Buoyancy effects on turbulent swirling flows

A three-parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time-averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T ′². Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl. The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results.     

The compressible Coanda wall jet—an experimental study of jet structure and breakaway

An underexpanded jet issuing from a convergent slot and blowing over a surface of convex streamwise curvature was studied experimentally. The jet was confined between side walls, with the slot aspect ratio varying between 40 and 6, but tests showed that in the area of interest close to the slot the flow was effectively two-dimensional. The ratio of slot width to the radius of curvature of the downstream surface varied between 0.05 and 0.33. The main techniques used were Schlieren and shadowgraph to show the jet structure, and surface flow visualization which revealed areas of separation and reattachment. Surface static pressures were also measured on the curved surface. The curved jet proved to have a shock cell structure similar to that of a plane jet. However, the cell structure disappeared more rapidly as the outer shear layer grew more quickly due to the destabilizing effect of the curvature on the turbulence in the shear layer. Even at modest upstream jet pressures, a separated region on the Coanda surface became evident. This region was characterized by a stagnant constant pressure part followed by a region of strongly reversed flow before reattachment took place. The separation was caused by the compression at the end of the first shock cell, with reattachment taking place where expansion in the second cell started. The separated region grew rapidly as the upstream pressure was increased, until, finally, reattachment failed to occur and the jet suddenly broke away from the surface. This work is related to studies of the Coanda flare, where the jet is axisymmetric. The high level of turbulence causes rapid entrainment of air and so gives us clean combustion. However there should be more general application to devices that use the Coanda effect, varying from fluidic devices to blown jet flaps on wings.     

Experimental study of stratified jet by simultaneous measurements of velocity and density fields

Stratified flows with small density difference commonly exist in geophysical and engineering applications, which often involve interaction of turbulence and buoyancy effect. A combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system is developed to measure the velocity and density fields in a dense jet discharged horizontally into a tank filled with light fluid. The illumination of PIV particles and excitation of PLIF dye are achieved by a dual-head pulsed Nd:YAG laser and two CCD cameras with a set of optical filters. The procedure for matching refractive indexes of two fluids and calibration of the combined system are presented, as well as a quantitative analysis of the measurement uncertainties. The flow structures and mixing dynamics within the central vertical plane are studied by examining the averaged parameters, turbulent kinetic energy budget, and modeling of momentum flux and buoyancy flux. At downstream, profiles of velocity and density display strong asymmetry with respect to its center. This is attributed to the fact that stable stratification reduces mixing and unstable stratification enhances mixing. In stable stratification region, most of turbulence production is consumed by mean-flow convection, whereas in unstable stratification region, turbulence production is nearly balanced by viscous dissipation. Experimental data also indicate that at downstream locations, mixing length model performs better in mixing zone of stable stratification regions, whereas in other regions, eddy viscosity/diffusivity models with static model coefficients represent effectively momentum and buoyancy flux terms. The measured turbulent Prandtl number displays strong spatial variation in the stratified jet.     

Direct Numerical Simulation of Transitional Noncircular Buoyant Reactive Jets

The near field dynamics of transitional buoyant reactive jets established on noncircular geometries, including a rectangular nozzle with an aspect ratio of 2:1 and a square nozzle with the same cross-sectional area, are investigated by three-dimensional spatial direct numerical simulations. Without applying external perturbations at the inflow boundary, large vortical structures develop naturally in the flow field due to buoyancy effects. Simulation results and analysis describe the details and clarify mechanisms of vortex dynamics of the noncircular buoyant reactive jets. The interaction between density gradients and gravity initiates the flow vorticity. Among the major vorticity transport terms, the gravitational term mainly promotes flow vorticity in the cross-streamwise direction. For the baroclinic torque, it can either create or destroy flow vorticity depending on the local flow structure. The vortex stretching term has different effects on the streamwise and cross-streamwise vorticity. Streamwise vorticity is mainly created by vortex stretching, while this term can either create or destroy cross-streamwise vorticity. Under the coupling effects of buoyancy and noncircular nozzle geometry, three-dimensional vortex interactions lead to the transitional behavior of the reactive jets. Simulations also show that the rectangular jet is more vortical than the square jet. The rectangular jet has a stronger tendency of transition to turbulence at the downstream due to the aspect ratio effect. Mean flow property calculations show that the rectangular buoyant reactive jet has a higher entrainment rate than its square counterpart. Received 13 December 2000 and accepted 24 July 2001     

