Role of Vorticity in Generation of Pressure Sources and its Implication for Maintenance of Turbulence

The Poisson equation for pressure, together with the evolutions equations for the velocity gradients, reveals the role of vorticity in generation of pressure sources. Specifically, it was shown how a pressure field created by a local source, acting on nearby vorticity, would create new pressure sources. It was further established that a moving pressure field, which moves with the velocity of its source, but extends well beyond the source location, could lead to generation of fast and slow streaks as wells as contribute to formation of flow structures in the wall region. These processes, which are part of central mechanisms of maintenance of turbulence, suggest that turbulence could be self-sustaining only if the perturbation pressure force could overcome the diffusion effects; the value of friction Reynolds number reflects the balance between the two.     

An experimental study of a turbulent wing-body junction and wake flow

Extensive measurements were conducted in an incompressible turbulent flow around the wing-body junction formed by a 3∶2 semi-elliptic nose/NACA 0020 tail section and a flat plate. Mean and fluctuating velocity measurements were performed adjacent to the wing and up to 11.56 chord lengths downstream. The appendage far wake region was subjected to an adverse pressure gradient. The authors' results show that the characteristic horseshoe vortex flow structure is elliptically shaped, with ? (W)/?Y forming the primary component of the streamwise vorticity. The streamwise development of the flow distortions and vorticity distributions is highly dependent on the geometry-induced pressure gradients and resulting flow skewing directions. The primary goal of this research was to determine the effects of the approach boundary layer characteristics on the junction flow. To accomplish this goal, the authors' results were compared to several other junction flow data sets obtained using the same body shape. The trailing vortex leg flow structure was found to scale on T. A parameter known as the momentum deficit factor (MDF = (Re _T)² (θ/T)) was found to correlate the observed trends in mean flow distortion magnitudes and vorticity distribution. Changes in δ/T were seen to affect the distribution of u′, with lower ratios producing well defined local turbulence maxima. Increased thinning of the boundary layer near the appendage was also observed for small values of δ/T.     

Boundary Vorticity Dynamics Since Lighthill's 1963 Article: Review and Development

In his well-known 1963 article: “Introduction. Boundary Layer Theory,” Lighthill explained for the first time how to describe quantitatively the vorticity creation rate from a solid surface and how this creation rate is dominated by the tangent pressure gradient. This was the first cornerstone of boundary vorticity dynamics, which has now been developed to a complete theory on the vorticity creation from solid or fluid boundaries and the reaction of the created vorticity to the boundaries. In this paper we present a general formulation of boundary vorticity dynamics, briefly review the theoretical progress for Newtonian fluid since 1963, examine the effect of variable viscosity and turbulence on the vorticity creation, and, of many applications, exemplify the use of the theory in aerodynamic diagnosis and optimization. Received 14 November 1996 and accepted 14 March 1997     

Effect of Roughness on Wall-Bounded Turbulence

Direct numerical simulation of turbulent incompressible plane-channel flow between a smooth wall and one covered with regular three-dimensional roughness elements is performed. While the impact of roughness on the mean-velocity profile of turbulent wall layers is well understood, at least qualitatively, the manner in which other features are affected, especially in the outer layer, has been more controversial. We compare results from the smooth- and rough-wall sides of the channel for three different roughness heights of h ⁺= 5.4, 10.8, and 21.6 for Re _τ of 400, to isolate the effects of the roughness on turbulent statistics and the instantaneous turbulence structure at large and small scales. We focus on the interaction between the near-wall and outer-layer regions, in particular the extent to which the near-wall behavior influences the flow further away from the surface. Roughness tends to increase the intensity of the velocity and vorticity fluctuations in the inner layer. In the outer layer, although the roughness alters the velocity fluctuations, the vorticity fluctuations are relatively unaffected. The higher-order moments and the energy budgets demonstrate significant differences between the smooth-wall and rough-wall sides in the processes associated with the wall-normal fluxes of the Reynolds shear stresses and turbulence kinetic energy. The length scales and flow dynamics in the roughness sublayer, the spatially inhomogeneous layer within which the flow is directly influenced by the individual roughness elements, are also examined. Alternative mechanisms involved in producing and maintaining near-wall turbulence in rough-wall boundary layers are also considered. We find that the strength of the inner/outer-layer interactions are greatly affected by the size of the roughness elements.     

