Spiral vortices between concentric cylinders

Spiral vortices appearing in Couette-Taylor flows are studied by means of numerical simulation. Transition curves from Couette to spiral vortices for different radius ratios and wavenumbers have been calculated in order to test our technique. Critical Reynolds numbers, angular velocities and slopes of the spirals at the onset of the instability agree with previous results [1]. Non-linear solutions obtained by a pseudospectral collocation method are studied, and they show a weak net axial flow. In order to counteract this effect, which is absent in the usual experimental set-up, an axial pressure gradient has been included. This procedure has proved to be sufficient to make the axial flow negligible. The onset of a quasiperiodic flow for larger Reynolds numbers, corresponding to a secondary bifurcation is also presented.     

Görtler vortices in Falkner–Skan flows with suction and blowing

In this paper, we use nonlinear calculations to study curved boundary‐layer flows with pressure gradients and self‐similar suction or blowing. For an accelerated outer flow, stabilization occurs in the linear region while the saturation amplitude of vortices is larger than for flows with a decelerating outer flow. The combined effects of boundary‐layer suction and a favourable pressure gradient can give a significant stabilization of the flow. Streamwise vortices can be amplified on both concave and convex walls for decelerated Falkner–Skan flow with an overshoot in the velocity profile. The disturbance amplitude is generally lower far downstream compared with profiles without overshoot. Copyright © 2007 John Wiley & Sons, Ltd.     

Influence of suspended particles on the structure of a turbulent flow in a tube

The results of an experimental investigation into the dispersed flow of a system subject to negative pressure gradients are presented. The measurements were based on an optical time-of-flight method in a water channel, using polystyrene spheres as the solid phase. The average and pulsational characteristics of the dispersed flow were obtained in the boundary (wall) region and also in the center (core) of the flow. For zero pressure gradient the influence of the solid phase expressed itself as a reduction in the level of turbulence and an increase in the extent of the viscous sublayer, leading to a fall in the coefficient of friction. For a negative pressure gradient the pressure of the solid phase generated small-scale vortices, reduced the extent of the viscous sublayer, and hence increased the coefficient of surface friction.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 111–118, March–April, 1976.The author wishes to thank Yu. A. Buevich for interest in this work and V. L. Zalukaev for participation in the experiments.     

Nonisothermal Couette flow of a non-Newtonian fluid under the action of a pressure gradient

Nonisothermal Couette flow has been studied in a number of papers [1–11] for various laws of the temperature dependence of viscosity. In [1] the viscosity of the medium was assumed constant; in [2–5] a hyperbolic law of variation of viscosity with temperature was used; in [6–8] the Reynolds relation was assumed; in [9] the investigation was performed for an arbitrary temperature dependence of viscosity. Flows of media with an exponential temperature dependence of viscosity are characterized by large temperature gradients in the flow. This permits the treatment of the temperature variation in the flow of the fluid as a hydrodynamic thermal explosion [8, 10, 11]. The conditions of the formulation of the problem of the articles mentioned were limited by the possibility of obtaining an analytic solution. In the present article we consider nonisothermal Couette flows of a non-Newtonian fluid under the action of a pressure gradient along the plates. The equations for this case do not have an analytic solution. Methods developed in [12–14] for the qualitative study of differential equations in three-dimensional phase spaces were used in the analysis. The calculations were performed by computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 26–30, May–June, 1981.     

Effect of plastic properties of fluids on phase permeabilities

The linearity of Darcy's law is known to be disturbed at both high and low flow velocities [1–3]. In the first case, this is associated with the increase in the inertial component of the hydraulic losses in the presence of large pressure gradients. The effect was theoretically investigated, for example, in [4]. In the second case, the nonlinearity is associated with the interphase interaction of the fluids and the skeleton of the porous material on the contact surface [5]. Here, within the context of the percolation approach [6, 7], the behavior of the phase permeabilities is analyzed for low flow velocities, when on the microlevel (flow in an individual pore channel) the fluids display plasticity properties [8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 110–115, March–April, 1991.     

Linear theory of unsteady gas flow under the influence of nonpotential external forces

We determine in the linear formulation the velocity and pressure fields excited in a compressible medium by a lifting filament that displaces and deforms arbitrarily. For general unsteady motion of such a filament we give explicit formulas that express the velocity at a given point in terms of the intensity of the free vortices entering the audio signal audibility zone constructed for this point. We examine gas flow caused by an arbitrary external body force field.Studies devoted to the determination of gas velocity fields for flow past slender bodies relate primarily to translational motion of a body with a dominant constant velocity [1–3]. Gas velocities for helical motion of a rectilinear lifting filament within the gas have been examined in [4].     

