Free convection of fluid in a vertical tube filled with porous material

1962 ◽  
Vol 13 (1) ◽  
pp. 129-144 ◽  
Author(s):  
R. A. Wooding
Keyword(s):  
Porous Material ◽  
Cross Section ◽  
Hyperbolic Equations ◽  
Circular Cross Section ◽  
Vertical Tube ◽  
Finite Amplitude ◽  
Theoretical Interpretation ◽  
Approximate Methods ◽  
Inertial Flow ◽  
The Mean

The problem of an unstable fluid overturning in a vertical tube filled with porous material is treated by an approximation of boundary-layer type. It is shown that the fluid can experience a pseudo-inertial effect, in which variations in density across the tube exhibit properties analogous to variations of momentum in an inertial flow. The mean fluid density and mean-square vertical velocity over a horizontal cross-section of the tube are related by a pair of hyperbolic equations, for which there exist two systems of characteristics. It is shown that changes in the mean density of the fluid can be propagated as discontinuities. For discontinuities of finite amplitude, two jump conditions are derived, one of which is found to involve an undetermined parameter λ. The theory is applied to the case of a vertical tube containing porous material saturated with water, which is attached at the top to a reservoir filled with an aqueous solution (an analogue of Taylor's (1954) experiment). The motion of a finite discontinuity which arises at the initial unstable interface is calculated by two approximate methods. These results compare satisfactorily with the data from three experiments, using tubes of circular cross-section, provided that the value of λ is about 0·75. If the theoretical interpretation is correct, it appears that convective flow ceases when the vertical density gradient is slightly less than the neutral value.

scholarly journals Analogue tuning of particle focusing in elasto-inertial flow

Meccanica ◽  
2021 ◽  
Author(s):  
I. Banerjee ◽  
M. E. Rosti ◽  
T. Kumar ◽  
L. Brandt ◽  
A. Russom
Keyword(s):  
Numerical Simulations ◽  
Cross Section ◽  
Immersed Boundary Method ◽  
Circular Cross Section ◽  
Finite Size ◽  
Reynolds Numbers ◽  
Immersed Boundary ◽  
Particle Focusing ◽  
Inertial Flow ◽  
Particle Behaviour

AbstractWe report a unique tuneable analogue trend in particle focusing in the laminar and weak viscoelastic regime of elasto-inertial flows. We observe experimentally that particles in circular cross-section microchannels can be tuned to any focusing bandwidths that lie between the “Segre-Silberberg annulus” and the centre of a circular microcapillary. We use direct numerical simulations to investigate this phenomenon and to understand how minute amounts of elasticity affect the focussing of particles at increasing flow rates. An Immersed Boundary Method is used to account for the presence of the particles and a FENE-P model is used to simulate the presence of polymers in a Non-Newtonian fluid. The numerical simulations study the dynamics and stability of finite size particles and are further used to analyse the particle behaviour at Reynolds numbers higher than what is allowed by the experimental setup. In particular, we are able to report the entire migration trajectories of the particles as they reach their final focussing positions and extend our predictions to other geometries such as the square cross section. We believe complex effects originate due to a combination of inertia and elasticity in the weakly viscoelastic regime, where neither inertia nor elasticity are able to mask each other’s effect completely, leading to a number of intermediate focusing positions. The present study provides a fundamental new understanding of particle focusing in weakly elastic and strongly inertial flows, whose findings can be exploited for potentially multiple microfluidics-based biological sorting applications.

Effects of Pin Shape and Array Orientation on Heat Transfer and Pressure Loss in Pin Fin Arrays

1984 ◽  
Vol 106 (1) ◽  
pp. 252-257 ◽  
Author(s):  
D. E. Metzger ◽  
C. S. Fan ◽  
S. W. Haley
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Pressure Loss ◽  
Flow Direction ◽  
Circular Cross Section ◽  
Cycle Performance ◽  
Mean Flow ◽  
Pin Fin ◽  
The Mean ◽  
Cooling Air

Modern high-performance gas turbine engines operate at high turbine inlet temperatures and require internal convection cooling of many of the components exposed to the hot gas flow. Cooling air is supplied from the engine compressor at a cost to cycle performance and a design goal is to provide necessary cooling with the minimum required cooling air flow. In conjunction with this objective, two families of pin fin array geometries which have potential for improving airfoil internal cooling performance were studied experimentally. One family utilizes pins of a circular cross section with various orientations of the array with respect to the mean flow direction. The second family utilizes pins with an oblong cross section with various pin orientations with respect to the mean flow direction. Both heat transfer and pressure loss characteristics are presented. The results indicate that the use of circular pins with array orientation between staggered and inline can in some cases increase heat transfer while decreasing pressure loss. The use of elongated pins increases heat transfer, but at a high cost of increased pressure loss. In conjunction with the present measurements, previously published results were reexamined in order to estimate the magnitude of heat transfer coefficients on the pin surfaces relative to those of the endwall surfaces. The estimate indicates that the pin surface coefficients are approximately double the endwall values.

