Vortical Disturbances Research Articles

Excitation and stability of nonlinear compressible Görtler vortices and streaks induced by free-stream vortical disturbances

We study the generation, nonlinear development and secondary instability of unsteady Görtler vortices and streaks in compressible boundary layers exposed to free-stream vortical disturbances and evolving over concave, flat and convex walls. The formation and evolution of the disturbances are governed by the compressible nonlinear boundary-region equations, supplemented by initial and boundary conditions that characterise the impact of the free-stream disturbances on the boundary layer. Computations are performed for parameters typical of flows over high-pressure turbine blades, where the Görtler number, a measure of the curvature effects, and the disturbance Reynolds number, a measure of the nonlinear effects, are order-one quantities. At moderate intensities of the free-stream disturbances, increasing the Görtler number renders the boundary layer more unstable, while increasing the Mach number or the frequency stabilises the flow. As the free-stream disturbances become more intense, vortices over concave surfaces no longer develop into the characteristic mushroom-shaped structures, while the flow over convex surfaces is destabilised. An occurrence map identifies Görtler vortices or streaks for different levels of free-stream disturbances and Görtler numbers. Our calculations capture well the experimental measurements of the enhanced skin friction and wall-heat transfer over turbine-blade pressure surfaces. The time-averaged wall-heat transfer modulations, termed hot fingers, are elongated in the streamwise direction and their spanwise wavelength is half of the characteristic wavelength of the free-stream disturbances. Nonlinearly saturated disturbances are unstable to secondary high-frequency modes, whose growth rate increases with the Görtler number. A new varicose even mode is reported, which may promote transition to turbulence at the stem of nonlinear streaks.

Influence of spanwise wall vibration on non-modal perturbations subject to freestream vortical disturbances in hypersonic boundary layers

In this paper, we study the effect of lateral wall vibrations on the excitation and evolution of non-modal perturbations in hypersonic boundary layers subject to low-frequency freestream vortical disturbances (FSVDs). A novel, high-efficiency numerical approach, combining the harmonic weakly nonlinear Navier–Stokes and nonlinear parabolised stability equation approaches, is developed, which is sufficient to accommodate both the rapid distortion of the perturbation in the leading-edge vicinity and the nonlinear development of finite-amplitude high-order harmonics in the downstream region. The boundary-layer response to low-frequency FSVDs shows a longitudinal streaky structure, for which the temperature perturbation shows much greater magnitude than the streamwise velocity perturbation. The lateral vibration induces a Stokes layer solution for the spanwise velocity perturbation, which interacts with the FSVD-induced perturbations and leads to a suppression of the non-modal perturbation and an enhancement of the downstream modal perturbation. The new perturbations excited by the FSVD–vibration interaction strengthen as the vibration intensifies, and they could become comparable with the FSVD-induced perturbations in downstream locations at a high vibration intensity, indicating a remarkable modification of the streaky structure and its instability property. Secondary instability (SI) analyses based on the streaky base flow indicate that the vibration could enhance or suppress the SI modes, depending on their initial phases over the vibration period. Overall, the average effect is that the low-frequency and high-frequency SI modes are stabilised and destabilised by the vibration, respectively. Since the high-frequency SI modes undergo higher amplifications, the subsequent bypass transition is likely to be promoted by relatively strong vibrations.

Passive Control of the Flow Around a Rectangular Cylinder with a Custom Rough Surface

Motivated by existing techniques for implementing roughness on cylinders to control flow disturbances, we performed delayed detached eddy simulations (DDES) at Re = 6×106 that generated unsteady turbulent flow around a rectangular cylinder with a controlled wrinkled surface and a 1:4 aspect ratio. A systematic study of the roughness effect was carried out by implementing different configurations of equally spaced grooves and bumps on the top-surface of the cylinder. Our results suggest that groove geometries reduce energy dissipation at higher rates than the smooth reference case, whereas bumped cylinders produce relative pressures characterized by a sawtooth pattern along the middle-upper part of the cylinder. Moreover, cylinders with triangular bumps increase mean drag and lift forces by up to 8% and 0.08 units, respectively, while circular bumps increase vorticity and pressure disturbances on the wrinkled surface. All of these effects impact energy dissipation, vorticity, pressure coefficients, and flow velocity along the wrinkled surface. Both the surface-manufactured cylinders and the proposed visualization techniques could be replicated in a variety of engineering developments involving flow characterization in the presence of roughness.

