Study of Density Effects in Turbulent Buoyant Jets Using Large-Eddy Simulation

Large-Eddy simulations (LES) of spatially evolving turbulent buoyant round jets have been carried out with two different density ratios. The numerical method used is based on a low-Mach-number version of the Navier–Stokes equations for weakly compressible flow using a second-order centre-difference scheme for spatial discretization in Cartesian coordinates and an Adams–Bashforth scheme for temporal discretization. The simulations reproduce the typical temporal and spatial development of turbulent buoyant jets. The near-field dynamic phenomenon of puffing associated with the formation of large vortex structures near the plume base with a varicose mode of instability and the far-field random motions of small-scale eddies are well captured. The pulsation frequencies of the buoyant plumes compare reasonably well with the experimental results of Cetegen (1997) under different density ratios, and the underlying mechanism of the pulsation instability is analysed by examining the vorticity transport equation where it is found that the baroclinic torque, buoyancy force and volumetric expansion are the dominant terms. The roll-up of the vortices is broken down by a secondary instability mechanism which leads to strong turbulent mixing and a subsequent jet spreading. The transition from laminar to turbulence occurs at around four diameters when random disturbances with a 5% level of forcing are imposed to a top-hat velocity profile at the inflow plane and the transition from jet-like to plume-like behaviour occurs further downstream. The energy-spectrum for the temperature fluctuations show both −5/3 and −3 power laws, characteristic of buoyancy-dominated flows. Comparisons are conducted between LES results and experimental measurements, and good agreement has been achieved for the mean and turbulence quantities. The decay of the centreline mean velocity is proportional to x ^−1/3 in the plume-like region consistent with the experimental observation, but is different from the x ⁻¹ law for a non-buoyant jet, where x is the streamwise location. The distributions of the mean velocity, temperature and their fluctuations in the near-field strongly depend upon the ratio of the ambient density to plume density ρ_a/ρ₀. The increase of ρ_a/ρ₀ under buoyancy forcing causes an increase in the self-similar turbulent intensities and turbulent fluxes and an increase in the spatial growth rate. Budgets of the mean momentum, energy, temperature variance and turbulent kinetic energy are analysed and it is found that the production of turbulence kinetic energy by buoyancy relative to the production by shear is increased with the increase of ρ_a/ρ₀. Received 16 June 2000 and accepted 26 June 2001     

Accounting for Buoyancy Effects in the Explicit Algebraic Stress Model: Homogeneous Turbulent Shear Flows

Most explicit algebraic stress models are formulated for turbulent shear flows without accounting for external body force effects, such as the buoyant force. These models yield fairly good predictions of the turbulence field generated by mean shear. As for thermal turbulence generated by the buoyant force, the models fail to give satisfactory results. The reason is that the models do not explicitly account for buoyancy effects, which interact with the mean shear to enhance or suppress turbulent mixing. Since applicable, coupled differential equations have been developed describing these thermal turbulent fields, it is possible to develop corresponding explicit algebraic stress models using tensor representation theory. While the procedure to be followed has been employed previously, unique challenges arise in extending the procedure for developing the algebraic representations to turbulent buoyant flows. In this paper the development of an explicit algebraic stress model (EASM) is confined to the homogeneous buoyant shear flow case to illustrate the methodology needed to develop the proper polynomial representations. The derivation is based on the implicit formulation of the Reynolds stress anisotropy at buoyant equilibrium. A five-term representation is found to be necessary to account properly for the effect of the thermal field. Thus derived, external buoyancy effects are represented in the scalar coefficients of the basis tensors, and structural buoyancy effects are accounted for in additional terms in the stress anisotropy tensor. These terms will not vanish even in the absence of mean shear. The performance of the new EASM, together with a two-equation (2-Eq) model, the non-buoyant EASM of Gatski and Speziale (1993) and a full second-order model, is assessed against direct numerical simulations of homogeneous, buoyant shear flows at two different Richardson numbers representing weak and strong buoyancy effects. The calculations show that this five-term representation yields better results than the 2-Eq model and the EASM of Gatski and Speziale where buoyancy effects are not explicitly accounted for. Received 5 March 2001 and accepted 15 January 2002     

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。     

Numerical predictions of the bifurcation of confined swirling flows

The bifurcation of confined swirling flows was numerically investigated by employing both the k-? and algebraic stress turbulence models. Depending upon the branch solution examined, dual flow patterns were predicted at certain swirl levels. In the lower-branch solution which is obtained by gradually increasing the swirl level from a low-swirl flow, the flow changes with increasing swirl number from the low-swirl flow pattern to a high-swirl flow pattern. In the upper-branch solution which is acquired by gradually decreasing the swirl level from a high-swirl flow, on the other hand, the flow can maintain itself in the high-swirl flow pattern at the swirl levels where it exhibits the low-swirl flow pattern in the lower branch. The bifurcation of confined swirling flows was predicted with either the k-? model or the algebraic stress model being employed. Both the k-? and algebraic stress models result in comparable and sufficiently good predictions for confined swirling flows if high-order numerical schemes are used. The reported poor performance of the k-? model was clarified to be mainly attributable to the occurrence of the bifurcation and the use of low-order numerical schemes.     

