Turbulence-driven secondary flows in a curved pipe

If the torque exerted on a fluid element and the source of streamwise vorticity generation are analyzed, a turbulence-driven secondary flow is found to be possible in a curved pipe. Based on this analysis, it is found that the secondary flow is primarily induced by high anisotropy of the cross-stream turbulent normal stresses near the outer bend (furthest from the center of curvature of the bend). This secondary flow appears as a counterrotating vortex pair embedded in a Dean-type secondary motion. Recent hot-wire measurements provide some evidence for the existence of this vortex pair. To verify the formation and extent of this turbulence-driven vortex pair further, a near-wall Reynolds-stress model is used to carry out a detailed numerical investigation of a curved-pipe flow. The computation is performed specifically for a U-bend with a full developed turbulent flow at the bend entrance and a long straight pipe attached to the exit. Numerical results reveal that there are three vortex pairs in a curved pipe. The primary one is the Dean-type vortex pair. Another pair exists near the pipe core and is a consequence of local pressure imbalance. A third pair is found near the outer bend and is the turbulence-driven secondary flow. It starts to appear around 60° from the bend entrance, grows to a maximum strength at the bend exit, and disappears altogether at about seven pipe diameters downstream of the bend. On the other hand, calculations of developing laminar curved-pipe flows covering a range of pipe-to-bend curvature ratios, Reynolds number, and different inlet conditions fail to give rise to a third cell near the outer bend. Therefore, experimental and numerical evidence together lend support to the formation of a pair of turbulence-driven secondary cells in curved-pipe flows.Research supported by the Office of Naval Research under Grant No. N0014-81-K-0428 and by the David Taylor Research Center, Annapolis, Maryland, under Contract No. N00167-86-K0075.     

Approximate two-dimensional equations of vortex flow in a plane layer with solid boundaries

Approximate two-dimensional equations governing turbulent vortex flows in plane fluid layers are considered. The equations were derived by the author in his earlier studies using the shallow water approximation and neglecting circulatory flows in the layer cross-sections. It is shown that, due to the centrifugal effect in the vortex flow, return flows in the layer cross-sections have only a slight influence on the fluid flow in the plane layer and can be neglected.     

Variational model of a turbulent rotating flow

A model of effectively viscous turbulent flows satisfying the Navier-Stokes equations and certain slip conditions at the walls is analyzed. The turbulent viscosity is determined on the basis of the principle of minimum energy dissipation rate, whose significance and conditions of applicability are discussed in detail. A new separated turbulent flow model is outlined. The problem of turbulent flow in a porous rotating tube is solved. The existence of two metastable flow regimes is predicted: one with an axial circulation zone, the other straight-through. In the case of a strongly swirled flow the first of these has a greater probability of realization; however, as the rotation weakens, in a certain critical situation the circulation zone collapses, after which the flow can only be straight-through. Despite the absence of empirical content, every aspect of the proposed theory is in good agreement with the experimental research on vortex chamber flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–32, May–June, 1985.     

Prediction of periodic boundary layers

A relatively simple, yet efficient and accurate finite difference method is developed for the solution of the unsteady boundary layer equations for both laminar and turbulent flows. The numerical procedure is subjected to rigorous validation tests in the laminar case, comparing its predictions with exact analytical solutions, asymptotic solutions, and/or experimental results. Calculations of periodic laminar boundary layers are performed from low to very high oscillation frequencies, for small and large amplitudes, for zero as well as adverse time-mean pressure gradients, and even in the presence of significant flow reversal. The numerical method is then applied to predict a relatively simple experimental periodic turbulent boundary layer, using two well-known quasi-steady closure models. The predictions are shown to be in good agreement with the measurements, thereby demonstrating the suitability of the present numerical scheme for handling periodic turbulent boundary layers. The method is thus a useful tool for the further development of turbulence models for more complex unsteady flows.     

Nichtisotherme ebene Freistrahlen unter Schwerkrafteinfluß

Higher-order boundary layer theory is used to study the behaviour of nonisothermal laminar and turbulent free jet flows. In addition to the Prandtl boundary layer equations, an equation is used to describe the equilibrium of forces normal to the flow direction. This equilibrium exists between the buoyancy forces caused by gravity and the centrifugal forces resulting from the curvature in the flow. The proper selection of reference values permits the characteristics of the jet flow to be expressed as universal functions in which only the initial jet orientation and the Prandtl number in the case of laminar flow are input parameters. When the volume flow is given in addition to the momentum and thermal energy, the characteristic parameter are the Archimedes number for turbulent flow and the modified Archimedes number for laminar flow. The jet flow is calculated using an integral method in which the eddy viscosity and the turbulent Prandtl number are given as functions of the local Archimedes number. Comparison of experimental data from the literature and from our laboratory on nonisothermal free jets with the theoretical results, show satisfactory agreement. The universal diagrams given in the paper are valid forall plane laminar (Pr=0.7) and turbulent nonisothermal jets.     

