Direct numerical simulation of turbulent flow and heat transfer in a square duct with natural convection

In this paper, a direct numerical simulation of a fully developed turbulent flow and heat transfer are studied in a square duct with an imposed temperature difference between the vertical walls and the perfectly insulated horizontal walls. The natural convection is considered on the cross section in the duct. The numerical scheme employs a time-splitting method to integrate the three dimensional incompressible Navier-Stokes equation. The unsteady flow field was simulated at a Reynolds number of 400 based on the Mean friction velocity and the hydraulic diameter (Re _m = 6200), while the Prandtl number (Pr) is assumed 0.71. Four different Grashof numbers (Gr = 10⁴, 10⁵, 10⁶ and 10⁷) are considered. The results show that the secondary flow and turbulent characteristics are not affected obviously at lower Grashof number (Gr ≤ 10⁵) cases, while for the higher Grashof number cases, natural convection has an important effect, but the mean flow and mean temperature at the cross section are also affected strongly by Reynolds stresses. Compared with the laminar heat transfer at the same Grashof number, the intensity of the combined heat transfer is somewhat decreased.     

Combined forced and free convective flow of water at 4°C past a semi-infinite vertical plate

Effects of buoyancy forces on forced and free convective flow of water at 4°C past a semi-infinite vertical plate at constant temperature are studied. Flow is assumed to be vertically upwards. Similarity solutions are derived and the resulting equations are solved numerically on a computer. Velocity and temperature profiles are shown graphically and numerical values of the skin friction and the rate of heat transfer are entered in tables. It is observed that the skin friction and the Nusselt number increase with increasing Gr/Re², where Gr is the Grashof number and Re is the Reynolds number     

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.     

Heat transfer characteristics of staggered wing-shaped tubes bundle at different angles of attack

An experimental and numerical study has been conducted to clarify heat transfer characteristics and effectiveness of a cross-flow heat exchanger employing staggered wing-shaped tubes at different angels of attack. The water-side Re_w and the air-side Re_a were at 5 × 10² and at from 1.8 × 10³ to 9.7 × 10³, respectively. The tubes arrangements were employed with various angles of attack θ_1,2,3 from 0° to 330° at the considered Re_a range. Correlation of Nu, St, as well as the heat transfer per unit pumping power (ε) in terms of Re_a and design parameters for the studied bundle were presented. The temperature fields around the staggered wing-shaped tubes bundle were predicted by using commercial CFD FLUENT 6.3.26 software package. Results indicated that the heat transfer increased with the angle of attack in the range from 0° to 45°, while the opposite was true for angles of attack from 135° to 180°. The best thermal performance and hence the efficiency η of studied bundle occurred at the lowest Re_a and/or zero angle of attack. Comparisons between the experimental and numerical results of the present study and those, previously, obtained for similar available studies showed good agreements.     

Numerical study of transient laminar natural convection heat transfer over a sphere subjected to a constant heat flux

Transient laminar natural convection over a sphere which is subjected to a constant heat flux has been studied numerically for high Grashof numbers (10⁵ ≤ Gr ≤ 10⁹) and a wide range of Prandtl numbers (Pr = 0.02, 0.7, 7, and 100). A plume with a mushroom-shaped cap forms above the sphere and drifts upward continuously with time. The size and the level of temperature of the transient cap and plume stem decrease with increasing Gr and Pr. Flow separation and an associated vortex may appear in the wake of the sphere depending on the magnitude of Gr and Pr. A recirculation vortex which appears and grows until “steady state” is attained was found only for the very high Grashof numbers (10⁵ ≤ Gr ≤ 10⁹) and the lowest Prandtl number considered (Pr = 0.02). The appearance and subsequent disappearance of a vortex was observed for Gr = 10⁹ and Pr = 0.7. Over the lower hemisphere, the thickness of both the hydrodynamic (δ_H) and the thermal (δ_T) boundary layers remain nearly constant and the sphere surface is nearly isothermal. The surface temperature presents a local maximum in the wake of the sphere whenever a vortex is established in the wake of the sphere. The surface pressure recovery in the wake of the sphere increases with decreasing Pr and with increasing Gr. For very small Pr, unlike forced convection, the ratio δ_T/δ_H remains close to unity. The results are in good agreement with experimental data and in excellent agreement with numerical results available in the literature. A correlation has also been presented for the overall Nusselt number as a function of Gr and Pr.     

