A numerical study of laminar heat transfer at bottom surface of a cavity submerged in separated flow region of duct

For the two cavity models whose upward and downward wall heights are different from each other, laminar heat transfer is studied numerically in a finite difference method. The effects of cavity configuration, free-stream velocity and buoyancy force on flow and temperature fields as well as heat transfer at the bottom surface are discussed. The flow pattern of DOF (Downward-Facing cavity)-model is more intricated than that of UPF (Upward-Facing cavity)-model, depending on the aspect ratio of cavity or main flow velocity. The mean Nusselt numberNu _m at the bottom surface of both cavity models tends generally to increase with increasing Re_HorGr _w/Re _H ² . However, in the flow region ofRe _H & 500 for DOF-cavity, theNu _m for 0.4 ≦ D₂/D₁ ≦ 0.6 is somewhat lower than that obtained from the other cavities and does not always increase with increasingRe _H.     

Transient behavior of heat removal from a cylindrical heat storage vessel packed with spherical porous particles

The transient heat transfer behavior in the case of heat removal from a cylindrical heat storage vessel packed with spherical particles was investigated experimentally for various factors (flow rate, diameter of spherical particles packed, temperature difference between flowing cold air and spherical particles accumulating heat, and physical properties of spherical particles). The experiments were covered in ranges of Reynolds number based on the mean diameter of spherical particles packed Re_d = 10.3–2200, porosity?=0.310 to 0.475, ratio of spherical particle diameter to cylinder diameterd/D = 0.0075–0.177 and ratio of length of the cylinder to cylinder diameterL/D=2.5–10. It was found that especially the flow rate and the dimension of spherical particles played an important role in estimating the transient local heat transfer characteristics near the wall of the cylindrical vessel in the present heat storage system. As flow rate and diameter of spherical particles were increased under a given diameter of the cylinder heat storage vessel, the mean heat transfer coefficient between the flow cold air and the hot spherical particles increased and the time period to finish removing heat from the vessel reduced. In addition, the useful experimental correlation equations of mean heat transfer coefficient between both phases and the time period to finish removing heat from the vessel were derived with the functional relationship of Nusselt numberNu _d=f [modified Prandtl numberPr ^* (d/D), Re_d) and Fourier numberFo = f(d/D, L/D, Pr^*, Re_d).     

Delay in response of turbulent heat transfer against acceleration or deceleration of flow in a pipe

To predict the heat transfer enhancements that result from the application of a pulsating flow in a pipe, we experimentally investigated the turbulent heat transfer variations produced in response to sudden accelerations or decelerations to flows within a pipe. To accomplish this, the Reynolds numbers with the valve open (Re₁) and close (Re₀) were systematically varied in the range of 8,000 ≤ Re₁ ≤ 34,000 and 700 ≤ Re₀ ≤ 23,000, respectively, and in-pipe spatiotemporal heat transfer variations were measured using infrared thermography simultaneously with temporal variations to the in-pipe flow properties. Based on the experimental results, it was found that the heat transfer delays that occur in response to accelerations or decelerations can be characterized using the corresponding time lag Δt and first-order time constant τ. The values of Δt and τ can be expressed as non-dimensional forms of Δt/(ν/u_τ²) and τ/(R/u_τ), respectively, where u_τ is the pipe wall friction velocity, ν is the kinematic viscosity of the fluid, and R is the pipe radius.     

Flow structures and heat transfer on dimples in a staggered arrangement

Vortex structures and heat transfer enhancement mechanism of turbulent flow over a staggered array of dimples in a narrow channel have been investigated using Large Eddy Simulation (LES), Laser Doppler Velocimetry (LDV) and pressure measurements for Reynolds numbers Re_H = 6521 and Re_H = 13,042.The flow and temperature fields are calculated by LES using dynamic mixed model applied both for the velocity and temperature. Simulations have been validated with experimental data obtained for smooth and dimpled channels and empiric correlations. The flow structures determined by LES inside the dimple are chaotic and consist of small eddies with a broad range of scales where coherent structures are hardly to detect. Proper Orthogonal Decomposition (POD) method is applied on resolved LES fields of pressure and velocity to identify spatial–temporal structures hidden in the random fluctuations. For both Reynolds numbers it was found that the dimple package with a depth h to diameter D ratio of h/D = 0.26 provides the maximum thermo-hydraulic performance. The heat transfer rate could be enhanced up to 201% compared to a smooth channel.     

