Turbulent air flow in a round pipe at high temperatures

The calculation of the heat exchange and fractional resistance during the turbulent flow of a gas with variable physical properties represents a complicated problem, which can be solved only with the help of a computer (see [1, 2], for example). Fundamentally new devices, the working substance of which is a gas heated to high temperatures, have been undergoing intensive development recently in engineering. The velocity and enthalpy profiles at the entrances of such devices can be nonuniform, not coinciding with the profiles typical of developed turbulent flow; the channel walls can consist of strongly cooled metal sections and weakly cooled ceramic sections; the ceramic materials used may be rough. The enumerated properties additionally complicate the calculation of the flow of a gas with variable physical properties. In the present report we consider two cases: the flow of air heated to high temperatures in a channel with a constant wall temperature under the conditions of strong cooling, and the flow in a pipe consisting of a strongly cooled metal section and a weakly cooled ceramic section. The results are obtained numerically using an implicit finite-difference scheme. They are in satisfactory agreement with the available experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 162–166, March–April, 1978.In conclusion, the author thanks A. N. Sekundov, I. P. Smirnova, and A. B. Lebedev for useful advice on questions connected with the development of the calculation program and A. B. Vatazhin for constant attention to the work.     

Heating and flow of a conducting gas

A model is proposed for the laminar flow of a conducting gas in the channel of a conical plasmatron (plasma source) and in the surrounding motionless medium. The boundary-layer approximation equations are written taking the intrinsic magnetic fields into account. The flow of an argon plasma in argon and air is analyzed numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 190–193, September–October, 1975.     

Theoretical and experimental investigations of the flow of a viscous fluid near the line of intersection of a cylindrical surface and a flat surface

Flow along a corner was investigated at large Reynolds numbers in, for example, [1–3]. The present author [4] considered flow in the neighborhood of a corner formed by the intersection of a plane and a concave cylindrical surface, the main attention being devoted to the formation of the three-dimensional boundary layer on the plane near the corner. It was shown that the curvature of one of the intersecting surfaces changes the flow pattern qualitatively. In the present paper, we report an investigation of the formation of the flow on a concave cylindrical surface near such a corner and consider how the flow is rearranged in the neighborhood of a corner in, for example, a channel of rectangular cross section that has an initial straight section and then a bend with a discontinuity of the curvature of the line of intersection of the concave and flat sides of the channel. The results are given of some experimental investigations of flow near the line of intersection of a flat wall and a curved (concave and convex) wall at a bend in a rectangular channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 64–68, January–February, 1983.I thank G. M. Bam-Zelikovich for constant interest in the work and A. I. Ruban for a number of extremely helpful comments.     

On the optimal distribution of the flow rate of gas blown through the side walls of the channel of a de plasmotron (plasma generator)

It is well known that the blowing of cold gas through the side walls of the channel of a dc plasmotron (plasma generator) with longitudinal blowing over the arc leads to an increase in the useful power of the plasmotron [1]. The increase is due to the increase in the combustion voltage of the arc and also the decrease in the heat fluxes to the wall of the channel. The present paper solves the problem of the optimal distribution of the flow rate of gas blown through the side walls into the channel of a dc plasmotron of arbitrary shape F(x). The flow in the main channel and in the ducts in the side walls is described by the quasi-one-dimensional gas-dynamic equations investigated qualitatively in [2] and verified experimentally in [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 120–124, May–June, 1981.     

Numerical investigation of unsteady subsonic viscous gas flows in a plane channel with a sudden expansion

The nonlinear processes of development of instability in an unsteady subsonic viscous gas flow in a plane channel with a sudden expansion are investigated numerically with allowance for acoustico-vortex interaction over a broad interval of the characteristic parameters. Effects associated with the acoustic self-excitation of the jet flowing into the wider part of the channel are determined. Approximate relations are obtained for the resonance conditions of self-excitation. The effect of the inlet mean-velocity profiles on the evolution of the flow is estimated. The processes of formation and subsequent interaction of the coherent structures are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 32–41, July–August, 1988.     