Topology of the vorticity field in three-dimensional shear layers and wakes

An experimental and numerical study of the three-dimensional transition of plane wakes and shear layers behind a flat plate is presented. Flow visualization techniques are used to monitor the response of laminar flows at moderate Reynolds numbers (≈100) to perturbations periodically distributed along the span. In this way, the formation and evolution of streamwise vortex tubes and their interaction with the spanwise vortices are analyzed. The flow was studied numerically by means of three-dimensional inviscid vortex dynamics. Assuming periodicity in the spanwise and the streamwise direction, we discretize the vorticity field into two layers of vortex filaments with finite core diameter. Comparison between experiment and visualization indicates that important features of the three-dimensional evolution can be reproduced by inviscid vortex dynamics. Vortex stretching in the strain field of the spanwise rollers appears to be the primary mechanism for the three-dimensional transition in this type of flows.     

Pressure drop for flow in channels subjected to strong system rotation

A disc stack centrifuge is an industrial example of a fluid machine in which all the internal flow takes place in a rapidly rotating frame. The present report gives a survey of the experimental and theoretical work performed at Alfa-Laval in order to estimate the pressure drops in the different internal passages in the centrifuge, including both laminar and turbulent flow.For the laminar flow between the discs, a theory has been developed using the concept of a rotating Hele Shaw cell and conformal mapping. The theory is valid in the limit of very small Rossby numbers. For moderately large Rossby numbers, this model overestimates the pressure drop. The linear theory was extended by introducing advecting vortices in a computer model. The vortices cause vertical fluid transport between the Ekman and geostrophic layers by Ekman pumping, an effect which decreases the pressure drop in the disc stack. The linear model and the enhanced model have both been confirmed by experiments.The flow is turbulent in most parts of the centrifuge, except in the disc stack. The theoretical or numerical modelling for rotating turbulent flows is very difficult and no reliable models exist so far. We therefore have to rely on measurements, which show that the pressure is significantly influenced by rotation for Rossby numbers below unity.     

Aerodynamics of end-wall boundary layer in a vortex chamber

The need for the inclusion of end-wall boundary layers in the study of the aerodynamics of vortex chambers has been frequently mentioned in the literature. However, owing to limited experimental data [1–3] with reliable information on the wall layers, the existing computational methods for end-wall boundary layers are not well-founded. The question of which parameters determine the formation of end-wall flow remains debatable. In some studies [4, 5], the vortex chambers are conditionally divided into short and long chambers. However, there is no unique opinion on the role of end-wall flows in vortex chambers of different lengths. It has also not been established for what geometric and flow parameters the chamber could be considered long or short. In the present study, as in [1, 5–8], solution is obtained for the end-wall boundary-layer equations using integral methods, considering the boundary layer in the radial direction in the form of a submerged wall jet. Such an approach made it possible to use the laws for the development of wall jets [9], and obtain fairly simple relations for integral parameters, skin friction, mass flow in the boundary layer, and other characteristics. Results are compared with available experimental data and computations of others authors; turbulent flow is considered; results for laminar boundary layer are given in [10].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 117–126, September–October, 1986.     

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.     

基于全局动态Vreman模型的复杂非定常湍流的大涡模拟

在湍流数值模拟方法中,大涡模拟方法可以提供丰富的大涡旋信息,已逐渐成为复杂湍流问题数值研究的重要方法。而大涡模拟中,最重要的一环是尽量准确地构建能反映流场物理本质特征的亚格子应力模型。基于该思想,将一种新型的大涡模拟亚格子应力模型-Vreman亚格子应力模型用于高雷诺数三维后台阶流动的求解,计算结果与实验结果进行对比分析结果较吻合,验证了该模型的可靠性。这是对该模型用于无任何均匀流动方向的高雷诺数复杂湍流非定常流动的首次检验,计算结果优于基于传统的Smagorinsky涡粘性的动态亚格子模型。     

