FREE CONVECTIVE DRAFT INDUCED BY THERMAL AND CONCENTRATION GRADIENTS INSIDE AN ISOTHERMAL,VERTICAL CYLINDER†

Laminar, free convective flow through a vertical cylinder induced by the thermal and concentration buoyancy forces is investigated. The numerical studies involve development of a steady-state, two-dimensional heat and mass transfer model for the moist air core of the vertical tube. The stream function-vorticity method is employed to simplify the governing, coupled conservation equations which were then numerically solved by the successive over-relaxation (SOR) and alternating direction implicit ((ADI) methods.

A graphical correlation was found between dimensionless flow rate and dimensionless tube length as a function of the buoyancy force ratio N = Gr/Grc. Excellent agreement was obtained for the dimensionless flow rale results with those of Davis and Perona¹⁶ and Kageyama and Izumi¹³ for the case when only the-thermal buoyancy force is considered.

The combined buoyancy force from thermal and species diffusion provides larger local Nusselt Nu and local Sherwood Sh numbers relative to the case when just one buoyancy force is accounted for. Both local Nu and local Sh are seen to asymptotically approach a constant value as flow develops.     

CONJUGATE HEAT TRANSFER WITH TURBULENT FLOW IN A CIRCULAR TUBE

A steady heat transfer problem has been analyzed as a conjugate problem with turbulent flow in a circular tube. The three kinds of thermal boundary conditions considered here are specified as constant temperature, constant heat flux and constant heat transfer coefficient at the outer surface of the wall.

From the results of numerical calculation for Prandtl numbers in the range 0.01 ≤ Pr ≤ 10 and for Reynolds numbers in the range 10⁴ ≤ Re ≤ 10⁵, it was confirmed that the dimensionless parameter R_c could have significant effects on the heat transfer and the temperature field in the fluid adjacent to the wall.     

高热流低流速条件下超临界CO2在小圆管内的对流传热特性

为获取高热流、低流速条件下超临界CO₂的传热规律，开展了超临界CO₂在内径2 mm水平小圆管内对流传热试验研究，并重点探讨了变物性、浮升力和热加速等效应对传热过程的影响。试验参数范围：系统压力7.6~8.4 MPa，质量流速400~500 kg/(m²?s)，热通量0~200 kW/m²，流体温度20~60℃，Reynolds数1.2×10⁴~4.3×10⁴。分别采用Gr/Re ²和Kv作为浮升力效应和热加速效应的判别因子。结果显示，在高热流低流速工况下，浮升力效应显著（Gr/Re ² > 10^-3），同一个截面处的上壁面传热系数始终小于下壁面传热系数。浮升力效应是高热流低流速工况下传热恶化的主要诱发因素。试验中热加速因子较小（Kv < 8.5×10^-7），其效应可以忽略。将试验数据与典型的传热经验关联式作对比，结果表明Liao-Zhao关联式的计算结果与试验结果最吻合。     

A NUMERICAL STUDY OF FLUID FLOW AND HEAT/MASS TRANSFER OVER A STACK OF PLANKS

Heat/mass transfer by air flow over a sample stack of planks is studied numerically. For the simulations, the low Re k-epsilon turbulence model and bounded QUICK scheme are used. The calculated Nusselt numbers are in good agreement with the experimental data

The results of our study show that the low Re turbulence models have advantages over the conventional high Re models for this type of industrial application. This is mainly due to the small height of separation bubbles resulting from the selected large blockage ratios (more than 50 percent) occurring in such flows

Numerical simulations were carried out to study the effect of the vertical air gap due to shrinkage and non uniform sawing as well as the non uniformity in the height of boards on the flow field and heat/mass transfer characteristics. The results show that the selected gap size significantly affects the local and average Nu numbers across the stack. We have suggested optimum gap sizes for maximum heat/mass for different flow velocities (Re numbers).     

A GENERALIZED BUBBLE RISE VELOCITY CORRELATION

A generalized bubble rise velocity correlation is developed to cover the range of conditions:

liquid-phase density = 45.1 to 74.7 lb/ft³,

liquid-phase viscosity = 0.233 to 59 cP., and

interfacial tension = 15 to 72 dynes/cm

The gas-phase is air and the bubble size ranged from 1.2 to 15 mm. The developed correlation is based upon new dimensionless groups which contain the parameters affecting bubble rise velocity as well as their interaction, The correlation is independent of flow regimes and applicable for Reynolds numbers from 0.1 to 10⁴. It is in good agreement with work appearing in the literature.     

