Finite-element analysis of fluid flow and heat transfer for staggered bundles of cylinders in cross flow

The two-dimensional Navier-Stokes equations and the energy equation governing steady laminar incompressible flow are solved by a penalty finite-element model for flow across finite depth, five-row deep, staggered bundles of cylinders. Pitch to diameter ratios of 1·5 and 2·0 are considered for cylinders in equilateral triangular and square arrangements. Reynolds numbers studied range from 100 to 400, and a Prandtl number of 0·7 is used. Velocity vector fields, streamline patterns, vorticity, pressure and temperature contours, local and average Nusselt numbers, pressure and shear stress distributions around the cylinder walls and drag coefficients are presented. The results obtained agree well with available experimental and numerical data.     

CONVECTIVE HEAT TRANSFER FROM A CIRCULAR CYLINDER UNDER THE EFFECT OF A SOLID PLANE WALL

The purpose of this investigation is to study the convective heat transfer from a horizontal circular cylinder under the effect of a solid plane wall. The full Navier–Stokes and energy equations for two-dimensi onal steady flow are solved by a finite element method. The variations in surface shear stress, local pressure and Nusselt number around the surface of the cylinder as well as the predicted values of average Nusselt number, location of separation and some flow and temperature fields are presented. It is found that the average Nusselt number and drag force increase as the gap between the cylinder and the wall is increased.     

Forced‐convection heat transfer from tandem square cylinders in cross flow at low Reynolds numbers

This paper presents the results of a numerical study on the flow characteristics and heat transfer over two equal square cylinders in a tandem arrangement. Spacing between the cylinders is five widths of the cylinder and the Reynolds number ranges from 1 to 200, Pr=0.71. Both steady and unsteady incompressible laminar flow in the 2D regime are performed with a finite volume code based on the SIMPLEC algorithm and non‐staggered grid. A study of the effects of spatial resolution and blockage on the results is provided. In this study, the instantaneous and mean streamlines, vorticity and isotherm patterns for different Reynolds numbers are presented and discussed. In addition, the global quantities such as pressure and viscous drag coefficients, RMS lift and drag coefficients, recirculation length, Strouhal number and Nusselt number are determined and discussed for various Reynolds numbers. Copyright © 2008 John Wiley & Sons, Ltd.     

Finite element solutions of laminar flow and heat transfer of air in a staggered and an in-line tube bank

A finite element method is used to solve the full Navier-Stokes and energy equations for the problems of laminar flow and heat transfer characteristics of air around three isothermal heated horizontal cylinders in a staggered tube bank and around four isothermal heated horizontal cylinders in an in line tube bank. The variations of surface shear stress, pressure and Nusselt number are obtained over the entire cylinder surface, including the zone beyond the separation point. The predicted values of total drag, pressure drag and friction drag coefficients, average Nusselt number, and the plots of velocity flow fields and isotherms are also presented.     

Combined natural convection heat and mass transfer in an enclosure having finite thickness walls

Unsteady three-dimensional conjugate heat and mass transfer in an enclosure having finite thickness heat-conducting walls has been analyzed numerically. The governing unsteady, three-dimensional flow, energy and contaminant transport equations for the gas cavity and unsteady heat conduction equation for solid walls, written in dimensionless terms of the vector potential functions, the vorticity vector, the temperature and the concentration, have been solved using an iterative implicit finite-difference method. Main attention was paid to the effects of the Rayleigh number, buoyancy ratio and the dimensionless time on the flow structure and heat and mass transfer regimes. It should be noted that the dominant cause of the oscillations in the dimensionless time dependences of the average Nusselt number on the heat source surface and the average Sherwood number on the contaminant source surface at Ra>5?10⁵ is the mutual influence of the analyzed object geometry and the thermo-diffusivity impact on the flow. The change in the buoyancy ratio can lead to the essential modifications of the flow, temperature and concentration fields owing to the significant influence of the concentration gradient.     

Fluid flow and heat transfer characteristics for a square prism (blockage ratio = 0.1) placed inside a wind tunnel

