Heat Capacity Rate Ratio Research Articles

Experimental investigation on the thermal and flow performance of a thermodynamically-balanced packed bed humidification system

In this paper, a packed bed humidification system filled with corrugated wire mesh was experimentally investigated to obtain a better humidification performance. To thermodynamically balance the simultaneous heat and mass transfer process, multiple water injection bypasses were fabricated at different packing heights based on the entropy generation minimization method. In addition to the inlet water temperature, the influences of the liquid–gas ratio and injection ratio on the humidification capacity, energy effectiveness, and pressure drop were respectively studied and discussed. The experimental and comparison results demonstrated that the established humidification device was robust and superior. It was summarized that raising the number of injections can significantly elevate the humidification capacity, and synchronously magnify the pressure drop for all the cases, while the effectiveness behaved a reverse trend. Additionally, a higher value of the inlet water temperature could increase the humidification capacity and effectiveness, as well as the pressure drop. And, an elevation amplitude of the humidification capacity emerged as 35.51% for the double water injections with a maximum value of 1.48 × 10−2 kgs−1 once the liquid–gas ratio increased from 1 to 1.36, while the value was 39.13% as the injection ratio raised from 0.33 to 0.7. Furthermore, it was illustrated that increasing the mass flow rate of the liquid will reduce the effectiveness when the heat capacity rate ratio is larger than 1, and the effectiveness can reach 0.97 at Twi = 70 °C. In the process of thermodynamic balancing, the increase in the pressure drop of humid air should receive more attention for the designer and researcher related to the packed bed humidifier.

An optimization of a pre-cooling system for batch processes: A case study of the tubular ice production process

Mathematical models for predicting the thermal behavior of feed water precooling systems for tubular ice makers were developed. A commercial water chiller and plate type heat exchanger were used as the cooling source and heat exchanging device. The simulation results suggest that the system, in which the feed water is circulated through the heat exchanger, provides a higher effectiveness (ε) with a lower heat capacity rate ratio of the feed water to the chilled water (wr) for a certain number of transfer units (NTU). In the range of the ice maker capacities popularly used, at a NTU of unity, the optimum heat capacity rate ratio of the feed water to the chilled water (wr) could be estimated to be 0.48. The water chillers would operate in the range of their minimum specific power consumptions when the feed water temperature was higher than 11 °C. The system has the potential to reduce the energy consumption about 6.7–11.6%. In addition, it can improve the productivity. The system was tested with a conventional ice maker. The energy consumption can be reduced as predicted by the model. The results could be also applied to a precooling or preheating of any production process.

Sensible heat recovery systems for batch processes with waste heat fluid drained at the end of the process

Mathematical models for modelling the behaviors of heat recovery systems of batch processes with waste heat fluid drained at the end of the process were developed. The results show that the optimum heat capacity rate ratio of the feed to the drain fluids might be estimated to be unity. For the drained fluid circulated (Dc), and flowing through heat exchanger (Dt) systems, the optimum number of transfer units might be estimated to be 1 and 4, and the effectiveness increases as the heat capacity rate ratio of the feed water to the drain water decreases and increases, respectively. The drained fluid circulated with the feed flowing through the heat exchanger system provides not only the highest effectiveness but also the lowest number of transfer units. A prototype of energy recovery system for the drained water from a 30 ton/day conventional tubular ice maker was developed according to the obtained result. It shows that the system is able to increase the productivity about 1600 kg/day and decrease the energy consumption by 5%. This concept has never been found. It may be applied to recover energy from batch processes having high or low temperature fluid drain after the end of the process.

