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.     

Experimental investigation of flow in a trench

An experimental investigation was made of the flow of a viscous incompressible liquid in a trench of square transverse cross section, using a laser Doppler velocimeter. The investigation was made with two values of the Reynolds number Re, corresponding to laminar and turbulent flow conditions in the channel. The experimental data show that a core with a constant vorticity is formed in the trench, that a jet propagates near the walls of the trench, and that there are secondary eddies in the corners of the trench. The motion of a viscous liquid in a trench of rectangular cross section is part of a broad class of breakaway flows. Experimental data on the investigation of flow in trenches are extremely few. A majority of the existing information is limited to visual observations [1–4]. In [2, 5, 6] the question of the unstable character of flow in trenches was discussed. Quantitative measurements of stable eddy flows in trenches were made in [7–9] using a thermoanemometer, and in [7] measurements were made of the pressure at the bottom and walls of trenches; there are data on the distribution of the velocity in the middle sections of trenches. In [8] the mean velocity, the intensity of the turbulence, and the stress of the turbulent flow were obtained in several sections parallel to the side walls of the trench, In [9] a measurement was made of the velocities also in two cross sections of a trench in which one component of the velocity prevails. A brief analysis of the existing experimental results shows that these data are insufficient to form a detailed representation of the character of flow in a trench.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 76–86, March–April, 1976.     

Effect of finite cavity width on flow oscillation in a low-Mach-number cavity flow

The current study is focused on examining the effect of the cavity width and side walls on the self-sustained oscillation in a low Mach number cavity flow with a turbulent boundary layer at separation. An axisymmetric cavity geometry is employed in order to provide a reference condition that is free from any side-wall influence, which is not possible to obtain with a rectangular cavity. The cavity could then be partially filled to form finite-width geometry. The unsteady surface pressure is measured using microphone arrays that are deployed on the cavity floor along the streamwise direction and on the downstream wall along the azimuthal direction. In addition, velocity measurements using two-component Laser Doppler Anemometer are performed simultaneously with the array measurements in different azimuthal planes. The compiled data sets are used to investigate the evolution of the coherent structures generating the pressure oscillation in the cavity using linear stochastic estimation of the velocity field based on the wall-pressure signature on the cavity end wall. The results lead to the discovery of pronounced harmonic pressure oscillations near the cavity’s side walls. These oscillations, which are absent in the axisymmetric cavity, are linked to the establishment of a secondary mean streamwise circulating flow pattern near the side walls and the interaction of this secondary flow with the shear layer above the cavity.     

Spanwise characteristics of the separated flow in a suddenly expanding duct

Summary The secondary flow due to the growth of the streamwise vortices near the side walls serves to diminish the spanwise uniformity of the time-mean flow properties. In the region adjacent to the side walls, momentum mixing is enhanced due to the existence of the secondary flow and the separated shear layer spreads faster. There is a corresponding increase in the non-coherent turbulence in this region near the side walls. The increased spreading rates and overall turbulence in the shear layer, in turn, tend to suppress the rolling-up of the separated shear layer into organized structures. This effect is rapidly carried into the core two-dimensional flow region as the streamwise vortex grows under the influence of the adverse pressure gradient. The surface visualizations provide further evidence of the existence of secondary flows near the side walls.     

Unsteady flow of an Oldroyd-B fluid generated by a constantly accelerating plate between two side walls perpendicular to the plate

The velocity field and the adequate tangential stresses corresponding to the unsteady flow of an Oldroyd-B fluid induced by a constantly accelerating plate between two side walls perpendicular to the plate are established by means of Fourier sine transforms. The solutions corresponding to Maxwell, second grade and Newtonian fluids, performing the same motion, appear as limiting cases of the solutions obtained here. In the absence of the side walls, namely when the distance between walls tends to infinity, all solutions that have been determined reduce to those corresponding to the flow over an infinite plate. Finally, for comparison, the velocity field at the middle of the channel as well as the shear stress on the bottom wall is plotted as a function of y for several values of t and of the material constants. The influence of the side walls on the motion of the fluid is also emphasized by graphical illustrations.     

