Analytic model for transient heat exchanger response

The temperature transient response of a single-phase fluid and a wall in a heat exchanger is investigated for when the other constant temperature fluid is subjected to a step change in temperature or when the single-phase fluid is subjected to a step change in mass flow rate. The dynamic behavior of the heat exchanger is approximated by an integral method assuming that the single-phase fluid temperature distribution can be expressed by a combination of the initial and final temperature distributions and a determined time function. The results are validated by comparison against numerical simulations. Excellent agreement is obtained.     

热负荷阶跃变化条件下热回流式换热系统缺陷机理及优化方法研究

针对国内某北方核电厂的设备冷却水系统热回流式换热器,分析了不同热负荷下热回流式换热系统的稳态特性及负荷阶跃变化下热回流式换热系统缺陷机理,提出了热回流式换热器系统优化方法。研究表明:在不同热负荷下热回流式换热器系统切换的关键是与不同热负荷对应的具有特定温度的伴流的形成;热负荷阶跃变化下状态转换瞬态过程中存在系统缺陷,其根本原因在于单纯采取调节热回流率的方法,具有较大的时间滞后性;调节换热器冷介质侧的流体流量,改变换热器传热系数,强化了对状态改变的快速响应;采取热回流叠加换热器旁流方法,可以解决原有系统状态转换瞬态过程中存在的缺陷。     

Comparison of dynamic performance for direct and fluid coupled indirect heat exchange systems

Three different arrangements of heat exchange from a hot fluid stream to a cold fluid stream such as, direct heat exchanger and fluid coupled indirect heat exchanger both with forced circulation loop as well as thermally driven natural circulation loop have been considered in the present work. Dynamic performance of these three arrangements has been studied for four different excitations namely, step, ramp, exponential and sinusoidal. These excitations are imposed at the hot fluid inlet temperature. Finite element technique is used to solve the transient one-dimensional conservation equations. A thorough comparison of the dynamic performance of these three arrangements is made. It is found that the direct heat exchanger does not have any time delay between the response and the excitation function. Moreover, the phase difference between the sinusoidal excitation and response is the lowest in this case.     

Counter-current tubular heat exchanger: Modeling and adaptive predictive functional control

The control of the outlet temperature of a counter-current tubular heat exchanger in heater configuration with the predictive functional control is presented in this paper. The outlet temperature of the cold fluid is controlled by variation of the flow of the hot fluid while the inlet temperatures corresponding to the principal inputs are maintained constant. An approximated first order model, corresponding to the response of the heat exchanger to a step change of the flow rate is used to apply the functional predictive control. The gain and the time-constant of this model depend on the initial and final steady state temperatures according to the flow rates. This nonlinear dynamic model, obtained from the partial differential equations (PDE) is taken into account to apply the functional predictive control, which was validated experimentally in various configurations. The robustness of this controller is also examined when the system is subjected to the sudden change of the flow rate of the cold fluid.     

An analytical method for determining transient temperature field in a parallel-flow three-fluid heat exchanger

In this paper we solve analytically, by the method of Laplace transforms, the set of partial differential equations describing the transient temperature field in a parallel-flow three-fluid heat exchanger. The analytical solution is obtained for a special case of the heat exchanger with two heat connections between the fluids, constant temperature in one channel, and step increase of the inlet temperature of one fluid. The analysis is illustrated by exemplary calculations.     

一次表面回热器动态特性的数值模拟与实验研究

对一次表面回热器(Primary Surface Recuperator,PSR)流量阶跃变化时的动态特性进行了数值分析和实验研究.根据能量守恒原理和一次表面回热器(PSR)的结构特点,导出回热器冷热流体和固体间壁非稳态温度变化的微分方程式,研究流体流量发生阶跃变化时PSR的响应时间.在冷热空气进口参数和换热量相同的条件下,当冷热侧流量分别增加为原来3倍的情况下,PSR的响应时间只有管壳式换热器的1/8,板翅式的1/3.数值分析结果与实验结果相符.由于PSR的固体壁面时间常数远小于板翅式和管壳式回热器,因此这种轻重量结构的先进回热器响应特性明显优于常规回热器.     

