外文翻译--冷凝器和蒸发器的热力设计 制定和应用.docx

附录B：参考英文文献及译文Thermodynamic design of condensers and evaporators:Formulation and applicationsChristian J.L. Hermesa b s t r a c t This paper assesses the therm-hydraulic design approach introduced in a previous publication (Hermes, 2012) for condensers and evaporators aimed at minimum entropy generation. An algebraic model which expresses the dimensionless rate of entropy generation as a function of the number of transfer units, the uid properties, the thermal-hydrauliccharacteristics, and the operating conditions is derived. Case studies are carried out with different heat exchanger congurgitations for small-capacity refrigeration applications. The theoretical analysis led to the conclusion that a high effectiveness heat exchanger does not necessarily provide the best thermal-hydraulic design for condenser and evaporator coils, when the rates of entropy generation due to heat transfer and uid friction are of the sameorder of magnitude. The analysis also indicated that a high aspect ratio heat exchanger produces a lower amount of entropy than a low aspect ratio one.Conception thermodynamic condenser et desse evaporate: formulation et applications.Keywords: floating head;heat exchanger;design;industry1. Introduction Condensers and evaporators are heat exchangers with fairly uniformwall temperature employed in a wide range of HVACR products, spanning from household to industrial applications. In general, they are designed aiming at accomplishing a certain heat transfer duty at the penalty of pumping power.There are two well-established methods available for the thermal heat exchanger design, the log-mean temperature difference (LMTD) and the effectiveness/number of transfer units (-NTU) approach (Kakac and Liu, 2002; Shah andSiliculose, 2003). The second has been preferred to the former for the sake of compact heat exchanger design as the effectiveness (), dened as the ratio between the actual heattransfer rate and the maximum amount that can be transferred, provides a 1st-law criterion to rank the heat exchanger.performance, whereas the number of transfer units (NTU) compares the thermal size of the heat exchanger with its capacity of heating or cooling fluid. Furthermore, the -NTU approach avoids the cumbersome iterative solution required by the LMTD for outlet temperature calculations.Nonetheless, neither -NTU or LMTD approaches are suitable to address the heat transfer/pumping power trade-off,which is the crux for a balanced heat exchanger design. For this purpose, Bajan (1987) established the so-called thermodynamic design method, later renamed as entropy generation minimization method (Bajan, 1996), which balances the thermodynamic irreversibilities due to the heat transfer with a nite temperature difference to those associated with the viscous uid ow, thus providing a 2nd-law criterion that has been widely used for the sake of heat exchanger design and optimization (San and Jan, 2000; Leprous et al., 2005; Achaean and Wongwises, 2008; Mishap et al., 2009; Kotcioglu et al.,2010; Pussoli et al., 2012; Hermes et al., 2012). However, the models adopted in those studies do not provide a straightforward indication of howthe design parameters (geometry, uid properties, working conditions) affect the rate of entropygeneration. They also require complex numerical solutions,being therefore not suitable for back-of-the-envelope calculations in the industrial environment.In a recent publication, Hermes (2012) advanced an explicit, algebraic formulation which expresses the dimensionless rate of entropy generation as a function of the number of transfer units, the uid properties, the thermal hydraulic characteristics ( j and f curves), and the operating.conditions (heat transfer duty, core velocity, and coil surface temperature) for heat exchangers with uniform wall temperature. An expression for the optimum heat exchanger effectiveness, based on the working conditions, heat exchanger geometry and uid properties, was also presented. The present paper is therefore aimed at assessing the formulation introduced by Hermes (2012) for designing condensers and evaporators for refrigeration systems