Experimental study of the velocity field in a vortex-flow heat exchanger with isothermal conditions

The velocity field in a vortex heat cell was investigated experimentally using laser Doppler velocimetry for a wide range of flow conditions. Experimental results point out the three dimensionality of the exchanger's flow, which is composed into a main vortex flow developing along the side walls. The strength of the flow increases up to a limiting value reached for a Reynolds number ranging between 15,000 and 30,000; a secondary flow, caused by interaction between centrifugal and inertial forces, extends perpendicularly to the main flow and remains Reynolds number dependent. It is composed of multiple counter-rotating structures occurring at the exchanger periphery with low inlet Reynolds numbers, thus reducing the rate of centripetal momentum transfer. With increasing inlet Reynolds number, the secondary flow extends across the whole exchanger radius, thus increasing the rate of mixing of the treated fluid. The appearance of so-called Taylor–Görtler vortices tends to reduce the z- and r-axis vorticity transfer.     

Iterative control of Görtler vortices via local wall deformations

Görtler vortices develop along concave walls as a result of the imbalance between the centrifugal force and radial pressure gradient. In this study, we introduce a simple control strategy aimed at reducing the growth rate of Görtler vortices by locally modifying the surface geometry in spanwise and streamwise directions. Such wall deformations are accounted in the boundary region equations by using a Prandtl transform of dependent and independent variables. The vortex energy is then controlled via a classical proportional control algorithm for which either the wall-normal velocity or the wall shear stress serves as the control variable. Our numerical results indicate that the control algorithm is quite effective in minimizing the wall shear stress.     

Nonlinear evolution of Görtler vortices in the near-wall part of a boundary layer

The evolution of Görtler vortices with wavelength smaller than the thickness of the boundary layer on a concave surface is modelled asymptotically at high Reynolds and Görtler numbers. It is known that in the initial linear stage of their evolution such vortices have the largest increment of amplitude growth. Numerical results demonstrate that taking the nonlinear interaction of the flow parameters into account considerably reduces the growth rate and leads to the forming of a perturbed vortex region core; profiles of the flow characteristics in the different stages of vortex evolution are presented.     

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].     

The onset of Görtler vortices in laminar boundary layer flow over a slightly concave wall

The onset of convective instability in the laminar boundary layer over the slightly curved wall is analyzed theoretically and compared with the existing experimental data. A new set of stability equations are derived by the propagation theory considering the relative instability under the linear stability theory. In this analysis the disturbances are assumed to have the form of longitudinal vortices and also to grow themselves in streamwise direction. The critical position to mark the onset of Görtler instability is obtained as a function of the Görtler number, where disturbances at the critical state are mainly confined to the hydrodynamic boundary layer. Comparing the theoretical predictions with available experimental and other theoretical results, the present predictions follow experimental trends fairly well with slightly higher critical Görtler numbers than those from the local stability theory. The propagation theory commanding the local eigenvalue analysis is successful to obtain stability conditions reasonably in Görtler vortex problems, relaxing the limitations by the conventional analyses.     

Görtler vortices: Are they amenable to local eigenvalue analysis?

It is often quoted that Görtler vortices cannot be described by a local eigenvalue analysis. In this work, by using the inverse of the Görtler number as a small expansion parameter, we derive an asymptotic sequence continuable to all orders which is similar, in principle, to the one that justifies the application of the Orr-Sommerfeld equation to two-dimensional boundary-layer instabilities. Existing local theories from the literature can be framed within the leading term of this expansion; however, none of the heuristically proposed non-parallel corrections fully captures the next higher term. We show that, when this term is included, locally computed growth rates' quickly collapse onto those obtained from numerical simulations of the parabolic linear stability equations, with initial conditions applied at the leading edge. The Görtler number (or, equivalently, the downstream distance) beyond which this non-parallel local theory is found out to be accurate encloses the commonly recognized experimental range. The small Görtler number (short distance) effect of initial conditions is described in a companion paper.     

