Vorticity Production Research Articles

Flow transition behind a heated cylinder

For more than a century the wake flow behind a cylinder has been the subject of many investigations. Most attention has been focussed on the first instability and the transition towards 3D for the flow around an unheated cylinder. The wake stability for a heated cylinder has until now received very little attention compared to the forced convection case. After a review of the literature on the wake flow behind an unheated and heated cylinder, in this paper the 2D wake behaviour and the 3D flow transition behind a heated cylinder are described. In the analysis performed, the Reynolds number is set around Re D=100 and the Richardson number is varied between Ri D=0 (forced convection case) and Ri D=1.5 (mixed convection case). From the results it is seen that for a relatively small heat input ( Ri D<1) the vortex street undergoes a negative deflection, i.e. downwards, caused by a strength difference between the upper and lower vortices which, in turn, is induced by baroclinic vorticity production. This strength difference also results in a rotational drift of the lower vortex around the upper vortex. For a higher heat input ( Ri D>1) an early 3D transition is observed. Mushroom-type structures appear on top of the upper vortex row. This flow transition is initiated by the occurrence of 3D flow structures at the rear end of the cylinder.

Vorticity production in shock diffraction

The production of vorticity or circulation production in shock wave diffraction over sharp convex corners has been numerically simulated and quantified. The corner angle is varied from 5° to 180°. Total vorticity is represented by the circulation, which is evaluated by integrating the velocity along a path enclosing the perturbed region behind a diffracting shock wave. The increase of circulation in unit time, or the rate of circulation production, depends on the shock strength and wall angle if the effects of viscosity and heat conductivity are neglected. The rate of vorticity production is determined by using a solution-adaptive code, which solves the Euler equations. It is shown that the rate of vorticity production is independent of the computational mesh and numerical scheme by comparing solutions from two different codes. It is found that larger wall angles always enhance the vorticity production. The vorticity production increases sharply when the corner angle is varied from 15° to 45°. However, for corner angles over 90°, the rate of vorticity production hardly increases and reaches to a constant value. Strong shock waves produce vorticity faster in general, except when the slipstream originating from the shallow corner attaches to the downstream wall. It is found that the vorticity produced by the slipstream represents a large proportion of the total vorticity. The slipstream is therefore a more important source of vorticity than baroclinic effects in shock diffraction.

Vorticity production and turbulent cooling of “hot channels” in gases: Three dimensions versus two dimensions

Hot channels (HCs), created in a gas by a rapid energy release in the quasi-cylindric geometry, cool anomalously fast by turbulent flow. Picone and Boris [Phys. Fluids 26, 365 (1983)] suggested that turbulent mixing results from the vorticity generation by the baroclinic mechanism during the early, shock-wave dominated stage of the dynamics. This scenario was confirmed, with important modifications, in a recent series of two-dimensional (2D) hydrodynamic simulations. This work reports three-dimensional (3D) hydrodynamic simulations of the HC evolution, and compares the results with those of 2D simulations. Assuming a small perturbation of the cylindric shape of the energy release region, we followed a typical HC up to 200 acoustic times. The simulations capture well the phenomenology of the HC cooling. The details of vorticity production, that results in a fast mixing of the cold ambient gas into the HC, are clearly identified. The cooling process can be interpreted as turbulent diffusion. The empiric diffusion coefficient and cooling time agree with experiment. The late-time morphology of the HC and the empiric turbulent diffusion coefficient are dimension-dependent, the 3D cooling being faster than 2D cooling.

