Theoretical Analysis of Oscillating and Streaming Fields Between Two Parallel Beams and Numerical Investigation of the Cooling Efficiency

2003 ◽  
Author(s):  
Qun Wan ◽  
A. V. Kuznetsov
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Boundary Layers ◽  
Standing Wave ◽  
Critical Value ◽  
Core Region ◽  
Wave Number ◽  
Wave Form ◽  
Channel Height ◽  
The Core

The main purpose of this paper is to investigate the oscillating and streaming flow fields and the heat transfer efficiency across a channel between two long parallel beams, one of which is stationary and the other oscillating in standing wave form. The oscillating amplitude is assumed much smaller than the channel height. When the Reynolds number, which is defined by the oscillating frequency and the standing wave number, is much greater than unity, boundary layer structures are found near both beams, which are separated by a core region in the center of the channel. The oscillating fields within the core region and both boundary layers are obtained analytically. Based on the oscillating fields, the streaming fields within both boundary layers are also analytically obtained. Further investigation of boundary layer streaming fields shows that the streaming velocities approach constant values at the edges of the boundary layers and provide slip velocities for the streaming field in the core region. The core region streaming velocity field is numerically obtained by solving the mass and momentum conservation equations in their stream function–vorticity form. The temperature field is also computed for two cases: both beams are kept at constant but different temperatures (case A) or the oscillating beam is kept at a constant temperature and the stationary beam is prescribed a constant heat flux (case B). Cases of different channel heights are computed and a critical height is found. When the channel height is smaller than the critical value, for each half standing wavelength distance along the beams, two symmetric eddies are observed, which occupy the whole channel. In this case, the Nusselt number increases with the increase of the channel height. After the critical value, two layers of asymmetric eddies are observed near the oscillating beam and the Nusselt number decreases and approaches unity with the increase of the gap size. The abrupt change of the streaming field and the Nusselt number as the channel height goes through its critical value may be due to the bifurcation caused by instability of the vortex structure in the fluid layer.

scholarly journals Sound propagation in a lined nozzle with shear and bias flows

2018 ◽  
Vol 18 (1) ◽  
pp. 3-48
Author(s):  
LMBC Campos ◽  
C Legendre
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Boundary Layers ◽  
Lower Boundary ◽  
Cross Flow ◽  
Core Flow ◽  
The Core ◽  
Wide Range ◽  
Bias Flow ◽  
Number Formula

In this study, the propagation of waves in a two-dimensional parallel-sided nozzle is considered allowing for the combination of: (a) distinct impedances of the upper and lower walls; (b) upper and lower boundary layers with different thicknesses with linear shear velocity profiles matched to a uniform core flow; and (c) a uniform cross-flow as a bias flow out of one and into the other porous acoustic liner. The model involves an “acoustic triple deck” consisting of third-order non-sinusoidal non-plane acoustic-shear waves in the upper and lower boundary layers coupled to convected plane sinusoidal acoustic waves in the uniform core flow. The acoustic modes are determined from a dispersion relation corresponding to the vanishing of an 8 × 8 matrix determinant, and the waveforms are combinations of two acoustic and two sets of three acoustic-shear waves. The eigenvalues are calculated and the waveforms are plotted for a wide range of values of the four parameters of the problem, namely: (i/ii) the core and bias flow Mach numbers; (iii) the impedances at the two walls; and (iv) the thicknesses of the two boundary layers relative to each other and the core flow. It is shown that all three main physical phenomena considered in this model can have a significant effect on the wave field: (c) a bias or cross-flow even with small Mach number [Formula: see text] relative to the mean flow Mach number [Formula: see text] can modify the waveforms; (b) the possibly dissimilar impedances of the lined walls can absorb (or amplify) waves more or less depending on the reactance and inductance; (a) the exchange of the wave energy with the shear flow is also important, since for the same stream velocity, a thin boundary layer has higher vorticity, and lower vorticity corresponds to a thicker boundary layer. The combination of all these three effects (a–c) leads to a large set of different waveforms in the duct that are plotted for a wide range of the parameters (i–iv) of the problem.

