A NUMERICAL INVESTIGATION OF THE FLOW IN A FULLY BLOCKED DIFFERENTIALLY HEATED ROTATING FLUID ANNULUS

1994 ◽  
Vol 05 (02) ◽  
pp. 203-206 ◽  
Author(s):  
Q.G. RAYER
Keyword(s):  
Computational Model ◽  
Horizontal Plane ◽  
Computer Modelling ◽  
Temperature Gradients ◽  
Rotating Fluid ◽  
Dynamical Equations ◽  
Radial Temperature ◽  
Rotation Rates ◽  
Horizontal Circulation ◽  
Simply Connected

A computational model has been used to determine the terms in the dynamical equations which are responsible for the formation of a certain horizontal circulation seen in a simply connected, differentially heated rotating fluid annulus. Experiments with a differentially heated rotating fluid annulus that is fully blocked by a thin, rigid, vertical radial barrier at rotation rates of up to 5 rad.sec−1 and with an externally applied radial temperature difference of 4 or 10 °C show two principal circulations. This paper is concerned with the mechanism for one of those circulations, which occurs in a horizontal plane. Computer modelling shows that this circulation is caused by small radial temperature gradients in the fluid, rather than centrifugal effects.

Modeling of Thermal Stresses and Thermal Cracking During Heating of Large Ingots

1996 ◽  
Vol 118 (2) ◽  
pp. 235-243 ◽  
Author(s):  
M. K. Alam ◽  
R. L. Goetz ◽  
S. L. Semiatin
Keyword(s):  
Thermal Stresses ◽  
Titanium Aluminides ◽  
Temperature Gradients ◽  
End Effects ◽  
Radial Temperature ◽  
Stress Criterion ◽  
Intermetallic Materials ◽  
Analytical Series ◽  
Biot Numbers ◽  
Selection Of

The development of temperature gradients and thermal stresses during the heating of large ingots has been investigated with special reference to the selection of heating schedules for brittle intermetallic materials such as titanium aluminides. A 1-D analytical (series) solution for radial temperature transients was used in conjunction with an elasticity analysis to determine the maximum thermal stresses that would be generated during ingot heating. The temperature gradients and stresses were seen to be strongly dependent on Fourier and Biot Numbers. In addition, finite element method simulations incorporating end effects and variations of thermal and elastic properties with temperature were performed and compared to the analytical results. Comparison of the predicated thermal stresses and actual ingot heating observations suggest that cracking is controlled by a maximum normal stress criterion.

Stabilization and destabilization of turbulent shear flow in a rotating fluid

1992 ◽  
Vol 241 ◽  
pp. 503-523 ◽  
Author(s):  
D. J. Tritton
Keyword(s):  
Experimental Data ◽  
Shear Flow ◽  
Reynolds Stress ◽  
Rotation Rate ◽  
Turbulent Shear ◽  
Rotating Fluid ◽  
Mean Flow ◽  
Rotation Rates ◽  
Principal Axes ◽  
The Mean

We consider turbulent shear flows in a rotating fluid, with the rotation axis parallel or antiparallel to the mean flow vorticity. It is already known that rotation such that the shear becomes cyclonic is stabilizing (with reference to the non-rotating case), whereas the opposite rotation is destabilizing for low rotation rates and restabilizing for higher. The arguments leading to and quantifying these statement are heuristic. Their status and limitations require clarification. Also, it is useful to formulate them in ways that permit direct comparison of the underlying concepts with experimental data.An extension of a displaced particle analysis, given by Tritton & Davies (1981) indicates changes with the rotation rate of the orientation of the motion directly generated by the shear/Coriolis instability occurring in the destabilized range.The ‘simplified Reynolds stress equations scheme’, proposed by Johnston, Halleen & Lezius (1972), has been reformulated in terms of two angles, representing the orientation of the principal axes of the Reynolds stress tensor (αa) and the orientation of the Reynolds stress generating processes (αb), that are approximately equal according to the scheme. The scheme necessarily fails at large rotation rates because of internal inconsistency, additional to the fact that it is inapplicable to two-dimensional turbulence. However, it has a wide range of potential applicability, which may be tested with experimental data. αa and αb have been evaluated from numerical data for homogeneous shear flow (Bertoglio 1982) and laboratory data for a wake (Witt & Joubert 1985) and a free shear layer (Bidokhti & Tritton 1992). The trends with varying rotation rate are notably similar for the three cases. There is a significant range of near equality of αa and αb. An extension of the scheme, allowing for evolution of the flow, relates to the observation of energy transfer from the turbulence to the mean flow.