Steady and unsteady Görtler boundary-layer instability on concave wall

The subject of the present combined experimental and theoretical investigation is the steady and unsteady linear Görtler instability. The majority of previous experiments were devoted to the steady Görtler vortices, despite the unsteady ones are also observed in real transitional flows. Moreover, even for the steady Görtler vortices no quantitative agreement between the experimental and theoretical linear-stability characteristics was obtained, especially for disturbance amplification rates. The experimental difficulties were connected, in particular, with a rather poor accuracy of measurements at zero disturbance frequency, a possible influence of nonlinearity, and an admixture of non-modal (transient) growth mechanism. All these difficulties have been overcome in the experimental part of the present study by means of: (i) tuning-out of the exact zero frequency of Görtler vortices and working, instead, with quasi-steady perturbations of very low frequencies, (ii) performing measurements at low disturbance amplitudes, and (iii) minimization and careful estimation of the disturbance-source near-field by means of utilizing a special controlled disturbance source and performing special numerical computations for exact experimental conditions. A detailed study of all linear-stability characteristics for essentially unsteady Görtler vortices was performed in this paper as well. The results are obtained in a range of Görtler numbers 13 ? Gö ? 17.3, frequency parameters F = 0.56–22.70, and spanwise wavelength parameters Λ = 149–775 (close to the most amplified Görtler modes).Appropriate calculations based on locally-parallel and non-local non-parallel linear-stability theories were performed and compared quantitatively with experimentally obtained linear-stability characteristics. For the first time all stability characteristics measured for steady Görtler vortices (in quasi-steady regimes) are found to agree very well with those calculated for the most amplified first discrete-spectrum mode of the linear Görtler-instability problem. Similar good agreement is obtained for essentially unsteady Görtler vortices. The roles of effects of the base-flow non-parallelism and the disturbance-source near-field are examined.     

Investigation of the spectrum of short-wave Görtler vortices in a gas

The linear stage of short-wave Görtler vortices in the boundary layer near a concave surface is studied for the regime of weak hypersonic viscid-inviscid interaction at high Reynolds and Görtler numbers. It is assumed that the gas is perfect and the viscosity is a linear function of the enthalpy. It is found that neutral vortices are located near the surface if it has zero temperature. When the surface is heated, the vortices move away from it, whereas all newly incipient vortices are located near the surface. It is shown that the growth rate of the vortices has a maximum and the heating of the surface has a stabilizing effect on the vortices.     

Reynolds stress modelling of jet and swirl interaction inside a gas turbine combustor

Influences of the inlet swirl levels on the interaction between the dilution air jets and the swirling cross‐flow to the interior flow field inside a gas turbine combustor were investigated numerically by Reynolds stress transport model (RSTM). Due to the intense swirl and jet interaction, a high level of swirl momentum is transported to the centreline and hence, an intense vortex core is formed. The strength of the centreline vortex core was found to depend on the inlet swirl levels. For the higher swirling inlet, the decay of the swirling motion causes strong streamline variation of pressure; and consequently leads to an elevated level of deceleration of its axial velocity. Predictions contrasted with measurements indicate that the stress model reproduces the flow correctly and is able to reflect the influences of inlet swirl levels on the interior flow structure. Copyright © 1999 John Wiley & Sons, Ltd.     

阻旋栅对梳齿密封动静特性影响研究

阻旋栅可改变密封进口流体周向流动与进口预旋，是提高系统稳定性的主要方法之一. 本文作者应用计算流体力学方法研究了阻旋栅几何参数对梳齿密封动静特性的影响，计算分析了阻旋栅在不同长度、间隙、周向个数及不同进口预旋比下密封流场分布与动力特性系数，并与无阻旋栅梳齿密封进行对比. 研究表明:阻旋栅能够有效抑制密封进口周向流动、降低密封腔室周向压力；随着阻旋栅周向个数与阻旋栅间隙的减小，其抑制效果增强，阻旋栅长度的增加对周向速度影响则越来越小；提高预旋比将使密封内流体周向速度增加. 与传统梳齿密封相比，具有阻旋栅的梳齿密封直接阻尼增加，交叉刚度降低，进而有效阻尼提高. 阻旋栅间隙s=0.20 mm、长度l=3.25 mm、数量n=90时密封有效阻尼较大，系统稳定性最好.      