Nonlinear evolution of vortical disturbances entrained in the entrance region of a circular pipe

The nonlinear evolution of free-stream vortical disturbances entrained in the entrance region of a circular pipe is investigated using asymptotic and numerical methods. Attention is focused on the low-frequency disturbances that induce streamwise elongated structures. A pair of vortical modes with opposite azimuthal wavenumbers is used to model the free-stream disturbances. Their amplitude is assumed to be intense enough for nonlinear interactions to occur inside the pipe. The formation and evolution of the perturbation flow are described by the nonlinear unsteady boundary-region equations in the cylindrical coordinate system, derived and solved herein for the first time. Matched asymptotic expansions are employed to construct appropriate initial conditions and the initial–boundary value problem is solved numerically by a marching procedure in the streamwise direction. Numerical results show the stabilising effect of nonlinearity on the intense algebraic growth of the disturbances and an increase of the wall-shear stress due to the nonlinear interactions. A parametric study is carried out to evince the effect of the Reynolds number, the streamwise and azimuthal wavelengths, and the radial length scale of the inlet disturbance on the nonlinear flow evolution. Elongated pipe-entrance nonlinear structures (EPENS) occupying the whole pipe cross-section are discovered. EPENS with $h$ -fold rotational symmetry comprise $h$ high-speed streaks positioned near the wall, and $h$ low-speed streaks centred around the pipe core. These distinct structures display a striking resemblance to nonlinear travelling waves found numerically and observed experimentally in fully developed pipe flow. Good agreement of our mean-flow and root mean square data with experimental measurements is obtained.

Nonlinear transient disturbance growth analysis for the compressible external flow and application to a flow around circular cylinder

The property of nonlinear optimal perturbation (NLOP) analysis for the flow around the circular cylinder was investigated with a comparison with the linear optimal perturbation analysis (LOP). Our analysis revealed that NLOP is highly dependent on the initial disturbance norm and highlighted the limitation of linear prediction in triggering instability in the flow field. This NLOP shows an asymmetric and deformed vortex structure on the cylinder wall, with the angle of the maximum wall vorticity shifting in relation to the initial disturbance norm. We also observed that the circulation and disturbance vorticity at the shear layer in boundary layer efficiently contributed to larger disturbance growth of the separation vortex behind the cylinder compared with the LOP.

Instability in strongly stratified plane Couette flow, with application to supercritical fluids.

This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjørtoft's criterion of instability when a minimum of kinematic viscosity is present in the base flow. The characteristic scales associated with this minimum are identified as the primary controlling parameters of the associated instability, regardless of the type of stratification. To support this finding, analytical stability models are derived in the long wave approximation using piecewise linear base flows. Numerical stability calculations are carried out to validate these models and to provide further information on the production of disturbance vorticity. All instabilities are interpreted as arising from the interaction between two vorticity waves. Depending on the type of stratification, these two waves are produced by different physical mechanisms. When both strong density and viscosity stratifications are present, we show that they result from the concurrent action of shear and inertial baroclinic effects. The stability models developed for simple fluid models ultimately shed light on a recently observed unstable mode in supercritical fluids (Ren et al., J. Fluid Mech., vol. 871, 2019, pp. 831-864), providing a quantitative prediction of the stability diagram and identifying the dominant mechanisms at play. Furthermore, our study suggests that the minimum of kinematic viscosity reached at the Widom line in these fluids is the leading cause of their instability. The existence of similar instabilities in different fluids and flows (e.g., miscible fluids) is finally discussed.

