Effects of uniform suction and surface tension on laminar filmwise condensation on a horizontal elliptical tube in a porous medium

This study performs a theoretical investigation into the problem of steady filmwise condensation flow over the external surface of a horizontal elliptical tube embedded in a porous medium with suction at the tube surface. The combined effects of the surface tension force and the gravitational force in driving the flow of the liquid film within the porous medium are modeled using Darcy's law. An effective suction function, f, is introduced to model the effect of the suction force at the wall on the thickness of the condensate film. The theoretical results presented in this study show that the heat transfer performance can be enhanced by applying a suction effect at the wall. Furthermore, it is shown that the surface tension force has a negligible effect on the mean Nusselt number.     

Numerical Simulation of Mixed Convection in a Two-Dimensional Laminar Plane Wall Jet Flow

A two-dimensional, laminar, incompressible mixed convection with plane wall jet is simulated numerically using the stream function–vorticity method. The buoyancy is assisting the main flow. The flow and heat transfer study is carried out for Re = 300–600, Gr = 10³–10⁷, and Pr = 0.01–15. The streamlines, isotherm contours, similarity profiles, vorticity at the walls, and the local and average Nu values are presented and analyzed. In some cases, similarity behaviour is observed. The vorticity profile at the wall is similar to boundary-layer-type flow. However, for high Gr, the wall vorticity increases in the downstream direction. The average Nusselt number increases when Re, Gr, and Pr are increased.     

NUMERICAL FORCED CONVECTION IN A CIRCULAR PIPE WITH NONUNIFORM BLOWING OR SUCTION THROUGH THE POROUS WALL

Numerical experiments have been performed to study the effect of nonuniform blowing or suction through the porous wall of a circular pipe with a constant heat flux at Us outer surface on the conjugated heat transfer. The Navier-Stokes equations were solved by using the vorticity -stream function formulation and a finite differences alternating direction implicit method. The results show the effect of both the angle and the velocity profile of the incoming flow through the porous wall on the internal wall temperature, Nusselt number, and wall shear stresses for nonisotkermal laminar flows with Péclet numbers between 10 and 1000.     

Effects of suction and injection on self-similar solutions of second-order boundary-layer equations

Effects of suction and injection on self-similar boundary-layer flows at moderately large Reynolds numbers are studied. The general form of normal velocity at the wall is assumed to be $\text{v}{}_{\mathrm{w}}\text{= R}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{v}{}_{\mathrm{w1}}\text{+ R}{}^{\mathrm{?1}}\text{v}{}_{\mathrm{w2}}\text{+…}$ In addition to the usual five second-order effects (due to longitudinal curvature, transverse curvature, displacement speed, external vorticity, temperature gradient) an additional sixth effect due to $\text{v}{}_{\mathrm{w2}}$ is linearly separated. Both the cases of the momentum and heat transfer are studied. For heat transfer two cases of prescribed wall temperature and that of insulated wall with full similarity with viscous dissipation considered. Numerical solutions are displayed graphically and critically discussed.     

Vortical structures and heat transfer augmentation of a cooling channel in a gas turbine blade with various arrangements of tip bleed holes

Abstract

This study investigates the internal cooling processes affected by the tip bleed holes in gas turbine blades. Double bleed holes are fixed at the center of the blade tip near the pressure side and suction side, respectively. Five different arrangements of the holes along the center line of the tip are studied. The purely double holes are set as the Baseline. The purpose of the present study is to provide a new perspective of the tip film cooling to understand the internal flow processes, vorticity evolution and the mechanism of the heat transfer augmentation. A topological analysis and the boundary layer analysis methods are introduced to better understand the tip heat transfer. The total extraction area and volume is kept at the same level for all the studied cases. The results show that the Dean vortices and the near-wall vortices induced by the secondary flow contribute to the high heat transfer coefficient on the tip surface. The mixing effect of the Dean vortices and the hole extraction helps to enhance heat transfer upstream of the tip. Different arrangement of the bleed holes can affect the internal flow processes and heat transfer performance. The suction effect of the center-line bleed hole can accelerate the near-hole flow and reduce the thickness of the boundary layer. The center-line hole fitted at the middle of the tip affects significantly the rear side of the hole. Thus, the holes aligned in the middle of the tip provide the highest heat transfer and thermal performance. The thermal performance is enhanced by up to 4.7% compared with the Baseline.     

