A family of steady, translating vortex pairs with distributed vorticity

1980 ◽  
Vol 99 (1) ◽  
pp. 129-144 ◽  
Author(s):  
R. T. Pierrehumbert
Keyword(s):  
Steady State ◽  
Vortex Pair ◽  
Relaxation Method ◽  
Numerical Results ◽  
Inviscid Fluid ◽  
Approximate Theory ◽  
Experimental Production ◽  
Vortex Pairs ◽  
The Family ◽  
Axis Of Symmetry

An efficient relaxation method is developed for computing the properties of a family of vortex pairs with distributed vorticity, propagating without change of shape through a homogeneous, inviscid fluid. The numerical results indicate that a steady state exists even when the gap between vortices is arbitrarily small, and that as the gap closes the steady state approaches a limiting vortex pair with a cusp on the axis of symmetry. Comparison is made with an approximate theory due to Saffman, and agreement is found to be good until the vortices are almost touching. The energy of members of the family is computed, and possible means of experimental production are discussed.

scholarly journals Computational Performance of Disparate Lattice Boltzmann Scenarios under Unsteady Thermal Convection Flow and Heat Transfer Simulation

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 65
Author(s):  
Aditya Dewanto Hartono ◽  
Kyuro Sasaki ◽  
Yuichi Sugai ◽  
Ronald Nguele
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Natural Convection ◽  
Lattice Boltzmann ◽  
Numerical Results ◽  
Convection And Heat Transfer ◽  
Steady State Condition ◽  
Physical Systems ◽  
Flow And Heat Transfer ◽  
Computational Performance

The present work highlights the capacity of disparate lattice Boltzmann strategies in simulating natural convection and heat transfer phenomena during the unsteady period of the flow. Within the framework of Bhatnagar-Gross-Krook collision operator, diverse lattice Boltzmann schemes emerged from two different embodiments of discrete Boltzmann expression and three distinct forcing models. Subsequently, computational performance of disparate lattice Boltzmann strategies was tested upon two different thermo-hydrodynamics configurations, namely the natural convection in a differentially-heated cavity and the Rayleigh-Bènard convection. For the purposes of exhibition and validation, the steady-state conditions of both physical systems were compared with the established numerical results from the classical computational techniques. Excellent agreements were observed for both thermo-hydrodynamics cases. Numerical results of both physical systems demonstrate the existence of considerable discrepancy in the computational characteristics of different lattice Boltzmann strategies during the unsteady period of the simulation. The corresponding disparity diminished gradually as the simulation proceeded towards a steady-state condition, where the computational profiles became almost equivalent. Variation in the discrete lattice Boltzmann expressions was identified as the primary factor that engenders the prevailed heterogeneity in the computational behaviour. Meanwhile, the contribution of distinct forcing models to the emergence of such diversity was found to be inconsequential. The findings of the present study contribute to the ventures to alleviate contemporary issues regarding proper selection of lattice Boltzmann schemes in modelling fluid flow and heat transfer phenomena.

scholarly journals The approach of a vortex pair to a plane surface in inviscid fluid

1979 ◽  
Vol 92 (3) ◽  
pp. 497-503 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Approximate Calculation ◽  
Plane Surface ◽  
Vortex Pair ◽  
Plane Wall ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Axis Ratio ◽  
Local Rate

It is shown that a symmetrical vortex pair consisting of equal and opposite vortices approaching a plane wall at right angles must approach the wall monotonically in the absence of viscous effects. An approximate calculation is carried out for uniform vortices in which the vortices are assumed to be deformed into ellipses whose axis ratio is determined by the local rate of strain according to the results of Moore & Saffman (1971).

Analysis of Twisting Stiffness for a Multifiber Composite Layer

1974 ◽  
Vol 41 (3) ◽  
pp. 658-662 ◽  
Author(s):  
C. W. Bert ◽  
S. Chang
Keyword(s):  
Cross Section ◽  
Least Squares Method ◽  
Rectangular Cross Section ◽  
Torsional Rigidity ◽  
Composite Layer ◽  
Circular Cross Section ◽  
Relaxation Method ◽  
Fiber Composites ◽  
Numerical Results ◽  
Torsion Problem

The twisting stiffness of a rectangular cross section consisting of a single row of solid circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Dirichlet torsion problem of a multielement region and solved by the boundary-point least-squares method. Numerical results for a single-fiber square cross section compare favorably with previous relaxation-method results. New numerical results for three and five-fiber composites suggest that the torsional rigidity of a multifiber composite can be approximated from the torsional rigidities of single and three-fiber models.

The Effects of Energy Dissipation on the Transition to Planing of a Boat

1989 ◽  
Vol 33 (01) ◽  
pp. 35-46
Author(s):  
P. M. Naghdi ◽  
M. B. Rubin
Keyword(s):  
Steady State ◽  
Energy Dissipation ◽  
Detailed Analysis ◽  
Leading Edge ◽  
Steady State Solution ◽  
State Solution ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Spray Formation ◽  
Propulsion Force

The problem of the transition to planing of a boat, in the presence of the effect of spray formation at the boat's leading edge, is investigated using a nonlinear steady-state solution of the equations of the theory of a directed fluid sheet for two-dimensional motion of an incompressible inviscid fluid. The motion of the fluid is coupled with the motion of the free-floating boat and detailed analysis is undertaken pertaining to such features as trim angle, sinkage, and propulsion force. The effects of the rate of energy dissipation arising from spray formation at the boat's leading edge, and changes in equilibrium depth, propulsion angle, and the boat's weight, are studied and shown to significantly influence the boat's planing characteristics.