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.     

Turbulent jet flows with buoyancy and swirl

Übersicht Das gleichzeitige Auftreten von Auftrieb und Drall in vertikalen, runden, turbulenten Freistrahlen wird mit einer Integralmethode untersucht. Durch Hinzunahme der Bewegungs- und Energiegleichung an der Strahlachse kann auf die Verwendung eines empirischen Entrainmentkoeffizienten verzichtet werden. Es zeigt sich, daß zwischen Druck- und Axialgeschwindigkeitsprofilen eine ganz bestimmte Beziehung bestehen muß, um unrealistische Singularitäten im Strömungsfeld zu vermeiden. Die Beziehung wird durch Meßergebnisse annähernd bestätigt. Der Einfluß des Dralls auf alle Strömungsgrößen ist in der Nähe des Ursprungs am stksten. Eine Zunahme der dimensionslosen Drallzahl bewirkt eine starke Aufwertung des Strahls mit 180° Öffnungswinkel im Ursprung und eine Abnahme der axialen Geschwindigkeit. Im Grenzfall sehr hoher Drallzahlen entsteht eine neue Strahlströmung, die als drallbehafteter, auftriebserzeugter Strahl bezeichnet wird. Stromabwärts klingen die Dralleffekte rasch ab und Auftriebseffekte nehmen an Bedeutung zu. Das asymptotische Verhalten entspricht einem auftriebserzeugten Strahl (plume).

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Turbulent jet flows with buoyancy and swirl

Summary Vertical, round, turbulent jets with combined effects of buoyancy and swirl are investigated by an integral method. The method avoids application of an empirical entrainment coefficient by including the differential equations of motion and energy at the jet axis. It is shown that pressure and velocity profiles have to be related to each other in order to avoid unrealistic singularities in the flow field. This relationship is approximately confirmed by measurements. With respect to all flow quantities, the influence of swirl is felt strongest near the origin. Increasing the dimensionless swirl number strongly increases the width of the jet (with infinite derivative at the origin) and decreases the axial velocity. In the limiting case of very high swirl numbers a new type of jet flow is found which can be called a swirling plume. Further, downstream swirl effects decay rapidly and buoyancy becomes relatively more important. The asymptotic behaviour resembles that of a plume.

     

Density effects on jet characteristics in confined swirling flow

Density effects on isothermal jet mixing in confined swirling flow are investigated. The experiment is carried out with helium/air as the jet fluid in the same facility as that used by So et al. (1984a, b) and the test conditions are chosen to be the same as before. Contrary to the homogeneous mixing results, the helium jet is preserved up to 40 jet diameters downstream. The behavior of the mean and turbulence field depends highly on the initial jet velocity. Since the jets are fully turbulent and the jet momentum fluxes for inhomogeneous mixing are less than those for homogeneous mixing, the cause of this difference in behavior is directly attributed to the combined action of density difference and swirl. In spite of this, near isotropy of the turbulence field is again observed at 40 jet diameters downstream.     

Direct numerical simulation of confined swirling jets

This study investigates the Lagrangian acceleration and velocity of fluid particles in swirling flows via direct numerical simulation. The intermittency characteristics of acceleration and velocity of fluid particles are investigated at different swirl numbers and Reynolds numbers. The flatness factor and trajectory curvature are used to analyse the effect of Lagrangian intermittency. The joint probability density function of Lagrangian acceleration and turbulence intensity is shown to explain the augmentation effect of Lagrangian intermittency by the strongly swirling levels under the relatively low intensity of turbulence. In addition, the correlation between the Lagrangian acceleration and the turbulence intensity is enhanced as the swirl level increases. It shows the important effect of swirl on the motion behaviour of fluid particles in the strongly swirling flows.     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

Mass and momentum transport in the near field of swirling turbulent jets. Effect of swirl rate