Transient heat transfer behaviors in cylindrical porous beds at relatively large Reynolds numbers

The transient behavior of heat transfer in a cylindrical porous bed was examined experimentally under various factors (flow rate, diameter of spherical solid particle, temperature of flowing fluid and physical properties of porous bed). In these factors, it was understood that especially flow rate and the diameter of the particled have important role in evaluating the transient behavior of heat transfer in the porous bed. That is, as the flow rate and the diameter of the particle under a constant diameterD of the cylindrical bed are increased, mean heat transfer coefficient between flowing fluid and the solid particles is increased and the time period to reach a thermally steady state is decreased. The useful experimental correlation equations of mean heat transfer coefficient and the time period to reach the steady state were derived with the functional relationships of Nusselt numberNu _d =f(d/D, Reynolds numberRe _d ) and Fourier numberFo =f (modified Prandtl numberPr*, d/D, Re _d ).     

Heat transfer in asymmetric transverse flows over bundles of tubes

Heat transfer was studied on a separate transverse row of tubes with the relative pitch ofs ₁/d=1.5 and a staggered bundle with the relative pitches ofs ₁/d×s ₂/d=1.15×0.98. A test tube in the transverse row was used with a variable displacement from the symmetric position. The tube bundle was placed at different gaps from the shell wall. Experiments were performed in air and water in the range ofRe from 10³ to 6×10⁵. Asymmetric flows over transverse rows are accompanied by augmented heat transfer rates and steady state lift force which becomes higher with the amount of displacement. The presence of the shell wall introduces alterations in the thermal and fluid dynamics over outside tubes in a bundle.     

Mixed convection adjacent to inclined flat surfaces embedded in a porous medium

An analysis is performed to study the flow and heat transfer characteristics of laminar mixed convection boundary layer flows from inclined (including horizontal and vertical) surfaces embedded in a saturated porous medium with constant aiding external flows and uniform surface temperature. Both the streamwise and normal components of the buoyancy forces are retained in the momentum equations. Nondimensionalization of the boundary layer equations results in the following three governing parameter: (1)Gr/Re, the ratio of the Grashof number to the Reynolds number; (2)Pe _x =Re _x Pr, the Peclet number; (3) φ, the angle of inclination from the horizontal. The resulting nonsimilar equations are solved by an efficient implicit finite-difference scheme. Numerical results are presented for flows with different values ofGr/Re in the range of 0 to 50, over a wide range of the Peclet numbersPe _x, and various values of φ ranging from 0 to 90 degrees. It is found that the local surface heat transfer rate increases with increasing the local Peclet number. In addition, as the plate is tilted from the horizontal to the vertical orientation, the local Nusselt number increases for a given Peclet number and the effect of the buoyancy force on the surface heat transfer rate increases.     

Numerical study of turbulent flow and heat transfer of Al2O3–water mixture in a square duct with uniform heat flux

Turbulent flow and convective heat transfer of a nanofluid made of Al₂O₃ (1–4 vol.%) and water through a square duct is numerically studied. Single-phase model, volumetric concentration, temperature-dependent physical properties, uniform wall heat flux boundary condition and Renormalization Group Theory k-ε turbulent model are used in the computational analysis. A comparison of the results with the previous experimental and numerical data revealed 8.3 and 10.2 % mean deviations, respectively. Numerical results illustrated that Nu number is directly proportional with Re number and volumetric concentration. For a given Re number, increasing the volumetric concentration of nanoparticles does not have significant effect on the dimensionless velocity contours. At a constant dimensionless temperature, increasing the particle volume concentration increases the size of the temperature profile. Maximum value of dimensionless temperature increases with increasing x/D_h value for a given Re number and volumetric concentration.     

Effects of aspect ratio on the drag of a wall-mounted finite-length cylinder in subcritical and critical regimes