并联双通道内超临界水的脉动传热特性

在压力26~30 MPa,时均质量流速420 kg·m^-2·s^-1、热通量0~130 kW·m^-2工况范围内,对垂直上升并联双通道内超临界水的脉动传热特性进行了实验研究。根据实验数据分析了流量脉动对壁温的影响,脉动振幅率(A_f)和脉动频率数（Wo）对时均Nusselt数的影响,并将脉动时均Nu与超临界传热关联式进行了比较。结果表明：壁温随流量脉动而波动,脉动周期相同,相位相反,流量脉动振幅越大,壁温波动也越大;低频脉动时均Nu随脉动振幅率的增大逐渐减小,随脉动频率数的增大先减小后基本不变;高频脉动时均Nu随脉动振幅率的增大而缓慢增大,随脉动频率数的增大而减小;关联式预测的Nu较实验值普遍偏高。     

THERMAL CONDUCTIVITY OF GASEOUS AMMONIA IN THE TEMPERATURE RANGE 358-925 K.

Thermal conductivity of research grade pure ammonia gas has been measured by the column method at pressures of 12.9, 26.5, and 45.0 kN/m² over the temperature range 358 to 925 K. The maximum probable error of measurement is 1.5% at 874 K and it increases in magnitude as the temperature decreases. At 405 K, it is about 4.8%. The experimental data are correlated by the following cubic polynomial in temperature:

k(T)=5.237× 10^-3 + 5.179 × 10^-4 T + 8.404 × 10^-7 T² + 1.557 × 10^-10 T³.

Here k is in mW/cm-K and T is in K.

The experimental values are compared with three kinetic theory expressions for thermal conductivity of polyatomic gases in conjunction with the Stockmayer (12-6-3) potential. It is concluded that none of the theories can accurately predict the thermal conductivity of ammonia and probably of polar gases in general. The diffusion coefficient characterizing the transport of vibrational energy is computed as a function of temperature and on the basis of experimental data and the theory due to Ahtye. It has been long known that the transfer of energy by polyatomic and polar molecules is quite complex because of the presence of internal degrees of freedom and the possibility of resonant energy transfer in the latter (Hirschfelder, Curtiss and Bird, 1964).     

SURFACE TENSION AND BUOYANCY DRIVEN INSTABILITIES IN A LAYER OF LIQUID TIN HEATED FROM BELOW

The linear theory of Pearson (1958) and Nield (1964) is modified here to study liquid tin and include the finite thermal resistances of the bounding layers of boron nitride, copper and air (∼10^-2 torr) in the experiments of Ginde et al. (1989). The magnitude of the ΔT_c across the layer of liquid tin required for the onset of convection depends on the ratios of the thermal conductivities and thicknesses of the supporting layers of boron nitride and copper to those of the tin.

According to our theory surface tension contributes more than buoyancy to the instability observed experimentally. The critical ΔT_c observed required for the onset of convection in the layer of tin, is up to 25% lower than that predicted, which shows the layer is less stable than the theory indicates. Thus the surface of the tin was uncontaminated, or a significantly larger observed critical ΔT_c would be expected.

The boundary condition on the thermal fluctuations at the base of the supporting layer of copper does not appear to be important in these experiments. However, the thermal resistance of the boron nitride would have to be assumed to be unrealistically large to obtain agreement within experimental error with the theory.     

螺旋缠绕波节管传热与流动性能分析

以水为工质,对螺旋缠绕波节管湍流状态下传热与流阻性能进行数值计算,分析了其强化换热的机理,并分析了波节深度H与波节间距P对其传热与流动阻力的影响。结果表明:相同工况下,螺旋缠绕波节管的综合换热性能优于螺旋缠绕光管;流体在管内做螺旋运动,由于离心力的作用,在垂直流体主流方向上产生二次流;管横截面周期性的扩张与收缩,使流体在波节内产生沿流体主流方向上的回流,它们对流体边界层产生很强的破坏作用,使湍流程度增强,对换热有较好的强化作用;随着波节深度H的增大,Nu提高,f增大,综合传热性能逐渐提高;随着波节间距P的减小,Nu提高,f降低,综合传热性能逐渐提高。     

FLOW OF A SUSPENSION THROUGH A VERTICAL TUBE

Jiang el at. (1986) have developed the local volume averages of the equations of motion as well as the appropriate boundary conditions for a flowing suspension of non-neutrally buoyant, uniform spheres in an incompressible Newtonian fluid under conditions such that inertial effects can be neglected. Neither the equations nor the boundary conditions involve any free or undetermined parameters.

