Combining reinforcement learning with mathematical programming:An approach for optimal design of heat exchanger networks

Heat integration is important for energy-saving in the process industry.It is linked to the persistently challenging task of optimal design of heat exchanger networks(HEN).Due to the inherent highly nonconvex nonlinear and combinatorial nature of the HEN problem,it is not easy to find solutions of high quality for large-scale problems.The reinforcement learning(RL)method,which learns strategies through ongoing exploration and exploitation,reveals advantages in such area.However,due to the complexity of the HEN design problem,the RL method for HEN should be dedicated and designed.A hybrid strategy combining RL with mathematical programming is proposed to take better advantage of both methods.An insightful state representation of the HEN structure as well as a customized reward function is introduced.A Q-learning algorithm is applied to update the HEN structure using theε-greedy strategy.Better results are obtained from three literature cases of different scales.

New Optimization Method, the Algorithms of Changes, for Heat Exchanger Design

Heat exchangers are widely used in the process engineering such as the chemical industries, the petroleum industries, and the HVAC applications etc. An optimally designed heat exchanger cannot only help the optimization of the equipment size but also the reduction of the power consumption. In this paper, a new optimization approach called algorithms of changes (AOC) is proposed for design and optimization of the shell-tube heat exchanger. This new optimization technique is developed based on the concept of the book of changes (I Ching) which is one of the oldest Chinese classic texts. In AOC, the hexagram operations in I Ching are generalized to binary string case and an iterative process, which imitates the I Ching inference, is defined. Before applying the AOC to the heat exchanger design problem, the new optimization method is examined by the benchmark optimization problems such as the global optimization test functions and the travelling salesman problem (TSP). Based on the TSP results, the AOC is shown to be superior to the genetic algorithms (GA). The AOC is then used in the optimal design of heat exchanger. The shell inside diameter, tube outside diameter, and baffles spacing are treated as the design (or optimized) variables. The cost of the heat exchanger is arranged as the objective function. For the heat exchanger design problem, the results show that the AOC is comparable to the GA method. Both methods can find the optimal solution in a short period of time.

Optimal design of the separate type heat pipe heat exchanger

Separate type heat pipe heat exchangers are often used for large-scale heat exchanging. The arrangement of such a heat exchanger conveniently allows heat input to and output from the heat exchanger at remote locations. The traditional method of designing an ordinary HPHE (heat pipe heat exchanger) is commonly applied in the separate type exchanger design, but the calculations have to be carried out separately, which makes it very complicated. In this work, the ε-NTU (effectiveness-Number of Transfer Units) method was applied for optimization analysis of single- or multi-level separate type heat pipe heat exchangers. An optimizing formula for single-level separate type heat pipe heat exchangers was obtained. The optimizing principles of effec- tiveness-NTU and heat transfer rate by the equal distribution method for multi-level separate type heat pipe heat exchanger are presented. The design of separate type heat pipe heat exchangers by the optimizing method is more convenient and faster than by the traditional method.

Flexibility analysis and design of heat exchanger network for syngas-to-methanol process

The heat exchanger network(HEN)in a syngas-to-methanol process was designed and optimized based on pinch technology under stable operating conditions to balance the energy consumption and economic gain.In actual industrial processes,fluctuations in production inevitably affect the stable operation of HENs.A flexibility analysis of the HEN was carried out to minimize such disturbances using the downstream paths method.The results show that two-third of the downstream paths cannot meet flexibility requirements,indicating that the HEN does not have enough flexibility to accommodate the disturbances in actual production.A flexible HEN was then designed with the method of dividing and subsequent merging of streams,which led to 13.89%and 20.82%reductions in energy consumption and total cost,respectively.Owing to the sufficient area margin and additional alternative heat exchangers,the flexible HEN was able to resist interference and maintain production stability and safety,with the total cost increasing by just 4.08%.