Experimental investigations in fluid flow and heat transfer have been carried out to study the effect of wall proximity due to flow separation around a square prism at Reynolds number 2.6 × 10⁴, blockage ratio 0.1, different height-ratios and various angles of attack. The static pressure distribution has been measured on all faces of the square prism. The results have been presented in the form of pressure coefficient, drag coefficient for various height-ratios. The pressure distribution shows positive values on the front face whereas on the rear face negative values of the pressure coefficient have been observed. The positive pressure coefficient for different height-ratios does not vary too much but the negative values of pressure coefficient are higher for all points on the surface as the bluff body approaches towards the upper wall of the wind tunnel. The drag coefficient decreases with the increase in angle of attack as the height-ratio decreases. The maximum value of drag coefficient has been observed at an angle of attack nearly 50° for the square prism at all height-ratios. The heat transfer experiments have been carried out under constant heat flux condition. Heat transfer coefficient are determined from the measured wall temperature and ambient temperature and presented in the form of Nusselt number. Both local and average Nusselt numbers have been presented for various height-ratios. The variation of local Nusselt number has been shown with non-dimensional distance for different angles of attack. The variation of average Nusselt number has also been shown with different angles of attack. The local as well as average Nusselt number decreases as the height-ratio decreases for all non-dimensional distance and angle of attack, respectively, for the square prism. The average Nusselt number for the square prism varies with the angle of attack. But there is no definite angle of attack at which the value of average Nusselt number is either maximum or minimum.     

Experimental investigation to study flow and heat transfer characteristics over a NACA0018 aerofoil for different height ratios

Experiments are carried out to study flow and heat transfer characteristics over NACA0018 aerofoil when the body approaches the wall of a wind tunnel. Investigations have been done to study the effect of wall proximity due to flow separation around the body at Reynolds number 2.5 × 10⁵, different height ratios and various angles of attack. The static pressure distribution has been measured on upper and lower surfaces of the aerofoil. The results have been presented in the form of pressure coefficient, drag coefficient for different height ratios. Pressure coefficient values are decreased and then increased on the lower surface of the aerofoil and decreased on the upper surface of the aerofoil at all angles of attack. The negative pressure coefficient and drag coefficient decreases as the body approaches the upper wall of wind tunnel. The maximum value of drag coefficient has been observed at an angle of attack 30° for the aerofoil at all height ratios. The Heat transfer experiments have been carried out under constant heat flux condition. Heat transfer coefficients are determined from the measured wall temperature and ambient temperature and presented in the form of Nusselt number. The variation of local as well as average Nusselt number has been shown with non dimensional distance for different angles of attack and for various height ratios. The local as well as average Nusselt number decreases as the height ratio decreases for all non-dimensional distance and angles of attack respectively. Maximum value of average Nusselt number has been observed at an angle of attack 40°.     

A SPECTRAL METHOD FOR UNSTEADY FLOW AND HEAT TRANSFER PAST A SPHERICAL DROPLET: PRIMITIVE VARIABLE FORMULATION

Abstract

A spectral method is developed based on the primitive variables for the time-dependent solution of the flow and the temperature past a spherical droplet. Both Chebyshev and Legendre polynomials are used to expand the velocity, pressure, and temperature in the radial and angular directions, respectively. The fractional time-stepping method suggested by Orszag (Orszag et al., 1980) is used for solving the flow and the pressure fields. Euler backward differencing is used for the integration of the energy equation. The computed steady-state drag coefficients are compared to those found in the literature for Reynolds numbers in the range from 0.5 to 50 for both the continuous and the dispersed phase. The transient drag coefficients and Nusselt numbers are compared with our previous study using a stream function-vorticity formulation (Nguyen et al, 1993). The comparison indicates that the present model is capable of predicting the correct nature of the flow and heat transfer associated with a droplet.     

Hydrodynamic and heat transfer characteristics of laminar flow past a parabolic cylinder with constant heat flux

 Steady, two-dimensional, symmetric, laminar and incompressible flow past parabolic bodies in a uniform stream with constant heat flux is investigated numerically. The full Navier–Stokes and energy equations in parabolic coordinates with stream function, vorticity and temperature as dependent variables were solved. These equations were solved using a second order accurate finite difference scheme on a non-uniform grid. The leading edge region was part of the solution domain. Wide range of Reynolds number (based on the nose radius of curvature) was covered for different values of Prandtl number. The flow past a semi-infinite flat plate was obtained when Reynolds number is set equal to zero. Results are presented for pressure and temperature distributions. Also local and average skin friction and Nusselt number distributions are presented. The effect of both Reynolds number and Prandtl number on the local and average Nusselt number is also presented. Received on 5 July 2000     

Effect of thermo‐solutal stratification on recirculation flow patterns in a backward‐facing step channel flow

This paper presents results on the combined effect of thermo‐solutal buoyancy forces on the recirculatory flow behavior in a horizontal channel with backward‐facing step and the ensuing impact on heat and mass transfer phenomena. The governing equations for double diffusive mixed convection are represented in velocity–vorticity form of momentum equations, velocity Poisson equations, energy and concentration equations. Galerkin's finite‐element method has been employed to solve the governing equations. Recirculatory flow fields with heat and mass transfer are simulated for opposing and aiding thermo‐solutal buoyancy forces by assuming suitable boundary conditions for energy and concentration equations. The effect of Richardson number (0.1?Ri?10) and buoyancy ratio (?10?N?10) on the recirculation bubble and Nusselt and Sherwood numbers are studied in detail. For Richardson number greater than unity, distinct variations in the gradients of Nusselt number and Sherwood number with buoyancy ratio are observed for flow regimes with opposing and aiding buoyancy forces. Copyright © 2009 John Wiley & Sons, Ltd.     