Heat transfer in subsonic high-temperature gas flow through three-dimensional curved channels

The heat transfer in subsonic high-temperature (T 2000°K) gas flow through a curved channel of rectangular cross section has been experimentally investigated. The local heat flow into the channel wall was measured by the modified gradient method, which consists in subdividing the walls by means of thin annular thermally-insulating partitions, measuring the temperature in the upper (gas) and lower (coolant) sections of the modules thus formed, and using these measurements to determine the local heat flux q_w on the assumption that the thermal field in the module is homogeneous. The soundness of this method has been demonstrated theoretically and experimentally and the expediency of using it in the intensive wall cooling regime has been confirmed. The method is employed to find the local heat flux fields over the- entire surface of the channel. The integrated fluxes q_w coincide to within 5% with the independently determined total increase in the enthalpy of the water in the cooling channels. A distinguishing feature of the investigation is the high relative curvature of the bend in the channel, which leads to the formation of a zone of intense separation on the convex (inner) wall. Three types of channel are examined. These differ with respect to the section beyond the bend which is either long or short or short with a contraction. A close correlation between the characteristics of the q_w fields and the hydrodynamic effects is detected and explained. These effects comprise: separation and reattachment of the flow, secondary effects in the bend, the formation of an unclosed separation zone in the short outlet section, the localization of this zone when the outlet section includes a contraction, and specific gas dynamic effects near the intersection of the surfaces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 93–99, May–June, 1989.     

Effect of proximity of barrier on lifting force produced by vertical solid jets

The effect of proximity to the ground on the lifting force generated by a vertical solid jet is studied in connection with development of vertical takeoff and landing devices and of air cushion devices. Such a study was made in [1 ] for planar flow by an incompressible ideal fluid. There a generalization of the results obtained on a compressible fluid was made by the approximation method. In the present work the planar problem of streamline flow past a dihedral barrier of a gas jet emerging from a channel with parallel walls was solved by the Chaplygin-Fal'kovich method [2, 3], The results of [1, 4–9] follow as a particular case from the solution obtained. Calculations were carried out clarifying the effect of the proximity of a barrier and the lifting effect of a fluid on flow characteristics at subsonic speeds.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 123–131, September–October, 1971.     

Evaporation from a surface and vapor flow through a plane channel into a vacuum

Two-dimensional steady rarefied-gas channel flow between two parallel walls, from an evaporating face to a perfectly absorbing plane end face, is studied. The vapor is considered to be a monatomic gas. The corresponding problem for the kinetic equation with collision integral in BGK form is formulated and solved numerically by two different finite-difference methods. Attention is focused on the calculation of the total gas flow rate through the channel cross-section. The structure of the gas channel flow as a function of the flow rarefaction, the channel length, and the ratio of the evaporation temperature to the wall temperature is studied.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–158, January–February, 1996.     

Bubble generation and transport in a microfluidic device with high aspect ratio

Bubble generation and transport in a micro-device composed of a micro-T-junction and a following serpentine micro-channel was experimentally investigated. It has a rectangular cross-sectional with an aspect ratio of 7.425. Air and water were used as gas and liquid, respectively. Mixtures of water–glycerol and water–Tween-20 were used to study the effects of liquid viscosity and surface tension. Compared with previous T-junction bubble generation, the liquid and gas inlets orientation was switched in this work. The continuous flow was driven from the perpendicular channel and the dispersion flow was from the main channel. It shows that the break-up process has three periodic steps under certain operating conditions. The dimensionless bubble length L/w in the micro-channel with high aspect ratio is much larger than that in square microchannels. A correlation is proposed to correlate L/w with liquid flow rate J_L, gas flow rate J_G, and liquid viscosity μ_L. Surface tension σ can change the bubble shape but almost does not affect the bubble length in this fast break-up process. Additionally, a long bubble may be broken up at the corners at the same time because the locations of gas and liquid are exchanged relative to the concave and convex portions of an elbow after a turn which may result in the change of fluid velocities and gas–liquid pressure drop.     

