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     

Experimental investigation of the unsteady structure of a transitional plane wall jet

 A laminar wall jet undergoing transition is investigated using the particle image velocimetry (PIV) technique. The plane wall jet is issued from a rectangular channel, with the jet-exit velocity profile being parabolic. The Reynolds number, based on the exit mean velocity and the channel width, is 1450. To aid the understanding of the global flow features, laser-sheet/smoke flow visualizations are performed along streamwise, spanwise, and cross-stream directions. Surface pressure measurements are made to correlate the instantaneous vorticity distribution with the surface pressure fluctuations. The instantaneous velocity and vorticity field measurements provide the basis for understanding the formation of the inner-region vortex and the subsequent interactions between the outer-region (free-shear-layer region) and inner-region (boundary-layer region) vortical structures. Results show that under the influence of the free-shear-layer vortex, the local boundary layer becomes detached from the surface and inviscidly unstable, and a vortex is formed in the inner region. Once this vortex has formed, the free-shear-layer vortex and the inner-region vortex form a vortex couple and convect downstream. The mutual interactions between these inner- and outer-region vortical structures dominate the transition process. Farther downstream, the emergence of the three-dimensional structure in the free shear layer initiates complete breakdown of the flow. Received: 8 November 1995/Accepted: 6 November 1996     

Experimental investigation of the wall shear stress and the vortex dynamics in a circular impinging jet

The wall shear stress and the vortex dynamics in a circular impinging jet are investigated experimentally for Re = 1,260 and 2,450. The wall shear stress is obtained at different radial locations from the stagnation point using the polarographic method. The velocity field is given from the time resolved particle image velocimetry (TR‐PIV) technique in both the free jet region and near the wall in the impinging region. The distribution of the momentum thickness is also inspected from the jet exit toward the impinged wall. It is found that the wall shear stress is correlated with the large-scale vortex passing. Both the primary vortices and the secondary structures strongly affect the variation of the wall shear stress. The maximum mean wall shear stress is obtained just upstream from the secondary vortex generation where the primary structures impinge the wall. Spectral analysis and cross-correlations between the wall shear stress fluctuations show that the vortex passing influences the wall shear stress at different locations simultaneously. Analysis of cross-correlations between temporal fluctuations of the wall shear stress and the transverse vorticity brings out the role of different vortical structures on the wall shear stress distribution for the two Reynolds numbers.     

Properties of vortices in the self-similar turbulent jet

Instantaneous, two-dimensional velocity measurements were conducted in the axial plane of a self-similar turbulent axisymmetric jet. The velocity fields were high-pass filtered to expose the vortical structures. An automated method was used to identify the radial and axial coordinates of the vortex centers and rotational sense, and to measure their size, circulation, vorticity, and energy. New insights into turbulent jets are obtained by plotting statistical distributions for vortex properties as functions of Reynolds number and radial position. While the probability of finding a vortex is uniform up to the edge of the jet, the strongest eddies in the high-pass filtered field occur near the jet axis. The average circulation is directly proportional to the vortex size. The Reynolds number strongly affects the average vorticity, circulation, and energy of the eddies. However, the normalized curves show a good collapse implying that the jet is indeed self-similar. Results for the left and right half-planes of the jet are also presented. Interestingly, we find that contrary to customary drawings of jet flows, a substantial number of both clockwise and counter-clockwise rotating eddies exist on both sides of the jet axis, with almost equal numbers of oppositely rotating vortices close to the jet axis. Further, the disparity in the number of oppositely rotating eddies in each half-plane increases with the eddy size. Nevertheless, these results are consistent with the well-known radial vorticity distribution of axisymmetric jets.     

Three-dimensional numerical study of jet-in-crossflow characteristics at low Reynolds number

A numerical study of a square jet in a cross flow is carried out at a Reynolds number of 100. The flow field and heat transfer characteristic downstream of the jet have been explored by solving three-dimensional unsteady Navier–Stokes equations and energy equation using higher order spatial and temporal discretization. The projection of vortical structure on a plane is seen to give the component of vortex normal to the plane. Four combinations of velocity profile namely (1) uniform crossflow and uniform jet, (2) laminar boundary layer crossflow and uniform jet, (3) uniform crossflow and parabolic jet profile, and (4) laminar boundary layer crossflow and parabolic jet are compared at same phase to see their effect on the flow field and heat transfer characteristic. All the four cases are seen to exhibit unsteadiness but the jet with parabolic profile is seen to show stronger unsteadiness. The instantaneous vortical structures of all the cases at the same phase show that the structures are more complex for the jet with parabolic velocity profile. The temperature field is seen to be correlated with the vortical structures. Comparison of the time averaged flow field reveals that the jet penetration is the highest for the jet having parabolic profile and boundary layer crossflow. The adiabatic effectiveness is observed to be more for the jet with uniform velocity profile and uniform crossflow and was least for the jet with parabolic velocity profile and boundary layer crossflow.     