Effect of compressibility on the development of taylor-görtler vortices at high reynolds numbers

The development of disturbances in viscous compressible flows caused by centrifugal forces is investigated. On the basis of an asymptotic analysis of the Navier-Stokes equations at high Reynolds and Görtler numbers, mathematical models describing the development of three-dimensional unstable vortex structures are constructed. Various linear boundary-value problems are analytically solved. One type of boundary layer instability is that generated by a centrifugal force field. This kind of instability can manifest itself in the flow past concave surfaces or, in general, in flows with streamlines of positive curvature [1, 2]. Instability-driven Görtler vortices have been the subject of much research which was reviewed, for example, in [2–4].     

Uniqueness of the self-similar solutions of three-dimensional laminar boundary-layer equations

The equations of the three-dimensional laminar boundary layer on lines of flow outflow and inflow are studied for conical outer flow under the assumption that the Prandtl number and the productρμ are constant. It is shown that in the case of a positive velocity gradient of the secondary flow (α₁>0) the additional conditions which result from the physical flow pattern determine a unique solution of the system of boundary-layer equations. For a negative velocity gradient of the secondary flow (α₁≤0) these conditions are satisfied by two solutions. An approximate solution is obtained for the boundary layer equations which is in rather good agreement with the numerical integration results. Compressible gas flow in a three-dimensional laminar boundary layer is described by a system of nonlinear differential equations whose solution is not unique for given boundary conditions. Therefore additional conditions resulting from the physical pattern of the gas flow are imposed on the resulting solution. In the solution of problems with a negative pressure gradient these additional conditions are sufficient for a unique selection of the solution of the boundary-layer equations. However, in the case of a positive pressure gradient the solution of the boundary-layer equations satisfying the boundary and additional conditions may not be unique. In particular, in [1] in a study of a three-dimensional laminar boundary layer in the vicinity of the stagnation point it was shown that for $$c = {{\frac{{\partial v_e }}{{\partial y}}} \mathord{\left/ {\vphantom {{\frac{{\partial v_e }}{{\partial y}}} {\frac{{\partial u_e }}{{\partial x}}}}} \right. \kern-\nulldelimiterspace} {\frac{{\partial u_e }}{{\partial x}}}} > 0$$ the solution is unique, while for c<0 there are two solutions. In the present paper we study the question of the uniqueness of the self-similar solution of the three-dimensional laminar boundary-layer equations on lines of flow outflow and inflow for a conical outer flow.     

Asymptotic solution of incompressible boundary layer equations with negative pressure gradient and large injection rates

During entry of bodies into the Earth's atmosphere with high velocities, the mass removal from the body surface as a result of the large convective and primarily radiation fluxes may become arbitrarily large, i. e., the injection rate into the boundary layer may approach infinity. The present article presents a solution of the Prandtl equations for the incompressible boundary layer with negative pressure gradient (dp/dx<0) for large injection rates. The existence of a solution of the boundary layer equations with arbitrary injection rate under the condition dp/dx<0 was shown in Oleinik's work [1].The asymptotic solution obtained agrees with the exact numerical solution for those values of the injection rate for which the boundary layer approximation still remains valid. An analogous solution for the self-similar equations in the vicinity of the stagnation point was previously obtained in [2]. The use of the asymptotic solution makes it possible to find an expression for the friction coefficient which is convenient for concrete calculations in the case of arbitrary negative pressure gradients.In conclusion the author wishes to thank G. A. Tirskii for guidance in the work and I. Gershbein for permitting the use of the numerical solution.     

Direct Numerical Simulation of a Square Jet Ejected Transversely into an Accelerating, Laminar Main Flow

A numerical simulation of a square jet ejected transversely into a laminar boundary-layer flow was performed at a jet-to-main-flow velocity ratio of 9.78 and jet Reynolds number of 6330. The jet consisted of a single pulse with a duration equal to the time required for the jet fluid to travel 173 jet widths. A strongly-favourable streamwise pressure gradient was applied to the boundary layer and produced a freestream acceleration that is above the typical threshold required for relaminarization. The results of the simulation illustrate the effect of the favourable streamwise pressure gradient on the flowfield created by the transverse jet. Notably, the horseshoe vortex system created upwind of the jet remains steady in time and does not induce noticeable fluctuations in the jet flow. The upwind and downwind shear layers of the jet roll-up through a Kelvin–Helmholtz-like instability into discrete shear-layer vortices. Jet vorticity in the upwind and downwind shear layers accumulates near the corners of the jet and produces two sets of vortex pairs, the former of which couple with the shear-layer vortices to produce large, counter-rotating vortices in the freestream, while the latter are unstable and periodically produce hairpin vortices in the main-flow boundary layer and elongated vortices in the freestream behind the jet. The departure of the jet flowfield from the vortical structures typically observed in transverse jets illustrates the substantive effect of the favourable streamwise pressure gradient on the flowfield created by the jet.     