Acoustic resonance associated with vibrations of an array of plates in a subsonic flow

The acoustic resonance effect occurring in the vibrations of an array of profiles (cascade) in a gas flow has been studied by a number of authors [1–8]. Relying on assumptions of a heuristic nature [1, 2, 7, 8] and using rather crude models [4, 6], they have derived criteria governing the acoustic resonance regimes and given the effect a certain physical interpretation. However, many problems of a physical bearing with regard to the quantitative and qualitative principles of the effect have been left unresolved. For a more complete and rigorous solution of the problem the author has previously [9, 10] analyzed the natural modes of a gas flowing past an array of plates It was determined that in the array domain the vibrational modes of the gas are localized in the vicinity, of the array and the eigenvalues are determined by the characteristic dimensions of the interstitial channel (as an open resonator). Also, the eigenfrequences were determined for the gas in the flow plane with the array absent [9]. Under spatial periodic conditions, such that the flow in the plane can be considered as a certain model of flow in an annular duct, these eigenfrequencies concurred with those obtained earlier in [1, 2, 4–6]. The results of [9, 10] are used in the present study as a basis for investigating certain laws and relations governing the unsteady aerodynamic characteristics of arrayed profiles in or close to regimes such that the gas can execute natural vibrations in the array domain and in an annular duct in the absence of the array.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 139–144, September–October, 1972.     

Experimental and Numerical Investigation of Flows in Complex Shaped Axisymmetric Channels with Mass Injection

The results of an experimental and numerical investigation of the flow in an axisymmetric channel with radial cavities are presented. The experiments were performed with air in a wind tunnel. The theoretical results obtained by numerically solving the problem of viscous axisymmetric gas flow agree with the experimental data on the longitudinal velocity profiles in a channel with a radial cavity.     

Induced flow close to the entry of a jet into a channel

The flow investigated here appears as a result of the ejecting action of a turbulent jet in conditions when a jet, after emerging from a cylindrical nozzle, impinges into a gas flow channel. Such conditions occur in gas distribution systems. A review of the investigations of flows induced by jets and the solution of a number of problems are contained in [1]. A distinctive feature of the problem investigated below is the stronger development of local characteristics and the specific flow geometry, and also its spatial inhomogeneity. The method of integral transforms is used and formulas for determining the velocity about the nozzle and the flow in the vicinity of jet entry into the gas channel are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 126–133, January–February, 1976.The author thanks T. Kh. Sedel'nikov for valuable suggestions.     

Effect of the form of the electrodes on the current distribution in a magnetogasdynamic channel

A solution is given to the plane problem of the flow of a conducting gas across a homogeneous magnetic field in a magnetogasdynamic channel taking account of the Hall effect at small magnetic Reynolds numbers. The channel is formed by two long electrodes, and the cross section of the channel varies slightly and periodically along the gas flow. It is assumed that the electromagnetic forces are small. It is shown that the current distribution in the channel is nonuniform to a consider able degree and that inverse currents can form at the electrodes, with both subsonic and supersonic flows of the conducting gas. Transverse motion of the gas, due to a change in the cross section of the channel, leads to an increase of Joule energy losses. In [1] the current distribution was obtained in a flat channel formed by infinite dielectric walls, with the flow of a steady-state stream of plasma through the channel across a homogeneous magnetic field. With interaction between the flow and the magnetic field, closed current loops develop in the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 26–33, November–December, 1970.     

Gas flow in cylindrical capillaries under intermediate conditions

At present, there are sufficient solutions of the problem of free-molecular gas flow through a short cylindrical channel, for example, [1–3]. In intermediate flow conditions, for Knudsen number Kn 1, solutions have been obtained for the limiting cases: an infinitely long channel [4] and a channel of zero length (an aperture) [5]. However, no solution is known for short channels for Kn 1. The present work reports a calculation by the Monte Carlo method of the macroscopic characteristics of the gas flow through a short cylindrical channel (for various length—radius ratios), taking into account intermolecular collisions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 187–190, January–February, 1977.     

Effect of an inhomogeneous magnetic field on the structure of an ionized gas flow

Results of an experimental study of the flow of an ionized gas produced by a shock wave through an inhomogeneous magnetic field are presented. Braking of the gas flow produced by the end currents is determined at two fixed sections of the magnetogasdynamic channel from the value of the isolated shock wave formed in the vicinity of the hemispherical model over which the flow passes. Maximum recorded reduction in Mach number was 30%, and with a magnetogasdynamic interaction parameter greater than 1.5, a transition of supersonic flow to infrasonic at the exit of the magnetic zone was observed. Experimental results were compared with a solution of a model problem which assumed one-dimensional flow in the flow core. The gas used was argon, with a maximum magnetic field induction of 1.5 T.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–178, September–October, 1976.     