Formation mechanisms of persistent extreme precipitation events over the eastern periphery of the Tibetan Plateau: Synoptic conditions, moisture transport and the effect of steep terrain

The eastern periphery of the Tibetan Plateau (EPTP) is prone to frequent and severe Persistent Extreme precipitation (PEP) events in summer. Given the complexity of weather systems and the intricate nature of terrain over this region, the generation and development mechanisms of the PEP in the EPTP remain to be determined. In this study, the formation and persistence mechanisms are further explored from the perspective of the general features of large-scale circulations, moisture source diagnosis and the influence of steep topography by using a thermal-dynamical diagnosis method, a mesoscale numerical simulation and a Lagrangian identification of the main moisture sources. The results show that during PEP events, the corresponding atmospheric circulation systems are characterized by an anomalous Rossby wave train at middle levels, an intensified westerly jet, an eastward extension of the South Asian high and a westward extension of the western Pacific subtropical high, all of which are possible to facilitate the development of potential instability and anticyclonic convergence of water vapor transport. The evaporative moisture sources from the Southeastern Asia (SEA), Bay of Bengal (BOB), and Southern China Sea (SCS) are remarkably enhanced during PEP events, with a contribution of 56.44%, which is 28.5% higher than the climatic mean. The further sensitive experiment indicates that the steep terrain could enhance the continuous transport of positive potential vorticity and the downward propagation of upper-level isentropic potential vorticity disturbances, thereby playing an essential role in the triggering and development of PEP events.

Modeling Flame Transfer Functions of an Industrial Premixed Burner

Abstract This paper presents an analysis of the unsteady heat release rate response of industrially relevant axisymmetric premixed flames to harmonic velocity perturbations. The heat release rate response, quantified using the flame transfer function (FTF) definition, is measured from an acoustically forced swirl burner under perfectly premixed conditions. To understand the features of the measured FTF, a physics-based analytical model is developed in this study. To describe the heat release rate dynamics, a model for the flame spatiotemporal response is derived in the linear limit using the G-equation formulation. Inputs to the flame response model are selected to be consistent with values observed in the corresponding industrial burner, based on experimental and numerical studies. The relative contributions of acoustic and convecting vortical disturbances on specific features of the FTF are explored in this study. The results highlight the importance of capturing the appropriate disturbance velocity field as an input to the flame response model for accurate FTF predictions.

Scaling of boundary-layer disturbances exposed to free-stream turbulence

We present theoretical results related to the experimental findings of Matsubara & Alfredsson (J. Fluid Mech., vol. 430, 2001, pp. 149–168) on the scaling of the energy spectra of the Klebanoff modes, i.e. streamwise-elongated vortical disturbances generated by free-stream turbulence in a flat-plate transitional boundary layer. The scaling is explained by a model that describes the streamwise evolution of the streamwise and spanwise energy spectra. The theoretical framework is based on the quasi-steady asymptotic solution of the boundary-region equations, on an axial-symmetric model of the free-stream spectrum, and on the spectral response of the boundary layer to the external perturbations.

Global receptivity analysis: physically realizable input–output analysis

In the context of transition analysis, linear input–output analysis determines the worst-case disturbances to a laminar base flow based on a generic right-hand-side volumetric/boundary forcing term. The worst-case forcing is not physically realizable, and, to our knowledge, a generic framework for posing physically realizable worst-case disturbance problems is lacking. In natural receptivity analysis, disturbances are forced by matching (typically local) solutions within the boundary layer to outer solutions consisting of free-stream vortical, entropic and acoustic disturbances. We pose a scattering formalism to restrict the input forcing to a set of realizable disturbances associated with plane-wave solutions of the outer problem. The formulation is validated by comparing with direct numerical simulations of a Mach 4.5 flat-plate boundary layer. We show that the method provides insight into transition mechanisms by identifying those linear combinations of plane-wave disturbances that maximize energy amplification over a range of frequencies. We also discuss how the framework can be extended to accommodate scattering from shocks and in shock layers for supersonic flow.

