Multicomponent chemically-reacting turbulent viscous shock layer on a catalytic surface

Turbulent flows past blunt bodies at high supersonic speeds are mainly investigated within the framework of the boundary layer model. However, even at large Reynolds numbers owing to the strong entropy gradient on the lateral surface it becomes necessary to take boundary layer corrections into account in the higher approximations [1]. The use of viscous shock layer theory makes it possible to obtain fairly accurate results over a broad interval of variation of the Reynolds numbers without organizing iterations with respect to vorticity and displacement thickness. The nonequilibrium nature of both homogeneous and heterogeneous catalytic reactions is taken into account. The results obtained are compared with the experimental data [2, 3]. Previously, in [4, 5] turbulent flow was investigated within the framework of viscous shock layer theory in the case of equilibrium homogeneous reactions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 144–149, March–April, 1989.     

Turbulent boundary layer on a catalytic surface in a nonequilibrium dissociating gas

The majority of the studies which consider the flow of a dissociating gas in a turbulent boundary layer are devoted to the investigation of either frozen or equilibrium flows on a flat plate.The frozen turbulent boundary layer has been studied by Dorrance [1], Kutateladze and Leont'ev [2], and Lapin and Sergeev [3]. A study of the effect of catalytic recombination processes at the plate surface on the heat transfer in a frozen turbulent boundary layer was made by Lapin [4].Kosterin and Koshmarov [5], Ginzburg [6], Dorrance [7], and Lapin [8] have studied the turbulent boundary layer on a plate in equilibrium dissociating gas.The calculation of the heat transfer in a turbulent boundary layer on a catalytic plate surface with nonequilibrium dissociation was made by Kulgein [9]. In this study the nonequilibrium nature of the dissociation process was taken into account only in the laminar sublayer, while the flow in the turbulent core was considered frozen. The solution was found numerically using a computer by means of a laborious iteration process.The present paper reports a method for calculating the turbulent boundary layer on a flat catalytic plate with arbitrary dissociation rate. The method, constructed using the assumptions customary for turbulent boundary layer theory, is a successive approximation method. Good convergence of the method is assured by the fact that the effect of the nonequilibrium nature of the dissociation process on the parameter distribution in the boundary layer and, consequently, on the friction and heat transfer may be allowed for merely by finding corrections, usually relatively small, to the distribution of these parameters in the equilibrium or frozen flows. The basis of the study is the two-layer scheme of the turbulent boundary layer. The Prandtl and Schmidt numbers and also their turbulent analogs are taken equal to unity. As the model of the dissociating gas we use the Lighthill model of the ideal dissociating gas [10], extended by Freeman [11] to nonequilibrium flows.     

Slip boundary conditions on a catalytic surface in a multicomponent gas flow

The boundary conditions for the velocity slip and temperature and concentration jumps on the surface of a body in a rarefied multicomponent gas flow are obtained. The mathematical treatment is given in detail because of the need to examine critically some previous results which disagree with each other in spite of the fact that the initial premises and the methods of solution were the same. The results of this study, which are given in a convenient form, represent the boundary conditions for both the simplified and the complete Navier-Stokes equations in problems of hypersonic rarefied gas flow past bodies with a catalytically active surface.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 159–168, January–February, 1996.     

Boundary conditions for flows with chemical reactions occurring on a surface

With the use of a solution of a model Boltzmann equation for a binary mixture in the Knudsen layer, we obtain the boundary conditions for the equations of gas dynamics when the reactionl _iA_il _jA_j (l _i molecules of A_i change intol _j molecules of A_j, and vice versa) is occurring on a surface. The boundary condition that we obtain differs from those that are usually applicable by the presence of terms of the same order. This confirms the conclusion arrived at by the authors in [1], where it was shown that if the Knudsen layer is left out of account, which is precisely what is usually done, it is impossible to obtain correct boundary conditions.Moscow. Translated from Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 129–138, January–February, 1972.     

Effect of a pulsating flow on hydrodynamics and fluid catalytic cracking chemical reaction in a circulating fluidized bed riser

The three-dimensional computational fluid dynamics (3D-CFD) of a pulsating flow applied to the fluid catalytic cracking (FCC) reaction was investigated in the riser of a circulating fluidized bed reactor. The kinetic parameters of the FCC and coke burning reactions for predicting the reactant conversion and product yield percentages were applied. To increase the reactant conversion level and product yield, the effect of the pulsating flow operating parameters was considered using a 2^k statistical experimental design with four factors (amplitude, frequency, types of the waveform, and amplitude ratio). The 3D-CFD simulation was successfully validated from the experimental literature data. The frequency and type of the waveform were found to be the significant operating parameters. The expression of the fitted regression model and response surface contour were derived and revealed that the pulsating flow provides a higher reactant conversion level and product yield percentages compared to a non-pulsating or steady flow.     

Effect of surface catalytic activity on nonequilibrium heat transfer in a subsonic jet of dissociated nitrogen

The present paper investigates experimentally and numerically the effect of the heterogeneous recombination of atoms on the heat transfer of models in a subsonic jet of dissociated nitrogen for the conditions of an experiment in the VGU-2 plasma generator and determines the effective probabilities of the heterogeneous recombination of nitrogen atoms for a number of materials at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–172, May–June, 1985.     

