Pressure Drop Constraints Research Articles

Multi-field coupling in designing embedded microchannels for three-dimensional integrated chip: A topology optimization approach

Topology optimization methods have shown promise in enhancing the heat transfer performance of microchannel structures. However, the thermal-electrical-force multi-field coupling effects in three-dimensional integrated chips present a complex heat generation scenario that necessitates their consideration in the design of embedded microchannel structures. Here, we perform topology optimization of embedded microchannels specifically tailored for three-dimensional integrated chip, with a specific focus on the multi-field coupling effects of through-silicon-via structures within the topology optimization process. A new and improved 2D microchannel structure that exhibits superior heat transfer performance was obtained by analyzing the effects of pressure drop constraints within the channel, as well as fixing the microfin diameter and local heat flux of through-silicon-via. Furthermore, the obtained topology optimization results were validated through rigorous three-dimensional numerical simulations. The findings demonstrate that the new microchannel structure, when compared to the original microfin model, yields a significant improvement in the comprehensive heat transfer performance coefficient, achieving a remarkable enhancement factor of 1.43. Furthermore, under identical flow conditions, the structural stress within the chip experiences a substantial reduction of 43.9%. These outcomes underscore the efficacy of the topology optimization approach in effectively addressing the thermal management challenges associated with three-dimensional integrated chip.

Parametric shape optimization of pin fin arrays using a multi-fidelity surrogate model based Bayesian method

The current work aims to develop a multi-fidelity Bayesian optimization methodology to reduce computation time in CFD based design optimization of an internal cooling channel of a gas turbine blade. To build energy efficient gas turbine engines, it is important to increase the turbine inlet temperature, while preventing material failure of hot gas path components. Power lost due to pumping compressed air in turbine blade internal cooling channels can affect the overall efficiency of a power cycle. While designing such a cooling channel, it is important to ensure high heat transfer within a given pressure drop budget. Design optimization using CFD typically needs a sufficient number of computationally expensive high fidelity simulations to search for an optimum design. In the current work, a multi-fidelity Gaussian process surrogate based Bayesian optimization framework has been used to design a pin fin array channel, typically used for gas turbine blade trailing edge cooling, with the goal of maximizing Nusselt number at a constrained pressure loss. Data from a cheaper, low fidelity computation model has been leveraged, along with an expensive high fidelity one, in order to search for a design configuration that maximizes heat transfer at a given pressure drop constraint. The multi-fidelity approach improves upon single fidelity optimization results, at a low additional computational cost due to usage of simulation data from the cheap lowfidelity CFD model. A multifidelity approach outperformed the previous single fidelity case, with 6% higher objective while satisfying the pressure constraint, with 2% lower computational expense and 8 fewer high fidelity data point computations.

Meshless Optimization of Triply Periodic Minimal Surface Based Two-Fluid Heat Exchanger

Triply Periodic Minimal Surface (TPMS) is suitable for the heat transfer of fluids, but it is difficult to preserve the integrality of independent fluids channels during optimization. We present an effective meshless optimization framework of Triply Periodic Minimal Surface based two-fluid heat exchangers, which can be represented, analyzed and optimized using function representation. Our method is directly executed on continuous functions instead of time-consuming meshing (tetrahedral/hexahedral), thereby substantially promotes the efficiency and controllability. Specifically, a valid TPMS based two-fluid heat exchanger is first constructed by function expression. The heat exchanger consists of two independent fully-connected spaces, which are used to infill different fluids, respectively. The two spaces are divided by a smooth and continuous separating wall, which can be expressed by functions and inherits several good properties of TPMS, such as large heat exchange surface area, high-order smoothness, independence and full connectivity of each fluid channel, good mechanical properties and controllability. Then, we formulate the optimization model by controlling the thickness and topology of the separating wall directly using the function representation. Also, we adapt an efficient automatic optimization of the modeling problem by maximizing thermal energy exchange under maximum pressure drop constraint. Finally, we obtain an optimized two-fluid heat exchanger with continuous geometry changes and proper topology changes. To our knowledge, this is the first work to provide both design and optimization for the TPMS based two-fluid heat exchangers. Various numerical results demonstrate the effectiveness and efficiency of our method.