spanning from house-hold application, which amounts w10% of the electrical energy consumed worldwide (Malo and Silva, 2010).2. Mathematical formulation In general, condensers and evaporators for refrigeration applications are designed considering the coil ooded with two-phase refrigerant, and also a wall temperature equal to the refrigerant temperature (Barbarossa and Hermes, 2008), in such a way as the temperature proles along the streams are those represented in Fig. 1. In addition, the outer (e.g., air,water, brine) side heat transfer coefcient and the physical properties are assumed to be constant. Therefore, the heat transfer rate if calculated from: （1）where is the mass ow rate, Ti, To and Ts are the inlet, outlet and surface temperatures, respectively, Q hAs(TseTm) is the heat transfer rate, Tm is the mean ow temperature over the heat transfer area, As, and is the heat exchanger effectiveness, calculated from (Kays and London, 1984): （2）where NTU hAs/mcp is the number of transfer units. The pressure drop, on the other hand, can be calculated from(Kays and London, 1984): （3）where f is the friction factor, uc is the velocity in the minimum ow passage, Ac, and the subscripts “i” and “o” refer to the heat exchanger inlet and outlet ports, respectively. Oneshould note that Eqs. (1) and (3) can be linked to each other through the following approximation for the Gibbs relation, （4）where Tmz(Ti To)/2, and the entropy variation, soesi,is calculated from the 2nd-law of Thermodynamics, （5）where the rst term in the right-hand side accounts for the reversible entropy transport with heat ( _Q=Ts), whereas _Sg is the irreversible entropy generation due to both the heattransfer with nite temperature difference and the viscous ow. Substituting Eqs. (1), (3) and (5) into Eq. (4), it follows that: NS （6）where NS is the dimensionless rate of entropy generation. The errors associated to the approximation used in Eq. (4) are marginal: noting that DTm 20 K in most small-capacityrefrigeration applications, it follows that the difference between the exact and approximated mean temperature never exceeds 1 K, which in turn affects the dimensionless entropy generation by less than 1%. Now noting that both condensers and evaporators are designed to provide a heat transfer duty subjected to ow rate and face area constraints Eq. (6) can be re-written as follows (Hermes, 2012): （7） And Q(ToeTi)/Ts a dimensionless temperature difference with both To and Ti known from the application. One should note that the rst and second terms of the right-hand side of Eq. (7)stand for the dimensionless entropy generation rates associated with the heat transfer with nite temperature difference and the viscous ow, respectively. The optimum heat exchanger design NTUopt that minimizes the rate of entropy generation is obtained from (Hermes, 2012): （8）drop effects, which rule the entropy generation for the low aspect ratio designs, are attenuated for low NTU values where the entropy generation due to nite temperature difference isDominant.4. Case studies For the sake of heat exchanger design, Eq. (8) has to be solved concurrently with (ToeTi)/(TseTi) as the coil surface temperature, Ts,must be free to vary thus ensuring that Q (andso _Q and _ m) is constrained. However, the solution is implicit.for Ts, thus requiring an iterative calculation procedure:a guessed Ts value is needed to calculate the effectiveness and NTU eln(1e), which is used in Eq. (8) with j j(Re) and f f(Re) curves, and also with the dimensionless core velocity to come outwith Q,which in turn is used to recalculate Ts until convergence is achieved. Firstly consider an air-supplied tube-n condenser for small-capacity refrigeration appliances running under the following working conditions: _ Q 1kW, _ V 1000 m3h1Ti 300 K (Waltrich et al., 2011; Hermes et al., 2012). Lets assume two heat exchanger congurations: (i) circular tubes with at ns (i.e., Kays and Londons surface 8.0-3/8T), whose thermal-hydraulic characteristics are j 0.16$Re0.4,tubes and ns (Kays and Londons surface CF-8.72), whose thermal-hydraulic characteristics are j 0.22$Re0.4 f 0.20$Re0.2, s 0.524 and Dh 3.93 mm. Also note that