Joule-Thomson effects on turbulent graetz problem for gas flows in pipes with uniform wall temperature

The Joule-Thomson effect is known to be important in arctic gas pipelines. The Joule-Thomson effects on forced convective heat transfer in the thermal entrance region of pipes with uniform wall temperature are studied for steady fully developed turbulent gas flows by the Graetz method. Thermal entrance heat transfer results are presented for Prandtl number 0.72, Reynolds number 10⁵ and Brinkman number ± 0.1, ± 1.0 with Joule-Thomson parameter Jμ ranging from 0 to 1.0 to cover the possible range in practical applications. Bulk temperatures and Nusselt numbers are also presented for fully developed flow with Reynolds numbers from 5 × 10³ to 10⁶. For given Prandtl and Reynolds numbers, the asymptotic Nusselt number is found to be dependent on the Joule-Thomson parameter only and is independent of Brinkman number. The fully developed bulk temperature is a linear function of Brinkman number and a linear relationship exists between the bulk temperature parameter (-θ_bf/Br) and the Joule-Thomson parameter Jμ for given Prandtl and Reynolds numbers.     

Laminar mixed convection in the thermal entrance region of horizontal rectangular channels with uniform heat input axially and uniform wall temperature circumferentially

This paper presents a numerical study on laminar mixed convection in the thermal entrance region of horizontal rectangular channels with uniform heat input axially and uniform wall temperature circumferentially. A relatively novel numerical method of solution is developed to obtain the developing velocity and temperature fields. The values of Prandtl number are 0.7 and 7.2, corresponding to air and water, respectively. The values of Rayleigh number are 0, 10⁴, 3 × 10⁴ and 10⁵. The channel aspect ratios considered are 0.2, 0.5, 1, 2 and 5. Variations in local friction factor ratios and local Nusselt numbers are presented. It is found that the circumferential boundary condition of uniform wall temperature significantly increases the value of local Nusselt number as compared to that found in earlier works under the boundary condition of uniform wall heat flux. But the boundary condition effect on the friction factor is shown to be comparatively minor. The asymptotic solutions at z → are compared to the existing numerical data with good agreement.     

Mechanisms of heat and mass transfer during drying of mate (Ilex paraguariensis) twigs

Experimental results of surface temperature and moisture content of twigs of mate were obtained in a conveyor-belt dryer operated batchwise. The first response was determined with an infrared sensor, while the second was by conventional gravimetry. A set of 0.04-m-long cylindrical twigs classified manually into three different subgroups on the basis of their diameters (3.5 × 10^?3, 6.5 × 10^?3, and 10 × 10^?3 m) were used in the experiments. Drying always took place in a chamber fed with a thin single layer of material 0.5 m in length and 0.05 m wide. The fresh twigs without leaves at ambient temperature (≈27.2 ± 2.6°C) and with an initial moisture content close to 0.8 ± 0.1 were dried at three different average air temperatures (65.5, 80.2, and 83.8°C) for 7200 s. A full set of nine (3¹ × 3¹) drying experiments were performed by varying the examined factors (particle diameter and drying temperature) at three levels. The low estimated Biot numbers (<0.55) indicate that convection plays a much more important role than conduction in heat transfer. Because of this and since heating was much faster than drying, the Newton’s law of cooling alone was successfully applied to describe the increase of particle temperature with time. From a similar analysis involving a convective mass transfer coefficient calculated with the Chilton-Colburn analogy emerged high-mass-transfer Biot numbers (≈5.37 × 10³ ? 3.65 × 10⁵) that reveal drying of twigs is governed by diffusion. In fact, the equation that represents the Fick’s second law of diffusion in a long cylinder (one-dimensional transfer), solved analytically and coupled to the model of heat transfer, was able to describe the kinetics of drying of mate twigs.     

