Formation Of Longitudinal Vortices Research Articles

The impact of steady streaming and conditional turbulence on gas transport during high-frequency ventilation.

High-frequency ventilation is a type of mechanical ventilation therapy applied on patients with damaged or delicate lungs. However, the transport of oxygen down, and carbon dioxide up, the airway is governed by subtle transport processes which hitherto have been difficult to quantify. We investigate one of these mechanisms in detail, nonlinear mean streaming, and the impact of the onset of turbulence on this streaming, via direct numerical simulations of a model 1:2 bifurcating pipe. This geometry is investigated as a minimal unit of the fractal structure of the airway. We first quantify the amount of gas recirculated via mean streaming by measuring the recirculating flux in both the upper and lower branches of the bifurcation. For conditions modeling the trachea-to-bronchi bifurcation of an infant, we find the recirculating flux is of the order of 3–5% of the peak flux . We also show that for conditions modeling the upper generations, the mean recirculation regions extend a significant distance away from the bifurcation, certainly far enough to recirculate gas between generations. We show that this mean streaming flow is driven by the formation of longitudinal vortices in the flow leaving the bifurcation. Second, we show that conditional turbulence arises in the upper generations of the airway. This turbulence appears only in the flow leaving the bifurcation, and at a point in the cycle centered around the maximum instantaneous flow rate. We hypothesize that its appearance is due to an instability of the longitudinal-vortices structure.

Numerical Simulation of the Boundary Layer Control on the NACA 0015 Airfoil Through Vortex Generators

This paper studies the influence caused by a vortex generator (VG) on a wing section with NACA 0015 airfoil when this generator is located before and after a recirculation bubble caused by the boundary layer detachment. The study was numerically carried out and concentrated under conditions of flow with Rec = 2.38 × 105 and angles of attack AoA = 3 and 6, characterized by the fact that they undergo detachment of the boundary layer before and after the location of the VG, respectively. The use of the generator in AoA = 3 strongly influenced the reduction of the recirculation bubble, leading to a drag reduction of 1.43%. In AoA = 6 with a bubble recirculation, the effect was much lower, with no well-defined formation of longitudinal vortices, resulting in increased drag and lift at 0.33 and 0.35%, respectively.

Wind tunnel tests on drag reduction of heavy vehicles using sinusoidal boat tails

A sinusoidal boat tail (SBT) is developed and investigated to greatly reduce drag, side force, and yawing moment under crosswind conditions. The drag and side forces of a heavy vehicle model with the SBT are reduced by 15.9 % and 22.6 %, respectively, relative to those of a reference model without the SBT at a yaw angle of 7°. Therefore, the SBT improves the aerodynamic performance and driving stability of the vehicle model. Flow characteristics around the vehicle model are measured using a particle image velocimetry technique. Mean velocity field results show that the SBT effectively suppresses the formation of longitudinal vortices by enhancing the streamwise velocity of the region behind the boat tail. In addition, the streamwise momentum deficit is reduced in the wake region owing to the development of a secondary recirculating flow region.

Effect of surface modification of a rectangular vortex generator on heat transfer rate from a surface to fluid: An extended study

For many industrial applications, cooling of a hot surface is of greater importance for an improved performance of the system. The wetted surface area plays a vital role in heat transfer process. Increase of the wetted surface may improve the heat transfer rate from the hot surface to the flowing fluid. Further, the optimisation of the shape of the extended surface may promote superior thermal interaction between the surface and the fluid. These extended surfaces are responsible for creating an abrupt pressure difference across it. This results in formation of longitudinal vortices downstream of the surfaces. The induced longitudinal vortex may interact with the boundary layer, which in turn enhances the convective rate of heat transfer. In the current work, the vortex generators with surface textures are studied numerically, which is an extension of previous work performed by same group of authors Kashyap et al. (2018). The CFD results show that multiple textures on the leading and the trailing faces of the vortex generator enhances the strength of the primary vortex, downstream of the vortex generator. As a result, the heat transfer from the heated surface increases to about 14.4%. The phenomenon is realised by increment in the surface average skin friction coefficient along with the surface average Nusselt number of the plate. The surface temperature distribution of the plate downstream of the vortex generator show a downfall due to the stretching of the primary vortex with a minimal pressure drop.

