Probability for the DNA fragmentation as a function of pressure and molecular size was estimated with HPLC. The larger size of the DNA was more easily fragmented. A threshold pressure does not seem to exist for the DNA fragmentation.     

Unsteady mixed convection with double diffusion over a horizontal cylinder and a sphere within a porous medium

The combined effects of the permeability of the medium, magnetic field, buoyancy forces and dissipation on the unsteady mixed convection flow over a horizontal cylinder and a sphere embedded in a porous medium have been studied. The nonlinear coupled partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The skin friction, heat transfer and mass transfer increase with the permeability of the medium, magnetic field and buoyancy parameter. The heat and mass transfer continuously decrease with the stream-wise distance, whereas the skin friction increases from zero, attains a maximum and then decreases to zero. The skin friction, heat transfer and mass transfer are significantly affected by the free stream velocity distribution. The effect of dissipation parameter is found to be more pronounced on the heat transfer than on the skin friction and mass transfer.Untersucht wurden kombinierte Effekte der Permeabilität des Mediums, des magnetischen Feldes, der Auftriebskräfte und der Dissipation auf die instationäre Mischkonvektions-Strömung über einen horizontalen Zylinder und eine Kugel, die in einem porösen Medium eingebettet sind. Die nichtlinearen gekoppelten partiellen Differentialgleichungen mit drei unabhängigen Variablen wurden numerisch unter Benutzung eines impliziten Finite-Differenzen-Verfahrens in Verbindung mit der Quasi-Linearisierungstechnik gelöst. Die Oberflächenreibung und die Wärme- und Stoffübertragung steigen mit der Permeabilität des Mediums, dem magnetischen Feld und dem Auftriebsparameter an. Die Wärme- und Stoffübertragung fällt stetig in Strömungsrichtung ab, wohingegen die Oberflächenreibung von Null ansteigt, ein Maximum erreicht und wieder auf Null abfällt. Die Oberflächenreibung und die Wärme- und Stoffübertragung werden signifikant von der Verteilung der Freistromgeschwindigkeit beeinflut. Es wurde festgestellt, das der Dissipations-Parameter stärker die Wärmeübertragung als die Oberflächenreibung und die Stoffübertragung beeinflut.     

Experimental and Numerical Study of a Hypersonic Separated Flow in the Vicinity of a Cone‐Flare Model

An axisymmetric laminar separated flow in the vicinity of a coneflare model is studied experimentally and numerically for a Mach number M = 6. The distributions of pressure and Stanton numbers along the model surface and velocity profiles in the region of shock wave–boundary layer interaction are measured and compared with the calculated data. The influence of the laminar–turbulent transition on flow parameters is studied numerically.     

Surface shear stress measurements around multiple jets in crossflow using the fringe imaging skin friction technique

The skin friction distribution around multiple jets in crossflow determined using the fringe imaging skin friction (FISF) technique is examined experimentally for two supply channel configurations. The velocity field associated with the jets is correlated to the skin friction distribution. A counterflow supply channel configuration has a pronounced skin friction deficit downstream of the injection holes caused by the lifting of fluid away from the wall by the counterrotating vortex pair (CRVP). In the counterflow case, the CRVP remains closer to the wall than in the coflow case. A potential flow analysis of a pair of counterrotating vortices above a wall demonstrates that the distance of the CRVP from the wall has a greater effect on the wall pressure distribution, and hence the separation phenomena, than does the strength of the vortices.Nomenclature a Distance between vortices in Y direction (potential flow analysis) - b Distance between vortices in Z direction (potential flow analysis) - C _f Skin friction coefficient - D Hole diameter - L/D Hole length-to-diameter ratio - M Momentum (blowing) ratio=jet momentum/free stream momentum - n _O Oil index of refraction - p Static pressure - P/D Spanwise spacing of injection-hole-to-diameter ratio - q Dynamic head=1/2U ² - Re Reynolds number based on momentum thickness - s Fringe spacing - t Time - v, w Wall-normal and spanwise velocity components - X Streamwise distance downstream from hole centerline - Y Height from test section floor - Z Spanwise distance from hole centerline - U Free stream velocity - Wavelength of incident radiation - _O Oil dynamic viscosity - Air density - _w Wall shear stress - _r Angle of incidence of illumination for FISF - ₀ Initial boundary layer momentum thickness Acronyms CRVP Counterrotating vortex pair - FISF Fringe imaging skin friction - SFD Skin friction deficit     

Direct Numerical Simulation and Theory of a Wall-Bounded Flow with Zero Skin Friction

