Fluid Flow and Mixed Heat Transfer in a Horizontal Channel with an Open Cavity and Wavy Wall

Heat exchangers are utilized extensively in different industries and technologies.Consequently,optimizing heat exchangers has been a major concern among researchers.Although various studies have been conducted to improve the heat transfer rate,the use of a wavy wall in the presence of different types of heat transfer mechanisms has not been investigated.This study thus investigates the mixed heat transmission behavior of fluid in a horizontal channel with a cavity and a hot,wavy wall.The fluid flow in the channel is considered laminar,and the governing equations including continuity,momentum,and energy are all solved numerically.The numerical solution is stabilized by using a first-order multi-dimensional characteristic-based scheme in combination with a fifth-order Runge-Kutta method.The flow and heat transfer effects of varying Richardson numbers,Reynolds numbers,wave amplitude,wavelength,channel height,and cavity width are examined.The results indicate that the mean Nusselt number increases with an increase in Reynolds number,wave amplitude,and cavity width,while it decreases with an increase in Richardson number,wavelength,and channel height.The minimum Nusselt number is calculated to be 0.7,whereas the maximum Nusselt number is 27.09.The Nusselt number has only increased by 40%in the higher depths of the cavity,despite the Richardson number being 10,000 times larger.But this figure increases to 130%at lower depths.The mean Nusselt number is thus significantly influenced by channel height and cavity width.The influence of wave amplitude on the mean Nusselt number is twice that of wavelength.

TRPIV investigation of space-time correlation in turbulent flows over flat and wavy walls

The present experimental work is devoted to in- vestigate a new space-time correlation model for the turbulent boundary layer over a flat and a wavy walls. A turbulent boundary layer flow at Reo = 2460 is measured by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The space-time correlations of instantaneous streamwise fluctuation velocity are calculated at 3 different wall-normal locations in logarithmic layer. It is found that the scales of coherent structure increase with moving far away from the wall. The growth of scales is a manifestation of the growth of prevalent coherent structures in the turbulent boundary layer like hairpin vortex or hairpin packets when they lift up. The resulting contours of the space-time correlation exhibit elliptic-like shapes rather than straight lines. It is suggested that, instead of Taylor hypothesis, the elliptic model of the space-time correlation is valid for the wallbounded turbulent flow over either a flat wall or a wavy wall. The elliptic iso-correlation curves have a uniform preferred orientation whose slope is determined by the convection velocity. The convection velocity derived from the space-time correlation represents the velocity at which the large-scale eddies carry small-scale eddies. The sweep velocity rep- resents the distortions of the small-scale eddies and is intimately associated with the fluctuation velocity in the logarithmic layer of turbulent boundary layers. The nondimensionalized correlation curves confirm that the elliptic model is more proper for approximating the space-time correlation than Taylor hypothesis, because the latter can not embody the small-scale motions which have non-negligible distortions. A second flow over a wavy wall is also recorded using TRPIV. Due to the combined effect of shear layers and the adverse pressure gradient, the space-time correlation does not show an elliptic-like shape at some specific heights over the wavy wall, but in the outer region of the wavy wallbounded flow, the elliptic model remains valid.

Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall

The combined effects of thermal and mass convection of viscous incom- pressible and immiscible fluids through a vertical wavy wall and a smooth flat wall are analyzed. The dimensionless governing equations are perturbed into a mean part （the zeroth-order） and a perturbed part （the first-order）. The first-order quantities are ob- tained by the perturbation series expansion for short wavelength, in which the terms of the exponential order arise. The analytical expressions for the zeroth-order, the first-order, and the total solutions are obtained. The numerical computations are presented graph- ically to show the salient features of the fluid flow and the heat transfer characteristics. Separate solutions are matched at the interface by using suitable matching conditions. The shear stress and the Nusselt number are also analyzed for variations of the governing parameters. It is observed that the Grashof number, the viscosity ratio, the width ratio, and the conductivity ratio promote the velocity parallel to the flow direction. A reversal effect is observed for the velocity perpendicular to the flow direction.

An Integral Research of the Flow of a Liquid Film Along a Vertical Wavy Wall

An approximate research on the flow of a two dimensional, steady laminar liquid film along a vertical, long periodic wavy wall is conducted based on boundary layer integration. An ordinary equation about the film evolution is derived. By analyzing the integral equation of the hydrodynamic boundary layer under different Reynolds number domains, the flow characteristics are studied preliminarily. Influences of wall waviness, flow rate on the film development are discussed.

WATER TUNNEL EXPERIMENTAL INVESTIGATION ON THE DRAG REDUCTION CHARACTERISTICS OF THE TRAVELING WAVY WALL

Drag reduction experiment of the traveling wavy wall at high Reynolds number is conducted.A suit of traveling wavy wall device is developed.The drag forces of the traveling wavy wall with various wave speeds（c）are measured under different water speeds（U）in the K15 cavitation water tunnel and are compared with that of the flat plate.The results show that the mean drag force of the traveling wavy wall have decreased and then increased with oscillation frequency increasing at the same flow speed.Under different flow speeds,when traveling wave wall reached to the minimum of drag force,the corresponding the ratio of the wall motion phase speed c to flow speed U,c /U is slightly different.Within the parameters of the experiment,whenc /U reaches a certain value,the drag force of the traveling wavy wall can be less than that of the flat plate.The drag reduction can be up to 42%.Furthermore,as the value ofc /U increases,the traveling wavy wall can restrain the separation and improve the quality of flow field.

