Field synergy equation for turbulent heat transfer and its application

A field synergy equation with a set of specified constraints for turbulent heat transfer developed based on the extremum entransy dissipation principle can be used to increase the field synergy between the time-averaged velocity and time-averaged temperature gradient fields over the entire fluid flow domain to optimize the heat transfer in turbulent flow. The solution of the field synergy equation gives the optimal flow field having the best field synergy for a given decrement of the mean kinetic energy, which maximizes the heat transfer. As an example, the field synergy analysis for turbulent heat transfer between parallel plates is presented. The analysis shows that a velocity field with small eddies near the boundary effectively enhances the heat transfer in turbulent flow especially when the eddy height which are perpendicular to the primary flow direction, are about half of the turbulent flow transition layer thickness. With the guide of this optimal velocity field, appropriate internal fins can be attached to the parallel plates to produce a velocity field close to the optimal one, so as to increase the field synergy and optimize the turbulent heat transfer.     

CFD study on local fluid-to-wall heat transfer in packed beds and field synergy analysis

To reach the target of smaller pressure drop and better heat transfer performance, packed beds with small tube-to-particle diameter ratio (D/d _p<10) have now been considered in many areas. Fluid-to-wall heat transfer coefficient is an important factor determining the performance of this type of beds. In this work, local fluid- to-wall heat transfer characteristic in packed beds was studied by Computational Fluid Dynamics (CFD) at different Reynolds number for D/d _p=1.5, 3.0 and 5.6. The results show that the fluid-to-wall heat transfer coefficient is oscillating along the bed with small tube-to-particle diameter ratio. Moreover, this phenomenon was explained by field synergy principle in detail. Two arrangement structures of particles in packed beds were recommended based on the synergy characteristic between flow and temperature fields. This study provides a new local understanding of fluid-to-wall heat transfer in packed beds with small tube-to-particle diameter ratio.     

Two energy conservation principles in convective heat transfer optimization

Improving heat transfer performance is very beneficial to energy conservation because heat transfer processes widely existed in energy utilization systems. In this contribution, in order to effectively optimize convective heat transfer, such two principles as the field synergy principle and the entransy dissipation extremum principle are investigated to reveal the physical nature of the entransy dissipation and its intrinsic relationship with the field synergy degree. We first established the variational relations of the entransy dissipation and the field synergy degree with the heat transfer performance, and then derived the optimization equation of the field synergy principle and made comparison with that of the entransy dissipation extremum principle. Finally the theoretical analysis is then validated by the optimization results in both a fin-and-flat tube heat exchanger and a foursquare cavity. The results show that, for prescribed temperature boundary conditions, the above two optimization principles both aim at maximizing the total heat flow rate and their optimization equations can effectively obtain the best flow pattern. However, for given heat flux boundary conditions, only the optimization equation based on the entransy dissipation extremum principle intends to minimize the heat transfer temperature difference and could get the optimal velocity and temperature fields.     

Numerical study of fluid flow and heat transfer in a flat-plate channel with longitudinal vortex generators by applying field synergy principle analysis

Three dimensional numerical simulations are performed on laminar heat transfer and fluid flow characteristics of a flat-plate channel with longitudinal vortex generators (LVGs). The effects of two different shaped LVGs, rectangular winglet pair (RWP) and delta winglet pair (DWP) with two different configurations, common-flow-down (CFD) and common-flow-up (CFU), are studied. The numerical results indicate that the application of LVGs effectively enhances heat transfer of the channel. According to the performance evaluation parameter, (Nu/Nu₀)/(f/f₀), the channel with DWP has better overall performance than RWP; the CFD and CFU configurations of DWP have almost the same overall performance; the CFD configuration has a better overall performance than the CFU configuration for RWP. The basic mechanism of heat transfer enhancement by LVGs can be well described by the field synergy principle.     

Optimization design of slotted fin by numerical simulation coupled with genetic algorithm

Using a novel method that couples genetic algorithm (GA) with numerical simulation, the geometric configuration for a two-dimensional slotted fin has been optimized in this paper. The objective of optimization is to maximize the heat transfer capacity of slotted fin, and minimize the pressure drop penalty of fluid flow through the fin. The key of this method is the fitness function of GA, which were (j/j₀)/(f/f₀) and j/j₀. In this complex multiparameter problem, the numerical simulation is a crucial step to calculate the Colburn factor j and friction factor f. The results showed that for two-dimensional slotted fin considered, the j factor is increased by 229.22%, the f factor is increased by 196.30%, and the j/f ratio was increased by 11.11% at Re = 500 based on optimal integrated performance (j/j₀)/(f/f₀); the j factor is increased by 479.08% at Re = 500 based on optimal heat exchange capacity j/j₀. The feasibility of optimal designs was verified by the field synergy principle.     

Experimental verification of the field synergy principle

In this paper, the basic idea of the field synergy principle (FSP) is briefly reviewed and is validated experimentally by incompressible flow through a square duct with an imposed temperature difference between vertical walls and perfectly insulated on the horizontal walls. This creates a situation where the steamwise flow velocity is normal to the cross section temperature gradient. The experimental results show the independency of crosswise heat transfer rate on the steamwise flow velocity. Detailed discussion is provided to account for some minor deviation from the expected results of FSP.     