Finite amplitude effect on the stability of a jet of circular cross-section

1968 ◽  
Vol 34 (2) ◽  
pp. 299-313 ◽  
Author(s):  
D. P. Wang
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Direct Consequence ◽  
Finite Amplitude ◽  
Stable States ◽  
Characteristic Wavelength ◽  
Method Of Solution ◽  
Linearized Theory ◽  
The Stability ◽  
Unstable States

The effect of finite amplitude on the stable and unstable states of a column of an ideal fluid of circular cross-section under the action of surface tension is studied. The method of solution is a formal extension of the linearized theory; it consists of assuming that the exact solution may be expanded in a power series of a small parameter characterizing the amplitude. The calculation is carried out to the point where the first non-trivial term of the finite amplitude effect is obtained. For the stable states, the result shows that the characteristic wavelength of a disturbance which appears to be stationary with respect to an observer is decreased by the finite amplitude effect. For the unstable states, it reveals that the growth rate depends not only on the wavelength and the magnitude but also on the type of disturbance imposed initially. The last result is a direct consequence of the fact that two independent types of initial disturbance, the disturbance of the velocity field and the disturbance of the free surface, may be imposed simultaneously on the jet.

Analysis of Axially Loaded Annular Shells With Applications to Welded Bellows

1960 ◽  
Vol 82 (3) ◽  
pp. 741-753 ◽  
Author(s):  
M. Hetenyi ◽  
R. J. Timms
Keyword(s):  
Experimental Data ◽  
General Solution ◽  
Cross Section ◽  
Circular Cross Section ◽  
Radius Of Curvature ◽  
Approximate Design ◽  
Axial Forces ◽  
The Mean ◽  
Maximum Stresses ◽  
Toroidal Shells

A method is presented for the calculation of stresses and deflections in ring-shaped shells of circular cross section, subjected to axial forces. The solution is derived without the restriction imposed for toroidal shells by previous investigators, that the radius of curvature of the cross section is to be small in comparison with the mean radius of the torus. The range of applicability of the method is extended hereby to include the slightly arched convolutions used in the construction of welded bellows. By a rational reduction of the general solution approximate design formulas are obtained for the maximum stresses and deflections in bellows under axial forces and the calculated values are compared with experimental data.

scholarly journals The Sonic Resonance Method and the Impulse Excitation Technique: A Comparison Study

2021 ◽  
Vol 11 (22) ◽  
pp. 10802
Author(s):  
Tomáš Húlan ◽  
Filip Obert ◽  
Ján Ondruška ◽  
Igor Štubňa ◽  
Anton Trník
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Resonance Method ◽  
Resonant Frequencies ◽  
Mean Values ◽  
Impulse Excitation ◽  
The Mean ◽  
The Relationship ◽  
Resonant Method

In this study, resonant frequencies of flexurally vibrating samples were measured using the sonic resonant method (SRM) and the impulse excitation technique (IET) to assess the equivalency of these two methods. Samples were made from different materials and with two shapes (prism with rectangular cross-section and cylinder with circular cross-section). The mean values and standard deviations of the resonant frequencies were compared using the t-test and the F-test. The tests showed an equivalency of both methods in measuring resonant frequency. The differences between the values measured using SRM and IET were not significant. Graphically, the relationship between the resonant frequencies is a line with a slope of 0.9993 ≈ 1.

scholarly journals Diffraction of a plane wave by an almost circular cylinder

1961 ◽  
Vol 264 (1317) ◽  
pp. 246-268 ◽  
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Circular Cross Section ◽  
The Body ◽  
Maximum Deviation ◽  
Dimensional Problem ◽  
Plane Wave Incident ◽  
Method Of Solution ◽  
Watson Transformation ◽  
The Mean

The two-dimensional problem of an E-polarized plane wave incident on a perfectly conducting cylinder of almost circular cross-section is treated , the maximum deviation of the perimeter of the cross-section from a strict circle being regarded mathematically as an infinitesimal quantity whose second and higher powers are neglected. In the body of the paper the method of solution uses infinite Fourier transform techniques, but an analysis involving a Watson transformation, more traditional in this type of problem , is given in appendix A. Attention is for the most part directed to the case in which the mean radius of the cylinder is large compared to the wavelength, and the form of the solution then appropriate is examined in some detail. In particular, initial terms of asymptotic expansions in inverse powers of the mean radius to wavelength ratio are obtained for the ‘specular’ and for the ‘creeping’ contributions to the far field. It is shown that the former contributionis in agreement with that derived by the Luneberg—Kline method, and the latter with the prescription proposed by Keller. Various Bessel function results are required, some of which are derived in appendices.

