Numerical simulation of natural convective heat transfer and fluid flow around a heated cylinder inside an enclosure

 A collocated, non-orthogonal grid based finite volume technique has been applied for investigating the two dimensional natural convective flow and heat transfer around a heated cylinder kept in a square enclosure. The effects of different enclosure wall thermal boundary conditions, fluid Prandtl number and the ratio between enclosure and cylinder dimensions (aspect ratio) upon the flow and thermal features, have been systematically studied. It is observed that the patterns of recirculatory flow and thermal stratification in the fluid are significantly modified, if any of these parameters is varied. The overall heat transfer rates are also affected due to the changes in the flow and temperature patterns. The study presents useful observations regarding the variation of local Nusselt number along each wall, for the different cases considered. Received on 2 August 2000 / Published online: 29 November 2001     

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Reslts show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds numberRe and rotation parameter α, is built by a kinematic analysis of the steady flow fields. The project supported by the National Natural Science Foundation of China     

Stability of flow between two rotating cylinders in the presence of a constant heat flux at the outer cylinder and radial temperature gradient – wide gap problem

The stability of Couette flow of a viscous incompressible fluid between two concentric rotating cylinders in the presence of a radial temperature gradient due to a constant heat flux at the outer cylinder is studied. The critical values of `a' (the wave number) and Ta (the Taylor number) are listed in a table and some critical Taylor numbers are shown graphically. It is shown that as the heat flux is increased the flow becomes more unstable for all values of μ calculated, where μ is the ratio of the angular velocity of the outer cylinder to that of the inner cylinder. Received on 04 March 1997     

Phase-resolved flow characteristics between two shrouded co-rotating disks

Flow characteristics in the interdisk midplane between two shrouded co-rotating disks were experimentally studied. A laser-assisted particle-laden flow-visualization method was used to identify the qualitative flow behaviors. Particle image velocimetry was employed to measure the instantaneous flow velocities. The flow visualization revealed rotating polygonal flow structures (hexagon, pentagon, quadrangle, triangle, and oval) existing in the core region of the interdisk spacing. There existed a difference between the rotating frequencies of the polygon and the disks. The rotating frequency ratio between the polygonal flow structure and the disks depended on the mode shapes of the polygonal core flow structures—0.8 for pentagon, 0.75 for quadrangle, 0.69 for triangle, and 0.6 for oval. The phase-resolved flow velocities relative to the bulk rotation speed of the polygonal core flow structure were calculated, and the streamline patterns were delineated. It was found that outside the polygonal core flow structure, there existed a cluster of vortex rings—each side of the polygon was associated with a vortex ring. The radial distributions of the time-averaged and phase-resolved ensemble-averaged circumferential and radial velocities were presented. Five characteristic regions (solid-body rotation region, hub-influenced region, buffer region, vortex region, and shroud-influenced region) were identified according to the prominent physical features of the flow velocity distributions in the interdisk midplane. In the solid-body rotation region, the fluid rotated at the angular velocity of the disks and hub. In the hub-influenced region, the circumferential flow velocity departed slightly from the disks’ angular velocity. The circumferential velocities in the hub-influenced and vortex regions varied linearly with variation of radial coordinates. The phase-resolved ensemble-averaged relative radial velocity profiles in the interdisk midplane at various phase angles exhibited grouping behaviors in three ranges of polygon phase angles (θ = 0 and α/2, 0 < θ < α/2, and α/2 < θ < α) because three-dimensional flow induced similar flow patterns to appear in the same range of polygon phase angles.     

Numerical analysis of vortex cell efficiency in laminar and turbulent flows past a circular cylinder with embedded rotating bodies

The effect of flow intensification in small-sized vortex cells on the flow pattern in the near wake downstream of a cylinder and the cylinder drag in laminar and turbulent flows is analyzed on the basis of a numerical simulation of the two-dimensional steady-state flow past a circular cylinder with rotating cylindrical bodies built into the cylinder contour. St. Petersburg, Saratov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–96, July–August, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 99-01-01115 and 99-01-00772).     

