Effect of side ratio on fluid flow and heat transfer from rectangular cylinders using the PANS method

A computational study of heat transfer from rectangular cylinders is carried out. Rectangular cylinders are distinguished based on the ratio of the length of streamwise face to the height of the cross-stream face (side ratio, R). The simulations were performed to understand the heat transfer in a flow field comprising separation, reattachment, vortex shedding and stagnation. The Partially-Averaged Navier–Stokes (PANS) modeling approach is used to solve the turbulent flow physics associated and the wall resolve approach is used for the near wall treatment because of the flow separation involved. The simulations were performed using a finite volume based opensource software, OpenFOAM, at Reynolds number (Re) = 22,000 for rectangular cylinder at constant temperature kept in an air stream. Two critical side ratios were obtained, R = 0.62 and 3.0. At R = 0.62, the maximum value of the drag coefficient (C_d) = 2.681 was observed which gradually reduced by 54% at R = 4.0. The base pressure coefficient and global Nusselt number also attained the maximum value at R = 0.62 and from R = 2.5 to 3.0 a sharp discontinuous increase by 140% in the Strouhal number was observed. At R = 0.62, it was observed that the separated flow reattaches at the trailing edge after rolling over the side face and therefore increases the overall Nusselt number. The phase averaging was also performed to analyze the unsteady behavior of heat transfer.     

URANS of flow and endwall heat transfer in a pinned passage relevant to gas-turbine blade cooling

This paper presents some results of URANS study of flow and heat transfer in a matrix of wall-bounded 8 × 8 round pins, mimicking internal cooling passage of gas-turbine blades. The focus is on flow unsteadiness, its role in heat transfer and the capabilities of RANS models to reproduce these features in a set-up of industrial relevance. The results for two Reynolds numbers, 10 000 and 30 000, are compared with the available experiments and LES. It is shown that the elliptic-relaxation eddy-viscosity model, ζ-f captures vortex shedding and the consequent gross effects on the flow development. However, a closer look at flow details reveals discrepancies, especially around the first three pin rows, where the unsteadiness reproduced by URANS shows much weaker amplitudes as compared with LES. Only further downstream the succession of forcing from a series of pins produced unsteadiness akin to those captured by LES. The comparison suggests that smaller structures undetected by URANS need to be resolved to capture properly the separation and wake characteristics of each row. At Re = 10 000, the average endwall Nusselt number agrees well with the LES, both being about 20% lower than in the experiment. For Re = 30 000 the URANS Nusselt is within 10% of the experimental value.     

Lattice Boltzmann simulation of the convective heat transfer from a stream-wise oscillating circular cylinder

In this paper, we studied the convective heat transfer from a stream-wise oscillating circular cylinder. Two dimensional numerical simulations are conducted at Re = 100–200, A = 0.1–0.4 and F = f_o/f_s = 0.2–3.0 with the aid of the lattice Boltzmann method. In particular, detailed attentions are paid on the extensive numerical results elucidating the influence of oscillation frequency, oscillation amplitude and Reynolds number on the time-average and RMS value of the Nusselt number. Over the ranges of conditions considered herein, the heat transfer characteristics are observed to be influenced in an intricate manner by the value of the oscillation frequency (F), oscillation amplitude (A) and Reynolds number (Re). Firstly, the heat transfer is enhanced when the cylinder oscillates stream-wise with small amplitude and low frequency, while it will be reduced by large amplitude and high frequency. Secondly, the average Nusselt number (Nu (ave)) decreases against the increasing value of oscillation frequency, while the RMS value of the Nusselt number, Nu (RMS), displays an opposite trend. Third, we obtained a similar frequency effect on the heat transfer over the range of Reynolds numbers investigated in this paper. In addition, detailed analyses on phase portraits, energy spectrum are also made.     

Chimney effect due to different vertical position of an isothermal horizontal cylinder confined between two adiabatic walls

The variation of natural convection heat transfer from an isothermal horizontal cylinder confined between two adiabatic walls of constant height is investigated by Mach-Zehnder interferometry technique. This paper focuses on the chimney effect due to the vertical position changes of cylinder (Y) located between two walls with a constant distance of W measuring 1.5 cylinder diameter. The cylinder’s local and average Nusselt numbers are determined for ratio of vertical position to its diameter ranging from Y/D = (0 to 10), and the Rayleigh number ranging from 3.5 × 10³ to 1.4 × 10⁴. There is an optimum distance between the walls in which the Nusselt number is maximum. Results are indicated with a single correlation which gives the average Nusselt number as a function of the ratio of vertical position to cylinder diameter and the Rayleigh number. The experimental data shows that there is an optimum vertical position for the cylinder at which the Nusselt number has a maximum value at each Rayleigh number. This optimal vertical position is derived from the correlation and is presented by an equation. The value of the optimum vertical position increases as the Rayleigh number increases.     