On the generation of spatially growing waves in a boundary layer

1965 ◽  
Vol 22 (3) ◽  
pp. 433-441 ◽  
Author(s):  
M. Gaster
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Wave Number ◽  
Wave System ◽  
Velocity Fluctuations ◽  
Forced Wave ◽  
General Terms ◽  
Complex Wave ◽  
Complex Wave Number

The solution is obtained in general terms for the velocity fluctuations generated in a laminar boundary layer by an oscillating disturbance on the boundry wall. The form of excitation is chosen to represent a vibrating ribbon of the type used by Schubauer to force disturbance in boundary layers. The forced wave system generated by the ribbon is shown to be a spatially growing one, which is described far downstream by an eigenmode of the system which has a complex wave-number.

Intermittency of coherent structures in the core region of fully developed turbulent pipe flow

1976 ◽  
Vol 74 (4) ◽  
pp. 767-796 ◽  
Author(s):  
Jean Sabot ◽  
Geneviève Comte-Bellot
Keyword(s):  
Correlation Coefficient ◽  
Boundary Layers ◽  
Reynolds Stress ◽  
Pipe Flow ◽  
Core Region ◽  
Turbulent Pipe Flow ◽  
Time Interval ◽  
The Core ◽  
The Mean ◽  
Mean Time

The present investigation is oriented towards a better understanding of the turbulent structure in the core region of fully developed and completely wall-bounded flows. In view of the already existing results concerning the bursting process in boundary layers (which are semi-bounded flows), an amplitude analysis of the Reynolds shear stress fluctuation u1u2, sorted into four quadrants of the u1, u2 plane, was carried out in a turbulent pipe flow. For the wall side of the core region, in which the correlation coefficient u1u2/u’1u’2 does not change appreciably with the distance from the wall, the structure of the Reynolds stress is found to be similar to that obtained in boundary layers: bursts, i.e. ejections of low speed fluid, make the dominant contribution to the Reynolds stress; the regions of violent Reynolds stress are small fractions of the overall flow; and the mean time interval between bursts is found to be almost constant across the flow. For the core region, the large cross-stream evolution of the correlation coefficient u1u2/u’1u’2 is associated with a new structure of the Reynolds stress induced by the completely wall-bounded nature of the flow. Very large amplitudes of u1u2 are still observed, but two distinct burst-like patterns are now identified and related to ejections originating from the two opposite halves of the flow. In addition to this interaction, a focusing effect caused by the circular section of the pipe is observed. As a result of these two effects, the mean time interval between the bursts decreases significantly in the core region and reaches a minimum on the pipe axis. Investigation of specific space-time velocity correlations reveals the possible existence of rotating structures similar to those observed at the outer edge of turbulent boundary layers. These coherent motions are found to have a scale noticeably larger than that of the bursts.

Reimagining full wave rf quasilinear theory in a tokamak

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Peter J. Catto ◽  
Elizabeth A. Tolman
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Collision Frequency ◽  
Velocity Space ◽  
Wave Number ◽  
Temporal Behaviour ◽  
Full Wave ◽  
Effective Collision Frequency ◽  
Space Boundary ◽  
Effective Collision

The velocity dependent resonant interaction of particles with applied radiofrequency (rf) waves during heating and current drive in the presence of pitch angle scattering collisions gives rise to narrow collisional velocity space boundary layers that dramatically enhance the role of collisions as recently shown by Catto (J. Plasma Phys., vol. 86, 2020, 815860302). The behaviour is a generalization of the narrow collisional boundary layer that forms during Landau damping as found by Johnston (Phys. Fluids, vol. 14, 1971, pp. 2719–2726) and Auerbach (Phys. Fluids, vol. 20, 1977, pp. 1836–1844). For a wave of parallel wave number ${k_{||}}$ interacting with weakly collisional plasma species of collision frequency $\nu$ and thermal speed ${v_{\textrm{th}}}$ , the effective collision frequency becomes of order $\nu {({k_{||}}{v_{th}}/\nu )^{2/3}} \gg \nu $ . The narrow boundary layers that arise because of the diffusive nature of the collisions allow a physically meaningful wave–particle interaction time to be defined that is the inverse of this effective collision frequency. The collisionality implied by the narrow boundary layer results in changes in the standard quasilinear treatment of applied rf fields in tokamaks while remaining consistent with causality. These changes occur because successive poloidal interactions with the rf are correlated in tokamak geometry and because the resonant velocity space dependent interactions are controlled by the spatial and temporal behaviour of the perturbed full wave fields rather than just the spatially local Landau and Doppler shifted cyclotron wave–particle resonance condition associated with unperturbed motion of the particles. The correlation of successive poloidal circuits of the tokamak leads to the appearance in the quasilinear operator of transit averaged resonance conditions localized in velocity space boundary layers that maintain negative definite entropy production.

