Inviscid dipole-vortex rebound from a wall or coast

1997 ◽  
Vol 351 ◽  
pp. 75-103 ◽  
Author(s):  
G. F. CARNEVALE ◽  
O. U. VELASCO FUENTES ◽  
P. ORLANDI
Keyword(s):  
Numerical Simulations ◽  
Laboratory Experiments ◽  
Vortex Tube ◽  
Water Dynamics ◽  
Angle Of Incidence ◽  
Initial Angle ◽  
Viscous Boundary Layer ◽  
Dipole Vortex ◽  
Vorticity Generation ◽  
Viscous Boundary

A vortex approaching a no-slip wall ‘rebounds’ due to the creation of vorticity at the wall in a viscous boundary layer. Here it is demonstrated that a purely inviscid mechanism can also produce vortex rebound from a slip wall. In inviscid vortex rebound, vortex tube stretching generates the necessary vorticity to allow rebound, eliminating the need for viscous vorticity generation. This vortex stretching mechanism is demonstrated through numerical simulations and laboratory experiments on dipole-vortex rebound from a boundary. In an application to oceanography, numerical simulations of both quasi-geostrophic and shallow water dynamics are used to show that the β-effect at an eastern boundary can produce this inviscid rebound. Through a series of numerical experiments in which the strength of the β-effect is varied, a formula for predicting the point of separation of the vortices from the boundary in a dipole–coast collision is deduced. Through simulations, the flux of vorticity and fluid away from the boundary is measured as a function of β and initial angle of incidence. It is found that, in contrast to viscous vortex rebound, which typically does not produce a flux of material away from the boundary farther than a distance comparable to the initial vortex radius, the β-induced rebound does carry fluid far from the coast. Laboratory experiments in a rotating tank are used to show that a sloping bottom can also provide an inviscid mechanism for dipole-vortex rebound from the wall of the tank under certain conditions. A relation determining the conditions under which inviscid or viscous processes will dominate in the rebound of the dipole from a boundary is obtained.

Vortices in oscillating spin-up

2007 ◽  
Vol 573 ◽  
pp. 339-369 ◽  
Author(s):  
M. G. WELLS ◽  
H. J. H. CLERCX ◽  
G. J. F. VAN HEIJST
Keyword(s):  
Numerical Simulations ◽  
Power Law ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Passive Scalar ◽  
Decay Rates ◽  
Small Scale ◽  
Two Dimensional ◽  
Ekman Pumping ◽  
Viscous Boundary Layer

Laboratory experiments and numerical simulations of oscillating spin-up in a square tank have been conducted to investigate the production of small-scale vorticity near the no-slip sidewalls of the container and the formation and subsequent decay of wall-generated quasi-two-dimensional vortices. The flow is made quasi-two-dimensional by a steady background rotation, and a small sinusoidal perturbation to the background rotation leads to the periodic formation of eddies in the corners of the tank by the roll-up of vorticity generated along the sidewalls. When the oscillation period is greater than the time scale required to advect a full-grown corner vortex to approximately halfway along the sidewall, dipole structures are observed to form. These dipoles migrate away from the walls, and the interior of the tank is continually filled with new vortices. The average size of these vortices appears to be largely controlled by the initial formation mechanism. Their vorticity decays from interactions with other stronger vortices that strip off filaments of vorticity, and by Ekman pumping at the bottom of the tank. Subsequent interactions between the weaker ‘old’ vortices and the ‘young’ vortices result in the straining, and finally the destruction, of older vortices. This inhibits the formation of large-scale vortices with diameters comparable to the size of the container.The laboratory experiments revealed a k−5/3 power law of the energy spectrum for small-to-intermediate wavenumbers. Measurements of the intensity spectrum of a passive scalar were consistent with the Batchelor prediction of a k−1 power law at large wavenumbers. Two-dimensional numerical simulations, under similar conditions to those in the experiments (with weak Ekman decay), were also performed and the simultaneous presence of a k−5/3 and k−3−ζ (with 0 < ζ « 1) power spectrum is observed, with the transition occurring at the wavenumber at which vorticity is injected from the viscous boundary layer into the interior. For higher Ekman decay rates, steeper spectra are obtained for the large wavenumber range, with ζ = O(1) and proportional to the Ekman decay rate. Movies are available with the online version of the paper.

