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.     

Control volume finite element solution of confined turbulent swirling flows

A control volume finite element method that uses a triangular grid has been applied for solving confined turbulent swirling flows. To treat the velocity-pressure coupling, the vorticity-streamfunction formulation has been used. For turbulence effects the k-? model has been adopted. Consistent with the use of wall functions in the near-wall regions, a boundary condition for the calculation of the vorticity at computational boundaries is proposed and used effectively. The discretized equations are obtained by making use of an exponential interpolation function. Its use has been beneficial in reducing numerical diffusion. Comparisons of the current predictions with available experimental and numerical data from the literature showed generally fair agreement.     

Development of a hybrid k-ε turbulence model for swirling recirculating flows under moderate to strong swirl intensities

A hybrid k-ε turbulence model, based on the concept that the modification of anisotropic effects should not be made in the flow regions inherent to small streamline curvatures, has been developed and examined with the swirling recirculating flows, with the swirl levels ranging from 0·6 to 1·23 in abrupt pipe expansion. A fairly satisfactory agreement of model predictions with the experimental data shows that this hybrid k-ε model can perform better simulation of swirling recirculating flows as compared to the standard k-ε model and the modified k-ε model proposed by Abujelala and Lilley.     

Large-eddy structures of turbulent swirling flows and methane-air swirling diffusion combustion

Turbulent swirling flows and methane-air swirling diffusion combustion are studied by large-eddy simulation (LES) using a Smagorinsky-Lilly subgrid scale turbulence model and a second-order moment (SOM) SGS combustion model, and also by RANS modeling using the Reynolds Stress equation model with the IPCM+wall and IPCM pressure-strain models and SOM combustion model. The LES statistical results for swirling flows give good agreement with the experimental results, indicating that the adopted subgrid-scale turbulence model is suitable for swirling flows. The LES instantaneous results show the complex vortex shedding pattern in swirling flows. The initially formed large vortex structures soon break up in swirling flows. The LES statistical results of combustion modeling are near the experimental results and are as good as the RANS-SOM modeling results. The LES results show that the size and range of large vortex structures in swirling combustion are different from those of isothermal swirling flows, and the chemical reaction is intensified by the large-eddy vortex structures. The project supported by the Special Funds for Major State Basic Research (G-1999-0222-07). The English text was polished by Keren Wang.     

Surfactant-induced effects on turbulent swirling flows

 We employ digital particle imaging velocimetry (DPIV) to investigate the influence of a drag reducing cationic surfactant additive, cetyltrimethyl-ammonium chloride (CTAC), on turbulent swirling flows generated in a cylindrical vessel either by a rotating disk or a rotating disk fitted with vertical flat blades. The largest concentration of CTAC used in this study (0.05 ≤ C ≤ 0.5 mmol/l) is an order of magnitude smaller than those used in experimental investigations of surfactant induced drag reduction in turbulent pipe/channel flows. Even for such dilute systems, a number of dramatic and intriguing effects are observed. In the case of disk-driven flow, it is shown that the surfactant has a non-monotonic influence on turbulence intensity: both radial and axial root mean square velocity fluctuations first increase with increasing surfactant concentration C, reach a maximum and decrease upon further increase in C. Moreover, the maximum intensity is attained at a concentration that is practically independent of the angular frequency Ω of the disk. For the flow driven by bladed impeller, the introduction of the surfactant leads to flow reversal at the impeller plane for low concentrations. Enhancement in the radial and azimuthal mean velocities is also observed. For relatively larger concentrations (=0.5 mmol/l), a mean flow field that consists of multiple transient mixing pockets emerges as Ω exceeds a critical value. Plausible mechanisms are proposed to explain these observations. Received: 11 September 2000 Accepted: 10 April 2001     

Numerical predictions of flows over backward-facing steps

Predictions are reported for two-dimensional, steady, incompressible flows over rearward-facing steps for both laminar and turbulent conditions. The standard k-? turbulence model was used for the turbulent flow. Attention was focused on obtaining accurate solutions to the differential equations. It is concluded that some of the serious discrepancies that have occurred between prediction and observation, and attributed in earlier studies to the inadequacy of the turbulence model, may have been due to the inaccuracy of the solution.     