Drag Reduction of a Circular Cylinder Using an Upstream Rod

Experimental studies on the drag reduction of the circular cylinder were conducted by pressure measurement at a Reynolds number of 82 000 (based on the cylinder diameter). A rod was placed upstream of and parallel to the cylinder to control the flow around the cylinder. The upstream rod can reduce the resultant force of the cylinder at various spacing between the rod and the cylinder for α < 5^∘(α defined as the staggered angle of the rod and the cylinder). For α > 10^∘, the resultant force coefficient has a large value, so the upstream rod cannot reduce the force on the cylinder any more. For α = 0^∘ and d/D = 0.5 (where d and D are the diameter of the rod and the cylinder, respectively), the maximum drag of the cylinder reduces to 2.34% that of the single cylinder. The mechanism of the drag reduction of the cylinder with an upstream rod in tandem was presented by estimating the local contributions to the drag reduction of the pressure variation. In the staggered arrangement, the flow structures have five flow patterns (they are the cavity mode, the wake splitting mode, the wake merge mode, the weak boundary layer interaction mode and the negligible interaction mode) according to the pressure distribution and the hydrogen bubble flow visualization. The half plane upwind of the cylinder can be divided to four regions, from which one can easily estimates the force acting on the circular cylinder with an upstream rod in staggered arrangement.     

Experimental determination of the speed of sound in cavitating flows

This paper presents measurements of the speed of sound in two-phase flows characterized by high void fraction. The main objective of the work is the characterization of wave propagation in cavitating flows. The experimental determination of the speed of sound is derived from measurements performed with three pressure transducers, while the void fraction is obtained from analysis of a signal obtained with an optical probe. Experiments are first conducted in air/water mixtures, for a void fraction varying in the range 0–11%, in order to discuss and validate the methods of measurement and analysis. These results are compared to existing theoretical models, and a nice agreement is obtained. Then, the methods are applied to various cavitating flows. The evolution of the speed of sound according to the void fraction α is determined for α varying in the range 0–55%. In this second configuration, the effect of the Mach number is included in the spectral analysis of the pressure transducers’ signals, in order to take into account the possible high flow compressibility. The experimental data are compared to existing theoretical models, and the results are then discussed.     

Transverse subsonic flow past a cylinder

At around the critical Reynolds number Re = (1.5–4.0)·10⁵ there is an abrupt change in the pattern of transverse subsonic flow past a circular cylinder, and the drag coefficient C_x decreases sharply [1]. A large body of both experimental and computational investigations has now been made into subsonic flow past a cylinder [1–4]. A significant contribution to a deeper understanding of the phenomenon was made by [4], which gives a physical interpretation of a number of theoretical and experimental results obtained in a wide range of Re. Nevertheless, the complicated nonstationary nature of flow past a cylinder with separation and the occurrence of three-dimensional flows when two-dimensional flow is simulated in wind tunnels do not permit one to regard the problem as fully studied. The aim of the present work was to make additional experimental investigations into transverse subsonic flow past a cylinder and, in particular, to study the possible asymmetric stable flow regimes near the critical Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–157, March–April, 1980.     

Momentum and heat transport in a finite-length cylinder wake

This paper reports an experimental study of turbulent momentum and heat transport in the wake of a wall-mounted finite-length square cylinder, with its length-to-width ratio L/d = 3–7. The cylinder was slightly heated so that heat produced could be considered as a passive scalar. A moveable three-wire probe (a combination of an X-wire and a cold wire) was used to measure velocity and temperature fluctuations at a Reynolds number of 7,300 based on d and the free-stream velocity. Measurements were performed at 10 and 20d downstream of the cylinder at various spanwise locations. Results indicate that L/d has a pronounced effect on Reynolds stresses, temperature variance and heat fluxes. The downwash flow from the free end of the cylinder acts to suppress spanwise vortices and, along with the upwash flow from the cylinder base, makes the finite-length cylinder wake highly three-dimensional. Reynolds stresses, especially the lateral normal stress, are significantly reduced as a result of suppressed spanwise vortices at a small L/d. The downwash flow acts to separate the two rows of spanwise vortices further apart from the wake centerline, resulting in a twin-peak distribution in temperature variance. While the downwash flow entrains high-speed fluid into the wake, responsible for a small deficit in the time-averaged streamwise velocity near the free end, it does not alter appreciably the distribution of time-averaged temperature. It has been found that the downwash flow gives rise to a counter-gradient transport of momentum about the central region of the wake near the free end of the cylinder, though such a counter-gradient transport does not occur for heat transport.     