We study turbulent plane Couette-Poiseuille (CP) flows in which the conditions (relative wall velocity ΔU _w ≡ 2U _w , pressure gradient dP/dx and viscosity ν) are adjusted to produce zero mean skin friction on one of the walls, denoted by APG for adverse pressure gradient. The other wall, FPG for favorable pressure gradient, provides the friction velocity u _τ , and h is the half-height of the channel. This leads to a one-parameter family of one-dimensional flows of varying Reynolds number Re ≡ U _w h/ν. We apply three codes, and cover three Reynolds numbers stepping by a factor of two each time. The agreement between codes is very good, and the Reynolds-number range is sizable. The theoretical questions revolve around Reynolds-number independence in both the core region (free of local viscous effects) and the two wall regions. The core region follows Townsend’s hypothesis of universal behavior for the velocity and shear stress, when they are normalized with u _τ and h; on the other hand universality is not observed for all the Reynolds stresses, any more than it is in Poiseuille flow or boundary layers. The FPG wall region obeys the classical law of the wall, again for velocity and shear stress. For the APG wall region, Stratford conjectured universal behavior when normalized with the pressure gradient, leading to a square-root law for the velocity. The literature, also covering other flows with zero skin friction, is ambiguous. Our results are very consistent with both of Stratford’s conjectures, suggesting that at least in this idealized flow turbulence theory is successful like it was for the classical logarithmic law of the wall. We appear to know the constants of the law within a 10% bracket. On the other hand, that again does not extend to Reynolds stresses other than the shear stress, but these stresses are passive in the momentum equation.     

Gasdynamic Analogies in Problems of the Oblique Interaction of MHD Shock Waves

Gasdynamic analogies are constructed for the oblique interaction of MHD shock waves (counter colliding or overtaking). These analogies fairly adequately describe the complex dependences of the gas dynamic parameters of the medium on the magnetic field strength and inclination. The complete gas dynamic analogy in which the MHD interaction is simulated by the interaction of two gas dynamic shock waves with Mach numbers calculated on the basis of the fast magnetosonic speeds adequately describe the state of the medium for weak and moderate magnetic fields. The hybrid model, in which the state behind the interacting shock wave is calculated from the MHD relations on discontinuities and the gas dynamic analogy is then used, gives satisfactory results in a stronger field.     

Interaction of shock waves with a combined discontinuity in two-phase media. 2. Nonequilibrium approximation

Interaction of a shock wave and a motionless combined discontinuity separating two twocomponent mixtures with different initial volume concentrations is studied on the basis of numerical simulation of unsteady processes. The calculations were performed using a modified method of coarse particles and a highaccuracy TVD difference scheme adapted to calculation of twophase flows. Flow parameters determined by analytical dependences coincide with those obtained by numerical simulation at large times of the process. Upon interaction of the shock wave and the combined discontinuity, the type of the transient or reflected shock wave may coincide with or differ from the type of the incident shock wave. The possibility of existence of a pressure difference at the combined discontinuity boundary, which was earlier predicted analytically, is confirmed.     

Physical properties of the flow in the separation region for three-dimensional interaction of a boundary layer with a shock wave

In a supersonic stream we consider the three-dimensional flow in the plane of symmetry in the region of interaction of a boundary layer with a shock wave which arises ahead of an obstacle mounted on a plate. The principal characteristic of this flow is the penetration of a filament of the ideal fluid within the separation zone and the formation on the surface of the plate and obstacle of narrow segments with high pressures, high velocity gradients, and large heat transfer coefficients.Pressure distribution measurements were made, shadow and schlieren photos were taken, and photographs of the flow pattern on the surface were made using dye coatings and low-melting models. The basic physical characteristics of the separation flow are established. The independence of the separation zone length of the boundary layer thickness is shown. Local supersonic flows are detected in the separation region, flow regimes are identified as a function of the angle of encounter of the separating flow with the obstacles, characteristic flow zones in the interaction region are identified.Notation s coordinate of separation point on the plate - l length of separation zone - H obstacle height - d obstacle transverse dimension - u freestream velocity - velocity gradient on stagnation line of obstacle - b jet width - compression shock standoff from the body - p static pressure - p_* pressure at stagnation point on obstacle - density - viscosity coefficient - boundary-layer thickness - compression shock angle - effective angle of separation zone - setting angle of obstacle on plate - M Mach number - R Reynolds number - P Prandtl number     

Experiments on the interaction of a pair of cylindrical weak blast waves in air

This paper reports the results of experiments and computations on the interaction of a pair of cylindrical blast waves in air. The waves were generated by exploding wires, and both symmetrical and unsymmetrical interactions were observed. The experimental data includes schlieren photographs of the wave interactions, their radii, shock Mach number and pressure versus time, as well as various cross plots and data on the shock regular/irregular interaction transition condition. The flow fields were computed with the help of the Total Variation Diminishing (TVD) method, and appear to represent the experimental results reasonably well. Some attention is also given to the blast scaling laws of the type discussed by Sakurai (1965) and Oshima (1960).This article was processed using Springer-Verlag TEX Shock Waves macro package 1990.     