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.     

Computation of confined coflow jets with three turbulence models

A numerical study of confined jets in a cylindrical duct is carried out to examine the performance of two recently proposed turbulence models: an RNG-based K-? model and a realizable Reynolds stress algebraic equation model. The former is of the same form as the standard K-? model but has different model coefficients. The latter uses an explicit quadratic stress-strain relationship to model the turbulent stresses and is capable of ensuring the positivity of each turbulent normal stress. The flow considered involves recirculation with unfixed separation and reatachment points and severe adverse pressure gradients, thereby providing a valuable test of the predictive capability of the models for complex flows. Calculations are performed with a finite volume procedure. Numerical credibility of the solutions is ensured by using second-order-accurate differencing schemes and sufficiently fine grids. Calculations with the standard K-? model are also made for comparison. Detailed comparisons with experiments show that the realizable Reynolds stress algebraic equation model consistently works better than does the standard K-? model in capturing the essential flow features, while the RNG-based K-? model does not seem to give improvements over the standard K-? model under the flow conditions considered.     

Linear stability of swirling flows computed as solutions to the quasi-cylindrical equations of motion

The linear stability of numerical solutions to the quasi-cylindrical equations of motion for swirling flows is investigated. Initial conditions are derived from Batchelor's similarity solution for a trailing line vortex. The stability calculations are performed using a second-order-accurate finite-difference scheme on a staggered grid, with the accuracy of the computed eigenvalues enhanced through Richardson extrapolation. The streamwise development of both viscous and inviscid instability modes is presented. The possible relationship to vortex breakdown is discussed.     

Numerical simulation of swirling flow in diffusers

A reduced form of Navier–Stokes equations is developed which does not have the usual minimum axial step size restriction. The equations are able to predict accurately turbulent swirling flow in diffusers. An efficient single sweep implicit scheme is developed in conjunction with a variable grid size domain-conforming co-ordinate system. The present scheme indicates good agreement with experimental results for (1) turbulent pipe flow, (2) turbulent diffuser flow, (3) turbulent swirling diffuser flow. The strong coupling between the swirl and the axial velocity profiles outside of the boundary layer region is demonstrated.     

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.     

Hot flow analysis of swirling sudden-expansion dump combustor

Hot flow of a sudden-expansion dump combustor with swirling is analysed by employing an infinite chemical reaction rate. Turbulence properties are closed using one type of algebraic Reynolds stress model and two types of κ–? model. One of the κ–? models includes a swirling effect modification to the ε-equation. Computations have been performed by the SIMPLE-C algorithm with a power-law scheme. The calculated results of the momentum fields and turbulence quantities for swirling flow are compared with the available experimental data. It is shown that the standard κ–? model gives poor prediction of the mean velocity, particularly the tangential velocity. For the hot flow analysis of a sudden-expansion dump combustor with swirling flow it is suggested that it is necessary to use the modified κ–? model or algebraic Reynolds stress model.     

An experimental investigation on flow structures of confined and unconfined impinging air jets

The flow characteristics of both confined and unconfined air jets, impinging normally onto a flat plate have been experimentally investigated. The mean and turbulence velocities, and surface pressures were measured for Reynolds numbers ranging from 30,000 to 50,000 and the nozzle-to-plate spacings in range of 0.2–6. Smoke-wire technique is used to visualize the flow behavior. The effects of Reynolds number, nozzle-to-plate spacing and flow confinement on the flow structure are reported. In the case of confined jet, subatmospheric regions occur on both impingement and confinement surfaces at nozzle-to-plate spacings up to 2 for all Reynolds numbers in consideration and they lie up to nearly the same radial location at both surfaces. However, there is no evidence of the subatmospheric region in unconfined jet. It is concluded that there exists a linkage among the subatmospheric region, turbulence intensity and the peaks in heat transfer coefficients for low spacings in impinging jets.     

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.     

