Vorticity measurements in turbulent grid flows

Results of direct simultaneous measurements of vorticity and velocity are reported for a turbulent flow past a grid of air and (slightly salted) water by two qualitatively different methods. Both experiments were preformed in the same geometry and at the same Taylor microscale Reynolds number 75. The experiments with salted water flow were performed in water tunnel of the laboratory for vorticity-helicity studiesx Faculty of Engineering, Tel-Aviv University and the experiments with air flow were performed in the wind tunnel of the Turbulent Flow Laboratory, University of Maryland. One of the most striking results is that in both experiments the flow is found to lack reflexional symmetry.     

Computation of turbulent asymmetric wake

The development of asymmetric wake behind an aerofoil in turbulent incompressible flow has been computed using finite volume scheme for solving two-dimensional Navier-Stokes equations along with the k-ε model of turbulence. The results are compared with available experimental data. It is observed that the computed shift of the point of minimum velocity with distance is sensitive to the prescribed value of the normal component of velocity at the trailing edge of the aerofoil. Making the model constant C_u as a function of streamline curvature and changing the production term in the equation for ε, has only marginal influence on the results.     

Relaxation oscillations in the turbulent near wake

The method of [2] is used to examine the interaction of a shock or an expansion wave in the outer plane supersonic stream with a turbulent near wake. It is shown that the flow in the disturbed near wake may be two-valued, and for fixed conditions in the outer stream quasisteady transitional flows between these two steady states are possible. Under the influence of some external disturbing mechanism (believed to be turbulent pulsations of the large-vortex type) these quasi-steady flows become relaxation oscillations which lead to the experimentally observed base-pressure oscillations.The theoretical conclusions are confirmed by an experimental study of the base-pressure fluctuations which develop in a two-dimensional expansion-deflection nozzle with interaction of the off-design shock with the near wake.In conclusion the author wishes to thank G. G. Chernyi and G. N. Abramovich for helpful discussions of the study and L. V. Kapranova, T. S. Soboleva, and Z. A. Donskova for assistance in performing the calculations.     

Determination of the parameters of the far turbulent wake

The axisymmetric far turbulent wake in a perfect gas is considered. An integral method of computing both the first moments of the hydrodynamic fields and the turbulence intensity and the root-mean-square values of the enthalpy pulsations is proposed in Section 1. (The whole system of equations is closed by using semiempirical hypotheses.) Under the assumption of no inviscid gradients, an approximate analytical solution of the problem is obtained in Section 2, and asymptotic expressions (as x) are presented for all the designated quantities. Numerical values of the experimental constants are estimated in Section 3 by comparing the computation with known experimental results.Leningrad. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 32–40, November–December, 1972.     

Interaction of a turbulent wake with the outer flow

The integral methods of boundary-layer theory are used to examine the interaction of a turbulent wake with the outer flow for the example of planar flow.In contrast with the known Crocco-Lees theory [1], the turbulent layer in the gas is described with the aid of an appropriate family of velocity profiles rather than by means of a Dorodnitsyn-type transformation of the incompressible turbulent layer. The selection of the simplest among the possible systems of first order interaction equations is justified; this system reduces to a single differential equation and an estimate is given of the influence of the arbitrariness in the equation selection on the final results.The hydrodynamic meaning of the singular and nonsingular integral curves and the singular point of the interaction equation is clarified on the basis of an examination of the interaction of compression and rarefaction waves in the outer supersonic stream with the wake. The effect of blowing (suction) and the initial boundary layer on the base pressure and the supersonic interaction flow as a whole is examined on the basis of the integral conditions for the splicing of the interaction flow with the isobaric mixing flow behind the corner. It is shown that, with proper selection of the single constant in the turbulent viscosity formula, the computational results are in satisfactory agreement with experiment.In conclusion, the authors wish to thank G. G. Chernyi for helpful discussions of the study, and L. V. Kapranova and Z. A. Donskova for assistance in the calculations.     