Effect of ion‐slip current on the thermal instability of natural convection flow in a boundary layer flow past a horizontal flat plate

PurposeThe purpose of this paper is to study the effects of ion‐slip current and Hall current on the formation of longitudinal vortices in natural convection flow over a heated horizontal plate.Design/methodology/approachThe criterion on the position marking on the onset of longitudinal vortices is defined in the present paper. The results show that the onset position characterized by the Grashof number depends on the Prandtl number, the Reynolds number, the wave number, the Hall parameter, the ion‐slip parameter, and the Hartmann number.FindingsThe flow becomes more stable as the magnetic field increases. However, the destabilizing effect is found on the flow when the Hall and ion‐slip currents are presented.Research limitations/implicationsThe standard method of linear stability model is applied, with terms higher than first order in disturbance quantities being neglected.Practical implicationsThe problem of MHD natural convection flow with Hall and ion‐slip currents has many important engineering applications, e.g. power generators, Hall accelerators and flows in channels and ducts.Originality/valueThis study is to check the validity of the assumptions that the conditions of Hall and ion‐slip currents can be ignored.

High-speed granular chute flows

AbstractThis paper reports experimental findings on the flow of sand down a steep chute. Nearly all granular flow models have a maximum value for the friction and therefore predict that flows on steep slopes will accelerate at a constant rate until the interaction with the ambient fluid becomes important. This prediction has not been tested by previous work, which has focused on relatively low slope angles where steady, fully developed flows occur after short distances. We test this by investigating flows over a much greater range of slope angles (30–50${}^{\ensuremath{\circ} } $) and flow depths (4–130 particle diameters). We examine flows with two basal conditions, one flat and frictional, the other bumpy. The latter imposes a no-slip condition for slow, deep flows, but permits some degree of slip for high flow velocities. The data suggests that friction can be much larger than theories such as the $\ensuremath{\mu} (I)$ rheology proposed by Jop, Forterre & Pouliquen (Nature, vol. 441, 2006) suggest and that there may be constant velocity states above the angle of vanishing ${h}_{\mathit{stop}} $. Although these flows do not vary in time, all but the flows on the bumpy base at low inclinations accelerate down the slope. A recirculation mechanism sustains flows with a maximum mass flux of $20~\mathrm{kg} ~{\mathrm{s} }^{\ensuremath{-} 1} $, allowing observations to be made at multiple points for each flow for an indefinite period. Flows with Froude number in the range 0.1–25 and bulk inertial number 0.1–2.7 were observed in the dense regime, with surface velocities in the range 0.2–5.6 $\mathrm{m} ~{\mathrm{s} }^{\ensuremath{-} 1} $. Previous studies have focused on $I\lessapprox 0. 5$. We show that a numerical implementation of the $\ensuremath{\mu} (I)$ rheology does not fully capture the accelerating dynamics or the transverse velocity profile on the bumpy base. We also observe the transverse separation of the flow into a dense core flanked by dilute regions and the formation of longitudinal vortices.