Experiments on elongational flow of dilute polymer solutions Part I: Jet reaction and excess pressure drop for the flow through small apertures

Experiments have been made with dilute polymer solutions on the reaction of jets issuing from small orifices and the excess pressure drop for orifice and capillary flows.Under the flow conditions with vortices occurring upstream of the aperture, the jet reaction is nearly zero below some mean velocity for PEO solutions and similarly zero below some generalized Reynolds number for Separan solutions. The normalized jet reactions, when they possess positive values, are correlated with the generalized Reynolds number irrespective of the aperture diameters for both kinds of solution.In most cases, the pressure is higher than in the corresponding water flow, but for some flows with no vortex it is lower. For the vortex flow of PEO solutions the normalized excess pressure drop is inversely proportional to the Reynolds number for both orifices and capillaries, while for Separan solutions this quantity is not correlated with the generalized Reynolds number for orifice flow but is correlated with it for capillary flow.     

压力梯度对湍流逆梯度输运的影响

研究Birkhoff系统的一般Lie对称性导致的非Noether守恒量. 得到非Noether守恒 量的存在定理，举例说明结果的应用.     

Blowing into a supersonic stream through a permeable surface

Distributed blowing of gas into a supersonic stream from flat surfaces using an inviscid flow model was studied in [1–9]. A characteristic feature of flows of this type is the influence of the conditions specified on the trailing edge of the body on the complete upstream flow field [3–5]. This occurs because the pressure gradient that arises on the flat surface is induced by a blowing layer whose thickness in turn depends on the pressure distribution on the surface. The assumption of a thin blowing layer makes it possible to ignore the transverse pressure gradient in the layer and describe the flow of the blown gas by the approximate thin-layer equations [1–5]. In addition, at moderate Mach numbers of the exterior stream the flow in the blowing layer can be assumed to be incompressible [3]. In [7, 8] a solution was found to the problem of strong blowing of gas into a supersonic stream from the surface of a flat plate when the blowing velocity is constant along the length of the plate. In the present paper, a different blowing law is considered, in accordance with which the flow rate of the blown gas depends on the difference between the pressures on the surface over which the flow occurs and in the reservoir from which the gas is supplied. As in [8, 9], the solution is obtained analytically in the form of universal formulas applicable for any pressure specified on the trailing edge of the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 108–114, September–October, 1980.I thank V. A. Levin for suggesting the problem and assistance in the work.     

Existence and Stability of Asymmetric Burgers Vortices

Burgers vortices are stationary solutions of the three-dimensional Navier–Stokes equations in the presence of a background straining flow. These solutions are given by explicit formulas only when the strain is axisymmetric. In this paper we consider a weakly asymmetric strain and prove in that case that non-axisymmetric vortices exist for all values of the Reynolds number. In the limit of large Reynolds numbers, we recover the asymptotic results of Moffatt, Kida & Ohkitani [11]. We also show that the asymmetric vortices are stable with respect to localized two-dimensional perturbations.     

Turbulent boundary layer with positive pressure gradient on a permeable surface under nonisothermal conditions

It is known that the longitudinal pressure gradient can exert a strong influence on the friction law and the characteristics of a dynamic turbulent boundary layer. The thermal and diffusion boundary layers are more conservative to the effect of the pressure gradient, and, hence, methods of analyzing them are based, in the majority of cases, on the hypothesis of conservativity of the heat- and mass-transfer laws to the longitudinal pressure gradient [1]. This hypothesis is verified by experimental results [2, 3] on heat transfer on an impermeable surface in a turbulent stream with positive pressure gradient under almost isothermal conditions. However, such investigations under nonisothermal conditions are practically nonexistent. An approximate theoretical analysis of the heat transfer in a turbulent boundary layer of a nonisothermal stream with a positive pressure gradient is given in this paper. Experimental results are presented. The experimental investigation was conducted in a burned-out graphite diffuser both with and without injection of an inert gas through the wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 43–49, July–August, 1976.     

