Characterisation of flow and heat transfer patterns in low aspect ratio packed beds by a 3D network-of-voids model

Using an illustrative sphere packing assembly, it is demonstrated that flow structure and wall heat transfer patterns in low aspect ratio fixed bed reactors are more realistically modelled by properly accounting for the discrete void fraction variations. A 3D network-of-voids (NoV) model has been devised to characterise and examine the discrete flow and heat transfer phenomena in a low aspect ratio packed bed with d_t/d_p = 1.93. The model as formulated is deliberately designed to be not too complicated so as not to place severe demands on computational resources. Hence, the model can potentially easily be applied to simulate the typically large sets of tubes (often comprising more than 10,000) in the case of industrial multi-tubular reactors, where every tube is different due to the random insertion of the packing particles. Because of its simplicity, the model offers an opportunity of coupling the individual catalyst pellet level transport with the complex interstitial flows at the reactor scale. Illustrative studies of this NoV model on a random packed bed of spheres predict large variations of discrete in-void angular velocities and consequently wall heat transfer coefficients within a single tube. The wide variations of wall heat transfer coefficients imply that the different angular sections of the tube will transfer heat at radically different rates resulting in potentially large temperature differences in different segments of the tube. This may possibly result in local temperature runaway and/or hot spot development leading to several potentially unanticipated consequences for safety and integrity of the tube and hence the reactor. The NoV model predictions of the overall pressure drop behaviour are shown to be consistent with the quantitative and qualitative features of correlations available in the literature.     

Role of entropy generation during convective thermal processing in right-angled triangular enclosures with various wall heatings

Thermal energy conservation is at the heart of energy efficiency in process industries. This allows researchers to go for advances in CFD methods to track the requirement of thermal energy for various thermal processing applications. CFD models need to be incorporated into optimization principles to achieve efficient industrial process designs. In this study, entropy generation due to natural convection in right-angled triangular enclosures (cases 1–4) has been studied numerically for energy efficient processing of various fluids (Pr = 0.025, 7 and 1000). It is found that maximum value of entropy generation due to heat transfer (S_θ,max) occurs near the vertex of the enclosures for cases 1 and 3, near corner between left wall and bottom wall for case 2 and near lower portion of the right wall for case 4. On the other hand, maximum value of entropy generation due to fluid flow (S_ψ,max) is observed near middle portions of the side walls for all cases and the location of S_ψ,max mainly depends on the presence of high velocity gradients. The entropy generation rates and heat transfer rates were also shown for various angles. Triangular cavities with specific angles are recommended for various processing fluids.     

耦合表面张力的封闭腔体内管外自然对流传热特性

采用格子-玻尔兹曼方法（LBM）构建了考虑表面张力影响下封闭腔体内加热圆柱外自然对流数学模型。在分别对自然对流与表面张力模型模拟验证的基础上,探究了液固表面张力与重力场下浮升力同时作用下加热圆柱外流体自然对流的传热特性。结果表明,在给定Ra数下（10³≤Ra≤10⁶）,随着表面张力的增大（Oh数减小）,封闭腔体内管外自然对流扰动会加剧,流型会变复杂,壁面换热效率有明显提高。在Ra数为10⁵,长度比（加热圆柱半径和方腔长度之比）为1/10情况下,加入表面张力σ=0.076302N/mm（Oh=0.122）,腔体左侧壁面平均努塞尔数和加热圆柱壁面与未加表面张力相比分别提高了93.5%和60.35%。当表面张力大小和自然对流的浮升力相当时,此时的流场波动更加明显剧烈,在一定范围内增大浮升力反而减弱换热。     

Experimental investigation of flow resistance and convection heat transfer of CO2 at supercritical pressures in a vertical porous tube