Local transport of the flow momentum and scalar admixture in the near-field of turbulent swirling jets (Re = 5,000) has been investigated by using a combination of the particle image velocimetry and planar laser-induced fluorescence methods. Advection and turbulent and molecular diffusions are evaluated based on the measured distributions of the mean velocity and concentration and the Reynolds stresses and fluxes. As has been quantified from the data, the flow swirl intensifies the entrainment of the surrounding fluid and promotes mass and momentum exchange in the outer mixing layer. A superimposed swirl results in the appearance of a wake/recirculation region at the jet axis and, consequently, the formation of an inner shear layer. In contrast to the scalar admixture, the momentum exchange in the inner shear layer is found to be strongly intensified by the swirl. For the jet with the highest considered swirl rate, a substantial portion of the surrounding fluid is found to enter the unsteady central recirculation zone, where it mixes with the jet that is issued from the nozzle. The contribution of the coherent velocity fluctuations, which are induced by large-scale vortex structures, to the turbulent transport has been evaluated based on triple decomposition, which was based on proper orthogonal decomposition analysis of the velocity data sets. For the considered domain of the jet with the highest swirl rate and vortex breakdown, the contributions of detected helical vortex structures, inducing pressing vortex core, to the radial fluxes of the flow momentum and the scalar admixture are found to locally exceed 65% and 80%, respectively.     

Buoyancy modelling with incompressible SPH for laminar and turbulent flows

This work aims to model buoyant, laminar or turbulent flows, using a two‐dimensional incompressible smoothed particle hydrodynamics model with accurate wall boundary conditions. The buoyancy effects are modelled through the Boussinesq approximation coupled to a heat equation, which makes it possible to apply an incompressible algorithm to compute the pressure field from a Poisson equation. Based on our previous work [1], we extend the unified semi‐analytical wall boundary conditions to the present model. The latter is also combined to a Reynolds‐averaged Navier–Stokes approach to treat turbulent flows. The k ? ? turbulence model is used, where buoyancy is modelled through an additional term in the k ? ? equations like in mesh‐based methods. We propose a unified framework to prescribe isothermal (Dirichlet) or to impose heat flux (Neumann) wall boundary conditions in incompressible smoothed particle hydrodynamics. To illustrate this, a theoretical case is presented (laminar heated Poiseuille flow), where excellent agreement with the theoretical solution is obtained. Several benchmark cases are then proposed: a lock‐exchange flow, two laminar and one turbulent flow in differentially heated cavities, and finally a turbulent heated Poiseuille flow. Comparisons are provided with a finite volume approach using an open‐source industrial code. Copyright © 2015 John Wiley & Sons, Ltd.     

Jet characteristics in confined swirling flow

Jets in confined swirling flow are investigated in a facility where the swirling flow in the tube is produced by a vane-type swirler. The jet is located centrally in the swirler, and the diameter ratio of the tube to the jet is 14. Both the jet and the swirling flow are fully turbulent. Results show that the confined jet is highly dissipative in nature. Consequently, the flow in the tube does not resemble a free jet with axial pressure gradient. The presence of swirl increases the rate of dissipation and the jet decays even faster. A fairly isotropic turbulence field is observed in the confined swirling flow. However, the introduction of the jet does not significantly affect this behavior and near isotropy of the turbulence field is again observed at 30 jet diameters downstream.     

Turbulent pipe flow downstream a 90° pipe bend with and without superimposed swirl

In the present work, the turbulent flow downstream a 90° pipe bend is investigated by means of stereoscopic particle image velocimetry. In particular, the three dimensional flow field at the exit of the curved pipe is documented for non-swirling and swirling flow conditions, with the latter being generated through a unique axially rotating pipe flow facility. The non-swirling flow was examined through snapshot proper orthogonal decomposition (POD) with the aim to reveal the unsteady behaviour of the Dean vortices under turbulent flow conditions, the so-called “swirl-switching” phenomenon. In respect to the swirling turbulent pipe flow, covering a wide range of swirl strengths, POD has been employed to study the effect of varying strength of swirl on the Dean vortices as well as the interplay of swirling motion and Dean cells. Furthermore, the visualised large scale structures in turbulent swirling flows through the bend are found to incline and tear up with increasing swirl intensity. The present time-resolved, three component, experimental velocity field data will provide a unique and useful database for future studies; in particular for the CFD community.     

An experimental study of fluid flow and heat transfer in decaying swirl through a heated annulus

The mean and turbulent structures of turbulent swirling flow in a heated annulus have been measured. Both forced and free vortex swirling flows were generated, and the outer wall of the test section was heated uniformly. The maximum swirl number was 1.39, Reynolds numbers were up to 200000, and heat input was 10.5 kW. Mean and turbulent velocity components, air and wall temperatures, and wall static pressures were all measured. Hot-film techniques were developed to measure turbulence. From these parameters, the flow and temperature fields, pressure distribution, and heat transfer coefficients were determined. The mechanisms of heat transfer were identified.     

