Flow Past Rotating Cylinders: Effect of Eccentricity

2000 ◽  
Vol 68 (4) ◽  
pp. 543-552 ◽  
Author(s):  
S. Mittal
Keyword(s):  
Steady State ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Steady State Solution ◽  
Rotating Cylinder ◽  
Computational Results ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Mean Values ◽  
Flow Past

Computational results are presented for flows past a translating and rotating circular cylinder. A stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation. To validate the formulation and its implementation certain cases, for which the flow visualization and computational results have been reported by other researchers, are computed. Results are presented for Re=5, 200 and 3800 and rotation rate, (ratio of surface speed of cylinder to the freestream speed of flow), of 5. For all these cases the flow reaches a steady state. The values of lift coefficient observed for these flows exceed the limit on the maximum value of lift coefficient suggested by Goldstein based on intuitive arguments by Prandtl. These observations are in line with measurements reported, earlier, by other researchers via laboratory experiments. To investigate the stability of the computed steady-state solution, receptivity studies involving an eccentrically rotating cylinder are carried out. Computations are presented for flow past a rotating cylinder with wobble; the center of rotation of the cylinder does not match its geometric center. These computations are also important from the point of view that in a real situation it is almost certain that the rotating cylinder will be associated with a certain degree of wobble. In such cases the flow is unsteady and reaches a temporally periodic state. However, the mean values of the aerodynamic coefficients and the basic flow structure are still quite comparable to the case without any wobble. In this sense, it is found that the two-dimensional solution is stable to purely two-dimensional disturbances.

Flow past a rotating cylinder

2003 ◽  
Vol 476 ◽  
pp. 303-334 ◽  
Author(s):  
SANJAY MITTAL ◽  
BHASKAR KUMAR
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Stability Analysis ◽  
Vortex Shedding ◽  
Rotation Rate ◽  
Rotating Cylinder ◽  
Two Dimensional ◽  
Stabilized Finite Element ◽  
Rotation Rates ◽  
Flow Past

Flow past a spinning circular cylinder placed in a uniform stream is investigated via two-dimensional computations. A stabilized finite element method is utilized to solve the incompressible Navier–Stokes equations in the primitive variables formulation. The Reynolds number based on the cylinder diameter and free-stream speed of the flow is 200. The non-dimensional rotation rate, α (ratio of the surface speed and freestream speed), is varied between 0 and 5. The time integration of the flow equations is carried out for very large dimensionless time. Vortex shedding is observed for α < 1.91. For higher rotation rates the flow achieves a steady state except for 4.34 < α < 4:70 where the flow is unstable again. In the second region of instability, only one-sided vortex shedding takes place. To ascertain the instability of flow as a function of α a stabilized finite element formulation is proposed to carry out a global, non-parallel stability analysis of the two-dimensional steady-state flow for small disturbances. The formulation and its implementation are validated by predicting the Hopf bifurcation for flow past a non-rotating cylinder. The results from the stability analysis for the rotating cylinder are in very good agreement with those from direct numerical simulations. For large rotation rates, very large lift coefficients can be obtained via the Magnus effect. However, the power requirement for rotating the cylinder increases rapidly with rotation rate.

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.

scholarly journals Instability of transonic flow past flattened airfoils

2013 ◽  
Vol 3 (4) ◽  
Author(s):  
Alexander Kuzmin
Keyword(s):  
Numerical Modeling ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Simulations ◽  
Flow Past ◽  
Coefficient Versus

AbstractTransonic flow past a Whitcomb airfoil and two modifications of it at Reynolds numbers of the order of ten millions is studied. The numerical modeling is based on the system of Reynolds-averaged Navier-Stokes equations. The flow simulations show that variations of the lift coefficient versus the angle of attack become more abrupt with decreasing curvature of the airfoil in the midchord region. This is caused by an instability of closely spaced local supersonic regions on the upper surface of the airfoil.