Design and Construction of a Spiral Heat Exchanger

In this article, the performance and applications of a Spiral Plate Heat Exchanger are demonstrated. Also, governing equation of heat transfer phenomena in such heat exchangers is discussed. Regarding the governing equations, a LAB-sized model of this type of heat exchanger was designed and constructed. Galvanized Iron sheets were used as the heat transfer surfaces. Two Galvanized Iron sheets were rolled together around a central core and, as a result, two separated channels were made. Also, a predesign simulation of the heat exchanger was done using the Fluent software to predict the performance of the heat exchanger. First the geometry was made using Gambit software environment then the model was analyzed through Fluent. Because of less fouling, easier cleaning and high heat transfer coefficient, Spiral Heat Exchanger is a good alternative to the other types of heat exchangers, especially when it’s going to handle high fouling flows or highly viscous fluids. Low fouling rate of the heat exchanger, reduces the need of cleaning and therefore the out of service will be decreased. In the constructed heat exchanger, Nusselt number increases as the mass flow rate increases. Average Nusselt number is about 100 that is very good.

A Pole Assignment Design Method of Process Control System for Tubular Heat Exchanger

This Paper has first studied the simplified model of tubular heat exchanger which is widely used in the industry and other field.On the basis of reference 2,a new pole assignment design method of pro-cess control system with derivative control action is found.For the above system,the method and the for-mation which calculate the feedback matrix K and gain matrix L is given,and the simulation of the system is made.

Calculation Method of Passive Residual Heat Removal Heat Exchanger and Numerical Simulation

The tube inside and outside heat transfer mechanism of Passive Residual Heat Removal Heat Exchanger (PRHR HX) was analyzed. The calculation method of this special heat exchanger under natural convection condition in In-containment Refueling Water Storage Tank (IRWST) was carried out. The single-tube coupling model three-dimensional natural circulation in the IRWST was simulated numerically using Fluent. The heat transfer and flow characteristics of the fluid in IRWST were obtained. The comparison of the results between theoretical arithmetic and numerical simulation showed that the theoretical calculation method is suitable for the heat transfer calculation of PRHR HX.

PIV Investigations of Flow Patterns in the Entrance Configuration of Plate-fin Heat Exchanger

Flow characteristics in the entrance of plate-fin heat exchanger have been investigated by means of particle image velocimetry (PIV). The flow field was measured using the two-frame cross-correlation technique. Streamline and velocity contour graphs at different cross-sections were obtained in the experiment. The experimental results indicate that flow maldistribution in the conventional header is very serious, while the improved header configuration with punched baffle can effectively improve the uniformity. The flow maldistribution parameter in plate-fin heat exchanger has been reduced from 1.21 to 0.21, and the ratio of the maximum velocity to the minimum is reduced from 23.2 to 1.8 by install-ing the punched baffle. The results suggest room for the optimum design of plate-fin heat exchanger.

Research on ground heat exchanger of Ground Source Heat Pump technique

Ground Source Heat Pump technique and its operating principle are described in this paper. Ground heat exchanger is the key technique of ground source heat pump and its patterns are discussed. Software is helpful to design ground heat exchanger. A project of Chinese Ground Source Heat Pump is introduced and its market is more and more extensive.

Near ground air temperature calculation model based on heat transfer of vertical turbulent and horizontal air flow

In order to calculate the air temperature of the near surface layer in urban environment,the surface layer air was divided into several sections in the vertical direction,and some energy balance equations were developed for each air layer,in which the heat exchange due to vertical turbulence and horizontal air flow was taken into account.Then,the vertical temperature distribution of the surface layer air was obtained through the coupled calculation using the energy balance equations of underlying surfaces and building walls.Moreover,the measured air temperatures in a small area(with a horizontal scale of less than 500 m) and a large area(with a horizontal scale of more than 1 000 m) in Guangzhou in summer were used to validate the proposed model.The calculated results accord well with the measured ones,with a maximum relative error of 4.18%.It is thus concluded that the proposed model is a high-accuracy method to theoretically analyze the urban heat island and the thermal environment.

Entransy dissipation minimization for optimization of heat exchanger design

In this paper,by taking the water-water balanced counterflow heat exchanger as an example,the entransy dissipation theory is applied to optimizing the design of heat exchangers.Under certain conditions,the optimal duct aspect ratio is determined analytically.When the heat transfer area or the duct volume is fixed,analytical expressions of the optimal mass velocity and the minimal entransy dissipation rate are obtained.These results show that to reduce the irreversible dissipation in heat exchangers,the heat exchange area should be enlarged as much as possible,while the mass velocity should be reduced as low as possible.

