Numerical study of a swirled turbulent flow in the separation zone of a centrifugal air separator

A mathematical model of a swirled turbulent flow in the separation zone of a pneumatic centrifugal device is presented. The model is based on the known k-? model of turbulence proposed by Wilcox. The influence of rotation of the separation-zone walls, input swirl of the gas flow, and other characteristic parameters on the mean velocity field is demonstrated. A comparison of parameters is performed, which reveals good agreement between the numerical and experimental results for a turbulent fluid flow between parallel disks.     

Experimental flow analysis of three-dimensional separation zones in front of weirs

Some results of experimental studies are shown concerning subsonic flow in separation zones of three-dimensional turbulent boundary layers formed in front of cylindrical weirs and rectangular parallelepipeds or dashboards. The width to height ratio of the weirs was varied from 0.25 to 24, and the boundary layer thickness to weir height ratio at separation was varied from 0.2 to 2.0. Flow patterns are shown along with the effects of the setup ge-ometry, of the weir width to height ratio, of the boundary layer parameters, and of the Euler and Reynolds numbers on the flow pattern and on the coordinates of characteristic points in the separation zone. Data are furnished for determining the dimensions of three-dimensional separation zones in front of weirs. The flow and the heat transfer in three-dimensional separation zones at subsonic velocities have not yet been explored adequately. The separation data published in [1, 2, 3] are not sufficient for determining the flow pattern, the static pressure distribution, and the characteristic dimensions of a separation zone — all of which are needed for calculating the heat transfer in the separation zone [4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 50–54, January–February, 1972.The authors thank V. S. Avduevskii for reviewing the results.     

On the centrifugal separation of a bulk mixture

The centrifugal separation of a mixture of particles and fluid in an axisymmetric container is examined. The flow consists of three distinct regions—mixture, sediment and purified fluid—with Ekman boundary layers at the interfaces and walls. In the settling process, the mixture and pure fluid acquire retrograde and prograde rotations relative to the tank. This flow pattern, and the shape and locus of the interface which are easily determined, provide another simple means to compare mixture theory and experiment. It is shown that when the Coriolis force is important, the pure fluid layer on the “outwardly” inclined wall is not thin. Moreover the interface between the mixture and the pure fluid is not perpendicular to the centrifugal force. Both features contrast those of the gravitational Boycott effect. As a consequence, there is no obvious enhancement of settling due to geometrical configuration.     

Experimental investigation of the flow in the separation zones of a turbulent boundary layer upstream from a two-dimensional step

The flow in the separation zones of a turbulent boundary layer upstream from a two-dimensional rectangular step has been experimentally investigated at subsonic flow velocities. The flow pattern and the static pressure distributions on the surface of the plate and the step are analyzed and the characteristic dimensions of the separation zones and the boundary-layer parameters in the separation section are determined.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 145–149, March–April, 1972.     

Study of heat transfer in the separation zones formed in front of supersonic jets in a subsonic carrier flow

The heat transfer taking place between the gas and the surface of the plate in the zone of three-dimensional separation of the turbulent boundary layer in front of a set of supersonic jets injected perpendicularly to a subsonic carrier flow is considered. The aim of this investigation is to establish the main physical characteristics of heat transfer in the separation zones in front of jet obstacles and to obtain the distributions of the local heat-transfer coefficients and the temperature of the thermally insulating wall as functions of the parameters of the carrier flow and the injected jets. Analysis of the experimental results yields certain approximating relationships for the distribution of the local heat-transfer coefficients as functions of the Mach number of the carrier flow M, the Mach number of the jet M_j, the relative boundary-layer displacement thickness _s= _s ^* /d, and the degree of jet superheating T_ojT_o relative to the separation zones in front of supersonic jet obstacles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–72, July–August, 1975.     

Unsteady flow calculation in a radial flow centrifugal pump with spiral casing

The prediction of the two-dimensional unsteady flow established in a radial flow centrifugal pump is considered. Assuming the fluid incompressible and inviscid, the velocity field is represented by means of source and vorticity surface distributions as well as a set of point vortices. Using this representation, a grid-free (Lagrangian) numerical method is derived based on the coupling of the boundary element and vortex particle methods. In this context the source and vorticity surface distributions are determined through the non-entry boundary condition together with the unsteady Kutta condition. In order to satisfy Kelvin's theorem, vorticity is shed at the trailing edges of the impeller blades. Then the vortex particle method is used to approximate the convection of the free vorticity distribution. Results are given for a pump configuration experimentally tested by Centre Technique des Industries Mécaniques (CETIM). Comparisons between predictions and experimental data show the capability of the proposed method to reproduce the main features of the flow considered.     