scholarly journals Moisture gradients form a vapor cycle within the viscous boundary layer as an organizing principle to worker termites

2018 ◽  
Vol 66 (2) ◽  
pp. 193-209 ◽  
Author(s):  
R. Soar ◽  
G. Amador ◽  
P. Bardunias ◽  
J. S. Turner
Keyword(s):  
Boundary Layer ◽  
Viscous Boundary Layer ◽  
Viscous Boundary

Viscous boundary layers in reversing flow

1976 ◽  
Vol 74 (1) ◽  
pp. 59-79 ◽  
Author(s):  
T. J. Pedley
Keyword(s):  
Boundary Layer ◽  
Shear Rate ◽  
Leading Edge ◽  
Wall Shear Rate ◽  
Viscous Boundary Layer ◽  
Large Molecules ◽  
Displacement Thickness ◽  
The Mean ◽  
Wall Shear ◽  
Viscous Boundary

The viscous boundary layer on a finite flat plate in a stream which reverses its direction once (at t = 0) is analysed using an improved version of the approximate method described earlier (Pedley 1975). Long before reversal (t < −t1), the flow at a point on the plate will be quasi-steady; long after reversal (t > t2), the flow will again be quasi-steady, but with the leading edge at the other end of the plate. In between (−t1 < t < t2) the flow is governed approximately by the diffusion equation, and we choose a simple solution of that equation which ensures that the displacement thickness of the boundary layer remains constant at t = −t1. The results of the theory, in the form of the wall shear rate at a point as a function of time, are given both for a uniformly decelerating stream, and for a sinusoidally oscillating stream which reverses its direction twice every cycle. The theory is further modified to cover streams which do not reverse, but for which the quasi-steady solution breaks down because the velocity becomes very small. The analysis is also applied to predict the wall shear rate at the entrance to a straight pipe when the core velocity varies with time as in a dog's aorta. The results show positive and negative peak values of shear very much larger than the mean. They suggest that, if wall shear is implicated in the generation of atherosclerosis because it alters the permeability of the wall to large molecules, then an appropriate index of wall shear at a point is more likely to be the r.m.s. value than the mean.

On one-dimensional unsteady flow at infinite Mach number

1968 ◽  
Vol 304 (1478) ◽  
pp. 255-273 ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Blast Wave ◽  
Outer Part ◽  
The Body ◽  
Viscous Boundary Layer ◽  
Outer Flow ◽  
Hypersonic Speeds ◽  
Set Up ◽  
Viscous Boundary ◽  
Infinite Set

The use of the blast-wave analogy, as an aid to the interpretation of experimental data on the motion of a fluid past an obstacle at hypersonic speeds, has led to the theoretical study of its role in an asymptotic expansion of the solution to the governing equations at large distances downstream of the body. In all attempts to set up such an expansion it has proved necessary to divide the flow régime into two parts, an outer part dominated by the blast wave and an inner part consisting of streamlines which, originally, pass close by the body. The matching of these two regions is apparently only possible if a certain integral vanishes. In the present paper a numerical integration, in one particular set of circumstances, is carried out to test the validity of the asymptotic expansion proposed. Formally, an unsteady problem is tackled, for ease of computation, but the steady analogue follows immediately and is of exactly the form discussed in the earlier investigations. It is found that the main results are in line with the theory and that the integral in question is indistinguishable from zero. However, a deeper investigation of the asymptotic expansion shows that, for an expansion of the type envisaged, an infinite set of integrals must each vanish. The next integral does not appear to be zero according to our computations but this result is not believed to be conclusive. Assuming that all the integrals do vanish, then it appears that the inner layer, which although inviscid, has many of the characteristics of a viscous boundary layer, has the addi­tional, surprising property that it can exert no direct influence on the outer flow at large distances downstream of the body.

scholarly journals An experimental and theoretical investigation of particle–wall impacts in a T-junction

2013 ◽  
Vol 727 ◽  
pp. 236-255 ◽  
Author(s):  
D. Vigolo ◽  
I. M. Griffiths ◽  
S. Radl ◽  
H. A. Stone
Keyword(s):  
Flow Direction ◽  
Three Dimensional ◽  
Stokes Number ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Viscous Boundary Layer ◽  
Particle Tracing ◽  
Two Dimensional Model ◽  
Viscous Boundary ◽  
The Impact