The effects of the side walls on the flow of a second grade fluid in ducts with suction and injection

The effects of the side walls on the flow in ducts with suction and injection are examined. Three illustrative examples are given. The first example considers the effect of the side walls on the flow over a porous plate. The second example considers the flow between two parallel porous plates and the third example is devoted to the investigation of the flow in a rectangular duct with two porous walls. Exact solution of the governing equation using the no-slip boundary condition and an additional condition are obtained. The expression of the velocity, the volume flux and the vorticity are given. It is found that for large values of the cross-Reynolds number near the suction region the flow for a Newtonian fluid does not satisfy the boundary condition, but it does not behave in the same way for a second grade fluid. Three examples considered show that there are pronounced effects of the side walls on the flows of a second grade fluid in ducts with suction and injection.     

Effects of the side walls on unsteady flow of a second grade fluid over a plane wall

The effects of the side walls on unsteady flow of a second grade fluid over a plan wall are considered. The solution of the governing equation for velocity is obtained by the sine transform method. This gives a correct result for the shear stress at the bottom wall. The shear stress at the bottom wall is minimum at the middle of the plate and it increases near the side walls. It is shown that the mean thickness of the layer of the liquid over the plate increases with time and the ratio of the mean thickness to the distance between the side walls becomes ultimately 0.2714.     

Lattice of plates in an unsteady supersonic flow

The supersonic unsteady flow of a gas past a lattice of thin, slightly curved profiles has been investigated in several studies. The paper [1] is devoted to an evaluation of the effect of wind tunnel walls on the unsteady aerodynamic characteristics of a profile, and [2] investigates the effects of the boundaries of a free jet. These cases are equivalent respectively to the anti-phase and in-phase oscillations of the profiles of an unstaggered grid. In [3] consideration is given to a more general case of gas flow past a profile in a wind tunnel with perforated walls. Flow past a lattice of profiles with stagger is studied in [4], where the magnitude of the stagger angle is limited by the condition that the lattice leading edge is located in the undisturbed stream.In the present paper we present a method of calculation of the unsteady supersonic flow of a gas past a lattice of profiles with arbitrary stagger. As an example the results are presented of the calculation of the aerodynamic forces and moments acting on an oscillating profile in a wind tunnel with solid walls and in a free jet.     

Numerical simulation of magnetohydrodynamic flow in a toroidal duct of square cross-section

We present numerical simulation results of the quasi-static magnetohydrodynamic (MHD) flow in a toroidal duct of square cross-section with insulating Hartmann walls and conducting side walls. Both laminar and turbulent flows are considered. In the case of steady flows, we present a comprehensive analysis of the secondary flow. It consists of two counter-rotating vortex cells, with additional side wall vortices emerging at sufficiently high Hartmann number. Our results agree well with existing asymptotic analysis. In the turbulent regime, we make a comparison between hydrodynamic and MHD flows. We find that the curvature induces an asymmetry between the inner and outer side of the duct, with higher turbulence intensities occurring at the outer side wall. The magnetic field is seen to stabilize the flow so that only the outer side layer remains unstable. These features are illustrated both by a study of statistically averaged quantities and by a visualization of (instantaneous) coherent vortices.     

Large-eddy simulation of turbulent buoyancy-driven flow in a rectangular cavity

Turbulent buoyancy-driven flow in a rectangular cavity with two differentially heated opposite walls is investigated numerically by means of large-eddy simulation (LES). Different dynamic global-coefficient subgrid-scale models for weakly compressible flows are applied to simulate the natural convective flow. It is shown that transition of the boundary layer is delayed in cases where the model coefficients are fixed or changing dynamically according to the Germano identity. On the contrary, in the ‘global equilibrium’ approach, the result shows an earlier change in flow regime due to lower subgrid-scale viscosity. Further, it is also demonstrated that three-dimensional effects of the natural convective flow may be significant due to the presence of adiabatic side walls.     

The propagation of shock waves in a semibounded volume

When a shock wave emerges from a pipe situated in a semibounded volume a system of waves arises between the end of the pipe and the bottom of the volume, and also in the gap between the pipe and the side walls of the volume. Paper [1] considers the propagation of a shock wave after emerging from the pipe until touching the side walls of the volume. The present paper considers the gas motion in a semibounded volume after the shock wave has traversed the volume and made contact with the side walls. In part 1 a physical model is constructed of the gas motion up to the time when the primary shock wave reaches the bottom of the volume. In part 2 relations are found which enable us to determine the stream parameters in the semibounded volume up to the time when the primary shock wave arrives at the bottom of the volume. Section 3 considers the motion of the reflected shock wave between the pipe and the side walls of the volume.     

