Numerical prediction of turbulent flow and heat transfer in helically coiled pipes

Computational results were obtained for turbulent flow and heat transfer in curved pipes, representative of helically coiled heat exchangers. Following a grid refinement study, grid independent predictions from alternative turbulence models (k–?, SST k–ω and RSM–ω) were compared with DNS results and experimental pressure drop and heat transfer data. Using the SST k–ω and RSM–ω models, pressure drop results were in excellent agreement with literature data and the Ito correlation. For heat transfer, the literature is not comparably complete or accurate, but a satisfactory agreement was obtained in the range of available data. Unsatisfactory results, both for pressure drop and heat transfer, were given by the k–? model with wall functions. Following the validation study, the RSM–ω model was used to compute friction coefficients and Nusselt numbers in the range Re = 1.4·10⁴–8·10⁴, Pr = 0.7–5.6 and δ (coil curvature) = 3·10^?3–0.3. Power-law correlations were found unsuitable to fit the Re-, Pr- and δ-dependence of the Nusselt number, while the use of a properly formulated momentum-heat transfer analogy collapsed all results with high accuracy.     

Prediction of convection from a finned cylinder in cross flow using direct simulation,turbulence modeling,and correlation-based methods

Direct numerical simulation (DNS), two shear-stress transport (SST) turbulence models, and three k-ε models are used to predict mixed convection associated with air in cross flow over an isothermal, finned cylinder. The DNS predictions reveal complex time-variation in the flow field. Convection heat transfer coefficients predicted by the SST models are in good agreement with those generated by DNS, whereas the k-ε models do not accurately predict heat fluxes. Correlation-based predictions of heat transfer coefficients are, in general, in poor agreement with the DNS and SST predictions. The impact of various geometrical modifications on convection coefficients is also presented.     

Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure

A numerical investigation is carried out to analyze natural convection heat transfer inside a cavity with a sinusoidal vertical wavy wall and filled with a porous medium. The vertical walls are isothermal while the top and bottom horizontal straight walls are kept adiabatic. The transport equations are solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used is ascertained by comparing our results with previously published results. The importance of non-Darcian effects on convection in a wavy porous cavity is analyzed in this work. Different flow models for porous media such, as Brinkman-extended Darcy, Forchheimer-extended Darcy, and the generalized flow models, are considered. Results are presented in terms of streamlines, isotherms, and local heat transfer. The implications of Rayleigh number, number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics are investigated in detail while the Prandtl number is considered equal to unity.     

Optimum wall-to-wall spacing in solar chimney shaped channels in natural convection by numerical investigation

A numerical study on the laminar and turbulent flows induced by natural convection in channels, with solar chimney configuration, for a wide range of Rayleigh number, several values of the relative wall-to-wall spacing and different heating conditions has been performed. The low-Reynolds k–ω turbulence model has been employed to simulate the turbulent cases. Numerical results for the average Nusselt number and the non-dimensional induced mass-flow rate have been obtained for values of Rayleigh number varying from 10⁵ to 10¹² for symmetrically, isothermal heating. For this heating condition, a correlation for the thermal optimum aspect ratio has been presented. The sudden change reached in the flow pattern for given conditions drives to obtain a different behavior of the optimum aspect ratio that maximizes the mass-flow rate with respect to the thermal optimum aspect ratio.     

Conjugate turbulent natural convection with surface radiation in air filled rectangular enclosures

Conjugate turbulent natural convection and surface radiation in rectangular enclosures heated from below and cooled from other walls, typically encountered in Liquid Metal Fast Breeder Reactor (LMFBR) subsystems, have been investigated by a finite volume method for various aspect ratios. The formulation comprises the standard two equation k–ε turbulence model with physical boundary conditions (no wall functions), along with the Boussinesq approximation, for the flow and heat transfer. As far as radiation is concerned, the radiosity – irradiation formulation for a transparent fluid of Prandtl number 0.7 has been employed. The conjugate coupling on the walls has been handled by using a fin type formulation. The Rayleigh number based on the width of the enclosure is varied from 10⁸ to 10¹² and the aspect ratio is varied from 0.5 to 2.0. Detailed results including stream lines, temperature profiles, and convective, radiative and overall Nusselt numbers are presented. A correlation for the mean convection Nusselt number in terms of Rayleigh number and aspect ratio is proposed for design purposes. The influence of the wall emissivity and the external heat transfer coefficient on the heat transfer from the enclosure has also been investigated.     

