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.     

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     

Pressure losses in transitions between square and rectangular ducts of the same cross-sectional area

Experimental results are presented for the pressure loss in transitions between square and rectangular ducts where the two ends have the same cross-sectional area. The aspect ratios at the rectangular end ranged from 0.3 to 0.625, and the transition length from 1 to 2 times the hydraulic diameter. Reynolds numbers ranged from 50 000 to 125 000. The pressure drop may be divided into components arising from friction and velocity profile distortion. The friction component, which may be evaluated by normal pipe flow methods, accounts for the observed variation with Reynolds number. The velocity profile component increases as the aspect ratio of the rectangular end falls, and is significantly higher for rectangular to square than for square to rectangular transitions. There is an optimum length to hydraulic diameter ratio, for which the pressure loss is a minimum; it has not been found exactly, but is less than 2 and probably below 1.     

Laboratory observations of interactions of forced plumes with stratified shear layers

Plumes of fluid are often observed in nature to interact with stratified shear layers. Examples of this include chimney plumes hitting inversion-layer ceilings; sewage plumes impinging on unmixed fresh/saltwater interfaces; descending plumes of cold water formed at ice-leads interacting with the oceanic thermocline; and volcano plumes interacting with atmospheric interfaces. Controlled laboratory studies of these phenomena have not previously been described in the literature, and as a result there is a lack of understanding regarding their morphology and dynamics. Thus, a novel set of experiments is described here in which the behaviour of a turbulent plume is observed in the presence of a two-layer ambient. The lower layer, into which the plume initially emerges, is quiescent and at a relatively high density. The upper layer is forced to flow uniformly across the top of the lower layer, and has a lower density. The flow of the resulting plume is characterised by (a) its vertical and lateral spreading in the lower layer; (b) the nature of its extension upstream and downstream at the interface; and (c) the extent to which it penetrates into the upper layer. The behaviour is found to be governed by three non-dimensional parameters: the initial gradient Richardson number of the interface Ri_G, the ratio of the upper layer crossflow speed to the speed of the plume when it first impinges on the interface U_F/U_PI, and the ratio of the plume Monin–Obukhov lengthscale to the lower layer depth L_MO/H_L. Regime diagrams are presented showing the effects of changing these parameters on the plume flow, quantitative relationships are determined, and practical applications of the results are considered.     

Multiplicity of Steady Two-Dimensional Flows in Two-Sided Lid-Driven Cavities

The two-dimensional steady incompressible flow in rectangular cavities is calculated numerically by a finite volume method. The flow is driven by two opposing cavity side walls which move with constant velocities tangentially to themselves. Depending on the cavity aspect ratio and the two side-wall Reynolds numbers different flow states exist. Their range of existence and the bifurcations between different states are investigated by a continuation method accurately locating the bifurcation points. When both side walls move in opposite directions up to seven solutions are found to exist for the same set of parameters. Three of these are point-symmetric and four are asymmetric with respect to the center of the cavity, if the side-wall Reynolds numbers have the same magnitude. When the walls move in the same direction, up to five different flow states are found. In this case only a single mirror symmetric solution exists for equal Reynolds numbers. Received 9 February 2000 and accepted 9 October 2000     

Evolution of a wall-attached buoyant plume in confined boxes: Direct numerical simulations,entrainment coefficient and an integral model

The evolution of a wall-attached plume in a confined box is studied here with the aid of three dimensional direct numerical simulations (DNS). The plume originates from a local line heat source of length, L, placed at the bottom left corner of the box. The Reynolds number of the wall plume, based on box height and buoyant velocity scale, is ${\mathit{Re}}_H=14530$ and boxes of two different aspect ratios (ratio of box width to height) for a particular value of L are simulated. We observe that the plume develops along the vertical sidewall while remaining attached to it before spreading across the top wall to form a buoyant fluid layer and eventually moving downwards and filling the whole box. The original filling box model of Baines and Turner (1969) is modified to incorporate the wall shear stress, and the results from the DNS are compared against the new model. In modelling plumes, we find that the entrainment coefficient ($\alpha$) for wall-attached plumes is reduced to approximately half of that in the free plume, and the main reason is a diminished contribution of turbulence production to $\alpha$ resulting from a restricted ability of the large-scale eddies to transport momentum. Also, unlike the free plume where away from the source inertial forces balances buoyancy forces, here in our simulations of wall-attached plumes this balance is marginally off, likely due to wall friction. A reasonable agreement is observed between our model and DNS data for the volume and momentum fluxes in the quiescent uniform environment and also for the time-dependent buoyancy profile calculated far away from the plume.     

Effects of temperature-dependent viscosity variation on entropy generation,heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Peclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Raut [14].     