Investigation of transitional and turbulent heat and momentum transport in a rotating cavity

The paper gives the results of the DNS/LES which was performed to investigate the transitional and turbulent non-isothermal flows within a rotor/stator cavity. Computations were performed for the cavity of aspect ratio L = 2–35, Rm = 1.8 and for rotational Reynolds numbers up to 290000. The main purpose of the investigations was to analyze the influence of aspect ratio and Reynolds number on the flow structure and heat transfer. The numerical solution is based on a pseudo-spectral Chebyshev–Fourier–Galerkin collocation approximation. The time scheme is semi-implicit second-order accurate, which combines an implicit treatment of the diffusive terms and an explicit Adams–Bashforth extrapolation for the non-linear convective terms. In the paper we analyze distributions of the Reynolds stress tensor components, the turbulent heat flux tensor components, Nusselt number distributions and the turbulent Prandtl number and other structural parameters, which can be useful for modeling purposes. Selected results are compared with the experimental data obtained for single heated rotating disk by Elkins and Eaton (2000).     

Experimental and numerical investigation on air-side performance of fin-and-tube heat exchangers with various fin patterns

Air-side heat transfer and friction characteristics of five kinds of fin-and-tube heat exchangers, with the number of tube rows (N = 12) and the diameter of tubes (D_o = 18 mm), have been experimentally investigated. The test samples consist of five types of fin configurations: crimped spiral fin, plain fin, slit fin, fin with delta-wing longitudinal vortex generators (VGs) and mixed fin with front 6-row vortex-generator fin and rear 6-row slit fin. The heat transfer and friction factor correlations for different types of heat exchangers were obtained with the Reynolds numbers ranging from 4000 to 10000. It was found that crimped spiral fin provides higher heat transfer and pressure drop than the other four fins. The air-side performance of heat exchangers with the above five fins has been evaluated under three sets of criteria and it was shown that the heat exchanger with mixed fin (front vortex-generator fin and rear slit fin) has better performance than that with fin with delta-wing vortex generators, and the slit fin offers best heat transfer performance at high Reynolds numbers. Based on the correlations of numerical data, Genetic Algorithm optimization was carried out, and the optimization results indicated that the increase of VG attack angle or length, or decrease of VG height may enhance the performance of vortex-generator fin. The heat transfer performances for optimized vortex-generator fin and slit fin at hand have been compared with numerical method.     

Influences of peripherally-cut twisted tape insert on heat transfer and thermal performance characteristics in laminar and turbulent tube flows

Effects of peripherally-cut twisted tape insert on heat transfer, friction loss and thermal performance factor characteristics in a round tube were investigated. Nine different peripherally-cut twisted tapes with constant twist ratio (y/W = 3.0) and different three tape depth ratios (DR = d/W = 0.11, 0.22 and 0.33), each with three different tape width ratios (WR = w/W = 0.11, 0.22 and 0.33) were tested. Besides, one typical twisted tape was also tested for comparison. The measurement of heat transfer rate was conducted under uniform heat flux condition while that of friction factor was performed under isothermal condition. Tests were performed with Reynolds number in a range from 1000 to 20,000, using water as a working fluid. The experimental results revealed that both heat transfer rate and friction factor in the tube equipped with the peripherally-cut twisted tapes were significantly higher than those in the tube fitted with the typical twisted tape and plain tube, especially in the laminar flow regime. The higher turbulence intensity of fluid in the vicinity of the tube wall generated by the peripherally-cut twisted tape compared to that induced by the typical twisted tape is referred as the main reason for achieved results. The obtained results also demonstrated that as the depth ratio increased and width ratio decreased, the heat transfer enhancement increased. Over the range investigated, the peripherally-cut twisted tape enhanced heat transfer rates in term of Nusselt numbers up to 2.6 times (turbulent regime) and 12.8 times (laminar regime) of that in the plain tube. These corresponded to the maximum performance factors of 1.29 (turbulent regime) and 4.88 (laminar regime).     

