A numerical investigation of the effects of a transverse temperature gradient on the formation of regular and irregular acoustic streaming in an enclosure

2010 ◽  
Vol 225 (1) ◽  
pp. 132-144 ◽  
Author(s):  
M K Aktas ◽  
T Ozgumus
Keyword(s):  
Temperature Gradient ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Fluid Motion ◽  
Sound Field ◽  
Flow Patterns ◽  
Temperature Gradients ◽  
Left Wall ◽  
Steady Streaming ◽  
Transverse Temperature

The effects of a transverse temperature gradient on the formation of regular and irregular acoustic streaming structures in air-filled, two-dimensional, rectangular, shallow enclosures carrying a longitudinal sound field are investigated numerically. The fluid motion is induced by the harmonic vibration of the enclosure left wall. The fully compressible form of the Navier—Stokes equations is considered to predict the primary oscillatory and secondary pseudo-steady streaming flow fields. An explicit time-marching flux-corrected transport algorithm is used to simulate the acoustic wave formation, propagation, and the resulting flow patterns in the enclosure. The vertical walls of the enclosure are adiabatic whereas the horizontal walls are heated differentially or symmetrically. The transverse temperature gradients are found to strongly affect the acoustic streaming structures and the velocities. The steady streaming velocities significantly increase when the enclosure horizontal walls are asymmetrically heated for both regular and irregular streaming flows. For irregular streaming, the transverse temperature gradients completely change the flow patterns. The irregular streaming velocities are greatly reduced in case of the symmetric temperature increase of the horizontal walls.

Heat Transfer Enhancement by Irregular Acoustic Streaming in a Shallow Enclosure

2009 ◽  
Author(s):  
Murat K. Aktas ◽  
Turkuler Ozgumus
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Fluid Motion ◽  
Bottom Wall ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Left Wall ◽  
Time Marching ◽  
Transverse Temperature

The effects of classical and irregular acoustic streaming structures on convective heat transport in air-filled two dimensional rectangular enclosures are investigated numerically. The oscillatory fluid motion and the resulting streaming motion are driven by cyclic vibration of the enclosure left wall. The fully compressible form of the Navier – Stokes equations are employed to model the transport phenomenon in the enclosure. An explicit time-marching Flux-Corrected Transport (FCT) Algorithm is used to simulate the oscillatory flow field, streaming patterns and associated thermal convection in the enclosure. The vertical walls of enclosure are thermally insulated. The bottom wall is heated isothermally while the top wall is kept at the initial temperature. The transverse temperature gradients strongly affect the acoustic streaming velocities and structures. The irregular streaming significantly augments the heat transfer from the enclosure bottom wall.

Numerical Solutions of the Viscous Flow Equations for a Class of Closed Flows

1965 ◽  
Vol 69 (658) ◽  
pp. 714-718 ◽  
Author(s):  
Ronald D. Mills
Keyword(s):  
Moving Boundary ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Steady Flows ◽  
Flow Equations ◽  
Steady Streaming ◽  
Difference Formula ◽  
Surface Passing

The Navier-Stokes equations are solved iteratively on a small digital computer for the class of flows generated within a rectangular “cavity” by a surface passing over its open end. Solutions are presented for depth/breadth ratios ƛ=0.5 (shallow), 10 (square), 20 (deep) and Reynolds number 100. Flow photographs ore obtained which largely confirm the predicted flows. The theoretical velocity profiles and pressure distributions through the centre of the vortex in the square cavity are calculated.In an appendix an improved finite difference formula is given for the vorticity generated at a moving boundary.Since Thorn began his pioneering work some thirty-five years ago the number of numerical solutions which have been obtained for the equations of incompressible viscous fluid motion remains small (see bibliographies of Thom and Apelt, Fromm). The known solutions are principally for steady streaming flows, although two methods have now been used with success for non-steady flows (Payne jets and Fromm flow past obstacles). By contrast this paper is concerned with the class of closed flows generated in a rectangular region of varying depth/breadth ratio by a surface passing over an open end. This problem has been considered for a number of reasons.