Large-Eddy Simulations of Forced Three-Dimensional Impinging Jets

Large-eddy simulations of the flow field around twin three-dimensional impinging jets were carried out to simulate the near-ground hover configuration of a vertical takeoff and landing (VTOL) aircraft. Both the impinging jet and the upwash caused by the collision of the wall jets are modeled in this study. The evolution of the vortical structures in the impinging jet flow field, due to the introduction of axisymmetric and azimuthal perturbations at the jet exit, has been investigated. The vortical structures formed in the jet shear layer due to azimuthal forcing, show significant three-dimensional vortex stretching effects when compared to the structures formed during axisymmetric forcing. Breakdown of the large-scale structures into smaller vortices also occurs much earlier during azimuthal forcing. When compared to the upwash formed during axisymmetric forcing, the azimuthally perturbed jet forms an upwash that is less coherent and results in a weaker upload or lift-off force on the aircraft undersurface. Comparison with available experimental data indicates good agreement for the centerline velocity decay, the wall pressure variation and the phase speed of the vortical structures.     

Perturbed vortical layers and shear sheltering

New theoretical results and physical interpretations are presented concerning the interactions between different types of velocity fields that are separated by thin interfacial layers, where there are dynamically significant variations of vorticity across the layers and, in some cases within them. It is shown how, in different types of complex engineering and environmental flow, the strengths of these interactions vary from the weakest kind of superposition to those where they determine the flow structure, for example by mutual exclusion of velocity fields from the other region across the interface, or by local resonance near the interface. We focus here on the excluding kinds of interactions between, on the one hand, elongated and compact regions containing vortical flows and large variations in velocity, and on the other hand various kinds of weak perturbation in the surrounding external flow region: rotational, irrotational; time-varying, steady; large, small; coplanar, non-coplanar; non-diffusive, diffusive. It is shown how all these kinds of external disturbances can be wholly, or partially, ‘blocked’ at the interface with the vortical region, so that beyond a certain sheltering distance into the interior of this region the fluctuations can be very small. For the special case of quasi-parallel co-planar external straining motions outside non-directional shear flows, weak sheltering occurs if the mean velocity of the shear flow increases – otherwise the perturbations are amplified. For non-parallel flows, the sheltering effect can be greater when the vorticity is distributed in thin vortex sheets. The mechanism whereby the vortical flow induces ‘blocking’ and ‘shear-sheltering’ effects can be quantitatively explained in terms of the small adjustments of the vorticity in the vortical layers, and in some cases by the change in impulse of these layers. If the vorticity in the outer part of the vortical region is weak, it can be ‘stripped away’ by the external disturbances until the remaining vorticity is strong enough to ‘block’ the disturbances and shelter the inner flow of the vortical region. The mechanisms presented here appear to explain on the one hand some aspects of the observed robustness of vortical structures and jet or plume like shear flows in turbulent and geophysical flows, and on the other hand the levels of external perturbation needed to erode or breakdown turbulent shear flows.     

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.     

An experimental study of a radial wall jet formed by the normal impingement of a round synthetic jet

The flow field of a radial wall jet created by the impingement of a round synthetic jet normal to a flat surface was characterized using hot-wire anemometry. In the synthetic wall jets the width of the outer layer was observed to increase linearly with the radial distance along the wall, while the local maximum velocity varied inversely. The synthetic wall jet exhibits self-similar behavior as distinguished by the collapse of the mean and rms velocity profiles when normalized by the outer layer scaling variables. Increasing the actuator driving amplitude at a fixed frequency (i) increased the growth rate of the outer layer, and (ii) decreased the decay rate of the local velocity maximum. The flow field of the synthetic wall jet was dominated by vortical structures associated with the actuator driving frequency, and harmonics connected with the interaction of the produced vortex structures. For the actuator conditions investigated, neither the classical laminar nor fully turbulent analytical solutions for continuous wall jets were amenable to modeling the synthetic wall jet profile due to the transitional and unsteady nature of the synthetic wall jet.     

LARGE-SCALE VORTICAL STRUCTURES PRODUCED BY AN IMPINGING DENSITY JET IN SHALLOW CROSSFLOW

The large-scale vortical structures produced by an impinging density jet in shallow crossflow were numerically investigated in detail using RNG turbulence model. The scales, formation mechanism and evolution feature of the upstream wall vortex in relation to stagnation point and the Scarf vortex in near field were analyzed. The computed characteristic scales of the upstream vortex show distinguished three-dimensionality and vary with the velocity ratio and the water depth. The Scarf vortex in the near field plays an important role in the lateral concentration distributions of the impinging jet in crossflow. When the velocity ratio is relatively small, there exists a distinct lateral high concentration aggregation zone at the lateral edge between the bottom layer wall jet and the ambient crossflow, which is dominated by the Scarf vortex in the near field.     

