A numerical study of flow and heat transfer in internally finned rotating straight pipes and stationary curved pipes

In this article the effects of internal fins on laminar incompressible fluid flow and heat transfer inside rotating straight pipes and stationary curved pipes are numerically studied under hydrodynamically and thermally fully developed conditions. The fins are assumed to have negligible thickness with the same conditions as the pipe walls. Two cases, constant wall temperature and constant heat flux at the wall, are considered. First the accuracy of the numerical code written by a finite volume method based on SIMPLE algorithm is verified by the available data for the finless rotating straight pipes and stationary curved pipes, and then, the numerical results for those internally finned pipes are investigated in detail. The numerical results for different sizes and numbers of internal fins indicate that the flow and temperature field analogy between internally finned rotating straight pipes and stationary curved pipes still prevail. The effects of Dean number (K_L) versus friction factor, Nusselt number, and other non-dimensional parameters are studied in detail. From the numerical results obtained, an optimum fin height about 0.8 of pipe radius is determined for Dean numbers less than 100. At this optimum value, the heat transfer enhancement is maximum, and the heat transfer coefficient appears to be 6 times as that of corresponding finless pipes.     

Analogy of forced convective heat transfer between developing laminar flows in curved pipes and orthogonally rotating pipes

Based on a quantitative analogy between developing laminar flows in curved pipes and orthogonally rotating straight pipes, a corresponding analogy of forced convective heat transfer in the entry regions of the pipes is described through similarity arguments and computational studies. Three‐dimensional developments of these flows are characterized by secondary flows due to the centrifugal or the Coriolis forces. Similarity considerations taking the secondary flow into account suggest a remarkable effect of the Prandtl number or the heat transfer structure, which is demonstrated by the computational results. When the curvature parameter of curved pipe flow and the Rossby number of rotating pipe flow are sufficiently large, it is shown that the development of the temperature fields and the Nusselt numbers of the two flows are similar when the governing parameters and the Prandtl numbers of the two flows are equal. © 2000 Scripta Technica, Heat Trans Asian Res, 29(6): 512–522, 2000     

Heat transfer analysis of stratified flow in rotating heat pipes with cylindrical and stepped walls

This paper deals with the flow behavior and the related heat transfer characteristics of stratified flow in axially rotating heat pipes with cylindrical and stepped wall configurations. Flow patterns are presented with existing experimental data of heat transfer in cylindrical and stepped wall rotating heat pipes. Theoretical and semi-empirical models for calculation of the condensation and evaporation heat transfer coefficients are developed. Key dimensionless numbers such as Froude, Galileo, G and ξ-number are identified. Existing experimental data from a rotating cylindrical heat pipe are analyzed and used for regression based on semi-empirical models. Good agreement between the predicted results and experimental data was obtained. Comparison between the present heat transfer models rotating cylindrical wall heat pipes and experimental data from a stepped wall heat pipe shows that the present models can be used to predict the condensation and evaporation heat transfer coefficients in a rotating stepped wall heat pipe.     

Studying the effect of the force convection boundary condition and radius magnetic field on fluid flow and heat transfer between coaxial pipes

An investigation of the heat transfer of Newtonian fluid flow through coaxial two pipes with variable radius ratio has been conducted with the boundary conditions of forced convection on the inner pipe walls and a radius magnetic field. This paper presents an exact analytical solution to the momentum equation and a novel semi-analytic collocation method for solving the full-term energy equation that takes Joule heating into account as well as viscous dissipation. Based on the results of the numerical fourth-order Runge–Kutta method, it was found that increasing the magnetic parameter decreased the amount of friction on the surface of the pipe walls and the rate of heat transfer. As the radius ratio of the two pipes increases, so does the skin friction and heat transfer rate on the internal pipe walls. As Eckert (Ec) and Prandtl (Pr) numbers increase, the mean temperature as well as the dimensionless temperature between the two pipes increases. The increase in Biot number (Bi) has the opposite impact on the mean temperature. As Ec, Pr, and Bi increase, so does the rate of heat transfer on the inner wall of the pipe.     

A Numerical Study of Entropy Generation in the Entrance Region of Curved Pipes

In this study, developing incompressible viscous flow and heat transfer in curved pipes are studied numerically considering a constant heat flux at the wall to analyze the entropy generation. The governing equations including continuity, momentum and energy equations are solved using a second order finite difference method based on the projection algorithm. Entropy generation and thermodynamic optimization are investigated through the entrance region of the curved pipes with circular cross section by a general non-dimensional analysis both numerically and analytically. Optimal Reynolds number calculation based on the entropy generation minimization are carried out for two cases considering the two groups of non-dimensional parameters. The comparison of the numerical results in the entrance region with the analytical ones in the fully developed region indicates that both solutions predict nearly the same optimal Reynolds numbers.     

