Heat transfer for non-Newtonian laminar flow in internally finned pipes with uniform temperature

An analysis is presented for fully developed laminar convective heat transfer of non-Newtonian power-law fluids in pipes with internal longitudinal fins and uniform outside wall temperature. The governing momentum and energy equations have been solved numerically, with the influence of fin conductance. The distributions of fin temperature, fluid temperature and local heat flux (both at finned and unfinned surfaces) are presented. These are shown to be strongly dependent on finned pipe geometry, fluid flow behavior index and the fin conductance. Values of overall Nusselt number indicated significant heat transfer enhancement over finless pipes. The flow behavior index affects the no. of fins which maximizes the overall Nusselt number.     

Developing and fully developed turbulent flow in ribbed channels

Wall-mounted roughness features, such as ribs, are often placed along the walls of a channel to increase the convective surface area and to augment heat transfer and mixing by increasing turbulence. Depending on the relative roughness size and orientation, the ribs also have varying degrees of increased pressure losses. Designs that use ribs to promote heat transfer encompass the full range of having only a few streamwise ribs, which do not allow fully developed flow conditions, to multiple streamwise ribs, which do allow the flow to become fully developed. The majority of previous studies have focused on perturbing the geometry of the rib with little attention to the spatially and temporally varying flow characteristics and their dependence on the Reynolds number. A staggered rib-roughened channel study was performed using time-resolved digital particle image velocimetry (TRDPIV). Both the developing (entry region) and a fully developed region were interrogated for three Reynolds numbers of 2,500, 10,000, and 20,000. The results indicate that the flow was more sensitive to Reynolds number at the inlet than within the fully developed region. Despite having a similar mean-averaged flowfield structure over the full Reynolds number range investigated, the population and distribution of coherent structures and turbulent dissipation within the fully developed region were also found to be Reynolds number dependent. Exploring the time-accurate flow characteristics revealed that in addition to vortices shed from the rib shear layer, the region of the rib wake was governed by a periodic process of bursting of the wake vortices resulting in the intermittent ejection of the inter-rib recirculation region into the core flow. This periodic process was the driving mechanism resulting in mixing and heat transfer augmentation. A quadrant-splitting burst analysis was also performed to determine the characteristic frequency and duration of inter-rib bursting as well as the wake shedding frequency, both of which were determined to be Reynolds number dependent.     

Evolution of turbulence characteristics from straight to curved pipes

Fully developed, statistically steady turbulent flow in straight and curved pipes at moderate Reynolds numbers is studied in detail using direct numerical simulations (DNS) based on a spectral element discretisation. After the validation of data and setup against existing DNS results, a comparative study of turbulent characteristics at different bulk Reynolds numbers Re_b = 5300 and 11,700, and various curvature parameters κ = 0, 0.01, 0.1 is presented. In particular, complete Reynolds-stress budgets are reported for the first time. Instantaneous visualisations reveal partial relaminarisation along the inner surface of the curved pipe at the highest curvature, whereas developed turbulence is always maintained at the outer side. The mean flow shows asymmetry in the axial velocity profile and distinct Dean vortices as secondary motions. For strong curvature a distinct bulge appears close to the pipe centre, which has previously been observed in laminar and transitional curved pipes at lower Re_b only. On the other hand, mild curvature allows the interesting observation of a friction factor which is lower than in a straight pipe for the same flow rate.All statistical data, including mean profile, fluctuations and the Reynolds-stress budgets, is available for development and validation of turbulence models in curved geometries.     