Laminar natural convection in an inclined cavity with a wavy wall

In the present work, a numerical study of the effect of a hot wavy wall of a laminar natural convection in an inclined square cavity, differentially heated, was carried out. This problem is solved by using the partial differential equations, which are the vorticity transport, heat transfer and stream function in curvilinear co-ordinates. The tests were performed for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. Two geometrical configurations were used namely one and three undulations.The results obtained show that the hot wall undulation affects the flow and the heat transfer rate in the cavity. The mean Nusselt number decreases comparing with the square cavity. The trend of the local heat transfer is wavy. The frequency of the latter is different from the undulated wall frequency.     

Conjugate natural convection in air filled tube inserted a square cavity

Numerical analyses of fluid flow and heat transfer due to buoyancy forces in a tube inserted square cavity filled with fluid were carried out by using control volume method in this study. The cavity was heated from the left wall and cooled from the right isothermally and horizontal walls were adiabatic. A circular tube filled with air was inserted into the square cavity. The case that the inside and outside of the tube were filled with the same fluid (air) was examined. Varied solid materials were chosen as the tube wall. Results were obtained for different Rayleigh numbers (Ra = 10⁴, 10⁵ and 10⁶), thermal conductivity ratio of the fluid to the tube wall (k = 0.1, 1 and 10) and different location centers of the tube (c (0.25 ≤ x ≤ 0.75, 0.25 ≤ y ≤ 0.75)). Comparison with benchmark solutions of the natural convection in a cavity was performed and numerical results gave an acceptable agreement. It was found that varied location of the tube center can lead to different flow fields and heat transfer intensities which are also affected by the value of Rayleigh number.     

Hydromagnetic effect on mixed convection in a lid-driven cavity with sinusoidal corrugated bottom surface

The present numerical simulation is conducted to analyze the mixed convection flow and heat transfer in a lid-driven cavity with sinusoidal wavy bottom surface in presence of transverse magnetic field. The enclosure is saturated with electrically conducting fluid. The cavity vertical walls are insulated while the wavy bottom surface is maintained at a uniform temperature higher than the top lid. In addition, the transport equations are solved by using the finite element formulation based on the Galerkin method of weighted residuals. The implications of Reynolds number (Re), Hartmann number (Ha) and number of undulations (λ) on the flow structure and heat transfer characteristics are investigated in detail while, Prandtl number (Pr) and Rayleigh number (Ra) are considered fixed. The trend of the local heat transfer is found to follow a wavy pattern. The results of this investigation illustrate that the average Nusselt number (Nu) at the heated surface increases with an increase of the number of waves as well as the Reynolds number, while decreases with increasing Hartmann number.     

Experimental and numerical investigation of thermal -hydraulic performance in wavy fin-and-flat tube heat exchangers

To the more deeply understand the enhancement heat transfer mechanism and optimization design for wavy fin-and-flat tube heat exchangers, three-dimensional numerical simulations and experimental investigation of air flow and heat transfer characteristics over the wavy fin heat exchangers are presented in this study. The numerical simulation results compared with the wind tunnel test data, the results show that the numerical simulation results are in good with the test. The experimental results show that, in the range of Re = 1000–5500, the standard k-ε mode (SST) is more suitable to predict the air flow and heat transfer of wavy fin. The waviness amplitude has the distinct effect on the heat transfer and pressure drop of wavy fin, while the wavy fin profile (Triangular, Sinusoidal and Triangular round corner) has little effect on the heat transfer performance. In additional, the enhancement heat transfer mechanism of wavy fin is explained in view of field synergy principle. Reduction the synergy angle between velocity and temperature gradient will induce to the heat transfer coefficients increase of wavy fin.     

Effect of a wavy interface on the natural convection of a nanofluid in a cavity with a partially layered porous medium using the ISPH method

The effect of a wavy nanofluid/porous-medium interface on the natural convection of a Cu–water nanofluid in a differentially heated non-Darcy porous cavity was investigated using the ISPH method. Wall boundary conditions were applied by improved scheme using the analytical kernel renormalization function and its gradient based on the quintic kernel function. The effect of the Rayleigh number and the Darcy number on the heat transfer of Cu–water nanofluid with a various solid volume fraction were studied. Results showed that higher amplitude, height, and the undulation number of the sinusoidal interface between the nanofluid and porous medium layer lead to a decrease in the average Nusselt number.     

