Numerical Prediction of Fluid Flow and Heat Transfer in a Wavy Pipe

IntroductionA pipe with periodically converging-divergingcross-section is one Of the sevens devices employed forenhancing the heat and mass tusfer efficiency. Thenuid flow, to the now passages with a periodicallyvaling cross-section, attains a folly develOPed acmethat differs fundamentally from that for a convelltionalconstant-area flow channel. In the periodically vwigcross-seCtions, the ac developed VelM field repeatsitSelf at cormsponding edal locations in successivecycles. The change of…     

Turbulent transport in the transition flow region

The present author's model of turbulent viscosity published in Int. J. Heat Mass Transfer26, pp. 479–508, 1983 was applied to analyse the conditions in the transition region between laminar and developed turbulent pipe flow, making use of the Rothfus' experimental data from Chem. Eng. Prog.4, pp. 533–538, 1953. Theoretical value of the critical Reynolds number Re_crit = 2295.18 for transition from laminar to turbulent pipe flow was determined from the limit values of turbulent transport characteristics.     

Technical Note Flow characteristics in a heated rotating straight pipe

The flow in a rotating or in a heated straight pipe has been extensively studied not only for academic interest, but also for the great importance in mechanical applications such as in pipe heat exchangers, in cooling systems of rotor blades in gas turbines and in chemical mixing. The viscous flow in a straight pipe rotating about an axis perpendicular to its own, has as a result the generation of a secondary flow that is sustained by the Coriolis force introduced by the rotation of the pipe. Barua [1]used a regular perturbation about the Poiseuille flow limit, similar to Deans 2 and 3approach for stationary and curved pipe flow. He showed that rotation generates a secondary flow and that it depends on the non-dimensional parameter R_r = (2Ωα²?ν), where Ω is the angular frequency of rotation, α is the radius of the pipe and ν is the kinematic viscosity. Subsequent boundary-layer analysis also predicted a significant increase in the friction factor with rotational speed for small rotational rates and high axial pressure gradients (Mori and Nakayama [4], Ito and Nanbu [5]), the latter group also obtaining satisfactory agreement with their experimental results. Mansour [6]considered higher rotational velocities using a computer extension for the perturbation expansion, similar to a method that was applied by Van Dyke 7, 8 and 9who studied the flow in a stationary straight pipe. According to this method the equations of motion are modified, so that they are depend on a single parameter K = R_eR_r, under the assumption that R_e → ∞, R_r → 0, where R_e is the Reynolds number based on the axial velocity. Benton [10]considered small rotational velocities and constructed a small perturbation expansion about the Hagen–Poisseuille flow. Later, Benton and Boyer [11]assumed the case of a rapid rotating conduit with R_rR_e ≤ 1. Duck [12]used a numerical procedure, based on a combination of Fourier decomposition and finite difference discretization to study the flow structure in rotating circular ducts.The first experiments concerning a rotating pipe were conducted by Trefethen [13]who observed that rotation transfers the onset of turbulence to higher Reynolds numbers. Later, Euteneuer and Piesche [14]in their experimental studies in circular pipes confirmed that the pressure drop is significantly higher than that for straight pipes, in agreement with the theoretical results.The earliest analysis on the flow in a heated straight pipe was considered by Morton [15]. His study was restricted to small rates of heating and he obtained solutions for the axial velocity and temperature as power series depending on the parameters R_eR_a, where R_a is the Rayleigh number based on the temperature gradient along the pipe wall. Mori and Nakayama [16]assumed velocity and temperature boundary layers along the pipe wall and analysed theoretically the flow field and the temperature field. Van Dyke [17]modified Mortons variable in order to clarify the dependence of the problem on the parameters P_r, R_a and R_e, where P_r is the Prandtl number. The advantage of these simplifications was that the flow depended only on two parameters ε = P_rR_aR_e and P_r, respectively. Guiasu et al. [18]were able to compute many terms of the series on Mortons problem using symbolic computation packages.In the present work we study the fully developed steady flow in a straight rotating heated pipe with circular cross-section. The equations of motion and energy depend on three parameters that characterize the flow, the rotational Reynolds number R_r, the Reynolds number based on the axial flow R_e and the Rayleigh number R_a, and they are solved both analytically and numerically. In the analytical solution the functions of the flow are expanded in power series of the parameters R_r and R_a. Because of the difficulties of the problem introduced by the presence of these three parameters, we were able to compute only ten terms in each series, so that the range of values of the parameters for which the analytical solution converges is limited by the products R_eR_a < 1000 and R_eR_r < 250. However the analytic expression is of some value because it provides us with a mathematical expression showing the trend of the flow characteristics as well as with a benchmark for the numerical solution. In the numerical solution we consider a grid of mesh points in the circular domain and we modify the differential equations by approximating all partial derivatives with central differences. In this way we deduce an algebraic system of equations for all the points of the circular region that is solved using an iterative procedure. The limits of the products R_eR_a and R_eR_r for which the numerical solution is valid are R_eR_a < 20 000 and R_eR_r < 5000. We compared the results obtained by the two methods and finally we examined the influence of Coriolis and buoyancy forces on the flow and the dependence of some properties of the flow, as the axial and azimuthal stresses, the Nusselt number, on the previous products.     

