Three-dimensional numerical simulations of cross-flow around four cylinders in an in-line square configuration

This paper presents a numerical study of three-dimensional (3-D) laminar flow around four circular cylinders in an in-line square configuration. The investigation focuses on effects of spacing ratio (L/D) and aspect ratio (H/D) on 3-D flow characteristics, and the force and pressure coefficients of the cylinders. Extensive 3-D numerical simulations were performed at Reynolds number of 200 for L/D from 1.6 to 5.0 at H/D=16 and H/D from 6 to 20 at L/D=3.5. The results show that the 3-D numerical simulations have remedied the inadequacy of 2-D simulations and the results are in excellent agreement with the experimental results. The relation between 3-D flow patterns and pressure characteristics around the four cylinders is examined and discussed. The critical spacing ratio for flow pattern transformation was found to be L/D=3.5 for H/D=16, while a bistable wake pattern was observed at L/D=1.6 for the same aspect ratio. Moreover, a transformation of flow pattern from a stable shielding flow pattern to a vortex shedding flow pattern near the middle spanwise positions of the cylinders was observed and was found to be dependent on the aspect ratio, spacing ratio, and end wall conditions. Due to the highly 3-D nature of the flows, different flow patterns coexist over different spanwise positions of the cylinders even for the same aspect ratio. It is concluded that spacing ratio, aspect ratio, and the no-slip end wall condition have important combined effects on free shear layer development of the cylinders and hence have significant effects on the pressure field and force characteristics of the four cylinders with different spacing ratios and aspect ratios.     

On the effect of flow direction on mixed convection from a horizontal cylinder

The influence of free stream direction on mixed (natural and forced) convective heat transfer from a circular cylinder is investigated. The cylinder, which has an isothermal surface, is placed with its axis horizontal and normal to the oncoming flow. The free stream direction varies between the vertically upward (parallel flow) and the vertically downward (contraflow) directions. The investigation is based on the time integration of the unsteady, two-dimensional equations of motion and energy until reaching steady conditions. The study is limited to Reynolds numbers up to Re = 40 and Grashoff numbers of Gr = Re². The results are compared with the available experimental data and the agreement is satisfactory.     

Large Eddy Simulation of Turbulent Flow Through Submerged Vegetation

Large Eddy Simulations (LES) are performed for an open channel flow through idealized submerged vegetation with a water depth (h) to plant height (h _p) ratio of h/h _p = 1.5 according to the experimental configuration of Liu et al. (J Geophys Res Earth Sci, 2008). They used a 1D laser Doppler velocimeter (LDV) to measure longitudinal and vertical velocities as well as turbulence intensities along several verticals in the flow and the data are used for the validation of the present simulations. The code MGLET is used to solve the filtered Navier–Stokes equations on a Cartesian non-uniform grid. In order to represent solid objects in the flow, the immersed boundary method is employed. The computational domain is idealized with a box containing 16 submerged circular cylinders and periodic boundary conditions are applied in both longitudinal and transverse directions. The predicted streamwise as well as vertical mean velocities are in good agreement with the LDV measurements. Furthermore, fairly good agreement is found between calculated and measured streamwise and vertical turbulence intensities. Large-scale flow structures of different shapes are present in the form of vortex rolls above the vegetation tops as well as locally generated trailing and von- Karman-type vortices due to flow separation at the free end and the sides of the cylinders. In this paper, the flow field is analyzed statistically and evidence is provided for the existence of these structures based on the LES.     

