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.     

Experimental and numerical investigation on heat transfer characteristics of supercritical R1234ze(E) cooled in horizontal tubes

The heat transfer characteristics of supercritical fluids in tubes have been considered indispensable for the design and optimization of the heat exchanger and the energy conversion system. Specifically the cooling heat transfer of supercritical R1234ze(E) in horizontal tubes is a promising heat-power conversion technology; however, there is a scarcity of conducted research in available literature. The present work, the first-ever study in this direction, aims to thoroughly investigate the heat transfer characteristics of supercritical R1234ze(E) which is cooled in horizontal tubes. Experimental work was performed to thoroughly explore and inspect the heat transfer characteristics of supercritical R1234ze(E) passing through the tube of 4.12 mm diameter at 4–5 MPa pressure and 240–400 kg/m² s mass flux. Furthermore, the simulation study, supporting the experimental investigation under the same conditions of pressure and mass flux, extended the range of tube diameter up to 9.44 mm. The effects of pressure, mass flux and tube diameter on the heat transfer coefficient were carefully analyzed in the present research work. Based on the simulation results and experimental results, heat transfer correlations were newly developed by separating the region above and below the pseudo-critical temperature. The average absolute deviation between the calculated Nusselt numbers by the numerical correlation and the simulation results was found 2.87%; the average absolute deviation between the calculated Nusselt numbers by the experimental correlation and the experimental results was found 5.3%.     

Natural convection of nano-fluids

Fluids with nano size solid particles suspended in them have been given the name nano-fluid which in recent studies have shown tremendous promise as heat transfer fluids. However, before suggesting such fluids for applications a thorough knowledge of physical mechanism of heat transfer in such fluids is wanted. The present study deals with one such aspect of natural convection of nano fluids inside horizontal cylinder heated from one end and cooled from the other. An apparently paradoxical behaviour of heat transfer deterioration was observed in the experimental study. Nature of this deterioration and its dependence on parameters such as particle concentration, material of the particles and geometry of the containing cavity have been investigated. The fluid shows characters distinct from that of common slurries.     

An experimental study of nonrheometric flows of visco-elastic fluids: I. flow into a re-entrant tube

A laser anemometer has been used to study the developing flow both upstream and downstream from the entry plane in a re-entrant tube geometry. A 0.75% polyacrylamide/water solution was used and Reynolds numbers (based on wall conditions in the fully developed downstream flow) in the range 100–500 were obtained in 1.82-cm and 2.40-cm-diameter tubes.The shear stress-shear rate relationship for the fluid was measured using a cone and plate geometry in conjunction with a Weissenberg rheogoniometer. Theoretical fully developed velocity profiles were calculated numerically from these measurements. The measured fully developed velocity profiles were found to be in excellent agreement with those calculated.Velocity profiles measured at the tube entry plane showed the pronounced wall region distortion typically predicted by recent numerical solutions of the flow of purely-viscous fluids through an abrupt tube contraction.It was found that the major velocity rearrangements were achieved within only a few diameters (both upstream and downstream) of the entry plane. In particular, the velocity distribution near the tube wall varied negligibly over the relatively longer distance (many diameters) that it took for the centreline velocity to achieve its fully developed value. Entry lengths were found to be only about half those for purely-viscous fluids.Calculation of the time of flight along the central streamline confirmed that the major rearrangements of velocity suffered by the fluid occurred over a relatively short time period. This indicates that hereditary integral constitutive equations may have to be used in theoretical analyses of this type of flow situation.     

Numerical simulations of Boger fluids through different contraction configurations for the development of a measuring system for extensional viscosity

This paper reports the flow behaviour of Newtonian and Boger fluids through various axisymmetric contraction configurations by means of numerical predictions. A principal aim has been to evaluate the geometrical design choice of the hyperbolic contraction flow. The FENE-CR model has been used to reflect the behaviour of Boger fluids, with constant shear viscosity, finite (yet large) extensional viscosity and less than quadratic first normal stress difference. Numerical calculations have been performed on six different contraction configurations to evaluate an optimized geometry for measuring extensional viscosity in uniaxial extensional flow. The influence of a sharp or rounded recess-corner on the nozzle has also been investigated. Few commercial measuring systems are currently available for measurement of the extensional rheology of medium-viscosity fluids, such as foods and other biological systems. In this context, a technique based on the hyperbolic contraction flow would be a suitable alternative. The pressure drop, the velocity field, the first normal stress difference and the strain rate across the geometry have each been evaluated for Newtonian and Boger fluids. This numerical study has shown that the hyperbolic configuration is superior to the other geometry choices in achieving a constant extension rate. In this hyperbolic configuration, no vortices are formed, the measuring range is broader and the strain rate is constant throughout the geometric domain, unlike in the alternative configurations tested. The difference between sharp and rounded recess-corner configurations proved to be negligible and a rise in excess pressure drop (epd) for increasing deformation rates has been observed.     