Buoyancy effects on flow transition in low-density inertial gas jets

Effects of buoyancy on transition from laminar to turbulent flow are presented for a momentum-dominated helium jet injected into ambient air. The buoyancy was varied in a 2.2 s drop tower facility without affecting the remaining operating parameters. The jet flow in Earth gravity and microgravity was visualized using the rainbow schlieren deflectometry apparatus. Results show significant changes in the flow structure and transition behavior with change of buoyancy.     

Analysis of a turbulent buoyant confined jet modeled using realizable k–ɛ model

Through this paper, analyses of components of the unheated/heated turbulent confined jet are introduced and some models to describe them are developed. Turbulence realizable k–? model is used to model the turbulence of this problem. Numerical simulations of 2D axisymmetric vertical hot water confined jet into a cylindrical tank have been done. Solutions are obtained for unsteady flow while velocity, pressure, temperature and turbulence distributions inside the water tank are analyzed. For seeking verification, an experiment was conducted for measuring of the temperature of the same system, and comparison between the measured and simulated temperature shows a good agreement. Using the simulated results, some models are developed to describe axial velocity, centerline velocity, radial velocity, dynamic pressure, mass flux, momentum flux and buoyancy flux for both unheated (non-buoyant) and heated (buoyant) jet. Finally, the dynamics of the heated jet in terms of the plume function which is a universal quantity and the source parameter are studied and therefore the maximum velocity can be predicted theoretically.     

Computational study of buoyancy effects in a laminar starting jet

Vortical structures formed in evolving jets are important in applications such as fuel injection in diesel engines and fuel leaks. When the jet fluid is different from the ambient fluid, the buoyancy can play an important role in determining the jet flow structure, and hence, the entrainment and fluid mixing processes. In the present study, a jet of helium injected in air is investigated, with emphasis placed on delineating the buoyancy effects on vector–scalar fields during the starting phase. We utilize a computational model, previously validated to predict the flow field of low-density gas jets. The model incorporates finite volume approach to solve the transport equation of helium mass fraction coupled with conservation equations of mixture mass and momentum. Computations were performed for a laminar jet to characterize the advancing jet front, and to capture the formation and propagation of vortex rings and the related pinch-off process. Results show significant effects of buoyancy on jet advancement, as well as on vorticity and helium concentration in the core of the vortex rings.     

Direct numerical simulation of the near field dynamics of a rectangular reactive plume

Spatial direct numerical simulation (DNS) is used to study the near field dynamics of a buoyant diffusion flame established on a rectangular nozzle with an aspect ratio of 2:1. Combustion is represented by a one-step finite-rate Arrhenius chemistry. Without applying external perturbations at the inflow boundary, large vortical structures develop naturally in the flow field, which interact with the flame and temporally create localized holes within the reaction zone in which no chemical reactions take place. The interaction between density gradients and gravity plays a major role in the vorticity generation of the buoyant plume. At the downstream of the reactive plume, a more disorganized flow regime characterized by small scales has been observed, following the breakdown of the large vortical structures due to three-dimensional (3D) vortex interactions. Analysis of energy spectra shows that the spatially developing reactive plume has a tendency of transition to turbulence under the effects of combustion-induced buoyancy. The buoyancy effects are found to be very important to the formation, development, interaction, and breakdown of vortices in reactive plumes. In contrast with the relaminarization effects of chemical exothermicity via viscous damping and volumetric expansion on non-buoyant jet diffusion flames, the tendency towards transition to turbulence in reactive plumes is greatly enhanced by the buoyancy effects.     