Dynamics of a long tubular cantilever conveying fluid downwards,which then flows upwards around the cantilever as a confined annular flow

A theoretical model is developed for the dynamics of a hanging tubular cantilever conveying fluid downwards; the fluid, after exiting from the free end, is pushed upwards in the outer annular region contained by the cantilever and a rigid cylindrical channel. This configuration thus resembles that of a drill-string with a floating fluid-powered drill-bit. The linear equation of motion is solved by means of a hybrid Galerkin–Fourier method, as well as by a conventional Galerkin method. Calculations are conducted for a very slender system with parameters appropriate for a drill-string, for different degrees of confinement of the outer annular channel; and also for another, bench-top-size experiment. For wide annuli, the dynamics is dominated by the internal flow and, for low flow velocities, the flow increases the damping associated with the presence of the annular fluid. For narrow annuli, however, the annular flow is dominant, tending to destabilize the system, giving rise to flutter at remarkably low flow velocities. The mechanisms underlying the dynamics are also considered, in terms of energy transfer from the fluid to the cantilever and vice versa, as are possible applications of this work.     

Thermal study of an array of inline horizontal cylinders below a nearly adiabatic ceiling

Steady state two-dimensional free convection heat transfer from a horizontal, isothermal cylinder in a horizontal array of cylinders consists of three isothermal cylinders, located underneath a nearly adiabatic ceiling is studied experimentally. A Mach–Zehnder interferometer is used to determine thermal field and smoke test is made to visualize flow field. Effects of the cylinders spacing to its diameter (S/D), and cylinder distance from ceiling to its diameter (L/D) on heat transfer from the centered cylinder are investigated for Rayleigh numbers from 1500 to 6000. Experiments are performed for an inline array configuration of horizontal cylinders of diameters D = 13 mm. Results indicate that due to the nearly adiabatic ceiling and neighboring cylinders, thermal plume resulted from the centered cylinder separates from cylinder surface even for high L/D values and forming recirculation regions. By decreasing the space ratio S/D, the recirculation flow strength increases. Also, by decreasing S/D, boundary layers of neighboring cylinders combine and form a developing flow between cylinders. The strength of developing flow depends on the cylinders Rayleigh number and S/D ratio. Due to the developing flow between cylinders, the vortex flow on the top of the centered cylinder appears for all L/D ratios and this vortex influences the value of local Nusselt number distribution around the cylinder.Variation of average Nusselt number of the centered cylinder depends highly on L/D and the trend with S/D depends on the value of Rayleigh number.     

Natural convection in an inclined quadrantal cavity heated and cooled on adjacent walls

Natural convective flow and heat transfer in an inclined quadrantal cavity is studied experimentally and numerically. The particle tracing method is used to visualize the fluid motion in the enclosure. Numerical solutions are obtained via a commercial CFD package, Fluent. The working fluid is distilled water. The effects of the inclination angle, ? and the Rayleigh number, Ra on fluid flow and heat transfer are investigated for the range of angle of inclination between 0° ? ? ? 360°, and Ra from 10⁵ to 10⁷. It is disclosed that heat transfer changes dramatically according to the inclination angle which affects convection currents inside, i.e. flow physics inside. A fairly good agreement is observed between the experimental and numerical results.     

Large eddy simulations of the flow past two side-by-side circular cylinders

A LES Large Eddy Simulation is performed to study the flow past two side-by-side circular cylinders at a Reynolds number of 5800, based on the free-stream velocity and the cylinders diameter. The centre-to-centre transverse pitch ratio T/D is varied from 1.5 to 3. Both cylinders are slightly heated and the small amount of heat can be treated as a passive scalar. The numerical simulations are in good agreement with experimental observations.     

An analysis on effect of transverse convex curvature on turbulent flow and heat transfer

An analysis based on a model of modified mixing length by Hornby, Mistry und Barrow [1] was made on the effect of transverse convex curvature in turbulent boundary layer for incompressible axial flows along circular cylinders. The deviation of various turbulent flow and heat transfer properties from those of flat plates is presented. The agreement between the analyses and the experimental results for skin friction and heat transfer rate is good. The study demonstrated that, for a given condition, both the friction coefficient and Stanton number increase with decreasing value of the cyclinder radius and that their values are always greater than those for the flow over a flat plate.     