Transient behavior of run-around heat and moisture exchanger system. Part І: Model formulation and verification

In Part І, a numerical model for coupled heat and moisture transfer in a run-around heat and moisture exchanger with a liquid desiccant coupling fluid is developed. The numerical model is two dimensional, transient and is formulated using the finite difference method with an implicit time discretization. The results from the numerical model for the case of only heat transfer for a single heat exchanger are compared to an available analytical solution and good agreement is obtained. For the simultaneous heat and moisture transfer in the run-around membrane energy exchanger (RAMEE), a comparison between numerical model results and experimental measurements obtained from laboratory testing for both sensible and latent effectiveness showed satisfactory agreement at different operating conditions. Part II of this paper applies the model for a range of initial conditions [32].     

Transient temperature profile inside thermoacoustic refrigerators

The linear theory used to calculate the thermal quantities inside the stack in the classical thermoacoustic refrigerators always overestimates those measured. The causes of these discrepancies have to be found in the complex processes of thermal exchanges. The analytical study of the transient response should provide an interpretation of these complex processes. This present paper provides such analytical modelling. This modelling remains within the framework of the classical linear theory. It includes the effects of the thermoacoustic heat flux carried along the stack, the conductive heat flux returning in the solid walls of the stack and through the fluid inside the stack, the transverse heat conduction in the stack and the heat leakages through the duct walls, the heat generated by viscous losses in the stack, the heat generated by vorticity at the ends of the stack, and the heat transfer through both ends of the stack. A modal analytical solution for the temperature profile is proposed, assuming the usual approximations in such thermal problems to avoid intricate calculations and expressions. The theoretical transient response of a thermoacoustic refrigerator is compared with experimental data. A good qualitative agreement is obtained between analytical and experimental results after fitting empirical coefficients.     

结构参数对电厂翅片管散热器动态特性的影响

散热器经常处于变化的工作条件中,研究散热器的动态特性有助于改善间接空冷系统的安全和经济运行,而散热器的结构参数会影响其动态特性。根据能量守恒建立了散热器空气、管壁和循环水的热平衡偏微分方程,采用改进欧拉法对偏微分方程组进行求解。以迎面风速阶跃变化为典型工况,研究了换热面积、换热系数和工质体积对散热器动态特性的影响。结果如下:当空气侧换热面积增加时,散热器换热量增大,两个稳态之间的空气出口温度差值不变,循环水出口温度差值增加,空气侧响应时间增加,循环水侧响应时间不变。当循环水侧换热面积增加时,散热器换热量增大,两个稳态之间的空气和循环水出口温度差值不变,空气侧和循环水侧的响应时间也不变。换热系数变化时,散热器动态过程的变化规律与换热面积变化时类似。空气侧工质体积变化对散热器动态特性没有影响。循环水侧工质体积增大会使得动态响应时间变长。     

多股流换热器动态过程场协同分析

建立了多股流板翅式换热器动态数学模型,通过换热器入口温度及流量阶跃的改变,模拟过渡过程中温度场的动态响应,利用温差场均匀性因子对多股流换热器过渡过程动态特性进行了评价,通过分析内部温度场与速度场的协同关系,揭示温差场在动态过程中的变化特征.将温差场均匀性因子与过渡时间结合,建立了自组织能力系数,并对多股流换热器控制品质进行了分析.多股流换热器在流量阶跃时,温差场均匀性因子平缓迁移,而温度阶跃时变化剧烈且存有极值.多股流换热器自组织系数越大,越易达到新的热平衡.     

Dynamic performance of a natural circulation loop with end heat exchangers under different excitations

In the present work the dynamic performance of a natural circulation loop (NCL) has been studied under step, ramp, exponential and sinusoidal excitations. The loop is equipped with two heat exchangers at its lower and upper end for the heating and cooling of the loop fluid. For the analysis, transient one-dimensional conservation equations have been constructed for the loop fluid as well as for the two fluid streams of hot and cold end heat exchangers. The solution of a set of differential equations and one integro-differential equation has been obtained through a finite element method (FEM). For different excitations imposed to the inlet temperature of the hot fluid responses have been studied for the outlet temperature of the two fluid streams and the mass flow rate of the coupling fluid. It has been observed that all these quantities experience some initial transients before reaching the steady state. Time needed for the attainment of steady state varies with the type of excitation. A finite time delay is observed before the cold fluid stream temperature starts responding to the excitation. This delay is related to the time required for the advection of a fluid particle.     