Flow structure in a flat vortex chamber

We investigate a flow in a flat vortex chamber in which the distance between the end walls is smaller than the radius of the chamber. The study was mainly performed by optical methods: a Töpler device was employed, with the Foucault knife replaced by a diaphragm. It is shown that the flow in the chamber has a complicated spatial structure. In addition to the basic helical flow, an intense “transverse” rotation of the type of Taylor-Görtler vortices occurs. In contrast to previously studied flows, where these vortices were observed near a concave surface, in the motion considered transverse vortices occur in the entire working volume of the chamber. In this case, four parallel vortex filaments are formed. The high intensity of the vortices has allowed one to visualize them by the Töpler method and by “tinting” the flow by highly disperse particles. Quantitative dependences of the dimensions of the vortex cells on the flow regime, i.e., on the pressure of gas deceleration, were obtained.     

Sensitivity of an asymmetric 3D diffuser to vortex-generator induced inlet condition perturbations

Modifications of the turbulent separated flow in an asymmetric three-dimensional diffuser due to inlet condition perturbations were investigated using conventional static pressure measurements and velocity data acquired using magnetic resonance velocimetry (MRV). Previous experiments and simulations revealed a strong sensitivity of the diffuser performance to weak secondary flows in the inlet. The present, more detailed experiments were conducted to obtain a better understanding of this sensitivity. Pressure data were acquired in an airflow apparatus at an inlet Reynolds number of 10,000. The diffuser pressure recovery was strongly affected by a pair of longitudinal vortices injected along one wall of the inlet channel using either dielectric barrier discharge plasma actuators or conventional half-delta wing vortex generators. MRV measurements were obtained in a water flow apparatus at matched Reynolds number for two different cases with passive vortex generators. The first case had a pair of counter-rotating longitudinal vortices embedded in the boundary layer near the center of the expanding wall of the diffuser such that the flow on the outsides of the vortices was directed toward the wall. The MRV data showed that the three-dimensional separation bubble initially grew much slower causing a rapid early reduction in the core flow velocity and a consequent reduction of total pressure losses due to turbulent mixing. This produced a 13% increase in the overall pressure recovery. For the second case, the vortices rotated in the opposite sense, and the image vortices pushed them into the corners. This led to a very rapid initial growth of the separation bubble and formation of strong swirl at the diffuser exit. These changes resulted in a 17% reduction in the overall pressure recovery for this case. The results emphasize the extreme sensitivity of 3D separated flows to weak perturbations.     

Obstacle-induced spiral vortex breakdown

An experimental investigation on vortex breakdown dynamics is performed. An adverse pressure gradient is created along the axis of a wing-tip vortex by introducing a sphere downstream of an elliptical hydrofoil. The instrumentation involves high-speed visualizations with air bubbles used as tracers and 2D Laser Doppler Velocimeter (LDV). Two key parameters are identified and varied to control the onset of vortex breakdown: the swirl number, defined as the maximum azimuthal velocity divided by the free-stream velocity, and the adverse pressure gradient. They were controlled through the incidence angle of the elliptical hydrofoil, the free-stream velocity and the sphere diameter. A single helical breakdown of the vortex was systematically observed over a wide range of experimental parameters. The helical breakdown coiled around the sphere in the direction opposite to the vortex but rotated along the vortex direction. We have observed that the location of vortex breakdown moved upstream as the swirl number or the sphere diameter was increased. LDV measurements were corrected using a reconstruction procedure taking into account the so-called vortex wandering and the size of the LDV measurement volume. This allows us to investigate the spatio-temporal linear stability properties of the flow and demonstrate that the flow transition from columnar to single helical shape is due to a transition from convective to absolute instability.     

Computations of strongly swirling flows with second‐moment closures

The present study is concerned with simulating turbulent, strongly swirling flows by eddy viscosity model and Reynolds stress transport model variants adopting linear and quadratic form of the pressure–strain models. Flows with different inlet swirl numbers, 2.25 and 0.85, were investigated. Detailed comparisons of the predicted results and measurements were presented to assess the merits of model variants. For the swirl number 2.25 case, due to the inherent capability of the Reynolds stress models to capture the strong swirl and turbulence interaction, both the linear and quadratic form of the pressure–strain models predict the flow adequately. In strong contrast, the k–ϵ model predicts an excessively diffusive flow fields. For the swirl number 0.85 case, both the k–ϵ and Reynolds stress model with linear pressure–strain process, show an excessive diffusive transport of the flow fields. The quadratic pressure–strain model, on the other hand, mimics the correct flow development with the recirculating region being correctly predicted. Copyright © 1999 John Wiley & Sons, Ltd.     