Lateral Spreading Mechanism of a Turbulent Spot and a Turbulent Wedge

We examine the spreading of turbulent spots and wedges into a surrounding laminar Blasius boundary layer. The spreading is not due to the lateral propagation of turbulent eddies but rather to a developing disturbance in the surrounding spanwise vorticity of the laminar boundary layer. We concentrate on the mechanisms for generating streamwise vorticity. In particular, inclined generally streamwise vortex tubes along the spot/wedge boundary tilt mean shear vortex lines either up or down. These lines subsequently tend to either lag back or lead forward. As the leading or lagging vortex lines continue to wrap around and reinforce the causative inclined tube, the lines arch up or down. The outboard portion of the resulting arch must acquire a vertical, ω_y, component of vorticity which induces the rollup of a new inclined tube now outboard of the first. Close to the wall the arching mechanism is inhibited by the no through flow boundary condition while far from the wall the process is inhibited by the lack of sufficient mean spanwise vorticity.     

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     

On the Flame-generated Vorticity Dynamics of Bluff-body-stabilized Premixed Flames

This investigation considers the dynamics of flame-generated vorticity for a premixed, submerged bluff-body stabilized flame. Experimentation characterizes the far-field region in particular with a level of detail not previously afforded to this type of flow. Simultaneous particle imaging velocimetry (PIV), Mie scattering and CH ^? chemiluminescence are used to obtain velocity fields and flame location. Mean static pressure measurements at the combustion chamber wall capture the pressure field. Analysis of the flame fronts in relation to the mean velocity and vorticity fields provides useful insight into the interaction of the flame and the flow. The unique nature of the velocity and vorticity fields and their effect on downstream flame structures are explained by the baroclinic torque generation of vorticity. The coupling that exists among pressure, heat release, and baroclinic generation is acknowledged and will influence strategies for control of the baroclinic mechanism.     

A parametric study of adverse pressure gradient turbulent boundary layers

There are many open questions regarding the behaviour of turbulent boundary layers subjected to pressure gradients and this is confounded by the large parameter space that may affect these flows. While there have been many valuable investigations conducted within this parameter space, there are still insufficient data to attempt to reduce this parameter space. Here, we consider a parametric study of adverse pressure gradient turbulent boundary layers where we restrict our attention to the pressure gradient parameter, β, the Reynolds number and the acceleration parameter, K. The statistics analyzed are limited to the streamwise fluctuating velocity. The data show that the mean velocity profile in strong pressure gradient boundary layers does not conform to the classical logarithmic law. Moreover, there appears to be no measurable logarithmic region in these cases. It is also found that the large-scale motions scaling with outer variables are energised by the pressure gradient. These increasingly strong large-scale motions are found to be the dominant contributor to the increase in turbulence intensity (scaled with friction velocity) with increasing pressure gradient across the boundary layer.     

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.     

Finite volume solution of the Navier–Stokes equations in velocity–vorticity formulation

For the incompressible Navier–Stokes equations, vorticity‐based formulations have many attractive features over primitive‐variable velocity–pressure formulations. However, some features interfere with the use of the numerical methods based on the vorticity formulations, one of them being the lack of a boundary conditions on vorticity. In this paper, a novel approach is presented to solve the velocity–vorticity integro‐differential formulations. The general numerical method is based on standard finite volume scheme. The velocities needed at the vertexes of each control volume are calculated by a so‐called generalized Biot–Savart formula combined with a fast summation algorithm, which makes the velocity boundary conditions implicitly satisfied by maintaining the kinematic compatibility of the velocity and vorticity fields. The well‐known fractional step approaches are used to solve the vorticity transport equation. The paper describes in detail how we accurately impose no normal‐flow and no tangential‐flow boundary conditions. We impose a no‐flux boundary condition on solid objects by the introduction of a proper amount of vorticity at wall. The diffusion term in the transport equation is treated implicitly using a conservative finite update. The diffusive fluxes of vorticity into flow domain from solid boundaries are determined by an iterative process in order to satisfy the no tangential‐flow boundary condition. As application examples, the impulsively started flows through a flat plate and a circular cylinder are computed using the method. The present results are compared with the analytical solution and other numerical results and show good agreement. Copyright © 2005 John Wiley & Sons, Ltd.     