TRANSIENT TWO-DIMENSIONAL COMPRESSIBLE ANALYSIS FOR HIGH-TEMPERATURE HEAT PIPES WITH PULSED HEAT INPUT

Abstract

A complete mathematical model for transient two-dimensional heat pipes is presented. The numerical results for both simulated compressible vapor flow with high Mach numbers and the vapor flow of a high-temperature heat pipe are compared with the experimental data in the literature. The transient responses of heat pipes to a pulsed heat input are also investigated. It is very important to include the porous wick and the wall in the numerical calculations for the transient analysis of heat pipes and to treat the entire heat pipe as a single system rather than to analyze the vapor flow alone.     

Flow felid and heat transfer enhancement investigations by using a combination of corrugated tubes with a twisted tape within 3D circular tube based on different dimple configurations

Different dimple geometrical configurations with a combination of corrugated tubes and twisted tape are numerically investigated. Water is used as a working fluid for constant heat flux heat transfer conditions at the pipe wall. The dimensionless diameter of the dimples (d/D) used in this study is 0.09, 0.18, 0.27, and 0.36. However, the corrugation configuration diameter is 1 mm. The numerical simulations are carried out at the Reynolds number in the range of 1500–14,000. The outcomes reveal that the friction factor (f) and Nu number are augmented as the dimple diameter increases. The Nu number ratio of 1.25 is found for a dimple pipe tube with a diameter of 4 mm. The numerical outcome presented more mixing, secondary, and vortex produced in the main flow direction and near the pipe wall to the rotating flow induced by twisted tape. Moreover, mixed, secondary vortices and rotational flow originate behind and near the dimple, twisted tape, and corrugation surfaces. These rotational and vortices can promote mixing in flow between the thermal boundary layer and velocity boundary flow layer. So, increase the heat transfer enhancement. The improved pipes with different dimple diameters produce a maximum performance evaluation factor of is more than 1.25.     

A numerical investigation of entropy generation in the entrance region of curved pipes at constant wall temperature

In this study, developing incompressible viscous flow and heat transfer in the curved pipes are studied numerically to analyze the entropy generation and thermodynamic optimization in the entrance region at a constant wall temperature. The governing equations including continuity, momentum and energy equations are solved using a second order finite difference method based on the projection algorithm. Entropy generation and optimal Reynolds number calculation based on the entropy generation minimization are carried out for two cases considering the two groups of non-dimensional parameters both numerically and analytically. The comparison of the numerical results in the entrance region with the analytical ones in the fully developed region indicates that both solutions predict nearly the same optimal Reynolds numbers, specially, for the first group of the non-dimensional parameters.     

Numerical investigation on the mixing performance of H2 and air in curved micro-channel combustors

Curved micro-channels are frequently used in micro-Swiss roll combustors and other applications. The secondary flows (i.e., Dean vortices) play an important role in both the mixing performance of fuel and oxidant and the flame propagation characteristics in curved micro-channel combustors. In the present study, the helicity method was adopted and a mixing performance evaluation criterion (MPEC) was proposed to investigate the impacts of inlet velocity, nominal equivalence ratio (φ) and curvature radius on the Dean vortices and mixing performance of H₂ and air in curved micro-channels. First, it is found that with the increase of inlet velocity, the intensity of Dean vortices increases and their shape grow asymmetrical. When the inlet velocity is high enough, another pair of smaller vortices appear near the outer wall. Meanwhile, the mixing performance of H₂ and air becomes worse due to the reduced residence time of gas flow. Second, as the nominal equivalence ratio is decreased, the Dean vortices are intensified and the vortices shape become asymmetrical. Moreover, the mixing process is improved owing to the enhanced secondary flows. Thirdly, the intensity of Dean vortices increases significantly as the curvature radius is decreased. However, the mixing performance becomes worse due to the shortened length of the curved micro-channel. Finally, an empirical correlation between MPEC and the Reynolds number (Re), Dean number (De) and φ was obtained based on the numerical results, which may provide a guidance for the design and operation of curved micro-channel combustors.     

Heat Transfer Performance of Heat Pipe Radiator with SiO2/Water Nanofluids

The effect of nanofluids on thermal performance of the miniature heat pipe radiator which was assembled by two heat pipes containing 0.6 vol.% SiO₂/water nanofluids and 30 pieces of rectangular aluminum fins was investigated experimentally and theoretically. The wall temperatures of the miniature heat pipe and fin surface temperatures were measured. Results showed that the utilization of SiO₂/water nanofluids as a working fluid in the heat pipe enhanced the heat performance by reducing wall temperature differences. Compared with Deionized water (DI water), the thermal resistance of the miniature heat pipe with SiO₂/water nanofluids decreased by about 23% to 40%. Furthermore, the theoretical calculation on a basis of one dimension found that the fin heat dissipation in the miniature heat pipe radiator charged SiO₂/water nanofluids was about 1.17 times of that of the DI water radiator.     

