Heating load density optimization of an irreversible simple Brayton cycle heat pump coupled to counter-flow heat exchangers

This paper presents a theoretical investigation on the finite time thermodynamic performance for an irreversible Brayton cycle heat pump (BCHP) coupled to counter-flow heat exchangers. The heating load density, i.e. the ratio of heating load to the maximum specific volume in the cycle, is taken as the optimization objective. Relations between heating load density and pressure ratio and between COP (coefficient of performance) and pressure ratio for BCHP in which the irreversibilities of heat resistance losses in the hot and cold-side heat exchangers and non-isentropic losses in the compression and expansion processes are derived. The analytical expression obtained for the cycle performance enabled its optimization through addressing the effects of mechanical and thermal inefficiencies of all components comprising the cycle. The influences of the temperature ratio of the reservoirs, the efficiencies of the compressor and expander and the effectiveness of the heat exchangers on the heating load density are provided. The cycle performance optimizations are performed by searching the optimum distribution of heat conductance of the hot- and cold-side heat exchangers for the fixed total heat exchanger inventory and the optimum heat capacity rate matching between the working fluid and the heat reservoirs. The BCHP design with heat loading density optimization leads to a smaller size of all equipments comprising the heat pump.     

Finite time exergoeconomic performance for six endoreversible heat engine cycles: Unified description

The operation of a universal steady flow endoreversible heat engine cycle model consisting of two constant thermal-capacity heating branches, a constant thermal-capacity cooling branch and two adiabatic branches is viewed as a production process with exergy as its output. The finite time exergoeconomic performance optimization of the universal endoreversible heat engine cycle is investigated by taking profit optimization criterion as the objective. The analytical formulae for power, efficiency and profit rate function of the universal endoreversible heat engine cycle with heat resistance loss are derived. The focus of this paper is to search the compromised optimization between economics (profit) and the utilization factor (efficiency) for endoreversible cycles. Moreover, analysis and optimization of the model are carried out in order to investigate the effect of cycle process on the performance of the universal endoreversible heat engine cycle using numerical examples. The results obtained herein include the performance characteristics of six endoreversible heat engines, including Carnot, Diesel, Otto, Atkinson, Brayton and Dual cycles.     

Mathematical modeling and comparison of air standard Dual and Dual-Atkinson cycles with friction,heat transfer and variable specific-heats of the working fluid

Based on finite-time thermodynamics, a comparative performance analysis of air standard Dual and Dual-Atkinson cycles with heat-transfer loss, friction like term losses and variable specific-heats of the working fluid have been performed. Also the effects of heat loss, as characterized by a percentage of the fuel’s energy, friction and variable specific-heats of the working fluid, on performance of the mentioned irreversible cycles are analyzed. Moreover, detailed numerical examples show the relations between the power output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between the power output and the thermal efficiency of cycles. Results show the importance of consideration of heat loss effects on the both cycles’ performance. Also performance comparison of two cycles show that heat efficiency and power output of a Dual-Atkinson cycle are higher than a Dual cycle’s ones. The results obtained from this paper will provide guidance for the design of Dual-Atkinson engines.     

Thermodynamic optimization of an irreversible regenerative closed Brayton cycle based on thermoeconomic performance criterion

An irreversible regenerative closed Brayton cycle has been optimized using a thermoeconomic objective criterion which is defined as the ratio of net power output to the total cost rate. The total cost rate includes fuel, investment, environmental and operation & maintenance cost rates. In the considered model pressure drops, heat leakages, irreversibilities due to finite-rate heat transfer and internal dissipations have been included. The effects of design parameters, such as isentropic temperature ratio of compressor and turbine, regenerator effectiveness, pressure loss parameter of the cycle, on the general and optimal thermoeconomic performances have been investigated in detail. The results of the study will be helpful for the performance analysis and optimization of practical Brayton heat engine systems.     