These local volume-averaged equations of motion have been solved for flow through a vertical tube and the results compared with available measurements of velocity profiles and of apparent viscosities. The predictions of measured apparent viscosities are in error by no more than 3%, when the volume fraction of solids is less than 0.20. The errors in representing the velocity profiles are comparable, but based upon fewer data.     

STEAM CONDENSATION IN A VERTICAL CORRUGATED DUCT

An experimental investigation was made on the condensation of water steam in a vertical corrugated duct. The data have been correlated as follows

Co=5.11Re^-0.431 150 ≤ Re ≤ 350 Co = 0.034311Re^-0.425350 ≤Re ≤l000

The vertical corrugated duct is constructed of two corrugated plates with corrugation inclination angles of β = 0 and β = 45° respectively (relative to the overall flow direction).

The condensation heat transfer coefficient in the corrugated duct is more than two times higher than that of bulk condensation on a vertical plate. A physical model was proposed to explain the heat transfer enhancement. Attention was also paid to the effect of exit steam velocity on the heat transfer during partial condensation. It was demonstrated that the heat transfer in the corrugated duct was strongly affected even at a low exit velocity, which was different from the case of bulk condensation on a vertical plate. Experimental apparatuses and the method for examining their reliability are described in detail.     

HYDRODYNAMIC CHROMATOGRAPHY: THREE DIMENSIONAL LAMINAR DISPERSION IN RECTANGULAR CONDUITS WITH TRANSVERSE FLOW

Experimental observations^1,9 indicate much poorer separations than are predicted by two dimensional theory. The purpose of this work is to explain these differences and suggest ways in which system performance can be improved.

The large effect of span-wise variation in axial velocity caused by side walls on hydrodynamic separations carried out in rectangular conduits with transverse flow is studied theoretically. As the aspect ratio increases, the steady stale retentivity (convection coefficient) approaches an asymptotic value obtained by neglecting side wall effects. However, the dispersion coefficient does not reduce to that for a flow with no side walls. Indeed, the asymptotic steady state dispersion coefficient is at least six times larger than that obtained by two dimensional theory which neglects side wall effects. As the transverse Peclet number increases, the effect of side walls on the dispersion coefficient becomes much larger.

The present three dimensional theoretical predictions, in contrast to two dimensional ones, are in good agreement with the experimental data of Caldwell, et al.⁹ and Kesner, et al.¹ on electrical field flow fractionation. The results indicate that side wall effects may be of major importance in hydrodynamic chromatography even when the aspect ratio is 70 or more.

The adverse effect of side walls may be avoided by having the membranes enclose thin annular regions rather than rectangular conduits. This should improve performance significantly.     

微通道内超临界氮气三维热流场实验与数值模拟

利用实验与数值模拟相结合的方法研究了超临界氮气（SCN₂）三维热流场特性,在用实验数据验证数值方法可靠性基础上,分析了压力（3.6~7 MPa）和质量流速［800~1200 kg/（m²?s）］对SCN₂对流传热特性的影响,揭示了微通道圆管不同圆周方向上SCN₂热流场规律。结果表明：在低压力和高质量流速下,同一轴向位置处,径向内壁温最大值出现在圆管90°处;质量流速越大,内壁温最大值和对流传热系数最小值由圆管180°向90°处发生了转移;当浮升力系数Gr*/Re²>1时,浮升力有利于强化圆管底部区域流体传热能力;基于获得的数据,提出了一个新的适合预测微通道圆管内SCN₂对流传热特性的无量纲换热关联式,预测误差小于20%。研究结果为微通道换热器优化设计提供了参考。     

超临界压力下航空煤油传热恶化的分析与预测

对竖直上升圆管内超临界压力航空煤油的传热恶化进行了实验研究。考察了浮升力和热加速对换热的影响机制,通过判别准则的适用性分析,选取能较好描述传热恶化的因子组,修正得到了合理的临界值,从而获得了适用于航空煤油的判别准则。基于可控参数建立了传热恶化临界热通量预测公式。阐述了传热恶化引发热声流动不稳定的过程。通过浮升力因子和热加速因子修正建立了换热关联式。结果表明：浮升力因子Bu和热加速因子Ac分别高于1.57×10^-5和4.92×10^-6时,两者将削弱边界层内剪切力,引发传热恶化现象。拟沸腾也是传热恶化和热声流动不稳定的诱因。     