Short time step analysis of vertical ground-coupled heat exchangers: The approach of CaRM

In this paper an improvement of the model CaRM (CApacity Resistance Model) is presented to consider the borehole thermal capacitance, both of the filling material of the borehole and of the heat carrier fluid inside the ground heat exchanger. Several models, numerical and analytical, are available in literature for short time step analyses of ground-coupled heat pump systems. According to the modelling for the surrounding ground, the new approach for the inside of the borehole is based on electrical analogy. In this study the double U-tube ground heat exchanger is analyzed. The new model has been validated by means of a commercial software based on the finite elements method as well as measurements of ground response test, using a suitable plant system. In this last comparison, the contribution of the thermal capacitance of the circulating fluid is investigated, since it is frequently neglected in short time step simulations. In both cases, there is agreement between the CaRM results and data from numerical simulations and measurements as well.     

Analysis of a Parallel-Flow Heat Exchanger with a Heat Source

In this work, a modified analysis of a parallel-flow plate heat exchanger that takes into account a volumetrically uniform heat source in the hot fluid is presented. New expressions for the number of transfer units (NTU) and effectiveness of the heat exchanger are derived. These expressions are verified against the conventional effectiveness–NTU relations in the limit of zero heat source rate. This situation is of interest in applications such as the ammonia–water absorption absorber heat exchanger where a heat source is generated in the solution side. The model studies two cases based on the minimum and maximum heat capacities of the hot fluid. The results show that the number of transfer units and the effectiveness of the heat exchanger are the same for both cases. The analysis is applied to the absorber heat exchanger. Expressions of effectiveness and number of transfer units of a counterflow heat exchanger with a heat source in the hot fluid stream are also given from minimum and maximum heat capacities points of view.     

Transient Response of a Co-current Heat Exchanger to an Inlet Temperature Variation with Time Using an Analytical and Numerical Solution

In this article, we examine the transient response of a co-current double-pipe heat exchanger with respect to the inlet temperature change. For this investigation, a method whose main feature is analytical solution of the energy equation for one element of the heat exchanger is developed. The governing equations are linearized with respect to space and time in one element, and the temperature distribution for the element is obtained. Finally, the obtained temperature distribution for one element is utilized numerically for the whole length of the heat exchanger. Various boundary conditions (ramp, exponential, and sinusoidal) are applied, and the responses are investigated with respect to various parameters. A comparison of the results with data from previous studies shows that the method applied in this article is capable of predicting transient behavior accurately. In addition, because the energy equation is solved analytically, the present method has higher accuracy than those previously utilized, and the calculation time declines noticeably.     

地源热泵竖直埋管的有限长线热源模型

对地热换热器竖直埋管的非稳态传热模型进行了分析讨论。采用虚拟热源和格林函数法给出了半无限大介质中有限长线热源产生的非稳态温度场的解析解表达式。与稳态温度场的解进行比较,讨论了温度场达到名义上的“稳态”所需的时间,同时对于达到稳态时的温度场也进行了分析,指出了现行教科书中关于该问题的错误,提出了稳态时两个地热换热器孔壁代表性温度的定义,并对两者进行了比较,进而给出了可供工程应用的简化计算公式,并对两者进行了比较,进而给出了可供工程应用的简化计算公式。基于以上分析,进一步讨论了全年冷热负荷不平衡对地热换热器长期性能的影响。     

Heat Exchangers Design Under Variable Overall Heat Transfer Coefficient: Improved Analytical and Numerical Approaches

In typical heat exchanger design methods it is generally assumed that the overall heat transfer coefficient is constant and uniform; however, the heat transfer coefficients on the hot and cold sides of the heat exchanger may vary with flow Reynolds number, surface geometries, fluid thermophysical properties, and other factors. In this article we present simple analytical and numerical methods for calculating heat transfer area for data sets introduced earlier in the literature. For the analytical methods presented in the article, the variation in the overall heat transfer coefficient with the local hot and cold fluid temperature difference is expressed as a power-law model and as a general polynomial model. The procedure for calculating the heat transfer area with the power-law model is explained with respect to a simple closed-form solution, while the polynomial model can also provide an analytical solution that seems to be quite accurate for the data sets examined. It is also shown that a Chebyshev numerical integration scheme that requires four points compared to the Simpson method of three points is quite accurate (within 1% of the exact value).     