AbstractUnderstanding the behaviour of particles entrained in a fluid flow upon changes in flow direction is crucial in problems where particle inertia is important, such as the erosion process in pipe bends. We present results on the impact of particles in a T-shaped channel in the laminar–turbulent transitional regime. The impacting event for a given system is described in terms of the Reynolds number and the particle Stokes number. Experimental results for the impact are compared with the trajectories predicted by theoretical particle-tracing models for a range of configurations to determine the role of the viscous boundary layer in retarding the particles and reducing the rate of collision with the substrate. In particular, a two-dimensional model based on a stagnation-point flow is used together with three-dimensional numerical simulations. We show how the simple two-dimensional model provides a tractable way of understanding the general collision behaviour, while more advanced three-dimensional simulations can be helpful in understanding the details of the flow.

PC-Based Computer Modeling of Combustion Processes

1999 ◽  
Author(s):  
Greg W. Gmurczyk ◽  
Ashwani K. Gupta
Keyword(s):  
Numerical Simulations ◽  
Computer Modeling ◽  
Numerical Experiments ◽  
Laboratory Experiments ◽  
Combustion Process ◽  
Numerical Algorithms ◽  
Computer Hardware ◽  
Simplifying Assumptions ◽  
High Level ◽  
Analytical Approaches

Abstract Constant and significant progress in both computer hardware and numerical algorithms, in recent years, have made it possible to investigate complex phenomena in engineering systems using computer modeling and simulations. Advanced numerical simulations can be treated as an extension of traditional analytical-theoretical analyses. In such cases, some of the simplifying assumptions can usually be dropped and the nonlinear interactions between various processes can be captured. One of the most complex engineering processes encountered in industry is a combustion process utilized either for power/thrust generation or incineration. However, even nowadays, because of the high level of complexity of the general problem of a combustion process in practical systems, it is not currently possible to simulate directly all the length and time scales of interest. Simplifying assumptions still need to be made, but they can be less drastic than in analytical approaches. Therefore, another view of numerical simulations is as a tool to simulate idealized systems and conduct numerical experiments. Such numerical experiments can be complementary to laboratory experiments and can also provide more detailed, nonintrusive diagnostics. Therefore, simulations, along with theory and laboratory experiments, can provide a more complete picture and better understanding of a combustion process. As an example of computer modeling of industrial combustion systems, an enclosed spray flame was considered. Such a flame can frequently be encountered in power generation units, turbine engines, and incinerators. Both the physical and mathematical models were formulated based on data from earlier laboratory studies and results obtained for open air spray flames. The purpose of this study was to use those data as model input to predict the characteristics of a confined flame and provide a means of optimizing the system design with a PC computer.

A weakly nonlinear framework to study shock–vorticity interaction

2022 ◽  
Vol 933 ◽  
Author(s):  
Pranav Thakare ◽  
Vineeth Nair ◽  
Krishnendu Sinha
Keyword(s):  
Numerical Simulations ◽  
Acoustic Waves ◽  
Significant Contribution ◽  
Interaction Analysis ◽  
Nonlinear Effects ◽  
Normal Shock ◽  
Linear Interaction ◽  
Weakly Nonlinear ◽  
High Incidence ◽  
Vorticity Generation

Linear interaction analysis (LIA) is routinely used to study the shock–turbulence interaction in supersonic and hypersonic flows. It is based on the inviscid interaction of elementary Kovásznay modes with a shock discontinuity. LIA neglects nonlinear effects, and hence it is limited to small-amplitude disturbances. In this work, we extend the LIA framework to study the fundamental interaction of a two-dimensional vorticity wave with a normal shock. The predictions from a weakly nonlinear framework are compared with high-order accurate numerical simulations over a range of wave amplitudes ( $\epsilon$ ), incidence angles ( $\alpha$ ) and shock-upstream Mach numbers ( $M_1$ ). It is found that the nonlinear generation of vorticity at the shock has a significant contribution from the intermodal interaction between vorticity and acoustic waves. Vorticity generation is also strongly influenced by the curvature of the normal shock wave, especially for high incidence angles. Further, the weakly nonlinear analysis is able to predict the correct scaling of the nonlinear effects observed in the numerical simulations. The analysis also predicts a Mach number dependent limit for the validity of LIA in terms of the maximum possible amplitude of the upstream vorticity wave.

Sign in / Sign up

Export Citation Format

Share Document