Discussion on the convective heat transfer and field synergy principle

The convective “heat” transfer is actually mainly carried out by the motion of hotter or colder particles from one system into another system. Therefore, the best convective “heat” (strictly speaking, internal energy) transfer is the case where velocity vectors are always perpendicular to the isothermal surfaces (or isotherm in 2D cases). This conclusion has been named “field synergy principle”. In this paper, some field synergy exact solutions are presented to further develop the principle. The concrete physical meanings of the derived analytical solutions are analyzed. The method of separating variables with addition and other extraordinary approaches are adopted in the derivation.     

Field synergy optimization and enhanced heat transfer by multi-longitudinal vortexes flow in tube

The field synergy equation for steady laminar convection heat transfer was derived by conditional variation calculus based on the least dissipation of heat transport potential capacity. The optimum velocity field with the best heat transfer performance and least flow resistance increase can be obtained by solving the synergy equation. The numerical simulation of laminar convection heat transfer in a straight circular tube shows that the multi-longitudinal vortex flow in the tube is the flow pattern that enhances the heat transfer enormously. Based on this result, a novel enhanced heat transfer tube, the discrete double-inclined ribs tube (DDIR-tube), is developed. The flow field of the DDIR-tube is similar to the optimal velocity field. The experimental results show that the DDIR-tube has better comprehensive heat transfer performance than the current heat transfer enhancement tubes. The present work indicates that new heat transfer enhancement techniques could be developed according to the optimum velocity field.     

Effect of fluid thermal properties on the heat transfer characteristics in a double-pipe helical heat exchanger

Heat transfer characteristics of a double-pipe helical heat exchanger were numerically studied to determine the effect of fluid thermal properties on the heat transfer. Two studies were performed; the first with three different Prandtl numbers (7.0, 12.8, and 70.3) and the second with thermally dependent thermal conductivities. Thermal conductivities of the fluid were based on a linear relationship with the fluid temperature. Six different fluid dependencies were modeled. Both parallel flow and counterflow configurations were used for the second study.Results from the first study showed that the inner Nusselt number was dependent on the Prandtl number, with a greater dependency at lower Dean numbers; this was attributed to changing hydrodynamic and thermal entry lengths. Nusselt number correlations based on the Prandtl number and a modified Dean number are presented for the heat transfer in the annulus. Results from the second part of the study showed that the Nusselt number correlated better using a modified Dean number. The counterflow configuration had higher heat transfer rates than the parallel flow, but the ratio of these differences was not different when comparing thermally dependent properties and thermally independent properties.     

Optimization for a heat exchanger couple based on the minimum thermal resistance principle

Following the brief introduction to the concept of a physical quantity, entransy, the equivalent thermal resistance of a heat exchanger couple is defined based on the entransy dissipation. The minimum thermal resistance principle is applied to obtain the optimal heat capacity rate of the medium fluid and the optimal allocation of heat exchangers thermal conductance, which correspond to the maximum heat transfer rate in the heat exchanger couple. In addition, analytical expression for the optimal heat capacity rate of the medium fluid is derived, whose reciprocal equals the sum of the reciprocal of the individual heat capacity rate of the hot and cold fluids, just like the case of two electrical capacitors in series. Numerical results in the variation of the thermal resistance and the heat transfer rate with the medium fluid heat capacity rate or the thermal conductance allocation agree with the theoretical analyses. Finally, for comparison, the entropy generation rate is also calculated to obtain its relation with the thermal performance of the heat exchanger couple. The results show that there is no one-to-one correspondence of the minimum entropy generation rate and the maximum heat transfer rate. This indicates that the minimum entropy generation principle cannot be used for optimizing the heat exchanger couple.     

On the design of the tubesheet and the tubesheet-to-shell junction of a fixed tubesheet heat exchanger

For the (mechanical) design of an existing fixed tubesheet heat exchanger, a C2-Hydrogenation reactor in a petrochemical plant, various code solutions are compared with each other and with a Finite Element solution based on the Direct Route in Design by Analysis (EN 13445-3, Annex B). The codes and standards used in the investigation are ASME Section VIII, Division 1 and EN 13445-3, Clause 13 and Annex J.     

Thermodynamic optimization of a coiled tube heat exchanger under constant wall heat flux condition

In this paper the second law analysis of thermodynamic irreversibilities in a coiled tube heat exchanger has been carried out for both laminar and turbulent flow conditions. The expression for the scaled non-dimensional entropy generation rate for such a system is derived in terms of four dimensionless parameters: Prandtl number, heat exchanger duty parameter, Dean number and coil to tube diameter ratio. It has been observed that for a particular value of Prandtl number, Dean number and duty parameter, there exists an optimum diameter ratio where the entropy generation rate is minimum. It is also found that with increase in Dean number or Reynolds number, the optimum value of the diameter ratio decreases for a particular value of Prandtl number and heat exchanger duty parameter.     