Experiments were conducted to measure the convection heat transfer in a vertical porous tube with particle diameters of 0.2–0.28 mm at supercritical pressures. The local heat transfer coefficients, fluid bulk temperatures and wall temperatures were measured to investigate the influence of the inlet fluid temperature, pressure, heat flux and flow direction on the convection heat transfer in the porous tube. The measured friction factors in a heated tube are much larger than those predicted using the Aerov-Tojec correlation for both upward and downward flows. Therefore, two new correlations are presented for upward and for downward flows to predict the friction factors of supercritical pressure CO₂ in heated porous tubes. The experimental results also show that the inlet temperature, pressure and heat flux all significantly influence the convection heat transfer. When the inlet temperature (T₀) is higher than the pseudocritical temperature (T_pc), the local heat transfer coefficients are much less than those when the inlet temperature is lower than the pseudocritical temperature. The convection heat transfer coefficients are found to vary nonlinearly with heat flux. For T₀ < T_pc, the local heat transfer coefficients along the porous tube have a maximum for upward flow and have a peak value for downward flow when the local fluid bulk temperatures are near T_pc and the wall temperatures are slightly higher than T_pc. The different variations of the local heat transfer coefficients along the porous tube for upward and downward flows are attributed to the effect of buoyancy. However, when the wall temperatures are much higher than T_pc, the local heat transfer coefficients along the porous tube decrease continuously for both upward and downward flows.     

双周期温度边界下多孔介质方腔内自然对流传热数值模拟

采用局部非热平衡模型及方腔左右两侧壁面温度正弦波变化边界条件,数值分析了具有内热源多孔介质方腔内的稳态非达西自然对流传热。探讨了不同温度波动参数N及波动相位差τ对方腔内自然对流传热的影响。结果表明:方腔两侧壁面出现了周期性分布的温度场,随着N值的增加,方腔内流场及温度场分布逐渐趋向于壁面均一温度边界情况。壁面局部Nu沿着高度方向呈现周期性分布。相对于均一温度的边界条件而言,正弦波温度边界条件在一定程度上强化了多孔介质方腔内的整体传热过程,随着N值的增加,方腔处于温度波动边界时的散热值Q逐渐趋向于均一温度边界时的情况。     

密闭二维腔内水中热声波的数值模拟

以边长为1 mm密闭二维腔中的液态水为研究对象,用数值计算的方法,通过在左侧边界施加阶跃温度或阶跃热流来产生热声效应。分析水中热声波的产生与传播特性,并研究右侧边界中点产生的热通量的强度。计算结果表明,在相同的热边界和几何边界条件下,液态水中热声效应引起的压力波幅值和热通量远大于空气;当加热阶跃温度不同时,水中产生的压力波幅值和热通量随温度升高而急剧增大;当阶跃热流加热时,压力波和热通量与阶跃温度加热时的有较大差异。     

Heat transfer in a swirling fluidized bed with geldart type-D particles

A relatively new variant in fluidized bed technology, designated as the swirling fluidized bed (SFB), was investigated for its heat transfer characteristics when operating with Geldart type D particles. Unlike conventional fluidized beds, the SFB imparts secondary swirling motion to the bed to enhance lateral mixing. Despite its excellent hydrodynamics, its heat transfer characteristics have not been reported in the published literature. Hence, two different sizes of spherical PVC particles (2.61 mm and 3.65 mm) with the presence of a center body in the bed have been studied at different velocities of the fluidizing gas. The wall-to-bed heat transfer coefficients were measured by affixing a thin constantan foil heater on the bed wall. Thermocouples located at different heights on the foil show a decrease in the wall heat transfer coefficient with bed height. It was seen that only a discrete particle model which accounts for the conduction between the particle and the heat transfer surface and the gas-convective augmentation can adequately represent the mechanism of heat transfer in the swirling fluidized bed.     