Numerical study on the effect of jet spacing on the Swirl flow and heat transfer in the turbine airfoil leading edge region

ABSTRACT

In this paper, flow and heat transfer of a swirl chamber that models an internal cooling passage for a gas turbine airfoil leading edge is studied with numerical simulation. The geometry consists of a circular pipe, and rectangular section inlets that lead inlet flow to impinge tangentially on the circular pipe. The effects of the ratio of jet spacing to swirl chamber radius and Reynolds numbers on swirl cooling performance are investigated. The results indicate how the pressure loss and globally averaged Nusselt number on the swirl chamber wall increase with increases of Reynolds number and the ratio of jet spacing to swirl chamber radius. A Nusselt number correlation on these parameters is suggested. Also shown is how Nusselt numbers on the swirl chamber surface increase with the ratio of jet spacing to swirl chamber radius.     

Pressure of Newtonian fluid flow through curved pipes and elbows

Under conditions of high temperature and high pressure, the non-uniformity of pressure loads has intensified the stress concentration which impacts the safety of curved pipes and elbows. This paper focuses on the pressure distribution and flow characteristic in a curved 90 o bend pipe with circular cross-sections, which are widely used in industrial applications. These flow and pressure characteristics in curved bend pipes have been researched by employing numerical simulation and theoretical analysis. Based on the dimensionless analysis method a formula for the pressure of Newtonian fluid flow through the elbow pipes is deduced. Also the pressure distributions of several elbows with different curvature ratio R/D are obtained by numerical methods. The influence of these non-dimensional parameters such as non-dimensional curvature ratio, Reynolds number and non-dimensional axial angle α and circumferential angle β on the pressure distribution in elbow pipes is discussed in detail. A number of important results have been achieved. This paper provides theoretical and numerical methods to understand the mechanical property of fluid flow in elbow pipes, to analyze the stress and to design the wall thickness of elbow pipes.     

A Review of Heat Transfer and Pressure Drop Correlations for Laminar Flow in Curved Circular Ducts

Heat transfer and pressure drop correlations for fully developed laminar Newtonian fluid flow in curved and coiled circular tubes are reviewed. Curved geometry is one of the passive heat transfer enhancement methods that fits several heat transfer applications, such as power production, chemical and food industries, electronics, environment engineering, and so on. Centrifugal force generates a pair or two pairs of cross-sectional secondary flow (based on the Dean number), which are known as the Dean vortices, and improves the overall heat transfer performance with an amplified peripheral Nusselt number variation. The main purpose of this review paper is to provide researchers with a comprehensive list of correlations and concepts that they may need during their research. The paper begins with an introduction to the governing equations and important dimensionless numbers for the flow in curved tubes. The correlations for developing flow in curved and coiled circular tubes are also presented. The main contribution of this study is reviewing the numerical and experimental correlations to calculate friction factor and Nusselt number in curved circular tubes. Nusselt number correlations are categorized based on the thermal boundary condition, as well as on the method. A Dean number range of 1 to 20,000 for the pressure drop correlations and 1 to 7000 for the heat transfer correlations and a Prandtl number range of 0.1 to 7,000 are covered with the reviewed correlations.     

Entry flow in heated curved pipes

The flow in the entrance region of heated curved pipes is analysed. Two cases of heating—a constant temperature at the wall, and a constant flux of heat at the wall—are considered. Using boundary layer approximations and the method of matched asymptotic expansions, the combined effects of curvature, entrance region and the buoyancy is studied. It is found that buoyancy disturbs the symmetric secondary motion induced by curvature, the deviation depending on the type of thermal input at the wall. It is also found that the oscillatory nature of the Nusselt number in the constant temperature case decreases as the Peclet number is increased.     

Conjugate natural convection around a finned pipe in a square enclosure with internal heat generation

This work is focused on the numerical study of steady, laminar, conjugate natural convection around a finned pipe placed in the center of a square enclosure with uniform internal heat generation. Four perpendicular thin fins of arbitrary and equal dimensions are attached to the pipe whose internal surface is isothermally cooled. The sides of the enclosure are considered to have finite and equal thicknesses and their external sides are isothermally heated. The problem is put into dimensionless formulation and solved numerically by means of the finite-volume method. Representative results illustrating the effects of the finned pipe inclination angle and fins length on the streamlines and temperature contours within the enclosure are reported. In addition, results for the local and average Nusselt numbers are presented and discussed for various parametric conditions.     