Topology optimization design of a passive two-dimensional micromixer

In this study, a novel two-dimensional micromixer design is proposed using the topology optimization method. The pressure drop constraint is introduced to achieve a limited pressure drop. The mixing performance of the proposed micromixer is evaluated over a broad range of Reynolds numbers (Re) through numerical simulations and experiments. The results showed that the mixing efficiency of the one-period and multi-period micromixers could reach 96% and 99%, respectively, while still maintaining a relatively low pressure drop. In addition, the experiment on the preparation of silver nanoparticles demonstrate the applicability and practicality of using topology optimization in the design of micromixers.

Experimental and Computational Study of Enhanced Forced Convection Heat Transfer in Novel Slotted Wavy-Plate-Fin Channels

Abstract Forced convective enhanced heat transfer performance of airflows (50 ≤ Re ≤ 4000, Pr ∼ 0.71) in novel slotted sinusoidal wavy-plate-fins is investigated both experimentally and computationally. The slotted wavy fin core evaluated in the experiments was produced by direct metal laser sintering (DMLS). Compared with the equivalent or nonslotted wavy fin core, also produced by DMLS, while the heat transfer was found to be similar, the pressure drop was reduced by as much as 31%. This very attractively significant enhancement was further explored in a three-dimensional computational analysis. Besides validating experimental results, it is seen that a significant part of pressure loss in plain wavy-fin channels is due to form drag induced by flow recirculation in the trough region. This is shown to be reduced substantially if the fins are slotted at large form drag locations. Their position and size, characterized, respectively, by phase angle (β) and dimensionless slot size (δ), are varied in the simulations to explore their role in the enhanced thermal-hydrodynamic performance. One such modified design exhibits a characteristically unusual performance at low Re, where improvement in heat transfer (+17%) is accompanied by a reduction in pressure loss (–16.8%). Additionally, at high Re, though a slight decline in heat transfer (–7.6%) is evidenced, the pressure drop is nearly cut in half (–46.6%). Moreover, the overall thermal-hydrodynamic performance based on the metric of fixed heat transfer rate and pressure drop constraint shows that ∼15% reduction in the required heat transfer surface area can be achieved with slotted wavy fins.

Spirally wound tubular heat exchanger optimisation using Genetic Algorithm

• Spirally coiled (Giauque-Hampson) type heat exchanger optimization. • Thermal analysis of optimum tube geometry predicted by Genetic Algorithm. • Design aimed at minimum exchanger weight under pressure drop constraints. • Design aimed at minimum exchanger height under pressure drop constraints. • Effect of different process parameters on the optimum heat exchanger design. A Genetic Algorithm based optimization of spirally wound two-fluid stream exchanger is presented. The proposed method elaborates a design methodology consistent with the user-defined specifications while simultaneously fulfilling a design objective linking optimization of either weight, height or thermo-hydraulic performances, etc., depending on the customer requirement. Optimization variables include tube material, tube size, normalized transverse and longitudinal pitches, number of tubes in the innermost layer, increment in the number of tubes with each successive layer, and the total number of tube layers. The effectiveness-NTU approach is adopted for design calculations, including fluid property variations with temperature. This paper explores the effect of optimization criteria like minimum weight or height and variation in pressure drop constraints on the optimized design. A compromise in exchanger effectiveness can substantially reduce its weight. Among the exchangers of the same effectiveness, the one handling 10 times larger flow could be 35 times heavier (subjected to other constraints). Exchanger designed with the minimum height criterion is nearly two times shorter than the one created on a minimum weight basis, while the shorter unit could be two times heavier. The optimum design is a trade-off between achievable minimum mass and maximum allowable pressure drop.