Cattaneo–Christov flux and entropy in thermofluidics involving shrinking surface

The paper examines radiative Casson boundary layer flow over an exponentially shrinking permeable sheet in a Cattaneo–Christov heat flux environment. The sheet is placed at the bottom of the fluid-saturated porous medium and suction is applied normally to the sheet to contain the vorticity. The radiative heat flux in the energy equation is assumed to follow the Rosseland approximation. Similarity transformation is performed to convert the governing partial differential equations into ordinary differential equations. The resulting boundary value problem is treated numerically employing Runge–Kutta fourth-order integration scheme along with the shooting method. The effects of pertinent parameters on quantities of interest are showcased graphically/in tabular form and are discussed. The dual profiles for velocity and temperature lead to a dual solution regime for entropy. It is found that critical mass suction rate and Nusselt number are substantially responsive to various parameters' values. Critical suction values decrease with a rise in Casson parameter β and permeability parameter K. Skin friction coefficient and Nusselt number show peculiar behavior for distinct branches of solutions.     

Ecoulement turbulent en conduite annulaire avec aspiration aux parois

The effect of suction on a turbulent flow through a cylindrical conduit of annular section is investigated experimentally. The author presents the pattern of evolution of the mean longitudinal velocity profiles and of the coefficients of friction at the walls. The “pseudo-velocity” is correctly represented by an expression proposed by Simpson et al. The wall flows, relating to the small tube and the large tube, can be considered to be virtually independent of each other for the suction magnitudes used. The author also proposes an empirical relation which gives the position of the maximum mean velocity as a function of the ratio of the radii in the absence of suction.     

GDQ Method for Natural Convection in a Cubic Cavity Using Velocity–Vorticity Formulation

ABSTRACT

Natural convection in a differentially heated cubic enclosure is studied by solving the velocity–vorticity form of the Navier–Stokes equations by a generalized differential quadrature (GDQ) method. The governing equations in the form of velocity Poisson equations, vorticity transport equations, and energy equation are solved using a coupled numerical scheme via a single global matrix for velocities, vorticities, and temperature. Vorticity and velocity coupling at the solid boundaries is enforced through a higher-order approximation by the GDQ method, thus assuring accurate satisfaction of the continuity equation. Nusselt numbers computed for Ra = 10³, 10⁴, 10⁵, and 10⁶ show good agreement with the benchmark results. A mesh independence study indicates that the present numerical procedure requires much coarse mesh compared to other numerical schemes to produce the benchmark solutions of the flow and heat transfer problems.     

Suction/injection effects on thermophoresis particle deposition in a non-Darcy porous medium under the influence of Soret,Dufour effects

The effect of suction/injection on thermophoretic particle deposition in free convection on a vertical plate embedded in a fluid saturated non-Darcy porous medium is studied using similarity solution technique. The effect of Soret and Dufour parameters on convective transport, wall thermophoretic deposition velocity, heat transfer and mass transfer is discussed in detail for different values of dispersion parameters, (Ra_γ, Ra_ξ) inertial parameter F and Lewis number Le. The result indicates that in both suction, injection the Soret effect is more influential in increasing the concentration distribution in both aiding as well as opposing buoyancies. Also, it is worth mentioning here that the combined effect of opposing buoyancy and injection will have a more significant effect on the boundary layer thickness. In both the cases, suction as well as injection, magnitude of heat transfer is observed to be more when the second order effects are considered than when they are not. But, mass transfer and the wall thermophoretic deposition velocity V_tw becomes less when all effects are considered than when they are not.     