Simulations of Topographically Forced Mesocyclones in the Weddell Sea and the Ross Sea Region of Antarctica

Abstract Mesocyclones (MCs) are a frequently observed phenomenon in the coastal regions of Antarctica. Numerical simulations of topographically forced MCs in the Weddell Sea and the Ross Sea region are presented using a three-dimensional mesoscale weather forecast model. Simulations are performed for an idealized case without synoptic forcing, three realistic cases of smaller MCs with diameters of 200–300 km, and two larger systems with diameters of up to 1000 km. The simulation results show that the orography of the coastal regions can play an important role in mesocyclogenesis. One key factor is the katabatic wind system, which is able to initiate low-level MCs in areas of suitable orography structure. The second key factor is the support of the synoptic environment, leading to vorticity production by vertical stretching of the synoptically supported katabatic winds. Besides this stretching mechanism, katabatic winds can have a second impact on the generation of MCs by transporting cold air into the coa...

Shock-Vortex Interactions at High Mach Numbers

We perform a computational study of the interaction of a planar shock wave with a cylindrical vortex. We use a particularly robust High Resolution Shock Capturing scheme, Marquina's scheme, to obtain high quality, high resolution numerical simulations of the interaction. In the case of a very-strong shock/vortex encounter, we observe a severe reorganization of the flow field in the downstream region, which seems to be due mainly to the strength of the shock. The numerical data is analyzed to study the driving mechanisms for the production of vorticity in the interaction.

Particle image velocimetry measurements of a backward-facing step flow

Particle image velocimetry (PIV) measurements were carried out on a backward-facing step flow at a Reynolds number of Reh=U∞h/ν=4,660 (based on step height and freestream velocity). In-plane velocity, out-of-plane vorticity, Reynolds stress and turbulent kinetic energy production measurements in the x–y and x–z planes of the flow are presented. Proper orthogonal decomposition was performed on both the fluctuating velocity and vorticity fields of the x–y plane PIV data using the method of snapshots. Low-order representations of the instantaneous velocity fields were reconstructed using the velocity modes. These reconstructions provided insight into the contribution that the various length scales make to the spatial distribution of mean and turbulent flow quantities such as Reynolds stress and turbulent kinetic energy production. Large scales are found to contribute to the Reynolds stresses and turbulent kinetic energy production downstream of reattachment, while small scales contribute to the intense Reynolds stresses in the vicinity of reattachment.

Interaction of Decaying Freestream Turbulence with a Moving Shock Wave: Pressure Field

Theunsteady interaction of a moving shock wavewith nearly homogeneousand isotropic decaying compressible turbulence has been studied experimentally in a large-scale shock-tube facility by using rectangular grids of various sizes. The interaction has been investigated by measuring velocity, total pressure, and temperature inside thee owe eldandstaticpressureatthewalloftheshocktubewithinstrumentationoftemporalandspatialresolution. Attenuation of theshock wavestrength has been found to take placeas a result oftheinteraction with theturbulent e owe eld, which depends on the mesh size of the grid or its Reynolds number, the e ow Mach number, and the initial Mach number of the shock wave. Finer grids produce turbulence, which attenuates the shock wave more than coarse grids at the same Mach number. Amplie cation of pressure e uctuations after the interaction has been observed in all experiments, depending on grid size (initial turbulencelevel )and shock strength. Furthermore, this amplie cation is not the same through the whole range of wave numbers resolved. I. Introduction T RAVELINGshockwavesorexpansionwavescanbegenerated inside turbines or compressors of turbine engines as a result of unsteady e ow phenomena. These moving waves can interact with rotating or stationary blades, as well as with the e ow, and may result in phenomena that can affect the operation and performance of the engine. One of these phenomena is the interaction of passing shock waves with turbulence. Of particular interest to those studying turbomachinery is the interaction of traveling shock waves with freestream turbulence, which can be considered as nearly isotropic and nearly homogeneous. In general, interactions of shock waves with turbulent e ows are of great practical importance in external or internal aerodynamics of engineering applications because they considerably modify the e uid e eld by vorticity and entropy production and transport. PastworkthathasbeenrecentlyreviewedbyAndreopoulosetal. 1 hasshownthattheinteractionbetweentheshockwaveandturbulent e ow is mutual and that the coupling between them is very strong. Complex linear and nonlinear mechanisms are involved that can cause considerable changes in the structure of turbulence and its statistical properties and alter the dynamics of the shock wave motion. Amplie cation of velocity e uctuations and substantial changes in length scales are the most important outcomes of interactions of shock waves with turbulence. This indicates that such interactions may greatly affect mixing. The use of shock waves, for instance, has been proposed by Budzinski et al. 2 as means to enhance mixing

