Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

MINLP Model for the Synthesis of Heat Exchanger Networks with Handling Pressure of Process Streams

This paper introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs), wherein the handling pressure of process streams is used to enhance the heat integration. The proposed approach combines generalized disjunctive programming (GDP) and mixed-integer nonlinear programming (MINLP) formulation, in order to minimize the total annualized cost composed by operational and capital expenses. A multi-stage superstructure is developed for the HEN synthesis, assuming constant heat capacity flow rates and isothermal mixing, and allowing for streams splits. In this model, the pressure and temperature of streams must be treated as optimization variables, increasing further the complexity and difficulty to solve the problem. In addition, the model allows for coupling of compressors and turbines to save energy. A case study is performed to verify the accuracy of the proposed model. In this example, the optimal integration between the heat and work decreases the need for thermal utilities in the HEN design. As a result, the total annualized cost is also reduced due to the decrease in the operational expenses related to the heating and cooling of the streams.

Retrofit of heat exchanger networks with pressure recovery of process streams at sub-ambient conditions

This paper presents a new mathematical programming model for the retrofit of heat exchanger networks (HENs), wherein the pressure recovery of process streams is conducted to enhance heat integration. Particularly applied to cryogenic processes, HENs retrofit with combined heat and work integration is mainly aimed at reducing the use of expensive cold services. The proposed multi-stage superstructure allows the increment of the existing heat transfer area, as well as the use of new equipment for both heat exchange and pressure manipulation. The pressure recovery of streams is carried out simultaneously with the HEN design, such that the process conditions (streams pressure and temperature) are variables of optimization. The mathematical model is formulated using generalized disjunctive programming (GDP) and is optimized via mixed-integer nonlinear programming (MINLP), through the minimization of the retrofit total annualized cost, considering the turbine and compressor coupling with a helper motor. Three case studies are performed to assess the accuracy of the developed approach, including a real industrial example related to liquefied natural gas (LNG) production. The results show that the pressure recovery of streams is efficient for energy savings and, consequently, for decreasing the HEN retrofit total cost especially in sub-ambient processes.

Calculations for HRE no.2 heat exchanger /

"Subject category: Physics."--Cover.

Velocity distributions in a plate heat exchanger channel

The development of a Laser Doppler Anemometer technique to measure the velocity distribution in a commercial plate heat exchanger is described. Detailed velocity profiles are presented and a preliminary investigation is reported on flow behaviour through a single cell in the channel matrix. The objective of the study was to extend previous investigations of plate heat exchanger flow patterns in the laminar range with the eventual aim of establishing the effect of flow patterns on heat transfer performance, thus leading to improved plate heat exchanger design and design methods. Accurate point velocities were obtained by Laser Anemometry in a perspex replica of the metal channel. Oil was used as a circulating liquid with a refractive index matched to that of the perspex so that the laser beams were not distorted. Cell-by-cell velocity measurements over a range of Reynolds number up to ten showed significant liquid mal-distribution. Local cell velocities were found to be as high as twenty seven times average velocity, contrary to the previously held belief of four times. The degree of mal-distribution varied across the channel as well as in the vertical direction, and depended on the upward or downward direction of flow. At Reynolds numbers less than one, flow zig-zagged from one side of the channel to the other in wave form, but increases in Reynolds number improved liquid distribution. A detailed examination of selected cells showed velocity variations in different directions, together with variation within individual cells. Experimental results are also reported on the flow split when passing through a single cell in a section of a channel . These observations were used to explain mal-distribution in the perspex channel itself.

Modelling and measurements on a condensing counter-flow heat exchanger

Experimental investigations and computer modelling studies have been made on the refrigerant-water counterflow condenser section of a small air to water heat pump. The main object of the investigation was a comparative study between the computer modelling predictions and the experimental observations for a range of operating conditions but other characteristics of a counterflow heat exchanger are also discussed. The counterflow condenser consisted of 15 metres of a thermally coupled pair of copper pipes, one containing the R12 working fluid and the other water flowing in the opposite direction. This condenser was mounted horizontally and folded into 0.5 metre straight sections. Thermocouples were inserted in both pipes at one metre intervals and transducers for pressure and flow measurement were also included. Data acquisition, storage and analysis was carried out by a micro-computer suitably interfaced with the transducers and thermocouples. Many sets of readings were taken under a variety of conditions, with air temperature ranging from 18 to 26 degrees Celsius, water inlet from 13.5 to 21.7 degrees, R12 inlet temperature from 61.2 to 81.7 degrees and water mass flow rate from 6.7 to 32.9 grammes per second. A Fortran computer model of the condenser (originally prepared by Carrington[1]) has been modified to match the information available from experimental work. This program uses iterative segmental integration over the desuperheating, mixed phase and subcooled regions for the R12 working fluid, the water always being in the liquid phase. Methods of estimating the inlet and exit fluid conditions from the available experimental data have been developed for application to the model. Temperature profiles and other parameters have been predicted and compared with experimental values for the condenser for a range of evaporator conditions and have shown that the model gives a satisfactory prediction of the physical behaviour of a simple counterflow heat exchanger in both single phase and two phase regions.