The influence of boundary layers on supersonic inlet flow unstart induced by mass injection

A transverse jet is injected into a supersonic model inlet flow to induce unstart. Planar laser Rayleigh scattering from condensed CO₂ particles is used to visualize flow dynamics during the unstart process, while in some cases, wall pressure traces are simultaneously recorded. Studies conducted over a range of inlet configurations reveal that the presence of turbulent wall boundary layers strongly affect the unstart dynamics. It is found that relatively thick turbulent boundary layers in asymmetric wall boundary layer conditions prompt the formation of unstart shocks; in symmetric boundary conditions lead to the propagation of pseudo-shocks; and in both cases facilitate fast inlet unstart, when compared with thin, laminar boundary layers. Incident shockwaves and associated reflections are found to affect the speed of pressure disturbances. These disturbances, which induce boundary layer separation, are found to precede the formation of unstart shocks. The results confirm the importance of and need to better understand shock-boundary layer interactions in inlet unstart dynamics.     

Separated flow structures around a cylindrical obstacle in a narrow channel

A detailed experimental study is performed on the separated flow structures around a low aspect-ratio circular cylinder (pin-fin) in a practical configuration of liquid cooling channel. Distinctive features of the present arrangement are the confinement of the cylinder at both ends, water flow at low Reynolds numbers (Re = 800, 1800, 2800), very high core flow turbulence and undeveloped boundary layers at the position of the obstacle. The horseshoe vortex system at the junctions between the cylinder and the confining walls and the near wake region behind the obstacle are deeply investigated by means of Particle Image Velocimetry (PIV). Upstream of the cylinder, the horseshoe vortex system turns out to be perturbed by vorticity bursts from the incoming boundary layers, leading to aperiodical vortex oscillations at Re = 800 or to break-away and secondary vorticity eruptions at the higher Reynolds numbers. The flow structures in the near wake show a complex three-dimensional behaviour associated with a peculiar mechanism of spanwise mass transport. High levels of free-stream turbulence trigger an early instabilization of the shear layers and strong Bloor–Gerrard vortices are observed even at Re = 800. Coalescence of these vortices and intense spanwise flow inhibit the alternate primary vortex shedding for time periods whose length and frequency increase as the Reynolds number is reduced. The inhibition of alternate vortex shedding for long time periods is finally related to the very large wake characteristic lengths and to the low velocity fluctuations observed especially at the lowest Reynolds number.     

Application of the method of near-wall boundary conditions to an investigation of turbulent flows with longitudinal pressure gradients

The dynamic and thermal characteristics of steady near-wall boundary layers in flow deceleration regions are studied on the basis of differential turbulencemodels. The method of transferring the boundary conditions from the wall into the flow is tested for flows with variable longitudinal pressure gradients. Using differential turbulence models in the transition and low-Reynolds-number regions near surfaces the effect of the parameters of highly turbulent free stream on the development of dynamic processes in the developed turbulent boundary layer in the flow deceleration region is studied. The calculated profiles of the velocity, the kinetic energy of turbulence, the friction and thermal conductivity coefficients, and the temperature factor are compared with the experimental data in the cases in which the boundary conditions are preassigned both on the wall and in the flow. The effect of an intermediate boundary condition on the results of the calculations is analyzed.     

Curved shock theory

Curved shock theory (CST) is introduced, developed and applied to relate pressure gradients, streamline curvatures, vorticity and shock curvatures in flows with planar or axial symmetry. Explicit expressions are given, in an influence coefficient format, that relate post-shock pressure gradient, streamline curvature and vorticity to pre-shock gradients and shock curvature in steady flow. The effect of pre-shock flow divergence/convergence, on vorticity generation, is related to the transverse shock curvature. A novel derivation for the post-shock vorticity is presented that includes the effects of pre-shock flow non-uniformities. CST applicability to unsteady flows is discussed.     