Visualization of natural convection heat transfer on horizontal cylinders

Natural convection heat transfer phenomena on horizontal cylinders were investigated experimentally in order to explore the applicability of analogy experimental method using the copper electroplating system and to visualize the local heat transfer depending on the angular position and the diameter of the horizontal cylinder. The diameters of the cylinders are varied from 0.01 to 0.15 m, which correspond to the Rayleigh numbers of 1.73 × 10⁷–5.69 × 10¹¹. The measured mass transfer coefficients show good agreements with the existing heat transfer correlations. The patterns of copper plated on the aluminum cathodes for various Rayleigh numbers reveal and visualize the local heat transfer depending on the angular position and show good agreement with the works of Kitamura et al. The hydrogen bubbles produced at higher applied potential visualize the plumes appeared on top region of the cylinders.     

Unsteady pressure in the annular flow between two concentric cylinders,one of which is oscillating: Experiment and theory

The first objective of this paper is to present a series of accurate experimental measurements of the unsteady pressure in the annulus between two concentric cylinders, the outer one of which executes a harmonic planar motion, either transverse translational or rocking motion about a hinge, with and without annular flow. The second objective is the solution of the unsteady Navier–Stokes and continuity equations for the same annular geometry under the same boundary conditions for an incompressible fluid in the laminar regime. The solutions are obtained with a three-time-level implicit integration method in a fixed computational domain by assuming small amplitudes of oscillation of the outer cylinder. A pseudo-time integration method with artificial compressibility is used to advance the solution between consecutive real time levels. The finite difference method is used for spatial discretization on a stretched staggered grid. The problem is reduced to a scalar tridiagonal system, solved by a decoupling procedure which is based on a factored Alternating Direction Implicit (ADI) scheme with lagged nonlinearities. The third objective is the comparison of the experimental results with the theoretical ones. This comparison shows that the two are in good agreement in the case of translational motion, and in excellent agreement in the case of rocking motion. The experimental and theoretical work presented in this paper is useful for fluid–structure interaction and flow-induced vibration analyses in such geometries.     

Numerical modeling and experimental measurements of water spray impact and transport over a cylinder

This study compares experimental measurements and numerical simulations of liquid droplets over heated (to a near surface temperature of 423 K) and unheated cylinders. The numerical model is based on an unsteady Reynolds-averaged Navier–Stokes (RANS) formulation using a stochastic separated flow (SSF) approach for the droplets that includes submodels for droplet dispersion, heat and mass transfer, and impact on a solid surface. The details of the droplet impact model are presented and the model is used to simulate water spray impingement on a cylinder. Computational results are compared with experimental measurements using phase Doppler interferometry (PDI). Overall, good agreement is observed between predictions and experimental measurements of droplet mean size and velocity downstream of the cylinder.     

Numerical modeling of a two-dimensional vertical turbulent two-phase jet

The results of numerically modeling two-dimensional two-phase flow of the “gas-solid particles” type in a vertical turbulent jet are presented for three cases of its configuration, namely, descending, ascending, and without account of gravity. Both flow phases are modeled on the basis of the Navier-Stokes equations averaged within the framework of the Reynolds approximation and closed by an extended k-? turbulence model. The averaged two-phase flow parameters (particle and gas velocities, particle concentration, turbulent kinetic energy, and its dissipation) are described using the model of mutually-penetrating continua. The model developed allows for both the direct effect of turbulence on the motion of disperse-phase particles and the inverse effect of the particles on turbulence leading to either an increase or a decrease in the turbulent kinetic energy of the gas. The model takes account for gravity, viscous drag, and the Saffman lift. The system of equations is solved using a difference method. The calculated results are in good agreement with the corresponding experimental data which confirms the effect of solid particles on the mean and turbulent characteristics of gas jets.     