The control of a multipurpose reservoir

1976 ◽  
Vol 8 (03) ◽  
pp. 592-609 ◽  
Author(s):  
John Haslett
Keyword(s):  
Steady State ◽  
Cost Function ◽  
Optimal Policy ◽  
Numerical Results ◽  
Full Description ◽  
Potential Cost ◽  
Stochastic Behaviour ◽  
Accounting Procedure ◽  
Multipurpose Reservoir

A technique known as potential cost, used by Faddy [3] for assessing the operation of a dam is seen to be capable of extension to allow for (i) a very general cost function, as is required for a multipurpose reservoir (the norm nowadays) and (ii) the use of discounting of future costs, a very widespread accounting procedure. Numerical results are obtained for an optimal policy based on such an assessment, and demonstrate the need for an accurate specification of the costs associated with the operation of a reservoir. As a by-product a very full description of the steady-state stochastic behaviour of the dam is obtained.

Direct Numerical Simulation of Single and Multiple Square Jets in Cross-Flow

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Y. Yao ◽  
M. Maidi
Keyword(s):  
Cross Flow ◽  
Vortex Pair ◽  
Flow Structures ◽  
Computational Domain ◽  
Freestream Velocity ◽  
Adjacent Edge ◽  
Vortex Pairs ◽  
Jet In Cross Flow ◽  
Edge Distance ◽  
Square Jets

Direct numerical simulations (DNSs) have been carried out for single and multiple square jets issuing normally into a cross-flow, with the primary aim of studying the flow structures and interaction mechanisms associated with the jet in cross-flow (JICF) problems. The single JICF configuration follows a similar study previously done by Sau et al. (2004, Phys. Rev. E, 69, p. 066302) and the multiple JICF configurations are arranged side-by-side in the spanwise direction with a jet-to-jet adjacent edge distance (H) for the twin-jet case and an additional third jet downstream along the centerline with a jet-to-jet adjacent edge distance (L) for the triple-jet case. Simulations are performed for two twin-jet cases with H=1D,2D, respectively, and for one triple-jet case with H=1D, L=2D, where D is the jet exit width. Flow conditions similar to Sau et al. are considered, i.e., the jet to the cross-flow velocity ratio R=2.5 and the Reynolds number 225, based on the freestream velocity and the jet exit width. For the single jet in cross-flow, the vortical structures from our DNS are in good qualitative agreement with the findings of Sau et al. For the side-by-side twin-jet configuration, results have shown that the merging process of the two initially separated counter-rotating vortex pairs (CRVPs) from each jet hole exit is strongly dependent on the jet-to-jet adjacent edge distance H with earlier merging observed for the case H=1D. Downstream, the flow is dominated by a larger CRVP structure, accompanied by a smaller inner vortex pair. The inner vortex pair is found not to survive in the far-field as it rapidly dissipates before exiting the computational domain. These observations are in good agreement with the experimental findings in the literature. Simulations of the triple-jet in cross-flow case have shown some complicated jet-jet and jet-cross-flow interactions with three vortex pairs observed downstream, significantly different from that seen in the twin-jet cases. The evidence of these flow structures and interaction characteristics could provide a valuable reference database for future in-depth flow physics studies of laboratory experimental and numerical investigations.

scholarly journals Some estimates on the space scales of vortex pairs emitted from river mouths

2001 ◽  
Vol 8 (1/2) ◽  
pp. 1-7 ◽  
Author(s):  
V. P. Goncharov ◽  
V. I. Pavlov
Keyword(s):  
Point Vortex ◽  
Vortex Pair ◽  
Vortex Structures ◽  
Shelf Zone ◽  
Vortex Pairs ◽  
Polygonal Boundary ◽  
Dipole Vortex ◽  
Qualitative Classification ◽  
River Mouths

Abstract. Two-dimensional vortex pairs are frequently observed in geophysical conditions, for example, in a shelf zone of the ocean near river mouths. The main aims of the work are to estimate the space scales of such vortex structures, to analyze possible scenarios of vortex pair motion and to give the qualitative classification of their trajectories. We discuss some features of the motion of strong localized vorticity concentrations in a given flow in the presence of boundaries. The analyses are made in the framework of a 2D point vortex mo-del with an open polygonal boundary. Estimations are made for the characteristic parameters of dipole vortex structures emitted from river mouths into the open ocean.

Thermoplastic Instability for the Transient Contact Problem of Two Sliding Half-Planes

1986 ◽  
Vol 53 (3) ◽  
pp. 565-572 ◽  
Author(s):  
A. Azarkhin ◽  
J. R. Barber
Keyword(s):  
Steady State ◽  
Pressure Distribution ◽  
Half Plane ◽  
Initial Pressure ◽  
Approximate Solutions ◽  
Steady State Solution ◽  
Fourier Integral ◽  
Numerical Results ◽  
Initial Size ◽  
Transient Contact

We study the time dependent problem of a nonconducting half-plane sliding on the surface of a conductor with heat generation at the interface due to friction. The conducting half-plane is slightly rounded to give a Hertzian initial pressure distribution. Relationships are established for temperature and thermoelastic displacements due to a heat input of cosine type through the surface, and then these are used to obtain the solution in the form of a double Fourier integral. Numerical results show that, if the ratio of the initial size of the area of contact to that in the steady state is less than some critical value, the area of contact and the pressure distribution change smoothly toward the steady state solution. Otherwise the area of contact goes through bifurcation. The bifurcation accelerates the process. Numerical results are compared with previous approximate solutions.

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