Physical and mathematical modeling of a supersonic flow around a cylinder with a porous insert

Results of numerical and experimental modeling of a supersonic flow (M_∞ = 4.85) around a model of a streamwise-aligned cylinder with a cellular-porous insert permeable for the gas on the frontal face of the cylinder are described. Experimental data on the influence of the pore structure and the length of the porous cylindrical insert on the model drag, pressure on the frontal face of the cylinder, and flow pattern are obtained. Numerical modeling includes solving Favre-averaged Navier-Stokes equations, which describe the motion of a viscous compressible heat-conducting gas. The system is supplemented with a source term taking into account the drag of the porous body within the framework of the continuum model of filtration. Data on pressure and velocity fields inside the porous body are obtained in calculations, and the shape of an effective pointed body whose drag is equal to the drag of the model considered is determined. The calculated results are compared with the measured data and schlieren visualization of the flow field.     

Effect of a drainage slit on the hydrodynamic stabilization of flow through porous media with lateral barotropic fluid injection

The effect of the scheme of fluid injection into a stratum on the length and the hydraulic drag of the initial portion of the flow through the porous medium and on the flow rate intercepted by a drainage slit separating the stratum from and end wall is investigated. The asymptotics of large and small values of the hydraulic conductivity coefficient of this slit are constructed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 60–67, January–February, 1999. The work was carried out at the Moscow State Chemical Industry Academy.     

In-Situ Capillary Trapping of CO<Subscript>2</Subscript> by Co-Injection

Co-injection of water with CO₂ is an effective scheme to control initial gas saturation in porous media. A fractional flow rate of water of approximately 5–10% is sufficient to reduce initial gas saturations. After water injection following the co-injection, most of the gas injected in the porous media is trapped by capillarity with a low fractional volume of migrating gas. In this study, we first derive an analytical model to predict the gas saturation levels for co-injection with water. The initial gas saturation is controlled by the fractional flow ratio in the co-injection process. Next, we experimentally investigate the effect of initial gas saturation on residual gas saturation at capillary trapping by co-injecting gas and water followed by pure water injection, using a water and nitrogen system at room temperature. Depending on relative permeability, initial gas saturation is reduced by co-injection of water. If the initial saturation in the Berea sandstone core is controlled at 20–40%, most of the gas is trapped by capillarity, and less than 20% of the gas with respect to the injected gas volume is migrated by water injection. In the packed bed of Toyoura standard sand, the initial gas saturation is approximately 20% for a wide range of gas with a fractional flow rate from 0.50 to 0.95. The residual gas saturation for these conditions is approximately 15%. Less than approximately 25% of the gas migrates by water injection. The amount of water required for co-injection systems is estimated on the basis of the analytical model and experimental results.     

Influence of injection on stabilization of flow over an axisymmetric body with a recess facing into a supersonic oncoming stream

Numerical modeling of supersonic flow over a body with an annular step formed by two coaxial cylinders is performed by the Godunov method within the framework of the model of an ideal gas. Regimes of nonsteady streamline flow and peculiarities of the flow associated with the presence of a cylindrical recess in the nose part of the body are analyzed. The influence of the intensity of injection of an annular wall jet from the bottom of the recess on flow stabilization and the body drag is investigated. The domain of the existence of steady streamline flow is established. Khar'kov Aviation Institute, Khar'kov 310070. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 84–90, July–August, 1998.     

Effect of local heat supply to a turbulent boundary layer on the friction

The results of calculating a supersonic turbulent boundary layer on a flat plate in the presence of thermal energy supply to the boundary layer are presented. Two methods of energy supply are considered: heating a local interval of the surface, which is otherwise thermally insulated and using a local volume heat source. It is shown that for the same amount of heat supplied to the gas volume heating leads, under certain conditions, to greater friction reduction than the surface heating. Localization of the energy supply zone leads to the intensification of the viscous drag reduction effect and to a greater decrease in the local friction coefficient, which extends a considerable distance downstream. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 48–56, January–February, 1997. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 93-013-17600).     

Heat transfer characteristics in flow around a spherically blunted cone at incidence and gas injection from a blunted surface

New methods of controlling thermal regimes in a high-enthalpy spatial flow around a body are considered. They are related to gas injection from the blunted surface and heat overflow in the material of the shell. The effect of injection is analyzed for different thermal conductivities. It is shown that highly heat-conducting materials can be successfully used to decrease the maximum temperatures at the windward side due to intense heat removal to the region of a porous spherical bluntness. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 162–169, July–August, 1999.     

Experimental study of the drag of the forebody and the cylindrical part of the HB-1 model with an upstream injection of a fluid in a supersonic flow

Values of the gas-dynamic drag of the forebody and the cylindrical part of the HB-1 test model in a supersonic flow have been separately measured using an internal strain-gauge balance. It is shown that an upstream injection of a fluid jet from the model forebody decreases the drag of both the forebody and the cylindrical part. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 110–112, November–December, 1998.     