Optimal configuration design for plate heat exchangers

A screening method is presented for selecting optimal configurations for plate heat exchangers. The optimization problem is formulated as the minimization of the heat transfer area, subject to constraints on the number of channels, pressure drops, flow velocities and thermal effectiveness, as well as the exchanger thermal and hydraulic models. The configuration is defined by six parameters, which are as follows: number of channels, numbers of passes on each side, fluid locations, feed relative location and type of channel flow. The proposed method relies on a structured search procedure where the constraints are successively applied to eliminate infeasible and sub-optimal solutions. The method can be also used for enumerating the feasible region of the problem; thus any objective function can be used. Examples show that the screening method is able to successfully determine the set of optimal configurations with a very reduced number of exchanger evaluations. Approximately 5% of the pressure drop and velocity calculations and 1% of the thermal simulations are required when compared to an exhaustive enumeration procedure. An optimization example is presented with a detailed sensitivity analysis that illustrates the application and performance of the screening method.     

螺旋翅片管换热器的优化设计

本文以试验为基础,对螺旋翅片管换热器的管束结构进行了优化设计,建立了数学模型。对建模 过程中有关目标函数确定、变量分析、约束条件等进行了讨论。得到了一定限制条件下的最佳结构参 数,可为电站锅炉的省煤器、空气预热器等设备的优化设计提供参考。     

A novel design of a heat exchanger for a metal-hydrogen reactor

A metal-hydride reactor equipped by a spiral heat exchanger is experimentally studied. The inserted exchanger provides significant insights into the problem of minimizing the total storage time by manipulating the operating parameters. Performance studies are carried out by varying the supply pressure, volume of the tank, absorption temperature, and overall heat transfer coefficient.     

Nusselt number correlations for a microchannel heat exchanger hot water supplier with S-shaped fins

Using 3D-CFD code, Nusselt number correlations for a microchannel heat exchanger (MCHE) with S-shaped fins used for hot water suppliers are obtained through numerical experiments and then validated. The supercritical carbon dioxide working fluid is assumed to operate around the pseudo-critical point, where fluid properties change radically. Calculations with 20 different temperatures are executed to produce Nusselt number correlations for each side. The fluid inlet temperature in each calculation is defined as 2 °C lower or higher than the constant wall temperature, respectively, for cold and hot side simulations. The small temperature difference of 2 °C is sufficiently small to regard thermal–hydraulic properties as constant. A new integrating method using the correlations to calculate the heat-transfer-performance is proposed. The resultant heat-transfer-performance is compared with that of another numerical result, which is reduced from large geometry and integration. The results agree within 3% error; the calculation accuracy of the method is confirmed. Experimental results with MCHE verify the correlations. The difference is approximately 5%. Using few computer resources, these Nusselt number correlations and the heat-transfer-performance calculation methods using correlation information are sufficiently accurate to evaluate heat exchangers.     

Heat exchanger optimization for geothermal district heating systems: A fuel saving approach

One of the most commonly used heating devices in geothermal systems is the heat exchanger. The output conditions of heat exchangers are based on several parameters. The heat transfer area is one of the most important parameters for heat exchangers in terms of economics. Although there are a lot of methods to optimize heat exchangers, the method described here is a fairly easy approach. In this paper, a counter flow heat exchanger of geothermal district heating system is considered and optimum design values, which provide maximum annual net profit, for the considered heating system are found according to fuel savings. Performance of the heat exchanger is also calculated. In the analysis, since some values are affected by local conditions, Turkey's conditions are considered.     

Influence of heat exchanger effectiveness on performance of vapour absorption heat transformers

A thermodynamic analysis was made to study the effect of heat exchanger effectiveness on the performance of single stage vapour absorption heat transformers (VAHT). The working fluid pairs considered were R21-DMF and R21-DMETEG. Variations in the performance parameters such as coefficient of performance, exergetic efficiency, concentration difference and circulation ratio at different values of operating temperatures were studied. Among the two working pairs analysed, the R21-DMF pair yielded a high coefficient of performance and exergetic efficiency, whereas the R21-DMETEG pair yielded a high temperature lift at given operating conditions. The improvements in coefficient of performance and exergetic efficiency with heat exchanger effectiveness were more pronounced for R21-DMF than for R21-DMETEG. Correlations are presented for quick estimation of performance under various operating conditions.     

基于最优夹点温差的换热网络优化设计

介绍了夹点技术基本原理及其在换热网络优化设计中的原则。利用ASPENPinch软件设计了一个有三股热股流、两股冷股流的换热网络,求得最优夹点温差是23．7℃,设计时取值23℃。夹点温差分别取10、23、30％进行换热网络初步优化设计,在相同换热器情况下,三者的总费用分别是44279、41931、42156美元／a。这证明采用最优夹点温差的换热网络经济性最好。     

槽式太阳能光热发电油盐换热装置设计优化

简要介绍油盐换热装置的工作原理,熔盐、导热油介质的特性。分析在设计槽式太阳能光热发电的关键设备油盐换热装置时需要考虑的问题,并详细描述油盐换热设备的设计方案。