Conjugate turbulent heat transfer in a square cavity with a solar control coating deposited to a vertical semitransparent wall

This paper presents a numerical study of the conjugate heat transfer (natural convection, surface thermal radiation and conduction) in a square cavity with turbulent flow. The cavity has one vertical isothermal wall, two horizontal adiabatic walls and one vertical semitransparent wall with a selective coating applied to the inner side to control the solar radiation transmission. Later on the semitransparent wall is replaced with another one without the selective coating. The mathematical model for the turbulent flow in the cavity was solved using the finite volume method. The system had the following conditions: the uniform temperature in the isothermal wall was 21 °C, the external ambient temperature was fixed at 35 °C and on the semitransparent wall the direct normal solar irradiation of 750 W/m² was considered constant. The Rayleigh number was varied in the range of 10⁹ ? Ra ? 10¹² by changing the lengths of the cavity from 0.70 m to 6.98 m, respectively. The results show that, even though the air temperature of the cavity with the solar control film coating semitransparent wall (case A) is higher compared with the one without solar film coating (case B), the total amount of heat going through the cavity is lower compared to the one going through the cavity without solar control film. The total amount of energy transferred to the air in cavity for the case A was 41.98% less than for the case B. A set of correlations for the Nusselt number was obtained for both cases considering the conjugate heat transfer.     

Experimental studies on heat transfer and friction factor characteristics of Al2O3/water nanofluid in a circular pipe under laminar flow with wire coil inserts

In this paper, fully developed laminar flow convective heat transfer and friction factor characteristics of Al₂O₃/water nanofluid flowing through a uniformly heated horizontal tube with and without wire coil inserts is presented. For this purpose, Al₂O₃ nanoparticles of 43 nm size were synthesized, characterized and dispersed in distilled water to form stable suspension containing 0.1% volume concentration of nanoparticles. The Nusselt number in the fully developed region were measured and found to increase by 12.24% at Re = 2275 for plain tube with nanofluid compared to distilled water. Two wire coil inserts made of stainless steel with pitch ratios 2 and 3 were used which increased the Nusselt numbers by 15.91% and 21.53% respectively at Re = 2275 with nanofluid compared to distilled water. The better heat transfer performance of nanofluid with wire coil insert is attributed to the effects of dispersion or back-mixing which flattens the temperature distribution and make the temperature gradient between the fluid and wall steeper. The measured pressure loss with the use of nanofluids is almost equal to that of the distilled water. The empirical correlations developed for Nusselt number and friction factor in terms of Reynolds/Peclet number, pitch ratio and volume concentration fits with the experimental data within ±15%.     

The influence of pipe length on thermal statistics computed from DNS of turbulent heat transfer

We present results from direct numerical simulation of turbulent heat transfer in pipe flow at a bulk flow Reynolds number of 5000 and Prandtl numbers ranging from 0.025 to 2.0 in order to examine the effect of streamwise pipe length (πδ ≡ πD/2 ⩽ L ⩽ 12πδ) on the convergence of thermal turbulence statistics. Various lower and higher order thermal statistics such as mean temperature, rms of fluctuating temperature, turbulent heat fluxes, two-point auto and cross-correlations, skewness and flatness were computed and it is found that the value of L required for convergence of the statistics depends on the Prandtl number: larger Prandtl numbers requires comparatively shorter pipe length for convergence of most of the thermal statistics.     

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.     

The influence of pipe length on thermal statistics computed from DNS of turbulent heat transfer

We present results from direct numerical simulation of turbulent heat transfer in pipe flow at a bulk flow Reynolds number of 5000 and Prandtl numbers ranging from 0.025 to 2.0 in order to examine the effect of streamwise pipe length (πδ ≡ πD/2 ? L ? 12πδ) on the convergence of thermal turbulence statistics. Various lower and higher order thermal statistics such as mean temperature, rms of fluctuating temperature, turbulent heat fluxes, two-point auto and cross-correlations, skewness and flatness were computed and it is found that the value of L required for convergence of the statistics depends on the Prandtl number: larger Prandtl numbers requires comparatively shorter pipe length for convergence of most of the thermal statistics.     