环形通道内湍流旋流流动的数值模拟

本文应用一种考虑湍流－旋流相互作用及湍流脉动各向异性的新的代数Ｒｅｙｎｏｌｄｓ应力模型,对环形通道内的湍流旋流流动进行了数值模拟,研究了改主为旋流流数,进口轴向速度及半径比等参数对环形通道内湍流流动的影响,以及对强化环形通道内传热的作用。     

Volumetric three-component velocimetry measurements of the turbulent flow around a Rushton turbine

Volumetric three-component velocimetry measurements have been taken of the flow field near a Rushton turbine in a stirred tank reactor. This particular flow field is highly unsteady and three-dimensional, and is characterized by a strong radial jet, large tank-scale ring vortices, and small-scale blade tip vortices. The experimental technique uses a single camera head with three apertures to obtain approximately 15,000 three-dimensional vectors in a cubic volume. These velocity data offer the most comprehensive view to date of this flow field, especially since they are acquired at three Reynolds numbers (15,000, 107,000, and 137,000). Mean velocity fields and turbulent kinetic energy quantities are calculated. The volumetric nature of the data enables tip vortex identification, vortex trajectory analysis, and calculation of vortex strength. Three identification methods for the vortices are compared based on: the calculation of circumferential vorticity; the calculation of local pressure minima via an eigenvalue approach; and the calculation of swirling strength again via an eigenvalue approach. The use of two-dimensional data and three-dimensional data is compared for vortex identification; a ‘swirl strength’ criterion is less sensitive to completeness of the velocity gradient tensor and overall provides clearer identification of the tip vortices. The principal components of the strain rate tensor are also calculated for one Reynolds number case as these measures of stretching and compression have recently been associated with tip vortex characterization. Vortex trajectories and strength compare favorably with those in the literature. No clear dependence of trajectory on Reynolds number is deduced. The visualization of tip vortices up to 140° past blade passage in the highest Reynolds number case is notable and has not previously been shown.     

Computation of rotordynamic coefficients associated with leakage steam flow through labyrinth seal

A mathematical model of calculating rotordynamic coefficients associated with leakage steam flow through labyrinth seals was presented. Particular attention was given to incorporating thermal properties of the steam fluid into prediction of leakage flow and subsequent derivation of rotordynamic coefficients, which quantitatively characterize influence of aerodynamic forcing of the leakage steam flow on the rotordynamics. By using perturbation analysis, we determined periodic and analytic solutions of the continuity and circumferential momentum equations for the time-dependent flow induced by non-axisymmetric rotation of the rotor encompassed by a labyrinth seal. Pressure distributions along labyrinth seal cavities and rotordynamic coefficients were compared at the same condition for air and steam flows. Influence of steam flow through the labyrinth seal cavities on rotordynamic coefficients was analyzed in terms of inlet pressure, inlet swirl velocity and rotor speed.     

Mass and momentum transport in longitudinal vortical structures in liquid flow Example of Görtler vortices

The difference between mass and momentum transport in longitudinal vortical structures is shown in this paper. The patterns observed by visualization using laser induced fluorescence are the signature of the mass transport, while the flow structures revealed by anemometry show the momentum transport. Experiments and numerical simulations are performed in order to compare the velocity field of the Görtler instability with the mass distribution of a passive scalar. The typical scales involved in this problem are discussed with relation to the Schmidt number, in order to compare the size of the observed “mushrooms” with the size of the longitudinal Görtler vortices. It is found that the nonlinearities which strongly influence the velocity perturbation do not modify the shape and the size of the scalar structures.     

Flow field characteristics of an axisymmetric sudden-expansion pipe flow with different initial swirl distribution

The results of an experimental investigation depicting the effects of swirl profile on confined flows in a sudden-expansion coaxial dump combustor are presented. Three swirlers (free vortex, forced vortex, and constant angle) with the same nominal swirl number were designed and fabricated to study the effects of swirl type on the isothermal dump combustor flow field. Imparting swirl to the inlet flow resulted in a considerable reduction of the corner recirculation length, a marked increase in turbulent mixing activity, and in one case creation of a central recirculation zone. This article highlights the importance of the combustor inlet swirl profile and shows that swirl type as well as swirl strength can affect the flow field significantly. The present database is well suited for numerical codes development and validation.