Laminar natural convection of pure and saline water along a vertical isothermal cylinder

 In most studies concerning laminar natural convection along a vertical isothermal cylinder a linear relationship between fluid density and temperature has been used and kinematic viscosity and thermal diffusivity have been considered constant calculated at ambient temperature. However, it is known that the density–temperature relationship for water is non-linear at low temperatures and kinematic viscosity and thermal diffusivity are functions of temperature. In this study the problem of laminar natural convection of pure and saline water along a vertical isothermal cylinder has been investigated in the temperature range between 20 and 0 ^∘C taking into account the temperature dependence of ν, α and ρ. The results are obtained with the numerical solution of the boundary layer equations. The variation of ν, α and ρ with temperature has a strong influence on free convection characteristics. Received on 17 May 1999     

On the formation of Taylor–G?rtler vortices in RMF-driven spin-up flows

This paper is concerned with a liquid metal flow driven by a rotating magnetic field inside a stationary cylinder. We consider especially the secondary meridional flow during the time when the fluid spins up from rest. The developing flow is investigated experimentally and by direct numerical simulations. The vertical profiles of the axial velocity are measured by means of the ultrasound Doppler velocimetry. Evolving instabilities in the form of Taylor–G?rtler vortices have been observed just above the instability threshold (Ta ≥ 1.5· Ta ^cr). The rotational symmetry may survive over a distinct time even if a first Taylor–G?rtler vortex pair has been formed as closed rings along the cylinder perimeter. The transition to a three-dimensional flow in the side layers results from the advection or a precession and splitting of the Taylor–G?rtler vortex rings. The predictable behaviour of the Taylor–G?rtler vortices disappears with increasing magnetic field strength. The numerical simulations agree very well with the flow measurements.     

Numerical and experimental investigation of thermal convection for a thermodependent Herschel-Bulkley fluid in an annular duct with rotating inner cylinder

Thermal convection for an incompressible Herschel-Bulkley fluid along an annular duct, whose inner cylinder is rotating and outer is at rest, is analyzed numerically and experimentally. The outer cylinder is heated at constant heat flux density and the inner one is assumed adiabatic. The first part of this study deals with the effect of the rheological behavior of the fluid and that of the rotation of the inner cylinder on the flow field and heat transfer coefficient. All the physical properties are assumed constant and the flow is assumed fully developed. The critical Rossby number Ro_c = (R₁Ω/U_d)_c, for which the dimension of the plug flow is reduced to zero is determined with respect to the flow behavior index, the radius ratio and the Herschel-Bulkley number for axial flow. The rotation of the inner cylinder induces a decrease of the axial velocity gradient at the outer cylinder thereby reducing the heat transfer between the heated wall and the fluid. The second part of this study introduces the variation of the consistency K with temperature and analyzes the evolution of the flow pattern and heat transfer coefficient along the heating zone. Two cases are distinguished depending on the Rossby number: (i) Ro < Ro_c, the plug flow dimension increases along the heating zone; (ii) Ro < Ro_c, the decrease of K with temperature leads to the reappearance of the plug flow. For high angular velocities, it is possible to have a plug zone attached to the outer cylinder. Finally, a correlation is proposed for the Nusselt number. It shows clearly that the effect of thermodependency of K on the heat transfer becomes more important with increasing rotational velocity of the inner cylinder.     