Structure of inertial-admixture accumulation zones in a tornado-like flow

The motion of a dispersed inertial admixture in a steady-state axisymmetric 3D viscous incompressible flow formed by a semi-infinite vortex filament interacting with an orthogonally located substrate surface is considered. The carrier-phase parameters are found from the numerical solution of the Navier-Stokes equations under the assumption of flow self-similarity of a known type [1]. Different phase force interaction schemes corresponding to different ratios of the phase densities are considered. For calculating the dispersed-phase continuum parameters, a full Lagrangian approach is used, which makes it possible to calculate the dispersed-phase concentration in particle accumulation zones and regions of intersecting particle trajectories. On the basis of parametric calculations, it is found that in the case of heavy particles (whose density is greater than that of the carrier phase) a “cup-shaped” particle accumulation surface visualizing a high-vorticity region is formed. The dependence of this surface shape on the governing parameters is investigated. It is shown that for different phase density ratios the dispersed-phase concentration fields are qualitatively different.     

Existence of supersonic zones in three-dimensional separation flows

Up till now the region of three-dimensional separation flows which occur with supersonic flow past obstacles has received insufficient study. Supersonic flow with a Mach number of 2.5 past a cylinder mounted on a plate was studied in [1]. A local zone with supersonic velocities was found in the reverse subsonic flow region ahead of the cylinder. Its presence is explained by the three-dimensional nature of the flow. Similar supersonic zones are not observed in the case of supersonic flow over plane and axisymmetric steps.The present paper presents the results of experimental studies whose objective was refinement of the flow pattern ahead of a cylinder on a plate and the study of the local supersonic zones.The experiments were performed in a supersonic wind tunnel with a freestream Mach number M₁=3.11. The 24-mm-diameter cylinder with pressure taps along the generating line was mounted perpendicular to the surface of a sharpened plate. The distance from the plate leading edge to the cylinder axis wasl ₀=140 mm. The plate was pressure tapped along the flow symmetry axis. The Reynolds number was Rl ₀=u₀ l ₀/v ₁, Rl ₀=1.87.10⁷, where u₁ andv ₁ are the freestream velocity and the kinematic viscosity, respectively. The pressures were measured using a Pilot probe with internal and external diameters of 0.15 and 0.9 mm, respectively.The probe was displaced in the flow symmetry plane at a distance of 1.6 mm from the plate surface and at a distance of 1.1 mm along the leading generator of the cylinder. The flow on the surface of the plate and cylinder was studied with the aid of a visualization composition and the flow past the model was photographed with a schlieren instrument. Typical patterns of the visualization composition distribution and the pressure distribution curves over the plate surface, and also photographs of the flow past the model, are shown in [1].     

Stability of a flow with leading stall zones

The phenomenon of the instability of plane and axisymmetric separation zones, starting from the leading edge of a semiinfinite plate with a mounded plane step, and from the apex of a cone with a mounted axisymmetric step (with a flap) is investigated herein. The instability of the separation zone is understood to be the periodic strong expansion, total disappearance, and new formation of a separation zone.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 74–81, January–February, 1972.     

Stress separation in the photoelastic study of centrifugal stresses

This technical note refers to the problem of stress separation in the photoelastic analysis of plane models under centrifugal stresses. Two methods are described in order to determine the sum of principal stresses. These methods, which are based on the compatibility equation, reduce the determination of the sum of principal stresses to the solution of a Laplace's or Poisson's equations. As an example of application, the separation of stresses in a rotating disk with two eccentric holes is shown and comparison with the stresses obtained by using the shear-difference method is made.     

Stability in film flow of a viscous fluid in a centrifugal force field

International Applied Mechanics -     

Flow investigation in separation zones ahead of supersonic jets in a subsonic stream

The flow in the three-dimensional separation zone of a turbulent boundary layer on a plate in front of a supersonic jet injected perpendicularly to the subsonic drifing flow is considered. The purpose of the investigation is to establish the physical singularities of subsonic flow around a supersonic jet obstacle and to obtain dependences of the geometric flow characteristics on the free-stream and injected-jet parameters. Results of an experimental investigation permitted proposing approximate dependences of the geometric three-dimensional separation-zone characteristics which appear in the subsonic stream ahead of a jet obstacle.     

