Lower Bounds to the Critical Rayleigh Number in Completely Confined Regions

1967 ◽  
Vol 34 (2) ◽  
pp. 308-312 ◽  
Author(s):  
M. Sherman ◽  
S. Ostrach
Keyword(s):  
Rayleigh Number ◽  
Lower Bounds ◽  
Body Force ◽  
Critical Rayleigh Number ◽  
Convective Motion ◽  
The Body ◽  
Maximum Dimension ◽  
Fixed Temperature ◽  
Boussinesq Fluid ◽  
The Given

A method is presented for estimating lower bounds to the minimum Rayleigh number that will induce a state of convective motion in a quasi-incompressible (Boussinesq) fluid where the temperature gradient is in the direction of the body force. The fluid is completely confined by fixed-temperature, rigid bounding walls. For any arbitrary region, the critical Rayleigh number is greater than 1558(h/D)4 where h is the maximum dimension of the given region in the direction of the body force and D is the diameter of an equal volume sphere. In certain simple geometrical configurations, improved lower-bound estimates are calculated.

Convective Instabilities in Fully Developed Flows

1968 ◽  
Vol 90 (1) ◽  
pp. 84-86 ◽  
Author(s):  
M. Sherman
Keyword(s):  
Rayleigh Number ◽  
Temperature Gradient ◽  
Body Force ◽  
Critical Rayleigh Number ◽  
Arbitrary Cross Section ◽  
The Body ◽  
Circular Channel ◽  
Square Channel ◽  
Force Direction ◽  
Boussinesq Fluid

This paper considers the possibility of inducing a convective secondary flow in the fully developed channel flow of a quasi-incompressible (Boussinesq) fluid. Instabilities of this type can only occur when the temperature gradient in the direction of the body force exceeds a certain critical value. This temperature gradient is proportional to the Rayleigh number of the fluid. We find that for channels of arbitrary cross section, the critical Rayleigh number is Rc ≥ 1360 (h/d)4 where h is the arbitrary channel’s maximum dimension in the body force direction and d is the diameter of an equal area circular channel. For two special geometries it is possible to improve the foregoing lower bound estimate to the critical Rayleigh number. In a circular channel Rc ≥ 3450 and in a square channel Rc ≥ 2480.

Linear stability of rotating convection in an imposed shear flow

1997 ◽  
Vol 350 ◽  
pp. 271-293 ◽  
Author(s):  
PAUL MATTHEWS ◽  
STEPHEN COX
Keyword(s):  
Rayleigh Number ◽  
Shear Flow ◽  
Eigenvalue Problem ◽  
Linear Stability ◽  
Thermal Convection ◽  
Critical Rayleigh Number ◽  
Rotation Vector ◽  
Linear Stability Theory ◽  
Fixed Temperature ◽  
Differential Motion

In many geophysical and astrophysical contexts, thermal convection is influenced by both rotation and an underlying shear flow. The linear theory for thermal convection is presented, with attention restricted to a layer of fluid rotating about a horizontal axis, and plane Couette flow driven by differential motion of the horizontal boundaries.The eigenvalue problem to determine the critical Rayleigh number is solved numerically assuming rigid, fixed-temperature boundaries. The preferred orientation of the convection rolls is found, for different orientations of the rotation vector with respect to the shear flow. For moderate rates of shear and rotation, the preferred roll orientation depends only on their ratio, the Rossby number.It is well known that rotation alone acts to favour rolls aligned with the rotation vector, and to suppress rolls of other orientations. Similarly, in a shear flow, rolls parallel to the shear flow are preferred. However, it is found that when the rotation vector and shear flow are parallel, the two effects lead counter-intuitively (as in other, analogous convection problems) to a preference for oblique rolls, and a critical Rayleigh number below that for Rayleigh–Bénard convection.When the boundaries are poorly conducting, the eigenvalue problem is solved analytically by means of an asymptotic expansion in the aspect ratio of the rolls. The behaviour of the stability problem is found to be qualitatively similar to that for fixed-temperature boundaries.Fully nonlinear numerical simulations of the convection are also carried out. These are generally consistent with the linear stability theory, showing convection in the form of rolls near the onset of motion, with the appropriate orientation. More complicated states are found further from critical.

Lower Bounds to Thermal Instability Criteria of Completely Confined Fluids Inside Cylinders of Arbitrary Cross Section

1964 ◽  
Vol 31 (3) ◽  
pp. 376-379 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Cross Section ◽  
Lower Bounds ◽  
Thermal Instability ◽  
Critical Rayleigh Number ◽  
Arbitrary Cross Section ◽  
The Body ◽  
Instability Criterion ◽  
Confined Fluids ◽  
Force Direction ◽  
Rayleigh Numbers

A method is developed to compute the lower bounds for the thermal instability criterion (the critical Rayleigh number) for fluids completely confined inside cylinders of arbitrary cross section; i.e., Rayleigh numbers below which no spontaneous flow may occur in spite of the density gradient being opposite to the body force direction.

The Thermal Instability of Completely Confined Fluids Inside Some Particular Configurations

1963 ◽  
Vol 85 (4) ◽  
pp. 346-354 ◽  
Author(s):  
S. Ostrach ◽  
D. Pnueli
Keyword(s):  
Thermal Stability ◽  
Experimental Investigation ◽  
Rayleigh Number ◽  
Thermal Instability ◽  
Body Force ◽  
Critical Rayleigh Number ◽  
Upper Bounds ◽  
Instability Criterion ◽  
Confined Fluids ◽  
Thermal Stability Of

This paper deals with the thermal stability of completely confined fluids subject to a body force and a temperature gradient which are parallel and oriented in the same direction. It describes a method to obtain upper bounds to the instability criterion (the critical Rayleigh number) for piecewise cylindrical configurations, and demonstrates the use of this method treating some particular practical configurations. These upper bounds are shown to coincide with the critical Rayleigh number under some conditions. An account of experimental investigation of three of the particular configurations is presented and the experimental results compare favorably with the computed upper bounds.