Numerical simulation of confined laminar jet flows

Two‐dimensional incompressible jet development inside a duct has been studied in the laminar flow regime, for cases with and without entrainment of ambient fluid. Results have been obtained for the flow structure and critical Reynolds number values for steady asymmetric jet development and for the onset of temporal oscillations, at various values of the duct‐to‐jet width ratio (aspect ratio). It is found that at low aspect ratios and Reynolds numbers, jet development inside the duct is symmetric. For larger aspect ratios and Reynolds numbers, the jet flow at steady state becomes asymmetric with respect to the midplane, and for still higher values, it becomes oscillatory with respect to time. When entrainment is present, the instabilities of asymmetric development and temporal oscillations occur at a much higher critical Reynolds number for a given aspect ratio, indicating that the stability of the jet flow is higher with entrainment. Copyright © 2000 John Wiley & Sons, Ltd.     

A USM-Θ two-phase turbulence model for simulating dense gas-particle flows

A second-order moment two-phase turbulence model for simulating dense gas-particle flows (USM- model), combining the unified second-order moment two-phase turbulence model for dilute gas-particle flows with the kinetic theory of particle collision, is proposed. The interaction between gas and particle turbulence is simulated using the transport equation of two-phase velocity correlation with a two-time-scale dissipation closure. The proposed model is applied to simulate dense gas-particle flows in a horizontal channel and a downer. Simulation results and their comparison with experimental results show that the model accounting for both anisotropic particle turbulence and particle-particle collision is obviously better than models accounting for only particle turbulence or only particle-particle collision. The USM- model is also better than the k--kp- model and the k--kp-p- model in that the first model can simulate the redistribution of anisotropic particle Reynolds stress components due to inter-particle collision, whereas the second and third models cannot.The project supported by the Special Funds for Major State Basic Research of China (G-1999-0222-08), the National Natural Science Foundation of China (50376004), and Ph.D. Program Foundation, Ministry of Education of China (20030007028)     

Effect of swirling flow on platelet concentration distribution in small-caliber artificial grafts and end-to-end anastomoses

Platelet concentration near the blood vessel wall is one of the major factors in the adhesion of platelets to the wall.In our previous studies,it was found that swirling flows could suppress platelet adhesion in small-caliber artificial grafts and end-to-end anastomoses.In order to better understand the beneficial effect of the swirling flow,we numerically analyzed the near-wall concentration distribution of platelets in a straight tube and a sudden tubular expansion tube under both swirling flow and normal flow conditions.The numerical models were created based on our previous experimental studies.The simulation results revealed that when compared with the normal flow,the swirling flow could significantly reduce the near-wall concentration of platelets in both the straight tube and the expansion tube.The present numerical study therefore indicates that the reduction in platelet adhesion under swirling flow conditions in small-caliber arterial grafts,or in end-to-end anastomoses as observed in our previous experimental study,was possibly through a mechanism of platelet transport,in which the swirling flow reduced the near-wall concentration of platelets.     

The nonlinear evolution of swirling jets

We investigate the mechanisms of vorticity concentration, reorientation and stretching in a swirling jet, whose dynamics is dominated by the competition of a Kelvin-Helmholtz-type vortex sheet instability and a centrifugal Rayleigh instability. To this end, we employ an inviscid Lagrangian vortex filament technique. It is found that the axial jet velocity profile breaks the symmetry of the pure swirling flow. Conversely, the swirl is seen to modify the case dominated by a Kelvin-Helmholtz instability in that it results in the formation of counterrotating vortex rings. A pinch-off mechanism is observed which leads to a dramatic decrease in the local jet diameter. Furthermore, the vortex ring circulation is seen to be time dependent.

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Sommario In questo lavoro si analizza la dinamica della vorticità in un setto rotante in cui siano presenti, ed in competizione reciproca, fenomeni di instabilità di Kelvin-Helmholtz e di Rayleigh. A tale scopo si adotta una metodologia di soluzione non viscosa, Lagrangiana a filamenti vorticosi. Viene mostrato come il profilo di velocità assiale del getto altera la simmetria del moto di pura rotazione. Viceversa, la presenza della rotazione modifica il flusso dominato dall'instabilità di Kelvin-Helmholtz attraverso la formazione di anelli vorticosi controrotanti. L'interazione di questi due campi di velocità porta sia ad una considerevole riduzione del diametro locale del getto, sia ad una variazione temporale della circolazione degli anelli vorticosi.