Effect of laminar flow on the rate of mass transfer inside cubical cavities

An electrochemical technique which involved measuring the limiting current of the cathodic reduction of potassium ferricyanide was used to study the rate of mass transfer inside a cubical cavity machined in the wall of a vertical rectangular duct. Variables studied were side length, physical properties of the solution and flow rate of the solution. The mass transfer coefficient was found to decrease with increasing cavity size; in all cases, the mass transfer coefficient inside the cavity was less than that at the duct wall. Mass transfer data inside the cavity were correlated by the equation Sh_c = 0.525 (Sc Re d_e/L)^0.33. Comparison of the present results with the results obtained using other cavity geometries shows that cavity geometry plays an important role in determining the rate of mass transfer inside the cavity.     

Preparation and properties of waterborne poly(urethane acrylate)/silica dispersions and hybrid composites

Abstract

Simulations of the isothermal and non-isothermal filling of a rectangular cavity were carried out for polystyrene using a Giesekus viscoelastic constitutive equation, whereby in the non-isothermal case the thermal resistance at the mould wall was modelled with different heat transfer coefficients to investigate the effect of the thermal resistance on the development of the molecular orientation. Results for stress development along the flow front and the cold wall were compared showing that the principal stress differences in the middle of the flow front are lower than those at the mould wall. In case of the non-isothermal filling, the latter one will increase further while the melt is gradually cooling down, which is especially true if the thermal resistance at the mould wall has been properly considered. Consequently, the high molecular orientation at the wall seems to be rather a result of the non-isothermal shear flow than of the extension at the advancing front as usually assumed.     

Natural convection in a heat generating fluid bounded by two horizontal concentric cylinders

Convective flow and heat transfer of a Boussinesq fluid contained between two horizontal concentric cylinders is investigated under the effects of two driving mechanisms – an externally-imposed temperature gradient across the annulus, and a uniform internal heat generation. Numerical results for flow field and temperature distribution are obtained in terms of four dimensionless parameters, namely the radius ratio, R, the Prandtl number, Pr, the Rayleigh number, Ra*, and the ratio, S, between the characteristic temperature induced by internal heating and the applied temperature difference between the boundaries. Depending on the value of S, the flow pattern is made up of either one or two vortices in each half cavity, and heat is transferred into or out of the cavity through the hot wall. In particular, for a certain value of the applied temperature difference, the hot wall apparently acts as a thermally-insulated boundary, the internal heat is completely lost through the cold wall, and the fluid undergoes a transition from a bicellular to a unicellular flow regime.     

Pool boiling of water-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> and water-Cu nanofluids on horizontal smooth tubes

Experimental investigation of heat transfer during pool boiling of two nanofluids, i.e., water-Al₂O₃ and water-Cu has been carried out. Nanoparticles were tested at the concentration of 0.01%, 0.1%, and 1% by weight. The horizontal smooth copper and stainless steel tubes having 10 mm OD and 0.6 mm wall thickness formed test heater. The experiments have been performed to establish the influence of nanofluids concentration as well as tube surface material on heat transfer characteristics at atmospheric pressure. The results indicate that independent of concentration nanoparticle material (Al₂O₃ and Cu) has almost no influence on heat transfer coefficient while boiling of water-Al₂O₃ or water-Cu nanofluids on smooth copper tube. It seems that heater material did not affect the boiling heat transfer in 0.1 wt.% water-Cu nanofluid, nevertheless independent of concentration, distinctly higher heat transfer coefficient was recorded for stainless steel tube than for copper tube for the same heat flux density.     

Laminar film boiling on a porous vertical wall with uniform suction velocity

Laminar free convection film boiling on a porous vertical wall with uniform suction or blowing is analysed using boundary layer theory. The solutions are obtained assuming suction or blowing to be a disturbance superposed on the isothermal, impermeable wall case. Using a parameter involving the suction or blowing velocity, universal functions are derived for various values of Prandtl Number and c_p(T_w — T_sat)/h_fgPr. These universal functions can be used to estimate the heat transfer rate in the presence of suction or blowing. As expected, suction increases the heat transfer rate while blowing decreases the heat-transfer. Even small velocities of suction or blowing could significantly affect the heat transfer. It is also found that the effects of suction or blowing are more pronounced at lower wall superheats.     