Hydrodynamic characteristics of a plate heat exchanger

This thesis describes a detailed investigation of the hydrodynamic characteristics of a commercially-available three-dimensional plate heat exchanger.

Local heat transfer coefficient in a baffled shell and tube heat exchanger

Local shell side coefficient measurements in the end conpartments of a model shell and tube heat exchanger have been made using an electrochemical technique. Limited data are also reported far the second compartment. The end compartment average coefficients have been found to be smaller than reported data for a corresponding internal conpartment. The second compartment data. have been shown to lie between those for the end compartments and the reported internal compartment data. Experimental data are reported fcr two port types and two baffle orientations. with data for the case of an inlet compartment impingement baffle also being given . Port type is shown to have a small effect on compartment coefficients, these being largely unaffected. Likewise, the outlet compartment average coefficients are slightly snaller than those for the inlet compartment, with the distribution of individual tube coefficients being similar. Baffle orientation has been shown to have no effect on average coefficients, but the distribution of the data is substantially affected. The use of an impingement baffle in the inlet compartment lessens the efect of baffle orientation on distribution . Recommendations are made for future work.

Studies of the fouling of heat exchanger equipment

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Design and analysis of micro-channel heat-exchanger embedded in Low Temperature Co-fire Ceramic (LTCC)

Increased device density, switching speeds of integrated circuits and decrease in package size is placing new demands for high power thermal-management. The convectional method of forced air cooling with passive heat sink can handle heat fluxes up-to 3-5W/cm2; however current microprocessors are operating at levels of 100W/cm2, This demands the usage of novel thermal-management systems. In this work, water-cooling systems with active heat sink are embedded in the substrate. The research involved fabricating LTCC substrates of various configurations - an open-duct substrate, the second with thermal vias and the third with thermal vias and free-standing metal columns and metal foil. Thermal testing was performed experimentally and these results are compared with CFD results. An overall thermal resistance for the base substrate is demonstrated to be 3.4oC/W-cm2. Addition of thermal vias reduces the effective resistance of the system by 7times and further addition of free standing columns reduced it by 20times.

Design construction and testing of a heat loop for study of fouling and its interrelationship to corrosion in heat exchanger tubes

A heat loop suitable for the study of thermal fouling and its relationship to corrosion processes was designed, constructed and tested. The design adopted was an improvement over those used by such investigators as Hopkins and the Heat Transfer Research Institute in that very low levels of fouling could be detected accurately, the heat transfer surface could be readily removed for examination and the chemistry of the environment could be carefully monitored and controlled. In addition, an indirect method of electrical heating of the heat transfer surface was employed to eliminate magnetic and electric effects which result when direct resistance heating is employed to a test section. The testing of the loop was done using a 316 stainless steel test section and a suspension of ferric oxide and water in an attempt to duplicate the results obtained by Hopkins. Two types of thermal ·fouling resistance versus time curves were obtained . (i) Asymptotic type fouling curve, similar to the fouling behaviour described by Kern and Seaton and other investigators, was the most frequent type of fouling curve obtained. Thermal fouling occurred at a steadily decreasing rate before reaching a final asymptotic value. (ii) If an asymptotically fouled tube was cooled with rapid cir- ·culation for periods up to eight hours at zero heat flux, and heating restarted, fouling recommenced at a high linear rate. The fouling results obtained were observed to be similar and 1n agreement with the fouling behaviour reported previously by Hopkins and it was possible to duplicate quite closely the previous results . This supports the contention of Hopkins that the fouling results obtained were due to a crevice corrosion process and not an artifact of that heat loop which might have caused electrical and magnetic effects influencing the fouling. The effects of Reynolds number and heat flux on the asymptotic fouling resistance have been determined. A single experiment to study the effect of oxygen concentration has been carried out. The ferric oxide concentration for most of the fouling trials was standardized at 2400 ppM and the range of Reynolds number and heat flux for the study was 11000-29500 and 89-121 KW/M², respectively.

Coupling short-term (B2G model) and long-term (g-function) models for ground source heat exchanger simulation in TRNSYS. Application in a real installation

Ground-source heat pump (GSHP) systems represent one of the most promising techniques for heating and cooling in buildings. These systems use the ground as a heat source/sink, allowing a better efficiency thanks to the low variations of the ground temperature along the seasons. The ground-source heat exchanger (GSHE) then becomes a key component for optimizing the overall performance of the system. Moreover, the short-term response related to the dynamic behaviour of the GSHE is a crucial aspect, especially from a regulation criteria perspective in on/off controlled GSHP systems. In this context, a novel numerical GSHE model has been developed at the Instituto de Ingeniería Energética, Universitat Politècnica de València. Based on the decoupling of the short-term and the long-term response of the GSHE, the novel model allows the use of faster and more precise models on both sides. In particular, the short-term model considered is the B2G model, developed and validated in previous research works conducted at the Instituto de Ingeniería Energética. For the long-term, the g-function model was selected, since it is a previously validated and widely used model, and presents some interesting features that are useful for its combination with the B2G model. The aim of the present paper is to describe the procedure of combining these two models in order to obtain a unique complete GSHE model for both short- and long-term simulation. The resulting model is then validated against experimental data from a real GSHP installation.