Large-scale vorticity generation by breakers in shallow and deep water

Water wave breaking is of considerable importance in the transfer of momentum, and in other transfers, between the atmosphere and oceans. Typically breaking occurs on deep water as events that have finite duration and finite spatial extent. Near shore lines most of the water motions are dominated by breaking waves. Recent work on the generation of vorticity by breaking waves and bores in the surf zone on beaches is considered and typical vortical structures are briefly discussed. Consideration of deep water breaking leads to the proposal that the end result of a breaking event in deep water may be a coherent structure within the resulting current field. Such a structure is topologically equivalent to half a vortex ring.     

Some features of a turbulent wing–body junction vortical flow

Laser-Doppler velocimeter measurements of a wing/body junction flow field made within a plane to the side of the wing/wall junction and perpendicular both to a 3:2 elliptical nose—NACA 0020 tail wing, and a flat wall are presented. Reynolds number of the approach boundary layer was, Re_θ = 5940, and free-stream air velocity was, U_ref = 27.5 m/s. A large vortical structure residing in the outer region redirects the low-turbulence free-stream flow to the vicinity of the wing/wall junction, resulting in thin boundary layers with velocity magnitudes higher than free-stream flow. Lateral pressure gradients result in a three-dimensional separation on the uplifting side of the vortex. Additionally, a high vorticity vortical structure with opposite sense to the outer-layer vortex forms beneath the outer-layer vortex. Normal and shear stresses increase to attain values an order of magnitude larger compared to values measured in a three-dimensional boundary layer just outside the junction vortex. Bimodal histograms of the w fluctuating velocity occur under the outer-layer vortex near the wall due to the time-dependent nature of the horseshoe vortex. In such a flow the shear-stress angle (SSA) highly lags the flow-gradient angle (FGA), and the turbulence diffusion is highly altered due to presence of vortical structures.     

Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study

Wakes behind heated cylinders, circular, and square have been experimentally investigated at low-Reynolds numbers. The electrically heated cylinder is mounted in a vertical airflow facility such that buoyancy aids the inertia of main flow. The operating parameters, i.e., Reynolds number and Richardson number are varied to examine flow behavior over a range of experimental conditions from forced to mixed convection regime. Laser schlieren-interferometry has been used for visualization and analysis of flow structures. Complete vortex shedding sequence has been recorded using a high-speed camera. The results on detailed dynamical characteristics of vortical structures, i.e., their size, shape and phase, Strouhal number, power spectra, convection velocity, phase shift, vortex inception length, and fluctuations are reported. On heating, alteration of organized (coherent) structures with respect to shape, size and their movement is readily perceived from instantaneous Schlieren images before they reduce to a steady plume. For both cylinders, Strouhal number shows a slow increase with an increase in Richardson number. At a critical value, there is complete disappearance of vortex shedding and a drop in Strouhal number to zero. The corresponding spectra evolve from being highly peaked at the vortex shedding frequency to a broadband appearance when vortex shedding is suppressed. The geometry of vortex structures transforms to a slender shape before shedding is suppressed. At this heating level, absence of multiple peaks in power spectra at cylinder centerline indicates absence of interaction between opposite shear layers. The convection velocity of vortices increases in stream wise direction to an asymptotic value and its variation is a function of Richardson number. The convection speed abruptly falls to zero at critical Richardson number. The phase difference of shed vortices between upstream and downstream location increases with an increase in Richardson number. Velocity profiles show an increase in fluid speed and beyond the critical point, buoyancy forces add enough momentum to cancel momentum deficit due to the cylinder. Overall, the combined effect of temperature gradient on the separating shear layer velocity profile in near field and vortical structures interaction in far field influences wake instability of a heated cylinder. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Impingement of a low Reynolds number turbulent circular jet onto a flat plate at normal incidence

The velocity field of a circular water jet impinging onto a flat plate has been measured using particle image velocimetry, or PIV. The velocity field has been recorded at several instants in time, producing thousands of simultaneous two-dimensional velocity measurements for each realization. The instantaneous velocity, vorticity and rate-of-strain fields reveal the interaction of vortices near the impinging wall within the radial wall jet downstream from the stagnation point. An ensemble average of the instantaneous fields produces a mean velocity field of the jet flow, which reveals many of the processes leading to boundary layer separation and vortex breakaway within the wall jet. The PIV system extracts the velocity measurements using a two-dimensional autocorrelation method, and can obtain thousands of highly accurate velocity measurements within a few minutes. The structure found in these experiments may be similar to the ground level structure of atmospheric microburst phenomena.A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, 17–19 October 1988     