Scaling investigation of plasma-induced flows over curved and flat surfaces: Comparison to the wall jet

The present investigation deals with Dielectric Barrier Discharge (DBD) induced jets flowing over curved surfaces and studied in the framework of a circulation control application, carried out by acting near the rounded trailing-edge of an airfoil. These jets are characterized experimentally via Particle Image Velocimetry (PIV) in quiescent air conditions. The study assesses the evolution of these flows in terms of self-similarity of the mean flow and of its turbulent components. DBD wall jets evolution in the streaming direction is also analyzed through the rate of spread and the maximum velocity decay evolution as commonly done for fluidic wall jets, and also through several normalized quantities deriving from different length and velocity scales. A comparison with a canonical flow, such as the classical wall jet flowing over plane or curved surfaces, is made in order to find out the similarities and the discrepancies between these two flows. Results reveal that DBD wall jets and canonical fluidic wall jets show comparable properties in the diffusion zone. Compared to the plane DBD wall jet, centrifugal forces are responsible of the greater spread of curved DBD wall jets and are likely the source of instabilities leading to their transitional state. The momentum flux of the induced jet and the radius of curvature of the surface are two relevant scales for DBD induced flows developing over curved surfaces.     

Particle tracking method for measurements of turbulence properties in a curved channel

The turbulence properties of a curved channel flow have been measured by particle tracking method. The results reveal some characteristics of the structure for wall turbulence.     

Phase-locked analysis of velocity fluctuations in a turbulent free swirling jet after vortex breakdown

Large-scale organized vortical structures were studied experimentally in a free swirling jet of air experiencing vortex precession (PVC) at ambient conditions. Detailed measurements were performed in the region near the nozzle exit using phase-locked LDV and PIV, at a Reynolds number of Re ?? 24,400 and a swirl parameter S ?? 1.0. The investigation allowed reconstruction of the time-averaged flowfield, with the associated distribution of turbulent fluctuations, the phase-locked structure of the jet and the associated precessing vortex structure. An original joint analysis of power spectra and probability density functions of velocity data led to quantification of the PVC effect on turbulent fluctuations. This analysis showed that the PVC contribution can be properly separated from the background random turbulence, reproducing the results of phase-locked measurements. It is found that the background turbulence in the near field is substantially weaker if compared to the coherent fluctuations induced by vortex precession.     

Calculation of an axisymmetric turbulent wall jet over a surface of convex curvature

One of the many applications of curved wall jets of engineering importance is the Coanda Flare, which is used for burning waste gases in the petroleum industry and which gave rise to this work. The gas jet flows over an axisymmetric tulip shaped body, entraining ambient air and so promoting clean combustion. The object of this work was to calculate the development of the jet with the extra rates of strain imposed by both longitudinal curvature and divergence. A differential ‘partially-parabolic’ technique was used with uncoupling of the streamwise and cross-stream momentum equations, leading to an efficient computer program. The extra rates of strain were modelled by corrections to a mixing length model with the two effects being assumed to be additive. The calculation method was compared with seven test ccases of experimental data. The first five were from published literature, and included the plane wall jet and axisymmetric free jet, and the separate effects of longitudinal curvature and divergence. The lost two cases were measurements of the wall jet flow over a model Coanda Flare. The calculation method gave generally good results for the main features of the flow such as growth rate and velocity decay. Details of the flow were not so well predicted, particularly the turbulent shear stress, as a result of the relatively simple turbulence model employed. The calculation method should provide a useful engineering tool, but some profitable developments could be made, particularly in the area of turbulence modelling.     