Particle-scale modeling study of coaxial jets of gas-solid swirling flow in an industrial-scale annular pipe via CFD-DEM

In this work, the gas-solid swirling flow characteristics of coaxial jets in an industrial-scale annular pipe with a helical swirler is numerically simulated via the CFD-DEM. After validating the numerical model, the general flow pattern of coaxial jets, and gas-particle mixing behavior together with the particle-scale information are discussed. The effect of the geometry parameters of the swirler is studied and analyzed in terms of particle azimuthal velocity and particle Reynolds number. The results demonstrate that the presence of the swirler enhances both the turbulent disturbance and gas vorticity. Increasing vane angle and diameter of swirler is beneficial for the particle dispersion. The particle velocity slightly reduces with decreasing the height in the region 0.6 m < H < 0.7 m but dramatically increases with decreasing the height in the region of height H < 0.6 m. The entrainment of particles by the swirling flow increases the distribution width and azimuthal velocity of particles with decreasing the height.

The Henan extreme rainfall in July 2021: Modulation of the northward-shift monsoon trough on the synoptic-scale wave train

The synoptic-scale wave train is a dominant pattern of the synoptic variability over the tropical western Pacific and usually affects the extreme weather over South China and Southeast Asia. Whether it could extend its influence and contribute to the Henan extreme rainfall in July 2021 still needs to be unraveled. We found that during the Henan extreme rainfall days a positively synoptic-scale vorticity disturbance dominated Henan province, China, which was embedded in the synoptic-scale wave train that originated from the western North Pacific. Moreover, the propagating pathway of this synoptic-scale wave train located northward and was likely modulated by the latitudinal location change of the monsoon trough over the western North Pacific. A northernmost displacement of the monsoon trough in July 2021 (∼23.2°N) would facilitate the synoptic-scale wave train to propagate farther northwestward via shifting the related barotropic conversion northward. Therefore, the synoptic-scale wave train from the tropics could reach Henan, provide the necessary lifting forcing, and supply abundant water vapor associated with the anomalous southerly for the occurrence of Henan extreme rainfall event. The results implicate that the pre-existing synoptic-scale wave train regulated by the location of the monsoon trough may be a potential precursor for heavy rainfalls in northern Central China.

Coalescence characteristics of droplets dispersed in oil subjected to electric and centrifugal fields

The demulsification and dewatering process is an important link in the resource utilization of waste oil. Compared with a single method, a coupling device based on high-voltage electric and swirl centrifugal fields can better realize emulsion demulsification and dewatering. As the main factor affecting the separation performance of a coupling device, the droplet size distribution changes dynamically owing to droplet coalescence. However, the coalescence characteristics of droplets under double-field coupling are unclear. Therefore, a numerical model is established in this study by coupling the electric and flow fields governing equations, and the droplet population balance equation to imitate droplet coalescence and breakup. With the finite element method, the dynamic variation and coalescence characteristics of droplets under different double-field coupling conditions are analyzed. Results show that droplet size decreases as vorticity increases, and vorticity disturbance will cause droplet size distribution instability. Droplet size is inversely proportional to oil volume fraction under the same inlet conditions. When the inlet Reynolds numbers (Re) is less than 12940, the coalescence effect is the dominant factor, but when Re is 12940, the breakage effect is the dominant factor. The regions where the droplet coalescence effect are dominant mainly include the near-wall region of the coupling and small cone and underflow pipe sections. Furthermore, the degree of coalescence does not directly determine the grade efficiency.