The Influence of Core Capacitance on the Dynamic Performance of a Single-Phase Natural Circulation Loop With End Heat Exchangers

The effect of wall-core capacitance of heat exchangers on the dynamic behavior of a natural circulation loop (NCL) with end heat exchangers is studied under various excitations such as step, ramp, exponential, and sinusoidal. The transient one-dimensional conservation equations are derived for loop fluid, hot and cold fluid streams, and wall core of both heat exchangers. The solution of a set of transient partial differential equations and one integro-differential equation for loop fluid circulation rate is achieved through a finite-element technique. Imposing the excitations to the inlet temperature of hot fluid, the effects of wall-core capacitance on the responses of outlet temperatures of both hot and cold fluid streams and flow rate of loop fluid are studied. Wall-core capacitance diminishes the initial transients and delays the inception of hot and cold fluids outlet temperature profiles as well as loop fluid flow profile. Further, it has the ability to bring even unstable system behavior with reverse flows into a stable system with steady loop flow rate through quickly decaying oscillations. System responses are also greatly influenced by boundary conditions such as hot and cold fluids flow rates and their inlet temperature excitations such as step, ramp, and exponential. As flow stability is an important subject for single-phase NCLs, a stability map is constructed and compared with zero wall-core capacitance. Inclusion of wall-core capacitance in the present study reveals the important fact that the stable state operating zone widens with the wall-core capacitance.     

Assessment of Bejan’s heat exchanger allocation model under the influence of generalized thermal resistance,relaxation effect,bypass heat leak and internal irreversibility

This article reports an analytical investigation of the optimal heat exchanger allocation and the corresponding efficiency for maximum power output of a Carnot-like heat engine. To mimic a real engine, the generalized power law for the resistance in heat transfer external to the engine, relaxation effect in heat transfer, bypass heat leak and finally internal irreversibility of the power producing compartment of the engine is taken into consideration. From the engineering perspective the temperature ratio of the heat source and sink as well as to that of hot end and cold side of the working fluid is considered not to be the controllable parameters. A parametric study is presented for the other possible controllable variables. Selection of a power law over a linear model has a significant effect on the optimal heat exchanger allocation for maximum power output and the corresponding efficiency. For a higher degree of relaxation effect the drop in the maximum power efficiency is prominent along with the shift of equipartitioned allocation of heat exchanger inventory. Bypass heat leak and internal irreversibility exhibits relatively less pronounced effects on the maximum power efficiency and on the optimal heat exchanger allocation. Thus the endoreversible formulation of thermodynamic model is physically realistic. Strikingly when the optimal allocation of the heat exchanger inventory obeys the principle of equipartition in macroscopic organization for the linear law of the external heat resistance, the thermal efficiency appears to assume the representative documented value. Hence the linear model due to Bejan is also capable of capturing the essential features of a real power plant.     

Transient behavior of run-around heat and moisture exchanger system. Part IІ: Sensitivity studies for a range of initial conditions

Part І of this paper [17] developed and verified the numerical model for simultaneous heat and moisture transfer in the run-around membrane energy exchanger (RAMEE) system to determine the transient behavior of the system under different initial and operating conditions.This paper presents the transient response of the RAMEE system for step changes in the inlet supply air temperature and humidity ratio. Also the system quasi-steady state operating conditions are predicted as the system approaches its asymptotic operating condition. The transient responses are predicted with changes in various parameters. These include: the number of heat transfer units, thermal capacity ratio, heat loss/gain ratio, storage volume ratio and the normalized initial salt solution concentration. It is shown that the storage volume ratio and the initial salt solution concentration have significant impacts on the transient response of the system and heat transfer between the RAMEE system and the surrounding environment can change the system quasi-steady conditions substantially.     

Unsteady MHD flow and heat transfer with viscous dissipation past a stretching sheet

In this paper a study is carried out to analyze the unsteady heat transfer effects of viscous dissipation on the steady boundary layer flow past a stretching sheet with prescribed constant surface temperature in the presence of a transverse magnetic field. The sheet is assumed to stretch linearly along the direction of the fluid flow. The assumed initial steady flow and temperature field neglecting dissipation effects becomes transient by accounting dissipation effects when time t′ > 0. The temperature and the Nusselt number are computed numerically using an implicit finite difference method. The obtained steady temperature field with dissipation is of practical importance.