TURBULENT HEAT TRANSFER IN A CIRCULAR TUBE WITH VISCOUS DISSIPATION

Abstract

The problem of developed turbulent conveclive heat transfer with viscous dissipation is considered for flow in a circular tube. Two cases are considered, Prandtl number equal to unity and large Prandtl number. For Prandtl number equal to unity, an exact expression for the recovery factor is presented which accounts for the radial variation in velocity profile. This exact expression is evaluated using the turbulent logarithmic velocity distribution. For large Prandtl numbers, a general asymptotic expansion for the recovery factor is determined which includes both wall and core contributions. A comparison of these results suggests that the large Prandtl number formula found for the recovery factor should be accurate for all Prandtl numbers greater than about unity.     

Numerical prediction of wall mass transfer rates in turbulent flow through a 90° two-dimensional bend

The present paper reports a numerical study of mass transfer in a curved channel flow using a low Reynolds number k–ε model modified to include the influence of curvature on the turbulent transport. Predictions were obtained of flow through a 90° 2-D bend for Reynolds numbers of Re = 2 × 10⁴, 10⁵ and 10⁶, curvature ratio's of R_c/d = 1, 1.5 and 3, and Schmidt numbers of Sc = 500, 1 500 and 5 000. Based on the numerial simulations, the value of the mass transfer coefficient, k, was observed to generally decrease and increase along the inner and outer walls, respectively, compared to the value in a straight duct. The behaviour appears to be sensitive to both the curvature ratio and Reynolds number, being most pronounced for the case of tight bends and low Reynolds numbers.     

A model for velocity and eddy diffusivity distributions in fully turbulent pipe flow

A model was developed for the eddy diffusivity and mean velocity distributions in fully developed turbulent isothermal smooth pipe flow (4 × 10³ < Re < 5 × 10⁶). Reichardt's tworegion eddy diffusivity models were modified so as to fulfill the requirements that the eddy diffusivity be represented by a smooth, continuous curve, and vanish with the third power of the distance from the wall; the continuity equation be satisfied; and the ratio of the bulk velocity to centerline velocity agree with experimental data. The descripition is in excellent agreement with Laufer's experimental mean velocity data and, in general, provides a method of accurately predicting the mean velocity distribution.     

Some Characteristics of Stirred Vessel Flows of Dilute Polymer Solutions Powered by a Hyperboloid Impeller

Measurements of the power consumption and mean and turbulent velocities in the wall jet of a stirred vessel flow, powered by a hyperboloid impeller, were carried out. The fluids were aqueous solutions of tylose, CMC and xanthan gum (XG), at weight concentrations ranging from 0.1% to 0.6%, which exhibited varying degrees of shear‐thinning and viscoelasticity. The hyperboloid impeller parameter k of Metzner and Otto (1957) was found to be equal to 27.2 ±4. In the Reynolds number range of 10³ to 3 × 10⁴ the mixing power was reduced for all non‐Newtonian fluids, but never by more than 13%. The flows of the 0.2% CMC and 0.2% XG solutions were found to be less turbulent than those of water, especially for the latter fluid where a reduction in axial rms in excess of 50% was found in the wall jet. This was attributed to elasticity effects and especially to the high zero shear viscosity of the latter fluid.     

Particle cloud concentration profiles for a turbulent flat plate boundary layer

A model is presented that predicts spatial concentration of particles in a turbulent flat plate boundary layer. Them model solves the two-dimensional particle diffusion equation which describes the movement of aerosol without the influence of filed forces within a zero pressure gradient turbulent boundary layer under the assumtion of a constant average particle diffusivity through the layer. By using a value of D_p = 10^?3 cm²/sec, the numerical integration yields a wall value for the dimensionless cloud concentration of 1.7 × 10^?2versus 1.5 × 10^?2 for the value calculated from experimentally determined deposition results. This value of D_p is also substantiated heuristically and by comparison with values predicted by other models. The overall result is a universal cloud concentration profile for particles in a zero pressure gradient turbulent boundary layer allowing one to predict deposition from the cloud concentration existing at the surface.     

