Estimation of critical rotation rates for suppression of steady separation bubble behind a circular cylinder

Context. Eclipsing time variations are observed in many close binary systems. In particular, for several post-common-envelope binaries (PCEBs) that consist of a white dwarf and a main sequence star, the observed-minus-calculated (O–C) diagram suggests that real or apparent orbital period variations are driven by Jupiter-mass planets or as a result of magnetic activity, the so-called Applegate mechanism. The latter explains orbital period variations as a result of changes in the stellar quadrupole moment due to magnetic activity. Aims. In this work we explore the feasibility of driving eclipsing time variations via the Applegate mechanism for a sample of PCEB systems, including a range of different rotation rates. Methods. We used the MESA code to evolve 12 stars with different masses and rotation rates. We applied simple dynamo models to their radial profiles to investigate the scale at which the predicted activity cycle matches the observed modulation period, and quantifiy the uncertainty. We further calculated the required energies to drive the Applegate mechanism. Results. We show that the Applegate mechanism is energetically feasible in 5 PCEB systems. In RX J2130.6+4710, it may be feasible as well considering the uncertainties. We note that these are the systems with the highest rotation rate compared to the critical rotation rate of the main-sequence star. Conclusions. The results suggest that the ratio of physical to critical rotation rate in the main sequence star is an important indicator for the feasibility of Applegate’s mechanism, but exploring larger samples will be necessary to probe this hypothesis.

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Effect of high rotation rates on the laminar flow around a circular cylinder

Physics of Fluids ◽

10.1063/1.1492811 ◽

2002 ◽

Vol 14 (9) ◽

pp. 3160-3178 ◽

Cited By ~ 118

Author(s):

D. Stojković ◽

M. Breuer ◽

F. Durst

Keyword(s):

Laminar Flow ◽

Circular Cylinder ◽

Rotation Rates

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A note on the stability of inviscid zonal jet flows on a rotating sphere

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.356 ◽

2012 ◽

Vol 710 ◽

pp. 154-165 ◽

Cited By ~ 4

Author(s):

Eiichi Sasaki ◽

Shin-ichi Takehiro ◽

Michio Yamada

Keyword(s):

Linear Stability ◽

Shooting Method ◽

Jet Flows ◽

Zonal Flows ◽

Rotating Sphere ◽

Rotation Rates ◽

Critical Rotation ◽

Critical Layers ◽

The Stability ◽

Linear Stability Problem

AbstractThe linear stability of inviscid zonal jet flows on a rotating sphere is re-examined. A semi-circle theorem for inviscid zonal flows on a rotating sphere is proved. It is also shown that numerically obtained eigenvalues of the linear stability problem do not converge well with a spectral method which was adopted in previous studies, due to an emergence of critical layers near the poles. By using a shooting method where the integral path bypasses the critical layers in the complex plane, the eigenvalues are successfully obtained with ${\ensuremath{\sim} }10\hspace{0.167em} \% $ correction of the critical rotation rates compared to those obtained in Baines (J. Fluid Mech., vol. 73, 1976, pp. 193–213).

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Cavitation Inception on a Circular Cylinder at Critical and Supercritical Flow Range

Journal of Fluids Engineering ◽

10.1115/1.3242598 ◽

1986 ◽

Vol 108 (4) ◽

pp. 421-427 ◽

Cited By ~ 6

Author(s):

A. Ihara ◽

H. Murai

Keyword(s):

Circular Cylinder ◽

Separation Bubble ◽

Circular Cylinders ◽

Critical Flow ◽

Laminar Separation Bubble ◽

Supercritical Flow ◽

Laminar Separation ◽

Cavitation Inception ◽

Rear Part ◽

Axisymmetric Bodies

Cavitation tests were performed in the critical and supercritical flow range on circular cylinders with and without boundary layer trip. Mean and fluctuating static pressures were meausred on the smooth circular cylinder from θ = 0 to 180° and on the tripped surface at θ = 104 and 106° corresponding to tripping wire location α = 38 and 40 deg. Through these measurements it was found that cavitation that closely resembles bubble ring cavitation reported on axisymmetric bodies took palce in a reattachment region of the laminar separation bubble for the critical flow range where the laminar separation bubble was present. For the supercritical flow range where the laminar separation bubble disappeared, smooth cavitation with small irregular bubbles at its rear part took place at a location about 100° from the stagnation point.