scholarly journals Superrotation in Terrestrial Atmospheres

2015 ◽  
Vol 72 (11) ◽  
pp. 4281-4296 ◽  
Author(s):  
Anne L. Laraia ◽  
Tapio Schneider
Keyword(s):  
Angular Momentum ◽  
Momentum Flux ◽  
Rossby Waves ◽  
Wave Activity ◽  
Temperature Gradients ◽  
Convective Heating ◽  
Mean Flow ◽  
Rotation Rates ◽  
Planetary Rotation ◽  
Scaling Arguments

Abstract Atmospheric superrotation with prograde equatorial winds and an equatorial angular momentum maximum is ubiquitous in planetary atmospheres. It is clear that eddy fluxes of angular momentum toward the equator are necessary to generate it. But under what conditions superrotation arises has remained unclear. This paper presents simulations and a scaling theory that establish conditions under which superrotation occurs in terrestrial atmospheres. Whether superrotation arises depends on the relative importance of factors that favor or disfavor superrotation. Convection preferentially generates Rossby waves near the equator, where the Rossby number is O(1). Since the Rossby waves transport angular momentum toward their source regions, this favors superrotation. Meridional temperature gradients preferentially lead to baroclinic instability and wave generation away from the equator. Eddy transport of angular momentum toward the baroclinic source region implies transport out of low latitudes, which disfavors superrotation. Simulations with an idealized GCM show that superrotation tends to arise when the equatorial convective generation of wave activity and its associated eddy angular momentum flux convergence exceed the baroclinic eddy angular momentum flux divergence. Convective and baroclinic wave activity generation is related through scaling arguments to mean-flow properties, such as planetary rotation rates and meridional temperature gradients. The scaling arguments show, for example, that superrotation is favored when the off-equatorial baroclinicity and planetary rotation rates are low, as they are, for example, on Venus. Similarly, superrotation is favored when the convective heating strengthens, which may account for the superrotation seen in extreme global warming simulations.

Thermo-mechanical stress analysis of rotating fiber reinforced variable thickness disk

2021 ◽  
pp. 030932472110609
Author(s):  
Ömer Can Farukoğlu ◽  
İhsan Korkut
Keyword(s):  
Variable Thickness ◽  
Failure Criteria ◽  
Temperature Gradients ◽  
Fiber Reinforced ◽  
Displacement Fields ◽  
Disk Radius ◽  
Radial Temperature ◽  
Stress And Displacement Fields ◽  
Angular Velocities ◽  
Analytical Approaches

Circumferentially fiber reinforced composite disk, which has a variable thickness, is modeled via analytical approaches. The disk is subjected to rotation in traction free conditions and decreasing, constant, and increasing steady state radial temperature gradients along the disk radius. Limit angular velocities are calculated by operating Tsai-Wu and Norris failure indexes to the problem. Subsequently, these limit velocities are gradually decreased to examine the stress and displacement fields. Acquired results show that as the angular velocity drops, the effects of temperature gradients become more visible. At lower angular velocities, these gradients may even alter the stress field directions. Also, different failure criteria implementation may change the calculated limit velocities to a considerable degree. Therefore, the failure index should be chosen attentively to procure conservative results. In the investigation, the influence of disk geometry on the directional stresses is studied as well. Without further ado, it can be expressed that the geometry causes slight alterations in stresses and displacements.

scholarly journals The traditional approximation of rotation, including the centrifugal acceleration for slightly deformed stars

2019 ◽  
Vol 631 ◽  
pp. A26 ◽  
Author(s):  
S. Mathis ◽  
V. Prat
Keyword(s):  
Low Frequency ◽  
Vertical Direction ◽  
Centrifugal Acceleration ◽  
Dynamical Equations ◽  
Horizontal Projection ◽  
Coriolis Acceleration ◽  
Seismic Modelling ◽  
Rotation Rates ◽  
Complete Set ◽  
Analytical Expansion