An analytical solution to the heat transfer problem in thick-walled hunt flow

The flow of a liquid metal in a rectangular duct, subject to a strong transverse magnetic field is of interest in a number of applications. An important application of such flows is in the context of coolants in fusion reactors, where heat is transferred to a lead-lithium eutectic. It is vital, therefore, that the heat transfer mechanisms are understood. Forced convection heat transfer is strongly dependent on the flow profile. In the hydrodynamic case, Nusselt numbers and the like, have long been well characterised in duct geometries. In the case of liquid metals in strong magnetic fields (magnetohydrodynamics), the flow profiles are very different and one can expect a concomitant effect on convective heat transfer. For fully developed laminar flows, the magnetohydrodynamic problem can be characterised in terms of two coupled partial differential equations. The problem of heat transfer for perfectly electrically insulating boundaries (Shercliff case) has been studied previously (Bluck et al., 2015). In this paper, we demonstrate corresponding analytical solutions for the case of conducting hartmann walls of arbitrary thickness. The flow is very different from the Shercliff case, exhibiting jets near the side walls and core flow suppression which have profound effects on heat transfer.     

Study into thermal stresses due to turbulent flow in pipes

Flow through pipes with heat transfer finds wide applications in industry. The thermal stresses, which develop in the pipe limit the heat transfer rate in pipe flow. In the present study, a turbulent flow in thick pipe with external heating is considered. The flow and temperature fields in a pipe and in the fluid are predicted using a numerical scheme; which employs a control volume approach. A k- model is introduced to account for the turbulence. The thermal stresses developed in the pipe due to heat transfer are predicted. The simulations are repeated for different pipe materials and fluids. It is found that the temperature gradient in the pipe changes rapidly in the vicinity of the solid-fluid interface. This change is not affected considerably by the Reynolds number. The effective stress developed at mid-plane of the pipe is independent of the Reynolds number; however, the pipe material affects the effective stress considerably.     

Pressure drop, heat transfer and performance of single-phase turbulent flow in spirally corrugated tubes

The paper presents the results of an experimental study that was carried out to determine turbulent friction and heat transfer characteristics of four spirally corrugated tubes, which have various geometrical parameters, with water and oil as the working fluids. Experiments were performed under conditions of Reynolds number varying from 6000 to 93,000 for water, and from 3200 to 19,000 for oil, respectively. The results show that the thermal performance of these tubes was superior compared to a smooth tube, but the heat transfer enhancements were not as large as the friction factor increases. Friction factors and heat transfer coefficient in these rough tubes were analyzed on the basis of momentum and heat transfer analogy, and the correlations obtained were compared with the present data and also the results of previous investigators. A mathematical model to evaluate the performance of spirally corrugated tube, which takes account of the large variation of fluid Prandtl number with temperature, was developed by the extension of previous work of Bergles and Webb. The results reported enable practical designs with standard products and optimization of tube geometry for specific conditions.     

添加剂湍流减阻流动与换热研究综述

添加剂湍流减阻是指在液体的管道湍流中添加少量的高分子聚合物或某种表面活性剂从而使湍流阻力大大降低的现象.从其被发现至今,经过近半个世纪的研究(实验研究、理论分析、数值模拟和实际系统的应用研究),尽管对这一现象及其实际应用价值已有了较为深入的认识,但仍有许多方面尚有欠缺,例如对湍流减阻的机理仍然在探索中.本文归纳评述了高分子聚合物或表面活性剂添加剂湍流减阻流动与换热现象的研究现状,从湍流减阻剂的特性、减阻剂的湍流减阻机理、湍流减阻发生时的换热机理、减阻流动速度场分布和换热控制等几个方面综述了添加剂湍流减阻流动与换热特性,并综述了湍流减阻剂在实际工业系统中的应用情况,在对添加剂湍流减阻机理、有湍流减阻发生时的对流换热机理等的理解方面进行了新的总结.      

Mass transfer enhancement by longitudinal vortices

From numerical and experimental investigations it has been recently established that convective heat transfer can be dramatically enhanced by the generation of longitudinal vortices in the flow. The phenomenological similarity between heat and mass transfer suggests that longitudinal vortices should increase also mass transfer. The mixing between two parallel streams of two components in a rectangular channel with and without a pair of rectangular winglets as vortex generators has been numerically investigated. The results show that one pair of vortex generators can increase the global mixing by more than 50 for laminar flow. This global mixing has been defined as the sum of the square of the differences of concentrations.     