Optimization of the design of recuperative heat exchangers in the exhaust nozzle of an aero engine

Today the needs for safer, cleaner and more affordable civil aero engines are found to be of great importance. Five years ago, the EU initiated an action for the design and the construction of efficient and environmentally friendly aero engines (EEFAE). One of the major European gas turbine industries, MTU, has presented a new technology for an advanced aero engine design, which uses an alternative thermodynamic cycle. The basis of this cycle is the adoption of a recuperation part with the use of a system of heat exchangers, installed in the exhaust nozzle of the aircraft engine. Thermal energy in the turbine exhaust is used in the recuperator to pre-heat the compressor outlet air before combustion. The benefits of this technique are focused on reduced pollutants and decreased fuel consumption. In this work, the procedure of the optimization of this installation, by means of the imposed pressure drop downstream the aircraft engine and the balanced mass inflow to the heat exchangers is presented. The optimization is based on experimental measurements in laboratory conditions and preliminary 2D CFD modeling for the flow inside the exhaust duct and through the heat exchangers. It is shown that with a careful approach, a better arrangement of the heat exchangers can be achieved in order to have a minimum pressure drop in the exhaust nozzle which can positively affect the engine’s performance.     

Effects of engine design and operating parameters on the performance of a spark ignition (SI) engine with steam injection method (SIM)

The effects of engine design and operating parameters such as equivalence ratio (ER), compression ratio (CR), cycle pressure ratio (CPR), cycle temperature ratio (CTR), bore-stroke length ratio (D/L) inlet pressure, inlet temperature, friction coefficient (FC), mean piston speed (MPS) and engine speed on the performance characteristics such as brake thermal efficiency (BTE) and brake power output (BPO) are investigated for a steam injected gasoline engine (SIGE) with a simulation model validated with experiments using a realistic finite-time thermodynamics model (FTTM). Moreover, the energy losses arising from exhaust output (EO), heat transfer (HT), friction (FR) and incomplete combustion (IC), are illustrated by using graphs. The optimum values of engine speed, compression ratio, equivalence ratio, cycle temperature ratio and pressure ratio are presented by grid curves. Also, they are called performance maps. The results showed that the performance characteristics improve with enhancing inlet pressure, cycle pressure ratio and cycle temperature ratio; with diminishing inlet temperature and friction coefficient. The BPO can be increased up to 42%, 55% and 62% by using the optimum values of cycle pressure ratio, cycle temperature ratio and inlet pressure, respectively. Also, the BTE can be increased up to 8%, 12% and 15%, by the same way. On the other hand, the performance characteristics can improve or deteriorate with respect to different conditions of compression ratio, engine speed, equivalence ratio, stroke length and mean piston speed. Therefore, the optimum values should be determined to obtain the maximum performance conditions.     

射流通道内方柱发热器件的几何设计北大核心CSCD

基于构形理论,建立了二维射流通道内导热基座上方柱离散热源的散热优化模型.给定离散热源的总纵截面面积和热源高度为约束条件,以系统最高温度和熵产率为优化目标,以各热源的长度比为优化变量进行了几何设计,并分析了射流速度和热源间距对热源最优构形的影响.当射流速度和热源间距给定时,均存在最优长度比使系统最高温度和熵产率最低,但对应不同射流速度和热源间距的最优长度比不同.研究结果可为方柱发热器件的热设计提供理论指导.     

A fast running numerical model based on the implementation of volume forces for prediction of pressure drop in a fin tube heat exchanger

Numerical based design of geometrical structures is common when studying systems involving heat exchangers, a central component in several fields, such as industrial, vehicle and household systems. The geometrical structure of heat exchangers is generally comprised by closely placed fins and tube bundles. The creation of a mesh grid for a geometrically compact heat exchanger will result in a dense structure, which is not feasible for personal computer usage. Hence, volume forces were created based on Direct Numerical Simulations (DNS) on a Flow Representative Volume (FRV) of a tube fin heat exchanger in an internal duct system of a heat pump tumble dryer. A relation of the volume averaged velocity and the volume averaged force was established in two different FRV models with a finite element simulation in COMSOL. This relation was subsequently used to create flow resistance coefficients based on volume averaged expressions of fluid velocity and volume forces. These flow resistance coefficients were implemented in two respective porous models, which represent the entire heat exchanger except the interior arrangements of fins and tube bundles. Hence, the computation time was reduced thanks to the absence of a dense mesh grid. Experimental results of the entire heat exchanger showed good agreement with the second porous model in terms of pressure drop and volume flow rate.     