Variation of Nusselt number with flow regimes behind a circular cylinder for Reynolds numbers from 70 to 30 000

The dependence of the Nusselt number in the separated flow behind a circular cylinder to the cross-flow varies greatly with Reynolds number according to the flow regimes, i.e., laminar shedding, wake transition, and shear-layer transition regimes. The Nusselt number at the rear stagnation point, Nu_r/Re^0.5, increases with Reynolds number in the laminar shedding regime (Re < 150) and the shear-layer transition regime (3000 < Re < 15 000), corresponding to the shortening of the vortex formation region. On the contrary, the Nusselt number, Nu_r/Re^0.5, decreases with Reynolds number in the regime in which the wake develops to a complex three-dimensional flow (300 < Re < 1500), corresponding to the lengthening of the vortex formation region. This distinctive change affects the correlation of the overall Nusselt number with Reynolds number, i.e., the exponent of the Reynolds number has a lower value for 200 < Re < 2000 than that for 70 < Re < 200 and Re > 2000.     

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.     

Experimental study on heat transfer augmentation in a double pipe heat exchanger utilizing jet vortex flow

This paper examines experimentally the effect of jet vortex technology on enhancing the heat transfer rate within a double pipe heat exchanger by supplying the heat exchanger with water at different vortex strengths. A vortex generator with special inclined holes with different inlet angles was designed, manufactured, and integrated within the heat exchanger. In this study, four levels of Reynolds number for hot water in the annulus (Re_h) were used, namely, 10,000; 14,500; 18,030; and 19,600. Similarly, four levels of Reynolds number for cold water in the inner tube (Re_c) were used, namely, 12,000; 17,500; 22,500; and 29,000. As for the inlet flow angle (θ), four different levels were selected, namely, 0°, 30°, 45°, and 60°. The temperature along the heat exchanger was measured utilizing 34 thermocouples installed along the heat exchanger. It was found that increasing the inlet flow angle (θ) and/or the Reynolds number results in an increase in the local Nusselt number, the overall heat transfer coefficient, and the ratio of friction factor. It is revealed that the percentage increase in the average Nusselt number due to swirl flow compared to axial flow was 10%, 40%, and 82% for an inlet flow angle of 30°, 45°, and 60°, respectively.     

Numerical investigation of effective parameters in convective heat transfer of nanofluids flowing under a laminar flow regime

This article presents a numerical investigation on heat transfer performance and pressure drop of nanofluids flows through a straight circular pipe in a laminar flow regime and constant heat flux boundary condition. Al₂O₃, CuO, carbon nanotube (CNT) and titanate nanotube (TNT) nanoparticles dispersed in water and ethylene glycol/water with particle concentrations ranging between 0 and 6 vol.% were used as working fluids for simulating the heat transfer and flow behaviours of nanofluids. The proposed model has been validated with the available experimental data and correlations. The effects of particle concentrations, particle diameter, particles Brownian motions, Reynolds number, type of the nanoparticles and base fluid on the heat transfer coefficient and pressure drop of nanofluids were determined and discussed in details. The results indicated that the particle volume concentration, Brownian motion and aspect ratio of nanoparticles similar to flow Reynolds number increase the heat transfer coefficient, while the nanoparticle diameter has an opposite effect on the heat transfer coefficient. Finally, the present study provides some considerations for the appropriate choice of the nanofluids for practical applications.     