Employing controlled vibrations to predict fluid forces on a cylinder undergoing vortex-induced vibration

In the present study, we measure the fluid forces on a vertical cylinder that is forced to vibrate transversely to a water channel flow, and compare directly to the forces encountered by freely vibrating cylinders, under conditions where we carefully match the amplitude, frequency, and Reynolds number (Re) of the two cases. A key point is that we use precisely the same cylinder and submerged flow configuration for both the free and controlled cases. Where the free vibration exhibits closely sinusoidal motion, the controlled sinusoidal motion yields forces in close agreement with the free vibration case. Although this result might be expected, previous comparisons have not been uniformly close, which highlights the importance of matching the experimental conditions precisely, and of accurately measuring the phase between the force and body motion. For a lightly damped system, which is perhaps the most significant case to analyze, one typically finds that the maximum response amplitude is quite unsteady. One might conventionally expect prediction of forces to be difficult in such cases. However, it is of practical significance that, even in this case, a quasi-steady approximation is effective. This is a significant point because it suggests that controlled vibration measurements for constant amplitude motion might remain applicable to free vibration systems undergoing even transient or intermittent motions.     

Two-degree-of-freedom vortex-induced vibrations of a circular cylinder at Re=3900

The vortex-induced vibrations of an elastically mounted circular cylinder are investigated on the basis of direct numerical simulations. The body is free to move in the in-line and cross-flow directions. The natural frequencies of the oscillator are the same in both directions. The Reynolds number, based on the free stream velocity and cylinder diameter, is set to 3900 and kept constant in all simulations. The behavior of the coupled flow-structure system is analyzed over a wide range of the reduced velocity (inverse of the natural frequency) encompassing the lock-in range, i.e. where body motion and flow unsteadiness are synchronized. The statistics of the structural responses and forces are in agreement with prior experimental results. Large-amplitude vibrations develop in both directions. The in-line and cross-flow oscillations are close to harmonic; they exhibit a frequency ratio of 2 and a variable phase difference across the lock-in range. Distinct trends are noted in the force-displacement phasing mechanisms in the two directions: a phase difference jump associated with a sign change of the effective added mass and a vibration frequency crossing the natural frequency is observed in the cross-flow direction, while no phase difference jump occurs in the in-line direction. Higher harmonic components arise in the force spectra; their contributions become predominant when the cylinder oscillates close to the natural frequency. The force higher harmonics are found to impact the transfer of energy between the flow and the moving body, in particular, by causing the emergence of new harmonics in the energy transfer spectrum.     

Lattice Boltzmann simulation of a fluid flow around a triangular unit of three isothermal cylinders

The lattice Boltzmann method is employed to simulate heat transfer in the flow past three arrangements of elliptical and circular cylinders under an isothermal boundary condition. The lattice Boltzmann equations and the Bhatnagar–Gross–Krook model are used to simulate two-dimensional forced convection at 30 ≤ Re ≤ 100 and Pr = 0.71. Pressure distributions, isotherms, and streamlines are obtained. Vortex shedding maps are observed in detail for several cases. The present results are in good agreement with available experimental and numerical data.     

Use of turbulent energy balance equation in the theory of turbulent flows along walls

The turbulent flow of an incompressible fluid is considered in a plane channel, a circular tube, and the boundary layer on a flat plate. The system of equations describing the motion of the fluid consists of the Reynolds equations and the mean kinetic energy balance equation for turbulent fluctuations. On the basis of an analysis of experimental data, hypotheses are formulated with respect to the eddy kinematic viscosity and lengthl entering into the expression for specific dissipation of turbulent energy into heat. It is assumed that in the central (outer) region of the flow in a channel, andl are constants, and expressions are taken for them which are used for a free boundary layer; near the walll varies linearly and almost linearly. Results of calculations of the turbulent energy distribution, the mean velocity, and the drag coefficient are in good agreement with the existing experimental data. The values of two empirical coefficients, which enter into the system of equations as the result of the hypotheses, are close to those obtained for a free boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–33, May–June, 1973.     