内插不同形状涡产生器管内层流流动与传热特性的对比分析

内插扰流元件是一种可操作性强的管内强化传热方式,其强化传热机理主要是在管内诱导产生了二次流。在均匀壁温热边界条件下,对内插不同形状涡产生器管内层流流动与传热特性进行了数值分析。研究发现：在扭带基础上裁去部分面积相同的条件下,管内插等腰梯形涡产生器的换热能力最强,直角梯形涡产生器次之,矩形涡产生器的换热能力最差,管壁上的局部Nusselt数的峰值所在圆周位置及其大小与涡产生器形状有关,而不同形状的涡产生器对管内流动的阻力系数影响较小。插入涡产生器后,管内二次流强度参数Se和平均Nusselt数Nu均随Reynolds数Re的增大而增大,二者随Reynolds数Re的变化规律具有一致性。平均Nusselt数Nu与二次流强度参数Se呈幂函数相关,内插涡产生器管内的二次流强度决定了其对流换热强度。     

RIBBING INSTABILITY OF A TWO-ROLL COATER: NEWTONIAN FLUIDS

Data are presented for the critical conditions at which the ribbing instability appears on the surface of a Newtonian liquid film emerging from the nip between two rotating rolls. Data are obtained over two decades in Capillary number (Ca = μU/σ) for values of H₀/R in the range 3 × 10^-3 to 5 × 10^-2. The critical Capillary number is found to be given by the expression

$

Data are compared to the predictions that follow from a theory due to Savage, and agreement is found to be poor.     

圆管束中导流器对其自然对流换热的影响

对无限大空间中5根同规格圆管组成的圆管束在管间放置导流器的自然对流换热进行了数值模拟研究。考虑了Ra在10³～10⁴范围内,导流器偏转角为0°～60°,圆管间距为2～4倍圆管直径的自然对流换热,分析了5根圆管的局部Nusselt数（Nu_loc）和平均Nusselt数（Nu_ave）。研究结果表明,导流器对管束结构的自然对流换热影响体现在两方面：一是对导流器下方圆管而言相当于障碍物削弱其换热,二是对导流器上方圆管而言隔绝了下方羽状流的影响,从而增强系统的整体换热。在圆管间距较大时,与无导流器的圆管束相比,C1～C4各圆管换热下降趋势明显放缓,并且从C4、C5圆管换热趋势上升,系统整体换热增强。圆管间距S=2D,Ra=10³,导流器主要起障碍物的作用,削弱C1～C4各圆管换热,导致系统整体换热下降。当导流器偏转角度为45°时系统换热达到最大值,较无导流器时换热最多有着21%的提升。     

ACETIC ACID AS AN OXYGEN CARRIER BETWEEN TWO PHASES FOR EPOXIDATION OF OLEIC ACID

Acetic acid was found to be an effective oxygen carrier for epoxidation of oleic acid. The reaction model of oleic acid epoxidation in the two-phase reaction system was systematically analyzed and the rate determining step was experimentally identified.

The results indicated that the rate of oxidation of the unsaturated acid was independent of the concentration of oleic acid and depended on the mixing rate and the rate of formation peracetic acid which in turn depended on the concentration of acetic acid, strength of acid catalyst and the oxygen source, hydrogen peroxide. In the region of reaction control, the rate equation of epoxidation was found to be

$

where k = 2.98 × 10^-2 M^-2 min^-1 at temperature of 35^°C.     

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。     

半周加热横纹管内熔盐强化传热特性

半周加热太阳能吸热器管给管内对流传热系数带来影响,基于此,建立半周加热横纹管内熔盐对流传热的实验台和数值计算模型,分析横纹管槽宽、槽深对管内熔盐传热性能的影响规律,结果表明：从横纹管绝热侧到加热侧,周向管内壁温度逐渐升高,周向管内局部Nusselt数先减小后缓慢增大至稳定。横纹管凹槽处轴向管内壁温度明显低于平滑段,凹槽处轴向管内局部Nu较大,凹槽后与平滑段交界处管内局部Nu最小。横纹管槽越宽,加热侧轴向管内局部Nu越小,管内平均Nu越小,传热综合性能评价因子PEC越大。横纹管槽越深,轴向管内局部Nu越大,管内平均Nu越大,传热强化倍数Nu/Nu _ST越大。槽宽对横纹管PEC的影响比槽深明显,槽深对横纹管内Nu/Nu _ST影响比槽宽大。通过线性拟合得到半周加热横纹管内熔盐传热Nu的关联式,其计算Nu与模拟值最大偏差在±7%以内。