Correlations for modeling transitional boundary layers under influences of freestream turbulence and pressure gradient

This paper presents mathematical expressions for two significant parameters which control the onset location and length of transition in the γ–Re_θ transition model of Menter et al. [Menter, F.R., Langtry, R.B., Volker, S., Huang, P.G., 2005. Transition modelling for general purpose CFD codes. In: ERCOFTAC International Symposium on Engineering Turbulence Modelling and Measurements]. The expressions are formulated and calibrated by means of numerical experiments for predicting transitional boundary layers under the influences of freestream turbulence and pressure gradient. It was also found that the correlation for transition momentum thickness Reynolds number needs only to be expressed in terms of local turbulence intensity, so that the more complex form that includes pressure gradient effects is unnecessary. Transitional boundary layers on a flat plate both with and without pressure gradients are employed to assess the performance of these two expressions for predicting the transition. The results show that the proposed expressions can work well with the model of Menter et al. (2005).     

A potential-flow,deformable-body model for fluid–structure interactions with compact vorticity: application to animal swimming measurements

This paper presents an approach to quantify the unsteady fluid forces, moments and mass transport generated by swimming animals, based on measurements of the surrounding flow field. These goals are accomplished within a framework that is independent of the vorticity field, making it unnecessary to directly resolve boundary layers on the animal, body–vortex interactions, or interactions among vortex lines in the wake. Instead, the method identifies Lagrangian coherent structures in the flow, whose dynamics in flows with compact vorticity are shown to be well approximated by potential flow concepts, especially the Kirchhoff and deformation potentials from deformable body theory. Examples of the application of these methods are given for pectoral fin locomotion of the bluegill sunfish and undulatory swimming of jellyfish, and the methods are validated by analysis of a canonical starting vortex ring flow. The transition to a Lagrangian approach toward animal swimming measurements suggests the possibility of implementing recently developed particle tracking (vis-à-vis DPIV) techniques for fully three-dimensional measurements of animal swimming.     

Vortex shedding flow behind a slowly rotating circular cylinder

This paper investigates flow past a rotating circular cylinder at 3600?Re?5000 and α?2.5. The flow parameter α is the circumferential speed at the cylinder surface normalized by the free-stream velocity of the uniform cross-flow. With particle image velocimetry (PIV), vortex shedding from the cylinder is clearly observed at α<1.9. The vortex pattern is very similar to the vortex street behind a stationary circular cylinder; but with increasing cylinder rotation speed, the wake is observed to become increasing narrower and deflected sideways. Properties of large-scale vortices developed from the shear layers and shed into the wake are investigated with the vorticity field derived from the PIV data. The vortex formation length is found to decrease with increasing α. This leads to a slow increase in vortex shedding frequency with α. At α=0.65, vortex shedding is found to synchronize with cylinder rotation, with one vortex being shed every rotation cycle of the cylinder. Vortex dynamics are studied at this value of α with the phase-locked eduction technique. It is found that although the shear layers at two different sides of the cylinder possess unequal vorticity levels, alternating vortices subsequently shed from the cylinder to join the two trains of vortices in the vortex street pattern exhibit very little difference in vortex strength.     

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The experiments were conducted at a Reynolds number, based on the stack external diameter, of Re_D=2.3×10⁴. The stack, of aspect ratio AR=9, was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer, where the ratio of the boundary layer thickness to the stack height was δ/H≈0.5. The jet-to-cross-flow velocity ratio was varied from R=0 to 3, which covered the downwash, crosswind-dominated and jet-dominated flow regimes. In the downwash and crosswind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip vortex pair located close to the free end of the stack, and the base vortex pair located close to the ground plane within the flat-plate boundary layer, were similar to those found in the wake of a finite circular cylinder, and were associated with the upwash and downwash flow fields within the stack wake, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair had the same orientation as the base vortex pair and was associated with the jet rise. The peak vorticity and strength of the streamwise vortex structures were functions of the jet-to-cross-flow velocity ratio. For the tip vortex structures, their peak vorticity and strength reduced as the jet-to-cross-flow velocity ratio increased.