On the analysis of turbulent transport processes in nonreacting multijet burner flows

Measurements of time-resolved velocity characteristics have been obtained with a laser-Doppler velocimeter in the vicinity of a model of an industrial oxy-fuel burner. The burner consists of a central axisymmetric jet surrounded by 16 circular jets, simulating the injection of oxygen in practical burners. The experiments were carried out for isothermal flows and quantify the effect of swirl for 0 ≤ S ≤ 0.9 on the mixing efficiency of the burner assembly. The results show that the present flow develops faster than related coaxial free jets with similar velocity ratios between central and peripheral air streams and, for example, for the nonswirling flow the rate of decay of the centreline velocity increases by a factor of 2. Swirl attenuates the three-dimensional structure typical of multijet flows although the peripheral jets limit the radial spreading of the swirling flow and give rise to increased values of mean shear strain and, therefore, to turbulent production. The existence of zones characterized by large turbulence anisotropy indicate the need to take account of the individual normal stresses in any proposed mathematical model to simulate the flow characteristics. Inspection of the terms in the conservation equation for the turbulent stresses quantify the extent to which interaction of normal stresses with normal strains influences the flow and suggests the likely combined magnitude of turbulent diffusion and dissipation.     

Numerical study of hysteresis in annular swirling jets with a stepped‐conical nozzle

This study investigates the experimentally observed hysteresis in the mean flow field of an annular swirling jet with a stepped‐conical nozzle. The flow is simulated using the Reynolds‐averaged Navier–Stokes (RANS) approach for incompressible flow with a k–ε and a Reynolds stress transport (RSTM) turbulence model. Four different flow structures are observed depending on the swirl number: ‘closed jet flow’, ‘open jet flow low swirl’, ‘open jet flow high swirl’ and ‘coanda jet flow’. These flow patterns change with varying swirl number and hysteresis at low and intermediate swirl numbers is revealed when increasing and subsequently decreasing the swirl. The influence of the inlet velocity profile on the transitional swirl numbers is investigated. When comparing computational fluid dynamics with experiments, the results show that both turbulence models predict the four different flow structures and the associated hysteresis and multiple solutions at low and intermediate swirl numbers. Therefore, a good agreement exists between experiments and numerics. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density

An investigation on the predictive performance of cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density is presented. Comparisons of the prediction with the experiments show some improvements of cubic models over the linear k–ε model. The linear k–ε model does not contain any mechanism to represent the interaction of swirl and density variation and as a consequence it performs poorly. With appropriate modelling, two‐equation cubic turbulence models can capture the subcritical nature of the flow, represent the azimuthal velocity profiles of combined forced‐free vortex motion, and predict the combined effects of swirl and density variation fairly well. However, the calibration of model coefficients is still a topic of investigation. Further amendments are also needed for the equations of k and ε to take into account the effects of swirl and density gradients correctly. Copyright © 2004 John Wiley & Sons, Ltd.     

不同参数下环形通道内湍流旋流流动的模拟

应用一种合理考虑湍流一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．研究了旋流数、进口轴向速度和内外半径比等参数对环形通道内湍流旋流流动的影响,以及由此产生的流场变化对强化环形通道内传热的作用．     

Numerical aspects of calculation of confined swirling flows with internal recirculation

Predictions were performed for two different confined swirling flows with internal recirculation zones. The convection terms in the elliptic governing equations were discretized using three different finite differencing schemes: hybrid, quadratic upwind interpolation and skew upwind differencing. For each flow case, calculations were carried out with these schemes and successively refined grids were employed. For the turbulent flow case the k-ε turbulence model was used. The predicted cases were a laminar swirling flow investigated by Bornstein and Escudier, and a turbulent low-swirl case studied by Roback and Johnson. In both cases an internal recirculation zone was present. The laminar case is well predicted when account is taken of the estimated radial velocity component at the chosen inlet plane. The quadratic upwind interpolation and skew upwind schemes predict the main features of the internal recirculation zone also with a coarse grid. The turbulent case is well predicted with the coarse as well as the finer grids, the skew upwind and quadratic upwind interpolation schemes yielding results very close to the measurements. It is concluded that the skew upwind scheme reaches grid independence slightly before the quadratic upwind scheme, both considerably earlier than the hybrid scheme.