Round gas jets submerged in water

Water submerged gas jets are characterized by the interplay of inertia and buoyancy forces and can exhibit diverse behaviors ranging from bubbly plumes to stable jets. In this work, direct measurements of the interfacial behavior of water-submerged gas jets, with Mach numbers ranging from subsonic to supersonic, were performed using high-speed digital photography and shadowgraphs. The results indicate that the jets have a preferential pinch-off position that can be attributed and correspond to the location of the maximum streamwise-velocity turbulence fluctuations. A new, experimentally determined jet penetration distance is proposed; the jetting length is taken as the jet length corresponding to a 99% probability of the gas-jet outer boundary being attached to the orifice during the sampling period. Using the shadowgraph analysis and this criterion, we determined that the electro-resistivity probe measurements, previously used to determine the jet penetration length, may be significantly biased. This is attributed to the inability of the probe measurements to distinguish between a continuous gas jet and advecting bubbles. In addition, based on a simple force-balance of the jet cross-section, we introduce a new scaling relationship for the jet penetration distance. This relationship shows that the jetting length scales with the square of the Froude number and compares well with the experimental observations. Finally, measurements of the gas jet boundary acceleration coupled with estimations of the internal gas jet velocity suggest that both Rayleigh–Taylor and Kelvin–Helmholtz mechanisms are nearly equally responsible for governing the jet boundary dynamics.     

Wave structure in the radial film flow with a circular hydraulic jump

 A circular hydraulic jump is commonly seen when a circular liquid jet impinges on a horizontal plate. Measurements of the film thickness, jump radius and the wave structure for various jet Reynolds numbers are reported. Film thickness measurements are made using an electrical contact method for regions both upstream and downstream of the jump over circular plates without a barrier at the edge. The jump radius and the separation bubble length are measured for various flow rates, plate edge conditions, and radii. Flow visualization using high-speed photography is used to study wave structure and transition. Waves on the jet amplify in the film region upstream of the jump. At high flow rates, the waves amplify enough to cause three-dimensional breakdown and what seems like transition to turbulence. This surface wave induced transition is different from the traditional route and can be exploited to enhance heat and mass transfer rates. Received: 25 April 2000/Accepted: 1 June 2001     

Principles and Performance of TCL-Based Second-Moment Closures

The paper argues that to achieve the desired width of applicability for use in general CFD software, turbulence modelling at second-moment level needs to be based upon making the pressure-strain term and other major processes comply with the two-component limit (TCL), a strategy first advocated by Lumley [24]. The approach is especially powerful for flows close to surfaces that are far from flat and in applications to horizontal, stably-stratified flows where, due to the action of buoyancy, the stress tensor also approaches a two-component form. A range of recent applications of TCL modelling is presented including flow in curved ducts, three-dimensional wall jets, free-surface jets and stably-stratified mixing regions. This revised version was published online in August 2006 with corrections to the Cover Date.     

On Cascade Energy Transfer in Convective Turbulence

The paper is devoted to specificities of the cascade processes in developed turbulence existing on a background of the density (temperature) gradient either parallel (turbulence in a stably stratified (SS) medium) or antiparallel (convective turbulence (CT)) to the gravitational force. Our main attention is paid to the Obukhov–Bolgiano (OB) regime, which presumes a balance between the buoyancy and nonlinear forces in a sufficiently extensive part of the inertial interval. Up to now, there has been no reliable evidence of the existence of the OB regime, although fragments of spectra with slopes close to–11/5 and–7/5 were detected in some works on the numerical simulations of convective turbulence. The paper presents a critical comparison of these data with the results obtained in this work using the cascade model of convective turbulence, which makes it possible to consider a wide range of control parameters. The cascade model is new and was obtained by the generalization of the class of helical cascade models to the case of turbulent convection. It is shown that, in developed turbulence, which is characterized by an interval with a constant spectral flux of kinetic energy, the buoyancy force cannot compete with nonlinear interactions and has no essential effect on the dynamics of the inertial interval. It is the buoyancy force that supplies the cascade process with energy in convective turbulence but only in the maximum scales. Under the SS conditions, the buoyancy forces reduce the energy of turbulent pulsations. In the case of stable stratification, the buoyancy force reduces the turbulence pulsation energy. The OB regime arises in none of these cases, but, in the scales beyond the inertial interval, Kolmogorov’s turbulence with the “–5/3” law, in which temperature behaves like a passive admixture, is established. The observed deviations from the “–5/3” spectrum, erroneously interpreted as the OB regime, are manifested in the case of insufficient separation of the macroscale of turbulence and the dissipative scale.     