Frictional resistance to accelerated flow in a tube

A study is made of the development of the flow of a viscous incompressible fluid from the state of rest in a circular cylindrical tube with constant pressure gradient. The tangential frictional stress at an arbitrary point of the flow is found as a function of the pressure gradient and the ratio of the values, averaged over the flow, of the accelerations corresponding to the considered time and the initial time. An analysis is made of the exact solution of the linear equation [1], which shows that the development of the drag forces in the case of viscous flow is determined by a characteristic time which depends on the kinematic viscosity and the tube radius. The value of the hydraulic friction drag coefficient for the unsteady flow is determined more accurately by introducing a correction that takes into account the velocity profile of the flow. The equations of motion are analyzed, and six different cases of development of the flow are described for the characteristic values of the dimensionless numbers. These cases determine the methods of calculation of one-dimensional problems. This question has not been fully clarified in earlier work [2, 3].     

Investigation on Secondary Flow Characteristics in a Curved Annular Duct with Struts

Under the influence of duct curvature, cross-sectional area variation and internal struts, the internal flow field within a curved annular duct becomes rather complicated and contains strong secondary flow. In this paper, the secondary flow characteristics in an annular duct with struts are experimentally and numerically investigated. The results show that large pressure gradients exist on the bends of hub and shroud. Meanwhile, two counter-rotating vortex pairs appear both along the hub-side and shroud-side surfaces. The hub-side vortex pair of which the vortex cores travel downstream parallelly evolves from the horseshoe vortex which is induced by the leading edge of the upstream strut, whereas the shroud-side vortex pair originates from the strut trailing edge and the corresponding vortex cores develop in a divergent way. Additionally, the effects of the duct exit Mach number on the secondary flow characteristics are also studied. As the exit Mach number increases, the streamwise pressure gradients increase and lead to more intense vortices, higher total pressure loss and larger flow distortion.     

Experimental study of flow structures of a solitary wave propagating over a submerged thin plate in different angles using PIV technique

This research presents an experimental investigation into the interaction of a solitary wave and a submerged thin plate under different angles. Experiments are conducted to measure both velocity and vorticity by using the Particle Image Velocimetry (PIV) technique. Effects of changing the thin plate angle on the wave height and wave speed are analyzed through the use of wave height gages. Vortices are generated when the solitary wave is transmitted over the obstacle. Understanding the formation and location of the vortices will help analyze the obstacle effect on the flow. In the initial stage, a thin plate is located vertically, and flow structures are visualized. The plate is then deviated from the vertical direction towards positive angles (the direction of wave propagation) and towards negative angles in the opposite direction. In order to study the effects of the plate angle on the flow structures, experiments are carried out for three positive and three negative angles. Comparison of the formed vortices at different angles shows the formation of an additional vortex near the bottom of the channel for positive angles, as opposed to negative angles. The larger the angle is, the less the formation time of the vortex at the bottom of the channel will be. The study of the clockwise vortices formed behind the obstacle shows that increasing the plate angle in both directions decreases their strength. The clockwise vortices of negative angles are stronger than those of positive angles. In addition, changing the plate angle to the negative direction causes more wave height and wave speed reduction than changing it to the positive direction.     

Laminar mixing of homogeneous currents in the presence of a pressure gradient

The problem of the mixture of a current with a quiescent gas was solved by Chapman [1]. In this study, the results of certain calculations on the laminar mixing zone of homogeneous gas currents with a pressure gradient will be presented. On the basis of the data calculated and evaluations, it is shown that the concept of similarity, formulated by Less [2], is applicable to the problem of mixture with a pressure gradient. In variable similarities, the velocity profiles for gradient flow practically coincide with the profiles of nongradient flow for the same parameter values at the interior and exterior boundaries of the mixture zone. Moreover, it proves to be the case that the excess velocity profile depends weakly on the specific parameters of the problem.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 67–71, March–April, 1972.     

Streamwise vortices generated by impinging flows in a confined duct

Particle-tracer technique was employed for visualizing flow structures in a side-inlet square duct. The results obtained indicate that the streamwise vortices developed in the stagnation region of impinging flows are irregularly distributed. As the vortices convect downstream they are first stretched and merged, then squashed due to the non-zero pressure gradient effects caused by the flow separation regions existed along the side walls. The mechanism responsible for generating streamwise vortices in the stagnation region is suggested due to the hydrodynamic instability effect, similar to that previously found for three-dimensional disturbances growing in a two-dimensional stagnation flow.