The hydraulic and thermal performances of rectangular and square microchannel with different hydraulic diameters cooled by graphene–platinum hybrid nanofluid

The objective of this paper is to analyze the effect of hydraulic diameter and channel shape on the thermal and hydrodynamic characteristics of a microchannel cooled by Graphene–Platinum/water hybrid nanofluid for electronic cooling applications. The study was performed numerically using mathematical software called Maple 19.0. Microchannels having square and rectangular cross-sections, and hydraulic diameters ranging from 200 µm to 1,000 µm were taken into consideration. Thermal resistance, heat transfer coefficient, pressure drop, and friction factor were evaluated for different conditions and their corresponding graphs are presented and discussed. It was evident from the results that low thermal resistance and high heat transfer coefficient was achieved upon decreasing the hydraulic diameter, which is favorable for the cooling of electronic chips and devices. Based on the Reynolds number, the heat transfer coefficient increased by 2–4 times for both rectangular and square microchannels, on decreasing the hydraulic diameter from highest value (1,000 µm) to lowest value (200 µm). However, friction factor and pressure drop increased for channels with lower hydraulic diameters. In addition, rectangular microchannels exhibited better heat transfer performance, while square microchannels had lower friction factor and pressure drop. Rectangular microchannels presented a maximum enhancement of 30% in heat transfer coefficient and a reduction of 18% in thermal resistance, when compared to square microchannels. The results also suggested that the performance of microchannels with 500 µm hydraulic diameter is balanced, considering both heat transfer performance and pressure drop constraints.

Analysis of Fluid Flow and Heat Transfer in Corrugated Perforated Plate Fin Heat Sinks

Abstract This paper reports a mathematical model for predicting the fluid and heat flow characteristics of a Z-shaped corrugated perforated plate heat sink. Experiments were carried out to validate overall pressure drop as well as heat transfer predictions. A two-pronged approach was undertaken to design a corrugated perforated fin geometry: (a) macroscopic packaging, where the flow is distributed into conduits before being fed into perforated plates, and (b) microscopic design, where the pores are sized to maximize heat dissipation. A methodology typically used for predicting flow maldistribution is extended for packaging porous perforated plates in the macroscopic approach. An illustrative study is carried that estimates the optimum number of porous perforated plate fins that can be packaged within a given volume under fixed pressure drop constraint. In the microscopic approach, an order of magnitude analysis was carried out to decide the optimum diameter to maximize the heat transfer rate and expression for optimum diameter, and maximum achievable heat flux is proposed. Numerical simulations were carried out by considering full perforated plate porous fin geometry and single-channel geometry, and good agreement in their results was found. Finally, this study elaborates on the importance of achieving uniform flow distribution across the porous perforated plate fins.

Process control strategies for solar-powered carbon capture under transient solar conditions

This paper presents process control strategies commanding the novel solar stripper (So-St) network to effectively regenerate the rich solvent and ultimately replace the conventional desorption unit in the PCC. In this work, the effect of solar heat flux (SHF) is analyzed and categorized by the active control strategy in full synergy with the absorber operation. The mismatch in operation between the two ends of the solvent cycle (absorption vs. desorption) is buffered/regulated by solvent storage tanks. Three original and two combined control scenarios are developed and assessed based on their main controlled output and manipulated input variables. It is found that the lean loading control strategy provides the most consistent absorber operation, reliable CO2 productivity, and desirable thermodynamic regime. This superior performance of lean loading control stems from absorbing a relatively larger SHF range without violating solvent temperature and pressure-drop constraints in the So-St network. In practical applications, it is recommended that lean loading control should incorporate temperature control to monitor solvent temperature and provide appropriate remedy control actions when required. Such process control strategies can lead to effective operation of the “solar-powered” carbon capture (SP-PCC), allowing SP-PCC technology to be installed and operated independently and autonomously from the power plant, thus cutting the capture energy penalty by integrating renewable solar heat.