Effects of inlet conditions and surface roughness on the performance of transitions between square and rectangular ducts of the same cross-sectional area

A study has been made of the effects of inlet conditions and surface roughness on the performance of transitions between square and rectangular ducts of the same cross-sectional area. The conditions at entry were varied by using different approach lengths of straight duct and by means of a square screen of woven wire cloth. The surface roughening was accomplished by coating the surface of the transition with graded waterproof silicon carbide paper, whose surface roughness was measured with a Talysurf 4 instrument. All tests were run at Reynolds number 10⁵.

The results indicate that the static pressure loss coefficient significantly increases as the inlet boundary layer thickness increases. This variation is a function of aspect ratio at the rectangular end; the loss coefficient rises as the aspect ratio falls. The pressure drop slightly increases when the wall surface is roughened and is higher at low aspect ratios.     

Fluid flow in a rotating curved rectangular duct

The fluid flowing in a rotating curved duct is subjected to both the Coriolis force due to a rotation and the centrifugal force due to a curvature. In this paper, the combined effects of the two forces on the flows in rotating curved rectangular ducts are examined numerically. According to the aspect ratio of the cross-section, the rectangular ducts are divided into three types: η>1, η=1, η<1, where η is the aspect ratio. The variations of the flow structures with the force ratio F (the ratio of the Corislis force to the centrifugal force) are studied in detail and many hitherto unknown flow patterns are found. The effects of the force ratio and the aspect ratio of the cross-section on the friction factor are also examined. Present results show both the characteristics of the secondary flow, axial flow and the natures of the friction factor.     

Spatial Direct Numerical Simulation of the Large Vortical Structures in Forced Plumes

Direct numerical simulation (DNS) of forced plumes arising frominput of both momentum and buoyancy into an ambient fluid is presented.The large vortical structures in the near field of thermal and reactiveplumes are investigated. Boundary conditions associated with the spatialDNS of open-boundary buoyant flows that are compatible with the modernnon-dissipative, high-order, finite-difference schemes have beendeveloped. The governing equations for flow and combustion at the plumecenterline are put into a special form to circumvent the singularity atthe axis associated with the cylindrical coordinates. Mixing is found tobe stronger in the planar thermal plume than in the axisymmetric case.An explanation is provided based on the vorticity budget. Axisymmetricreactive plumes with a one-step reaction governed by the Arrheniuskinetics have also been studied. The unsteady effects of chemical heatrelease and combustion-induced buoyancy on the flow structures areinvestigated. Budgets of the vorticity transport are examined to revealthe mechanisms leading to the formation and evolution of large vorticalstructures in forced plumes. It is found that volumetric expansion dueto chemical heat release tends to destroy vorticity, whilecombustion-induced buoyancy under the gravitational effect generatesvorticity. The gravitational term in the vorticity transport equation isfound to be the main mechanism for the buoyant flow instability and thedevelopment of counter-rotating vortices in reactive plumes.     

Prediction of developing turbulent flow in 90°‐curved ducts using linear and non‐linear low‐Re k–ε models

This paper reports the outcome of applying two different low‐Reynolds‐number eddy‐viscosity models to resolve the complex three‐dimensional motion that arises in turbulent flows in ducts with 90^° bends. For the modelling of turbulence, the Launder and Sharma low‐Re k–ε model and a recently produced variant of the cubic non‐linear low‐Re k–ε model have been employed. In this paper, developing turbulent flow through two different 90^° bends is examined: a square bend, and a rectangular bend with an aspect ratio of 6. The numerical results indicate that for the bend of square cross‐section the curvature induces a strong secondary flow, while for the rectangular cross‐section the secondary motion is confined to the corner regions. For both curved ducts, the secondary motion persists downstream of the bend and eventually slowly disappears. For the bend of square cross‐section, comparisons indicate that both turbulence models can produce reasonable predictions. For the bend of rectangular cross‐section, for which a wider range of data is available, while both turbulence models produce satisfactory predictions of the mean flow field, the non‐linear k–ε model returns superior predictions of the turbulence field and also of the pressure and friction coefficients. Copyright © 2006 John Wiley & Sons, Ltd.     