Direct numerical simulations of two-phase laminar jet flows with different cross-section injection geometries

Direct numerical simulations are performed of spatial, three-dimensional, laminar jets of different inlet geometric configurations for the purpose of quantifying the characteristics of the flows; both single-phase (SP) and two-phase (TP) free jets are considered. The TP jets consist of gas laden with liquid drops randomly injected at the inlet. Drop evaporation ensues both due to the gaseous flow being initially unvitiated by the vapor species corresponding to the liquid drops, and to drop heating as the initial drop temperature is lower than that of the carrier gas. The conservation equations for the TP flow include complete couplings of mass, momentum, and energy based on thermodynamically self-consistent specification of the vapor enthalpy, internal energy, and latent heat of vaporization. Inlet geometries investigated are circular, elliptic, rectangular, square, and triangular. The results focus both on the different spreading achieved according to the inlet geometry, as well as on the considerable change in the flow field due to the presence of the drops. The most important consequence of the drop interaction with the flow is the production of streamwise vorticity that alters entrainment and species mixing according to the inlet geometry. Similar to their SP equivalent, TP jets are shown to reach steady-state entrainment; examination of the flows at this time station shows that the potential cores of TP jets are shorter by an order of magnitude than their SP counterpart. Moreover, whereas the TP circular jet exhibits a symmetric entrainment pattern well past the streamwise location of the potential core, noncircular jets display at the same location strong departures from symmetry. Furthermore, the SP-jet phenomenon of axis switching is no longer present in TP jets. The distributions of drop-number density, liquid mass, and evaporated species are compared for different inlet cross sections and recommendations are made regarding the optimal choice for different applications.

Early Evolution of Vertical Vorticity in a Numerically Simulated Idealized Convective Line

The generation and organization of mesoscale convective vortices (MCVs) is a recurring theme in midlatitude and tropical meteorology during the warm season. In this work a simulation of a finite-length idealized convective line in a westerly shear environment is investigated in the absence of ambient vertical vorticity. An asymmetry in average vertical vorticity forms rapidly at early times in the present simulation. This study focuses on the formation and organization of vertical vorticity at these early simulation times. Previous simulations suggest that tilting of either ambient or storm-generated horizontal vorticity is the primary mechanism responsible for the formation, organization, and maintenance of MCVs. This study confirms recent work regarding the generation of vertical vorticity at early times in the simulation. A Lagrangian budget analysis of the vertical vorticity equation, however, shows that vorticity convergence becomes a comparable, and at times dominant, mechanism for the enhancement and long-term organization of vertical vorticity early in the simulation. Despite differences in the initial ambient horizontal vorticity, hodograph, and convective available potential energy, the Lagrangian budget analysis in the present midlatitude case is consistent with the Lagrangian budget results of a previous tropical squall line simulation. The study of idealized convective lines in midlatitude environmental conditions therefore provide valuable insight into understanding vertical vorticity production in tropical squall lines and their potential relevance to tropical cyclogenesis.

Control of the viscous sublayer for drag reduction

We investigate the possibility of manipulating turbulence structures in the viscous sublayer for the purpose of drag reduction using a direct numerical simulation of a turbulent channel flow. Recognizing that a great portion of production of vorticity occurs in the viscous sublayer, a body force is used to suppress spanwise velocity in the sublayer, and a significant amount of drag reduction is obtained. A more realistic body force or wall movement in the spanwise direction using instantaneous wall-shear stress in a closed-loop control is shown to reduce drag as much as 35%. Implementation of such a body force using an electromagnetic force is also discussed.

