Groove geometry effects on turbulent heat transfer and fluid flow

The present work represents a two-dimensional numerical prediction of forced turbulent flow heat transfer through a grooved tube. Four geometric groove shapes (circular, rectangular, trapezoidal and triangular) were selected to perform the study, as well as two aspect ratios of groove-depth to tube diameter (e/D = 0.1 and 0.2). The study focuses on the influence of the geometrical shapes of grooves and groove-depth on heat transfer and fluid flow characteristics for Reynolds number ranging from 10,000 to 20,000. The characteristics of Nusselt number, friction factor and entropy generation are studied numerically by the aid of the computational fluid dynamics (CFD) commercial code of FLUENT. It is observed that the best performance occurs with the lower depth-groove ratio, whereas it is found that the grooved tube provides a considerable increase in heat transfer at about 64.4 % over the smooth tube and a maximum gain of 1.52 on thermal performance factor is obtained for the triangular groove with (e/D = 0.1).     

Numerical investigation of flow and combined natural-forced convection from an isothermal square cylinder in cross flow

Unsteady flow and heat transfer from a horizontal isothermal square cylinder is studied numerically using a three-dimensional computational model to investigate the influence of buoyancy on the forced flow and heat transfer characteristics. The numerical model is based on a horizontal square cylinder subjected to laminar fluid flow in an unconfined channel. The governing equations in 3D form are solved using a fractional step method based on the finite difference discretization in addition to a Crank–Nicholson scheme employed to the convective and the viscous terms. Two working fluids–air (Pr = 0.7) and water (Pr = 7)–are considered, and the flow and heat transfer simulations were carried out for the Reynolds and Richardson numbers in the intervals 55 ≤ Re ≤ 250 and 0 ≤ Ri ≤ 2, respectively. The flow characteristics such as time-averaged drag/lift, rms drag/rms lift coefficients as well as Strouhal number were computed. The heat transfer from the cylinder is assessed by mean Nusselt number (and rms Nusselt number) over the total heated cylinder walls. As the buoyancy increases, the mass and the velocity of the fluid flowing underneath the cylinder increases. The fluid is injected into the near wake region with an upward motion which significantly alters the flow field in the downstream as well as upstream regions. The effects of Reynolds, Richardson and Prandtl numbers on the flow field and temperature distributions are discussed in detail. It is shown that the flow and heat transfer characteristics are influenced more for air than water. To fill the void in the literature, useful empirical correlations of practical importance are derived for pure forced and pure natural as well as mixed convection. The mixed convection correlations, in terms of the ratio of pure forced convection, are also developed, and their implications are discussed.     

Steady flow of a power-law non-Newtonian fluid across an unconfined square cylinder

A two-dimensional flow of a non-Newtonian power-law fluid directed normally to a horizontal cylinder with a square cross section is considered in the present paper. The problem is investigated numerically with a finite volume method by using the commercial code Ansys Fluent with a very large computational domain so that the flow could be considered unbounded. The investigation covers the power-law index from 0.1 to 2.0 and the Reynolds number range from 0.001 to 45.000. It is found that the drag coefficient for low Reynolds numbers and low power-law index (n ≤ 0.5) obeys the relationship C_D = A/Re. An equation for the quantity A as a function of the power-law index is derived. The drag coefficient becomes almost independent of the power-law index at high Reynolds numbers and the wake length changes nonlinearly with the Reynolds number and power-law index.     

DNS of turbulent heat transfer in a channel flow with a high spatial resolution

Direct numerical simulations of turbulent heat transfer in a channel flow are performed to investigate the effects of Reynolds and Prandtl numbers on higher-order turbulence statistics such as a turbulent Prandtl number and the budget for the dissipation rate of the temperature variance. The Reynolds numbers based on the friction velocity and the channel half width are 180 and 395, and the molecular Prandtl numbers Pr’s 0.71–10.0. Careful attention is paid to ensure accuracy of the higher-order statistics through the use of a high spatial resolution comparable to Batchelor length scale. The wall-asymptotic value of the turbulent Prandtl number is mostly independent of Reynolds number for the current range of Pr’s. The budget for the dissipation rate of the temperature variance has been computed, and the negligible effect of a Reynolds number on the sum of all source and sink terms in near-wall region in the current computational range is found. This result is quite similar to the one in the budget for the dissipation rate of turbulent energy. In addition, a priori test for existing models is also performed to assess the Pr dependence on the individual terms and their summations in the budget.     