The influence of multiple tubes on the tube-to-bed heat transfer in a fluidised bed

There have been few studies modelling both flow and heat transfer in fluidised beds. The kinetic theory of granular flow (KTGF) has been used for flow prediction in the past without heat transfer modelling. In the present study, a two-fluid Eulerian–Eulerian formulation incorporating the KTGF was applied first to a tube-to-bed reactor with one immersed tube and compared with the results in the literature. The bed was then modified to introduce two and three heated tubes. The effects on the flow and temperature distribution, local heat transfer coefficients and averaged heat transfer coefficients over a 3.0 s time period were carried out. Results showed that increasing the number of tubes promotes heat transfer from tubes to the particles and flow. The heat transfer coefficients extracted from the single-tube to three-tube cases were analysed in detail, confirming the importance of linking flow/particle and heat transfer calculations.     

Investigation of the flow and heat transfer of viscous reacting fluids in long tubes

Heat transfer and resistance in the case of laminar flow of inert gases and liquids in a circular tube were considered in [1–4], the justification of the use of boundary-layer type equations for investigating two-dimensional flows in tubes being provided in [4]. The flow of strongly viscous, chemically reacting fluids in an infinite tube has been investigated analytically and numerically in the case of a constant pressure gradient or constant flow rate of the fluid [5–8]. An analytic analysis of the flow of viscous reacting fluids in tubes of finite length was made in [9, 10]. However, by virtue of the averaging of the unknown functions over the volume of the tube in these investigations, the allowance for the finite length of the tube reduced to an analysis of the influence of the time the fluid remains in the tube on the thermal regime of the flow, and the details of the flow and the heat transfer in the initial section of the tube were not taken into account. In [11], the development of chemical reactions in displacement reactors were studied under the condition that a Poiseuille velocity profile is realized and the viscosity does not depend on the temperature or the concentration of the reactant; in [12], a study was made of the regimes of an adiabatic reactor of finite length, and in [13] of the flow regimes of reacting fluids in long tubes in the case of a constant flow rate. The aim of the present paper is to analyze analytically and numerically in the two-dimensional formulation the approach to the regimes of thermal and hydrodynamic stabilization in the case of the flow of viscous inert fluids and details of the flow of strongly viscous reacting fluids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 17–25, January–February, 1930.     

Algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow

The study considers algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow, focusing in particular on momentum and heat transfer (so-called ‘convective boiling’) through the annular liquid film. In contrast with single-phase wall-bounded flow theory, shear-driven annular liquid films are assumed here to behave as fluid-bounded flows, mostly interacting with the shearing gas-entrained droplets core flow. Besides providing velocity and temperature profiles through the liquid film, the turbulence model proposed here predicts key parameters such as the average liquid film thickness, the void fraction and the convective boiling heat transfer coefficient with accuracies comparable or better than those of leading design correlations. This turbulence model is part of a unified annular flow modeling suite that includes methods to predict the entrained liquid fraction and the axial frictional pressure gradient. The underlying heat transfer database covers nine fluids (water, two hydrocarbons and six refrigerants) for vertical and horizontal tubes of 1.03-14.4 mm diameter and pressures of 0.1-7.2 MPa. Importantly, this study shows that there appears to be no macro-to-microscale transition when it comes to annular flow. Simply better physical modeling is required to span this range.     