Simulation of Acoustic Streaming in a Resonator

2004 ◽  
Author(s):  
Bakhtier Farouk ◽  
Murat K. Aktas
Keyword(s):  
Flow Field ◽  
Standing Wave ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Flow Patterns ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Streaming Flow

Formation of vortical flow structures in a rectangular enclosure due to acoustic streaming is investigated numerically. The oscillatory flow field in the enclosure is created by the vibration of a vertical side wall of the enclosure. The frequency of the wall vibration is chosen such that a standing wave forms in the enclosure. The interaction of this standing wave with the horizontal solid walls leads to the production of Rayleigh type acoustic streaming flow patterns in the enclosure. All four walls of the enclosure considered are thermally insulated. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to explicitly track the acoustic waves. Numerical solutions are obtained by employing a highly accurate flux corrected transport (FCT) algorithm for the convection terms. A time-splitting technique is used to couple the viscous and diffusion terms of the full Navier-Stokes equations. Non-uniform grid structure is employed in the computations. The simulation of the primary oscillatory flow and the secondary (steady) streaming flows in the enclosure is performed. Streaming flow patterns are obtained by time averaging the primary oscillatory flow velocity distributions. The effect of the amount of wall displacement on the formation of the oscillatory flow field and the streaming structures are studied. Computations indicate that the nonlinearity of the acoustic field increases with increasing amount of the vibration amplitude. The form and the strength of the secondary flow associated with the oscillatory flow field and viscous effects are found to be strongly correlated to the maximum displacement of the vibrating wall. Total number of acoustic streaming cells per wavelength is also determined by the strength and the level of the nonlinearity of the sound field in the resonator.

Oscillatory Flow Induced Developing Convection in a Shallow Enclosure: Effect of Sinusoidal Bottom Wall Temperature

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Saeid R. Angeneh ◽  
Murat K. Aktas
Keyword(s):  
Heat Transfer ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Acoustic Streaming ◽  
Fluid Motion ◽  
Side Wall ◽  
Convective Transport ◽  
Bottom Wall ◽  
Mean Flow

Abstract The influence of hydrodynamically developing nonzero mean acoustic streaming motion on transient convective heat transfer in an air-filled rectangular enclosure is studied numerically. The enclosure is two-dimensional with sinusoidal bottom wall spatial temperature distribution. The oscillatory flow under relatively large Womersley number regime conditions is actuated by the periodic vibrations of the enclosure side wall. The side walls of the enclosure are adiabatic, while the top wall is isothermal. The compressible form of the Navier–Stokes equations is considered to predict the oscillatory- and time-averaged mean flow fields. A control-volume method based explicit computational scheme is used to simulate the convective transport in the enclosure. The longitudinal and the transverse temperature gradients strongly affect the flow structure in the enclosure. The mean fluid motion alters the heat transfer behavior compared to the pure conduction.

Acoustic Streaming Induced Thermal Convection in an Enclosure Subject to Uniform Heat Flux

2010 ◽  
Author(s):  
Murat K. Aktas
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Transport Phenomena ◽  
Acoustic Streaming ◽  
Side Wall ◽  
Uniform Heat Flux ◽  
Uniform Wall ◽  
Transverse Temperature ◽  
Streaming Motion

The effects of acoustic streaming motion on transient convective heat transfer in an air-filled shallow enclosure with a vibrating side wall are investigated. The acoustic streaming phenomenon has been extensively studied by using theoretical and experimental methods. However, the investigations on the effects of longitudinal or transverse temperature gradients on acoustic streaming formation, associated transport phenomena and influence of various parameters on streaming structures are relatively scarce. To our knowledge, the influence of a transverse temperature gradient created by a uniform wall heat flux on streaming patterns has not been studied. In the present study, the fluid motion is driven by the periodic vibration of the enclosure side wall. The vertical walls of the enclosure are adiabatic while the bottom wall is subject to uniform heat flux and the top wall is isothermal or both bottom and top walls are subject to uniform, symmetric heat flux. The fully compressible form of the Navier–Stokes equations are considered to compute the primary oscillatory and secondary mean flow fields. A control-volume method based, explicit time-marching Flux-Corrected Transport (FCT) Algorithm is used to simulate the transport phenomena in the enclosure. The results of an isothermal test case simulation are compared with the existing literature for code validation. Transverse temperature gradient induced by uniform wall heating (symmetrically or non-symmetrically) strongly affects the acoustic streaming structures and velocities. The streaming motion significantly changes the transient behavior of heat transfer in the enclosure compared to pure conduction.