Effect of the pattern of initial perturbations on the steady pipe flow regime

The influence of the inlet flow formation mode on the steady flow regime in a circular pipe has been investigated experimentally. For a given inlet flow formation mode the Reynolds number Re* at which the transition from laminar to turbulent steady flow occurred was determined. With decrease in the Reynolds number the difference between the resistance coefficients for laminar and turbulent flows decreases. At a Reynolds number approximately equal to 1000 the resistance coefficients calculated from the Hagen-Poiseuille formula for laminar steady flow and from the Prandtl formula for turbulent steady flow are equal. Therefore, we may assume that at Re > 1000 steady pipe flow can only be laminar and in this case it is meaningless to speak of a transition from one steady pipe flow regime to the other. The previously published results [1–9] show that the Reynolds number at which laminar goes over into turbulent steady flow decreases with increase in the intensity of the inlet pulsations. However, at the highest inlet pulsation intensities realized experimentally, turbulent flow was observed only at Reynolds numbers higher than a certain value, which in different experiments varied over the range 1900–2320 [10]. In spite of this scatter, it has been assumed that in the experiments a so-called lower critical Reynolds number was determined, such that at higher Reynolds numbers turbulent flow can be observed and at lower Reynolds numbers for any inlet perturbations only steady laminar flow can be realized. In contrast to the lower critical Reynolds number, the Re* values obtained in the present study, were determined for given (not arbitrary) inlet flow formation modes. In this study, it is experimentally shown that the Re* values depend not only on the pipe inlet pulsation intensity but also on the pulsation flow pattern. This result suggests that in the previous experiments the Re* values were determined and that their scatter is related with the different pulsation flow patterns at the pipe inlet. The experimental data so far obtained are insufficient either to determine the lower critical Reynolds number or even to assert that this number exists for a pipe at all.     

Finite element solutions for laminar and turbulent compressible flow

The time-split finite element method is extended to compute laminar and turbulent flows with and without separation. The examples considered are the flows past trailing edges of a flat plate and a backward-facing step. Eddy viscosity models are used to represent effects of turbulence. It is found that the time-split method produces results in agreement with previous experimental and computational results. The eddy viscosity models employed are found to give accurate predictions in all regions of flow except downstream of reattachment.     

Some Swirling-flow Challenges for Turbulent CFD

The paper examines some of the continuing challenges, within a RANS framework, of computing turbulent swirling flows such as are encountered in industry and the environment. The principal focus is on modelling turbulent transport processes but serious problems also arise in handling numerical issues, too. Recent researches of two of these types of flow by the authors and their colleagues in the Turbulence Mechanics Group at Manchester are examined; namely, the confined flow within a rotor–stator disc cavity and the trailing wing-tip vortex. The former flow, while geometrically axisymmetric, has been found to create multiple rotating vortices necessitating a three-dimensional time-dependent analysis. The wing-tip vortex is extremely sensitive to the choice of turbulence model and only a second-moment closure that complies with the constraints of two-component turbulence has been found capable of handling both the flow over the wing and the wake vortex. Moreover, because of the large distances downstream of the aircraft to which, for practical cases, computations need to be carried, the numerical strategy is brought into question. Finally, arising from these two test cases, outline remarks are made about a swirling flow that poses one of the major computational challenges of the twenty-first century.     

Critical Reynolds number in plasma flows on a stabilized plasmatron section

A technique for determining the criterion of transition from the laminar to the turbulent flow regime on a stabilized plasmatron channel section is proposed. The technique uses experimental data and the methods of numerical simulation of plasma flows. A criterial generalization of the experimental data which for the first time makes it possible to establish the boundary of transition from the laminar to the turbulent flow regime on a stabilized plasmatron channel section is proposed. The experimental results are in good agreement with the theoretical dependences derived in the study. A curve (analog of the neutral curve) separating the domains of existence of laminar and turbulent plasma flows in a cylindrical channel is constructed in the space of the plasmatron working parameters.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 49–61. Original Russian Text Copyright © 2004 by Sinkevich and Chikunov.     

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.     