A Scalable Compact Additively Manufactured Molten Salt to Supercritical Carbon Dioxide Heat Exchanger for Solar Thermal Application

Abstract Design of an additively manufactured molten salt (MS) to supercritical carbon dioxide (sCO2) primary heat exchanger (PHE) for solar thermal power generation is presented. The PHE is designed to handle temperatures up to 720 °C on the MS side and an internal pressure of 200 bar on the sCO2 side. In the core, MS flows through a three-dimensional periodic lattice network, while sCO2 flows within pin arrays. The design includes integrated sCO2 headers located within the MS flow, allowing for a counterflow design of the PHE. The sCO2 headers are configured to enable uniform flow distribution into each sCO2 plate while withstanding an internal pressure of 200 bar and minimizing obstruction to the flow of MS around it. The structural integrity of the design is verified on additively manufactured (AM) 316 stainless steel sub-scale specimens. An experimentally validated, correlation-based sectional PHE core thermofluidic model is developed to study the impact of flow and geometrical parameters on the PHE performance, with varied parameters including the mass flowrate, surface roughness, and PHE dimensions. A process-based cost model is used to determine the impact of parameter variation on build cost. The model results show that a heat exchanger with a power density of 18.6 MW/m3 (including sCO2 header volume) and effectiveness of 0.88 can be achieved at a heat capacity rate ratio of 0.8. The impact of design and AM machine parameters on the cost of the PHE are assessed.

Effect of single-phase flow maldistribution on the thermal performance of brazed plate heat exchangers

This paper presents an experimental and numerical investigation of the effect of single-phase flow maldistribution on the thermal performance of brazed plate heat exchangers (BPHEs). A thermal performance model of the BPHEs is developed with the consideration of flow maldistribution among the channels. The proposed model is validated against the experimental results. The model simulations reveal that the flow maldistribution has a trivial impact on the overall thermal capacity of the BPHEs if two fluid streams are supplied from the same side of the heat exchangers; if two fluid streams are supplied from the opposite side, the overall thermal performance is significantly deteriorated due to mismatched flow distributions of two fluid streams. Moreover, other factors are also proven to act in this issue, including the number of plates, plate length, header/port size, sudden expansion flow at the heat exchanger entrance, and heat capacity rate ratio of two streams. They either directly change the flow distribution or potentially affect the thermal effectiveness of the BPHEs. Based on the simulation results, correlations are generated, which can evaluate the thermal capacity degradation due to flow maldistribution without the necessity of knowing the detailed flow distribution and building heat exchanger models.

Examination of Energy Efficiency of Air Handling Unit with Integrated Air to Air Heat Exchanger in Cooling Mode

Object of the present study is an experimental determination of parameters, showing efficiency of air handling unit with integrated air to air heat exchanger in cooling mode: effectiveness of supply side of air to air heat exchanger, coefficient of performance and specific fan power of air handling unit. A daily performance of air handling unit in cooling mode is conducted. Effectiveness of supply side of air to air heat exchanger in range of 50.5 % to 74.3 % is received. Coefficient of performance in range of 0.88 to 2.99 and specific fan power of air handling unit in range of 1.77 kW/(m3/s) to 3.06 kW/(m3/s) are received. A relation between effectiveness of supply side of air to air heat exchanger and ratio of heat capacity rates of supply and exhaust air is received. Effectiveness of supply side of air to air heat exchanger depends on values of mass flow of supply and the exhaust air. High values of mass flow of exhaust air responds to high effectiveness of supply side of air to air heat exchanger.

An additively-manufactured molten salt-to-supercritical carbon di-oxide primary heat exchanger for solar thermal power generation – Design and techno-economic performance

The design and techno-economic performance of a compact additively manufactured (AM) molten salt (MS)-to-supercritical carbon di-oxide (sCO2) primary heat exchanger (PHE) for solar thermal application is described. The PHE design consists of sCO2 flow through an array of microscale pin fins while the MS flows through mm-scale rectangular channels. Constraints imposed by AM using laser powder bed fusion method are considered in the design. Structural and fluid flow simulations are performed to arrive at a viable design of the core and headers. A simplified one-dimensional steady state model for the PHE is developed including the impact of surface roughness from the AM process. A process-based cost model is used to determine the tradeoff between thermofluidic design and manufacturing cost.A parametric study is performed using the thermo-fluidic and cost models to determine the set of geometrical and flow variables that result in high power density and low cost, while restricting the pressure drop on the sCO2 side to less than 2% of line pressure. Flow rates of MS and sCO2 were varied over heat capacity rate ratios ranging from 0.2 to 1. Results indicate that it is possible to design a low-pressure drop AM PHE with an effectiveness of 90% and a power density in excess of 10 MW/m3 (including headers). Fabrication of representative nickel superalloy specimens are shown to demonstrate that low-porosity parts with the requisite dimensional tolerance of PHE core can be generated.