TRANSIENT DYNAMICS OF STREAK AND LONGITUDINAL VORTICES IN SHEAR FLOW WITH WAVE

Langmuir circulations are alternating right and left helical vortices in the ocean having horizontal axes parallel to the wind. They are manifested by floating material on the ocean surface as streaks. The laboratory wind driven shear flow demonstrate streak feature with/without wave condition. When the wave is present the explanation of results with Craik-Leibovich instability mechanism, originally proposed for weak current shear in ocean, is not appropriate for some problem as in the laboratory the current shear is strong. The existing normal mode analysis based on the generalized Lagrangian mean formulation for wave with strong shear is not able to capture the fully dynamics of streak and longitudinal vortices. We extend Craik-Leibovich theory to strong shear in Eulerian framework but focusing on the fully perturbation evolution dynamics. Transient dynamics of perturbation is studied with an initial value problem. In this approach the effect of shear and wave and its interaction are made clear. The transient growth in the time period without wave is significant and is crucial to the initial preferred wave number observed in the experiments. The optimal longitudinal vortex form perturbation is searched and the preferred spanwise wave number predicted is well consistent with experimental data of wind shear and wave.

Effect of magnetic field on thermal instability in mixed convection flow over a rotating boundary layer

Effect of magnetic field on the formation of longitudinal vortices in mixed convection flow over a rotating heated flat plate is presented. The onset position is characterized by the Grashof number, the rotational number, the Prandtl number, the Eckert number, the magnetic field parameter, and the wave number. Negative rotation (clockwise) and external magnetic field stabilize the boundary layer flow. On the contrary, positive rotation (anti-clockwise), the Eckert number, and the Prandtl number destabilize the flow. The numerical data show agreement with the experimental data with the case of zero Hartmann number in the literature.

The onset of Görtler vortices in laminar boundary layer flow over a slightly concave wall

The onset of convective instability in the laminar boundary layer over the slightly curved wall is analyzed theoretically and compared with the existing experimental data. A new set of stability equations are derived by the propagation theory considering the relative instability under the linear stability theory. In this analysis the disturbances are assumed to have the form of longitudinal vortices and also to grow themselves in streamwise direction. The critical position to mark the onset of Görtler instability is obtained as a function of the Görtler number, where disturbances at the critical state are mainly confined to the hydrodynamic boundary layer. Comparing the theoretical predictions with available experimental and other theoretical results, the present predictions follow experimental trends fairly well with slightly higher critical Görtler numbers than those from the local stability theory. The propagation theory commanding the local eigenvalue analysis is successful to obtain stability conditions reasonably in Görtler vortex problems, relaxing the limitations by the conventional analyses.

Thermal instability in natural convection flow over a boundary layer subject to external electrical and magnetic fields

This paper presents a numerical study of external electrical and magnetic effects on the formation of longitudinal vortices in natural convection flow over a heated horizontal plate. The criterion on the position marking on the onset of longitudinal vortices is defined in the present paper. The onset position characterized by the Grashof number depends on the Prandtl number, the wave number, the electric field parameter, and the magnetic field parameter. The flow is found more stable as the value of the magnetic field parameter increases. Moreover, the stabilizing effect is also found on the flow when the positive electric field parameter Ec is applied. The results of the present numerical prediction show reasonable agreement with the experimental data with zero magnetic field and electric field parameters in literature.

An optimal path to transition in a duct

This paper is concerned with the transition of the laminar flow in a duct of square cross section. As in the similar case of pipe flow, the motion is linearly stable for all Reynolds numbers, rendering this flow a suitable candidate for a study of the 'bypass' path to turbulence. It has already been shown that the classical linear optimal perturbation problem, yielding optimal disturbances in the form of longitudinal vortices, fails to provide an 'optimal' path to turbulence, i.e. optimal perturbations do not elicit a significant nonlinear response from the flow. Previous simulations have also indicated that a pair of travelling waves generates immediately, by nonlinear quadratic interactions, an unstable mean flow distortion, responsible for rapid breakdown. By the use of functions quantifying the sensitivity of the motion to deviations in the base flow, the optimal travelling wave associated with its specific defect is found by a variational approach. This optimal solution is then integrated in time and shown to display a qualitative similarity to the so-called 'minimal defect', for the same parameters. Finally, numerical simulations of an 'edge state' are conducted, to identify an unstable solution that mediates laminar-turbulent transition and relate it to results of the optimization procedure.