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Instability and sensitivity of the flow around a rotating circular cylinder

Journal of Fluid Mechanics ◽

10.1017/s0022112009993764 ◽

2010 ◽

Vol 650 ◽

pp. 513-536 ◽

Cited By ~ 92

Author(s):

JAN O. PRALITS ◽

LUCA BRANDT ◽

FLAVIO GIANNETTI

Keyword(s):

Circular Cylinder ◽

Passive Control ◽

Base Flow ◽

Structural Sensitivity ◽

Rotation Rates ◽

Rotating Circular Cylinder ◽

Flow Stagnation ◽

Two Dimensional Flow ◽

Classic Approach ◽

Structural Sensitivity Analysis

The two-dimensional flow around a rotating circular cylinder is studied at Re = 100. The instability mechanisms for the first and second shedding modes are analysed. The region in the flow with a role of ‘wavemaker’ in the excitation of the global instability is identified by considering the structural sensitivity of the unstable mode. This approach is compared with the analysis of the perturbation kinetic energy production, a classic approach in linear stability analysis. Multiple steady-state solutions are found at high rotation rates, explaining the quenching of the second shedding mode. Turning points in phase space are associated with the movement of the flow stagnation point. In addition, a method to examine which structural variation of the base flow has the largest impact on the instability features is proposed. This has relevant implications for the passive control of instabilities. Finally, numerical simulations of the flow are performed to verify that the structural sensitivity analysis is able to provide correct indications on where to position passive control devices, e.g. small obstacles, in order to suppress the shedding modes.

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Drag and pressure fields for the MHD flow around a circular cylinder at intermediate Reynolds numbers

Journal of Applied Mathematics ◽

10.1155/jam.2005.183 ◽

2005 ◽

Vol 2005 (3) ◽

pp. 183-203 ◽

Cited By ~ 7

Author(s):

T. V. S. Sekhar ◽

R. Sivakumar ◽

T. V. R. Ravi Kumar

Keyword(s):

Circular Cylinder ◽

Drag Coefficient ◽

Stagnation Point ◽

Stokes Equations ◽

Separation Bubble ◽

Flow Direction ◽

Boundary Layer Separation ◽

Pressure Fields ◽

Correction Technique ◽

Rear Stagnation Point

Steady incompressible flow around a circular cylinder in an external magnetic field that is aligned with fluid flow direction is studied forRe(Reynolds number) up to 40 and the interaction parameter in the range0≤N≤15(or0≤M≤30), whereMis the Hartmann number related toNby the relationM=2NRe, using finite difference method. The pressure-Poisson equation is solved to find pressure fields in the flow region. The multigrid method with defect correction technique is used to achieve the second-order accurate solution of complete nonlinear Navier-Stokes equations. It is found that the boundary layer separation at rear stagnation point forRe=10is suppressed completely whenN<1and it started growing again whenN≥9. ForRe=20and 40, the suppression is not complete and in addition to that the rear separation bubble started increasing whenN≥3. The drag coefficient decreases for low values ofN(<0.1)and then increases with increase ofN. The pressure drag coefficient, total drag coefficient, and pressure at rear stagnation point vary withN. It is also found that the upstream and downstream pressures on the surface of the cylinder increase for low values ofN(<0.1)and rear pressure inversion occurs with further increase ofN. These results are in agreement with experimental findings.

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Uniaxial and biaxial nematic liquid crystals

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2006.1846 ◽

2006 ◽

Vol 364 (1847) ◽

pp. 2681-2696 ◽

Cited By ~ 48

Author(s):

T.J Dingemans ◽

L.A Madsen ◽

N.A Zafiropoulos ◽

Wenbin Lin ◽

E.T Samulski

Keyword(s):