High efficiency 3-D printed microchannel polymer heat exchangers for air conditioning applications

The design, fabrication, and experimental characterization of a counterflow Micro-pin array Polymer Heat eXchanger (MPHX) for HVAC applications is described. The design consists of water flow through microscale pin array plates, and airflow paths in a counterflow direction through adjacent rectangular channels. When compared to a Finned Tube Heat eXchanger (FTHX), the water plates take the place of fins and the crossflow tube bank is eliminated. The MPHX is fabricated by 3 D printing using a digital light synthesis method. A correlation-based model is developed and used to explore the parametric space to arrive at a baseline MPHX core geometry. Mechanical and fluidic simulations are performed on the baseline geometry to further develop the design. A sub-scale MPHX with a nominal cross duct area of 10.1 cm × 20.3 cm is designed and fabricated. Its thermal performance over a range of air and water flow rates corresponding to heat capacity rate ratios in the range of 0.25–1 is investigated. Results show that the effectiveness varies from 0.65 to 0.95 corresponding to a of 1 to 0.25. The experimental data are used to validate a correlation-based thermo-fluidic model of the MPHX. The validated model is further used to compare the performance advantages of the MPHX design over a FTHX. For a given heat exchanger volume and thermo-fluidic conditions, the MPHX transfers 55% more thermal energy when compared to a FTHX at comparable air-side pressure drops.

Fluid Friction Effects on the Thermodynamic Performance of Spiral Plate Heat Exchangers

This paper presents a detailed analysis of the thermodynamic performance of spiral plate heat exchangers (SPHEs) and their channels by considering the fluid friction effect and no heat leakage to the environment. An optimal design algorithm for SPHEs is developed to find higher compactness and the overall heat transfer coefficient by increasing channels pressure drops, maintaining the geometric aspect ratio, and minimizing total costs. To determine the internal temperature distributions and the rates of heat transfer, a mathematical model is proposed. Fluid friction effects are examined as viscous heating; for this purpose, new parameters of the viscous heating entransy number and viscous heating entransy resistance are defined. Finally, various single-phase countercurrent SPHEs assuming a constant heat transfer rate, are modeled and compared in terms of energy, entropy generation, and entransy criteria. The results show the fluid friction effects as pressure drop effects in entropy generation are insignificant when compared to those caused by heat transfer. However, fluid effects as viscous heating in entransy analysis show that these effects can be rather significant in SPHEs with large spiral turn numbers or small values of heat capacity rate ratios. The obtained data suggest the significant role of entransy methods and their reliability to entropy generation methods in thermodynamic performance evaluation of SPHEs.

주기적으로 작동하는 평행류 열교환기의 해석해와 그 응용

The objective of this study is to present an analytical model for a parallel-flow rotary wheel heat exchanger. The model is based on mathematical solution for an ideal parallel-flow heat exchanger with a periodic inlet temperature condition. Air and wheel matrix temperatures are given in an infinite series of the product of trigonometric and exponential functions. An analytical expression is also presented for the effectiveness of the heat exchanger, which has been validated using literature and numerical data. The model is confirmed to give an exact result when the NTU ratio between hot and cold region is unity. It tends to give a higher error for smaller heat capacity rate ratio as it deviates from the unity. Ranges of parameters are presented with distribution of the maximum absolute error. This study shows that the model is applicable to cross-flow heat exchangers when the split ratio approaches zero.