Experimental study of pre-swirl flow effect on the heat transfer process in the entry region of a convergent pipe

Experiments have been performed to study the heat transfer process of swirling flow issued into a heated convergent pipe with a convergent angle of 5° with respect to the pipe axis. A flat vane swirler situated at the entrance of the pipe is used to generate the swirling flow. During the experiments, the Reynolds number ranges from 7970 to 47,820, and the swirl number from 0 to 1.2. It is found that the convergence of the pipe can accelerate the flow which has an effect to suppress the turbulence generated in the flow and reduce the heat transfer. However, in the region of weak swirl (S = 0-0.65), the Nusselt numbers increase with increasing swirl numbers until S = 0.65, where turbulence intensity is expected to be large enough and not suppressible. In the region of strong swirl (S > 0.65), where recirculation flow is expected to be generated in the core of the swirling flow, the heat transfer characteristic can be altered significantly. At very high swirl (S ? 1.0), the accelerated flow in the circumferential direction is expected to be dominant, which leads to suppress the turbulence and reduce the heat transfer. The Nusselt number is found proportional to the swirl number. Correlations of the Nusselt numbers in terms of the swirl number, the Reynolds number and the dimensionless distance are attempted and are very successful in both the weak and the strong swirl regions.     

Confined impinging twin air jets at high Reynolds numbers

An experimental study is carried out to investigate flow characteristics of confined twin jets issuing from the lower surface and impinging normally on the upper surface. Pressure distributions on the impingement and confinement plates were obtained for Reynolds numbers ranging from 30,000 to 50,000, nozzle-to-plate spacing (H/D) in the range of 0.5-4 and jet-to-jet spacing (L/D) in the range of 0.5-2. Smoke-wire technique was used to visualize the flow behavior. The effects of Reynolds number, nozzle-to-plate spacing and jet-to-jet spacing on the flow structure are examined. The subatmospheric regions occur on both impingement and confinement plates at the nozzle-to-plate spacing up to 1 for all studied Reynolds numbers and jet-to-jet spacings in consideration. They lie nearly up to the same radial location at both surfaces and move radially outward from the stagnation points with increasing nozzle-to-plate spacing and jet-to-jet spacing. It is concluded that there exists a relation between the subatmospheric regions and peaks in heat transfer coefficients for low spacings in the impinging jets.     

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

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

Reynolds Number Effects on Statistics and Structure of an Isothermal Reacting Turbulent Wall-Jet

Three-dimensional direct numerical simulation (DNS) is used to investigate the effects of changing the Reynolds number on dynamics of a reacting turbulent wall-jet. The flow is compressible and a single-step isothermal global reaction is considered. At the inlet, fuel and oxidizer enter the domain separately in a non-premixed manner. In this study, the bulk Reynolds number of the flow, in terms of the inlet quantities, varies from Re = 2000 to Re = 6000, which results in a comparable change in friction Reynolds numbers. The DNS database in Pouransari et al. (Phys. Fluids 23(085104), 2011) is used for the lower Reynolds number case and for the higher Reynolds number case, a new DNS is performed. One of the main objectives of this study is to compare the influences of changing the Reynolds number of the isothermal flow with the heat-release effects caused by the chemical reaction, that we studied earlier in Pouransari et al. (Int. J. Heat Fluid Flows 40, 65–80, 2013). While, both turbulent and flame structures become finer at the higher Reynolds number, the effect of decreasing the Reynolds number and adding the combustion heat release are compared with each other and found to be similar for some aspects of the flow, but are not always the same.     

Statistical analysis of instantaneous turbulent heat transfer in circular pipe flows

Turbulent heat transfer in circular pipe flow with constant heat flux on the wall is investigated numerically via Large Eddy Simulations for frictional Reynolds number Re _τ  = 180 and for Prandtl numbers in the range 0.1 ≤ Pr ≤ 1.0. In our simulations we employ a second-order finite difference scheme, combined with a projection method for the pressure, on a collocated grid in cylindrical coordinates. The predicted statistical properties of the velocity and temperature fields show good agreement with available data from direct numerical simulations. Further, we study the local thermal flow structures for different Prandtl numbers. As expected, our simulations predict that by reducing the Prandtl number, the range of variations in the local heat transfer and the Nusselt number decrease. Moreover, the thermal flow structures smear in the flow and become larger in size with less sharpness, especially in the vicinity of the wall. In order to characterize the local instantaneous heat transfer, probability density functions (PDFs) for the instantaneous Nusselt number are derived for different Prandtl number. Also, it is shown that these PDFs are actually scaled by the square root of the Prandtl number, so that a single PDF can be employed for all Prandtl numbers. The curve fits of the PDFs are presented in two forms of log-normal and skewed Gaussian distributions.     