Immersed boundary method for the simulation of heat transfer and fluid flow based on vorticity–velocity formulation

ABSTRACT

The present paper, based on the vorticity–velocity formulation of the Navier–Stokes equations, proposes an immersed boundary method for the simulation of heat transfer problems within a geometrically complex domain. The desired boundary conditions are imposed by the direct modification of the initial conditions of vorticity transport and energy equations using smooth interpolations. The time advancement of both transport equations is performed by the explicit fourth-order Runge–Kutta method. One of the main objectives of this paper is to present global smooth interpolations to evaluate the local Nusselt number. The forced convection of moving and fixed circular cylinders, natural convection problem in complex geometries, and the mixed convection between two concentric cylinders—at various Reynolds numbers—are studied.     

Flow and convective heat transfer of a ferro-nanofluid in a double-sided lid-driven cavity with a wavy wall in the presence of a variable magnetic field

ABSTRACT

In this work, the effect of a variable spatial magnetic field on ferro-nanofluid flow and heat transfer in a double-sided lid-driven enclosure with a sinusoidal hot wall is investigated. The working fluid is a mixture of iron oxide (Fe₃O₄) nanoparticles and water and is referred to as a ferro-nanofluid. The control volume-based finite element method (CVFEM) is used to solve the governing equations in the stream function–vorticity formulation. In deriving the governing equations for this investigation, the effect of both ferro-hydrodynamics and magneto-hydrodynamics is taken into account. The numerical calculations are performed for different governing parameters namely; the Reynolds number, nanoparticle volume fraction, magnetic number (arising from Ferrohydrodynamics (FHD) consideration), and the Hartmann number (arising from Magnetohydrodynamics (MHD) consideration). The results show that an enhancement in heat transfer has a direct relationship with the Reynolds number and the Hartmann number, but it has an inverse relationship with the magnetic number. Also, it can be concluded that the Nusselt number increases with the increase of the nanoparticle volume fraction, magnetic number, and the Reynolds number while the opposite trend is observed for the Hartmann number.     

GDQ METHOD FOR NATURAL CONVECTION IN A SQUARE CAVITY USING VELOCITY–VORTICITY FORMULATION

ABSTRACT

This article describes a compact numerical algorithm based on the generalized differential quadrature (GDQ) method for the numerical analysis of natural convection in a differentially heated square cavity. The velocity–vorticity form of the Navier–Stokes equations and energy equation are used to represent the mass, momentum, and energy conservations of the fluid medium in the cavity. The GDQ form of the governing equations and the vorticity definition at the boundaries are solved by a coupled solution algorithm using a global matrix scheme for all the field variables. The vorticity values at the boundary are correctly imposed using the GDQ method, which approximates a given space derivative with higher-order accuracy compared to the existing schemes based on Taylor's series expansion. This has assured a divergence-free solution for the flow field by satisfying the continuity constraint, though the pressure term is not used directly in the present formulation. The proposed algorithm is validated for a lid-driven cavity flow for Reynolds number Re = 100, 400, and 1,000, and the predicted velocity profiles are in excellent agreement with the benchmark solutions. The algorithm is then used to compute the average Nusselt number and flow parameters for natural convection in a square cavity for Rayleigh number Ra = 10³, 10⁴, 10⁵, and 10⁶. These results are in better agreement with the benchmark solutions than the results obtained by other numerical schemes, which used much finer grids compared to the present scheme.     

Non-Darcy Mixed Convection in a Porous Square Enclosure Under Suction/Injection Effects with a Non-Isothermal Vertical Wall

The influence of suction/injection at bottom/top or top/bottom walls on non-Darcy mixed convection flow with a sinusoidally varying temperature on the left vertical wall in a two-dimensional square porous enclosure is analyzed. The Forchheimer extended Darcy model is considered for flow equations. The fully developed equations are nondimensionalized, and then solved numerically by the Galerkin finite element method. A parametric study is carried out and the results are obtained for various values of the parameters such as the Grashof number (Gr*), Rayleigh number (Ra), suction/injection velocity (a), suction/injection window width (D/H), and amplitude (λ) of the sinusoidally varying temperature profile. The computed flow and temperature fields are visualized through streamlines, isotherms, and loal/global cumulative heat flux plots.     