The effect of flow patterns on two-phase flow in a T junction

Two-phase air-water flows have been studied in sharp edged $\text{T}$ junctions. The behaviour of the flow is very dependent on the flow pattern upstream of the junction. If the flow pattern is annular or churn then usually the liquid preferentially enters the side tube. If the flow pattern is bubbly, then the gas preferentially enters the side tube. For annular flow the liquid entering the side tube comes from the thin film of liquid travelling on the walls of the tube rather than from the drops entrained into the gas. The proportion of the total liquid film entering the side tube is approximately linearly dependent on the flow rate of gas into the side tube.     

Calculation of the stability of the flow in a circular pipe with injection

An experimental investigation of the transition of a laminar flow regime into a turbulent one has been carried out in [1] for a flow in a circular pipe which is organized due to injection through the porous lateral surface with a jammed leading end of the pipe. It was established as a result that injection leads to an increase in stability of the laminar flow regime and increases the Reynolds number of the transition to 10,000 instead of the value 2300 which is characteristic of flow in a circular pipe with impenetrable walls. A similar effect was discovered in [2], in which it was also obtained that the Reynolds number of stability loss under the action of injection can take values significantly larger than in pipes with impenetrable walls. The phenomenon of relaminarization of a turbulent flow in the initial section of a circular pipe under the action of injection has been experimentally detected at the entrance for relatively low Reynolds numbers in [3, 4]. Theoretical investigations of stability of flow with injection have been performed only for a plane channel [5, 6]. A calculation is made in this paper of the stability of a hydrodynamically developed flow in a circular pipe with injection through a porous lateral surface.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 82–86, May–June, 1984.     

Effects of the side walls on the unsteady flow of a second-grade fluid in a duct of uniform cross-section

In this paper, the effects of the side walls on the unsteady flow of a second-grade fluid in a duct of rectangular cross-section are considered. Two types of unsteady flows are investigated. One of them is the unsteady flow in a duct of rectangular cross-section moving parallel to its length and the other is the unsteady flow due to an applied pressure gradient in a duct of rectangular cross-section whose sides are at rest. It is shown that a Newtonian fluid reaches steady-state earlier than a second-grade fluid and the effect of the side walls on a second-grade fluid is more effective than that on a Newtonian fluid.     

The effect of side walls on particles mixing in rotating drums

In this paper, we study the effects of the presence and shape of side walls and of the overall length of rotating cylindrical drums on the mixing of particles with differing sizes by application of the discrete element method (DEM). By varying the semi-axis of the spheroidally shaped side walls and the length of the overall drum, we observe the formation of circulation patterns near the side walls. Although there is a vast amount of literature studying mixing regimes in rotating drums, little is known about the effect of the side walls of the drum on particle mixing. The results of our study demonstrate that introducing curved side walls induces a strong circulation pattern near these side walls, but has, paradoxically, a negative impact on mixing and actually promotes segregation. The cause for this segregation is the difference in velocity of differently sized particles near the curved side walls. Large particles accumulate at the curved side walls, whereas small particles move away from the curved side walls. When the length of the drum is increased, the overall effect of the side walls is decreased, although it does remain observable, even in very large drums.     

Particle transport in Poiseuille flow in narrow channels

Particle-tracking experiments were performed to validate a model [Staben, M.E., Zinchenko, A.Z., Davis, R.H., 2003. Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Phys. Fluids 15, 1711–1733] for neutrally buoyant spherical particles convected by a Poiseuille flow in a thin microchannel for particles as large as d_p/H = 0.95, where d_p is the particle diameter and H is the channel width (narrow dimension). The measured and predicted velocities agree within experimental error and show that a particle’s velocity is more retarded when it is larger and/or closer to a channel wall. The particle distribution across the channel for a blunt entrance shows a focusing of small particles away from the walls and towards the center of the channel, whereas the particle distribution for an offset-angled entrance is slightly skewed towards the wall encountered first in the entrance region. As a result, the average particle velocities for the blunt entrance exceed those for the angled entrance. Moreover, due to the depletion of particles from the slow-moving region within one radius of the wall, the average particle velocity exceeds the average fluid velocity unless the particle diameter exceeds about 80% of the channel width.     