The effects of nose bluntness on broadband disturbance receptivity in hypersonic flow

While nose bluntness is known to have a large impact on the stability of hypersonic vehicles, its influence on the freestream receptivity process has not been fully characterized for a wide range of conditions. This paper investigates the effects of nose bluntness on the second mode receptivity coefficients and the development of boundary layer disturbances over two 7° half-angle circular blunt cones at Mach 10 after perturbation with broadband freestream pulses of different types. The cones have nose radii of 9.525 mm (case B) and 5.08 mm (case I). Unsteady direct numerical simulation (DNS) and linear stability theory (LST) results compare well and predict stronger second mode growth for case I in all pulse cases. Unsteady DNS also shows variations in extramodal excitation between the cones depending on freestream disturbance type. Spectral receptivity coefficients are generated by decomposing the unsteady DNS data into discrete frequency Fourier modes, which are then corrected with LST N-factors. Fast acoustic disturbances demonstrate minimal variation in receptivity coefficients, while temperature and vorticity disturbances have much higher coefficients in case I. Planar slow acoustic pulses induce stronger disturbances outside of the second mode in case I, resulting in higher peak receptivity coefficients. Results show significant variation in receptivity response based on nose bluntness, pulse geometry, and the type of incident perturbation.

Growth of vortical disturbances entrained in the entrance region of a circular pipe

The development and growth of unsteady three-dimensional vortical disturbances entrained in the entry region of a circular pipe is investigated by asymptotic and numerical methods for Reynolds numbers between $1000$ and $10\,000$ , based on the pipe radius and the bulk velocity. Near the pipe mouth, composite asymptotic solutions describe the dynamics of the oncoming disturbances, revealing how these disturbances are altered by the viscous layer attached to the pipe wall. The perturbation velocity profiles near the pipe mouth are employed as rigorous initial conditions for the boundary-region equations, which describe the flow in the limit of low frequency and large Reynolds number. The disturbance flow is initially primarily present within the base-flow boundary layer in the form of streamwise-elongated vortical structures, i.e. the streamwise velocity component displays an intense algebraic growth, while the cross-flow velocity components decay. Farther downstream the disturbance flow occupies the whole pipe, although the base flow is mostly inviscid in the core. The transient growth and subsequent viscous decay are confined in the entrance region, i.e. where the base flow has not reached the fully developed Poiseuille profile. Increasing the Reynolds number and decreasing the frequency causes more intense perturbations, whereas small azimuthal wavelengths and radial characteristic length scales intensify the viscous dissipation of the disturbance. The azimuthal wavelength that causes the maximum growth is found. The velocity profiles are compared successfully with available experimental data and the theoretical results are helpful to interpret the only direct numerical dataset of a disturbed pipe-entry flow.

Combined effect of passive vortex generators and leading-edge roughness on dynamic stall of the wind turbine airfoil

Dynamic stall causes the highly unsteady and nonlinear aerodynamic loads on wind turbines. Recently, dynamic stall with passive vortex generators (VGs) and leading-edge roughness (LER) has received considerable attention, but independently. Therefore, this paper presents a careful investigation into dynamic stall of the NREL S809 airfoil with both VGs and LER to reveal their combined effect. Fully-resolved URANS simulations are conducted to identify the unsteady flow characteristics, and equivalent sand-grain roughness is used to model LER. LER significantly increases the turbulence kinetic energy (TKE) and suction loss at the leading edge, thereby causing the earlier onsets of separated flow and dynamic stall. Increasing roughness height generally reduces linear lift-curve slope, increases aerodynamic hysteresis and makes the separated flow hard to be reattached. VGs increase near-wall TKE via streamwise vortices and effectively suppress the separated flow. Dynamic stall is therefore significantly delayed by VGs with higher maximum lift, and aerodynamic hysteresis is also greatly reduced with the flow reattachment accelerated. Interestingly, serious LER may cause strong vortical disturbances and change the dynamic stall behaviors from light stall into deep stall. Double-row VGs are also found better than single-row VGs in improving the aerodynamic performance of roughened airfoil. These findings imply that VGs effectively control dynamic stall and diminish the adverse LER effect. This study should advance the control of unsteady loads on wind turbines suffering from harsh environmental conditions.