Prediction of the temperature field in flat plate heat pipes with micro-grooves – Experimental validation

A liquid and vapour flow model coupled to a thermal model is presented for a flat plate heat pipe with micro-grooves. This model allows the calculation of the liquid and vapour pressures and velocities, the meniscus curvature radius in the grooves and the temperature field in the heat pipe wall from the heat source to the heat sink. The meniscus curvature radius is introduced in the thermal model to take into account the heat transfer at the liquid–vapour interface. Experimental measurements of the meniscus curvature radius as well as temperature measurements along a grooved heat pipe are compared to the model results. Both comparisons show the good ability of the numerical model to predict the maximum heat transport capability and the temperature field in the heat pipe. The model is used to optimize the heat pipe dimensions in order to improve its thermal performances.     

Numerical simulation of hydrothermal behavior in a concentric curved annular tube

This study performs a numerical investigation of the steady‐state fully developed laminar flow and forced convection heat transfer characteristics in a concentric curved annular tube with two different curvature angles, a 90°‐bend annular tube and a U‐bend annular tube. A wide range of aspect ratios (r* = 0.1, 0.25, 0.5, and 0.75) and three curvature ratios (δ_c = 0.1, 0.2, and 0.5) were adopted in this study. The governing equations consisting of continuity, momentum, and energy equations are solved by considering the outer wall to be insulated (adiabatic), and a constant temperature is applied at the inner wall by using the finite‐volume method (FVM) to investigate the hydrothermal performance for these two different bend angles.Features of axial velocity contours, temperature patterns, and secondary flow streamlines at different cross‐sectional locations along the angular coordinate of curved annulus are observed with a Dean number range of (De = 32‐632). Additionally, the circumferential friction factor and averaged Nusselt number are obtained along the concentric curved annulus flow direction. The numerical results indicate that the normalized average Nusselt number and Performance Evaluation Criteria (PEC) increase with increasing De and curvature ratio for both curvature angles of concentric curved annular tube. Moreover, the normalized average Nusselt number, normalized friction factor‐Reynolds number product, and PEC increase with decreasing the aspect ratio because the annular gap between the surfaces of the inner and outer tubes (the boundaries of annulus) increases with decreasing aspect ratio. The hydrothermal performance of the concentric curved annular tube is higher than that of the straight annular tube attributed to the formation of secondary flows (Dean's vortices) in a cross‐sectional direction and the impact of the inner tube wall boundary. The value of PEC for both curvature angles of the curved annular tube at aspect ratio = 0.1 and De = 632 is approximately two‐fold of the straight annular tube under the same conditions while at aspect ratio = 0.75, it increases by nearly 80%.     

The correlation between the number of fins and the discharge time for a finned heat pipe latent heat storage system

The concept of a solar energy heat pipe latent heat storage system is presented. In order to assure large charging and discharging rates, finned heat pipes are used to transfer heat to and from the phase-change material (paraffin in this case). The evolution of the solid - liquid interface is studied by considering the radial heat transfer (due to the heat pipe wall) and the angular one (due to the fin). Two mathematical models, corresponding to exponential, respectively polynomial functions describing the fin temperature profile are presented and the results are compared. The two models allow the evaluation of the discharge time of the storage unit for a certain number of fins for a single heat pipe. When the discharge time has a fixed value, the methods presented in the paper allow to conclude whether the number of fins is sufficiently large to assure the complete solidification of the phase-change material.     

Direct numerical simulation of fluid flow and heat transfer in periodic wavy channels with rectangular cross-sections

Fully-developed flow and heat transfer in periodic wavy channels with rectangular cross sections are studied using direct numerical simulation, for increasing Reynolds numbers spanning from the steady laminar to transitional flow regimes. The results show that steady flow is characterized by the formation of symmetric secondary flow or Dean vortices when liquid flows past the bends. It is found that the patterns of Dean vortices may evolve along the flow direction, thus leading to chaotic advection, which can greatly enhance the convective fluid mixing and heat transfer. With increasing Reynolds numbers, the flow undergoes transition from a steady state to a periodic one with a single frequency, and subsequently to a quasiperiodic flow with two incommensurate fundamental frequencies. Within these unsteady regimes, the flow is characterized by very complex Dean vortices patterns which evolve temporally and spatially along the flow direction, and the flow symmetry may even be lost. Further increase in Reynolds number leads to chaotic flow, where the Fourier spectrum of the velocity evolution becomes broadband. The bifurcation scenario in wavy channels may thus share some common features with the well-known Ruelle–Takens–Newhouse scenario. Heat transfer simulation in all flow regimes is carried out with constant wall temperature condition and liquid water as the coolant. It is found that due to the efficient mixing in wavy channels, the heat transfer performance is always significantly more superior to that of straight channels with the same cross sections; at the same time the pressure drop penalty of wavy channels can be much smaller than the heat transfer enhancement. The present study shows that these wavy channels may have advantages over straight channels and thus serve as promising candidates for incorporation into efficient heat transfer devices.