Three dimensional finite element analysis for Rayleight-Benard convection in rectangular enclosures

The pattern of Rayleigh-Benard convection of air in a rectangular box heated-from-below is studied by numerically solving the three-dimensional time-dependent Navier-Stokes equations under the Boussinesq approximation. Slightly supercritical Rayleigh number was adopted to track the evolutions of flow structure as a function of enclosure's aspect ratio (A=L/H). The flow will asymptotically evolve to different patterns, among which, two possible types of flow pattern are found. One consists of the pair of straight vortex rolls and the other appears as closed vortex rings. The transition between the flow patterns indicates that there exists a flow bifurcation with the variation of container's aspect ratio. In addition, both steady and oscillatory flows have been observed, corresponding to the pair of straight vortex rolls and the vortex ring, respectively. The complexity of flow structure tends to increase with the increasing aspect ratio of the rectangular enclosure. The project supported by the National Natural Science Foundation of China (19889210), the National Distinguished Young Fund (10125210), the Hundred Talents Program of CAS, and the Training Program for the Trans-Century Outstanding Young of MOE     

Fully developed magneto convection flow in a vertical rectangular duct

An analysis is performed to study the MHD free convection flow in a vertical rectangular duct for laminar and fully developed regime taking into consideration the effects of Ohmic heating and viscous dissipation. Numerical solutions are found using finite difference method of second-order accuracy. The effects of various physical parameters such as Hartmann number, aspect ratio, buoyancy parameter and circuit parameter are presented graphically. It is found that as Hartmann number, buoyancy parameter and aspect ratio increase, the upward and downward flow rates are increased for open circuit but decrease for short circuit.     

DNS study of passive plume interference emitting from two parallel line sources in a turbulent channel flow

Turbulent mixing of dual plumes emitting simultaneously from line sources in a turbulent channel flow has been studied using direct numerical simulation (DNS). Three test cases have been compared to investigate the effects of the source separation on turbulent mixing of the two instantaneous plumes. The dispersion and interference of dual plumes are investigated in both physical and spectral spaces, which include an analysis of statistical moments of the concentration field, cross-correlation between the two instantaneous plumes, pre-multiplied spectra of the velocity and concentration fields, and co-spectrum and coherency spectrum of the dual plumes. As the downstream distance from the line source increases, the plume development associated with a single source emission transitions from a turbulent convective stage to a turbulent diffusive stage. It is observed that a plume released from a ground-level source reaches the turbulent diffusive stage faster than that released from an elevated source. It is also observed that a smaller separation between the two line sources tends to facilitate a more rapid growth in the cross-correlation coefficient of two instantaneous plumes. In the near-source region, the maximum coherency spectrum is produced at lower frequencies indicating that dual-plume mixing is dominated by the external flapping effects of large-scale eddy motions. However, in the far downstream region of the sources, the coherency spectrum in the higher frequency range increases significantly, indicating that the spread of the total plume is larger than all scales of turbulent eddies, such that they all contribute to the in-plume mixing of the dual plumes.     

Improved-Delayed-Detached-Eddy Simulation of cavity-induced transition in hypersonic boundary layer

Hypersonic flow transition from laminar to turbulent due to the surface irregularities, like local cavities, can greatly affect the surface heating and skin friction. In this work, the hypersonic flows over a three-dimensional rectangular cavity with length-to-width-to-depth ratio, L:W:D, of 19.9:3.57:1 at two angles of attack (AoA) were numerically studied with Improved-Delayed-Detached-Eddy Simulation (IDDES) method to highlight the mechanism of transition triggered by the cavity. The present approach was firstly applied to the transonic flow over M219 rectangular cavity. The results, including the fluctuating pressure and frequency, agreed with experiment well. In the hypersonic case at Mach number about 9.6 the cavity is seen as “open” at AoA of −10° but “closed” at AoA of −15° unconventional to the two-dimensional cavity case where the flow always exhibits closed cavity feature when the length-to-depth ratio L/D is larger than 14. For the open cavity flow, the shear layer is basically steady and the flow maintains laminar. For the closed cavity case, the external flow goes into the cavity and impinges on the bottom floor. High intensity streamwise vortices, impingement shock and exit shock are observed causing breakdown of these vortices triggering rapid flow transition.     

EFFECTS OF LID-DRIVEN CAVITY SHAPE ON THE FLOW ESTABLISHMENT PHASE

Experiments are carried out to study the flow establishment phase inside closed cavities submitted to the impulsive translation from rest, of one of their walls at a Reynolds number of 1000. Three standard industrially machined or molded cylindrical cavity shapes are studied and are compared with respect to the efficiency of mixing process: square, rectangular and semi-circular of length-to-width ratio of 2:1. The flow structures in the mid-cross-section are analysed by means of fine topological and kinematic visualization series using two complementary techniques: continuous dye filament and discrete solid tracers both coupled with a laser sheet illumination. Particular attention is given to vorticity propagation and primary/secondary eddy formations. Although a roughly similar vortex generation is observed in all examined cavities, important differences appear with time. The semi-circular cavity flow results in a much more homogeneous and uniform recirculation with no secondary flow recirculation zone. On the contrary, the square and rectangular cavity flows develop a better flow mass dispersion and, respectively, one and two secondary eddies. At the final time of observation (t^*=12), both semi-circular and rectangular cavity flows seem to reach their steady state whereas the square one continues to evolve. Comparisons with 2-D computational results of other authors illustrate the three-dimensional flow aspect present in experiments.     