Experimental and numerical analysis of heat transfer including viscous dissipation in a scraped surface heat exchanger

Viscous dissipation plays an important role in the dynamics of fluids with strongly temperature-dependent viscosity because of the coupling between the energy and momentum equations. The heat generated by viscous friction causes a local temperature increase in the high shearing zone with a consequent decrease of the viscosity which may dramatically change the temperature and velocity distribution. These processes are mainly controlled by the Brinkman number, the rotating velocity and the thermal boundary conditions. This work analyses forced convection heat transfer including the viscous dissipation in a scraped surface heat exchanger (SSHE). In this study the increase of the temperature due to the viscous dissipation is analysed both experimentally and numerically for Newtonian and non-Newtonian fluids. Heat transfer simulations including viscous dissipation were carried out by means of the CFD code of the software Fluent, version 6.3, with solving momentum and energy equations. Two thermal boundary conditions were considered: pseudo-adiabatic wall and constant temperature on the stator wall exchange. In the case of Newtonian fluid (pure HV45), for both considered thermal boundary conditions, an important increase of the temperature was obtained. In the case of non-Newtonian shear thinning fluid (2 wt% CMC solution), viscous dissipation is neglected. The developed numerical model agrees well with experimental results. The validated numerical model was then used to study the effect of index and consistency behaviour of shear thinning fluid using power-law rheological behaviour on the viscous dissipation, and correlation using dimensionless analysis expressed with different dimensionless process numbers is proposed for Newtonian and non-Newtonian shear thinning fluid.     

A generalized approach to heat transfer in pipe flow with internal heat generation

In the last few years, there has been a renewed interest in the molten salt reactor (MSR), one of the “Generation IV International Forum” concepts, which adopts a circulating molten salt mixture as both heat generator (fuel) and coolant. The heat transfer of a fluid with internal heat generation depends on the strength of the source whose influence on the heat exchange process is significant enough to demand consideration. At present, few studies have been performed on the subject from either an experimental or a numerical point of view.This study considers fluids with a wide range of Reynolds numbers, flowing through smooth and straight circular tubes within which the flow is hydrodynamically developed but thermally developing (conditions of interest for MSR core channels). The study aims at an assessment of the heat transfer modelling for a large variety of fluids (with Prandtl numbers in the range 0≤Pr≤10⁴), in particular taking into account the influence of the internal heat generation on the temperature distribution, which plays an important role in the case of molten salts for nuclear reactors. To this purpose, the general and unified solution of the heat transfer equation is applied to the turbulent Graetz problem with boundary conditions of the third kind and arbitrary heat source distribution, incorporating recent formulations for turbulent flow and convection.Computed results are shown to be in a good agreement with experimental data concerning heat transfer evaluations for both fully developed and thermally developing flow conditions, over a large range of Prandtl numbers (10^?2<Pr<10⁴). Finally, a preliminary correlation, which includes the Prandtl number range of interest for molten salts, is proposed for the Nusselt number predictions in the case of simultaneous uniform wall heat flux and internal heat generation.     

稀疏气固两相湍流边界层拟序结构变动特性

应用PIV两相同时测量方法,对壁面Reynolds数为430的水平槽道稀疏气固两相湍流边界层拟序结构变动特性进行了研究。选取质量载荷为10^-4~10^-3的110 μm聚乙烯颗粒作为离散相。结果表明,低载荷颗粒仍能显著改变湍流拟序结构,进而影响宏观湍流属性。颗粒重力沉降形成的粗糙壁面增强了壁面附近湍流猝发行为,导致黏性底层中的气相法向脉动速度和雷诺剪切应力显著增大。颗粒与壁面的碰撞加强了低速流体上抛、削弱了高速流体下扫,同时增强了轨道交叉效应,从而抑制了湍流拟序结构发展,显著减小了黏性底层以上区域的法向脉动速度和雷诺剪切应力。此外,颗粒惯性还减小了黏性底层厚度、增大了流向速度梯度,导致气相流向脉动速度峰值增大,且其对应位置也更加靠近壁面。     

Effect of fluid motion on radiation-induced polymerization of ethylene in a tubular reactor