Performance of RNG Turbulence Modelling for Forced Convective Heat Transfer in Ducts

This investigation concerns numerical calculation of turbulent forced convective heat transfer and fluid flow in straight ducts using the RNG (Re-Normalized Group) turbulence method.

A computational method has been developed to predict the turbulent Reynolds stresses and turbulent heat fluxes in ducts with different turbulence models. The turbulent Reynolds stresses and other turbulent flow quantities are predicted with the RNG κ?ε model and the RNG non-linear κ-ε model of Speziale. The turbulent heat fluxes are modeled by the simple eddy diffusivity (SED) concept, GGDH and WET methods. Two wall functions are used, one for the velocity field and one for the temperature field. All the models arc implemented for an arbitrary three dimensional duct.

Fully developed condition is achieved by imposing cyclic boundary conditions in the main flow direction. The numerical approach is based on the finite volume technique with a non-staggered grid arrangement. The pressure-velocity coupling is handled by using the SIMPLEC-algorithm. The convective terms are treated by the QUICK, scheme while the diffusive terms are handled by the central-difference scheme. The hybrid scheme is used for solving the κ and ε equations.

The overall comparison between the models is presented in terms of friction factor and Nusselt number. The secondary flow generation is also of major concern.     

Numerical Analysis of Laminar-Turbulent Transition in a Circular Pipe with Periodic Inflow Perturbations

The problem of the spatio-temporal evolution of perturbations introduced into the inlet cross-section of a circular pipe is solved numerically. The case of time-periodic inflow perturbations is considered for Re = 4000. It is shown that for relatively small inflow perturbations periodic flow regimes and for greater perturbations chaotic regimes are established.Periodic regimes the flow is a superposition of steady flow and a damped wave propagating downstream. The velocity profile of the steady component differs essentially from both the parabolic Poiseuille and developed turbulent flows and is strongly inhomogeneous in the angular direction. The angular distortion of the velocity profile is caused by longitudinal vortices developing as a result of the nonlinear interaction of inflow perturbations.Chaotic flow regimes develop when the amplitude of the inflow perturbations exceeds a certain threshold level. Stochastic high-frequency pulsations appear after the formation of longitudinal vortices in the regions of maximum angular gradient of the axial velocity. In the downstream part of the flow, remote from the transition region, the developed turbulent regime is formed. The distributions of all the statistical moments along the pipe level off and approach the values measured experimentally and calculated numerically for developed turbulent flows.     

管内定型流传热过程的有效能损失

对管道内充分发展对流传热过程的有效能损失进行了分析．根据定型流状态下定热流与定壁温换热条件的特点,经代数推演,得到了这两种条件下的表征换热状态、流动功耗以及黏性变化的无量纲形式的有效能损失关系式,适用于不同截面形状的管道内的层流与湍流工况下的有效能分析．     

Experimental investigation on turbulent flow in a circular-sectioned 90-degree bend

 The steady, turbulent flow in a circular-sectioned 90° bend with smooth walls has been investigated experimentally. The bend had a curvature radius ratio of 4.0 with long, straight upstream and downstream pipes. The longitudinal, circumferential and radial components of mean and fluctuating velocities, and the Reynolds stresses in the pipe cross section at several longitudinal stations were obtained with the technique of rotating a probe with an inclined hot wire at a Reynolds number of 6×10⁴. The velocity fields of the primary and secondary flows, and the Reynolds stress distributions in the cross section were illustrated. Moreover, other characteristics of the bend flow, such as deviation of the primary flow and intensity of the secondary flow, were presented. Simultaneously, discussions were given on the transition of phenomena in the longitudinal direction and the structures of turbulence in the 90° bend. Received: 21 April 1997/Accepted: 14 November 1997     

Investigation of flow and heat transfer in corrugated-undulated plate heat exchangers