Separation zones in the flow near a small-angle convex corner

On the basis of an asymptotic analysis of the Navier-Stokes system of equations for large Reynolds numbers (Re → ∞), the plane incompressible fluid flow near a surface having a convex corner with a small angle 2θ* is investigated. It is shown that for θ* = O(Re^?1/4), in addition to the known solution that describes a separated flow completely localized in a thin “viscous” sublayer of the interaction region near the corner point, another solution corresponding to a flow with a developed separation zone is possible. For θ ₀ = Re^1/4 θ* = O(1), the longitudinal dimension of this zone varies from finite values up to values of the order of Re^?3/8. The nonuniqueness of the solution is established on a certain range of variation of the parameter θ ₀. The dependence of the drag coefficient on the angle θ* is found.     

Supersonic two-dimensional flow in a forward separation zone

Supersonic separated flow past a spiked body with a plane cap on the end of the spike (a flat plate or a wedge) is studied. The cases of both symmetric and nonsymmetric flow, with a rotating or nonrotating spike, are considered. The flow pattern, visualized by means of a Toepler instrument and a laser knife, and the limiting streamline patterns are analyzed. The reasons for the initiation of self-oscillations in the flow between the cap and the body are determined. The flow patterns for a rotating and nonrotating spike are compared.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–162, January–February, 1995.     

On centrifugal separation of particles of two different sizes

We consider flow in a centrifugal force field of a non-dilute suspension with particles or droplets of two sizes. The volume fraction and the velocity fields are determined assuming small convection and shear terms. The resulting flow field is quite different from that in a gravitational settling of a similar mixture. In particular, the volume fraction is a function of time and radius in the sectors separated by kinematic shocks and the settling velocity is a non-monotonic function of the particle size.     

Contribution to the theory of stationary separation zones

Experiment shows that the stationary flow pattern about a bluff body with closed separation zone, in the case of laminar flow about the body and in the separation zone, breaks down for a subsonic stream velocity in the Reynolds number range from 10¹ to 10². However, experiment shows that for a supersonic stream velocity a stable stationary flow pattern is observed with the existence of laminar stagnant zones adjacent to the body (the stagnant zone behind an aft-facing step on the body surface, the stagnant zone ahead of a gradual forward-facing step on the body surface, the forward separation zone formed by the tip of a spike, the stagnant zone formed when a shock impinges on a body surface) at high Reynolds numbers of the order of 10⁴–10⁶.Thus, experiments indicate that in certain ranges of variation of M and R, under certain boundary condition, stationary solutions of the viscous fluid equations of motion exist and are stable. Outside these ranges and under other boundary conditions the flow about a body with a closed separation zone has a more (Karman vortex street for M1) or less (pulsating flow in the near wake behind the body for M>1) marked unsteady nature, indicating instability of the stationary solutions of the equations of motion under these conditions. To date no theoretical justification has been presented for the existence of stable stationary flows with separation zones in the ranges indicated.In the following an attempt is made to find the region of existence of possible stationary flows with a closed separation zone in that range of Reynolds numbers in which the flow in the viscous mixing region may be described by the Prandtl equations. In so doing the boundary conditions for the flow within the separation zone are selected so that the flow pattern within the zone is significantly simplified and use of the analysis methods applicable in hydrodynamics becomes possible. In the first part (§§1–4) we study the field of possible stationary flows for the case of an incompressible fluid. It is shown that only under special boundary conditions within the separation zone (ideal dissipator) does the flow about a flat plat as R approach the Kirchhoff flow with fluid at rest within the zone. In this case the drag coefficient of the system consisting of the plate plus the ideal dissipator c_x/(^{+ +}4), i.e., it approaches a value which is half that obtained by Kirchhoff for an ideal fluid.A qualitative study of the field of possible stationary flows in the c_xR plane made it possible to discover the existence of a region, having an upper bound at R10², which degenerates into a line. In this region the stationary flows have a singular flow configuration with inviscid vortical-type attachment.The existence of a connection between the flow configuration in the inviscid vortical attachment region and the stability of the stationary solutions is investigated in the second part (§§6–7), both for the case of individual solutions obtained by the method of linear hydrodynamic stability theory and on the basis of the available experimental data obtained over a wide range of Reynolds numbers for both subsonic and supersonic flow velocities. This investigation makes it possible to formulate a rule for finding stable stationary flows with separation zones and to apply this rule to analyze separation-type flows, both laminar and in certain special cases turbulent.