Behavior of the vorticity vector in supersonic axisymmetric swirl flows behind a detonation wave

The behavior of the vorticity vector on a discontinuity surface arising in a supersonic nonuniform combustible gas flow with the formation of a shock or detonation wave is studied. In the general case, it is a vortex flow with prescribed distributions of parameters. It is demonstrated that the ratio of the tangential component of vorticity to density remains continuous in passing through the discontinuity surface, while the quantities proper become discontinuous. Results calculated for flow vorticity behind a steady-state detonation wave in an axisymmetric supersonic flow of a combustible mixture of gases are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 15–21, November–December, 2007     

Effect of the accommodation coefficient on transfer processes in a supersonic rarefied gas flow around a transversely aligned cylinder

A supersonic flow around a cylinder is studied by the direct statistical Monte Carlo method in a wide range of rarefaction: from regimes close to continuum to free-molecular flow. The effect of the accommodation coefficient on the flow near the cylinder and on heat transfer between the gas and the cylinder is examined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 64–72, May–June, 2008.     

Aerodynamic characteristics of a body of revolution with gas-permeable surface areas

Results of experimental studies and numerical calculations of aerodynamic characteristics of a supersonic flow around a body of revolution with a gas-permeable porous nose cone and an internal duct are presented. At a flow velocity corresponding to the Mach number M = 3, the body considered is found to have a lower drag coefficient (approximately by 9%) than a similar body impermeable for the gas and a lower streamwise static stability.     

The blunt-body problem in a nonuniform hypersonic viscous gas flow

The laws of heat transfer associated with the interaction of underexpanded supersonic gas jets and obstacles or blunt bodies have been investigated, for example, in [1–3]. Similar problems of nonuniform flow occur when bodies move in the wake behind other bodies; however, in this case the laws of heat transfer have so far received little attention [4–8]. It has been established that for a certain Reynolds number and flow nonuniformity parameters a zone of reverse-circulatory flow develops near the front of the blunt body. However, the conditions of transition to separated flow have not been determined. This paper presents a self-similar solution of the equations of the viscous shock layer near the stagnation line in supersonic flow past an axisymmetric blunt body located behind another body. On the basis of this solution a separationless flow criterion is proposed. The effect of the nonuniformity and the Reynolds number on the shock standoff distance, the convective heat flux and the friction drag of the blunt body is investigated. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 120–125, November–December, 1986. In conclusion the authors wish to thank I. G. Eremeitsev for useful suggestions and G. A. Tirskii for discussing their work.     

Drag and Separation Flow Past Solid Sphere with Porous Shell at Moderate Reynolds Number

Axisymmetric viscous, two-dimensional steady and incompressible fluid flow past a solid sphere with porous shell at moderate Reynolds numbers is investigated numerically. There are two dimensionless parameters that govern the flow in this study: the Reynolds number based on the free stream fluid velocity and the diameter of the solid core, and the ratio of the porous shell thickness to the square root of its permeability. The flow in the free fluid region outside the shell is governed by the Navier–Stokes equation. The flow within the porous annulus region of the shell is governed by a Darcy model. Using a commercially available computational fluid dynamics (CFD) package, drag coefficient and separation angle have been computed for flow past a solid sphere with a porous shell for Reynolds numbers of 50, 100, and 200, and for porous parameter in the range of 0.025–2.5. In all simulation cases, the ratio of b/a was fixed at 1.5; i.e., the ratio of outer shell radius to the inner core radius. A parametric equation relating the drag coefficient and separation point with the Reynolds number and porosity parameter were obtained by multiple linear regression. In the limit of very high permeability, the computed drag coefficient as well as the separation angle approaches that for a solid sphere of radius a, as expected. In the limit of very low permeability, the computed total drag coefficient approaches that for a solid sphere of radius b, as expected. The simulation results are presented in terms of viscous drag coefficient, separation angles and total drag coefficient. It was found that the total drag coefficient around the solid sphere as well as the separation angle are strongly governed by the porous shell permeability as well as the Reynolds number. The separation point shifts toward the rear stagnation point as the shell permeability is increased. Separation angle and drag coefficient for the special case of a solid sphere of radius r = a was found to be in good agreement with previous experimental results and with the standard drag curve.     

Nonlinear effects caused by pulsed periodic supply of energy in the vicinity of a symmetric airfoil in a transonic flow

Changes in the structure of a transonic flow around a symmetric airfoil and a decrease in the wave drag of the latter, depending on the energy-supply period and on localization and shape of the energy-supply zone, are considered by means of the numerical solution of two-dimensional unsteady equations of gas dynamics. Energy addition to the gas ahead of the closing shock wave in an immediate vicinity of the contour in zones extended along the contour is found to significantly reduce the wave drag of the airfoil. The nature of this decrease in drag is clarified. The existence of a limiting frequency of energy supply is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 64–71, May–June, 2006.     