Convective heat transfer to CO2 at a supercritical pressure flowing vertically upward in tubes and an annular channel

The Super-Critical Water-Cooled Reactor (SCWR) has been chosen by the Generation IV International Forum as one of the candidates for the next generation nuclear reactors. Heat transfer to water from a fuel assembly may deteriorate at certain supercritical pressure flow conditions and its estimation at degraded conditions as well as in normal conditions is very important to the design of a safe and reliable reactor core. Extensive experiments on a heat transfer to a vertically upward flowing CO₂ at a supercritical pressure in tubes and an annular channel have been performed. The geometries of the test sections include tubes of an internal diameter (ID) of 4.4 and 9.0 mm and an annular channel (8 × 10 mm). The heat transfer coefficient (HTC) and Nusselt numbers were derived from the inner wall temperature converted by using the outer wall temperature measured by adhesive K-type thermocouples and a direct (tube) or indirect (annular channel) electric heating power. From the test results, a correlation, which covers both a deteriorated and a normal heat transfer regime, was developed. The developed correlation takes different forms in each interval divided by the value of parameter Bu. The parameter Bu (referred to as Bu hereafter), a function of the Grashof number, the Reynolds number and the Prandtl number, was introduced since it is known to be a controlling factor for the occurrence of a heat transfer deterioration due to a buoyancy effect. The developed correlation predicted the HTCs for water and HCFC-22 fairly well.     

Thermal and friction characteristics of laminar flow through rectangular and square ducts with transverse ribs and wire coil inserts

The heat transfer and the pressure drop characteristics of laminar flow of viscous oil (195 < Pr < 525) through rectangular and square ducts with internal transverse rib turbulators on two opposite surfaces of the ducts and with wire coil inserts have been studied experimentally. Circular duct has also been used. The transverse ribs in combination with wire coil inserts have been found to perform better than either ribs or wire coil inserts acting alone. The heat transfer and the pressure drop measurements have been taken in separate test sections. Heat transfer tests were carried out in electrically heated stainless steel ducts incorporating uniform wall heat flux boundary conditions. Pressure drop tests were carried out in acrylic ducts. The flow friction and thermal characteristics are governed by duct aspect ratio, coil helix angle and wire diameter of the coil, rib height and rib spacing, Reynolds number and Prandtl number. Correlations developed for friction factor and Nusselt number have predicted the experimental data satisfactorily. The performance of the geometry under investigation has been evaluated. It has been found that on the basis of constant pumping power, up to fifty per cent heat duty increase occurs for the combined ribs and wire coil inserts case compared to the individual ribs and wire coil inserts cases in the measured experimental parameters space. On the constant heat duty basis, the pumping power has been reduced up to forty per cent for the combined enhancement geometry than the individual enhancement geometries.     

Flow instability in baffled channel flow

Flow instability in baffled channel flow, where thin baffles are mounted on both channel walls periodically in the direction of the main flow, has been numerically investigated. The geometry considered here can be regarded as a simple model for finned heat exchangers. The aim of this investigation is to understand how baffle interval (L) and Reynolds number (Re) influence the flow instability. With a fixed baffle length of one quarter of channel height (H), ratios of baffle interval to channel height (R_B = L/H) between 1 and 4 are considered. The critical Reynolds number of the primary instability, a Hopf bifurcation from steady flow to time-periodic flow, turned out to be minimum when R_B = 3.08. The friction factor (f) is strongly correlated with the critical Reynolds number for R_B ⩽ 2.5. For the particular cases of R_B = 1.456 and R_B = 1.0, we performed Floquet stability analysis in order to study the secondary instability through which time-periodic two-dimensional flow bifurcates into three-dimensional flow. The results obtained in this investigation are in good agreement with those computed from full simulations, and shed light on understanding and controlling flow characteristics in a finned heat exchanger, quite beneficial to its design.     

Numerical analysis of turbulent convection heat transfer from an array of perforated fins

Numerical investigation is made for three-dimensional fluid flow and convective heat transfer from an array of solid and perforated fins that are mounted on a flat plate. Incompressible air as working fluid is modeled using Navier–Stokes equations and RNG based k ? ? turbulent model is used to predict turbulent flow parameters. Temperature field inside the fins is obtained by solving Fourier’s conduction equation. The conjugate differential equations for both solid and gas phase are solved simultaneously by finite volume procedure using SIMPLE algorithm. Perforations such as small channels with square cross section are arranged streamwise along the fin’s length and their numbers varied from 1 to 3. Flow and heat transfer characteristics are presented for Reynolds numbers from 2 × 10⁴ to 4 × 10⁴ based on the fin length and Prandtl number is taken Pr = 0.71. Numerical computations are validated with experimental studies of the previous investigators and good agreements were observed. Results show that fins with longitudinal pores, have remarkable heat transfer enhancement in addition to the considerable reduction in weight by comparison with solid fins.     