Lee-Vortex Formation in Free-Slip Stratified Flow over Ridges. Part II: Mechanisms of Vorticity and PV Production in Nonlinear Viscous Wakes

The formation of orographic wakes and vortices is studied within the context of numerically simulated viscous flow with uniform basic-state wind and stability past elongated free-slip ridges. The viscosity and thermal diffusivity are sufficiently large that the onset of small-scale turbulence is suppressed. It is found in Part I of this study that wake formation in the viscous flow is closely tied to the dynamics of a low-level hydraulic-jump-like feature in the lee of the obstacle. Here the role of the hydraulic jump in producing the vorticity and potential vorticity (PV) of the viscous wake is considered. A method for diagnosing vorticity production is developed based on a propagator analysis of the Lagrangian vorticity equation that generalizes Cauchy's formula for the evolution of vorticity in a Lagrangian framework. Application of the method reveals that the vertical vorticity of the wake originates through baroclinic generation and tilting in the mountain wave upstream of the jump. However, upstream of the jump the vertical vorticity is relatively weak. Vertical stretching in the jump then amplifies this vorticity significantly to produce the pronounced vertical vorticity anomalies along the shear lines at the lateral edges of the wake. The PV of the wake is found to result mainly from thermal dissipation in the jump. In particular, thermal diffusion tends to diabatically modify the potential temperature field in the jump so as to create PV from the vertical vorticity already present. From the standpoint of PV conservation, the presence of both diabatic cooling (by thermal diffusion) and vertical vorticity at the base of the jump produces a vertical flux of PV through the lower boundary. The advective fluxes of PV along each side of the wake are then primarily balanced at steady state by fluxes of PV through the obstacle surface.

Nonlinear equation for curved stationary flames

A nonlinear equation describing curved stationary flames with arbitrary gas expansion, θ=ρfuel/ρburnt, subject to the Landau–Darrieus instability, is obtained in a closed form without an assumption of weak nonlinearity. It is proved that in the scope of the asymptotic expansion for θ→1, the new equation gives the true solution to the problem of stationary flame propagation with the accuracy of the sixth order in θ−1. In particular, it reproduces the stationary version of the well-known Sivashinsky equation at the second order corresponding to the approximation of zero vorticity production. At higher orders, the new equation describes influence of the vorticity drift behind the flame front on the flame velocity and the flame front structure. Its asymptotic expansion is carried out explicitly, and the resulting equation is solved analytically at the third order. For arbitrary values of θ, the highly nonlinear regime of fast flow burning is investigated, for which case a large flame velocity expansion of the nonlinear equation is proposed.

Effect of vorticity production on the structure and velocity of curved flames.

A nonlinear equation describing curved stationary flames with arbitrary gas expansion theta = rho(fuel)/rho(burnt) is obtained in a closed form without an assumption of weak nonlinearity. The equation respects all conservation laws and takes into account vorticity production in the flame. In the scope of the asymptotic expansion for theta -->1, the new equation solves the problem of stationary flame propagation with accuracy of the sixth order in theta - 1. Its analytical solutions give the flame velocity in tubes of arbitrary width, which agrees with available results of direct numerical modeling.

Shock bowing and vorticity dynamics during propagation into different transverse density profiles

A 2D numerical investigation is presented of shock wave propagation into a gas whose density is modulated in the transverse direction across the width of a shock tube. These density modulations represent temperature distributions in which low density corresponds to high temperature gas and high density corresponds to low temperature gas. This work is motivated by recent shock-plasma experiments, and mechanisms to explain the experimentally observed shock “splitting” signatures are investigated. It is found that the shock splitting signatures are more pronounced when the shock wave is more strongly curved or bowed. This occurs as the depth of the initial density profile is increased. The gross features of the shock splitting signatures are relatively insensitive to variations in the shape of the initial density profile (into which the shock propagates). Several interesting features of vorticity production and evolution are also indicated.