Determination of rough-surface skin friction coefficients from wake profile measurements

A technique for determining the skin friction coefficients from wake profile measurements is described, and is applied to symmetric turbine airfoils with rough surfaces, which operate in a compressible, high-speed flow environment. The procedure involves the measurement of profiles of streamwise momentum in the wakes which form downstream of different airfoils with different levels of surface roughness. Different physical phenomena which affect such wake profiles are discussed and related to different effects, such as surface roughness, form drag, flow separation zones, and laminar-to-turbulent transition. With the same inlet experimental condition for each case, overall skin friction coefficients for the rough airfoils are determined. Resulting values increase considerably as the magnitude of equivalent sandgrain roughness size increases.List of symbols A test airfoil surface area - A _i test section inlet area - A _e test section exit area - c chord length of airfoil - C _f/2 skin friction coefficient - (C _f/2)_smooth skin friction coefficient for smooth airfoil - (C _f/2)_rough skin friction coefficient for rough airfoil - F _s force from surface shear stress - F _p force from form drag due to airfoil blockage and separated flow - F _w force imposed by the top and bottom test section walls - F _s,smooth force from surface shear stress for smooth airfoil - F _s,rough force from surface shear stress for rough airfoil - h height of test section - k roughness height - k _s equivalent sand grain roughness - L total length of airfoil surface from leading edge to trailing edge - p airfoil passage effective pitch - P _o stagnation pressure - P _oe exit local stagnation pressure - P _oe, exit freestream stagnation pressure - P _oi inlet stagnation pressure - P _s static pressure - P _se exit static pressure - s distance along airfoil surface from leading edge - u local streamwise velocity - u _i local streamwise velocity at test section inlet - u _e local streamwise velocity at test section exit - u local freestream streamwise velocity at test section exit - w width of test section - x linear distance along airfoil centerline from airfoil leading edge - y normal coordinate measured from airfoil centerline Greek symbols ratio of specific heats - _s roughness parameter - _i local static air density at test section inlet - _e local static air density at test section exit - local static air density in freestream at test section exit     

Effects of magnetic field and variable viscosity on forced non‐darcy flow about a flat plate with variable wall temperature in porous media in the presence of suction and blowing

This paper presents a study of the effect of a magnetic field and variable viscosity on steady twodimensional laminar nonDarcy forced convection flow over a flat plate with variable wall temperature in a porous medium in the presence of blowing (suction). The fluid viscosity is assumed to vary as an inverse linear function of temperature. The derived fundamental equations on the assumption of small magnetic Reynolds number are solved numerically by using the finite difference method. The effects of variable viscosity, magnetic and suction (or injection) parameters on the velocity and temperature profiles as well as on the skinfriction and heattransfer coefficients were studied. It is shown that the magnetic field increases the wall skin friction while the heattransfer rate decreases.     

Direct numerical simulation of turbulent flows through concentric annulus with circumferential oscillation of inner wall

Periodic wall oscillations in the spanwise or circumferential direction can greatly reduce the friction drag in turbulent channel and pipe flows. In a concentric annulus, the constant rotation of the inner cylinder can intensify turbulence fluctuations and enhance skin friction due to centrifugal instabilities. In the present study, the effects of the periodic oscillation of the inner wall on turbulent flows through concentric annulus are investigated by the direct numerical simulation (DNS). The radius ratio of the inner to the outer cylinders is 0.1, and the Reynolds number is 2 225 based on the bulk mean velocity U_m and the half annulus gap H. The influence of oscillation period is considered. It is found that for short-period oscillations, the Stokes layer formed by the circumferential wall movement can effectively inhibit the near-wall coherent motions and lead to skin friction reduction, while for long-period oscillations, the centrifugal instability has enough time to develop and generate new vortices, resulting in the enhancement of turbulence intensity and skin friction.     

Discrete element simulation of shock wave propagation in polycrystalline copper

The implementation of the characteristic of compressive plasticity into the Discrete Element Code, DM2, while maintaining its quasi-molecular scheme, is described. The code is used to simulate the shock compression of polycrystalline copper at 3.35 and 11.0 GPa. The model polycrystal has a normal distribution of grain sizes, with mean diameter 14 μm, and three distinct grain orientations are permitted with respect to the shock direction; 〈1 0 0〉, 〈1 1 0〉, and 〈1 1 1〉. Particle velocity dispersion (PVD) is present in the shock-induced flow, attaining its maximum magnitude at the plastic wave rise. PVD normalised to the average particle velocity of and are yielded for the 3.35 and 11.0 GPa shocks, respectively, and are of the same order as those seen in the experiment. Non-planar elastic and plastic wave fronts are present, the distribution in shock front position increasing with propagation distance. The rate of increase of the spread in shock front positions is found to be significantly smaller than that seen in probabilistic calculations on nickel polycrystals, and this difference is attributed, in the main, to grain interaction. Reflections at free surfaces yield a region of tension near to the target free surface. Due to the dispersive nature of the shock particle velocity and the non-planarity of the shock front, the tensile pressure is distributed. This may have implications for the spall strength, which are discussed. Simulations reveal a transient shear stress distribution behind the shock front. Such a distribution agrees with that put forward by Lipkin and Asay to explain the quasi-elastic reloading phenomenon. Simulation of reloading shocks show that the shear stress distribution can give rise to quasi-elastic reloading on the grain scale.