A novel and simple jet-stirred reactor for homogeneous and heterogeneous reactions with short residence times

A novel and simple cylindrical jet-stirred reactor with short residence times (about one second) is described. Stirring is achieved by means of four turbulent jets issuing from nozzles. Perfect macromixing has been checked for space times between 0.5 and 4 s in the empty reactor and from 0.5 to 1.5 s in the reactor packed with glass rods. Heat transfer at the wall of both the empty and packed reactors has been studied in the perfect mixing range. For instance, the following correlation was obtained for the empty reactor:Nu = 12 + 0.0460 Re_Nozzle Pr^?1.5.This device was found to be a much better heat exchanger than an empty tube reactor with the same diameter and at the same flowrate. Finally, ten individually jet-stirred cells have been connected in series, allowing plug flow to be approached. Thanks to the high heat transfer rate at the wall, it was shown by computer simulations that the well-known “hot spot” problem could be avoided in the jet-stirred cascade if exothermic reactions were carried out in both empty and packed jet-stirred reactors.     

A numerical study of supercritical forced convective heat transfer of n-heptane inside a horizontal miniature tube

Supercritical convective heat transfer of hydrocarbon propellants plays a key role in the regenerative cooling technology development in aerospace applications. In this paper, a numerical study of the supercritical forced convective heat transfer of a typical hydrocarbon fuel, n-heptane, has been conducted based on a complete set of conservation equations of mass, momentum, and energy with accurate evaluations of the thermophysical properties. The present fundamental numerical study focuses on the effects of many key parameters, including the inlet pressure, inlet velocity, wall heat flux, and the inlet fluid temperature, on the supercritical heat transfer processes. Results indicate that under supercritical heat transfer processes, heat transfer deterioration could occur once the wall temperature or the fluid temperature in a large near-wall region reaches the pseudo-critical temperature, and increasing the fluid pressure would enhance heat transfer. The conventional empirical Gnielinski expression could only be used for supercritical heat transfer predictions of n-heptane under very limited operational conditions. It is found in the present numerical study that a supercritical heat transfer expression for CO₂, H₂O, and HCFC-22 applications can generally be employed for predicting the supercritical heat transfer coefficient of n-heptane when the inlet velocity is higher than 10 m/s.     

Laminar heat transfer in the thermal entrance region

Series solutions for heat transfer in the thermal entrance region are presented for laminar flow in conduits (plane ducts, tubes, annular passages). The present solution of the equation of energy has been obtained for either a step change in heat flux or wall temperature and is valid for all time-independent non-Newtonian fluids, providing that the flow-field is such that v_θ = 0, v_r = 0, v_g = v_g(r) From its general nature with regard to the flow-field, such a solution is a convenient alternative to the eigenvalue solutions when applied in the thermal entrance region where a large number of eigenvalues and eigencoefficients are required.     

Characteristics of the boundary layer with hydrogen combustion with variations of thermal conditions on a permeable wall

The paper describes a numerical study of the influence of thermal and boundary conditions on the structure of laminar and turbulent diffusion flames in the cases with hydrogen injection through a porous surface and with hydrogen combustion in an air flow. Two types of boundary conditions are compared: with a given constant temperature T _w = const over the length of the porous surface for arbitrary intensities of fuel injection and with a constant temperature T′ = const of the fuel injected through the porous wall. The first case occurs during combustion of a liquid fuel whose burning surface temperature remains unchanged. Injection of gaseous fuel usually leads to the second case with T′ = const. Despite significant differences in velocity and temperature profiles, the skin friction coefficients in the laminar flow are close to each other in these two regimes. In the turbulent regime, the effect of the thermal boundary conditions on friction and heat transfer is more pronounced. Moreover, the heat flux to the wall as a function of fuel-injection intensity is characterized by a clearly expressed maximum. A principal difference of the effect of combustion on friction and heat transfer in the laminar and turbulent flow regimes is demonstrated. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 3, pp. 3–11, May–June, 2009.     