Experimental investigation of the root flow in a horizontal axis wind turbine

This research investigates the flow behavior and its features in the blade's root region of a horizontal axis wind turbine by using stereoscopic particle image velocimetry (PIV) technique. Wind tunnel tests are conducted to measure the velocity field, phase‐locked with the blade motion, at different azimuth angles and at different spanwise positions. The pressure distribution is obtained from PIV velocity field by solving the Navier–Stokes momentum equations. In this paper, we aim to answer two questions: (i) How is the flow behavior in the root region? (ii) How is the evolution of the root vortex? The analysis of the velocity fields shows an outboard radial flow motion in the root region and a vorticity driven inboard motion at the blade?s maximum chord position. As a result of this vorticity driven flow, an increase in the axial velocity close to nacelle is measured. Wake sheets are observed and further discussed in the measured velocity and vorticity distributions. The formation and evolution of the root vortices conveyed downstream by the axial velocity are analyzed through vorticity and pressure distributions. Although the azimuthal vorticity in 3D representation is showing the trailing vorticity, the tilting of the root vortex tube is observed in the axial vorticity distribution. Moreover, the radial vorticity and azimuthal velocity from chordwise measurements show separation on the suction surface of the blade. This research concluded that the flow in the blade wake is driven by the root vortex; hence, the local effects of the root vortex cannot be ignored. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical study of mixed convective heat transfer in a lid‐driven enclosure with rotating cylinders

A numerical simulation is performed to characterize the mixed convective transport in a three‐dimensional square lid‐driven enclosure with two rotating cylinders. The top wall is moving in the positive x‐direction, and the bottom wall is at a higher fixed temperature compared with all other isothermal walls. Both cylinders are rotating in its own plane about their centroidal axis. On the basis of rotation of both cylinders in clockwise or counter‐clockwise directions, four rotational models are studied. Various controlling parameters considered in the present study are Grashof number (10 ³ < Gr < 10 ⁵), rotating speed of the cylinder (5 < ω < 50), and the Reynolds number based on top wall movement is fixed to 100. The effect of cylinder rotation on the heat transfer of bottom wall is reported with the help of streamlines, contour plots of z‐component of vorticity, averaged and local Nusselt number, ratios of secondary flow and drag coefficient. It is observed that the heat transfer at the bottom wall is substantially dependent on the rotational model and rotational speed of the cylinder.     

Molecular Dynamics Study of Interactions between the Water/ice Interface and a Nanoparticle in the Vicinity of a Solid Surface

ABSTRACT

In this study, non-equilibrium molecular dynamics simulations were conducted for a coexistence system of water and ice on a wall surface with a single nanoparticle to reveal the effects of water solidification on the nanoparticle in the vicinity of a wall surface. We further investigated the effect of the presence and size of particles on the density profile of water in the vicinity of the wall surface and the force acting on particles from water molecules, when the solidification interface contacted the wall and the particles. The results revealed that a strong mutual influence exists between the solidification interface and the nanoparticle on the wall’s surface; the nanoparticle on the wall prevents water solidification in proximity to the wall. Moreover, the force acting on the nanoparticle from water molecules changes as the solidification interface approaches; the cooling temperature is shown to affect the direction of this force. It indicates that the solidification process is a key influential factor which affects nanoparticle movements on a wall surface at molecular scales.     