Pr z 0.7 for air. Fig. 4 compares the performance characteristics ( j and f curves) of surfaces 8.0-3/8T and CF-8.72 as functions of Re rucDh/m. Fig. 5 compares the dimensionless entropy generation Observed for both surfaces as a function of NTU. A curve of (NTU), which the same for both surfaces, is also plotted to be used as a reference. It can be clearly seen that the (, NTU) design which minimizes the rate of entropy generation is (0.61, 0.95) for surface 8.0-3/8T and (0.57, 0.81) for surface CF-8.72. It can also be noted that the circular-n surfaceshowed a higher rate of entropy generation for all NTU span,which is mostly due to the viscous uid ow effect assurface CF-8.72 has a higher friction factor than surface 8.0-3/8T for the same Reynolds number (see Fig. 4). For low NTU values, where the entropy generation is ruled by NS,DT, both surfaces showed similar NS values as their j-curves are close (see Fig. 4).Fig. 6 compares three different condenser designs consid- ering surface 8.0-3/8T and face areas varying from 0.025 to 0.1 m2 running under the same working conditions. The heat exchanger length was also varied in order to accommodate the heat transfer surface area for different face areas. For a vertical, constant NTU line (i.e. same heat transfer area), it can be clearly observed that a heat exchanger design with high aspect ratio (higher face area, smaller length in the ow direction) produces a signicantly lower amount of entropy in comparison to a low aspect ratio design (lower face area, larger length). It can be additionally observed that the NS curves converge for low NTU values. This is so as the pressure drop effects, which rule the entropy generation for the low aspect ratio designs, are attenuated for low NTU values where the entropy generation due to nite temperature difference is Dominant. Now consider an air-supplied evaporator for household refrigeration appliances, comprised of 10 tube rows in the ow direction and 2 rows in the transversal direction, whose performance characteristics are as follows f z 5.8 is the nning factor, L z0.2 m is the heat exchanger Fig. 7 shows the rate of entropy generation as a function of NTU for the no-frost evaporator. It can be clearly seen that the length, Dt z 8 mm is the tube O.D., Af z 0.02 m is the face area, and s z 0.72. The working conditions are:Tiz260K. In the following analysis, the mass transfer and the related frost accretion phenomena have not been taken into account.minimum entropy generation takes place for NTU w 6.5 and /1, thus indicating that, in this type of evaporator, the pressure drop effects are negligible in comparison with the heat transfer with nite temperature difference. Nonetheless, these gures may change dramatically in presence of frost, which increases not only the pressure drop but also the thermal conduction resistance. also noted that the minimum dimensionless entropy generation rate not only increases as s decreases, but also that the optima move towards the left, Indicating that the pressure drop effects become dominant for lower NTU values as s decreases. It can also be noted that the curves for different s converge for low NTU values as mainly affects the pressure drop rather than the temperature difference, being the formerattenuated for low NTU values. In addition to the optima found for the number of transferunits and, consequently, for the heat exchanger effectiveness, two other important design parameters, the ow path, 4L/Dh, and the heat exchanger surface area density, b As/AfL, do also have optimum values (see Fig. 9) since both are strongly dependent on Ntu: 4L/Dh NTU/St (see Fig. 9a) and b 4s/Dh (see Fig. 9b) where St j/Pr 2/3 is the Stanton number. In both cases, the optimum ow path and heat exchanger surface area density are calculated as follows: （9） （10）Fig. 9 illustrates Eqs. (9) and (10). Unlike Fig. 8, the curves in Fig. 9a do not converge for low NTU values as lower s values imply on higher core velocities which enhance the heat transfer process (higher j or St) even in case of low NTU. In Fig. 9b, it can be noted that the curves cross each other in case of low NTU values, which is due to the inu- ence