Rigorous NLP distillation models for simultaneous optimization to reduce utility and capital costs

Two non-linear programming (NLP) models with rigorous stage-by-stage MESH calculations are proposed based on the concept of bypass efficiency. The models can be used to simultaneously optimize the number of stages, feed stage location and operating parameters such as the reflux ratio and column pressure. They can also be used for simultaneous flowsheet optimization with distillation columns and heat integration, as demonstrated in a case study. The first model removes an over-specification where the enthalpy of the outlet stream is calculated using an equation-of-state. A degrees of freedom (DOF) analysis shows that the calculation is not required since the enthalpy of the outlet stream is computed from the inlet stream and equilibrium stream and the outlet temperature does not need to be known for subsequent stage calculations. The second model reduces the number of free variables by grouping the bypass efficiencies in a systematic manner. This modification reduces the model size and solution time without sacrificing accuracy or the number of unique solutions. Other than that, the pressure drop equations were improved. The improvement proved to be significant as the original equations caused all stages to be active in a case study, while the same problem was not observed with the new set of pressure drop constraints. Both proposed models had shorter solution times, smaller model size and they yielded minimized objective values 1.5–5.4% lower compared to the original bypass efficiency model. • A modified bypass efficiency model with the removal of enthalpy equations is proposed in this work. • An NLP distillation model with grouped bypass efficiencies to reduce the free variables is presented in this paper. • A new set of pressure drop equations was developed to improve the original set of pressure drop constraints. • The proposed models performed better in terms of convergence, objective values and solution speed in the case studies.

Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers

We present a topology optimization approach for the design of fluid-to-fluid heat exchangers which rests on an explicit meshed discretization of the phases at stake, at every iteration of the optimization process. The considered physical situations involve a weak coupling between the Navier–Stokes equations for the velocity and the pressure in the fluid, and the convection–diffusion equation for the temperature field. The proposed framework combines several recent techniques from the field of shape and topology optimization, and notably a level-set based mesh evolution algorithm for tracking shapes and their deformations, an efficient optimization algorithm for constrained shape optimization problems, and a numerical method to handle a wide variety of geometric constraints such as thickness constraints and non-penetration constraints. Our strategy is applied to the optimization of various types of heat exchangers. At first, we consider a simplified 2D cross-flow model where the optimized boundary is the section of the hot fluid phase flowing in the transverse direction, which is naturally composed of multiple holes. A minimum thickness constraint is imposed on the cross-section so as to account for manufacturing and maximum pressure drop constraints. In a second part, we optimize the design of 2D and 3D heat exchangers composed of two types of fluid channels (hot and cold), which are separated by a solid body. A non-mixing constraint between the fluid components containing the hot and cold phases is enforced by prescribing a minimum distance between them. Numerical results are presented on a variety of test cases, demonstrating the efficiency of our approach in generating new, realistic, and unconventional heat exchanger designs.

Topology optimization of two fluid heat exchangers

A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for each of the fluids. A single design variable is used to describe the physical fields. The solid interface and the fluid domains are generated using an erosion-dilation based identification technique, which guarantees well-separated fluids, as well as a minimum wall thickness between them. Under the assumption of laminar steady flow, the two fluids are modelled separately, but in the entire computational domain using the Brinkman penalization technique for ensuring negligible velocities outside of the respective fluid subdomains. The heat transfer is modelled using the convection-diffusion equation, where the convection is driven by both fluid flows. A stabilized finite element discretization is used to solve the governing equations. Results are presented for two different problems: a two-dimensional case illustrating and verifying the methodology; and a three-dimensional case inspired by shell-and-tube heat exchangers. The optimized designs for both cases show an improved heat transfer compared to the baseline designs. For the shell-and-tube case, the full freedom topology optimization approach is shown to yield performance improvements of up to 113% under the same pressure drop.

Analysis of Fluid Flow and Heat Transfer in Corrugated Porous Fin Heat Sinks

This study reports on a mathematical model for predicting the fluid and heat flow characteristics of a Z-shaped corrugated foam heat sink. Experiments were carried out to validate local as well as overall pressure drop predictions. The mathematical model was further validated against corrugated carbon foam experimental measurements from the literature. A general flow parameter emerges from the formulation that is descriptive of flow uniformity. Based on a scaling analysis, it was found that a relatively low permeability foam, compared to the square of the conduit hydraulic diameter, is more effective than high permeability foam because of its ability to achieve uniform flow distribution. An illustrative study is carried that estimates the optimum number of porous fins that can be packaged within a given volume under fixed pressure drop constraint. Further, this study elaborates on the importance of achieving uniform flow distribution across the porous fins. The ideal condition of uniform flow was found to be useful in increasing the rate of heat transfer when compared with the actual condition of non-uniform flow for the range of parameters explored in this work. Finally, the impact of the flow non-uniformity parameter on the overall Nusselt number is illustrated.