Aerodynamic behavior of wind turbines with polygonal cross- sectional tower

2021 ◽  
Author(s):  
Yong Chul Kim ◽  
Yukio Tamura
Keyword(s):  
Cross Section ◽  
Wind Turbines ◽  
Cross Sections ◽  
Lift Force ◽  
Circular Cross Section ◽  
Force Coefficient ◽  
Cross Sectional ◽  
The World ◽  
The Mean ◽  
Power Generation Systems

<p>Wind turbines are commonly used power generation systems around the world and their application is becoming increasingly widespread. Traditionally, circular‐cross‐section wind towers have been used, but recent upsizing of wind turbines has exposed weaknesses of these structures, including problems related to manufacturing and inadequate strength. Thus, the concept of site‐ assembled modular towers with polygonal cross‐sections such as octagonal and/or tetradecagonal has been proposed, but their wind‐resistant performances have not been clearly investigated. In the present study, the wind‐resistant performances of polygonal cross‐sectional towers were investigated through wind tunnel tests. It was thus found that the maximum force coefficient of the upper structure is larger than that of the tower, which makes the effect of cross‐sectional tower shape rather small. The mean and fluctuating lift force coefficients of a helical square cross‐sectional tower were quite small for cases of tower only and wind turbine.</p>

The initial and ultimate motions of an impulsively started cylinder in a compressible fluid

1988 ◽  
Vol 418 (1854) ◽  
pp. 209-228 ◽  
Keyword(s):  
Cross Section ◽  
Compressible Fluid ◽  
Line Source ◽  
Sound Speed ◽  
Circular Cross Section ◽  
The Mean ◽  
Moving Line Source ◽  
Inviscid Compressible Fluid ◽  
Moving Line ◽  
Slow Timescale

A cylinder with circular cross section of radius a 0 , in an inviscid, compressible fluid, is subjected to an impulse so that it moves in a direction perpendicular to its length. In addition, a force, which is taken to be constant, acts in the direction of motion. The cylinder’s velocity is found to decrease rapidly during the initial stages of the motion on the timescale T 0 = a 0 / c 0 , where c 0 is the mean sound speed in the fluid. After a time of order T 0 it reaches a stage when the velocity varies more slowly. If u 0 is a typical value of the velocity and is small compared with c 0 , then a matching argument in time leads to the ultimate, slowly varying velocity defined on the slow timescale t 0 = a 0 / u 0 . The acoustic field induced by the cylinder’s motion is determined and, for the later stages of the motion, a matching argument in space leads to an expression for the field at distances much greater than a 0 from the cylinder in terms of moving line source and dipole potentials.

The mean inner potential of GaN measured from nanowires using off-axis electron holography

2005 ◽  
Vol 892 ◽  
Author(s):  
Andrew See Weng Wong ◽  
Ghim Wei Ho ◽  
Rafal E Dunin-Borkowski ◽  
Takeshi Kasama ◽  
Rachel A Oliver ◽  
...  
Keyword(s):  
Cross Section ◽  
Carbon Film ◽  
Circular Cross Section ◽  
Electron Holography ◽  
Amorphous Coating ◽  
Gan Nanowires ◽  
A Value ◽  
Accurate Knowledge ◽  
Transmission Electron ◽  
The Mean

AbstractThe mean inner potentials of wurtzite GaN nanowires are measured using off-axis electron holography in the transmission electron microscope (TEM). The nanowires have a circular cross-section and are suspended across holes in a holey carbon film, resulting in an accurate knowledge of their thickness profiles and orientations. They are also free of the implantation and damage that is present in mechanically-polished ion-milled TEM specimens. The effect of a thin amorphous coating, which is present on the surfaces of the nanowires, on measurements of their mean inner potential is assessed. A value for the mean inner potential of GaN of (16.7 ± 0.3) V is obtained from these samples.

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