Theoretical analysis of a method for segmented heat exchanger design

In the process of the design of heat exchangers,it is difficult to establish the factors governing the optimal points of the design objective functions due to the contradictions and uncertainties of the design objectives.The variation of fluid properties is one of the main factors causing this type of uncertainty.Conventional design methods have not completely solved these problems.In the present work,based on the logarithmic mean temperature difference,a new heat exchanger design method(called the segmented design method) is proposed which takes into account the variation of fluid properties with respect to the temperature.In this method,the whole heat exchanger is first divided into several segments.Then by applying the principle of the conservation of energy and taking into account the initial conditions as well as the connecting conditions of the adjacent segments,the inlet and outlet temperatures of each segment are determined.Finally,the application of the logarithmic mean temperature difference method on each segment defines the heat transfer area.

Shortcut Method of Design and Energy-Saving Analysis of Sargent Dividing Wall Column

The Sargent dividing wall column can implement four products separation sequences in one column based on Fully Thermally Coupled Distillation Column. The initial design parameters are required for the design optimization or dynamic control of the Sargent dividing wall column, and in order to make the rigorous simulation of the Sargent dividing wall column more conducive to convergence, a ten column model for complex Sargent column is established in this paper,and the shortcut design method of this model is proposed. The internal minimum vapor and liquid flow are obtained by the Underwood equations and the mass balance method and the V-min method. The separation for a 4-component shortcut mixture of pentane, hexane, heptane and octane was considered, while the initial values of design parameters and the ratio of vapor-liquid distribution of each column were calculated by using the shortcut design method of a ten column model. And by comparing the shortcut calculations with rigorous simulation results, the practicality and reliability of shortcut calculations were verified. The reason for energy saving was analyzed based on back-mixing. A virtual heat exchanger is proposed to make the Sargent dividing wall column more energy efficient.

Assessment of micro-scale heat exchangers efficiency using lattice Boltzmann method and design of experiments

The study is focused on the use of nanofluids in a micro-open tall cavity,which is a type of micro heat exchanger(MHE).The cavity is heated from the bottom sidewall in a sinusoidal pattern,and the effects of four input parameters(Ra,Ha,Kn,and Vf)on heat transfer and irreversibility are investigated using numerical simulations based on Lattice Boltzmann Method(LBM).The findings of the study suggest that the local heat transfer on the bottom sidewall is strongly influenced by Ra and Ha,while the surface distribution of entropy generation is mainly dependent on Kn.The study also shows that the optimization of the magnitude and wavelength of the sinusoidal temperature can improve both local heat transfer and surface distribution of entropy generation.The results of the study provide valuable insights into the design of micro heat exchangers and suggest that the optimization of micro-porous geometries using DOE could lead to increased energy efficiency.The study contributes to our understanding of the complex interactions between input parameters in micro heat exchangers and highlights the importance of considering multiple parameters in the design process.

Algebraic Calculation Method of One-Dimensional Steady Compressible Gas Flow

This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elements of a finite size for which mass, energy and momentum conservation laws are written in the integral form, assuming linear distribution of the parameters along the length. As a result, the calculation is reduced to finding the roots of a quadratic algebraic equation, thus providing an alternative to numerical methods based on differential equations. The advantage of this method is its high tolerance to coarse discretization of the calculation area as well as its good applicability for transonic flow calculations.