Experimental study of the effect of a passive porous coating on disturbances in a hypersonic boundary layer 2. Effect of the porous coating location

The effect of the location of a passive porous coating on natural disturbances in a hypersonic boundary layer is studied experimentally. The experiments are performed in the flow around a sharp cone aligned at a zero angle of attack with the free-stream Mach number M_∞ = 5.8, stagnation temperature T ₀ = 370 ± 5 K, and unit Reynolds numbers Re_1∞ = 2.6 · 10⁶, 4.6 · 10⁶, 6.6 · 10⁶, and 10⁷ m^?1. The wave characteristics of the boundary layer are calculated with the use of the linear stability theory for flow parameters corresponding to experimental values. A comparison of experimental and predicted results shows that the presence of a porous coating in the region where the second mode is unstable leads to reduction of its amplitude at the measurement point, whereas the presence of a porous coating in the region of second mode stability leads to enhancement of the amplitude.     

Turbulent film boiling from a vertical non-isothermal surface

The turbulent film boiling from a vertical non-isothermal surface is formulated with due consideration to thermal radiation from its lateral face. It is observed that the application of Reynolds analogy together with thermal conduction in the test surface has yielded a conjugate solution from which the case of an isothermal condition can be generated as a special case. The analysis has further paved the way in establishing a functional relation between the Nusselt numberNu, radiation parameterN _R , fin parameterM, temperature ratio termT _s /(T _w,0?T _s ), and a product of characteristic modified Grashof, Prandtl and superheating parameter defined as (Gr ² Pr S). In a fully developed turbulent film boiling i.e., modified Grashof number being greater than 10¹⁰, the temperature ratio term accounts for the non-linearities arising due to the inclusion of radiation from the lateral face of the fin. The results are in good agreement with experimental data over a wide range of system conditions.     

Experiments on sedimentation beneath downward-facing inclined walls

It has been known since Boycott (1920) that sedimentation rates can be several times higher within inclined walls than in vertical vessels. Beneath the downward-facing inclined wall a thin boundary-layer of clear liquid is formed with an upward velocity. Mass continuity brings about the observed effect. Ponder (1925), and Nakamura & Kuroda (1937) proposed a global kinematic model without any detail of the flow field to predict the sedimentation rate. Recently, two asymptotic theories for describing the flow field became available. The investigation by Acrivos & Herbolzheimer (1979) requires both Re²/Gr and Re⁴/Gr to be small, with Re being a sedimentation Reynolds number and Gr a sedimentation Grashof number. The analysis due to Schneider (1982) is valid for small values of Re²/Gr and large values of Re⁴/Gr. This paper presents experimental sedimentation data in a²/Gr and large values of symmetrical, roof-shaped vessel. The experiments with spherical glass beads in a variable mixture of glycerine and water cover the whole parameter range from very small to very large values of Re⁴/Gr. Therefore, both theories could be verified. In the case of small values of Re⁴/Gr, strong waves beneath the downward-facing wall were observed and graphically evaluated in order to find a basis for further theoretical approach. Furthermore, an upward flow of particles in a sublayer of the boundary-layer leads te protruding “borns” and an oscillation of the originally horizontal discontinuity separating the suspension from the clear liquid. The measured particle distribution and deviations from a monodispersed suspension seems to be a possible explanation for this effect, which is investigated theoretically in a separate paper (Schaflinger 1984). A further experimental shortcoming, the shallow depth of the settling vessel, that was necessary for an optoelectronic measuring of the actual volume fraction solids within the bulk, may affect the convective motion when the sedimentation Reynols number is small. However, in this case the experimental data are in conformity with the theoretical predictions which do not consider the influence of wall friction on the sedimentation behaviour.     

Heat transfer from the heated concave wall of a return bend with rectangular cross section

The characteristics of the turbulent heat transfer along the heated concave walls of return bends which have rectangular cross sections with large aspect ratio have been examined for various clearances of the ducts in detail. The experiments are carried out under the condition that the concave walls are heated at constant heat flux while the convex walls are insulated. Water as the working fluid is utilized. Using three kinds of clearance of 9, 34, and 55 mm, the Reynolds number in the turbulent range are varied from 5×10³ to 8×10⁴ with the Prandtl numbers ranging from 4 to 13. As a result it is elucidated that both the mean and the local Nusselt numbers are always greater than those for the straight parallel plates or for the straight duct, respectively. This is attributed to Görtier vortices, which are visualized here. It is also found that the more the clearance increases, the more both the local and the mean Nusselt numbers increase. Correlation equations for the mean and the local Nusselt numbers are determined in the range of parameters covered. Introducing the Richardson number, it appears that the local Nusselt number,Nu _x , may be described as the following equation:Nu _x =447.745 ·Re _x ^1.497 ·De _x ^?1.596 ·F ^0.960 ·Pr ^0.412     

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.     