Effect of flow geometry parameters on transient heat transfer for turbulent flow in a circular tube with baffle inserts

The effect of the flow geometry parameters on transient forced convection heat transfer for turbulent flow in a circular tube with baffle inserts has been investigated. The characteristic parameters of the tubes are pitch to tube inlet diameter ratio H/D = 1, 2 and 3, baffle orientation angle β = 45°, 90° and 180°. Air, Prandtl number of which is 0.71, was used as working fluid, while stainless steel was considered as pipe and baffle material. During the experiments, different geometrical parameters such as the baffle spacing H and the baffle orientation angle β were varied. Totally, nine types of baffle inserted tube were used. The general empirical equations of time averaged Nusselt number and time averaged pressure drop were derived as a function of Reynolds number corresponding to the baffle geometry parameters of pitch to diameter ratio H/D, baffle orientation angle β, ratio of smooth to baffled cross-section area S_o/S_a and ratio of tube length to baffle spacing L/H were derived for transient flow conditions. The proposed empirical correlations were considered to be applicable within the range of Reynolds number 3000 ⩽ Re ⩽ 20,000 for the case of constant heat flux.     

Forced convection in a helical pipe filled with a saturated porous medium

An analysis is made of laminar forced convection in a helical pipe of circular cross-section and filled by a porous medium saturated with a fluid, for the case when the curvature and torsion of the pipe are both small. The Darcy model is employed, and boundaries with either uniform flux or uniform temperature are considered. It is found that curvature induces a secondary flow at first order in the parameter ε = κa, where κ is the curvature and a is the radius of the pipe. On the other hand, the Nusselt number is unchanged to first order in ε but is increased at second order, for either set of thermal boundary conditions. The effect of torsion on the velocity appears at second order, but torsion does not affect the Nusselt number at second order.     

The effect of flow field and turbulence on heat transfer characteristics of confined circular and elliptic impinging jets

The flow field of confined circular and elliptic jets was studied experimentally with a Laser Doppler Anemometry (LDA) system. In addition, heat transfer characteristics were numerically investigated. Experiments were conducted with a circular jet and an elliptic jet of aspect ratio four, jet to target spacings of 2 and 6 jet diameters, and Reynolds number 10 000. The toroidal recirculation pattern was observed in the outflow region for both geometries at dimensionless jet to plate distance 2. Higher spreading rates in the minor axis direction of the elliptic jet have also been mapped. Along the target plate, different boundary layer profiles were obtained for circular and elliptic jets at H/d=2, but profiles became similar when dimensionless jet to plate distance was increased to 6. Positions of maximum radial and axial velocities and turbulence intensities have been determined for both geometries. For the confined circular and elliptic jet geometries, analysis of flow field measurements and numerical heat transfer results showed that inner peaks in local heat transfer closely relate to turbulence intensities in the jet and radial flow acceleration along the wall. Differences between the circular and elliptic jet, in terms of flow field and heat transfer characteristics, reduced with increase in the jet to plate distance.     

Unstable vortex flow and new inertia-driven vortex rolls resulting from an air jet impinging onto a confined heated horizontal disk

An experiment combining flow visualization and temperature measurement is carried out here to investigate the possible presence of new inertia-driven vortex rolls and some unique characteristics of the time-dependent mixed convective vortex flow in a high-speed round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber. How the jet Reynolds and Rayleigh numbers and jet-to-disk separation distance affect the unique vortex flow characteristics is examined in detail. Specifically, the experiment is conducted for the jet Reynolds number varying from 0 to 1623 and Rayleigh number from 0 to 63,420 for the jet-to-disk separation distance fixed at 10.0, 20.0 and 30.0 mm. The results indicate that at sufficiently high Re_j the inertia-driven tertiary and quaternary rolls can be induced aside from the primary and secondary rolls. At an even higher Re_j the vortex flow becomes unstable due to the inertia-driven flow instability. Only for H = 20.0 mm the flow is also subjected to the buoyancy-driven instability for the ranges of the parameters covered here. Because of the simultaneous presence of the inertia- and buoyancy-driven flow instabilities, a reverse flow transition can take place in the chamber with H = 20.0 mm. At the large H of 30.0 mm the flow unsteadiness results from the mutual pushing and squeezing of the inertia- and buoyancy-driven rolls since they are relatively large and contact with each other. It is also noted that the critical Re_j for the onset of unsteady flow increases with ΔT for H = 10.0 and 20.0 mm. But for H = 30.0 mm the opposite is true and raising ΔT can destabilize the vortex flow. Based on the present data, flow regime maps delineating the temporal state of the flow are provided and correlating equations for the boundaries separating various flow regimes are proposed.     