Prediction of Equivalent Thermal Conduction Resistance of Printed Circuit Heat Exchangers

Printed circuit heat exchangers(PCHEs) have great potential to be employed in the advanced nuclear reactor systems. In this work, the equivalent thermal conduction resistance of PCHE is studied. The influences of thermal convection resistance are analyzed. The results indicate that the equivalent thermal conduction resistance of PCHEs with unequal numbers of hot plates and cold plates are sensitive to the thermal convection resistance of hot side and cold side. Specifically, for case C which has unequal number of hot and cold channels, the maximum value of equivalent thermal conduction resistance can be 1.7-2.4 times the minimum value. The equivalent thermal conduction resistance is underestimated under the isothermal boundary. In addition, the non-uniformity of the lengths of all the heat flux lines determines the influence degree of thermal convection resistance on the equivalent thermal conduction resistance. For further investigation, Latin hypercube sampling method is adopted to generate a large number of design points for each PCHE configuration. Based on the sample data, mathematical correlations and artificial neural network(ANN) for prediction of equivalent thermal conduction resistance for each case are developed. The proposed correlations of equivalent thermal conduction resistance for each case have acceptable accuracy of prediction with a wide range covering general engineering applications. The ANN model can achieve much better prediction accuracy than the proposed correlations thus it is recommended in the cases that the prediction accuracy is considered as the priority need.

A refined design method for precoolers with consideration of multi-parameter variations based on low-dimensional analysis

The precooler is a distinctive component of precooled air-breathing engines but constitutes a challenge to conventional thermal design methods.The latter are based upon assumptions that often reveal to be limited for precooler design.In this paper,a refined design method considering the variations of fluid thermophysical properties,flow area and thermal parameters distortion,was proposed to remediate their limitations.Firstly,the precooler was discretized into a fixed number of sub-microtubes based on a new discretization criterion.Next,in-house one-dimensional(1D)and two-dimensional(2D)segmented models were established for rapid thermal design and precooler rating with non-uniform airflow,respectively.The heat transfer experimental studies of supercritical hydrocarbon fuel were performed to verify the Jackson correlation for precooler design and the in-house models were validated against the reported data from open literature.On this basis,the proposed method was employed for the design analysis of hydrocarbon fuel precoolers for precooled-Turbine Based Combined Cycle(TBCC)engines.The results show that the local performance of precoolers is intrinsically impacted by the aforementioned three variations.In the case study,the local heat transfer performance is drastically affected by coolant flow transition.While the circumferential temperature distortion of airflow is weakened by heat transfer.With consideration of additional parameter variations,this novel method improves design accuracy and shortens the design time.

Deep convolutional surrogates and freedom in thermal design

A deep learning approach is presented for heat transfer and pressure drop prediction of complex fin geometries generated using composite Bézier curves.Thermal design process includes iterative high fidelity simulation which is complex,computationally expensive,and time-consuming.With the advancement in machine learning algorithms as well as Graphics Processing Units(GPUs),parallel processing architecture of GPUs can be used to accelerate thermo-fluid simulation.In this study,Convolutional Neural Networks(CNNs)are used to predict results of Computational Fluid Dynamics(CFD)directly from topologies saved as images.A design space with a single fin as well as multiple morphable fins are studied.A comparison of Xception network and regular CNN is presented for the case with a single fin design.Results show that high accuracy in prediction is observed for single fin design particularly using Xception network.Xception network provides 98 percent accuracy in heat transfer and pressure drop prediction of the single fin design.Increasing the design freedom to multiple fins increases the error in prediction.This error,however,remains within three percent of the ground truth values which is valuable for design purpose.The presented predictive model can be used for innovative BREP-based fin design optimization in compact and high efficiency heat exchangers.

Modeling of Air Temperature for Heat Exchange due to Vertical Turbulence and Horizontal Air Flow

In order to calculate the air temperature of the near surface layer in urban environment,the surface layer air was divided into several layers in the vertical direction,and some energy balance equations were developed for each air layer,in which the heat exchange due to vertical turbulence and horizontal air flow was taken into account.Then,the vertical temperature distribution of the surface layer air was obtained through the coupled calculation using the energy balance equations of underlying surfaces and building walls.Moreover,the measured air temperatures in a small area(with a horizontal scale of less than 500 m)and a large area(with a horizontal scale of more than 1 000 m)in Guangzhou in summer were used to validate the proposed model.The calculated results agree well with the measured ones,with a maximum relative error of 4.18%.It is thus concluded that the proposed model is a high-accuracy method to theoretically analyze the urban heat island and the thermal environment.