Incompressible fluid flow past a circular cylinder with linear relation between the vorticity and the stream function

Incompressible fluid flow with a linear relationship between the vorticity and the stream function past a circular cylinder is studied.Vortical flows about profiles have been considered in several studies [1–15], but in all these studies with the exception of [15] a constant vorticity was assumed (in [15] an approximate solution is found of the problem of incompressible fluid flow about a Zhukovskii profile with parabolic distribution of the velocities in the approaching stream).A freestream velocity profile similar to that considered below occurs, for example, in a planar jet (laminar or turbulent), in the wake behind a bluff body, in the boundary layer along an infinite plane [4,13], in turbulent jet flows with reverse fluid currents [16]. A similar situation also arises in the flow past an array of cylinders with large spacing which is located in the wake of another array.The author wishes to thank V. E. Davidson for posing the problem and for guidance in its solution.     

Motion of a nonisothermal jet in a field of centrifugal forces

Considerable interest attaches to the study of a jet of viscous liquid in a field of body forces that depend on an axial coordinate. Such flows are realized when slag cotton is obtained by the action on a molten mineral of the centrifugal force of drums rotating in the vertical plane [1]. The behavior of a film of liquid on a rotating cylinder was considered in [2, 3]. The instability of a molten layer and jet separation are explained on the basis of the Taylor mechanism in [4]. In the present paper, a particular solution is given for accelerating nonisothermal jets of a viscous incompressible liquid. This solution is used to explain the dynamics of jet separation from a uniformly rotating drum. The flow stability is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 27–36, September–October, 1980.We thank A. A. Zaitsev for discussing the results of the work.     

Large Eddy Simulation of the sound field of a round turbulent jet

In this paper we will use Large Eddy Simulation (LES) to obtain the flow field of a turbulent round jet at a Reynolds number based on the jet orifice velocity of 11000. In the simulations it is assumed that the flow field is incompressible. The acoustic field of the jet is calculated with help of the Lighthill acoustic analogy. The coupling between the flow solver and the acoustic solver is discussed in detail. The Mach number used in the acoustic calculation was equal to 0.6. It is shown that the decay of the jet centerline velocity and centerline rms are in good agreement with experimental data of [12]. Furthermore, it is shown that the influence of the LES modeling on the acoustic field is very small, if the dynamic subgrid model is used.     

Experimental and numerical analysis of the jet dispersion from a bent chimney around an obstacle

An experimental study and a numerical modelling analysis were carried out simultaneously to study the flow field structure issuing from a chimney around an obstacle. The main purpose of this study is to evaluate the impact of the jet emitted from a chimney (bent or straight) on the dynamics and the turbulent features of the surrounding flow. The consideration of these features is particularly pertinent to the understanding of mixing between the interacting flows which may be very important in controlling pollutant dispersion in the atmosphere. The experimental data are depicted by means of a PIV technique; whereas the numerical three-dimensional model is simulated through the resolution of the different governing Navier–Stokes equations. The volume finite method, together with the second order turbulent closure model (RSM), was adopted. Variations in obstacle form (cylindrical or parallelepiped) and chimney configuration (bent or straight) were tested and features studied were: the global jet plume, the windward and leeward jet spread; the size, location and magnitude of the reverse flow region; the penetration and the deflection of the jet trajectory around the obstacle. All these considerations allowed us to characterize well the impact of the injection of the jet emitted from the chimney within the crossflow, and its spreading around the obstacle and within the whole domain. Such characterization is very important with regard to pollutant dispersion and consequently to the environmental impact. Indeed, the different species contained within the emitted fumes are mainly directed by the velocity components and their mixing and progression within the domain and around the obstacle are closely related.     

熔喷双槽形喷嘴气体射流流场初探

在熔喷非织造布加工中,气体射流作为工作介质使聚合物熔体实现拉伸,气体射流流场的研究对熔喷气流拉抻数学模型研究非常重要。熔喷双槽形喷嘴形成的流场可以看作两股平面射流的合成。从单个点涡的性质出发,研究了涡偶的性质和涡偶代替射流的可行性。研究表明,在喷丝孔轴线附近,涡偶和射流的速度分布趋势相同,且有比较相近的速度分布,从而说明以涡偶代替射流是可行的。在此基础上,用两个涡偶分别代替两股射流,然后进行合成,推导出两股射流合成后速度分布的理论公式,该公式的计算结果与实验结果吻合较好。将该公式引入熔喷气流拉伸数学模型,预测出的纤维直径与采用经验公式时的预测结果几乎完全相同。结果表明,应用涡偶代替射流推导出的气流速度分布公式能够较好地描述熔喷双槽形喷嘴气体射流流场,可以用于完善熔喷气流拉伸数学模型。     

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.     