The effect of cylinder aspect ratio (??H/d, where H is the cylinder height or length, and d is the cylinder diameter) on the drag of a wall-mounted finite-length circular cylinder in both subcritical and critical regimes is experimentally investigated. Two cases are considered: a smooth cylinder submerged in a turbulent boundary layer and a roughened cylinder immersed in a laminar uniform flow. In the former case, the Reynolds number Re _d (??U _?? d/??, with U _?? being the free-stream velocity and ?? the fluid viscosity) was varied from 2.61?×?10⁴ to 2.87?×?10⁵, and two values of H/d (2.65 and 5) were examined; in the latter case, Re _d ?=?1.24?×?10⁴?C1.73?×?10⁵ and H/d?=?3, 5 and 7. In the subcritical regime, both the drag coefficient C _D and the Strouhal number St are smaller than their counterparts for a two-dimensional cylinder and reduce monotonously with decreasing H/d. The presence of a turbulent boundary layer causes an early transition from the subcritical to critical regime and considerably enlarges the Re _d range of the critical regime. No laminar separation bubble occurs on the finite-length cylinder immersed in the turbulent boundary layer, and consequently, the discontinuity is not observed in the C _D?CRe _d and St?CRe _d curves. In the roughened cylinder case, the Re _d range of the critical regime grows gradually with decreasing H/d, while the C _D crisis becomes less obvious. In both cases, H/d has a negligible effect on the critical value of Re _d at which transition occurs from the subcritical to critical regime.     

Aerodynamics and heat transfer in a separated flow in an axisymmetric diffuser with sudden expansion

Results of a numerical study of the influence of a positive pressure gradient in an axisymmetric diffuser with sudden expansion of a circular tube on aerodynamics and turbulent heat transfer in regions of flow separation, reattachment, and relaxation are reported. The air flow prior to separation is assumed to be fully turbulent and to have a constant Reynolds number Re _D1 = 2.75 · 10⁴. The tube expansion degree is 1.78, and the apex half-angle of the diffuser is varied from 0 to 5°. It is found that an increase in the pressure gradient leads to a decrease in the heat transfer intensity in the separation region, and the maximum heat release point moves away from the flow separation point. The calculated results are compared with experimental data. It is shown that the behavior of the separated flow behind the step becomes significantly different as the streamwise pressure gradient changes.     

Measurements of heat transfer coefficients between turbulent liquid jets and a radially finned heated disk placed at the bottom of an open vertical circular cavity

 Experiments have been performed to assess the impact of an extended surface on the heat transfer enhancement for axisymmetric, turbulent liquid jet impingement on a heated round disk. The disk, with an array of integral radial fins mounted on its surface, is placed at the bottom of an open vertical circular cavity. Hydrodynamic and heat transfer data were obtained for a dielectric fluorocarbon liquid FC-77. For a fixed circular heater of diameter D=22.23 mm, several geometric parameters were tested: the nozzle diameter (4.42≤d≤9.27 mm), the confining wall diameter of the vertical cavity (22.23≤D _c≤30.16 mm), and the nozzle-to-heater spacing (0.5≤S/d≤5.0). The FC-77 flow rates varied from =0.2 to 11.0 l/min producing Reynolds numbers in the wide interval 700≤Re _d ≤44,000. For d=4.42 mm, the heat transfer response to the separation distance S/d was small but increased gradually with increasing nozzle diameter up to d=9.27 mm. The thermal resistance R _th increased with the confining wall diameter D _c and also with the nozzle diameter d. A minimum value of the thermal resistance of R _th,min=0.4 cm² K/W was attained for a combination of d=4.42 mm, D _c=22.23 mm, S/d=1, and =7.5 l/min. Based on a simplified heat transfer model, reasonable agreement was obtained between measured values of the thermal resistance and the R _th-predictions. The total fin effectiveness ɛ_f was shown to increase with increasing nozzle diameter, but was invariant with the flow rate (or the jet exit velocity). More than a three-fold heat transfer enhancement was realized through the addition of the array of integral radial fins on the heated round disk. Received on 30 August 2000 / Published online: 29 November 2001     

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.     

“Magnetic-ribs” in fully developed laminar liquid–metal channel flow

This paper documents the numerical investigation of the effects of non-uniform magnetic fields, i.e. magnetic-ribs, on a liquid–metal flowing through a two-dimensional channel. The magnetic ribs are physically represented by electric currents flowing underneath the channel walls. The Lorentz forces generated by the magnetic ribs alter the flow field and, as consequence, the convective heat transfer and wall shear stress. The dimensionless numbers characterizing a liquid–metal flow through a magnetic field are the Reynolds (Re) and the Stuart (N) numbers. The latter provides the ratio of the Lorentz forces and the inertial forces. A liquid–metal flow in a laminar regime has been simulated in the absence of a magnetic field (Re_H = 1000, N = 0), and in two different magnetic ribs configurations for increasing values of the Stuart number (Re_H = 1000, N equal to 0.5, 2 and 5). The analysis of the resulting velocity, temperature and force fields has revealed the heat transport phenomena governing these magneto-hydro-dynamic flows. Moreover, it has been noticed that, by increasing the strength of the magnetic field, the convective heat transfer increases with local Nusselt numbers that are as much 27.0% larger if compared to those evaluated in the absence of the magnetic field. Such a convective heat transfer enhancement has been obtained at expenses of the pressure drop, which increases more than twice with respect to the non-magnetic case.     