Transient natural convection between concentric and vertically eccentric spheres with mixed boundary conditions

Transient analysis has been investigated numerically to determine heat transfer by natural convection between concentric and vertically eccentric spheres with constant heat flux on the inner wall and a specified isothermal temperature on the outer wall. The governing equations, in terms of vorticity, stream function and temperature are expressed in a spherical polar coordinate system. The alternating direction implicit method and the successive over-relaxation techniques are applied to solve the finite difference form of governing equations. A physical model is introduced which accounts for the effects of fluid buoyancy as well as eccentricity of the outer sphere. Transient solutions of the entire flow field are obtained for a range of modified Rayleigh number (10³<Ra?<5×10⁵), for a Prandtl number of 0.7 and a radius ratio of 2.0, with the outer sphere near the top and bottom of the inner sphere (ε=±0.625). Results of the parametric study conducted further reveal that the heat and flow fields are primarily dependent on the modified Rayleigh number and the eccentricity of the spherical annulus. The results of average Nusselt numbers are also compared with the results obtained for flow between two isothermal spheres.     

Mixed Convection in a Vertical Porous Channel

A numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces is studied by taking into account the effect of viscous and Darcy dissipations. The flow is modeled using the Brinkman–Forchheimer-extended Darcy equations. The two boundaries are considered as isothermal–isothermal, isoflux–isothermal and isothermal–isoflux for the left and right walls of the channel and kept either at equal or at different temperatures. The governing equations are solved numerically by finite difference method with Southwell–Over–Relaxation technique for extended Darcy model and analytically using perturbation series method for Darcian model. The velocity and temperature fields are obtained for various porous parameter, inertia effect, product of Brinkman number and Grashof number and the ratio of Grashof number and Reynolds number for equal and different wall temperatures. Nusselt number at the walls is also determined for three types of thermal boundary conditions. The viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. The Darcy and inertial drag terms suppress the flow. It is found that analytical and numerical solutions agree very well for the Darcian model. An erratum to this article is available at .     

On the friction drag reduction mechanism of streamwise wall fluctuations

Understanding how to decrease the friction drag exerted by a fluid on a solid surface is becoming increasingly important to address key societal challenges, such as decreasing the carbon footprint of transport. Well-established techniques are not yet available for friction drag reduction. Direct numerical simulation results obtained by Józsa et al. (2019) previously indicated that a passive compliant wall can decrease friction drag by sustaining the drag reduction mechanism of an active control strategy. The proposed compliant wall is driven by wall shear stress fluctuations and responds with streamwise wall velocity fluctuations. The present study aims to clarify the underlying physical mechanism enabling the drag reduction of these active and passive control techniques. Analysis of turbulence statistics and flow fields reveals that both compliant wall and active control amplify streamwise velocity streaks in the viscous sublayer. By doing so, these control methods counteract dominant spanwise vorticity fluctuations in the near-wall region. The lowered vorticity fluctuations lead to an overall weakening of vortical structures which then mitigates momentum transfer and results in lower friction drag. These results might underpin the further development and practical implementation of these control strategies.     

Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method

The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.     

Numerical analysis on longitudinal location optimization of vortex generator in compact heat exchangers

In this paper, numerical, curvilinear and turbulent model has been used to investigate the effect of vortex generator's longitudinal displacement on heat transfer and fluid flow in different Reynolds numbers ranging from 500 to 3000. The numerical model has been validated with experimental results of a former study, which is resembled in a particular case. Numerical simulation shows that the vorticity enhancement would increase both Nusselt number and pressure drop. Proposed trend is not constant and the pattern in which parameters change is dependent on Reynolds number. Finally, a conjugated optimization of pressure drop and the Nusselt number has been suggested based on the order of parameter changes. Copyright © 2010 John Wiley & Sons, Ltd.     

Turbulent natural convection in vertical parallel-plate channels

The problem of buoyancy driven turbulent flow in parallel-plate channels is investigated. The investigation is limited to vertical channels of uniform cross-section with different modes of heating. The details of the flow and thermal fields are obtained from the solution of the conservation equations of mass, momentum, and energy in addition to equations of the low Reynolds number turbulence model. The study covers Rayleigh number ranging from 10⁵ to 10⁷ and focuses on the effect of channel geometry on the characteristic of the flow and thermal fields as well as the local and average Nusselt number variation. A Nusselt number correlation has been developed in terms of a modified Rayleigh number and channel aspect ratio for the cases of symmetrically heated isothermal and isoflux conditions.     