Numerical simulation of stabilization of the boundary layer on a surface with a porous coating in a supersonic separated flow

Stability of a supersonic (M _∞ = 5.373) boundary layer with local separation in a compression corner with a passive porous coating partly absorbing flow perturbations is considered by solving two-dimensional Navier-Stokes equations numerically. The second mode of disturbances of a supersonic boundary layer is demonstrated to be the most important one behind the boundary-layer reattachment point. The possibility of effective stabilization of these disturbances behind the reattachment point with the use of porous coatings is confirmed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 39–47, March–April, 2007.     

Flow around the afterbody of a plate in a longitudinal gas stream with transverse injection from the lateral surface

The flow around the afterbody of a plate of finite thickness in a supersonic gas stream is investigated on the basis of a numerical solution of the time-dependent Navier-Stokes equations for a compressible viscous heat-conducting gas. The change in the flow pattern with the onset of transverse slot injection from the body surface in the vicinity of the base section is studied. For constant supersonic injection, both steady and unsteady flow regimes could be obtained depending on the values of certain relevant parameters.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 157–163, March–April, 1996.     

Mixed Convection in a Vertical Porous Channel

A numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces is studied by taking into account the effect of viscous and Darcy dissipations. The flow is modeled using the Brinkman–Forchheimer-extended Darcy equations. The two boundaries are considered as isothermal–isothermal, isoflux–isothermal and isothermal–isoflux for the left and right walls of the channel and kept either at equal or at different temperatures. The governing equations are solved numerically by finite difference method with Southwell–Over–Relaxation technique for extended Darcy model and analytically using perturbation series method for Darcian model. The velocity and temperature fields are obtained for various porous parameter, inertia effect, product of Brinkman number and Grashof number and the ratio of Grashof number and Reynolds number for equal and different wall temperatures. Nusselt number at the walls is also determined for three types of thermal boundary conditions. The viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. The Darcy and inertial drag terms suppress the flow. It is found that analytical and numerical solutions agree very well for the Darcian model. An erratum to this article is available at .     

An experimental study on the effects of uniform injection through one perforated surface of a square cylinder on some aerodynamic parameters

It is well known that injection/suction (transpiration) through a perforated surface is an efficient way of influencing the characteristics of a turbulent boundary layer. Injection application creates a thicker boundary layer on a flat plate and it thus decreases drag. In aeronautical applications, suction is frequently used to delay boundary layer separation. This paper presents an experimental study on the effects of uniform injection through one perforated surface of a square cylinder on the pressure distribution and drag coefficient in a two-dimensional turbulent flow. For this purpose, surface pressure measurements around a square cylinder have been performed at three different Reynolds numbers in a wind tunnel. The parameters taken into account were injection rate, position of perforated surface (i.e., front, top, and rear), and pressure coefficient and drag coefficient. The results show that variation in pressure coefficient around the square cylinder and drag coefficient were influenced by the position of perforated surface and by injection rate.     

Interaction of heated filaments with a blunt cylinder in supersonic flow

A computational study is performed to examine the influence of pulsed energy deposition on a cylinder in supersonic flow. A code is written to solve the compressible Navier–Stokes equations. The energy deposition is modeled as a high temperature, low density filament introduced at the inflow boundary, and the frequency of energy deposition pulses is varied. It is shown that the energy deposition reduces both the average drag and the average heat transfer to the front face of the cylinder. The effectiveness of drag reduction is shown to be inversely proportional to the energy deposition pulsation period. The efficiency of drag reduction is shown to be approximately 100. The average heat transfer to the face is reduced from the steady state, with a maximum reduction of 30%.     

Drag reduction by coupled systems: microbubble injection with homogeneous polymer and surfactant solutions

 The influence of homogeneous surfactant and homogeneous polymer solutions on the performance of microbubble skin friction reduction was investigated on an axisymmetric body. Carbon dioxide was injected into water, homogeneous surfactant (Aerosol OT) solutions, and homogeneous dilute polymer (Polyethylene oxide) solutions. Integrated skin friction measurements were obtained at two freestream velocities as a function of gas injection rate and polyethylene-oxide concentration. A moderate (50%) decrease in surface tension had little to no effect on the drag reducing characteristics of microbubble injection. At similar gas injection rates, microbubble injection exhibited more drag reduction in the polymer solutions than obtained with microbubble injection into water. However, the increased drag reduction obtained with polymer additives was no more than a multiplicative factor related to the baseline levels of drag reduction achieved by the individual methods, and suggests the mechanism for microbubble skin friction reduction acts independently of the polymer drag reduction. Received: 17 April 1998 / Accepted: 12 October 1998     

Formation of a gas hydrate due to injection of a cold gas into a porous reservoir partly saturated by water

Specific features of formation of gas hydrates due to injection of a gas into a porous medium initially filled by a gas and water are considered. Self-similar solutions of an axisymmetric problem, which describe the distributions of the basic parameters in the reservoir, are constructed. The existence of solutions is demonstrated, which predict gas hydrate formation both on the frontal surface and in the volume zone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 137–150, May–June, 2008.