Finite amplitude convection cells

1967 ◽  
Vol 30 (3) ◽  
pp. 577-600 ◽  
Author(s):  
J. L. Robinson
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Boundary Conditions ◽  
Boundary Layers ◽  
Cross Section ◽  
Circular Cross Section ◽  
Maximum Heat ◽  
Mean Field Equations

In this paper we consider two-dimensional steady cellular motion in a fluid heated from below at large Rayleigh number and Prandtl number of order unity. This is a boundary-layer problem and has been considered by Weinbaum (1964) for the case of rigid boundaries and circular cross-section. Here we consider cells of rectangular cross-section with three sets of velocity boundary conditions: all boundaries free, rigid horizontal boundaries and free vertical boundaries (referred to here as periodic rigid boundary conditions), and all boundaries rigid; the vertical boundaries of the cells are insulated. It is shown that the geometry of the cell cross-section is important, such steady motion being not possible in the case of free boundaries and circular cross-section; also that the dependence of the variables of the problem on the Rayleigh number is determined by the balances in the vertical boundary layers.We assume only those boundary layers necessary to satisfy the boundary conditions and obtain a Nusselt number dependence $N \sim R^{\frac{1}{3}}$ for free vertical boundaries. For the periodic rigid case, Pillow (1952) has assumed that the buoyancy torque is balanced by the shear stress on the horizontal boundaries; this is equivalent to assuming velocity boundary layers beside the vertical boundaries (rather than the vorticity boundary layers demanded by the boundary conditions) and leads to a Nusselt number dependence N ∼ R¼. If it is assumed that the flow will adjust itself to give the maximum heat flux possible the two models are found to be appropriate for different ranges of the Rayleigh number and there is good agreement with experiment.An error in the application of Rayleigh's method in this paper is noted and the correct method for carrying the boundary-layer solutions round the corners is given. Estimates of the Nusselt numbers for the various boundary conditions are obtained, and these are compared with the computed results of Fromm (1965). The relevance of the present work to the theory of turbulent convection is discussed and it is suggested that neglect of the momentum convection term, as in the mean field equations, leads to a decrease in the heat flux at very high Rayleigh numbers. A physical argument is given to derive Gill's model for convection in a vertical slot from the Batchelor model, which is appropriate in the present work.

Laminar Boundary-Layer Flow Near the Entry of a Curved Circular Pipe

1980 ◽  
Vol 47 (4) ◽  
pp. 697-702 ◽  
Author(s):  
W. S. Yeung
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Cross Flow ◽  
Outer Edge ◽  
Core Region ◽  
Large Reynolds Number ◽  
Normal Velocity ◽  
Curved Pipe ◽  
The Core ◽  
Layer Flow

The fluid mechanics of a viscous, incompressible fluid entering a circular curved pipe at large Reynolds number is investigated numerically. The flow field is divided into two regions, the boundary-layer region and the inviscid core region. The boundary layer is assumed to be laminar and the method of integral relations is used to solve the governing equations. The core region, on the other hand, is assumed irrotational and is solved by a modified version of Telenin’s method. The coupling of the two regions is accounted for through the imposition of the outer edge normal velocity as a boundary condition for the core region. Results are presented for a Reynolds number of 104 and a curvature ratio of 0.1. It has been shown that the cross flow in the core region is initially directed from the outer to the inner bend and reverses its direction downstream for the entry condition of uniform axial motion. The core velocity profiles are consistent with a recent experimental investigation, while the boundary-layer results are qualitatively similar to those of Yao and Berger, although a direct quantitative comparison is not applicable, due to the different range of Reynolds number considered.