Heat transfer enhancement in a tube with equilateral triangle cross sectioned coiled wire inserts

The heat transfer and pressure drop were experimentally investigated in a coiled wire inserted tube in turbulent flow regime. The coiled wire has equilateral triangular cross section and was inserted separately from the tube wall. The experiments were carried out with three different pitch ratios (P/D = 1, 2 and 3) and two different ratio of equilateral triangle length side to tube diameter (a/D = 0.0714 and 0.0892) at a distance (s) of 1 mm from the tube wall in the range of Reynolds number from 3500 to 27,000. Uniform heat flux was applied to the external surface of the tube and air was selected as fluid. The experimental results obtained from a smooth tube were compared with those from the studies in literature for validation of experimental set-up. The use of coiled wire inserts leads to a considerable increase in heat transfer and pressure drop over the smooth tube. The Nusselt number rises with the increase of Reynolds number and wire thickness and the decrease of pitch ratio. The highest overall enhancement efficiency of 36.5% is achieved for the wire with a/D = 0.0892 and P/D = 1 at Reynolds number of 3858. Consequently, the experimental results reveal that the best operating regime of all coiled wire inserts is detected at low Reynolds number, leading to more compact heat exchanger.     

Periodic boiling in parallel micro-channels at low vapor quality

Based on experimental investigations the present study evaluates instability and heat transfer phenomenon under condition of periodic flow boiling of water and ethanol in parallel triangular micro-channels. Tests were performed in the range of hydraulic diameter 100–220 μm, mass flux 32–200 kg/m² s, heat flux 120–270 kW/m², vapor quality x = 0.01–0.08. The period between successive events depends on the boiling number and decreases with an increase in the boiling number. The initial film thickness decreases with increasing heat flux. When the liquid film reached the minimum initial film thickness CHF regime occurred. Temporal variations of pressure drop, fluid and heater temperatures were periodic. Oscillation frequency is the same for the pressure drop, for the fluid temperature at the outlet manifold, and for the mean and maximum heater temperature fluctuations. All these fluctuations are in phase. The CHF phenomenon is different from that observed in a single channel of conventional size. A key difference between micro-channel heat sink and single conventional channel is amplification of parallel-channel instability prior to CHF. The dimensionless experimental values of the heat transfer coefficient are presented as the Nusselt number dependence on the Eotvos number and the boiling number.     

Experimental evaluation of cooling performance of circular heat sinks for heat dissipation from electronic chips using nanofluid

In this work, an experimental investigation on cooling performance of using nanofluid to replace the pure water as the coolant in a minichannel heat sink is conducted. The heat sink comprises of four circular channels with hydraulic diameter of 6 mm. Thermal and hydraulic performances of the nanofluid cooled minichannel heat sink are evaluated from the results obtained for the Nusselt number, friction factor, thermal resistance and pumping power, with the volume flow rate ranging from 0.3 to 1.5 L/min. The experimental results show that the nanofluid cooled heat sink outperforms the water-cooled one, having significantly higher average heat transfer coefficient. Despite the marked increase in dynamic viscosity due to dispersing the nanoparticles in water, the friction factor for the nanofluid-cooled heat sink is found slightly increased only.     

Flow boiling heat transfer of R134a,R236fa and R245fa in a horizontal 1.030 mm circular channel

This research focuses on acquiring accurate flow boiling heat transfer data and flow pattern visualization for three refrigerants, R134a, R236fa and R245fa in a 1.030 mm channel. We investigate trends in the data, and their possible mechanisms, for mass fluxes from 200 to 1600 kg/m²s, heat fluxes from 2.3 kW/m² to 250 kW/m² at T_sat = 31 °C and ΔT_sub from 2 to 9 K. The local saturated flow boiling heat transfer coefficients display a heat flux and a mass flux dependency but no residual subcooling influence. The changes in heat transfer trends correspond well with flow regime transitions. These were segregated into the isolated bubble (IB) regime, the coalescing bubble (CB) regime, and the annular (A) regime for the three fluids. The importance of nucleate boiling and forced convection in these small channels is still relatively unclear and requires further research.