Transition to turbulence in duct flow

The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the ‘bypass’ path to turbulence. Initially the so-called ‘linear optimal perturbation problem’ is formulated and solved, yielding optimal disturbances in the form of longitudinal vortices. Such optimals, however, fail to elicit a significant response from the system in the nonlinear regime. Thus, streamwise-inhomogeneous sub-optimal disturbances are focused upon; nonlinear quadratic interactions are immediately caused by such initial perturbations and an unstable streamwise-homogeneous large-amplitude mode rapidly emerges. The subsequent evolution of the flow, at a value of the Reynolds number at the boundary between fully developed turbulence and relaminarization, shows the alternance of patterns with two pairs of large-scale vortices near opposing parallel walls. Such edge states bear a resemblance to optimal disturbances.

Magnetic effect on the formation of longitudinal vortices in natural convection flow over a rotating heated flat plate

A numerical study of magnetic effect on the formation of longitudinal vortices in natural convection flow over a rotating heated flat plate is presented. The onset position characterized by the local Grashof number, depends on the rotational Reynolds number, the Prandtl number, the Hartmann number, and the wave number. The Coriolis force and the Lonertz force have significant effects on the formation of longitudinal vortices and the associated instability. Positive rotation stabilizes the flow on the rotating flat surface. On the contrary, a negative rotation destabilizes the flow. The flow is found more stable as the value of Hartmann number increases. The numerical data show reasonable agreement with the experimental results with the case of thermal instability in natural convection over a flat plate heated from below.

The Onset of Darcy–Forchheimer Convection in Inclined Porous Layers Heated from Below

It is well known that the onset of convection in an inclined porous layer heated from below takes the form of longitudinal vortices when Darcy’s law is valid. In this paper we consider briefly how the onset criterion alters when form drag, as modelled by the Forchheimer terms, is significant. In general, the critical Rayleigh number increases substantially as form drag effects strengthen, but the wavenumber rises by only a small amount. This numerical study is supplemented by a brief asymptotic analysis of the case when the Forchheimer terms dominate and it is shown that the critical Rayleigh number increases in direct proportion with the form drag parameter.

Magnetic effect on the formation of longitudinal vortices in a rotating laminar boundary layer

AbstractThis paper presents a numerical study of magnetic effect on the formation of longitudinal vortices in a rotating laminar boundary layer. The criterion for the position marking the onset of longitudinal vortices is defined in this paper. The onset position characterized by the rotational Goertler number Gδ,rot, depends on the local rotation number, Reynolds number, the magnetic field parameter, the Prandtl number and the wave number. The results show that positive rotation destabilizes the flow. The flow is found to become more unstable to the vortex mode of instability as the value of magnetic field parameter M increases. The numerical data shows good agreement with the experimental results. Copyright © 2005 John Wiley & Sons, Ltd.

Effect of rotation on the formation of longitudinal vortices in mixed convection flow over a flat plate

This paper presents a numerical study of the effect of rotation on the formation of longitudinal vortices in mixed convection flow over a flat plate. The criterion on the position of marking the onset of longitudinal vortices is defined in this paper. The onset position characterized by the Goertler number G δ depends on the Grashof number, the rotation number Ro, the Prandtl number Pr and the wave number. The results show that negative rotation stabilizes the boundary layer flow on the surface. On the contrary, positive rotation destabilizes the flow. The numerical data are compared with the experimental results.

Longitudinal vortices in granular flows.

We present a new instability observed in rapid granular flows down rough inclined planes. For high inclinations and flow rates, the free surface of the flow experiences a regular deformation in the transverse direction. Measurements of the surface velocities imply that this instability is associated with the formation of longitudinal vortices in the granular flow. From the experimental observations, we propose a mechanism for the longitudinal vortex formation based on the concept of granular temperature.