Calculation of aerodynamic characteristics of a wing profile with discharge of a controllable jet into the external flow

A wing profile of infinite span, whose lower surface is replaced by a system of guide vanes, is placed in a flow of an ideal incompressible fluid. Fluid flows out through the system of guide vanes from the internal cavity of the wing into the external stream, forming a jet in the wake (Fig. 1). The total pressure in the wing cavity and in the jet differs from the total pressure in the outer free stream. The jet boundaries are streamlines extending to infinity, along which there is a discontinuity of the velocity value. The flow of fluid in the internal wing cavity is simulated by a flow caused by a system of suitably located sources, and the system of guide vanes is replaced by discrete vortices.The form of the profile arc is selected so that the fluid flow from the sources in the direction which is nearly opposite the direction of the freestream velocity is restrained by the segment of the contour with high curvature in the vicinity of the leading edge. We consider the flow regime about the profile with an exhausting jet for which the two ends of the arc the points of detachment of the stream and the velocity discontinuity line (profile arc, jet boundary) is a smooth curve, which imposes an additional condition on the magnitude of the circulation. As the model for the study of the flow about a profile with jet blowing we take the arc of a logarithmic spiral.Formulas are obtained for determining the over-all characteristics of the stream forces acting on the profile in the presence of the jet and the total pressure discontinuity. On the basis of the calculations made for a thin wing a qualitative analysis is made for the stream force acting on the profile.The authors wish to thank S. A. Khristianovich for formulating the problem and for his advice.     

Some problems in the theory of plane jets of conducting fluid

Using the boundary-layer equations as a basis, the author considers the propagation of plane jets of conducting fluid in a transverse magnetic field (noninductive approximation).The propagation of plane jets of conducting fluid is considered in several studies [1–12]. In the first few studies jet flow in a nonuniform magnetic field is considered; here the field strength distribution along the jet axis was chosen in order to obtain self-similar solutions. The solution to such a problem given a constant conductivity of the medium is given in [1–3] for a free jet and in [4] for a semibounded jet; reference [5] contains a solution to the problem of a free jet allowing for the dependence of conductivity on temperature. References [6–8] attempt an exact solution to the problem of jet propagation in any magnetic field. An approximate solution to problems of this type can be obtained by using the integral method. References [9–10] contain the solution obtained by this method for a free jet propagating in a uniform magnetic field.The last study [10] also gives a comparison of the exact solution obtained in [3] with the solution obtained by the integral method using as an example the propagation of a jet in a nonuniform magnetic field. It is shown that for scale values of the jet velocity and thickness the integral method yields almost-exact values. In this study [10], the propagation of a free jet is considered allowing for conduction anisotropy. The solution to the problem of a free jet within the asymptotic boundary layer is obtained in [1] by applying the expansion method to the small magnetic-interaction parameter. With this method, the problem of a turbulent jet is considered in terms of the Prandtl scheme. The Boussinesq formula for the turbulent-viscosity coefficient is used in [12].This study considers the dynamic and thermal problems involved with a laminar free and semibounded jet within the asymptotic boundary layer, propagating in a magnetic field with any distribution. A system of ordinary differential equations and the integral condition are obtained from the initial partial differential equations. The solution of the derived equations is illustrated by the example of jet propagation in a uniform magnetic field. A similar solution is obtained for a turbulent free jet with the turbulent-exchange coefficient defined by the Prandtl scheme.     

Application of the ultrasonic velocity profile method to the mapping of liquid metal flows under the influence of a non-uniform magnetic field

An ultrasonic velocity profile (UVP) method has been successfully applied to the investigation of a liquid metal channel flow under the influence of an inhomogeneous magnetic field. Using velocity profiles obtained by the ultrasonic velocimeter and their numerical post processing, two-dimensional time-averaged flow maps were efficiently produced. A single transducer immersed directly into the working fluid was used in order to simplify alignment of measurement lines and avoid the undesirable refraction of the acoustic beam on the walls. An M-shaped flow and wake behind a magnetic obstacle were reconstructed as the patterns of shear and large-scale vortical flows.     