The influence of the turbulence of reactant on the radiation-induced polymerization of ethylene in 40 mole-% Freon-114 (C₂Cl₂F₄) was studied using a tubular reactor at 400 kg/cm² and 25°C with a dose rate of 1.3 × 10⁵ rad/hr. At constant linear velocity and tube diameter, the polymer concentration was shown to increase linearly with the reactor tube length. This indicates that the polymerization is in a stationary state. By changing the linear velocity from 3.5 to 42.7 cm/sec and the tube diameter from 5 to 14 mm, the space time yield and the molecular weight of polymer were found to vary between 0.21 and 0.46 mole ethylene/1.-hr and from 5.0×10³ to 10.5×10³, respectively. The space time yield and molecular weight decreased sharply to about one half those in the static polymerization with increasing fluid turbulence and then slowly increased in the highly turbulent state. Similar effects were observed in a tank reactor when the stirring speed was changed.     

Turbulent flow friction reduction effectiveness and hydrodynamic degradation of polysaccharides and synthetic polymers

Two water-soluble synthetic polymers and several polysaccharides were compared for friction reduction effectiveness during increased exposure to turbulent flow. Solutions were passed through a 0.117 × 41.0 cm fine bore tube at a constant solvent wall shear stress of 4200 dynes/cm² and wall shear rate of 4 × 10⁵ sec^?1. After one pass through the tube, greatest friction reduction at low polymer concentrations was in the order poly(ethylene oxide) > polyacrylamide > bacterial polysaccharide from Xanthomonas campestris > guar gum. As a result of mechanical degradation, after 40 passes of 40 ppm solutions, friction reduction effectiveness was in the order polyacrylamide > polysaccharide from Xanthomonas campestris > poly(ethylene oxide) > guar gum. Degradation curves, the effect of concentration on degradation, and boundary layer and pipe flow applications are discussed.     

Effect of vitrification pressure on radius of gyration,specific heat and density of amorphous polymers

The effects of vitrification pressure (to 500 MPa) and temperature (to 180°C) on the radius of gyration (as determined by small-angle neutron scattering), specific heat, and density were measured for polystyrene and poly(methyl methacrylate). The radius of gyration increased slightly (5 × 10^?3/°C) in both polymers; this increase is near the experimental uncertainty in the measurements. The small observed values are due to either small intrinsic effects of temperature or pressure on the conformation or competing effects of temperature and pressure. Density and specific heat showed changes which have been observed before and are attributed to intermolecular factors.     

Simultaneous heat and mass transfer through laminar boundary layers in combined forced and free convection

Heat and mass transfer rates from a vertical plate are reported for combined free and forced convection. Heat transfer coefficients were obtained from temperature gradients at the wall and mass transfer rates from thickness decrease measurements of naphthalene coatings. The free convection data cover a Grashof number range from 100 to 2 × 10⁸ and the combined flow parameters Gr/Re² and Gr'/Re² vary from 0.2 to 100 and 2 × 10^?8 to 3.25, respectively. Predictions from boundary layer solutions are in good agreement with the data. Absorption of ultraviolet light by naphthalene vapor was used to measure free convection concentration profiles. Results prove the versatility of this method.     

Superimposed effects in high‐shear‐rate capillary rheology of polystyrene melt

During micro‐injection molding, the polymer melt may undergo a shear rate up to 10⁶ s^?1, at which the rheological behaviors are obviously different from those in conventional molding process. Using both online and commercial rheometers, high‐shear‐rate capillary rheology of polystyrene (PS) melt is analyzed systematically in this work. The accurate end pressure drop and pressure coefficient of viscosity are determined via the enhanced exit pressure technique. Experimental and theoretical investigations are conducted on four significant effects, that is, the dissipative heating, end pressure loss, pressure dependence, and melt compressibility in capillary flow. For the PS melt, which exhibits distinct temperature and pressure dependence of viscosity, both dissipation and end effects become pronounced as the shear rate exceeds 2 × 10⁵ s^?1. From lower to higher shear rates (10³–10⁶ s^?1), the competition between dissipation and pressure effects results in the overestimation to underestimation of Bagley‐corrected pressure drop, and finally the comprehensively corrected viscosity becomes about half of the uncorrected one owing to the enhanced superimposed effects. Moreover, the compressibility shows a minor influence on the shear viscosity. Under the shear rate range investigated, the power‐law relationship is sufficient for describing the corrected viscosity curve of PS melt used. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Microstructure and permeability of porous YSZ ceramics fabricated by freeze casting of oil-in-water suspension