Three-dimensional vorticity in a turbulent cylinder wake

The three components of the vorticity vector in the intermediate region of a turbulent cylinder wake were measured simultaneously using a multi-hot-wire probe. This probe has an improved spatial resolution compared with those reported in the literature. The behavior of the instantaneous velocity and vorticity signals is examined. Both coherent and incoherent vorticity fields are investigated using a phase-averaged technique. The iso-contours of the phase-averaged longitudinal and lateral vorticity variances, and , wrap around the spanwise structures of opposite sign and run through the saddle point along the diverging separatrix. The observation conforms to the previous reports of the occurrence of the longitudinal structures based on flow visualizations and numerical simulations. The magnitude of these contours is about the same as that of the maximum coherent spanwise vorticity at the vortex center, indicating that the strength of the longitudinal structures is comparable to that of the spanwise vortices. Furthermore, and exhibit maximum concentration away from the vortex center, probably because of a combined effect of the large-scale spanwise vortices and the intermediate-scale longitudinal structures. Coherent structures contribute about 36% to the spanwise vorticity variance at x/d=10. The contribution decreases rapidly to about 5% at x/d=40. The present results suggest that vorticity largely reside in relatively small-scale structures.     

Memory effects in a turbulent plane wake

Memory effects in turbulent plane wakes have been investigated for various wake generators (circular, triangular and square cylinders and a screen of 50% solidity) using orthogonal arrays of X-wires, eight in the (x,y) plane and eight in the (x, z) plane. In the far-wake region, discernible differences are observed for different generators, in the measured Reynolds stresses, spectra of v and approximations to the rms spanwise and lateral vorticities. These differences, which reflect variations in various aspects of the organised large-scale structures, are quantified through the contributions these structures make to the Reynolds stresses. The difference between the screen and the solid body wakes is especially pronounced.The support of the Australian Research Council is gratefully acknowledged     

Swirling turbulent wake behind a self-propelled body

The development of the swirling turbulent axisymmetric wake of a self-propelled body is modeled numerically. The flow pattern is calculated within the framework of the thin shear layer approach for nonclosed system of the motion and continuity equations. The closed system of equations is written for two different formulations of the closure relations. The numerical solution of the problem is performed with the use of the finite-difference algorithm realised on moving grids. The algorithm is conservative with respect to the laws of conservation of the momentum and the angular momentum. The experimentally measured distributions are used as the initial conditions. Both the models described agree well with the experimental data of Gavrilov N., Demenkov A., Kostomakha V., Chernykh G. (2000), Experimental and numerical modelling of turbulent wake behind self-propelled body, J. Appl. Mech. Tech. Phys., 41 (4), 619–627. It is demonstrated that at the large distances downstream from the body the solution of the problem approaches the self-similar one.     

Asymptotic behavior of the far region of turbulent wake vortices

An approximate mathematical model, formulation of the problem, and its approximate solution are proposed for the far region of a turbulent vortex wake past a moving body, where the departure of the horizontal velocity component from the uniform flow is slight. It is assumed that the single important parameter that defines the main flow characteristics in this region is the vortex momentum per unit length produced in the fluid by the lift equal to the weigth of the moving body uncompensated by the buoyancy force. Thus, the flow is self-similar, and the self-similarity law determines the intensity, shape, and location of vortex lines as functions of the downstream distance with accuracy up to a constant factor, which cannot be determined theoretically and should be obtained by comparison of theory with experiment. A boundary-value problem is formulated to determine the flow structure of vortex lines (vorticity distribution). A solution of the problem is obtained numerically in the limit of “vanishing turbulent viscosity.” The variation in the maximum velocity of a vortex line with distance, determined by self-similarity, is in agreement with available experimental data. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 13–23, March–April, 1999.     

Internal waves generated by the turbulent wake of a sphere

Internal waves generated by the turbulent wake of a sphere travelling horizontally through a linearly stratified fluid were studied using shadowgraph and particle-streak photography. The Reynolds and internal Froude number ranges considered were 2,000 Re 12,900 and 2.0 Fi 28.0, respectively. Two quite distinct flow regimes based on the structure of the turbulent wake were identified. In one, the wake is characterized by large-scale coherent structures. In the other, the wake, as viewed on a side-view shadowgraph, grows in a roughly symmetric fashion to a maximum height and then collapses slowly; such flows are termed the smallscale structures regime.Wave lengths and maximum wave heights of the internal waves were measured as functions of Nt and Fi, where N is the Brunt-Väisälä frequency and t the time. It was found that the wave lengths scale well with the streamwise dimension of the spiralling coherent structures. The maximum amplitude of the internal waves were found to scale with the vertical dimension of the turbulent wake, upon varying the internal Froude number.     

Self-similar solutions of the second-order model of the far turbulent wake

A second-order semi-empirical two-dimensional model of turbulence in the approximation of the far turbulent wake is considered. The sought quantities are the velocity defect, kinetic turbulent energy, energy dissipation, and Reynolds stress. The full group of transformations admitted by this model is found. Self-similar solutions satisfying natural boundary conditions are constructed. The solutions obtained agree with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 74–78, March–April, 2008.     