Intelligent optimization design of shell and helically coiled tube heat exchanger based on genetic algorithm

The intelligent optimization design of a helically coiled tube heat exchanger is proposed. The structural design, meshing, and numerical calculations are integrated into the genetic algorithm to perform intelligent optimization in selecting the structural and thermodynamic parameters. Compared with the experimental results, the heat flux and heat transfer rate of the heat exchanger with the optimal structure increase by 110% and 101%, respectively, which can be proved by the decrease of the average intersection angle between the velocity vector and temperature gradient on both the shell side and tube side. Considering the pressure drop constraint, the maximum heat flux increases by 12% compared with the value obtained from the optimization criterion when the total heat transfer rate is maximized, indicating its potentials in reducing the financial cost. Finally, this method provides an automatic solution to the optimization design of a diversity of heat exchangers.

Practical Energy Retrofit of Heat Exchanger Network Not Containing Utility Path

The paper presents a method developed for the energy retrofit of specific Heat Exchanger Networks not containing Utility Paths. This useful and highly practically oriented method involves a systematic approach to obtaining the most efficient minimal modification topology of a Heat Exchanger Network, which brings the greatest benefits in terms of energy savings of the modified process. In principle, it is focused on finding the most suitable location for a new heat exchanger insertion to create the most efficient Utility Path. The next step of the developed retrofit method is the detailed design of the newly integrated heat exchanger using commercial software in combination with several heuristic rules regarding the cost-free investment and maintenance cost minimization of a new heat exchanger and considering heat transfer enhancement within the available exchanger type, space, and fluids pressure drop constraints. The detail design stage of the method also includes observation and reassessment of the performance and operational parameters of the existing heat exchangers. Then, the developed method is applied to the case of the Heat Exchanger Network retrofit in the process of the hydrogenation of oil.

Computationally efficient optimization of wavy surface roughness in cooling channels using simulated annealing

This article reports a computationally efficient optimization for wavy surface roughness in cooling channels based on simulated annealing. Our approach rapidly calculates the performance metrics of cooling channels using closed-form models and approximates an optimum design via a random optimization technique, simulated annealing. The proposed method optimizes the wall roughness of cooling channels for maximizing the heat transfer rate while satisfying the pressure drop constraint. The channel wall smoothly converges and diverges throughout to locally modulate the heat transfer rate and the pressure drop. For a given pressure constraint and heat load distribution, the optimizer is able to compare more than 10,000 possible channel designs within a minute and generate a distinct channel design that achieves the optimization objective. The channel temperature predicted by the optimizer differs up to 10.9% to the estimations by a finite volume model. Lastly, optimized wavy channel designs are introduced that exhibit up to 2.7 times greater performance factor than a conventional channel geometry. This work demonstrates the potential of algorithm-based optimization techniques for designing efficient thermodynamic systems.

Convexification for natural gas transmission networks optimization

Natural gas transmission is energy consuming due to significant pressure loss during the transportation process. Despite considerable effort to reduce its energy consumption in optimization study, the nonconvex behavior of mathematical models, mainly resulted from nonconvex pressure drop constraints, have made the problem challenging to tackle. To address this issue, this paper presents two convex formulation techniques to convexify the pressure drop constraints. The techniques use logical constraints to handle unknown gas flow direction to avoid absolute values and bilinear terms in the constraints. Modeling techniques are also presented to reformulate nonconvex compressor constraints into convex/concave ones. The proposed techniques are applied to two different scale natural gas transmission networks. Computational results suggest that the convexification relieves the models from local optima, and greatly improves solution quality and solution efficiency.