Near-wall imaging using toluene-based planar laser-induced fluorescence in shock tube flow

A quantitative thermometry technique, based on planar laser-induced fluorescence (PLIF), was applied to image temperature fields immediately next to walls in shock tube flows. Two types of near-wall flows were considered: the side wall thermal boundary layer behind an incident shock wave, and the end wall thermal layer behind a reflected shock wave. These thin layers are imaged with high spatial resolution (15μm/pixel) in conjunction with fused silica walls and near-UV bandpass filters to accurately measure fluorescence signal levels with minimal interferences from scatter and reflection at the wall surface. Nitrogen, hydrogen or argon gas were premixed with 1–12% toluene, the LIF tracer, and tested under various shock flow conditions. The measured pressures and temperatures ranged between 0.01 and 0.8 bar and 293 and 600 K, respectively. Temperature field measurements were found to be in good agreement with theoretical values calculated using 2-D laminar boundary layer and 1-D heat diffusion equations, respectively. In addition, PLIF images were taken at various time delays behind incident and reflected shock waves to observe the development of the side wall and end wall layers, respectively. The demonstrated diagnostic strategy can be used to accurately measure temperature to about 60 μm from the wall.     

Variational problem of optimum side wall design for a narrow three-dimensional nozzle

The optimum design of the side walls of the supersonic section of a three-dimensional nozzle with two planes of symmetry is considered in the narrow channel model approximation, which reduces three-dimensional to two-dimensional flow. This nozzle realizes maximum thrust for given sonic or supersonic inlet flow, upper and lower walls, maximum permissible length and pressure outside the nozzle. In general, an approximate solution of the variational problem can be obtained by the indeterminate control contour method [1]. For nozzles with nonexpanding end sections of the upper and lower walls this is a rigorous solution. Numerical algorithms, based on the method of characteristics, for constructing the optimum, side walls and calculating the flow in narrow channels are developed in the formulation adopted using the optimality conditions found, which generalize the wellknown conditions for plane and axisymmetric configurations [1]. In addition, the three-dimensional supersonic flow in the nozzles thus designed has been calculated in accordance with a shock-capturing marching scheme [2], which for the uniform grids employed in the calculations gives a second-order approximation. A rather complex relation is established between the thrust of the optimum configurations constructed and the shape of their inlet cross sections.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 102–112, March–April, 1992.The authors are grateful to L. E. Sternin for drawing their attention to the problem and to V. A. Vostretsova for assisting with the work.     

Transonic flow of a gas jet from a vessel with plane walls

The problem of transonic flow of a gas jet with equilibrium excitation of the vibrational degrees of freedom of the molecules from an infinite symmetrical vessel with plane walls is reduced to a generalized Tricomi boundary-value problem for an equation of Chaplygin type. It is solved using a difference scheme [13] based on the decomposition of the difference operator in accordance with the type of differential operator. Calculation results are presented for a mixture of oxygen and nitrogen simulating air. The effect of the angle between the walls, the stagnation temperature and the back-pressure coefficient on the flow coefficient is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 128–135, November–December, 1987.The authors are grateful to F. Yu. Stepanov for his useful comments.     

An analytical solution to the heat transfer problem in thick-walled hunt flow

The flow of a liquid metal in a rectangular duct, subject to a strong transverse magnetic field is of interest in a number of applications. An important application of such flows is in the context of coolants in fusion reactors, where heat is transferred to a lead-lithium eutectic. It is vital, therefore, that the heat transfer mechanisms are understood. Forced convection heat transfer is strongly dependent on the flow profile. In the hydrodynamic case, Nusselt numbers and the like, have long been well characterised in duct geometries. In the case of liquid metals in strong magnetic fields (magnetohydrodynamics), the flow profiles are very different and one can expect a concomitant effect on convective heat transfer. For fully developed laminar flows, the magnetohydrodynamic problem can be characterised in terms of two coupled partial differential equations. The problem of heat transfer for perfectly electrically insulating boundaries (Shercliff case) has been studied previously (Bluck et al., 2015). In this paper, we demonstrate corresponding analytical solutions for the case of conducting hartmann walls of arbitrary thickness. The flow is very different from the Shercliff case, exhibiting jets near the side walls and core flow suppression which have profound effects on heat transfer.