Thermal lattice-BGK model based on large-eddy simulation of turbulent natural convection due to internal heat generation

To simulate turbulent convection at high Rayleigh number (Ra), we propose a new thermal lattice-BGK (LBGK) model based on large eddy simulation (LES). Two-dimensional numerical simulations of natural convection with internal heat generation in a square cavity were performed at Ra from 10⁶ to 10¹³ with Prandtl numbers (Pr) at 0.25 and 0.60. Simulation results indicate that our model is fit to simulate high Ra flow for its better numerical stability. At Ra = 10¹³, a global turbulent has occurred. With a further increase in Ra, the flow will arrive in a fully turbulence regime. The Nusselt–Rayleigh relationship is also discussed.     

Numerical simulation of laminar and turbulent buoyancy-driven flows using a lattice Boltzmann based algorithm

The capability of simulating natural and forced convection has been recently developed and integrated into PowerFLOW, a general purpose CFD solver based on the lattice Boltzmann algorithm. Several benchmark tests have been performed to validate this buoyancy model. Two typical cases of Rayleigh-Bénard convection with the Rayleigh number slightly above (Ra=2000) and below (Ra=1500) the critical Rayleigh number of 1708 were tested to verify the conceptual and algorithmic correctness of the buoyancy model. Then simulations of turbulent natural convection in an enclosed tall cavity with two different Rayleigh numbers, Ra=0.86×10⁶ and Ra=1.43×10⁶, were carried out and found to be in a very good agreement with the experiments of Betts and Bokhari.     

Heat transfer enhancement in cubical enclosures with vertical fins

Natural convection of air in a cubical enclosure with a thick partition fitted vertically on the hot wall is numerically investigated for Rayleigh numbers of 10³–10⁶. A three dimensional convective circulation is generated, in which the cold flow sweeps the fin faces and the hot wall, with low flow blockage. The combined contributions of these faces cause heat transfer enhancements over 40% at high Rayleigh numbers and thermal conductivity ratios (R_k). These enhancements significantly exceed the ones obtained with horizontal fins. Even low R_k values cause heat transfer enhancements, except at Ra = 10⁴.     

Conjugate turbulent natural convection in the roof enclosure of a heavy construction building during winter

This paper presents the results of a study of conjugate turbulent natural convection inside a building attic in the shape of a rectangular enclosure bounded by realistic walls made from composite construction materials under winter day boundary conditions. The effects of cavity aspect ratio, Rayleigh number (Ra), depth of the external concrete beam, and external wall construction materials on the flow and heat transfer characteristics were the main focus of the investigation. The Shear stress transport k–ω turbulence model is implemented to calculate air-flow velocities and temperatures in a steady, turbulent, two-dimensional conjugate natural convection heat transfer inside an attic. The governing equations were solved by employing the line-by-line tri-diagonal matrix algorithm (TDMA) control volume method. For Ra ranging from 10⁷ to 10¹⁰, steady-state results of the streamline and temperature contours in addition to local and mean Nusselt numbers at all surfaces of the cavity were obtained. The results show that the values of Ra, attic aspect ratio and the composite wall materials have significant effect on the temperature and stream function contours within the enclosure, and the heat flux out of the room through the enclosure.     

NATURAL CONVECTION OVER A ROTATING CYLINDRICAL HEAT SOURCE IN A RECTANGULAR ENCLOSURE

A numerical study of laminar two-dimensional natural convection heat transfer from a uniformly heated horizontal cylinder rotating about its center, and placed in an isothermal rectangular enclosure, is performed using a spectral element method. The physical aspects of the flow and its thermal behavior are studied for a wide range of pure natural convection to mixed convection at low and high rotational speeds of the cylinder. The computer program has been validated against experimental correlations available on pure natural convection of heated bodies in enclosures. The rotation of the cylinder has been found to enhance the heat transfer. At low ratios of Rayleigh number to the square of the rotational Reynolds number, Ra / Re_ω ², the maximum temperature on the cylinder surface is decreased by as much as 25–35% from similar cases with fixed cylinders. At moderate values of Ra/ Re_ω ², the thermal plume rising above the cylinder is shifted in the rotation direction and the angular shift decreases as Ra / Re_ω increases. The rotation produces more uniform temperature and shear stress distributions around the cylinder surface. At high Rayleigh numbers the increase in rotation reduces the cylinder mean Nusselt number by 2–10% as compared with the fixed cylinder.     