Effect of cross-stream buoyancy and rotation on the free-stream flow and heat transfer across a cylinder

Cross-stream buoyancy-induced formation of VS (vortex shedding) past a rotating cylinder maintained at constant wall temperature is studied at Re = 40 and 100. The non-dimensional rotational velocity (α) is varied from 0 to 8 and Richardson number from 0 to 1 with air as the working fluid. Semi-explicit finite-volume method code implemented on colocated Cartesian multi-block grid is used. Buoyancy-induced onset of vortex shedding is found for stationary/rotating cylinder at sub-critical Re = 40. Steady-VS flow transition map is shown for the different rotational velocity and Ri; and reasoned using vorticity dynamics. At higher rotational velocity, origin of buoyancy-induced secondary frequency for Re = 40 at α = 6 and for 100 at α = 5 is discussed using spectral analysis and phase portrait technique. The VS frequency is much smaller at higher as compared to lower rotational velocity and increases with increasing Ri. A monotonic increase in the downward lift force and a reversal in the direction of drag force is found with increasing rotational velocity. Rotation can be used as a drag reduction and heat transfer suppression technique.     

Parametric influence on convective heat transfer for an outlet guide vane

ABSTRACT

Improved understanding of the impact of the operating conditions on the heat transfer and fluid flow behaviors of an outlet guide vane (OGV) is essential for accurate prediction of the lifetime of jet engines. In this article, the heat transfer characteristics of an OGV at various Reynolds numbers (Re), free stream turbulence levels, Mach number (Ma), and surface roughness are studied numerically. The Re is kept at 300,000 and 450,000, respectively, the free stream turbulence intensity ranges from 3.2% to 13%, and the turbulent length scale is varied from 1.2 to 11 mm. The Ma is selected as 0.06, 0.25, and 0.35, and the sandy grain roughness height is increased from the smooth wall level up to 160 µm. Mid-span pressure coefficient and Nu distributions are presented. Basically, the heat transfer patterns and pressure profiles are weak functions of the Re and Ma. Increasing the Re slightly moves the transition position upstream, while the Ma has no effect on the transition process. On the suction side, the transition is induced by flow separation and a bump is visible in the pressure profile. However, the turbulence intensity, turbulence length scale, and surface roughness levels have significant effects on the heat transfer and pressure distributions. On the suction side, the bump is invisible and the “separation-induced transition” is replaced by the “by pass transition”. It is also found that the transition position moves upstream as the turbulence intensity, length scale, and roughness level increase.     

Reduction in Performance Due to Recirculation in Mechanical Draft Cooling Towers

Abstract

The influence of recirculating warm plume air on the performance of mechanical-draft cooling towers is investigated analytically, numerically, and experimentally. It is shown that the amount of recirculation that occurs is a function of the flow and the thermal and geometric characteristics of the tower. The presence of a wind wall tends to reduce the amount of recirculation. An equation is presented with which the performance effectiveness due to recirculation can be evaluated approximately for a mechanical-draft cooling tower.     

Velocity–vorticity formulation for 3D natural convection in an inclined cavity by DQ method

The present work proposes a novel numerical solution algorithm based on a differential quadrature (DQ) method to simulate natural convection in an inclined cubic cavity using velocity–vorticity form of the Navier–Stokes equations. Since the DQ method employs a higher-order polynomial to approximate any given differential operator, the vorticity values at the boundaries can be computed more accurately than the conventionally followed second-order accurate Taylor’s series expansion scheme. The numerical capability of the present algorithm is demonstrated by the application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the continuity equation, the vorticity transport equations and the energy equation are all solved as a coupled system of equations for the seven field variables consisting of three velocities, three vorticities and temperature. Thus coupling the velocity and the vorticity transport equations allows the determination of the vorticity boundary values implicitly without requiring the explicit specification of the vorticity boundary conditions. The present algorithm is proved to be an efficient method to resolve the non-linearity involved with the vorticity transport equations and the energy equation. Test results obtained for an inclined cubic cavity with different angle of inclinations for Rayleigh number equal to 10³, 10⁴, 10⁵ and 10⁶ indicate that the present coupled solution algorithm could predict the benchmark results for temperature and flow fields using a much coarse computational grid compared to other numerical schemes.