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.     

Coherent structure in the turbulent wake behind a circular cylinder

A wake behind a circular cylinder at Reynolds number 850–1700 was visualized by the smoke-wire method. The observations of the How together with the results of quantitative measurements, such as various velocity correlation coefficients, illustrated the formation process of spoon-shaped large eddies in the region 90 ⩽x/d⩽ 230 attained through the deformation and rearrangement of the regular Karman vortices. A spoon vortex was likely to pair with the counterpart on the opposite side of the wake. The large-scale bulges of the turbulent and non-turbulent interface of the wake were shown to correspond to these spoon vortices.These results indicate that some coherent structures are organized by rearrangement and deformation of initially regular vortices in turbulent flow.     

A bypass wake induced laminar/turbulent transition

The process of laminar to turbulent transition induced by a von Karman vortex street wake, was studied for the case of a flat plate boundary layer. The boundary layer developed under zero pressure gradient conditions. The vortex street was generated by a cylinder positioned in the free stream. An X-type hot-wire probe located in the boundary layer, measured the streamwise and normal to the wall velocity components. The measurements covered two areas; the region of transition onset and development and the region where the wake and the boundary layer merged producing a turbulent flow. The evolution of Reynolds stresses and rms-values of velocity fluctuations along the transition region are presented and discussed. From the profiles of the Reynolds stress and the mean velocity profile, a ‘negative' energy production region along the transition region, was identified. A quadrant splitting analysis was applied to the instantaneous Reynolds stress signals. The contributions of the elementary coherent structures to the total Reynolds stress were evaluated, for several x-positions of the near wall region. Distinct regions in the streamwise and normal to the wall directions were identified during the transition.     

再入飞行器湍流尾迹流场研究

再入飞行器湍流尾迹流场状况，直接关系到飞行器的雷达散射特性。对再入飞行器湍流尾迹等离子体场理论模型，试图通过湍流模式理论来表达，即使用κ－ε－g模型方程来封闭平均化的全Navier-Stokes方程，从而准确获得流动平均场和脉动场信息。使用的N－S平均方程由质量加权平均过程产生，湍流模型方也经过可压缩性修正。真实气体效应重点考察空气处于局部热化学平衡状态。流动控制方程运用一个二阶TVD格式的有限体积法求解，以一典型小钝锥体零攻角再入飞行为例，计算了在两种高程（H－40km和H＝30km)条件下的高超声速湍流尾迹流场。获得的尾迹流场参数与流动物理状况符合，并且湍流脉动参数与已有相应的实验结果定性一致，初步证实该方法合理。     

Particle mixing and diffusion in the turbulent wake of cylinder arrays

The collection of 10 DOP droplets from an aerosol flow around an array of five circular cylinders in a turbulent air stream was measured. Axial and angled alignments of the target array, normal to the flow, were examined. Cylinder Reynolds numbers ranged from 1,300 to 5,100, and effective Stokes numbers from 0.50 to 1.58. A continuous line source turbulent diffusion model was used with the centerline velocity and concentration distributions to derive the eddy diffusion coefficients for momentum and particle concentration in the near wake of the cyinders. Angled collection results showed an optimal target alignment at the edge of the momentum wake of the lead cylinder. Further examination with an LDA system suggests the peak in collection is due to a particle velocity surplus in the wake.List of symbols A _k projected area of cylinder k - A _t cross sectional area of flow - b wake width - C particle concentration - C ₁ concentration deficit - C _D.n drag coefficient of nth cylinder - d diameter - vortex shedding frequency - L _c length of cylinder - n cylinder rank - Q strength of line source - R _L Lagrangian time autocorrelation coefficient - Re Reynolds number (U d/) - T _L Lagrangian integral time scale - U x-directed velocity - U ₁ velocity deficit - u fluctuating axial velocity component - v fluctuating lateral velocity component - V drop volume - x intercylinder spacing - y lateral displacement - mixing length proportionality constant - A measured droplet diameter - eddy diffusivity - ^* corrected collection efficiency - contact angle of droplet on surface - viscosity of air - density - time - non-Stokesian drag correction factor - c cylinder - g gas - M momentum - p particles - theoretical (Stokes efficiency) - aneth freestream value - 1, n cylinder rank 1 or n