Transient finite element analysis of generalized Newtonian coextrusion flows in complex geometries

A two-dimensional transient finite element model capable of simulating problems related to two-layer polymer flows has been developed. This technique represents an effective tool which can be used to study the possibility of the onset of interfacial instability in coextrusion flows, considering melt rheology as well as the fluid–geometry interaction. A code has been developed to solve the transient problem of the flow of bi-component systems of Newtonian and generalized Newtonian fluids through parallel plates and complex geometries, such as: 2:1 abrupt expansion, 2:1 (30°) expansion, 4:1 abrupt contraction and 4:1 tapered (30°) contraction. Solutions are compared with experimental data from the literature and results provided by linear stability analysis (LSA) for the case of parallel plate flows. Numerical results are in agreement with LSA results for the parallel plate geometry cases studied. The expansion geometries tend to stabilize flows in the parallel plate section downstream of the expansion. Contractions may give rise to break-up of the interface depending on the flow conditions. © 1998 John Wiley & Sons, Ltd.     

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.     

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.     

Pulsatile flows of Leslie–Ericksen liquid crystals

Capillary pulsatile flows of calamitic (rod-like) and discotic nematic liquid crystals are analyzed using the Leslie–Ericksen equations for low-molar mass liquid crystals, using computational, analytical, and scaling methods. The dependence of flow-enhancement and power requirement on frequency, amplitude, pressure drop wave-form, molecular geometry is characterized. The unique roles of orientation-dependent local viscosity and backflow (orientation-driven flow) on flow-enhancement and power requirement are elucidated. The local viscosity effect is shown to be a significant factor in flow-enhancement at all pressure drops, but only affects power requirement at higher pressure drops. Backflow has weak effects on flow-enhancement and large effects on power requirements at low average pressure drops. Amplitude, frequency, and molecular geometry effects are clearly manifested through viscosity and backflow. A detailed comparison with predictions for power law fluids shows a clear correspondence between these non-Newtonian fluids and nematic liquid crystals. The unique distinguishing feature of pulsatile flows of liquid crystals is found to be backflow, such that power increases with increasing frequency, a featured that does not exist in other non-Newtonian fluids due to lack of a strong flow driven by restructuring/re-orientation processes. Future use of these new results may include measurements of viscoelastic parameters that control backflow.     

Flow boiling performance in horizontal microfinned copper tubes with the same geometric characteristics

This article reports an experimental investigation on flow boiling heat transfer and pressure drop of refrigerant R-134a in a smooth horizontal and two microfinned tubes from different manufacturers with the same geometric characteristics. Experiments have been carried out in an experimental facility developed for change of phase studies with a test section made with 9.52 mm external diameter, 1.5 m long copper tubes, electrically heated by tape resistors wrapped on the external surface. Tests have been performed under the following conditions: inlet saturation temperature of 5 °C, vapor qualities from 5% to 90%, mass velocity from 100 to 500 kg/s m², and a heat flux of 5 kW/m². Experimental results indicated that the heat transfer performance was basically the same for both microfin tubes. The pressure drop is higher in the microfinned tubes in comparison to the smooth tube over the whole range of mass velocities and vapor qualities. The enhancement factor, used to evaluate the combination of heat transfer and pressure drop, is higher than one for both tubes for mass velocities lower than 300 kg/s m². Values lower than one have been obtained for both tubes in the mass velocity upper range as a result of a significant pressure drop increment not followed by a correspondent increment in the heat transfer coefficient. Some images, illustrating the flow patterns, were obtained from the visualization section, located in the exit of the test section with the same internal diameter of the tested tube.     

Transient free convection of non-Newtonian fluids along a wavy vertical plate including the magnetic field effect

A Prandtl transformation method is applied to study the transient free convection of non-Newtonian fluids along a wavy vertical plate in the presence of a magnetic field. A simple transformation is proposed to transform the governing equations into the boundary-layer equations and solved numerically by the cubic spline approximation. A simple coordinate transformation is employed to transform the complex wavy surface to a vertical flat plate for a constant wall temperature by the numerical method. The effects of the magnetic field parameter, the wavy geometry and the non-Newtonian nature of the fluids on the flow characteristics and heat transfer are discussed in detail.     