A three‐dimensional vortex particle‐in‐cell method for vortex motions in the vicinity of a wall

A new vortex particle‐in‐cell method for the simulation of three‐dimensional unsteady incompressible viscous flow is presented. The projection of the vortex strengths onto the mesh is based on volume interpolation. The convection of vorticity is treated as a Lagrangian move operation but one where the velocity of each particle is interpolated from an Eulerian mesh solution of velocity–Poisson equations. The change in vorticity due to diffusion is also computed on the Eulerian mesh and projected back to the particles. Where diffusive fluxes cause vorticity to enter a cell not already containing any particles new particles are created. The surface vorticity and the cancellation of tangential velocity at the plate are related by the Neumann conditions. The basic framework for implementation of the procedure is also introduced where the solution update comprises a sequence of two fractional steps. The method is applied to a problem where an unsteady boundary layer develops under the impact of a vortex ring and comparison is made with the experimental and numerical literature. Copyright © 2001 John Wiley & Sons, Ltd.     

Discretization of the vorticity field of a planar jet

In data assimilation, information from sensors is used to correct the state variables of a numerical model. This has been used to great advantage by the weather prediction community in the context of direct numerical simulation (DNS) models, but has seen comparatively little use in point-vortex models. This is due in large part to data-processing issues. In order to keep up with the speeds necessary for effective data assimilation, one must extract and discretize the vortex structures from velocity field data in a computationally efficient fashion—i.e., using as few discrete vortices as possible to model the measured flow. This paper describes a new strategy for accomplishing this and evaluates the results using data from a laboratory-scale vortex-dominated planar jet. Large-scale vortex structures are found using a family of variants on traditional vortex extraction methods. By augmenting these methods with simple computational topology techniques, one obtains a new method that finds the boundaries of the coherent structures in a manner that naturally follows the geometry of the flow. This strategy was evaluated in the context of two standard vortex extraction methods, vorticity thresholding and Okubo–Weiss, and tested upon velocity field data from the experimental fluid flow. The large-scale structures found in this manner were then modeled with collections of discrete vortices, and the effects of the grain size of the discretization and the parameters of the discrete vortex model were studied. The results were evaluated by comparing the instantaneous velocity field induced by the discrete vortices to that measured in the jet. These comparisons showed that the two extraction techniques were comparable in terms of sensitivity and error, suggesting that the computationally simpler vorticity thresholding method is more appropriate for applications where speed is an issue, like data assimilation. Comparisons of different discretization strategies showed that modeling each large-scale vortex structure with a single discrete vortex provided the best compromise between mean-squared error and computational effort. These results are of potential interest in any situation where one must balance accuracy and expense while extracting vortices from a snapshot of a flow field; data assimilation is only one example.     

Turbulent structure during transition to self-similarity in a round jet

 The developing turbulent region of a round jet was investigated using an improved implementation of digital particle image velocimetry (DPIV). The two-dimensional flow field in planes normal and parallel to the axial velocity was measured at locations between 15 and 30 diameters downstream, for two Reynolds numbers of 5500 and 16,000. The study consisted of instantaneous snapshots of the velocity and vorticity fields as well as measurements of velocity correlations up to third order. In this regime, the Reynolds number had a significant effect on both the instantaneous flow structure and the profiles of mean velocity across the jet. Coherent streamwise structures were present in the jet core for the lower Reynolds number. Additional structures whose evolution was governed by time scales two orders of magnitude larger than the convective scale inside the jet were observed in the entrainment field. The velocity correlations provided further support for the validity of DPIV turbulence measurements. The data was consistent with the equations of motion and momentum was conserved. DPIV measurements of turbulent kinetic energy components agreed with the hot-wire measurements of previous studies. Received: 27 November 1996/Accepted: 14 July 1997     

Wavelet multi-scale analysis of the circular cylinder wake under synthetic jets control

The wavelet method is used to study the multi-scale vortical structures of the flow around a circular cylinder without and with synthetic jet control at Re = 950. The velocity field is decomposed into 9 wavelet components, including one approximation component and 8 detail components. The first component shows the flow characteristics at low frequency. The dominant components represent large-scale vortical structures in the flow and they show similar distributions for the same wake pattern. Other detail components reflect the characteristics of relatively small-scale structures. The individual vortex dynamics underlying the complex flow can be extracted and thus reconstructed by the approximation and dominant components. Thus, we show an effective approach to reveal the flow physics from the complex flow.     

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.