Nematic Phase ◽

Mean Field ◽

Rotation Frequency ◽

General Context ◽

Rotation Rates ◽

Critical Rotation ◽

Biaxial Nematics ◽

Nematic Phases ◽

Lower Temperature ◽

Biaxial Nematic

The unusual exhibition of a biaxial nematic phase in nonlinear thermotropic mesogens derived from the 2,5-oxadiazole biphenol (ODBP) core is placed in a general context; the uniaxial nematic phase of the prototypical rod-like mesogen para -quinquephenyl does not follow the classical mean-field behaviour of nematics, thus questioning the utility of such theories for quantitative predictions about biaxial nematics. The nuclear magnetic resonance spectra of labelled probe molecules dissolved in ODBP biaxial nematic phases suggest that a second critical rotation frequency, related to the differences in the transverse diamagnetic susceptibilities of the biaxial nematic, must be exceeded in order to create an aligned two-dimensional powder sample. Efforts to find higher viscosity and lower temperature biaxial nematics (with lower critical rotation rates) to confirm the above conjecture are described. Several chemical modifications of the ODBP mesogenic core are presented.

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Time-dependent viscous flow past an impulsively started rotating and translating circular cylinder

Journal of Fluid Mechanics ◽

10.1017/s0022112085002725 ◽

1985 ◽

Vol 158 ◽

pp. 447-488 ◽

Cited By ~ 123

Author(s):

H. M. Badr ◽

S. C. R. Dennis

Keyword(s):

Circular Cylinder ◽

Differential Equations ◽

Numerical Study ◽

Separated Flow ◽

Time Dependent ◽

Initial Development ◽

Rotation Rates ◽

Finite Set ◽

Small Times ◽

Two Dimensional Flow

A numerical study is made of the development with time of the two-dimensional flow of a viscous, incompressible fluid around a circular cylinder which suddenly starts rotating about its axis with constant angular velocity and translating at right angles to this axis with constant speed. The governing partial differential equations in two space variables and time are reduced to sets of time-dependent equations in one space variable by means of Fourier analysis. By truncating the Fourier series to a finite number of terms, a finite set of differential equations is solved to give an approximation to the theoretical flow. The solutions are obtained by numerical methods. Results are given for the initial development with time of the asymmetrical wake at the rear of the cylinder at Reynolds numbers R [ges ] 200, based on the diameter of cylinder, and at small rotation rates. The detailed results show the formation of a Kármán vortex street. The time development of this separated flow is compared in detail at R = 200 with recent experimental results. The details of the formation and movement of the vortices behind the cylinder and the velocity profiles in several locations are virtually identical in the experimental and theoretical studies. The variations with time of the lift, drag and moment exerted by the fluid on the cylinder are determined both by calculations and by means of approximate analytical expressions. The agreement between these results at small times is excellent.

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An investigation into the nonstationary characteristics of separation-bubble formation on a smooth circular cylinder in the critical transition range

Journal of Mechanics ◽

10.1093/jom/ufab011 ◽

2021 ◽

Vol 37 ◽

pp. 415-431

Author(s):

Yi-Huei Lai ◽

Jiun-Jih Miau

Keyword(s):

Circular Cylinder ◽

Time Scales ◽

Time Scale ◽

Separation Bubble ◽

Bubble Formation ◽

Small Scale ◽

Critical Transition ◽

Transitional Regime ◽

Transition Range ◽

Pressure Signal

Abstract To investigate the characteristics of the separation-bubble formation of flow over a smooth circular cylinder in the critical transition range, a sliding-window (SW) method and a peak-valley (PV) method were proposed to identify the intermittent jumps, named the characteristic events, in the real-time pressure signal obtained on both sides of the cylinder model. By evaluating the counts of the qualified events of the SW and PV methods, the PV method was found less sensitive to the small-scale disturbances in the pressure signal, therefore was adopted for later analysis. With the PV method, the characteristic events were identified from the pressure signal and categorized into two types: Type-1 is referred to the events of pressure descending and Type-2 is referred to the events of pressure ascending. Subsequently, the count per minute of the characteristic events was determined for describing the intermittency of the separation-bubble formation, and the time scale of each of the characteristic event was regarded as the time length of the separation-bubble formation. The count per minute of the characteristic events appeared to be the highest in the transitional regime. While the time scales of the characteristic events were varying with Reynolds number, the weighting-averaged normalized time scales in the transitional regime of the three cases studied were found comparable to the normalized time scale of the lift jump noted in the literature. Physically, the characteristic events found in the pressure signals in this study can be attributed to the three-dimensional aspect of separation-bubble formation.

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