Very Large Eddy Simulation of Flow and Heat Transfer in a Pulsating Impinging Jet

2020 ◽  
Author(s):  
Fangyuan Liu ◽  
Junkui Mao ◽  
Xingsi Han ◽  
Zhaoyang Xia
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Large Eddy Simulation ◽  
Impinging Jet ◽  
Core Region ◽  
Wall Jet ◽  
The Core ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Pulsating Jets

Abstract The steady impinging jets applied in turbomachine have been comprehensively studied but the pulsating jets still need to be further researched. The flow field and heat transfer characteristics of pulsating impinging jet impinging on a flat plate have been simulated using the improved very large eddy simulation established with SST k–ω model. Two time-mean Reynolds numbers (6,000 and 23,000) in the conditions of frequency = 10Hz and steady state at the constant jet–to–surface distance (6D) were considered. The velocity, vortices, and Nusselt number distributions on the plate surface were investigated to emphasize on the vortex structures in the flow and its relation to the heat transfer. The investigation has revealed the advantage of the improved very large eddy simulation for predicting the dynamical generating process of flow structures in pulsating jets. Calculated results showed pairs of vortices were organized and induced from the jet exit, and propagated along with the jet region periodically. The vortices grew with the entrainment towards the ambient fluid and resulted in accelerated interaction in the wall jet region. Meanwhile, the vortices had strong interaction with the core region and weakened velocity in the core region. Results showed that the time–mean local Nusselt number of pulsating jet was lower in the stagnation region at both investigated Re numbers but not reduced in the wall jet region.

Effect of Wall Movement on a Jet Depositing on a Moving Wall at Moderate Reynolds Number

2010 ◽  
Author(s):  
Md. Yahia Hussain ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Surface ◽  
Core Region ◽  
Relaxation Length ◽  
Moving Wall ◽  
The Core ◽  
Wall Movement ◽  
Moderate Reynolds Number ◽  
Surface Jet

The steady flow of a moderately inertial jet depositing on a moving wall, is examined theoretically near channel exit. The free surface jet emerges from a channel and adheres to a wall, which may move in the same or opposite direction to the acting channel pressure gradient. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse Reynolds number. The flow field is obtained as a composite expansion by matching the flow in the boundary layer regions near the free surface, with the flow in the core region. The influence of inertia and wall velocity on the shape of the free surface, the velocity and stress is emphasized. It is found that the viscous relaxation length is essentially uninfluenced by the velocity of a forward moving wall. In contrast, it diminishes rapidly with the velocity of a backward moving wall.

Intramitochondrial Viruses of Reptilian Cell Origin

1972 ◽  
Vol 30 ◽  
pp. 318-319
Author(s):  
Philip D. Lunger ◽  
H. Fred Clark
Keyword(s):  
Particle Production ◽  
Outer Zone ◽  
Density Variation ◽  
Core Region ◽  
Mitochondrial Membranes ◽  
Virus Particles ◽  
The Core ◽  
Vipera Russelli ◽  
Maturation Stages ◽  
Type Particle

In the course of fine structure studies of spontaneous “C-type” particle production in a viper (Vipera russelli) spleen cell line, designated VSW, virus particles were frequently observed within mitochondria. The latter were usually enlarged or swollen, compared to virus-free mitochondria, and displayed a considerable degree of cristae disorganization.Intramitochondrial viruses measure 90 to 100 mμ in diameter, and consist of a nucleoid or core region of varying density and measuring approximately 45 mμ in diameter. Nucleoid density variation is presumed to reflect varying degrees of condensation, and hence maturation stages. The core region is surrounded by a less-dense outer zone presumably representing viral capsid.Particles are usually situated in peripheral regions of the mitochondrion. In most instances they appear to be lodged between loosely apposed inner and outer mitochondrial membranes.

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