Investigation on the potential of multiple water injections in thermodynamic optimization of heat and mass transfer process in air humidifier

In this paper, several thermodynamic optimization strategies are implemented to tap the potential of multiple water injections in thermodynamic balancing of combined heat and mass transfer process in air humidifier. The all-state of humid air including unsaturation, saturation and supersaturation states are particularly considered. Based on finite difference method, theoretical models are integrated with multiple injection methods. In the off-design analysis, the equipartition process of the driving forces including heat transfer temperature difference and mass transfer pressure difference are full of attention and interest. The research results present that entropy generation minimization is achieved when the values of heat capacity rate ratio equal to unity for all the cases. A larger value of the number of injections will improve the equipartition process of the driving forces, resulting in a reduction of total normalized entropy generation. In addition, it is found that these driving forces can be better balanced with larger number of injections and smaller injection ratio, when the heat capacity rate ratio is constant. Moreover, it is observed that energy effectiveness can be improved and the total normalized entropy generation is diminished as the inlet relative humidity augments, with a minimum normalized entropy generation of 0.0045 emerged at φi=0.85. Furthermore, it is also highlighted that controlling and adjusting the relative humidity of inlet humid air for the optimization of thermal devices and engineering systems is significant and available, especially referred to the all-state of humid air.

Use of single air extraction and injection to thermodynamically balance the combined heat and mass transfer process

In order to thermodynamically balance the combined heat and mass transfer process at the conditions of unsaturated, saturated and supersaturated state of humid air, measures like single air injection and extraction are implemented to address the distribution of driving forces. From the microscopic point of view, integrated mathematical models for simultaneous heat and mass transfer process are built, coupled with zero, single air extraction and single air injection methods. Off-design analysis for the balance process of driving forces including the heat transfer temperature difference and mass transfer pressure difference are accomplished. The research results exhibit that single air extraction is the preferable measure to lower the total entropy generation in general operating regions for simultaneous heat and mass transfer process (the liquid gas ratio less than 2.9), compared with single air injection. It is found that a minimum value for normalized entropy generation is appeared for all the cases, as the heat capacity rate ratio is unity, and a specific extraction ratio is obtained to minimize the entropy generation with fixed liquid-gas ratio. In addition, it is observed that higher inlet relative humidity will decrease the total normalized entropy generation, while an optimal value is obtained as 0.0064 at inlet relative humidity of 0.85. Meanwhile, inlet relative humidity represents a positive effect on system energy efficiency. It is also confirmed that as the number of extractions is constant and other measures are limited, adjusting the extraction height is an available additional option for further optimizing the thermodynamic performance.

Thermal performance analysis of fin-and-tube heat exchangers operating with airflow nonuniformity

This study develops a tube element method for thermal performance analysis of fin-and-tube heat exchangers operating with airflow nonuniformity. Experimental investigations have been performed on two fin-and-tube heat exchangers to validate the proposed tube element method. The heat exchanger tubes are discretized into a finite number of tube elements. These tube elements are observed as distinctive sub-exchangers, described by the appropriate heat transfer relations. The tube element method is capable of predicting the effectiveness in heat exchangers with complex tube circuitries, operating with either uniform or nonuniform airflows. The following general conclusions are obtained: the size of the effectiveness deterioration depends mainly on the heat exchanger operating point and on the degree of airflow nonuniformity. The effectiveness deterioration is highest when the heat capacity rate ratio is 1 and lowest when the heat capacity rate ratio is 0, for airflow nonuniformities with orientation perpendicular to the tube axis. The opposite is seen for airflow nonuniformities with orientation parallel to the tube axis. The heat exchanger effectiveness deterioration is up to 5.2% and 14.5% for complex nonuniform airflow profiles encountered in real-world operation, having airflow nonuniformity degrees of 0.43 and 0.81, respectively. Further, it was found that the heat exchanger tube circuitry design, the thermal resistance ratio and the airflow regime also influence the size of the effectiveness deterioration.