Array measurements of the surface pressure beneath a forced axi-symmetric separation bubble

An array of microphones is used to study the space–time characteristics of the wall-pressure field beneath a forced separation bubble downstream of an axi-symmetric backward-facing step. To excite the flow, an externally driven Helmholtz resonator is employed. A unique aspect of the present study is the utilization of an amplitude-modulated forcing scheme in order to avoid contamination of the measured hydrodynamic pressure fluctuations by acoustic radiation from the forcing device. The results lead to the hypothesis that the optimal forcing frequency is achieved when the forced disturbance originates near the center of the unforced separation bubble in the limit of very low levels of forcing. Moreover, a frequency–wavenumber spectrum analysis highlights the possibility for achieving separation control while minimizing potential acoustic radiation due to coupling between the forced disturbance and resonant modes of the underlying surface.     

Three-dimensional chemically nonequilibrium viscous shock layer on a catalytic surface with allowance for associated heat transfer

A three-dimensional flow of dissociating air past blunt bodies is investigated in the framework of the thin viscous shock layer theory. Multicomponent diffusion and homogeneous chemical reactions, including dissociation, recombination, and exchange reactions, are taken into account. The generalized Rankine-Kugoniot conditions are specified on the shock wave and the conditions which take into account the heterogeneous catalytic reactions, on the surface of the body. The viscous shock layer equations are solved together with the heat equations inside the coating, which is carbon with a deposited thin film of SiO₂, or quartz. The case of a thermally insulated surface is also considered. The problem for the case of the motion of a body along the re-entry trajectory into Earth's atmosphere is investigated numerically. The temperature of the surface and the heat flux toward it are given as a dependence on the height (tine) of the flight for different cases of the specification of the catalytic reactions. It is shown that the difference between the heat fluxes towards the thermally insulated surface and the fluxes toward the heat-conducting surface in the neighborhood of the stagnation point is of the order of 6–12% for all the cases considered. This makes it possible to decouple the solution of the problem of heat conduction in the body.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 140–146, November–December, 1985.deceased     

Allowance for longitudinal diffusion in the neighborhood of a discontinuity of catalytic surface properties

In the investigation of flow near surfaces with discontinuous changes in the catalytic properties the question arises of the applicability of parabolic boundary and viscous shock layer equations in the neighborhood of the discontinuity. In the present paper, three types of problem are solved in which longitudinal diffusion is taken into account. In the first an insertion with different catalytic properties is placed in the neighborhood of the stagnation point, in the second the discontinuity lines of the catalytic properties are perpendicular to the oncoming flow, while in the third they are parallel. On the main surface and on the insertion surface the heterogeneous catalytic reactions are assumed firstorder reactions with various rate constants whose values vary in a wide range. The data of the solution are compared with the solution obtained using the boundary layer approximation and the regions of influence of the longitudinal diffusion are estimated. In [1–4] a problem similar to the second one was solved by the numerical method of [1] and the Wiener-Hopf method for the case of transition from a noncatalytic to a perfectly catalytic surface and the region of applicability of the boundary layer was estimated [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 99–105, July–August, 1986.     

Diffusion problems in the linear theory of gasdynamic and chemical lasers

The system of linear equations of multicomponent convective diffusion is reduced consistently with allowance for the features of the relevant laser devices. A criterion for the realization of a purely diffusion regime is established. A method of diagonalization of the diffusion coefficient matrix is given; it reduces the multicomponent problem to a series of one-component problems. The superposition of relaxation modes is discussed. A diffusion type hydrofluoric laser illustrates the influence of angular asymmetry of the particles on the output power of the radiation.     

A hypersonic chemically nonequilibrium viscous shock layer oh wings with a catalytic surface

Within the framework of the theory of a hypersonic viscous shock layer a study is made of flow round wings of infinite span with blunt leading edges at various angles of attack and slip. Account is taken of multicomponent diffusion, and homogeneous chemical reactions, including dissociation-recombination reactions and exchange reactions. On the shock wave the generalized Rankine-Hugoniot conditions are given, and on the surface of the body conditions which allow for heterogeneous catalytic reactions of the first order with reaction rate constants depending [1] or not depending [2] on the temperature. The cases of an ideally catalytic and a noncatalytic surface are also considered. The surface of the body is assumed to be heatinsulated. A numerical study was made of the problem in a broad range of variation in the angles of attack and slip for different cases of prescribed constants representing the rates of the heterogeneous reactions. The conditions of the flow corresponded to the motion of a body which possess a lifting force along the trajectory of entry into the Earth's atmosphere [3]. The dependences are given of the equilibrium temperature of the surface along the stagnation line of the wing on the height of the flight and the distribution of this temperature along the surface of wings with parabolic and hyperbolic contours. It is shown that for flow regimes with a relatively high degree of dissociation in cases when the proportion of atoms recombined on the surface of the body is small, the dependences of the heat flow and the temperature of the surface on the angle of slip are of a nonmonotonic nature.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza., No. 6, pp. 127–135, November–December, 1984.