Porous yttria-stabilized zirconia (YSZ) ceramics are fabricated through freeze casting of oil-in-water suspension followed by sintering at 1250−1550 °C. The pore structure, compressive strength and permeability of porous YSZ ceramics are tailored via altering the emulsion content and sintering temperature. The samples obtained using higher emulsion content or at lower sintering temperature show larger Darcian and non-Darcian constants due to their higher open porosity and larger pore size. Furthermore, the investigation on individual contributions of viscous and inertial resistances on the total pressure drop during permeation process indicates that the viscous resistance increases but the inertial resistance decreases with increasing the emulsion content or decreasing the sintering temperature for samples. Porous YSZ ceramics obtained in this work with a k₁ range of 3.14 × 10⁻¹³–1.12 × 10⁻¹² m² are appropriate for applications in filters and membrane supports.     

Mixed conductivity of garnet phases based on gadolinium ferrite

Incorporation of Pr and Ca into the garnet lattice of Gd₃Fe₅O_12±δ was found to increase the electronic conductivity, and to decrease the thermal expansion coefficients and oxygen ion transference numbers. The ionic conductivity of Gd_2.2Pr_0.8Fe₅O_12±δ ceramics is similar to that of undoped gadolinium ferrite, whilst Gd_2.5Ca_0.5Fe₅O_12-δ exhibits slightly higher ionic transport, suggesting an enhanced vacancy contribution. The activation energies for ionic conduction in Gd₃Fe₅O₁₂-based materials vary in the narrow range 211–224 kJ/mol. Due to a significantly lower activation energy for the total conductivity (24–81 kJ/mol), the oxygen ion transference numbers in air increase with temperature, from 4 × 10⁻⁵ – 5×10⁻³. Steady-state oxygen permeation fluxes through dense garnet membranes are limited by bulk ambipolar conductivity. The thermal expansion coefficients of the ferrite ceramics (100–1000 °C) were found linear and in the range 10.36–10.86 × 10⁻⁶ K⁻¹.     

Dissociation et hydratation de nitrates alcalins dans le carbonate de propylene aqueux

Dissociation of lithium, sodium, potassium and tetraethylammonium nitrates and perchlorates in propylene carbonate has been studied by conductometry. Dissociation constants of alkali nitrates are 3·14 × 10^?3 (LiNO₃), 8·35 × 10^?3 (NaNO₃ and 1·92 × 10^?2 (KNO₃) at 25°C. The perchlorates and tetraethylammonium nitrate are strong electrolytes. The solubility products are 4·1 × 10^?4 (LiNO₃), 1·2 × 10^?5 (NaNO₃ and 2·5 × 10^?5 (KNO₃). The conductivity of saturated solutions of nitrates in the aqueous solvent has been determined up to 0·6 M water. Results are used to calculate the equilibrium constants for the reaction I^± + H₂O = I^± H₂O; Li⁺ 6·5, Na⁺ 2·5, K⁺ 0·5 and NO^?₃ 2·4. Dissociation constants, solubility products and hydration constants are compared with values reported for other solvents.     

Longitudinal gas dispersion in transitional and turbulent flow through a straight tube

Longitudinal dispersion data are reported for a straight tube (internal dia. 1¼′ (2.77 cm)). Three binary gas systems were examined over the regime 3 × 10² < Re < 10⁴ with special emphasis on the transition from laminar to turbulent flow. Effect of Schmidt number is studied in detail over the transition regime, and practical variation with Sc for the lower turbulent regime is compared with the predicted effect based on existing theories of turbulence. In the laminar regime results are reported which diverge from Taylor's theory at Re lower than the normally accepted value for the onset of turbulence.