Mixed convection film condensation from downward flowing vapors onto a sphere with variable wall temperature

A model is developed for the study of mixed- convection film condensation from downward flowing vapors onto a sphere with variable wall temperature. The model combined natural convection dominated and forced convection dominated film condensation, concerning effects of pressure gradient (P), interfacial vapor shear drag and non-uniform wall temperature variation (A), has been investigated and solved numerically. The effect of pressure gradient on the dimensionless mean heat transfer, NuˉRe^−1/2 will remain almost uniform with increasing P until for various corresponding available values of F. Meanwhile, the dimensionless mean heat transfer, NuˉRe^−1/2 is increasing significantly with F for its corresponding available values of P. Although the non-uniform wall temperature variation has an appreciable influence on the local film flow and heat transfer; however, the dependence of mean heat transfer on A can be almost negligible. Received on 10 October 1996     

Development of empirical correlations to predict the secondary droplet size of impacting droplets onto heated surfaces

The present article reports an experimental analysis of the mechanisms of secondary atomization which occur at the impact of individual droplets onto heated targets. The experiments follow those reported in a previous article (Moreira et al. 2007) and encompass the use of different liquids and impact conditions. An image analysis system is combined with a phase Doppler interferometer to measure extended size distributions, which cover the full range of diameters generated at all heat transfer regimes. The results evidence that disintegration mechanisms depend on the heat transfer regimes; therefore, a universal relation cannot be devised for the outcome of droplet impact. Analysis shows that droplets impacting within the nucleate-boiling regime break-up by a thermal-induced mechanism associated with the vapour pressure at bubble nucleation sites, combined with liquid surface tension. On the other hand, within the film-boiling regime, disintegration is associated with radial disruption of the rim at the early instants after impact, as in non-heated targets, and with the rupture of the ligaments of the cellular structures. Functional relations available at the literature, mostly developed for impacts onto non-heated surfaces, are well fitted to the experimental results obtained within the film-boiling regime, since the break-up mechanisms are qualitatively similar. On the other hand, such relations cannot predict the secondary atomization occurring within the nucleate-boiling regime, as the break-up mechanisms within this regime have significantly different characteristics. In this context, the present article recognizes the relevance of the relations devised for ‘cold impacts’, to fit the size of secondary droplets within the film-boiling regime, as the correlation formulated here has a similar form: SMD/D ₀ = f(We, Re) ~ A ₁ We _N ^?0.6 Re ^?0.23 and proposes a new correlation for impacts within the nucleate-boiling regime: SMD/D ₀ = f(We, Re, Ja) ~ A ₂ We _N ^?0.14 Re ^?011 Ja ^?03. These correlations are observed to hold for impacts onto rough surfaces with dimensionless roughness R _a/D ₀ smaller than 2E-3, but not for larger roughness amplitudes, for which the data are quite scattered.     

Heat transfer in supersonic flow over a single spherical cavity

The flow and heat transfer on a plate with a single spherical cavity has been experimentally investigated for M=4 and Re_,L=3.1 · 10⁶. The flow pattern over the cavity has been obtained. Zones of enhanced heat transfer have been detected, and the heat transfer coefficients in and near the cavity have been determined. It has been established that a single spherical cavity has almost no effect on the integral heat flux.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 48–52, September–October, 1991.The authors are grateful to V. N. Brazhko for assistance in carrying out the experiments and to T. A. Ershova for assistance in analyzing the results.     

Large-scale structures of turbulent flows over an open cavity

Low Mach number turbulent flows over an open cavity were studied to investigate the quantitative characteristics of large-scale vortical structures responsible for self-sustained oscillations. Wind tunnel experiments with particle image velocimetry (PIV) were conducted in the range of the ratio of cavity length (L) to depth (D), 1<L/D<4, when the incoming boundary layer is turbulent at Re_θ=830 and 1810. Self-sustained oscillation modes were classified by varying the conditions of L/D and Re_θ. The oscillation modes were consistent with the number of vortical structures existing between the leading and trailing edges of the cavity. Proper orthogonal decomposition (POD) was employed to the spatial distributions of vertical velocity correlations on the lip line of cavity geometry. By examining the conditionally averaged distributions of the correlation coefficients of POD, the spatial characteristics of large-scale vortical structures for self-sustained oscillations were examined.     