Numerical simulation of natural convective heat transfer and fluid flow around a heated cylinder inside an enclosure

 A collocated, non-orthogonal grid based finite volume technique has been applied for investigating the two dimensional natural convective flow and heat transfer around a heated cylinder kept in a square enclosure. The effects of different enclosure wall thermal boundary conditions, fluid Prandtl number and the ratio between enclosure and cylinder dimensions (aspect ratio) upon the flow and thermal features, have been systematically studied. It is observed that the patterns of recirculatory flow and thermal stratification in the fluid are significantly modified, if any of these parameters is varied. The overall heat transfer rates are also affected due to the changes in the flow and temperature patterns. The study presents useful observations regarding the variation of local Nusselt number along each wall, for the different cases considered. Received on 2 August 2000 / Published online: 29 November 2001     

Large-eddy simulation of buoyancy-driven natural ventilation in an enclosure with a point heat source

Rising buoyant plumes from a point heat source in a naturally ventilated enclosure have been investigated using large-eddy simulation (LES). The aim of the work is to assess the performance and the accuracy of LES for modelling buoyancy-driven displacement ventilation of an enclosure and to shed more light on the transitional behaviour of the plume and the coherent structures involved. The Smagorinsky sub-grid scale model is used for the unresolved small-scale turbulence. The Rayleigh number, Ra is chosen to be in the range where spatial transition from laminar to turbulent flow takes place (Ra = 1.5 × 10⁹). The plume properties (source strength and rate of spread) as well as the ventilation properties (stratification height and temperature of stratified layer) estimated using the theory of Linden et al. are found to agree reasonably well with the LES results. The variation of the plume width with height indicates a linear variation of the entrainment coefficient rather than a constant value used by Linden et al. for a fully turbulent thermal plume. Flow visualisation revealed the nature of the large-scale coherent structures involved in the transition to turbulence in the plume. The most excited modes observed in the velocity, pressure and temperature fields spectra correspond to Strouhal number in the range 0.3 ≤ St ≤ 0.55 which is in agreement with those observed by Zhou et al. for a turbulent forced plume. Excited modes less than thisvalue (St = 0.2) were observed and may be due to low-frequency motions felt throughout the flow.     

Numerical study of flow and thermal behaviour of lid‐driven flows in cavities of small aspect ratios

Numerical study has been performed to investigate the effects of cavity shape on flow and heat transfer characteristics of the lid‐driven cavity flows. Dependence of flow and thermal behaviour on the aspect ratio of the cavities is also evaluated. Three types of the cross‐sectional shape, namely, circular, triangular, and rectangular, and four aspect ratios, 0.133, 0.207, 0.288, and 0.5, are taken into account to construct twelve possible combinations; however, attention is focused on the small‐aspect‐ratio situations. Value of the Reynolds number considered in this study is varied between 100 and 1800. For the cases considered in this study a major clockwise vortex driven by the moving lid prevailing in the cavity is always observed. When the Reynolds number is fixed, the rectangular cavity produces strongest lid‐driven flow, and the triangular cavity weakest. For the cases at small aspect ratio and low Reynolds number, the streamlines appear symmetric fore‐and‐aft with respect to the central line at x/L = 0.5. Data for the local and average Nusselt numbers are also provided. For rectangular cavities, it is observed that case 1/5R produces the highest average Nusselt number at any Reynolds number. Among the twelve possible geometric cases considered herein, the highest and lowest average Nusselt numbers are found with cases 1/6T and 1/2C, respectively. Copyright © 2006 John Wiley & Sons, Ltd.     

Flow over rectangular porous block in a fixed width channel: influence of porosity and aspect ratio

Flow over a rectangular porous block placed in a fixed width channel is considered and the influence of block aspect ratio on the heat transfer rate from the block is examined. A non-porous solid block is also accommodated to compare the effect of porosity on the flow field and heat transfer characteristics. Aspect ratio and the porosity of the block are varied in the simulations. A numerical scheme employing a control volume approach is considered when predicting the flow and temperature fields. The Reynolds number is selected to yield the mix convection situation in the flow field. It is found that the aspect ratio significantly influences Nu and Gr numbers, in which case increasing the aspect ratio enhances Nu while lowering Gr. Increasing porosity improves the heat transfer rates from the porous block, provided that at high aspect ratios, this situation ceases due to blockage effect of the body in the channel.