Free Convection in a Two-Dimensional Porous Loop

1986 ◽  
Vol 108 (2) ◽  
pp. 277-283 ◽  
Author(s):  
L. Robillard ◽  
T. H. Nguyen ◽  
P. Vasseur
Keyword(s):  
Steady State ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Outer Boundary ◽  
Convective Motion ◽  
Steady State Solution ◽  
Temperature Fields ◽  
Maximum Temperature ◽  
Two Dimensional ◽  
Convective Cells

A study is made of the natural convection in an annular porous layer having an isothermal inner boundary and its outer boundary subjected to a thermal stratification arbitrarily oriented with respect to gravity. For such conditions, no symmetry can be expected for the flow and temperature fields with respect to the vertical diameter and the whole circular region must be considered. Two-dimensional steady-state solutions are sought by perturbation and numerical approaches. Results obtained indicate that the circulating flow around the annulus attains its maximum strength when the stratification is horizontal (heating from the side). This circulating flow is responsible for an important heat exchange between the porous layer and its external surroundings. The flow field is also characterized by the presence of two convective cells near the inner boundary, giving rise to flow reversal on this surface. When the maximum temperature on the outer boundary is at the bottom of the cavity, the convective motion becomes potentially unstable; for a Rayleigh number below 80, there exists a steady-state solution symmetrical with respect to both vertical and horizontal axes; for a Rayleigh number above 80, an unsteady periodic situation develops with the circulating flow alternating its direction around the annulus.

scholarly journals Simulation of flow past two tandem cylinders using deterministic vortex method

2012 ◽  
Vol 16 (5) ◽  
pp. 1460-1464 ◽  
Author(s):  
Guo Huang ◽  
Haiming Huan ◽  
Xiaoliang Xu ◽  
Yu Liu
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Sudden Change ◽  
Vortex Method ◽  
Simulation Method ◽  
Critical Distance ◽  
Navier Stokes ◽  
Tandem Cylinders ◽  
Flow Past

The vortex method is a direct numerical simulation method for solving the Navier-Stokes equations. In order to reveal the influence of Reynolds number and distances between the cylinders, the incompressible flow past a pair of tandem cylinders is solved on the base of the vortex method. The results show that for the flow past two tandem cylinders, there is a critical distance of the tandem cylinders. Over the critical distance, the flow field will have a sudden change, and the drag coefficient, lift coefficient and Strouhal number will also change dramatically. The critical distance will diminish as the Reynolds number rises.

scholarly journals On the uniqueness of steady flow past a rotating cylinder with suction

2000 ◽  
Vol 411 ◽  
pp. 213-232 ◽  
Author(s):  
E. V. BULDAKOV ◽  
S. I. CHERNYSHENKO ◽  
A. I. RUBAN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Cross Flow ◽  
Rotation Velocity ◽  
Rotating Cylinder ◽  
Large Reynolds Number ◽  
Order Unity ◽  
Flow Past ◽  
Exponentially Small

The subject of this study is a steady two-dimensional incompressible flow past a rapidly rotating cylinder with suction. The rotation velocity is assumed to be large enough compared with the cross-flow velocity at infinity to ensure that there is no separation. High-Reynolds-number asymptotic analysis of incompressible Navier–Stokes equations is performed. Prandtl's classical approach of subdividing the flow field into two regions, the outer inviscid region and the boundary layer, was used earlier by Glauert (1957) for analysis of a similar flow without suction. Glauert found that the periodicity of the boundary layer allows the velocity circulation around the cylinder to be found uniquely. In the present study it is shown that the periodicity condition does not give a unique solution for suction velocity much greater than 1/Re. It is found that these non-unique solutions correspond to different exponentially small upstream vorticity levels, which cannot be distinguished from zero when considering terms of only a few powers in a large Reynolds number asymptotic expansion. Unique solutions are constructed for suction of order unity, 1/Re, and 1/√Re. In the last case an explicit analysis of the distribution of exponentially small vorticity outside the boundary layer was carried out.

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