Explosive boiling of water in parallel micro-channels

The objective of this study is to visualize the flow pattern and to measure heat transfer coefficient during explosive boiling of water in parallel triangular micro-channels. Tests were performed in the range of inlet Reynolds number 25–60, mass flux 95–340 kg/m²s, and heat flux 80–330 kW/m².The flow visualization showed that the behavior of long vapor bubbles, occurring in a micro-channel at low Reynolds numbers, was not similar to annular flow with interposed intermitted slugs of liquid between two long vapor trains. This process may be regarded as explosive boiling with periodic wetting and dryout.In the presence of two-phase liquid–vapor flow in the micro-channel, there are pressure drop oscillations, which increase with increasing vapor quality.This study shows strong dependence of the heat transfer coefficient on the vapor quality. The time when liquid wets the heated surface decreases with increasing heat flux. Dryout occurs immediately after venting of the elongated bubble.     

Laboratory investigation and commercial test for rotors-assembled strand applied in smooth tube

In the commercial test for smooth tube inserted with rotors-assembled strand comparing with non-inserted ones on condensers in electric power plant, using water as working fluid, the single-phase pressure drop and heat transfer were measured. It was found difficult to receive reliable and accurate enough data through commercial test. Meanwhile, the single-phase pressure drop and heat transfer in a rotors-assembled strand inserted tube were measured in laboratory, with the tube side Prandtl numbers varying from 5.67 to 5.80 and the tube side Reynolds numbers varying from 21,300 to 72,200. Before that, a validation experiment based on the same smooth tube was carried out to testify the experimental system and the data reduction method, in which fixed mounts were employed to eliminate entrance effects. The Prandtl numbers varied from 5.64 to 5.76 and the Reynolds numbers varied from 19,000 to 56,000 in the tube. The annular side Reynolds numbers remained nearly constant at the value of around 50,000 for all experiments, with the annular side Prandtl numbers varying from 8.02 to 8.22. The experimental results of smooth tube show that employment of fixed mounts leads to a visible bias of friction factor at relative low Reynolds numbers while it hardly affects the Nusselt numbers. On the other hand, experiment for the tube inserted with rotors-assembled strand show remarkable improvement for heat transfer with the Nusselt number increased by 9.764–11.87% and the overall heat transfer coefficient increased by 7.08–7.49% within the range of Reynolds number from about 21,300 to 55,500. Meanwhile, friction factor increases inevitably by 278.1–353.9% within the same range of Reynolds number. Based on through multivariant linear normal regression method, the Reynolds number and Prandtl number dependencies of the Nusselt number and friction factor were determined to be Nu = 0.0031Re^0.9Pr^1.0849 and f = 0.993Re^−0.22.     

Flow structure and heat transfer characteristics of an unconfined impinging air jet at high jet Reynolds numbers

The flow and heat transfer characteristics of an unconfined air jet that is impinged normally onto a heated flat plate have been experimentally investigated for high Reynolds numbers ranging from 30,000 to 70,000 and a nozzle-to-plate spacing range of 1–10. The mean and turbulence velocities by using hot-wire anemometry and impingement surface pressures with pressure transducer are measured. Surface temperature measurements are made by means of an infrared thermal imaging technique. The effects of Reynolds number and nozzle-to-plate spacing on the flow structure and heat transfer characteristics are described and compared with similar experiments. It was seen that the locations of the second peaks in Nusselt number distributions slightly vary with Reynolds number and nozzle-to-plate spacing. The peaks in distributions of Nusselt numbers and radial turbulence intensity are compatible for spacings up to 3. The stagnation Nusselt number was correlated for the jet Reynolds number and the nozzle-to-plate spacing as Nu _st∝Re ^0.69(H/D)^0.019.     

Wall modeling for implicit large-eddy simulation and immersed-interface methods

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re _τ  = 395 up to Re _τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re _h = 5,000 and the periodic hill at Re _H = 10,595 and Re _H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.     

Convection heat transfer of closely-spaced spheres with surface blowing

A validated computer simulation model has been developed for the analysis of colinear spheres in a heated gas stream. Using the Galerkin finite element method, the steady-state Navier-Stokes and heat transfer equations have been solved describing laminar axisymmetric thermal flow past closely-spaced monodisperse spheres with fluid injection. Of interest are the coupled nonlinear interaction effects on the temperature fields and ultimately on the Nusselt number of each sphere for different free stream Reynolds numbers (20 ≤Re ≤ 200) and intersphere distances (1.5 ≤d _ij ≤ 6.0) in the presence of surface blowing (0 ≤v _b < 0.1). Fluid injection (i.e. blowing) and associated wake effects generate lower average heat transfer coefficients for each interacting sphere when the Reynolds number increases (Re>100). Heat transfer is also reduced at small spacings especially for the second and third sphere. A Nusselt number correlation for each interacting (porous) sphere has been developed based on computer experiments.     