Nonlinear turbulence models for predicting strong curvature effects

Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applications and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent Uduct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models （NLEVM） （quadratic and cubic）, a quadratic explicit algebraic stress model （EASM） and a Reynolds stress model （RSM） developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be employed to simulate the turbulent curved flows in engineering applications.     

Experimental investigation on the similarity of a 3D rectangular turbulent jet

 The paper presents an experimental investigation of turbulent jets issuing from rectangular nozzles. Nozzles with aspect ratios between 3 and 10 were used. Eight different initial conditions were studied. The following jet parameters were measured and evaluated: mean velocity components, jet boundaries, jet momentum, jet entrainment, turbulence intensities and Reynolds stresses. A DISA 55M thermoanemometer and a data acquisition system BE256 were used. The influence of the initial conditions on the similarity of the flow was determined with respect to the mean axial velocity, turbulence intensity and the Reynolds stresses. A significant influence of the initial conditions on the flow structure was observed. The possibility for jet control is discussed and suggestions are given about the need to investigate different parameters. Received: 25 November 1996/Accepted: 30 October 1997     

Near-field development of gas-phase horizontal laminar jets with positive and negative buoyancy measured with filtered Rayleigh scattering

Near-field mixing characteristics of horizontally issuing jets, alternatively positively and negatively buoyant, are explored. The cross-sectional mass fraction of a buoyant horizontal jet consisting of helium flowing into ambient air is measured using a non-intrusive technique, filtered Rayleigh scattering, for Reynolds numbers ranging from 50 to 1,200, Froude numbers ranging as low as 0.71, and Schmidt numbers on the order of unity for all tests. Several corresponding experiments were carried out using carbon dioxide in place of helium in order to determine whether the direction of the buoyancy changes the characteristic shape of the jet cross-section. Consistent with the literature, mixing rates were consistently higher on the side of the jet where instability, due to density stratification, was present. At jet Froude numbers ranging between 1.5 and approximately 3, the jet cross-section takes a shape consistent with a single plume of fluid being ejected from the core in a vertical direction—upward for a jet with positive buoyancy and downward for a jet with negative buoyancy. Remarkably, for Froude numbers less than unity, the distortion of the jet is quite different in that two separate plumes emanate from each side of the jet while ejection from the center is suppressed. Both the positively and negatively buoyant jet cross-sections exhibited this trait, suggesting that the mechanism that determines the cross-sectional shape of the jet core is only mildly influenced by centripetal effects brought about by streamline curvature. The location of the jet centroid at varied streamwise locations was computed from the mass fraction data, yielding jet trajectory.     

等离子体激励器诱导射流的湍流特性研究

为了进一步掌握等离子体流动控制机理, 完善等离子体激励器数学模型, 提升等离子体激励器扰动能力, 采用粒子图像测速技术, 在静止空气下开展了介质阻挡放电等离子体激励器诱导射流特性研究. 实验时, 将非对称布局激励器布置在平板模型上, 随后将带有激励器的模型放置在有机玻璃箱内, 从而避免环境气流对测试结果的影响. 基于激励器诱导流场, 分析了激励电压对诱导射流特性的影响, 揭示了较高电压下诱导射流近壁区的拟序结构, 获得了卷起涡、二次涡等拟序结构的演化发展过程, 计算了卷起涡脱落频率, 阐述了卷起涡与启动涡的区别, 初步探索了卷起涡的耗散机制. 结果表明: (1)层流射流不能完全概括等离子体诱导射流特性, 激励电压是影响射流特性的重要参数. 当电压较低时, 诱导射流为层流射流; 当电压较高时, 诱导射流的雷诺数提高, 射流剪切层不稳定, 层流射流逐渐发展为湍流射流. (2)等离子体诱导湍流射流包含着卷起涡、二次涡等拟序结构; 在固定电压下, 这些涡结构存在恒定的卷起频率. (3)当激励电压较高时, 流动不稳定使得卷起涡发生了拉伸、变形, 引起了流场湍动能增大, 从而加速了卷起涡的耗散. 研究结果为全面认识激励器射流特性, 进一步挖掘激励器卷吸掺混能力, 提升激励器控制能力积累基础.