Entrainment and growth of vortical disturbances in the channel-entrance region

The entrainment of free-stream unsteady three-dimensional vortical disturbances in the entry region of a channel is studied via matched asymptotic expansions and by numerical means. The interest is in flows at Reynolds numbers where experimental studies have documented the occurrence of intense transient growth, despite the flow being stable according to classical stability analysis. The analytical description of the vortical perturbations at the channel mouth reveals how the oncoming disturbances penetrate into the wall-attached shear layers and amplify downstream. The effects of the channel confinement, the streamwise pressure gradient and the viscous/inviscid interplay between the oncoming disturbances and the boundary-layer perturbations are discussed. The composite perturbation velocity profiles are employed as initial conditions for the unsteady boundary-region perturbation equations. At a short distance from the channel mouth, the disturbance flow is mostly confined within the shear layers and assumes the form of streamwise-elongated streaks, while farther downstream the viscous disturbances permeate the whole channel although the base flow is still mostly inviscid in the core. Symmetrical disturbances exhibit a more significant growth than anti-symmetrical disturbances, the latter maintaining a nearly constant amplitude for several channel heights downstream before growing transiently, a unique feature not reported in open boundary layers. The disturbances are more intense as the frequency decreases or the bulk Reynolds number increases. We compute the spanwise wavelengths that cause the most intense downstream growth and the threshold wall-normal wavelengths below which the perturbations are damped through viscous dissipation.

Thermochemical effects on hypersonic shock waves interacting with weak turbulence

The interaction between a weakly turbulent free stream and a hypersonic shock wave is investigated theoretically by using linear interaction analysis (LIA). The formulation is developed in the limit in which the thickness of the thermochemical nonequilibrium region downstream of the shock, where relaxation toward vibrational and chemical equilibrium occurs, is assumed to be much smaller than the characteristic size of the shock wrinkles caused by turbulence. Modified Rankine–Hugoniot jump conditions that account for dissociation and vibrational excitation are derived and employed in a Fourier analysis of a shock interacting with three-dimensional isotropic vortical disturbances. This provides the modal structure of the post-shock gas arising from the interaction, along with integral formulas for the amplification of enstrophy, concentration variance, turbulent kinetic energy (TKE), and turbulence intensity across the shock. In addition to confirming known endothermic effects of dissociation and vibrational excitation in decreasing the mean post-shock temperature and velocity, these LIA results indicate that the enstrophy, anisotropy, intensity, and TKE of the fluctuations are much more amplified through the shock than in the thermochemically frozen case. In addition, the turbulent Reynolds number is amplified across the shock at hypersonic Mach numbers in the presence of dissociation and vibrational excitation, as opposed to the attenuation observed in the thermochemically frozen case. These results suggest that turbulence may persist and get augmented across hypersonic shock waves despite the high post-shock temperatures.

Elevated low-frequency free-stream vortical disturbances eliminate boundary-layer separation

Abstract

Modelling of sound-vortex interaction for the flow through an annular aperture

The acoustic characteristics of bluff-body burners play a critical role in the combustion stability for combustors using this type of burners. The acoustic modelling of an axisymmetric bluff-body burner entails properly capturing the sound-vortex interaction for the flow through the annular aperture of the burner. Such a problem pertaining to annular apertures can also be of relevance to other engineering applications, such as acoustic dampers or turbofan duct systems. The methodology of combining suitable acoustic Green’s functions with a vortex sheet model has been applied extensively in previous theoretical studies of the acoustic response of a short circular orifice with a mean flow passing through it. In this work, the Green’s function and vortex sheet model theory is generalised in order to efficiently predict the acoustic characteristics of thin annular apertures sustaining a mean flow, which effectively emulate the typical axisymmetric bluff-body burner configurations in realistic combustors. This requires the incorporation of multiple Kutta conditions for modelling the vortex shedding and multiple vortex sheets for modelling the interaction of the shed vorticity and the acoustics. A high-resolution compressible Large Eddy Simulation (LES) of a simplified representative geometry is performed for validation; the analytical prediction and numerical findings show very good agreement, and the LES further provides key insights into the speed with which vortical disturbances convect downstream.