Reynolds number effects on the behavior of a non-buoyant round jet

The behavior of a non-buoyant circular water jet discharged from a contraction nozzle was experimentally investigated. In this experiment, the Reynolds number of the jet, based on the mean velocity results obtained by particle image velocimetry (PIV), ranged from 177 to 5,142. From the experimental results, we found that the cross-sectional profile of the axial velocity for a laminar flow near the nozzle did not show a top-hat distribution, whereas the profiles with Reynolds number higher than 437 were almost top-hat. The length of the zone of flow establishment (ZFE) was found to decrease with increasing Reynolds number. The measured centerline velocity decayed more rapidly and, consequently, approached the theoretical equation earlier near the nozzle as the Reynolds number increased. The decay constant for the centerline velocity of the turbulent cases was relatively lower than that discovered in theory. It is assumed that this probably resulted from the use of the contraction nozzle. Verifying the similarity of the lateral velocity profiles demonstrated that the Gaussian curve was properly approximated only for the turbulent jets and not for the laminar or transitional flows. The jet half width seldom grew for the laminar or transitional flows, whereas it grew with increasing axial distance for the turbulent flows. The spreading rates for the turbulent flows gradually decreased with increasing Reynolds number. The normalized turbulence intensity along the jet centerline increased more rapidly with the axial distance as the Reynolds number increased, and tended to the constant values proposed by previous investigators. The Reynolds shear stress levels were also found to increase as the Reynolds number increased for the turbulent jets.     

自由剪切湍流中颗粒-拟序结构相互作用研究进展

从实验和数值模拟两方面评述了颗粒-湍流拟序结构相互作用的近期研究进展.关于Stokes数不同对颗粒行为和拟序结构影响的试验研究,从单点激光多普勒测量到粒子图像全场测速,并与流场显示定性方法结合,揭示了不同Stokes数范围颗粒-拟序结构相互作用的规律.基于涡方法、直接数值模拟和大涡模拟等的模拟研究,进一步揭示颗粒-拟序结构的相互耦合作用和外界激励的调制作用等规律,同时推动了算法的发展.      

Instantaneous structure and statistical feature of unsteady flow in a channel obstructed by a square rod

A two-dimensional numerical computation has been made for an unsteady flow in a channel obstructed by an inserted square rod. The results of the computation made for the flow with a parabolic inlet velocity profile at a specific value of channel Reynolds number are analyzed in detail. The obtained results reveal that momentum transfer is enhanced due to the apparent shear stress resulting from the nonzero value of cross-correlation between the streamwise and normal components of fluctuating velocity, , just as in turbulent shear flows, although the studied flow is quite different from turbulent flows in the sense that it is highly periodical and therefore free from randomness. This periodicity leads to a quick recovery of the velocity defect in some region of the wake of the rod. Special attention is paid to the time variation of flow structure. The crisscross motion of the Karman vortex previously found to occur is discussed again, and how it appears is explained in terms of the interaction between the Karman vortex and the disturbed wall shear layer. In the discussion of this relationship, wavering motion of the separation vorticity layers formed on both sides of the rod and the periodic formation of an isolated vortex island from the lifted tip of the wall vorticity layer are analyzed. The vortex island is found to play an important role not only for the occurrence of the crisscross motion of Karman vortex but also for the generation of the nonzero value of .     

Applications of URANS on predicting unsteady turbulent separated flows

Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practi cal challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS （URANS）. Some typical linear and nonlinear eddy viscosity turbulence models （LEVM and NLEVM） and a quadratic explicit algebraic stress model （EASM） are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding.     

Laser-Doppler measurements of laminar and turbulent flow in a pipe bend

Laser-Doppler measurements are reported for laminar and turbulent flow through a 90° bend of circular cross-section with mean radius of curvature equal to 2.8 times the diameter. The measurements were made in cross-stream planes 0.58 diameters upstream of the bend inlet plane, in 30, 60 and 75° planes in the bend and in planes one and six diameters downstream of the exit plane. Three sets of data were obtained: for laminar flow at Reynolds numbers of 500 and 1093 and for turbulent flow at the maximum obtainable Reynolds number of 43 000. The results show the development of strong pressure-driven secondary flows in the form of a pair of counter-rotating vortices in the streamwise direction. The strength and character of the secondary flows were found to depend on the thickness and nature of the inlet boundary layers, inlet conditions which could not be varied independently of Reynolds number. The quantitative anemometer measurements are supported by flow visualization studies. Refractive index matching at the fluid-wall interface was not used; the measurements consist, therefore, of streamwise components of mean and fluctuating velocities only, supplemented by wall pressure measurements for the turbulent flow. The displacement of the laser measurement volume due to refraction is allowed for in simple geometrical calculations. The results are intenden for use as benchmark data for calibrating flow calculation methods.