A novel single and multi-objective optimization approach based on Bees Algorithm Hybrid with Particle Swarm Optimization (BAHPSO): Application to thermal-economic design of plate fin heat exchangers

As a novel hybrid optimization approach, the single and multi-objective BAHPSO are investigated for thermal designing of the cross-flow plate fin heat exchanger (PFHE) under given heat duty and pressure drop constraints. Because both of the Particle Swarm Optimization (PSO) and Bess Algorithm (BA) are operating with a random primary population of solutions, the current study combined their searching abilities for the first time, and presented a novel searching procedure named BAHPSO. In the current investigation, Multi-Objective optimization (MO) of BAHPSO is simultaneously employed to acquire the maximum effectiveness and the minimum total annual cost (TAC) of a heat exchanger as two contradict objectives and then results are compared with MOPSO and MOBA. Hot and cold side length, fin frequency, number of fin layers, fin thickness, fin height, and fin lance length are chosen as seven decision parameters. Also, a sensitivity analysis is performed to study the impact of geometrical parameters on each objective function. Finally, accuracy and efficiency of the presented algorithm is proven via illustrative single-objective optimization case studies which adopted from the references. Results demonstrate that the BAHPSO can detect optimal shape with higher accuracy compared to other algorithms.

Numerical evaluation of a compact generator design for steam driven H2O/LiBr absorption chiller application

The objectives of this study are to analyze effects of design parameters of a generator with a steam heat source on condensation heat transfer and flow characteristics inside tubes and to design optimum configuration of the generator with minimum volume that satisfies design constraints for H2O/LiBr absorption chiller application. To that end, the heat transfer and flow characteristics of a straight-pipe tube and a tube with return bends were analyzed through numerical analysis according to the tube diameter, number of tubes, and the diameter of return bends. It was found that the minimum tube volume satisfying the design constraints was obtained for Ntube=2 and Dtube=12mm in the case of the straight tube. The smaller the diameter of the return bend was, the greater the flow separation area, which caused a large local flow velocity. In the case of the return bend tubes, the smallest tube volume that satisfies both the flow and pressure drop constraints was obtained for Ntube=2 and Dturn/Dtube=1.0. In the case Dturn/Dtube=1.5, where the pressure drop was the smallest, the pressure drop was higher by 9% compared to the pressure drop constraint (1 bar), but the tube volume that satisfies the flow constraints decreased by 49%.

The role of insert devices on enhancing heat transfer in a flat-plate solar water collector

This work presents a comparative experimental study of heat transfer enhancement in a flat-plate solar water collector using insert devices. Three wire-coils and three twisted-tapes were selected with representative geometrical characteristics typically employed in industrial applications. Isothermal pressure drop tests were carried out to obtain the fully-developed Fanning friction factor for a range of Reynolds numbers Re = [80–9000]. The increase in friction factor in comparison to smooth tube was computed for all the devices. Depending on Reynolds number and insert geometry fi/fs values ranged from 1.3 to 79.8. Furthermore, detailed temperature profiles were obtained for different sections along the absorber plate and the risers for five different mass flow rates covering the Reynolds range from [400–2500]. The increase of the inner heat transfer coefficient by the inserts caused an important decrease of the absorber temperature. At increasing mass flow rates (from Re ≈ 1000), all the inserts showed a very similar thermal performance which make them suitable for inserting within harp-type solar collectors, where pressure drop is not a constraint. The best inserts TT03, WC01 and WC02 gave at Re ≈ 1500 maximum absorber temperature decreases (insert vs smooth tube) of 5.05 °C, 5.40 °C and 5.34 °C. In serpentine-type solar collectors, due to pressure drop constraints, the wire coil WC01 with a moderate pitch to wire-diameter ratio (p/d = 1.5 and e/d = 0.07), is the best specimen to insert. WC01 presents a moderate pressure drop increase (fi/fs = 2.8 at Re ≈ 1000), an early promotion of turbulent flow (at Re ≈ 700), and a significant reduction of the absorber temperature (decreasing 4.84 °C vs smooth tube at Re ≈ 1000).