Numerical Study for Turbulent Flow of Drag and Flow Noise with Wavy Wall

In this paper,a numerical simulation of flow-induced noise by the low Mach number turbulent flow with a sinusoidal wavy wall was presented based on the unsteady incompressible Navier-Stokes equations and Lighthill's acoustic analogy.Large eddy simulation (LES) was used to investigate the space-time flow field and the Smagorinsky sub-grid scale (SGS) model was introduced for turbulence model.Using Lighthill's acoustics analogy,the flow field simulated by LES was taken as near-field sound sources and radiated sound from turbulent flow was computed by the Curle's integral formulation under the low Mach number approximation.Both spanwise wavy wall and streamwise wavy wall with various wall wave amplitudes were discussed to investigate their effects on reducing the drag and flow noise.The relationship between flow noise and drag on the wavy wall is also studied.

EXPERIMENTAL INVESTIGATION ON THE DRAG REDUCTION CHARACTERISTICS OF TRAVELING WAVY WALL AT HIGH REYNOLDS NUMBER IN WIND TUNNEL

Drag reduction experiments of the traveling wavy wall at high Reynolds number, ranging from 1.46×106 to 5.83×106 based on the free-stream velocity and the model length, were conducted. A suit of traveling wavy wall device was developed and its characteristics of drag reduction at high Reynolds number were investigated. The drag forces of the traveling wavy wall with various wave speeds （ c ） were measured at different wind speeds （U ） in the FL-8 low-speed wind tunnel and compared with the drag force of the flat plate. The results show that the mean drag force of the traveling wavy wall decreases as the value of c /U increases, at different wind velocities, the values of c /U corresponding to minimal drag force of the traveling wavy wall are different, when the values of c /U are larger than 0.6, the mean drag forces of the traveling wavy wall are smaller than those of the flat plate, and the drag reduction can be up to 60%. The drag reduction effectiveness of traveling wavy wall is thus achieved. Furthermore, as the value of c /U increases, the traveling wavy wall can restrain the separation and improve the quality of flow field.

Transport of Cu-H2O nanofluid through a channel with wavy walls under velocity slip and connective boundary conditions

Present study examines the mixed convective peristaltic transport of Cu-H2O nanofluid with velocity slip and convective boundary conditions. Analysis is performed using the two-phase model of the nanofluid. Viscous dissipation and heat generation/absorption effects are also taken into account. Problem is formulated using the long wavelength and low Reynolds number approach. Numerical solutions for the pressure rise per wavelength, pressure gradient, axial velocity, temperature and heat transfer rate at the boundaxy are obtained and studied through graphs. Results show that the area of peristaltic pumping decreases with an increase in the nanoparticles volume fraction. Increase in the velocity slip parameter shows an increase of the pressure gradient in the occluded part of the channel. Further, addition of copper nanoparticles reduces both the axial velocity and temperature of the base fluid. Temperature of the nanofluid also decreases sufficiently for an increase in the value of Blot number.

Unsteady Flow of Hybrid Nanofluid with MagnetohydrodynamicsRadiation-Natural Convection Effects in a U-Shaped Wavy Porous Cavity

In this paper,the unsteady magnetohydrodynamic(MHD)-radiation-natural convection of a hybrid nanofluid within a U-shaped wavy porous cavity is investigated.This problem has relevant applications in optimizing thermal management systems in electronic devices,solar energy collectors,and other industrial applications where efficient heat transfer is very important.The study is based on the application of a numerical approach using the Finite Difference Method(FDM)for the resolution of the governing equations,which incorporates the Rosseland approximation for thermal radiation and the Darcy-Brinkman-Forchheimer model for porous media.It was found that the increase of Hartmann number(Ha)causes a reduction of the average Nusselt number(Nu),with a maximum decrease of 25%observed as Ha increases from 0 to 50.In addition,the influence of the wall’s wave amplitude and the heat source length on the heat transfer rate was quantified,and it was revealed that at high wave amplitude,the average Nu increases by up to 15%.These findings suggest that manipulating magnetic field strength and cavity geometry can significantly enhance thermal performance.The novelty of this is related to the exploration of a U-shaped wavy cavity,which is not covered in previous studies,and to the detailed examination of the combined effects of magnetic fields,radiation,and hybrid nanofluids.

Noise control for high subsonic jet flows by inner wall treatment

Subsonic jet nozzles,commonly used in passenger aircrafts,generate significant noise that travels both downstream and upstream due to large-scale or fine-scale turbulence in the jet plume.To reduce jet noise,a novel wall treatment method,termed the wavy inner wall(WIW),is proposed.With this method,the smooth inner wall near the exit of the nozzle is replaced by treated walls that carry small wavy patterns.Numerical simulations were conducted to investigate the effects of the WIW treatment.Large eddy simulations(LES)were used to predict the unsteady flow field and the far-field noise,followed by the analogy method proposed by Ffowcs Williams and Hawkings.To better understand the mechanism behind the noise reduction achieved by the WIW treatment,the shear-layer instability,radial and azimuthal auto-correlation functions,turbulent kinetic energy,and acoustic source term from the Tam-Auriault(TA)jet-noise model were analyzed.Results indicated that the WIW treatment advances the onset of jet flow instability in the shear-layer,leading to the early breakdown of jet shear-layer and production of different scales of downstream turbulent structures.As a result,the distribution and production of turbulent kinetic energy are affected,and the genera-tion and emission of jet noise are controlled.The WIW treatment enables the control of fine scale turbulence,resulting in the reduction of mid-to high-frequency noise in the far field,while ensuring a low thrust loss.This feature makes the WIW method a promis-ing approach for jet noise control.