Optimal static pricing for a service facility with holding costs

We study a service facility modelled as a single-server queueing system with Poisson arrivals and limited or unlimited buffer size. In systems with unlimited buffer size, the service times have general distributions, whereas in finite buffered systems service times are exponentially distributed. Arriving customers enter if there is room in the facility and if they are willing to pay the posted price. The same price is charged to all customers at all times (static pricing). The service provider is charged a holding cost proportional to the time that the customers spend in the system. We demonstrate that there is a unique optimal price that maximizes the long-run average profit per unit time. We also investigate how optimal prices vary as system parameters change. Finally, we consider buffer size as an additional decision variable and show that there is an optimal buffer size level that maximizes profit.     

Mathematical modelling of spark-ignition engines

The flow field, scavenging efficiency, power output, heat transfer losses, and unburned hydrocarbon emissions have been numerically studied by means of a two-equation model of turbulence in a four-stroke, homogeneous-charge, spark-ignition engine. The engine is equipped with an intake valve, an exhaust valve, and a constant rate heat source which simulates the spark plug. Combustion has been modelled by means of a one-step irreversible chemical reaction whose rate is controlled by an Arrhenius-type expression. The numerical results indicate that the intake stroke is characterized by the formation of two eddies which persist in the compression stroke. Turbulence is generated at the shear layers of the air jet drawn into the cylinder, but its level decreases in the compression stroke. Due to the heat released by the spark plug and the chemical reaction, a spherical flame kernel is formed. This kernel evolves into a cylindrical flame when the flame front reaches the piston. Fuel remains unburnt at the corner between the cylinder head and the cylinder wall due to heat transfer losses. The numerical results also indicate that despite uncertainties about the turbulence and heat transfer models, an engine model such as the one studied here can be used to understand the flow field, heat transfer losses, scavenging efficiency, and power output in conventional spark-ignition engines. Such capabilities are very helpful in the development and optimization stages of engines. For example, here the engine model thermal and scavenging efficiencies are 15.69% and 94%, respectively. The peak pressure is 33 atm and occurs at 6° ATDC. The unburnt hydrocarbon emissions are 7.41% of the total fuel admitted into the cylinder.     

Generalized model and optimum performance of an irreversible thermal Brownian microscopic heat pump

A generalized model of an irreversible thermal Brownian microscopic heat pump is established in this paper. It is composed of Brownian particles which are moving in a periodic sawtooth potential with external forces and contacting with alternating hot and cold reservoirs along the space coordinate. The generalized irreversible Brownian heat pump model incorporates heat flows driven by both the potential and kinetic energies of the particles as well as the heat leakage between the hot and cold reservoirs. This paper derives the expressions for heating load, power input and coefficient of performance (COP) of the Brownian heat pump. The optimum performance of the generalized heat pump model is analyzed by using the theory of finite time thermodynamics (FTT). Effects of the design parameters, i.e., the external force, the heat leakage coefficient, barrier height of the potential, asymmetry of the sawtooth potential and heat reservoir temperature ratio on the performance of the Brownian heat pump are discussed in detail. The performance of the Brownian heat pump depends strictly on the design parameters. Through the proper choice of these parameters, the Brownian heat pump can operate in the optimal regimes. The optimum COP performance and the fundamental optimal relations between COP and heating load are studied by detailed numerical examples. It is shown that due to the heat leakage between the heat reservoirs and heat flow via the change of kinetic energy of the particles, both the heating load and COP performances of the Brownian heat pump will decrease. The effective ranges of the external force and barrier height of the potential in which the Brownian motor system can operate as a heat pump are further determined.     