of s on b.Summary and conclusions This study assessed an analytical formulation that conates two different heat exchanger design methodologies, the Kays and Londons (1984) -NTU approach and the Bejans (1996) method of entropy generation minimization. Expressions for optimum heat exchanger effectiveness, number of transfer units, ow path and heat exchanger surface area density arealso devised. It was shown that there does exist a particular -NTU design for condensers and evaporators that minimizes the dimensionless rate of entropy generation. To this obser-vation follows the conclusion that a high effectiveness heat exchanger has not necessarily the best thermal-hydraulic design, as the effectiveness does not account for the pumping power effect.Case studies considering a tube-n condenser for light commercial refrigeration applications and an evaporator for frost-free refrigerators were also carried out. In case of thecondenser coil, where the entropy production due to viscous uid ow is of the same order of that due to nite temperature difference, the analytical formulation of Hermes (2012)showed to be suitable for thermodynamic optimizations. The analysis also indicated that a heat exchanger design with a high aspect ratio is preferable to a lowaspect ratio one as theformer produces a dramatically lower amount of entropy. In addition, it was found that in case of a “no-frost” evaporator working under dry coil conditions, the pressure drop effect onthe dimensionless entropy production is negligible in comparison to the nite temperature difference, thus indi- cating that Eq. (8) should be used with great care to avoid an economically unfeasible (high NTU) design.On one hand, since the coil temperature is treated as a oating parameter during the optimization exercise, the design for heat transfer enhancement leads to lower average temperature differences and, therefore, to lower condensing temperature and higher evaporating temperature. On the otherhand, theoptimizationfor pressuredropreductionyields a higher mass ow rate for the same pumping power, thus improving the heat transfer coefcient which also tends to reduce the condenser temperature or increase the evaporating temperature. Since the refrigeration system COP obeys the Tevap/(TcondeTevap) scale, it can be stated that the heat exchanger design that presents the best local (component level) performance in terms of minimum entropy generation also leads to the best global (system-level) performance.冷凝器和蒸发器的热力设计: 制定和应用摘 要这份评估旨在用以前出版物中的最小熵产生法介绍的蒸发器及冷凝器中热液的设计方法。其中表示无量纲率的熵产生作为函数的转让单位、 液体属性、 热-水力特性和运行条件数的代数模型产生而来。与不同换热器配置为小容量制冷的应用进行了个体案例研究。理论分析得出的结论为高效率换热器并不一定提供冷凝器和蒸发器的线圈，最佳的热工水力设计时的热转移和 液体 摩擦的熵产生率的数量级相同。分析报告也表明高纵横比换热器产生熵比低的纵横比一个较低的数额。关键字：冷凝器；蒸发器；概念；优化介绍冷凝器和蒸发器是具有相当均匀壁温的换热器，是被用于范围较大的的暖通空调的研发产品，是跨越从家庭到工业的应用。一般情况下，它们设计旨在以很大的功率完成一种特定的热转换任务。如今有两种有效的方法可用于热换热器设计、 温度平均对数比和效能/传质单元数的办法，第二个一直是首选，前者主要用于板式换热器的设计，为了紧凑式换热器设计的有效性，定义为实际的热传递率之间的比率，可以传输的最大金额。提供了一个第一定律标准等级的热交换器的性能，而数量的传输单位比较热的大小与它的容量换热器的加热或冷却液, 此外,-NTU方法避免了繁琐的解决方案所需的温度平均对数比对于出口温度的计算.尽管如此,无论是-NTU或温度平均对数比方法都不适合解决传热/泵功率交换,这是一个平衡的换热器设计的关键。为此，Bejan（1987）建立了叫做的热力学设计方法，后改名为熵产生最小化方法，平衡的热力学不可逆性，由于传热的粘性流体流相关联的那些具有有限的温度差，从而提供了已被广泛应用为换热器设计与优化。从而提供了一种第二法的标准，已被广泛用于热交换器的设计和优化的缘故，然而，在这些研究中所采用的模型并没有提供一个简单的标志的设计参数是如何影响的熵产生率。在最近的一份出版物中，爱马仕（2012年）提出一个明确的，代数的配方，它表示的无量纲熵产率的函数的传质单元数流体性质水力特性（j和f曲线），和热交换器的运行条件具有均匀壁温。并根据工作条件给出了一个表达式的优化换热器效率和换热器几何和流体性质, 因此，本论文旨在评估制定出台爱马仕（2012年）设计的冷凝器和蒸发器的制冷系统，涵盖从家庭到轻型商用应用程序，这相当于全球10的电能消耗。数学模型板式换热器数值分析法用到了对流结构和U型结构中。四个APV SR3标准的板形成三个流动通道。两侧的通道有向下流的热流体，然而中间通道有向上流动的冷流体。换热器的中间通道的V型区域被分为五个轴向部分，这样流体从一个轴向部分进入下一个部分。进口和出口处是在板的左下角和右上角。可是相对中间通道而言，两侧通道进口和出口处是与之相反的。应该指出的，在换热器的不同区域，三角形分布器的存在会使热交换部位每一单元长度都是有区别的。然而这种区别在本文并不值得推崇，因为这些节点是在主要的V型部位，这样轴向分段被假设是均等的。板的几何体和流程在(Haseler高庆宇,1992年)中用于局部温度测量实验。这使两种数据的对比更加有意义。数学模型基于以下假设条件可通过能量平衡方程建立：1 轴向流传导在流动通道和板上表现不显著;2 换热器的尾部板是绝缘的;3 稳态条件;4 热流体均匀分布在两侧边通道;5 忽略热损失;6 没有相变（沸腾和冷凝）;7 除了粘度，其他物理性质不变;8 一维流动;9 通过子通道的温度变化忽略不计。假设在每条通道的垂直方向，一维流动的流体会保持一个平均速度运动。假设均匀分布的流体在冷热流体通道的流速是恒定的。基于以上的假设，图1控制体的能量方程是： （1）采用稳态假定条件，方程（1）可简化为： (2)对称的几何形状和流动使控制体（如图1）从两侧的通道均等的吸收能量，并且th在侧边通道与之相同，由于这个原因，方程（2）可变为： (3) 无论是左手边的通道还是右手边的通道，一个相似的控制体只从一边的通道来吸收能量。其中一边通道的控制体的能量平衡方程是： 将方程（3）和（4）组成方程组，通过方程组来控制换热器相邻通道流体的温度分布。对U很大变化的