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.     

Heat transfer augmentation by swirl generators inserted into a tube with constant heat flux

A novel conical injector type swirl generator (CITSG) is devised in this study. Performances of heat transfer and pressure drop in a pipe with the CITSG are experimentally examined for the CITSGs' angle (α) of 30°, 45° and 60° in Reynolds number (Re) range of 10,000–35,000. Moreover, circular holes with different numbers (N) and cross-section areas (A_h) are drilled on the CITSG. In this way, total areas (A_t = N · A_h) of the holes on the CITSG are equaled each other. Besides, flow directors having three different angles (β = 30°, 60° and 90°) to radial direction are attached to every one of the holes. This study is a typical example for decaying flow. All experiments were conduced with air accordingly; Prandtl number was approximately fixed at 0.71. The local Nusselt number (Nu_x), heat transfer enhancement ratio (Nu_ER) and heat transfer performance ratio (Nu_PR) are calculated and discussed in this paper. It is found that the Nu_ER decreases with increase in Reynolds number, the director angle (β), the director diameter (d), and with decrease in the CITSG angle (α). Likewise, variation of Nu_PR and Nu_ER is also essentially similar for the same independent parameters.     

Performance of a hybrid photovoltaic/thermal system utilizing water‐Al2O3 nanofluid and fins

Innovative hybrid solar panels combining photovoltaic cells along with an efficient heat exchanger with attached fins to the parallel plates and water‐Al₂O₃ nanofluid as a working fluid is presented in this work. Twenty‐seven fins at the upper wall and 27 fins at the lower wall in labyrinth arrangement are used in simulations with fin lengths of 0, ¼, ½, and ¾ of the flow path height. Moreover, nanosolid particles dispersed in the base fluid range as 0 ≤ ? ≤ 0.2 . In addition, Reynolds number Re at the inlet was varied such that 10 < Re < 80. Numerical finite element analysis using COMSOL software is utilized to investigate flow and thermal characteristics as well the overall efficiency of the hybrid system. Results show that as the Reynolds number, the length of the fin, and the volume fraction of the nanosolid particles increase, the overall efficiency increases. Moreover, increasing nanoparticle volume fraction and the fin length was found to increase the friction coefficient.     

Lagrangian simulation of deposition of CO2 gas-solid sudden expansion flow

Freezing and blockage resulting from the deposition of solid CO₂ formed because of sudden expansion of the downstream pipe during the release of CO₂ through safety valves, will endanger the protected equipment. To overcome this problem, the characteristics of the CO₂ gas2solid sudden expansion flow are studied by using the disperse Lagrangian model. A comparison of the calculated deposition of the solid CO₂ with the experimental results shows that they are in reasonable agreement. The simulation results show that the size of the solid CO₂ formed should not be in the range of 0.04–0.07 mm (St number 3.2–9.8). This can be achieved by using an appropriate flow cross section of the safety valve. __________ Translated from Journal of Shanghai Jiaotong University, 2007, 41(3): 419–423 [译自: 上海交通大学学报]     

Experimental study for the stratified to slug flow regime transition mechanism of gas-oil two-phase flow in horizontal pipe

Theoretical relations that predict the transition from a stratified pattern to a slug pattern, including a onedimensional wave model that contains less empiricism than the commonly used Taitel-Dukler model, and the ideal model for stratified flow for the gas-liquid flow in horizontal pipes are presented. Superficial velocities of each phase, as the onset of slugging occurs, were predicted, and theoretical analysis was conducted on the stratified to slug flow regime transition. The friction, existing between the fluid and pipe wall, and on the interface of two phases, was especially taken into account. A theoretical model was applied to an experiment about air-oil two-phase flow in a 50 mm horizontal pipe. The effect of pipe diameter on the transition was also studied. The results show that this approach gives a reasonable prediction over the whole range of flow rates, and better agreement has been achieved between predicted and measured critical parameters. __________ Translated from Journal of Shanghai Jiaotong University, 2006, 40(10): 1782–1785, 1789 [译自: 上海交通大学学报]     

Convective Transport Around a Rotating Square Cylinder at Moderate Reynolds Numbers