Investigation of turbulent flows via pseudo flow visualization part I: Axisymmetric jet mixing layer

Hot-wire anemometer measurements obtained in the near-field axisymmetric jet mixing layer by Glauser and George [1] are examined using a pseudo flow visualization (PFV) technique. Pseudo flow visualization is a visualization procedure used to manipulate data obtained from an array of probes to create a graphical representation of the instantaneous and fluctuating velocity components of a flow field. An indicator function was employed to identify the frequency content of each velocity-time trace, giving insight into the analysis of the visualizations. From this application, the natural shedding frequency, or preferred mode, of the large-scale structures was determined and compared with the conventional streamwise and radial spectral measurements acquired by Glauser and George [1]. Furthermore, the wavelength of the preferred mode, nondimensionalized by the jet exit diameter, was determined to be approximately 2.4, a result consistent with the work of Crowe and Champagne [2]. In Part 1 the technique is developed and discussed for the fundamental and fairly well-researched mixing layer of the axisymmetric jet. Our aim is to verify the effectiveness of PFV in the context of a well-documented flow. In Part 2, this technique is then applied to an industrial flow field, namely, the mixing region of a lobed mixer     

Density-stratified Sadovskii flow in a channel

Stably density-stratified and nonstratified flows in a channel past a pair of symmetrical closed-streamline vortices on the channel axis are considered. The numerical results obtained cover the whole range of subcritical stratification and eddy lengths. An asymptotic solution for a very long closed-streamline region is found. The results can be used directly in the asymptotic theory of separated flows at high Reynolds number. Sadovskii flows are plane potential inviscid flows past a pair of closed-streamline regions of uniform vorticity. The flow velocity may be discontinuous at the boundary of the closed-streamline region. The analysis below is restricted to the specific case of continuous velocity distribution, so that the Bernoulli constant jump at the eddy boundary is zero. Unbounded nonstratified flows of this kind were studied in [1, 2]. Calculations of the corresponding channel flow were restricted to relatively wide channels. Closely related problems were also considered in [3, 4].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 118–123, May–June, 1993.     

Interaction of a heavy fluid flow in a channel with a transverse jet barrier

An experimental and numerical analysis of the interaction between a plane horizontal water flow in a rectangular channel (free water current) and a plane thin water jet (water jet curtain) is presented; the jet flows out vertically from either a slot nozzle in the bottom of the channel or the crest of a rigid spillway at a velocity appreciably (several times) greater than the water velocity in the channel. Numerical calculations were carried out using the STAR-CD software package preliminarily tested against the experimental data obtained. The dependence of the water level in the channel at a certain distance ahead of the jet barrier on the main jet parameters and the water flow rate in the horizontal channel is studied. It is found that in the region of the interface between the flows both steady and unsteady (self-oscillatory) flow patterns can be realized. Steady stream/jet interaction patterns of the “ejection” and “ejection-spillway” types are distinguished and a criterion separating these regimes is obtained. The notion of a rigid spillway equivalent to a jet curtain is introduced and an approximate dependence of its height on the relevant parameters of the problem is derived. The possibility of effectively controlling the water level ahead of a rigid spillway with a sharp edge by means of a plane water jet flowing from its crest is investigated. The boundary of transition to self-oscillation interaction patterns in the region of the flow interface is determined. The structure of these flows and a possible mechanism of their generation are described. Within the framework of the inviscid incompressible fluid model in the approximate formulation for a “thin” jet, an analytical dependence of the greatest possible depth of a reservoir filled with a heavy fluid at rest and screened by a vertical jet barrier on the jet parameters is obtained.     

Far nonlinear field of a nonlifting airfoil for a generalised equation of transonic flow

The transonic flow equation [1] for plane unsteady irrotational idealgas flows is extended to the case of subsonic, transonic or supersonic flows in a region with an almost constant value of the velocity using orthogonal flow coordinates (family of equipotential lines and streamlines). A solution for the nonlinear far field of steady transonic flow past an airfoil has been obtained for the transonic equation [2]. In this paper it is obtained for a generalized transonic equation and its asymptotic expansion is given. In using difference methods of calculating the flow past an airfoil in the transonic regime a knowledge of the nonlinear field makes it possible to reduce the dimensions of the calculation region (near field) as compared with the region determined by the far field of the linear theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 87–91, January–February, 1986.     