满液式蒸发器中螺旋扁管的池沸腾传热

对螺旋扁管在满液式蒸发器中的池沸腾传热进行了实验研究。螺旋扁管由外径为15.88 mm的圆形满蒸管加工而得,其外径、壁厚以及长度分别为19.50 mm×11.28 mm、1.09 mm和3310 mm。通过实验研究了管程Reynolds数Re_i、制冷剂饱和温度T_sat、管壁过热度T_sup以及热通量q_b对于池沸腾传热性能的影响。结果表明,随着Re_i、T_sat和q_b的增加,螺旋扁管满液式蒸发器以及原有满液式蒸发器的沸腾传热性能都随之增强,而随着T_sup的增加,两者的沸腾传热性能却呈下降趋势。同时,对装有两种满液式蒸发器的螺杆式冷水机组分别进行了测试,结果表明在换热量相同的条件下,螺旋扁管满液式蒸发器比原有蒸发器的总传热系数提高了15%左右,证明螺旋扁管满液式蒸发器在螺杆式冷水机组中的应用是可行的。     

Effects of anisotropic scattering of radiation in laminar forced convection in a parallel-plate duct

Effects of anisotropic scattering to heat transfer in hydrodynamically-developed, thermally-developing steady laminar forced flow of a gray fluid between two infinite parallel plates are investigated for the case when the inlet temperature of the fluid is less than the wall temperature. An implicit finite difference scheme is applied to solve the energy equation, while the high order P_N method is used to solve the radiation part of this problem. The effects of the anisotropy, the conduction-to-radiation parameter, the optical thickness, the reflectivity of the plates and the inlet temperature on the local Nusselt number are studied.     

A model to predict fire resistance of non‐load bearing wood‐stud walls

The author has developed a series of computer models to predict the fire resistance of wood‐framed walls and floors. The models utilize two‐dimensional heat‐conduction equations and thermo‐physical property data to describe heat transfer through the assemblies. The model for wall assemblies WALL2D, the basic version of the wall model, has already been published in Fire and Materials. Recently, WALL2D has been extended to WALL2DN to analyse heat transfer through insulated walls and walls that experience openings at the joints between adjacent sheets of gypsum board. Since gypsum board shrinks at high temperatures, the joints between adjacent sheets of gypsum board open. Hot fire gases, thereby, enter the openings and heat the edge of the gypsum board and wood studs. The new model WALL2DN simulates the joint opening and describes the resultant effect of openings. The model also calculates heat transfer through insulation in the stud cavity and depicts the effect of insulation on the fire resistance of non‐load bearing wall assemblies. Insulation selected in WALL2DN is glass‐fibre insulation, rock‐fibre insulation, polystyrene foam and polyurethane foam. When walls are exposed to fire, the insulation in the cavity shrinks (and/or melts) and an empty space appears at the interface between insulation and gypsum board. The model simulates this shrinking behaviour of insulation in the cavity. Finally, the model was validated by comparing the predicted results to those from full‐scale standard fire‐endurance tests. Copyright © 2003 John Wiley & Sons, Ltd.     

A mathematical model for the dehydrogenation of methylcyclohexane in a packed bed reactor

A model for the dehydrogenation of methylcyclohexane in a tubular reactor over an industrial catalyst Pt-Sn/Al₂O₃ has been established. This model takes into account the axial dispersion at the inlet of the catalytic bed reactor as well as the heat transfer at the wall of the reactor. The heat transfer at the wall is satisfactorily represented by using a heat transfer coefficient correlation for which the parameters are obtained by fitting to the experimental data. The model provides a good representation of the radial and axial temperature profiles in the packed bed and can be also used to calculate the conversion.