 An experimental and numerical investigation of heat transfer and fluid flow was conducted for corrugated-undulated plate heat exchanger configurations under transitional and weakly turbulent conditions. For a given geometry of the corrugated plates the geometrical characteristics of the undulated plates, the angle formed by the latter with the main flow direction, and the Reynolds number were made to vary. Distributions of the local heat transfer coefficient were obtained by using liquid-crystal thermography, and surface-averaged values were computed; friction coefficients were measured by wall pressure tappings. Overall heat transfer and pressure drop correlations were derived. Three-dimensional numerical simulations were conducted by a finite-volume method using a low-Reynolds number k–ɛ model under the assumption of fully developed flow. Computed flow fields provided otherwise inaccessible information on the flow patterns and the mechanisms of heat transfer enhancement. Received on 5 February 1999     

Experimental study on heat transfer of thermally developing and developed, turbulent, horizontal pipe flow of dilute air-solids suspensions

Heat transfer characteristics of a turbulent, dilute air-solids suspension flow in thermally developing/developed regions were experimentally studied, using a uniformly heated, horizontal 54.5 mm-ID pipe and 43-μm-diameter glass beads. The local heat transfer was measured at 27 locations from the inlet to 120-dia downstream of the heated section over a range of Reynolds numbers 3×10⁴−1.2×10⁵ and solids loading ratio 0–3, and the fully developed profiles of air velocity/temperature and particle mass flux were measured at a location 140-dia downstream of the heated section using specially designed probes, inserted into the suspension flow. The effects of the Reynolds number, solids loading ratio, and azimuthal/longitudinal locations on the heat transfer characteristics and their interactions are discussed through comparison of the present results with the data obtained by other investigators. Received on 14 October 1996     

Experimental investigation on turbulent flow through a circular-sectioned 180° bend

The steady, developing turbulent flow in a circular-sectioned 180° bend has been investigated. The bend had a radius of 104 mm and a curvature radius ratio of 4.0 with long, straight upstream and downstream pipes. Measurements of the longitudinal, radial and circumferential components of mean velocity, and corresponding components of the Reynolds stress were obtained with a hot wire anemometer at a Reynolds number of 6×10⁴ and at various longitudinal stations. The velocity fields of the primary and secondary flows and the Reynolds stresses were illustrated in the form of contour map or vector diagram. Moreover, the mean quantities characterizing the bend flow, i.e., the deflection of the primary flow in the cross section, the intensity of the secondary flow and the turbulence energy, were shown in a graphic form against the longitudinal distances. In the section upstream from a bend angle of about 60°, both the flows through the 180° and the 90° bend are closely similar in their behavior. In the section from the bend angle of 90°, the high-velocity regions, however, occur near the upper and lower walls as a result of strong secondary flow and the turbulence with high level emerges in the central region of the bend. Just behind the bend exit, an additional pair of vortices appears in the outer part of the cross section owing to the transverse pressure difference. In the downstream tangent, the flow returns slowly to the proper flow in a straight pipe, but it needs a longer distance for recovery than in the 90° bend. Received: 23 April 1998/Accepted: 24 April 1999     

Investigation of thermal dispersion and intra-pore turbulent heat flux in porous media

In the present study, the importance of the thermal dispersion and the turbulent heat flux in porous media and their effects on the macroscopic distribution of thermal energy are investigated. To this end, turbulent flow and heat transfer within five unit-cells mimicking porous media are solved using large eddy simulation. It is shown that the thermal dispersion and the turbulent heat flux are negligible as compared to the convection term in the macroscopic energy equation. When further scrutinizing this equation, it is revealed that except for the longitudinal components of the thermal dispersion, the other components of thermal dispersion and turbulent heat flux may be neglected away from the boundaries as compared to the interfacial heat transfer. Visualizations of vortices show that the size of the turbulence structures within the cells is of the same order as the size of the pores; therefore, the turbulent heat flux is limited to the intra-pore level. Finally, a discussion is provided on the accuracy of the gradient type diffusion model commonly used for turbulent heat flux in porous media in the absence of macroscopic turbulence. It is shown that the intra-pore turbulence does not affect the macroscopic transport of thermal energy within the porous media studied.     