Similarity autooscillations in a plane jet

Experimental investigations into the stability of a plane jet [1, 2] show that after the stationary flow has lost its stability a stable autooscillatory regime arises. In the present paper, an autooscillatory flow in a jet is studied theoretically on the basis of a plane-parallel flow in a fairly wide channel in the presence of a field of external forces. The external forces are such that at zero amplitude of the autooscillations they produce a Bickley—Schlichting velocity profile. The excitation of the secondary regimes is studied by the methods of bifurcation theory [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 26–32, May–June, 1979.We thank M. A. Gol'dshtik and V. N. Shtern for discussing the formulation of the problem and the results.     

Three-dimensional numerical study of jet-in-crossflow characteristics at low Reynolds number

A numerical study of a square jet in a cross flow is carried out at a Reynolds number of 100. The flow field and heat transfer characteristic downstream of the jet have been explored by solving three-dimensional unsteady Navier–Stokes equations and energy equation using higher order spatial and temporal discretization. The projection of vortical structure on a plane is seen to give the component of vortex normal to the plane. Four combinations of velocity profile namely (1) uniform crossflow and uniform jet, (2) laminar boundary layer crossflow and uniform jet, (3) uniform crossflow and parabolic jet profile, and (4) laminar boundary layer crossflow and parabolic jet are compared at same phase to see their effect on the flow field and heat transfer characteristic. All the four cases are seen to exhibit unsteadiness but the jet with parabolic profile is seen to show stronger unsteadiness. The instantaneous vortical structures of all the cases at the same phase show that the structures are more complex for the jet with parabolic velocity profile. The temperature field is seen to be correlated with the vortical structures. Comparison of the time averaged flow field reveals that the jet penetration is the highest for the jet having parabolic profile and boundary layer crossflow. The adiabatic effectiveness is observed to be more for the jet with uniform velocity profile and uniform crossflow and was least for the jet with parabolic velocity profile and boundary layer crossflow.     

Calculation of the momentum and heat transfer in turbulent gas-particle jet flows

The equations for the second moments of the dispersed-phase velocity and temperature fluctuations are used for calculating gas-suspension jet flows within the framework of the Euler approach. The advantages of introducing the equations for the second moments of the particle velocity fluctuations has previously been quite convincingly demonstrated with reference to the calculation of two-phase channel boundary flows [9–11]. The flows considered below have a low solid particle volume concentration, so that interparticle collisions can be neglected and, consequently, the stochastic motion of the particles is determined exclusively by their involvement in the fluctuating motion of the carrier flow. In addition to the equations for the turbulent energy of the gas and its dissipation, the calculation scheme includes the equations for the turbulent energy and turbulent heat transfer of the solid phase; however, the model constructed does not contain additional empirical constants associated with the presence of the particles in the flow.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 69–80, May–June, 1992.     

Simulation of ordered structures in open turbulent flows

Extensive experimental material [1–4] indicates that ordered (coherent) structures play an important part in determining the nature of the flow, the generation of Reynolds stresses and turbulence energy, and the transport of heat, momentum, and passive admixtures in a turbulent flow. In the present paper, a model is constructed for describing coherent structures in which, given the profile of the mean velocity, one can determine the characteristic sizes, the propagation velocities, and also the frequency and amplitude characteristics of these ordered motions. The model is based on the analogy between the ordered formations and secondary flows in a subsidiary laminar flow whose velocity profile is the same as the turbulent profile of the mean velocity. The influence of small-scale pulsations is described by the introduction of the coefficient of turbulent viscosity. In the framework of the model, numerical calculations are made for two-dimensional turbulent flows in a mixing layer, a jet, and a wake behind a cylinder. The results of the calculations are compared with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 45–52, July–August, 1981.     