LINEAR AND NONLINEAR DYNAMICS OF CANTILEVERED CYLINDERS IN AXIAL FLOW. PART 2: THE EQUATIONS OF MOTION

In this paper a nonlinear equation of motion is derived for the dynamics of a slender cantilevered cylinder in axial flow, generally terminated by an ogival free end. Inviscid forces are modelled by an extension of Lighthill's slender-body work to third-order accuracy. The viscous, hydrostatic and gravity-related terms are derived separately, to the same accuracy. The equation of motion is obtained via Hamilton's principle. The boundary conditions related to the ogival free end are also derived separately. The paper is concluded by a discussion of the methods used to obtain the solutions presented in Part 3 of this study.     

Numerical investigation of mixed convection heat transfer past an in-line bundle of cylinders

Two dimensional unsteady Navier-Stokes and the energy equations are solved using finite element method for the case of flow past five row deep in-line bundle of circular cylinders with pitch to diameter ratios (PDR) of 1.5 and 2.0. Numerical solutions of governing equations have been obtained using Euler's explicit algorithm. Analysis have been made for Reynolds number of 100 and Prandtl number of 0.71. The effect of Richardson number (Ri=Gr/Re ²) on the flow and heat transfer have been investigated forRi=?1.0, ?0.5, 0.0, +0.5 and +1.0. Streamlines, isovorticity lines, pressure and temperature contours, local and average Nusselt numbers, pressure and shear stress distribution around the cylinders are presented. Results obtained for forced convection (Ri=0.0) agree well with the available experimental and numerical results. There is considerable effect of buoyancy over tube bundles both in buoyancy aiding and opposing flows.     

Effect of flow diverters on free convection heat transfer from a pair of vertical arrays of isothermal cylinders

Laminar free convection heat transfer from two vertical arrays of five isothermal cylinders separated by flow diverters is studied experimentally using a Mach-Zehnder interferometer. The width of flow diverters is kept constant to two-cylinder diameters and the cylinders vertical center-to-center spacing is equal to three-cylinder diameter. Effect of the ratio of the horizontal spacing between two cylinder arrays to their diameter (S_h/D) on heat transfer from the cylinders is investigated for various Rayleigh numbers. The experiments are performed for S_h/D = 2-4, and the Rayleigh number based on the cylinder diameter ranging from 10³ to 3 × 10³. It is observed that for small S_h/D ratios, the flow diverters have a negative effect on the total rate of heat transfer from the arrays; while by increasing the horizontal center to center spacing, they tend to enhance the overall cooling rate of the array. Moreover, increasing Ra and S_h/D generally results in a higher average Nusselt number for each cylinder in the array.     

Numerical study of convective heat transfer and fluid flow around two side by side square cylinders using k - \omega - \overline{{\upsilon^{2} }} - f turbulence model

The effect of spacing between two identical square cylinders placed side by side on the fluid flow and heat transfer is numerically investigated using $ k - \omega - \overline{{\upsilon^{2} }} - f $ turbulence model. The present study is performed at Pr = 0.7 and Re = 10,000, 21,000 for different scaled gap spacing between cylinders in the range of Gl = 0.5–6. It should be noted all geometrical lengths such as Gl are scaled with cylinders side. In order to show the accuracy of $ k - \omega - \overline{{\upsilon^{2} }} - f $ model, part of the results such as various flow patterns (flip-flop, in-phase and anti-phase) and global quantities are compared with the available numerical and experimental results and also a Large Eddy Simulation study of the present work. Based on this comparison, a close agreement is observed. The local and averaged flow and thermal quantities are also compared for two side by side square and circular cylinders and some significant similarities and differences are presented. Progressive increasing and decreasing of the distance between cylinders indicates that the hysteresis phenomenon appears for the gap spacing in the range of Gl = 1–2.5. In the hysteresis range, two different patterns are observed for each distance in the aforementioned range. Also in this range, two different values are found for different quantities such as lift and drag coefficients, Strouhal number and Nusselt number.