Evaluation of two RANS turbulence models in predicting developing mixed convection within a heated horizontal pipe

The developing weakly turbulent regime of mixed convection in a uniformly heated horizontal pipe was first studied experimentally, by means of heat transfer measurements in the following ranges of dimensionless numbers: 3.19 < Re × 10^? 3 < 6.39, 1.80 < Gr _h  × 10^? 8 < 4.20. The working fluid was FC-72?, with Pr = 12.4.

In order to gain a better insight into the thermo-fluid dynamics involved in the phenomenon and obtain the velocity and temperature fields at every point of the fluid domain, numerical simulations were performed by means of commercial software. Turbulence was modelled by using the Reynolds averaged Navier–Stokes equations (RANS) approach. Two closures of the governing equations were evaluated: realizable κ–? (RKE) model and renormalization-group κ–? (RNG) model.

Both models were capable of reproducing the observed physical trends. However, deviations from the experimental data lower than 20% were obtained only in the entry-zone with the RKE model, while the RNG model gave fair predictions only in developed or quasi-developed flow.     

Experimental investigation of mixed convection in a rectangular duct with a heated plate in the middle of cross section

The flow and heat transfer in an inclined and horizontal rectangular duct with a heated plate longitudinally mounted in the middle of cross section was experimentally investigated. The heated plate and rectangular duct were both made of highly conductive materials, and the heated plate was subjected to a uniform heat flux. The heat transfer processes through the test section were under various operating conditions: Pr ≈ 0.7, inclination angle ϕ = −60° to +60°, Reynolds number Re = 334–1,911, Grashof number Gr = 5.26 × 10²–5.78 × 10⁶. The experimental results showed that the average Nusselt number in the entrance region was 1.6–2 times as large as that in the fully developed region. The average Nusselt numbers and pressure drops increased with the Reynolds number. The average Nusselt numbers and pressure drops decreased with an increase in the inclination angle from −60° to +60° when the Reynolds number was less than 1,500. But when the Reynolds number increased to over about 1,800, the heat transfer coefficients and pressure drops were independent of inclination angles.     

Characterisation of gas-liquid two-phase flow in minichannels with co-flowing fluid injection inside the channel,part I: unified mapping of flow regimes

Present research highlights the potential of apparatuses with integrated minichannel packings to intensify gas-liquid-solid contacting. Especially an operation of these devices within the Taylor flow regime gained extraordinary attention due to its excellent heat and mass transfer and the segmented flow characteristics. However, criteria for flow regime transitions are mainly developed from water-similar fluids and are contradictory which hinders uniform flow regime prediction.This work presents a systematic analysis of adiabatic gas-liquid downflow in a square minichannel of 1.0 mm hydraulic diameter. In the mixing zone located within the flow channel, gas was injected into the co-flowing liquid by so-called capillary injectors with variable inner diameter (0.184, 0.317, 0.490 mm). Experiments were conducted using water, water-glycerol, and water-ethanol mixtures to cover a broad range of material properties. The gas and liquid superficial velocities were varied between 9.81·10^-4…2.72 m/s and 1.7·10⁻⁴…0.80 m/s, respectively. Taylor flow, Taylor-annular flow, annular flow, churn flow, and bubbly flow were observed. Using the Pi-theorem, 8 significant dimensionless groups dictating the flow transition were identified, namely u_{G, s}/u_{L, s}, Re_G, Re_L, We_G, We_L, Θ*, d_{In, CI}/d_h, and d_{Ou, CI}/d_h. Based on more than 1500 experimental data, criteria for the regime transitions of Taylor flow are provided. The derived flow regime map shows good agreement for all applied liquids and for the two larger injector geometries.     

A convective weakly viscoelastic rotating flow with pressure Neumann condition

The objective of this work is to investigate through the numeric simulation, the effects of the weakly viscoelastic flow within a rotating rectangular duct subject to a buoyancy force due to the heating of one of the walls of the duct. A direct velocity–pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure field is directly updated without any iteration. Numerical simulations were done for several Weissemberg numbers (We) and Grashof numbers (Gr) . The numerical results show that for high Weissemberg numbers (We>7.4 × 10^?5) and for ducts with aspect ratio 2:1 and 8:1, the secondary flow is restabilized with a stretched double vortex configuration. It is also observed that when the Grashof number is increased (Gr>17 × 10^?4) , the buoyancy force neutralizes the effects of the Coriolis force for ducts with aspect ratio 8:1. Copyright © 2008 John Wiley & Sons, Ltd.     