Asymptotic theory of the flow around an obstacle by a sonic flow

The first investigation of the problem of the flow around an obstacle by a gas flow whose velocity is equal to the speed of sound at infinity was carried out in [1, 2], where it is shown in particular that the principal term of the appropriate asymptotic expansion is a self-similar solution of Tricomi's equation, to which the problem reduces in the first approximation upon a hodographic investigation. The requirement that the stream function be analytic as a function of the hodographic variables on the limiting characteristic was an important condition determining the selection of the self-similarity exponent n (xy^–n is an invariant of the self-similar solution). The analytic nature of the velocity field everywhere in the flow above the shock waves, which arise from necessity upon flow around an obstacle, follows from this condition. The latter was found in [3], where one of the branches of the solution obtained in [1] was used in the region behind the shock waves. The principal and subsequent terms of the asymptotic expansion describing a sonic flow far from an obstacle were discussed in [4], where the author restricted himself to Tricomi's equation. Each term of the series constructed in [4] contains an arbitrary coefficient (we will call it a shape parameter) which is not determined within the framework of a local investigation, and consideration of the problem of flow around a given obstacle as a whole is necessary in order to determine these shape parameters. It follows from the results of [4] that the problem of higher approximations to the solution of [1] coincides with the problem, of constructing a flow in the neighborhood of the center of a Laval nozzle with an analytic velocity distribution along the longitudinal axis (a Meyer-type flow). Along with the Meyer-type flow in the vicinity of the nozzle center, which corresponds to a self-similarity exponent n=2, two other types of flow are asymptotically possible with n=3 and 11, given in [5]. The appropriate solutions are written out in algebraic functions in [6]. The results of [5] show that the condition that the velocity vector be analytic on the limiting characteristic in the flow plane is broader than the condition that the stream function be analytic as a function of the hodographic variables, which is employed in [1, 2, 4]. Therefore, the necessity has arisen of reconsidering the problem of higher approximations for the obstacle solution of F. I. Frankl'. It has proved possible for the region in front of the shock waves to use a series which is more general than in [4], which implies the inclusion of an additional set of shape parameters. The solution is given in the hodograph plane in the form of the sum of two terms; the series discussed in [4] corresponds to the first one, and the series generated by the self-similar solution with n=3 or with n=11 corresponds to the second one.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 99–107, May–June, 1979.The authors thank S. V. Fal'kovich for a useful discussion.     

Investigation of the microstructure a turbulent jet in a wake

The study of the characteristics of the turbulence in the boundary layer and in free jets is one of the most important problems of the aerodynamics of viscous fluids. The accumulation of information on the pulsation characteristics of jet flows and the establishment of the corresponding governing laws may serve to verify the basic hypotheses of the semiempirical theories of turbulence, and also for the development of more advanced computational methods. In many cases the measurement of the pulsation characteristics of turbulent jets is of practical interest.The studies made up till now [1–5] of the microstructure of turbulent flow in the primary region of submerged axisymmetric jets have made it possible to obtain several interesting results. In particular, in addition to the average velocity profiles, hot-wire anemometric equipment has been used to measure the normal and tangential Reynolds stresses and also the intermittency factor in cross sections of the jet, the distribution of the intensity of the longitudinal and lateral velocity pulsations along the axis, the correlation coefficients and the corresponding integral turbulence scales, etc. These measurements have made it possible to draw several important conclusions on the mechanism of turbulent exchange, on the order of the terms omitted in the equation of motion, and on the semiempirical theories of turbulence [6–9].The common deficiency of the studies mentioned above is that near the boundary of a submerged jet, where the average velocity is practically equal to zero, the intensity of the pulsations is so great that it makes the reliability of the results obtained by means of the hotwire anemometer questionable. In this connection Townsend [6] indicated the advisability of studying the microstructure of a turbulent jet issuing into a low-velocity ambient flow.The present study had as its objective the investigation of the microstructure of the primary region of an axisymmetric jet in a wake flow over quite a broad range of the flow ratio parameter m=u/u₀;here u₀ is the average velocity at the nozzle exit, u is the velocity of the ambient stream. For various values of the parameter m in the primary region of the jet measurements were made of the profiles of the three components of the pulsation velocity and the Reynolds shear stresses, and also the values of the average velocity and two components of the pulsation velocity at a large number of points on the jet axis. The measured profiles of the Reynolds shear stresses were compared with the corresponding profiles calculated on the basis of the boundary layer equations from the experimentally determined average velocity profiles. For two values of the parameter m, in one of the sections of the jet measurements were made of the correlation coefficients of the longitudinal components of the pulsation velocity and the variation across the jet of the integral turbulence scale was determined.The results obtained give an idea of the influence of the parameter m on the characteristics of the turbulent jet in an ambient stream.