Supersonic two-phase flow around a wedge

Supersonic two-phase flow around bodies is encountered in calculating the flow around the last stages of blades of condensing turbines, in studying the motion of airplanes under cloudy conditions, etc. In the latter case, there is, along with erosion of the forward edges of the wing profiles, a change in the wave structure and interference situation in the flow about the airplane, leading to off-design regimes of motion. Supersonic flow of a two-phase mixture around a wedge, without taking account of the influence of the particles on the flow, was investigated in [1–3]. In [4], also in this kind of simplified setting, a study was made of the interaction of particles with the surface of a wedge in which reflection of the particles from the wall was taken into account. Morganthaler [5] made an experimental study of the flow of a mixture of air and aluminum oxide particles around a wedge. In [6] a theoretical study was made of a supersonic two-phase flow around thin flat axially-symmetric bodies. In particular, for the flow around a wedge, closed form solutions were obtained for the form of the shock wave, the gas streamlines and particle paths, and the distribution of all the parameters along the surface of the wedge. On the basis of the equations given in [7] and the method of characteristics, which were developed for flows consisting of a mixture of a gas and heterogeneous particles in nozzles [8,9], we present below a study of a supersonic two-phase flow around a wedge.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 83–88, March–April, 1972.     

Airflow behind strong shock front with account for nonequilibrium ionization and radiation

We consider the gas state behind a shock wave front in air with a velocity v10 km/sec. Nonequilibrium ionization and radiative transport are taken into account. We take into consideration the real air spectrum — the numerous lines, bands, and continuua. Account for the radiation leads to an integrodifferential system of equations for which a solution method is developed. As a result we obtain the gas parameter profiles behind the shock wave, which are affected by the relaxation processes and radiative cooling. The calculations were made for v=10–16 km/sec and a pressure p=10^–5–10^–2 atm ahead of the front.In order to obtain realistic results, we consider only the gas layer bounded by the shock and a surface parallel to it. It is assumed that the gas bounded by these planes is not irradiated from without. In this formulation still another defining parameter appears—the distancel between the planes. The calculations were made forl=1–100 cm.     

Characteristics of film condensation of supersaturated steam–air mixture on a flat plate

Experimental and numerical work was performed for the laminar film condensation of steam–air mixture flow over a flat plate. For small temperature difference between the gas mixture and the cold wall, the gas mixture in the boundary layer can be treated as superheated gas. When the temperature difference is large, the gas mixture becomes supersaturated near the interface. In that case, mist formed near the interface, the temperature profile of the gas mixture was greatly concaved toward the interface and the heat transfer was enhanced. However the velocity profile measured by the laser Doppler anemometer (LDA) showed the same trend without mist formation. A calculation model is proposed and compared with the experimental data and previous models for the superheated or the saturated conditions.     

Mixed boundary-value problems of profiling of supersonic nozzles and channels

In the framework of the inverse method of numerical profiling of the supersonic part of nozzles and channels, two new mixed boundary-value problems of gas dynamics are formulated and solved with boundary conditions specified both along and across the flow. A modification of the grid-characteristic method with respect to layers formed by streamlines is constructed. The solution of the posed mixed problems makes it possible to profile a class of flat and axisymmetric nozzles and channels larger than the known class. Transition channels, which transform one expanding flow into another for which the flow at the exit is close to that from a source, are constructed Channel profiles are obtained with a bend in the generator that suppress shock waves on the wall. The results are presented of profiling of exit channels with contact discontinuity, and also channels that realize discontinuities in the exit sections, these being made isentropic by means of compression characteristics focused at the points of the discontinuity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 112–118, July–August, 1983.We thank U. G. Pirumov, M. Ya. Ivanov, and A. N. Kraiko for helpful discussions.     

Flow of viscous gas out of a cylindrical channel into vacuum

A study is made of the exhausting of a jet of viscous gas from a cylindrical channel into vacuum in the presence of a flat bounding surface outside the channel in the plane of its exit section. The problem is solved numerically using the complete system of Navier—Stokes equations. The developed flow model makes it possible to take into account the influence of an external medium into which the jet exhausts on the structure of the flow in the exit section of the channel, and also the influence of the subsonic part of the boundary layer in the channel on the flow field of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–128, January–February, 1981.