Context. The traditional approximation of rotation (TAR) is a treatment of the dynamical equations of rotating and stably stratified fluids in which the action of the Coriolis acceleration along the direction of the entropy (and chemicals) stratification is neglected, while assuming that the fluid motions are mostly horizontal because of their inhibition in the vertical direction by the buoyancy force. This leads to the neglect of the horizontal projection of the rotation vector in the equations for the dynamics of gravito-inertial waves (GIWs) that become separable, such as in the non-rotating case, while they are not separable in the case in which the full Coriolis acceleration is taken into account. This approximation, first introduced in geophysical fluid dynamics for thin atmospheres and oceans, has been broadly applied in stellar (and planetary) astrophysics to study low-frequency GIWs that have short vertical wavelengths. The appoximation is now being tested thanks to direct 2D oscillation codes, which constrain its domain of validity. The mathematical flexibility of this treatment allows us to explore broad parameter spaces and to perform detailed seismic modelling of stars. Aims. The TAR treatment is built on the assumptions that the star is spherical (i.e. its centrifugal deformation is neglected) and uniformly rotating while an adiabatic treatment of the dynamics of the waves is adopted. In addition, their induced gravitational potential fluctuations is neglected. However, it has been recently generalised with including the effects of a differential rotation. We aim to carry out a new generalisation that takes into account the centrifugal acceleration in the case of deformed stars that are moderately and uniformly rotating. Methods. We construct an analytical expansion of the equations for the dynamics of GIWs in a spheroidal coordinates system by assuming the hierarchies of frequencies and amplitudes of the velocity components adopted within TAR in the spherical case. Results. We derive the complete set of equations that generalises TAR by taking the centrifugal acceleration into account. As in the case of a differentially rotating spherical star, the problem becomes 2D but can be treated analytically if we assume the anelastic and JWKB approximations, which are relevant for low-frequency GIWs. This allows us to derive a generalised Laplace tidal equation for the horizontal eigenfunctions and asymptotic wave periods, which can be used to probe the structure and dynamics of rotating deformed stars thanks to asteroseismology. A first numerical exploration of its eigenvalues and horizontal eigenfunctions shows their variation as a function of the pseudo-radius for different rotation rates and frequencies and the development of avoided crossings.

Infrared Imaging of 2-D Temperature Distribution During Cryogen Spray Cooling

2002 ◽  
Vol 124 (6) ◽  
pp. 669-675 ◽  
Author(s):  
Bernard Choi ◽  
Ashley J. Welch
Keyword(s):  
Temperature Distribution ◽  
Spray Cooling ◽  
Temperature Gradients ◽  
Measured Temperature ◽  
Back Side ◽  
Surface Cooling ◽  
Radial Temperature ◽  
Cooling Temperature ◽  
Temperature Distributions ◽  
Cryogen Spray Cooling

Cryogen spray cooling (CSC) is used in conjunction with pulsed laser irradiation for treatment of dermatologic indications. The main goal of this study was to determine the radial temperature distribution created by CSC and evaluate the importance of radial temperature gradients upon the subsequent analysis of tissue cooling throughout the skin. Since direct measurement of surface temperatures during CSC are hindered by the formation of a liquid cryogen layer, temperature distributions were estimated using a thin, black aluminum sheet. An infrared focal plane array camera was used to determine the 2-D backside temperature distribution during a cryogen spurt, which preliminary measurements have shown is a good indicator of the front-side temperature distribution. The measured temperature distribution was approximately gaussian in shape. Next, the transient temperature distributions in skin were calculated for two cases: 1) the standard 1-D solution which assumes a uniform cooling temperature distribution, and 2) a 2-D solution using a nonuniform surface cooling temperature distribution based upon the back-side infrared temperature measurements. At the end of a 100-ms cryogen spurt, calculations showed that, for the two cases, large discrepancies in temperatures at the surface and at a 60-μm depth were found at radii greater than 2.5 mm. These results suggest that it is necessary to consider radial temperature gradients during cryogen spray cooling of tissue.

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