Numerical study of formation of longitudinal vortices in natural convection flow over horizontal and inclined surfaces

This paper presents a numerical study of the formation of longitudinal vortices in natural convection flow over horizontal and inclined plates. The criterion on the position marking on the onset of longitudinal vortices is defined in the present paper. The results show that the onset position characterized by the Grashof number depends on the Prandtl number, wave number, and the inclined angle φ from the horizontal. The flow is found to become more stable to the vortex mode of instability as the value of inclined angle increases, owing to a decrease in buoyancy force in the normal direction. However, the Prandtl number has a destabilizing effect on the flow. The results of the present numerical prediction show a reasonable agreement with the experimental data in the literature.

Finite‐amplitude Rotational Waves in Viscous Shear Flows

Growing finite‐amplitude initially spanwise‐independent two‐dimensional rotational waves and their nonlinear interaction with unidirectional viscous shear flows of various strengths are considered. Both primary and secondary instabilities are studied, but only secondary instabilities are permitted to vary in the spanwise direction. A generalized Lagrangian‐mean formulation is employed to describe wave‐mean interactions, and a separate theory is constructed to account for the back effect of the developing mean flow on the wave field. Viscosity is seen to significantly complicate calculation of the back effect. The primary instability is seen to act as a platform for, and catalyst to, secondary instabilities. The analysis leads to an eigenvalue problem for the initial growth of the secondary instability, this being a generalization of the eigenvalue problem constructed by Craik for inviscid neutral waves. Two inviscid secondary instability mechanisms to longitudinal vortex form are observed: the first has as its basis the Craik–Leibovich type 2 mechanism. The second, which is as yet unproven, requires that both the wave and flow field distort in concert at all levels of shear. Both mechanisms excite exponential growth on a convective rather than diffusive scale in the presence of neutral waves, but growing waves alter that growth rate.

On the formation of longitudinal vortices in a turbulent boundary layer over wavy terrain

Parallel inviscid O(1) shear interacting with O(ε) spanwise-independent neutral rotational Rayleigh waves are used to model turbulent boundary layer flow over small-amplitude rigid wavy terrain. Of specific interest is the instability of the flow to spanwise-periodic initially exponentially growing longitudinal vortex modes via the Craik–Leibovich CL2-O(1) instability mechanism and whether it is this instability mechanism that gives rise to longitudinal vortices evident in the recent experiments of Gong et al. (1996). In modelling the flow, wave and turbulence length scales are assumed sufficiently disparate to cause minimal interaction. This allows the primary mean velocity profile to be specified. Two profiles were chosen: a power law and the logarithmic law of the wall. Important in wave–mean interactions of this class are the effect of wave-induced fluctuations upon the mean state and the influence of the developing mean flow on the fluctuating part of the motion. The former is described by a generalized Lagrangian-mean formulation; the latter by a modified Rayleigh equation. Together they comprise an eigenvalue problem for the growth rate appropriate to the initial stages of the instability. Both primary mean flows are unstable to longitudinal vortex form in the presence of Rayleigh waves whose amplitudes diminish with altitude. Moreover the interaction is most unstable for streamwise wavenumbers α = O(1), the growth rate increasing with increased spanwise wavenumber. In comparing the results with experiment, it is first shown that spanwise-independent waves excited in Gong et al.'s experiment depict velocity fluctuations whose amplitudes diminish with altitude in accord with those for appropriate Rayleigh waves. Concordantly, the longitudinal vortices depict transverse velocity components that are weaker by a factor of ε than the axial perturbation and are observed to grow at a rate consistent with exponential growth. All are key features of CL2-O(1), although the observed growth rate is not in accord with the maximal suggested by inviscid instability theory. Rather it appears that the spanwise wavenumber takes a value at which energy is extracted from the mean motion in an optimal volume-averaged sense while minimizing energy loss to both viscous dissipation and small-scale turbulence. It is concluded that the CL2-O(1) instability mechanism is physically realizable and that the data of Gong et al. represent the first documented observations thereof.