Experimental study and mathematical simulation of the characteristics of a turbulent flow in a straight circular pipe rotating about its longitudinal axis

The vorticity formed in the cross section of a turbulent flow in a straight circular pipe rotating about its longitudinal axis decreases the values of the turbulent stresses, turbulence energy, and dissipation rate along the pipe. The results of laboratory experiments and calculations by the second-order closure model of turbulent transfer are presented. On the whole, the model using a system of transport equations yields better agreement with experimental data than the models with algebraic relations for second-order moments. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 103–116, March–April, 1998.     

Experimental study of developing turbulent flow and heat transfer in ribbed convergent/divergent square ducts

The local heat transfer and pressure drop characteristics of developing turbulent flows of air in three stationary ribbed square ducts have been investigated experimentally. These are: ribbed square duct with constant cross-section (straight duct), ribbed divergent square duct and ribbed convergent square duct. The convergent/divergent duct has an inclination angle of 1°. The measurement was conducted within the range of Reynolds numbers from 10 000 to 77 000. The heat transfer performance of the divergent/convergent ducts is compared with the ribbed straight duct under three constraints: identical mass flow rate, identical pumping power and identical pressure drop. Because of the streamwise flow acceleration or deceleration, the local heat transfer characteristics of the divergent and convergent ducts are quite different from those of the straight duct. In the straight duct, the fluid flow and heat transfer become fully developed after 2–3 ribs, while in the divergent and convergent ducts there is no such trend. The comparison shows that among the three ducts, the divergent duct has the highest heat transfer performance, the convergent duct has the lowest, while the straight duct locates somewhere in between.     

Convective heat transfer of aqueous alumina nanosuspensions in a horizontal mini-channel

This work reports an experimental study of convective heat transfer of aqueous alumina nanofluids in a horizontal mini-channel under laminar flow condition 40 < Re < 1,000. The variation of local heat transfer coefficients, in both entrance and developed flow regimes, was obtained as a function of axial distance. The heat transfer coefficient of nanofluids was found to be dependent on not only nanoparticle concentration but also mass flow rate. Different to the behavior in conventional-sized channels, the major heat transfer coefficient enhancement is shown in the fully developed regime in the minichannel where up to 40% increase is observed. Discussions of the results suggest that apart from the need of a careful assessment of different thermo-physical properties of nanofluids, i.e., viscosity, specific heat and thermal conductivity, the heterogeneous nature of nanoparticle flow should be considered especially under high flow rate conditions.     

Large eddy simulation and self-similarity analysis of the momentum spreading in the near field region of turbulent submerged round jets

Self-Similarity in turbulent round jets has been the object of investigation from several decades. The evolution of turbulent submerged jets is characterized by the presence of two regions: the region of flow establishment, or near field region (NFR) and the fully developed region (FDR), or far-field region (FFR). The momentum spreading in the FDR is known to be self-similar and few mathematical models have been presented in the past to describe it. The flow evolution in the NFR has been rarely studied since there is a certain consensus on the idea that the flow in the NFR is not self-similar. In this work, we study the flow evolution of a turbulent submerged round jet by means of large eddy simulation (LES) at several Reynolds numbers ranging from 2492 to 19,988. Three new self-similar laws are proposed to describe the flow evolution in the NFR, one for the initial region, called Undisturbed Region of Flow, (URF), and two for the final region, the potential core region (PCR). The numerical results presented in this work are also validated with the self-similar laws for the FDR proposed by Tollmien (1926) and Görtler (1942), and the experimental data of Hussein et al. (1994), and Panchapakesan and Lumley (1993), in the FDR; those of Davies et al. (1963), in the PCR; and van Hout et al. (2018), in the URF. The conclusion is that previous inability to find the self-similarity law in the NFR is due to the attempt to find a unique self-similar variable to describe the momentum spreading in both the URF and the PCR.