An advanced study of forced turbulent-flow film boiling for subcooled liquid with high velocity in a circular tube

A further advanced semi-empirical theory for the turbulent film boiling heat transfer of subcooled liquid flowing with high velocity in a circular tube is presented in this paper. A new analytical expression has been obtained theoretically and it is found that the exponent ofRe _D in the expression can be predicted analytically with an universal constant value of 4/5 for different fluids. Meanwhile, it is revealed that the coefficientk is correlated withk′, and thatk determined for flowing along plate can be extended to the case for flowing in a circular tube. The analyses show that new analytical expression concides really with the results presented before [5].     

Three-dimensional simulations of flow past two circular cylinders in side-by-side arrangements at right and oblique attacks

The flow past two identical circular cylinders in side-by-side arrangements at right and oblique attack angles is numerically investigated by solving the three-dimensional Navier–Stokes equations using the Petrov–Galerkin finite element method. The study is focused on the effect of flow attack angle and gap ratio between the two cylinders on the vortex shedding flow and the hydrodynamic forces of the cylinders. For an oblique flow attack angle, the Reynolds number based on the velocity component perpendicular to the cylinder span is defined as the normal Reynolds number Re_N and that based on the total velocity is defined as the total Reynolds number Re_T. Simulations are conducted for two Reynolds numbers of Re_N=500 and Re_T=500, two flow attack angles of α=0° and 45° and four gap ratios of G/D=0.5, 1, 3 and 5. The biased gap flow for G/D=0.5 and 1 and the flip-flopping bistable gap flow for G/D=1 are observed for both α=0° and 45°. For a constant normal Reynolds number of Re_N=500, the mean drag and lift coefficients at α=0° are very close to those at α=45°. The difference between the root mean square (RMS) lift coefficient at α=0° and that at α=45° is about 20% for large gap ratios of 3 and 5. From small gap ratios of 0.5 and 1, the RMS lift coefficients at α=0° and 45° are similar to each other. The present simulations show that the agreement in the force coefficients between the 0° and 45° flow attack angles for a constant normal Reynolds number is better than that for a constant total Reynolds number. This indicates that the normal Reynolds number should be used in the implementation of the independence principle (i.e., the independence of the force coefficients on the flow attack angle). The effect of Reynolds number on the bistable gap flow is investigated by simulating the flow for Re_N=100–600, α=0° and 45° and G/D=1. Flow for G/D=1 is found to be two-dimensional at Re_N=100 and weak three-dimensional at Re_N=200. While well defined biased flow can be identified for Re_N=300–600, the gap flow for Re_N=100 and 200 changes its biased direction too frequently to allow stable biased flow to develop.     

Near Field Round Jet Flow Downstream from an Abrupt Contraction Nozzle with Tube Extension

Round air jet development downstream from an abrupt contraction coupled to a uniform circular tube extension with length to diameter ratio L/D?=?1.2 and L/D?=?53.2 is studied experimentally. Smoke visualisation and systematic hot film velocity measurements are performed for low to moderate Reynolds numbers 1130?<?Re _b ?<?11320. Mean and turbulent velocity profiles are quantified at the tube exit and along the centerline from the tube exit down to 20 times the diameter D. Flow development is seen to be determined by the underlying jet structure at the tube exit which depends on Reynolds number, initial velocity statistics at the tube exit and the presence/absence of coherent structures. It is shown that the tube extension ratio L/D as well as the sharp edged abrupt contraction influence the initial jet structure at the tube exit. For both L/D ratios, the presence of the abrupt contraction results in transitional jet flow in the range 2000?<?Re _b ?<?4000 and in flow features associated with forced jets and high Reynolds numbers Re _b ?>?10⁴. The tube extension ratio L/D downstream from the abrupt contraction determines the shear layer roll up so that for L/D?=?1.2 flow visualisation suggests the occurrence of toroidal vortices for Re _b ?<?4000 whereas helical vortices are associated with the transitional regime for L/D?=?53.2. Found flow features are compared to features reported in literature for smooth contraction nozzles and long pipe flow.