Combined forced and natural convection heat transfer from a horizontal cylinder embedded in a porous medium

This paper reports the results of an experimental study of heat transfer by combined forced and natural convection from a horizontal cylinder embedded in a porous medium composed of randomly packed glass spheres saturated with water. The direction of the flow of water was horizontal and normal to the longitudinal axis of the cylinder. The diameter of the cylinder, D, was 11.45mm and the equivalent diameter of the glass spheres was 3.072mm. It is shown that the condition Gr_k/Re²_D ⩽ 0.5 represents a conservative criterion for segregating heat transfer data that are predominantly governed by forced convection from those in which natural convection effects are significant. A correlation hypothesis for convection heat transfer which is based upon four assumptions, primary among which is that the flow can be (conceptually) regarded as being composed of ‘coarse’ and ‘fine’ components, is presented. This hypothesis is shown to provide a basis for successfully correlating a set of experimental heat transfer data that extends from the Darcy regime into the turbulent regime and spans the intervening Forchheimer and transition regimes. It is suggested that the correlation procedure adopted here may yield useful results if applied to other geometries such as, for example, forced convection heat transfer in ducts packed with porous media.     

Optimum tip gap and orientation of multi-piezofan for heat transfer enhancement of finned heat sink in microelectronic cooling

Piezoelectric fans can be manipulated to generate airflow for cooling microelectronic devices. Their outstanding features include noise-free operation, low power consumption and suitability for confined spaces. This paper presents experimental optimization of tip gap and orientation angle of three piezoelectric fans (multi-piezofan) to maximize the heat removal performance of finned heat sink for microelectronic cooling. Design of experiments (DOE) approach is used for the optimization, and a three dimensional simulation using FLUENT 6.3.2 is carried out to better understand the flow induced by the multi-piezofan and the resulting heat transfer from the heat sink surface. For the optimization, the Central Composite Design (CCD) of response surface methodology (RSM) is exploited from the Design Expert software. In the numerical model, the flow induced by the piezofan is treated as incompressible and turbulent; the turbulence is taken care by the shear stress transport (SST) k–ω model. The experimental results are found to be in good agreement with the predictions. Out of 13 experimental trials determined by CCD, the optimum tip gap and fan orientation are found to be δ = 0.17 and 90° respectively. At this condition, an enhancement in convective heat transfer coefficient exceeding 88% is achieved, compared to natural convection.     

Asymptotic analysis of heat transfer in turbulent Rayleigh–Bénard convection

Based on asymptotic considerations a heat transfer law for turbulent Rayleigh–Bénard convection is found that differs from existing correlations which often are of a power law type with respect to their Rayleigh number dependence. From the asymptotic temperature profile, derived by matching temperature gradients in the overlap region of the wall layer and the core layer, a Nusselt number follows which includes a logarithmic term. This correlation is in good agreement with data from highly accurate Rayleigh–Bénard experiments for Rayleigh numbers between 10⁵ and 10¹⁵ and Prandtl numbers larger than 0.5. It is an alternative to existing power laws or more complicated correlations for Nu = Nu(Ra,Pr).     

Heatline method for the visualization of natural convection in a complicated cavity

In this paper, natural convection inside a two-dimensional cavity with a wavy right vertical wall has been carried out. The bottom wall is heated by a spatially varying temperature and other three walls are kept at constant lower temperature. The integral forms of the governing equations are solved numerically using finite-volume method in non-orthogonal body-fitted coordinate system. SIMPLE algorithm with higher-order upwinding scheme are used. The method of numerical visualization of heat transport for convective heat transfer by heatlines is studied. The heatfunction equation in the transformed plane is solved in terms of dimensionless variables. Results are presented in the form of streamlines, isotherms, heatlines, local and average Nusselt number distribution for a selected range of Rayleigh number (10⁰–10⁶). The results are presented for three different undulations (1–3) with different wave amplitude (0.00–0.10) and a fluid having Prandtl number 0.71.     

Evaluation of Turbulent Models for Natural Convection of Compressible Air in a Tall Cavity

Numerical simulation of turbulent natural convection of compressible air in a tall cavity is carried out. In order to evaluate the accuracy of turbulent models, various turbulent models are applied to solve the natural convection in a tall cavity that has different temperatures imposed on two opposing vertical walls. For the large-eddy simulation (LES) model, Smagorinsky subgrid scale (SGS) and dynamic Smagorinsky SGS are also applied to the same cases in order to investigate the differences in temperature and velocity caused by different turbulent models. It is found that the k–? model has a high accuracy of predicting velocity distribution at various sampled lines by comparing with experimental data at Rayleigh number of 2.03 × 10¹⁰ and 3.37 × 10¹⁰, while the LES model has good performance in predicting temperature distributions.