A characteristic line based method to build finite-dimensional medoels of heat exchangers

surface heat exchngers are typical simulated with simplified models obtained through segmentation of the heat exchanging fluid path in a number of consecutive lumps In order to aviod major drawbacks of this approach, which may be very misleading for control design purpose, we propose a method, based on the intergration of the PDE system by the method of characteristic lines, for the construction of numerical heat exchangers models. It can be proved that the time response of such new models is indeed rid of parasitic oscillation and suitable for the understanding of complex dynamic phenomena occurring and suitable for the understanding of complex dynamic phenomena occurring in long residence time heat exchangers, both with one- and two- phase flow. In this paper, particular attention is paid to the problem of generating finite dimensional dynamic system by application of the characteristic lines method and computing the frequency responce of such models. Actually, since the characteristic lines method is not naturally is not straightforward to define Finally, the accuracy of CL models is compared with classical models of comparable complexity, with special reference to real application cases, taken from the power generation field.     

A collaborative inventory system with permissible delay in payment for deteriorating items

A collaborative inventory system of single vendor and single buyer is developed to maximize the total profit of the whole system. However, the optimal solution for the whole system is not always beneficial to both players. To ensure mutual benefit, a negotiation factor is incorporated to share the profit between the two players according to their contributions. The permissible delay in payment is a win–win strategy for sharing profit in the collaborative system. A deteriorating inventory model with finite replenishment rate and price sensitive demand is assumed to occur in a high-tech, short life cycle and perishable electronic product. A numerical example is provided to illustrate our models. The sensitivity analysis of the demand rate, replenishment rate, deterioration factor, and other related parameters shows that the percentage extra total profit is significant when both the collaboration strategy and the deterioration factor are considered.     

需求依赖销售努力库存系统的随机比较

研究需求依赖销售努力库存系统中需求不确定性对系统最优订货量、利润和销售努力的影响.对一般需求模型给出期望利润关于订货量和努力水平为联合凹的充分条件,证明期望利润函数的超模性质.对加乘需求模型证明系统最优利润和最优努力水平都可由一类与需求分布有关的广义TTT变换来表示.通过引入定义在不同支撑分布集合上一阶、二阶和三阶随机占优,得到广义TTT变换之差与二阶和三阶随机占优之间的关系式,建立了比较库存系统最优利润或努力水平的理论基础.在一阶和二阶随机占优意义下对加乘需求模型得到比较系统最优利润和努力水平的充分条件或充分必要条件.进一步,证明存在一类需求分布当系统关键比(或市场价格)足够大时系统最优利润和努力水平随需求可变性的增加而增加.最后给出几个数值例子验证了研究结果.     

Strong controllability and optimal control of the heat equation with a thermal source

In this paper we consider an optimal control system described byn-dimensional heat equation with a thermal source. Thus problem is to find an optimal control which puts the system in a finite time T, into a stationary regime and to minimize a general objective function. Here we assume there is no constraints on control. This problem is reduced to a moment problem.We modify the moment problem into one consisting of the minimization of a positive linear functional over a set of Radon measures and we show that there is an optimal measure corresponding to the optimal control. The above optimal measure approximated by a finite combination of atomic measures. This construction gives rise to a finite dimensional linear programming problem, where its solution can be used to determine the optimal combination of atomic measures. Then by using the solution of the above linear programming problem we find a piecewise-constant optimal control function which is an approximate control for the original optimal control problem. Finally we obtain piecewise-constant optimal control for two examples of heat equations with a thermal source in one-dimensional.     