Measurement of velocity profiles in a rectangular microchannel with aspect ratio <Emphasis Type="Italic">α</Emphasis> = 0.35

In this work, we measured 14 horizontal velocity profiles along the vertical direction of a rectangular microchannel with aspect ratio α = h/w = 0.35 (h is the height of the channel and w is the width of the channel) using microPIV at Re = 1.8 and 3.6. The experimental velocity profiles are compared with the full 3D theoretical solution, and also with a Poiseuille parabolic profile. It is shown that the experimental velocity profiles in the horizontal and vertical planes are in agreement with the theoretical profiles, except for the planes close to the wall. The discrepancies between the experimental data and 3D theoretical results in the center vertical plane are less than 3.6%. But the deviations between experimental data and Poiseuille’s results approaches 5%. It indicates that 2D Poiseuille profile is no longer a perfect theoretical approximation since α = 0.35. The experiments also reveal that, very near the hydrophilic wall (z = 0.5–1 μm), the measured velocities are significantly larger than the theoretical velocity based on the no-slip assumption. A proper discussion on some physical effects influencing the near wall velocity measurement is given.     

Prediction of flow and heat transfer in narrow rotating rectangular channels using Reynolds stress model

A computational study is performed on three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with aspect ratio (AR) of 10:1, oriented 120° from the direction of rotation. The Focus is on high rotation and high-density ratios effects on the heat transfer characteristics of the 120° orientation. The Reynolds stress model (RSM), which accounts for rotational effects are used to compute the turbulent flow and heat transfer in the rotating channel. The effects of rotation and coolant-to-wall density ratio on the fluid flow and heat transfer characteristics is reported on a range of rotation numbers and density ratios (0 < Ro < 0.25 and 0.07 < Δρ/ρ < 0.4). The computational results are in good agreement with experimental data within ±15%. The results show that the density ratio, rotation number and channel orientation significantly affect the flow field and heat transfer characteristics in the rotating rectangular channel. Flow reversal occurs at high rotation number and density ratio.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

Investigation of the stability of a natural circulation two-pass boiler

In this paper, the results of a theoretical analysis of the static flow instability, namely the reverse flow, for a two-pass steam generator (see Fig. 1) will be presented. The aim of the work was the development of design criteria to avoid the reversal of flow. To determine the critical heat absorption ratio between the two riser systems of a two-pass boiler several dynamic simulations of a warm start-up of the two-pass boiler with different heat absorption ratios, different heat profiles along the lower heated riser system 1 and modified geometry of the boiler (influence of the flow resistance) are done. On the basis of the results of this investigations it can be shown that for every natural circulation system with unequally heated risers and a common downcomer a special critical heat absorption ratio exists. The investigations clearly indicate that such types of steam generators should be designed only in that way that the operation below the critical heat absorption ratio is possible. The modification of the flow resistance in the riser systems can help to extend the range of stable operation.     

Numerical study of adverse pressure gradient generation over a flat plate using a rotating cylinder

Generating an adverse pressure gradient (APG), using a rotating cylinder in the proximity of a plane wall under a laminar freestream flow, is studied numerically in this work. The magnitude of the generated APG is a function of the gap, G, between the cylinder and the wall, and the rotational speed of the cylinder, Ω. The flow in such a configuration is characterized by periodic transient vortex shedding at high Reynolds number. A numerical model for the computation of the transient flow for this configuration is developed using the ANSYS CFD simulation tool. The model is validated against published experimental and numerical data for similar flow configurations and excellent agreement is observed. A parametric study is carried out for different combinations of G and Ω for two different Reynolds numbers of 200 and 1000 to examine the development of the resulting separation bubble due to the generated APG. The mechanism of the boundary layer separation over the plane wall and the corresponding wake dynamics is investigated. Results are presented in terms of the distribution of the pressure coefficient as well as skin friction coefficient along the wall and flow patterns around and downstream of the cylinder in the proximity of the wall. The results of these computations confirm that using a rotating cylinder over a plane wall in a freestream flow is an effective technique to generate a controlled range of adverse pressure gradients.     

Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel

An experimental study was conducted of incompressible, moderate Reynolds number flow of air over heated rectangular blocks in a two-dimensional, horizontal channel. Holographic interferometry combined with high-speed cinematography was used to visualize the unsteady temperature fields in self- sustained oscillatory flow. Experiments were conducted in the laminar, transitional and turbulent flow regimes for Reynolds numbers in the range from Re = 520 to Re = 6600. Interferometric measurements were obtained in the thermally and fluiddynamically periodically fully developed flow region on the ninth heated block. Flow oscillations were first observed between Re = 1054 and Re = 1318. The period of oscillations, wavelength and propagation speed of the Tollmien–Schlichting waves in the main channel were measured at two characteristic flow velocities, Re = 1580 and Re = 2370. For these Reynolds numbers it was observed that two to three waves span one geometric periodicity length. At Re = 1580 the dominant oscillation frequency was found to be around 26 Hz and at Re = 2370 the frequency distribution formed a band around 125 Hz. Results regarding heat transfer and pressure drop are presented as a function of the Reynolds number, in terms of the block-average Nusselt number and the local Nusselt number as well as the friction factor. Measurements of the local Nusselt number together with visual observations indicate that the lateral mixing caused by flow instabilities is most pronounced along the upstream vertical wall of the heated block in the groove region, and it is accompanied by high heat transfer coefficients. At Reynolds numbers beyond the onset of oscillations the heat transfer in the grooved channel exceeds the performance of the reference geometry, the asymmetrically heated parallel plate channel. Received on 26 April 2000     

Three-dimensional viscoelastic simulation of coextrusion process: comparison with experimental data

 Three-dimensional numerical simulation of viscoelastic coextrusion process has been performed and numerical results were compared with the experimental data of Karagiannis et al. (1990). By varying the magnitude of the second normal stress difference and its ratio of Fluid I and Fluid II, we were able to control the interface profile and the degree of encapsulation along the downstream direction. By increasing the parameter α (α_Fluid I=α_Fluid II) from 0.1 to 0.4 in the Giesekus model and increasing the α ratio (α_Fluid Iα_Fluid II) between Fluid I and Fluid II from 2.0 to 4.0 in the permissible range of realistic polymeric systems, the interface profile and the degree of encapsulation along the downstream direction were fitted with the experimental results. There was little difference between the numerical results and the experimental data in the interface profile and the degree of encapsulation along the downstream direction when the α ratio was set to 3.0 (0.3:0.1). Fluid I with larger magnitude of the second normal stress difference protrudes into Fluid II with smaller magnitude of the second normal stress difference around the symmetric plane, while Fluid II wraps around Fluid I near the side walls. As the ξ ₁ ratio (ξ _{1 ,Fluid I}ξ _{1 ,Fluid II}) increases from 1.0 to 3.0 for the two-mode Phan-Thien and Tanner model, it was found that the curvature of the interface profile increased, and the difference between the numerical results and the experimental data in the interface profile and the degree of encapsulation along the downstream direction was almost negligible when the ξ ₁ ratio was set to 3.0 (0.54:0.18). Although the parameters of viscoelastic models were fitted by using the shear viscosity data only, quantitative agreements between the numerical results and the experimental coextrusion data were quite satisfactory. Received: 24 April 2001 Accepted: 5 June 2001     

Investigation of the rarefied gas flow around a circular cylinder in stationary and oscillatory regimes

Numerically, on the basis of the Krook kinetic equation, the rarefied gas flow around a circular cylinder is investigated in stationary and oscillatory regimes. The flows around a rotating cylinder and a cylinder with a nonuniformly heated surface are considered. The Knudsen numbers at which the lift force acting on the rotating cylinder changes sign are calculated. It is shown that at low Knudsen numbers a lift force acts on the nonuniformly heated cylinder.