Micro Cooling Based on Acoustic Streaming

2008 ◽  
Author(s):  
Hongming Sun ◽  
Hang Guo
Keyword(s):  
Heat Transfer ◽  
Analytical Study ◽  
Stokes Equations ◽  
Acoustic Radiation ◽  
Acoustic Streaming ◽  
Fluid Motion ◽  
Radiation Force ◽  
Cooling Effect ◽  
Navier Stokes ◽  
Navier Stokes Equations

Heat transfer due to forced convection caused by acoustic streaming in microfluidic devices is shown to have potential in cooling effect. However, few studies are made for theoretically studying the fluid motion induced by the acoustic field and forced heat transfer for micro cooling in microdevices. In this paper, Navier-Stokes equations are first employed to study acoustic radiation force and acoustic streaming in microchannel actuated by ultrasonic vibration. Then, an analytical study of fluid motion acoustically induced and the temperature field in microchannel is investigated to determine the enhancement of cooling effect in microchannel with acoustic streaming.

Experimental and Numerical Study of Acoustic Streaming in a Cylindrical Enclosure

2005 ◽  
Author(s):  
Yiqiang Lin ◽  
Bakhtier Farouk
Keyword(s):  
Flow Field ◽  
Acoustic Waves ◽  
Stokes Equations ◽  
Numerical Study ◽  
Acoustic Streaming ◽  
Digital Camera ◽  
Sound Field ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Cylindrical Resonator

Acoustic streaming motion generated by finite-amplitude resonant oscillations in an air-filled two-dimensional cylindrical enclosure was experimentally studied and numerically simulated. The oscillatory flow field in the enclosure was created by the vibration of one end of the cylindrical resonator (L = 325 mm, R = 12.5 mm). The frequency of the wall vibration was chosen as f = 1062 Hz, such that the corresponding wavelength is equal to the length of the resonator. A standing wave was then generated in the closed tube. In the experiment, the flow field was visually studied by a smoke generator, He-Ne Laser and a digital camera. The pressure wave in the axial points was measured by a piezoresistive pressure transducer (Endvco #4428A). To simulate the flow field, the full compressible form of the Navier-Stokes equations in cylindrical coordinates was considered and solved by a highly accurate flux-corrected transport algorithm for convection terms and a central differencing scheme for the viscous and diffusive terms. In both of the experimental and numerical studies, outer acoustic streaming due to interaction of acoustic waves with viscous boundary layers was observed, and the effects of sound field intensity on the formation of streaming structures were studied.

Influences of Recess Geometry and Restrictor Dimension on Flow Patterns and Pressure Distribution of Hydrostatic Bearings

2007 ◽  
Author(s):  
Cheng-Hsien Chen ◽  
Yuan Kang ◽  
Yeon-Pun Chang ◽  
De-Xing Peng ◽  
Ding-Wen Yang
Keyword(s):  
Pressure Distribution ◽  
Stokes Equations ◽  
Flow Patterns ◽  
Lubricant Film ◽  
Navier Stokes ◽  
Width Ratio ◽  
Navier Stokes Equations ◽  
Hydrostatic Bearing ◽  
Lubricant Flow ◽  
Land Width

This paper studies the influences of recess geometry and restrictor dimensions on the flow patterns and pressure distribution of lubricant film, which are coupled effects of hybrid characteristics of a hydrostatic bearing. The lubricant flow is described by using the Navier-Stokes equations. The Galerkin weighted residual finite element method is applied to determine the lubricant velocities and pressure in the bearing clearance. The numerical simulations will evaluate the effects of the land-width ratio and restriction parameter as well as the influence of modified Reynolds number and the jet-strength coefficient on the flow patterns in the recess and pressure distribution in lubricant film. On the basis of the simulation drawn from this study, the simulated results are expected to help engineers make better use of the design of hydrostatic bearing and its restrictors.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

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