Optimal pricing,EOL (end of life) warranty,and spare parts manufacturing strategy amid product transition

We study firm’s strategy to determine its product price and warranty period, and plan the spare parts manufacturing so as to maximize its profit and at the same time to fulfill its commitment to providing the customer with the key part continuously over the relevant decision time horizon, i.e., the product’s life cycle plus its EOL service (warranty) period. To examine the research question, we develop and solve a two-stage optimal control theory model. From the numerical analysis, we infer as follows. It is not always true that the longer the EOL warranty period, the better for the company’s profitability, implying there exists an optimal EOL warranty period that balances all the relevant forces like market demand and cost structures. The relationship between optimal EOL warranty period and failure rate (defect rate) is concave: when the defect rate is moderate, the company has to increase its EOL warranty period as the defect rate increases so as to compensate for the deteriorating quality; but, when the defect rate is beyond a threshold level, the company needs to curtail its EOL warranty commitment as the defect rate increases in order to avoid excessive cost to service the failed parts. By depicting key dynamics in this managerial problem, this paper sheds light on how to make decision for optimal pricing and warranty when the product life cycle is finite and the company is obliged to provide after-sales services to customers for an extended period of time after the current product is no longer produced.     

Lumped thermal model for switched reluctance motor applied to mechanical design optimization

Switched reluctance motors (SRM) are attracting much attention because of their special advantages. Generated heat, due to losses, can reduce the life time of SRMs. Therefore, taking into account thermal modeling helps to improve their performance and increase their life time. In this paper, a lumped thermal model of SRM based on the analogue circuit of conductive and convective thermal resistances is proposed. First the heat transfer equations were applied for modeling of each motor part as a thermal equivalent circuit. Then, the thermal modeling of whole SRM was done via assembling all these sub-circuits. For validity of the obtained model on a wide range of geometrical and structural properties of motor, apt heat transfer relations have been used. This comprehensive model is used to investigate the influence of dimensions on heat transfer in SRM. Finally, an optimal design of the stator yoke dimensions has been reached concerning the mechanical aspects without degrading electromagnetic characteristics of SRM.     

Optimal production stopping time for perishable products with ramp-type quadratic demand dependent production and setup cost

A single item economic production quantity (EPQ) model is discussed to analyse the behaviour of the inventory level after it’s introduction to the market. It is assumed that demand is time dependent accelerated growth-effect of accelerated growth-steady type. Unlike the conventional EPQ models, which are restricted to general production cycle over the finite or infinite time horizon, we consider the production sale scenario of the very first production cycle for newly introduced perishable product. Shortage is not allowed. Set up cost of an order cycle depends on the total amount of inventory produced. The finite production rate is proportional to demand rate. Optimal production stopping time is determined to maximize total unit profit of the system. A numerical example is presented to illustrate the development of the model. Sensitivity analysis of the model is carried out.     

多级制造系统的最优化模型及其应用

多级制造系统是现代制造业的主要加工方式，系统的每一级的加工速度和加工周期是系统设计的主要决策变量，正确确定这两个变量是系统得到优化的主要目标。本文导出了系统优化的基本模型，它包括系统各级的生产时间、等待时间、生产速度、生产成本以及系统的循环时间、总成本、产品利润和利润率等，并给出了一个应用实例。     

Thermal stress state of a bimaterial with a closed interfacial crack having rough surfaces

We have formulated the problem of thermoelasticity for a bimaterial whose components differ only in their shear moduli, with a closed interfacial crack having rough surfaces. The bimaterial is subjected to the action of compressive loads and heat flow normal to the interfacial surface. We have taken into account the dependence of thermal conductance of the defect on the contact pressure of its faces and heat conductivity of the medium that fills it. The problem is reduced to a Prandtl-type nonlinear singular integro-differential equation for temperature jump between the crack surfaces. An analytical solution of this problem has been constructed for the case of action of the heat flow only. We have analyzed the dependence of contact pressure of the defect faces, temperature jump between them, and the intensity factor of tangential interfacial stresses on the value of given heat flow, roughness of the surfaces, and ratio between the shear moduli of joined materials.