Stress-Dependent Porosity and Permeability of Porous Rocks Represented by a Mechanistic Elastic Cylindrical Pore-Shell Model

The stress dependency of the porosity and permeability of porous rocks is described theoretically by representing the preferential flow paths in heterogeneous porous rocks by a bundle of tortuous cylindrical elastic tubes. A Lamé-type equation is applied to relate the radial displacement of the internal wall of the cylindrical elastic tubes and the porosity to the variation of the pore fluid pressure. The variation of the permeability of porous rocks by effective stress is determined by incorporating the radial displacement of the internal wall of the cylindrical elastic tubes into the Kozeny–Carman relationship. The fully analytical solutions of the mechanistic elastic pore-shell model developed by combining the Lamé and Kozeny–Carman equations are shown to lead to very accurate correlations of the stress dependency of both the porosity and the permeability of porous rocks.

     

Effective Correlation of Apparent Gas Permeability in Tight Porous Media

Gaseous flow regimes through tight porous media are described by rigorous application of a unified Hagen–Poiseuille-type equation. Proper implementation is accomplished based on the realization of the preferential flow paths in porous media as a bundle of tortuous capillary tubes. Improved formulations and methodology presented here are shown to provide accurate and meaningful correlations of data considering the effect of the characteristic parameters of porous media including intrinsic permeability, porosity, and tortuosity on the apparent gas permeability, rarefaction coefficient, and Klinkenberg gas slippage factor.     

Soret and Dufour effect on double diffusion mixed convection from a vertical surface in a porous medium saturated with a non-Newtonian fluid

A non-similar boundary layer analysis is presented to study the flow, heat and mass transfer characteristics of non-Darcian mixed convection of a non-Newtonian fluid from a vertical isothermal plate embedded in a homogeneous porous medium with the effect of Soret and Dufour and in the presence of either surface injection or suction. The value of the mixed-convection parameter lies between 0 and 1. In addition, the power-law model is used for non-Newtonian fluids with exponent n < 1 for pseudoplastics n = 1 for Newtonian fluids and n > 1 for dilatant fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection, from the pure forced-convection limit to the pure free-convection limit, and the whole domain of non-Newtonian fluids, from pseudoplastics to dilatant fluids. The numerical solution of the problem is derived using a Runge–Kutta integration scheme with Newton–Raphson shooting technique. Distributions for velocity, temperature and concentration, as well as for the rate of wall heat and mass transfer, have been obtained and discussed for various physical parametric values.     

Optimization of the vane geometry

The use of nonstandard geometries like the vane is essential to measure the rheological characteristics of complex fluids such as non-Newtonian fluids or particle dispersions. For this geometry which is of Couette type, there is no analytical simple model defining the relation between the shear stress and the torque or relating the angular velocity to the shear rate. This study consists on calibrating a nonstandard vane geometry using a finite volume method with the Ansys Fluent software. The influence of geometrical parameters and rheological characteristics of the complex fluids are considered. First, the Newtonian fluid flow in a rotative vane geometry was simulated and a parametric model is derived therefrom. The results show an excellent agreement between the calculated torque and the measured one. They provide the possibility to define equivalent dimensions by reference to a standard geometry with concentric cylinders where the relationships between shear stress (resp. shear rate) and the torque (resp. the angular rotation) are classical. Non-Newtonian fluid flows obeying a power law rheology with different indices were then simulated. The results of these numerical simulations are in very good agreement with the preceding Newtonian-based model in some ranges of indices. The absolute difference still under 5 % provided the index is below 0.45. Finally, this study provides a calibration protocol in order to use nonstandard vane geometries with various heights, gaps, and distance to the cup bottom for measuring the rheology of complex fluids like shear thinning fluids and concentrated suspensions.     

Heat transfer to laminar flow of nongray gases through a circular tube

Analyses are presented for infrared radiative energy transfer in gases when other modes of energy transfer simultaneously occur. Fully developed laminar flow of an absorbing emitting gas in a circular tube is considered under the conditions of uniform wall heat flux. Nongray as well as gray formulations are presented, and results are obtained for illustrative cases. Appropriate limiting solutions of the governing equations are obtained and conduction-radiation interaction parameters are evaluated. The influence of variable wall emittance (gray and nongray) upon radiative energy transfer in nongray gases is investigated. In particular, nongray results are obtained, in the large path length limit, for the flow of CO₂ through stainless steel tubes of various compositions. Finally, a correlation is presented which can be utilized to extend all nongray results for the parallel plate geometry, already available in literature, to yield results for the corresponding case of a circular tube. This work was supported by the National Science Foundation through Grant No. GK-16755.