Laminar fluid convection between concentric and eccentric heated horizontal rotating cylinders for low-Prandtl-number fluids

Numerical experiments are performed to study rotational effects on the mixed convection of low-Prandtlnumber fluids enclosed between the annuli of concentric and eccentric horizontal cylinders. The inner cylinder is assumed to be heated and rotating. The rotational Reynolds number considered is in the range where the effect of Taylor vortices is negligible. The Prandtl number of the fluid considered is in the range 0·01–1·0. The Rayleigh number considered is up to 10⁶. A non-uniform mesh transformation technique coupled with the introduction of ‘false transient’ parameters to the vorticity and streamfunction-vorticity expressions was used to solve the governing set of equations. Results show that when the inner cylinder is made to rotate, the multicellular flow patterns observed in stationary cylindrical annuli subside in a manner depending on the Prandtl number of the fluids. Eventually the flow tends toward a uniform flow similar to that of a solid body rotation. For a fixed Rayleigh number and with a Prandtl number of the order of 1·0, when the inner cylinder is made to rotate, the mean Nusselt number is observed to decrease throughout the flow. For lower Prandtl number of the order 0·1–0·01 the mean Nusselt number remained fairly constant when the inner cylinder was made to rotate. The mean Nusselt numbers obtained were also compared with available data from other investigators.     

Numerical investigation of flow and combined natural-forced convection from an isothermal square cylinder in cross flow

Unsteady flow and heat transfer from a horizontal isothermal square cylinder is studied numerically using a three-dimensional computational model to investigate the influence of buoyancy on the forced flow and heat transfer characteristics. The numerical model is based on a horizontal square cylinder subjected to laminar fluid flow in an unconfined channel. The governing equations in 3D form are solved using a fractional step method based on the finite difference discretization in addition to a Crank–Nicholson scheme employed to the convective and the viscous terms. Two working fluids–air (Pr = 0.7) and water (Pr = 7)–are considered, and the flow and heat transfer simulations were carried out for the Reynolds and Richardson numbers in the intervals 55 ≤ Re ≤ 250 and 0 ≤ Ri ≤ 2, respectively. The flow characteristics such as time-averaged drag/lift, rms drag/rms lift coefficients as well as Strouhal number were computed. The heat transfer from the cylinder is assessed by mean Nusselt number (and rms Nusselt number) over the total heated cylinder walls. As the buoyancy increases, the mass and the velocity of the fluid flowing underneath the cylinder increases. The fluid is injected into the near wake region with an upward motion which significantly alters the flow field in the downstream as well as upstream regions. The effects of Reynolds, Richardson and Prandtl numbers on the flow field and temperature distributions are discussed in detail. It is shown that the flow and heat transfer characteristics are influenced more for air than water. To fill the void in the literature, useful empirical correlations of practical importance are derived for pure forced and pure natural as well as mixed convection. The mixed convection correlations, in terms of the ratio of pure forced convection, are also developed, and their implications are discussed.     

Simultaneous quantitative flow measurement using PIV on both sides of the air–water interface for breaking waves

An experimental method for simultaneously measuring the velocity fields on the air and water side of unsteady breaking waves is presented. The method includes a novel technique for seeding the air flow such that the air velocity can be resolved in the absence of wind. Low density particles that have large Stokes drag and ability to respond to high-frequency flow fluctuations are used to seed the air flow. Multi-camera, multi-laser particle image velocimetry setups are applied to small-scale unsteady breaking waves, yielding fully time-resolved velocity fields. The surface tension of the fluid is altered and controlled to form spilling breaking waves. Results for the velocity and vorticity fields of representative spilling breakers, which show shedding of an air-side vortex and well-documented generation of water-side vorticity, are presented and discussed.     

Numerical modeling of a viscous incompressible unsteady separated flow past a rotating cylinder

For studying unsteady flow past a rotating circular cylinder the Navier-Stokes equations are used. The numerical algorithm is based on an artificial-compressibility method, an implicit three-layer second-order scheme with subiterations with respect to time, a third-order scheme with splitting of the flux vectors for the convective terms, and a central-difference scheme for integrating the viscous terms. The calculated velocity profiles, the vorticity fields, the Strouhal numbers, the distribution of the pressure and friction coefficients over the cylinder surface, and the coefficients of the drag and lift forces for the laminar flow regime are analyzed.