Two-dimensional numerical simulation is performed to analyze the thermofluidic transport around a rotating square cylinder in an unconfined medium. The convective transport originates as a consequence of the interaction between a uniform free-stream flow and the flow evolving due to the rotation of the sharp-edged body. A finite volume-based method and a body-fitted grid system along with the moving boundaries are used to obtain the numerical solution of the incompressible Navier–Stokes and energy equations. The Reynolds number based on the free-stream flow is considered in the range 10 ≤ Re ≤ 200, and the dimensionless rotational speed of the cylinder is kept 0 ≤ Ω ≤ 5. Depending on the Reynolds number and the rotational speed of the cylinder, the transport characteristics change. For the range 10 ≤ Re < 50, the flow remains steady irrespective of the rotational speed. In the range 50 ≤ Re ≤ 200, regular low-frequency Kármán vortex shedding (VS) is observed up to a critical rate of rotation (Ω_cr ). Beyond Ω_cr , the global convective transport shows a steady nature. The rotating circular cylinder also shows likewise degeneration of Kármán VS at some critical rotational speed. However, the heat transfer behavior varies significantly with a rotating circular cylinder. Such thermofluidic transport around a spinning square in an unconfined free-stream flow is reported for the first time.     

Experimental investigation of turbulent flow and convective heat transfer characteristics of alumina water nanofluids in fully developed flow regime

In this paper the convective heat transfer and friction factor of the nanofluids in a circular tube with constant wall temperature under turbulent flow conditions were investigated experimentally. Al₂O₃ nanoparticles with diameters of 40 nm dispersed in distilled water with volume concentrations of 0.1–2 vol.% were used as the test fluid. All physical properties of the Al₂O₃–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient were measured. The results show that the heat transfer coefficient of nanofluid is higher than that of the base fluid and increased with increasing the particle concentrations. Moreover, the Reynolds number has a little effect on heat transfer enhancement. The experimental data were compared with traditional convective heat transfer and viscous pressure drop correlations for fully developed turbulent flow. It was found that if the measured thermal conductivities and viscosities of the nanofluids were used in calculating the Reynolds, Prandtl, and Nusselt numbers, the existing correlations perfectly predict the convective heat transfer and viscous pressure drop in tubes.     

Computational research on rotating channel by a modified anisotropic turbulence model

Based on the simplified format of the Reynolds stress equations,a fire-new rotational-modification method for the anisotropic turbulence model has been presented.A three-dimensional Navier-Stokes code with this new rotational modified k-ω turbulence models(β=0.1 and β=1) and the standard k-ω turbulence model have been used for the prediction of flow and heat transfer characteristics in a rotating smooth square channel.The Reynolds number Re based on the inlet velocity of the cooling air and hydraulic diameter is 6000.The rotating speed are 300,600,900,1200rpm respectively.The calculations results of using three turbulence models have been compared with the experimental data.The research results show that(1) the rotational modification coefficient Rf13 used in the new anisotropic k-ω model would increased/decreased the predictions of heat transfer on the trailing surface/leading surface compared to the standard k-ω model.And this tendency would be increased with the increased β.(2) The simulation performance of the standard k-ω model was well on the leading surface.However,on the trailing surface it under-predicted the heat transfer at high rotating speed.(3) The calculation results of the new anisotropic k-ω model with β=0.1 proposed by the present paper agreed well with experimental data,both on the leading and trailing surfaces.Besides,compared to 1,0.1 is a more appropriate magnitude of β at conditions in the present paper.     

Flow characteristics of single-phase flow in narrow annular channels

The characteristics of single-phase flow in narrow annular channels were analyzed and theoretical model was proposed. Based on the present model, the theoretical calculation was performed to predict the flow characteristics for the developed flow in narrow annuli with the gap sizes of 1.0, 1.5 and 2.0 mm, respectively. The results were in good agreement with the experimental data. In addition, the gap size of narrow annuli has great impact upon the flow characteristics. The decrease of gap size reduces friction factor. The higher the Reynolds number, the more remarkable the effect of gap size upon friction coefficient during single-phase flowing through narrow annular channels. The effect of gap size upon friction coefficient is dependent on the Reynolds number, and will decrease with the decrease of the Reynolds number. __________ Translated from Atomic Energy Science and Technology, 2007, 41(5): 575–579 [译自 : 原子能科学技术]