PENGEMBANGAN TANAMAN RAMI (Boehmeria nivea L. Gaud) DAN PEMANFAATAN LIMBAH DAUN RAMI UNTUK PENGGEMUKKAN DOMBA WONOSOBO

2018 ◽  
Vol 16 (2) ◽  
pp. 201-210
Author(s):  
Muryanto Muryanto ◽  
Pita Sudrajad ◽  
Amrih Prasetyo
Keyword(s):  
Body Weight ◽  
Weight Gain ◽  
Plant Development ◽  
Body Weight Gain ◽  
Survey Methods ◽  
The Body ◽  
Boehmeria Nivea ◽  
Central Java ◽  
Potential Capacity ◽  
The Given

The aim of the study was to determine the development of ramie plants (Boehmeria nivea L. Gaud) and the effect of using ramie leaves on feed on the body weight gain of Wonosobo Sheep (Dombos). Research on the development of ramie plants using survey methods in the area of ramie plant development in Wonosobo Regency. While the research on the use of ramie leaves for fattening was carried out in Butuh Village, Kalikajar District, Wonosobo Regency in 2018. 21 male Dombos were divided into 3 feed treatments with forage proportions of 70%, 50% and 30 ramie leaves respectively. %. The results showed that currently ramie plants were being developed in Wonosobo Regency by CV. Ramindo Berkah Persada Sejahtera in Gandok Village, Kalikajar District, Wonosobo Regency, Central Java. Until now the area of the crop has reached 13 ha. Of this area will produce ramie leaves 195,000 kg / year. If one sheep needs 4 kg of ramie / tail / day leaves, then the potential capacity of sheep is 135 heads / year, if the given one is 50% then the Jurnal Litbang Provinsi Jawa Tengah, Volume 16 202 Nomor 2 – Desember 2018potential capacity is 270 heads / year and if it is reduced again to 25% of ramie leaves then the potential capacity 440 heads / year. The use of ramie leaves as a feed for Wonosobo Sheep fattening can be given as much as 30% in fresh form.

scholarly journals Computational Modeling of Vortex Generators for Turbomachinery

2002 ◽  
Author(s):  
R. V. Chima
Keyword(s):  
Computational Models ◽  
Body Force ◽  
Secondary Flows ◽  
The Body ◽  
Vortex Generators ◽  
Force Model ◽  
Suction Surface ◽  
Near Surface ◽  
Compressor Rotor ◽  
Surface Particle

In this work computational models were developed and used to investigate applications of vortex generators (VGs) to turbomachinery. The work was aimed at increasing the efficiency of compressor components designed for the NASA Ultra Efficient Engine Technology (UEET) program. Initial calculations were used to investigate the physical behavior of VGs. A parametric study of the effects of VG height was done using 3-D calculations of isolated VGs. A body force model was developed to simulate the effects of VGs without requiring complicated grids. The model was calibrated using 2-D calculations of the VG vanes and was validated using the 3-D results. Then three applications of VGs to a compressor rotor and stator were investigated: 1. The results of the 3-D calculations were used to simulate the use of small casing VGs used to generate rotor preswirl or counterswirl. Computed performance maps were used to evaluate the effects of VGs. 2. The body force model was used to simulate large partspan splitters on the casing ahead of the stator. Computed loss buckets showed the effects of the VGs. 3. The body force model was also used to investigate the use of tiny VGs on the stator suction surface for controlling secondary flows. Near-surface particle traces and exit loss profiles were used to evaluate the effects of the VGs.

Heat transport by parallel-roll convection in a rectangular container

1987 ◽  
Vol 185 ◽  
pp. 205-234 ◽  
Author(s):  
R. W. Walden ◽  
Paul Kolodner ◽  
A. Passner ◽  
C. M. Surko
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Critical Rayleigh Number ◽  
Equation Model ◽  
Onset Of Convection ◽  
Infinite Layer ◽  
Lateral Extent ◽  
Prandtl Numbers ◽  
Rayleigh Numbers ◽  
Good Agreement

Heat-transport measurements are reported for thermal convection in a rectangular box of aspect’ ratio 10 x 5. Results are presented for Rayleigh numbers up to 35Rc, Prandtl numbers between 2 and 20, and wavenumbers between 0.6 and 1.0kc, where Rc and kc are the critical Rayleigh number and wavenumber for the onset of convection in a layer of infinite lateral extent. The measurements are in good agreement with a phenomenological model which combines the calculations of Nusselt number, as a function of Rayleigh number and roll wavenumber for two-dimensional convection in an infinite layer, with a nonlinear amplitude-equation model developed to account for sidewell attenuation. The appearance of bimodal convection increases the heat transport above that expected for simple parallel-roll convection.

scholarly journals Optimization of a k-covering of a bounded set with circles of two given radii

2021 ◽  
Vol 11 (1) ◽  
pp. 232-240
Author(s):  
Alexander V. Khorkov ◽  
Shamil I. Galiev
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Lower Bounds ◽  
Integer Linear Programming ◽  
Numerical Results ◽  
Programming Models ◽  
Bounded Set ◽  
The Given

Abstract A numerical method for investigating k-coverings of a convex bounded set with circles of two given radii is proposed. Cases with constraints on the distances between the covering circle centers are considered. An algorithm for finding an approximate number of such circles and the arrangement of their centers is described. For certain specific cases, approximate lower bounds of the density of the k-covering of the given domain are found. We use either 0–1 linear programming or general integer linear programming models. Numerical results demonstrating the effectiveness of the proposed methods are presented.

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