Experimental study of the laminar-turbulent transition on a blunt cone

Results of an experimental study of the laminar-turbulent transition in a hypersonic flow around cones with different bluntness radii at a zero angle of attack, free-stream Mach number M _∞ = 6, and unit Reynolds number in the interval Re _∞,1 = 5.79 · 10⁶–5.66 · 10⁷ m^?1 are presented. Flow regimes in which a reverse of the laminar-turbulent transition (decrease in the length of the laminar segment with increasing bluntness radius) are studied. Heat flux distributions over the model surface are obtained with the use of temperature-sensitive paints. Lines of the beginning of the transition in the boundary layer are analyzed by using heat flux fields. The critical Reynolds number Re _∞,R ≈ 1.3 · 10⁵ beginning from which the laminar-turbulent transition substantially depends on uncontrolled disturbances, such as the model tip roughness, is found. In supercritical regimes, the line of the transition beginning is shifted in most cases toward the model tip (reverse of the transition). The results obtained are compared with available experimental data.     

Scalar dispersion in the near wake of a simplified model car

Experimental results on tracer gas diffusion within the near wake of a simplified model car (Ahmed model with a rear slant angle of 25°) are presented. Pollutant emission is simulated using heated air injected through a small pipe at one side of the model base. Fine cold wire thermometry is used to measure instantaneous temperature excess in the near wake. Characteristics of the temperature field over the Reynolds number range (1.3×10⁴<Re _L<7×10⁴) show strong differences as a result of transition in the wake at a critical Reynolds number Re _Lc=2.7×10⁴.     

Effect of acoustic disturbances on a free convective flow

A gas-dynamic flow in an axisymmetric convective jet is studied experimentally. It is demonstrated that the jet flow with Grashof numbers Gr = (0.4–2.0) · 10⁶ is self-similar. Acoustic oscillations directed perpendicular to the axis of symmetry transform the profiles of the gas-flow parameters; two temperature maximums located outside the axis can appear. The results obtained indicate that flow instability is generated in high-gradient regions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 27–33, September–October, 2006.     

Flow past a square cylinder at low Reynolds numbers

Results are presented for the flow past a stationary square cylinder at zero incidence for Reynolds number, Re ? 150. A stabilized finite‐element formulation is employed to discretize the equations of incompressible fluid flow in two‐dimensions. For the first time, values of the laminar separation Reynolds number, Re_s, and separation angle, θ_s, at Re_s are predicted. Also, the variation of θ_s with Re is presented. It is found that the steady separation initiates at Re = 1.15. Contrary to the popular belief that separation originates at the rear sharp corners, it is found to originate from the base point, i.e. θ_s=180^° at Re = Re_s. For Re > 5, θ_s approaches the limit of 135 ^°. The length of the separation bubble increases approximately linearly with increasing Re. The drag coefficient varies as Re^?0.66. Flow characteristics at Re ? 40 are also presented for elliptical cylinders of aspect ratios 0.2, 0.5, 0.8 and 1 (circle) having the same characteristic dimension as the square and major axis oriented normal to the free‐stream. Compared with a circular cylinder, the flow separates at a much lower Re from a square cylinder leading to the formation of a bigger wake (larger bubble length and width). Consequently, at a given Re, the drag on a square cylinder is more than the drag of a circular cylinder. This suggests that a cylinder with square section is more bluff than the one with circular section. Among all the cylinder shapes studied, the square cylinder with sharp corners generates the largest amount of drag. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental investigation of mixed convection from an array of discrete heat sources at the bottom of a horizontal channel

Mixed convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally under various operating conditions for air. The lower surface of the channel was equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux, sidewalls and the upper wall are insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR = 10, Reynolds numbers 241 Re_Dh 980, and modified Grashof numbers Gr^* = 9.53 × 10⁵ to 1.53 × 10⁷ . From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers, with emphasis on changes obtained for different discrete heat source locations. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit, especially for low Reynolds numbers.     

Measurement and decomposition of periodic flow structures downstream of a test turbine

The temperature dissipation rate inferred from the balance of $\overline{\theta^{2}}/2$ budget is used for the purpose of studying different methods employed to directly measure dissipation. The terms involved in the budget equation of temperature variance are measured with laser Doppler velocimetry and cold-wire thermometry used simultaneously. This study focuses on the centerline of a turbulent round jet, in the far field, at high Reynolds number (x/D = 30, Re _D  = 1.5 × 10⁵ and Re _λ  = 548). Particular attention is devoted to statistical convergence of second- and third-order moments of velocity and temperature fluctuations. Temperature dissipation obtained by Taylor’s hypothesis and radial temperature derivative spectra confirm local isotropy. A high level of low wave number content is reported for the longitudinal derivative spectra, probably due to transverse mode spectral aliasing and noise contamination for small wire separation. A parallel is drawn between finite difference formulations and the behavior of the autocorrelation coefficient for small wire separations. The temperature dissipation estimates found are close to the budget reference value, but spectral analysis cast doubts on the validity of the streamwise derivative obtained with a pair of probes.