Direct numerical simulation of the interaction between a shock wave and various types of isotropic turbulence

Direct Numerical Simulation (DNS) is used to study the interaction between normal shock waves of moderate strength (M 1= 1.2 and M 1 = 1.5) and isotropic turbulence. A complete description of the turbulence behaviour across the shock is provided and the influence of the nature of the incoming turbulence on the interaction is investigated. The presence of upstream entropy fluctuations satisfying the Strong Reynolds Analogy enhances the amplification of the turbulent kinetic energy and transverse vorticity variances across the shock compared to the solenoidal (pure vorticity) case. Budgets for the fluctuating-vorticity variances are computed, showing that the baroclinic torque is responsible for this additional production of transverse vorticity. More reduction of the transverse Taylor microscale and integral scale is also observed in the vorticity-entropy case while no influence can beseen on the longitudinal Taylor microscale. When the upstream turbulence is dominated by acoustic and vortical fluctuations, less amplification of the kinetic energy (for Mach numbers between 1.25 and 1.8), less reduction of the transverse microscale and more amplification of the transverse vorticity variance are observed through the shock compared to the solenoidal case. In all cases, the classic estimation of Batchelor relating the dissipation rate and the integral scale of the flow proves to be invalid. These results are obtained with the same numerical tool and similar flow parameters, and they are in good agreement with Linear Interaction Analysis (LIA).

Stability Theory on a Circular Jet with Near-Critical Mixing Surface.

The stability of a circular liquid jet with near-critical mixing surface is analyzed in the frame-work of inviscid linear stability theory. The phase equilibrium condition results in vanishing small surface tension and surface density difference at high pressures. Because of very low mass diffusivity, the density changes only in the vicinity of the near-critical mixing surface. The analysis shows that the small surface density difference enhances the instability to a great degree, coupling with the effects of gas-phase velocity boundary layer flow and baroclinic vorticity production.

The vortex wake of the free-swimming larva and pupa of Culex pipiens (Diptera).

The kinematics and hydrodynamics of free-swimming pupal and larval (final-instar) culicids were investigated using videography and a simple wake-visualisation technique (dyes). In both cases, swimming is based on a technique of high-amplitude, side-to-side (larva) or up-and-down (pupa) bending of the body. The pupa possesses a pair of plate-like abdominal paddles; the larval abdominal paddle consists of a fan of closely spaced bristles which, at the Reynolds numbers involved, behaves like a continuous surface. Wake visualisation showed that each half-stroke of the swimming cycle produces a discrete ring vortex that is convected away from the body. Consecutive vortices are produced first to one side then to the other of the mean swimming path, the convection axis being inclined at approximately 25 degrees away from dead aft. Pupal and larval culicids therefore resemble fish in using the momentum injected into the water to generate thrust. Preliminary calculations for the pupa suggest that each vortex contains sufficient momentum to account for that added to the body with each half-stroke. The possibility is discussed that the side-to-side flexural technique may allow an interaction between body and tail flows in the production of vorticity.

Theoretical investigation of unsteady flow interactions with a premixed planar flame

This paper presents the results of a theoretical study of the interactions between a laminar, premixed flame front and a plane acoustic wave. Its objective is to elucidate the processes that damp or drive acoustic waves as they interact with flames. Using linear analysis, the characteristics of the acoustic field, the flame's movement and wrinkling in response to acoustic perturbations, and the acoustic energy that is produced or dissipated at the flame are calculated. These calculations show that the net acoustic energy flux out of the flame is controlled by competing acoustic energy production and dissipation processes. Energy is added to the acoustic field by unsteady heat release processes resulting from the unsteady flux of unburned reactants through the flame by fluctuations in the flame speed or density of the unburned reactants. Energy is dissipated by the transfer of acoustic energy into fluctuations in vorticity that are generated at the flame front because of the misaligned fluctuating pressure and mean density gradients (i.e. the baroclinic vorticity production mechanism). The paper concludes by showing how these results can be generalized to determine the response of planar flames to an arbitrarily complex acoustic field. The principal contribution of this work is its demonstration that the excitation of vorticity and fluctuations in the flame speed have significant qualitative and quantitative affects on the interactions between flames and acoustic waves.