3D Numerical study of the effect of aspect ratio on mixed convection air flow in upward solar air heater

A 3D Numerical study of mixed convection air flow in upward solar air heater with large spanwise aspect ratio (A = 10 to 40) was performed using CFD commercial code Fluent 14.5 (ANSYS). The main objective of this study is to investigate the channel height's effect (aspect ratio) on flow pattern and heat transfer in upward solar air heater in the particular case of low Re and high aspect ratio. The bottom plate (absorber) was submitted to Constant Heat Flux (CHF) in the range of 200 to 1000 W/m² and Reynolds number was varied from 50 to 1000. Our results are in concordance with most of authors conclusions about Poiseuille–Rayleigh–Benard flows. In mixed convection, increasing heat flux enhances heat transfer unlike forced convection flows. Simulation results of flow visualizations and Nusselt number calculations have shown that depending on Ri*, the velocity and temperature distributions in SAH vary greatly with the channel's height. The obtained results were different from previous studies. Indeed, our investigation of channel's height was achieved for the same heat flux but different Grashof numbers. For low channel's heights (high aspect ratio), increasing heat flux has not a significant effect but for higher channel's heights, an augmentation of heat flux enhances buoyancy effects in the flow and causes high turbulence. Also, increasing Reynolds number in low channel's heights (high A), can enhance substantially heat transfer. For higher channel's heights (low A), increasing Reynolds number decreases Ri* and thus buoyancy forces. Heat transfer is reduced and so Nusselt number. The obtained results may be very useful for engineers in designing and testing solar collectors.     

Enhanced heat transfer performances of molten salt mixed convection in a vertical annular duct

The mixed convection heat transfer of upward molten salt flow in a vertical annular duct is experimentally and numerically studied. The heat transfer performances of mixed convection are measured under Reynolds number 2,500–12,000 and inlet temperature 300–400 °C, and Nusselt number of molten salt flow with cooled inner wall monotonically increases with buoyancy number. The mixed convection is further simulated by low-Reynolds number k-ε model and variable properties, and the heat transfer tendency from numerical results agrees with that from experiments. At low Reynolds number, the natural convection plays more important role in the mixed convection. As the buoyancy number rises, the thickness of flow boundary layer near the inner wall increases, while the effective thermal conductivity remarkably rises, so the enhanced heat transfer of mixed convection is mainly affected by the effective thermal conductivity due to turbulent diffusion.     

Effect of particles on turbulent thermal field of channel flow with different Prandtl numbers

The direct numerical simulation(DNS) of heat transfer in a fully developed non-isothermal particle-laden turbulent channel flow is performed.The focus of this paper is on the modulation of the particles on turbulent thermal statistics in the particle-laden flow with three Prandtl numbers(P r = 0.71,1.5,and 3.0) and a shear Reynolds number(Reτ = 180).Some typical thermal statistics,including normalized mean temperature and their fluctuations,turbulent heat fluxes,Nusselt number and so on,are analyzed.The results show that the particles have less effects on turbulent thermal fields with the increase of Prandtl number.Two reasons can explain this.First,the correlation between fluid thermal field and velocity field decreases as the Prandtl number increases,and the modulation of turbulent velocity field induced by the particles has less influence on the turbulent thermal field.Second,the heat exchange between turbulence and particles decreases for the particle-laden flow with the larger Prandtl number,and the thermal feedback of the particles to turbulence becomes weak.     

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.     

Numerical simulation of fluid flow and heat transfer characteristics in channel with V corrugated plates

A detailed numerical study is carried out to investigate fluid flow and heat transfer characteristics in a channel with heated V corrugated upper and lower plates. The parameters studied include the Reynolds number (Re = 2,000–5,500), angles of V corrugated plates (θ = 20°, 40°, 60°), and constant heat fluxs (q″ = 580, 830, 1,090 W/m²). Numerical results have been validated using the experimented data reported by Naphon, and a good agreement has been found. The angles of V corrugated plates (θ) and the Reynolds number are demonstrated to significantly affect the fluid flow and the heat transfer rate. Increasing the angles of V corrugated plates can make the heat transfer performance become better. The increasing Reynolds number leads to a more complex fluid flow and heat transfer rate. The numerical calculations with a non-equilibrium wall function have a better accuracy than with a standard wall function for solving high Reynolds numbers or complex flow problems.     

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.