The Sensitivity of Simulated Supercell Structure and Intensity to Variations in the Shapes of Environmental Buoyancy and Shear Profiles

Convective storm simulations are conducted using varying thermal and wind profile shapes, subject to the constraints of strict conservation of convective available potential energy (CAPE) and hodograph trace. Small and large CAPE regimes and straight and curved hodographs are studied, each with a matrix of systematically varying thermal and wind profile shapes having identical levels of free convection and bulk Richardson numbers favorable to supercell development. Differences in storm intensity and morphology resulting from changes in the profile shapes can be profound, especially in the small CAPE regime, where, for the moderate shears studied here, storms are generally weak except when the buoyancy is concentrated at low levels. In stronger CAPE regimes, less dramatic relative enhancements of storm updraft intensity are found when both the buoyancy and shear are concentrated at low levels. Peak midlevel vertical vorticity correlates roughly with peak updraft speed in the small CAPE regime, but it shows less sensitivity to buoyancy and shear stratification at larger CAPE. Although peak low-level vertical vorticity can be large in either CAPE regime, it is generally larger in the large CAPE regime, where evaporation of rain leads to the formation of stronger surface cold pools, zones of enhanced horizontal shear, and baroclinic production of horizontal vorticity that can be tilted onto the vertical by storm updrafts. The present parameter space study strongly suggests that, while bulk CAPE and shear are important determinants of gross storm morphology and intensity, significant modulation is possible within a given bulk CAPE and shear class by changing only the shapes of the profiles of buoyancy and shear, either alone or in combination.

On the structure and formation of spiral Taylor–Görtler vortices in spherical Couette flow

A direct numerical simulation of the spherical Couette flow between two spheres with the inner sphere rotating was performed to investigate the detailed structure, formation process and mechanism of the spiral Taylor–Görtler (TG) vortices. For comparison with our previous experiments, a moderate gap case with clearance ratio β = 0.14 is chosen in the present numerical study. With adequate initial and boundary conditions, we have sucessfully simulated the supercritical spiral TG vortex flow in this system. Analysis of the numerical results reveals the structure and features of the spiral TG vortices. The flow consists of one toroidal TG vortex, one toroidal vortex cell, three spiral TG vortices and a secondary flow circulation in each hemisphere, and this supercritical flow solution features rotational and equatorial asymmetries. It is found that the spiral TG vortices are composed of a pair of counter-rotating, unequal spiral vortices with essentially different structural forms. One begins in the secondary flow circulation at higher latitude and ends with a connection to the toroidal vortex cell at lower latitude while the other one starts on the inner rotating spherical surface at lower latitude and ends on the outer stationary spherical surface at higher latitude. Through sucessive visualizations which display the transient features of the spiral TG vortices, we observe that vortex tearing, splitting, tilting, reconnecting, stretching and compressing occur in the formation of the spiral TG vortices. Pairing of two alternating helical vortices is the key process in their evolution. To understand the formation mechanism, we consider the vorticity production in the azimuthal vorticity component equation. The important vorticity tilting and stretching terms play different roles in the formation process of these two counter-rotating spiral vortices. The vorticity tilting term is responsible for generating both of the spiral vortices. The vorticity stretching term acts to stretch one of the spiral vortices from the inner sphere to the outer sphere while suppressing the stretching of the other in the azimuthal direction. The different formation mechanisms for these two counter-rotating spiral vortices lead to the structure of the spiral TG vortices.