Performance analysis of a multi-stage humidification–dehumidification desalination system with different salinity levels

Humidification–dehumidification (HDH) technology is an innovative desalination technology that is inexpensive and reliable for small-scale applications. With the development of research, increasing scholars are beginning to adopt a closed-water cycle configuration to improve the HDH system efficiency. The resulting problems of salt accumulation and salinity regulation have not yet been effectively addressed. This paper presents a thermodynamic analysis of a closed-water multi-stage HDH desalination system with different salinity levels. The increase in salinity results in a decrease in the water productivity (~0.75% per 1% increase in the salinity) and maximum energy efficiency (in an average of 11.44% for 20% salinity). It is suggested that the salinity level in the system should be kept below 15% to prevent the maximum energy efficiency of the system lower than that of the open-water system. Additionally, the parameter referred to as the pinch point heat capacity rate ratio is introduced to assess the system performance with different salinity levels. The energy efficiency is maximised when the pinch point heat capacity rate ratio of the 1st-stage dehumidifier is equal to unity at any salinity level. Meanwhile, the effect of salinity on energy efficiency can be judged as an enhanced or diminished role based on whether the pinch point heat capacity rate ratio of the 1st-stage dehumidifier is less or greater than unity.

Transient performance of coupled heat and mass transfer in cross-flow hollow fiber membrane module for air dehumidification

Membrane-based liquid desiccant dehumidification has great advantages over traditional method, particularly in avoiding liquid droplets moving into the process air. This paper proposes a simple model to predict the transient performance of the hollow fiber membrane-based dehumidification module. To simplify the fiber-to-fiber influence, the modeled membrane module is assumed to be a parallel-plates heat mass exchanger. The model has been calibrated and validated with a transient experiment reasonably well. Impacts of various parameters on the transient performance were studied by using the proposed model. The results show that the variation of air temperature is more significant than air humidity. The absorption heat of water vapor is the main resistance of heat and mass transfer. It initially restricts the growth of the cooling effectiveness, and then limits the driving potential for moisture transfer. Therefore, it brings the dehumidification effectiveness down. It is found that reducing the heat capacity rate ratio can reduce the equilibrium time, and increase the cooling and dehumidification effectiveness. The high packing density increases the dehumidification effectiveness with a negligible effect of somewhat drop in cooling effectiveness. By contrast, the geometry of the fiber packing arrangement has little influence on dynamic performance of the module formed by numerous fibers. The membrane module can fit the change of weather conditions by varying solution temperature on the inlet of the dehumidifier with the help of this dynamic model. The cooling and dehumidification effectiveness also increase to improve heat and mass transfer performance of the dehumidifier under the adjustment.

Thermodynamic analysis of a two-stage humidification–dehumidification system with reflux configuration

Humidification–dehumidification technology is an innovative desalination technology which is promising for small-scale desalination applications. The relative low energy efficiency made the early system less competitive. Multi-stage humidification–dehumidification technology is one of the approaches that effectively improve the system energy efficiency. In this study, an air extraction/injection two-stage humidification–dehumidification system with reflux configuration is proposed. The reflux configuration is introduced into the two-stage system to improve the energy efficiency by eliminating the difference between the air temperatures at the extraction and injection points. A thermodynamic model is developed to investigate the system performance. It is found that the air temperatures at the extraction and injection points are only identical when the pinch point heat capacity rate ratio of first-stage dehumidifier less than unity and that of second-stage dehumidifier greater than unity. The influence of liquid-to-air mass flow rate ratio in the second stage on the energy efficiency of the system is negligible when the pinch point heat capacity rate ratio of first-stage and second-stage dehumidifier both greater than unity. The energy efficiency peaks when the pinch point heat capacity rate ratio of first-stage or second-stage dehumidifier equals unity. Additionally, the reflux configuration can improve the energy efficiency of two-stage system by 30%.

Experimental study of a membrane-based liquid desiccant dehumidifier based on internal air temperature variation

A membrane-based liquid desiccant dehumidifier with the separated air stream and liquid desiccant channels has the ability to solve its working fluid carryover problem in the traditional direct contact system. The sensible, latent, total effectiveness and air moisture removal rate are adopted for the dehumidifier performance evaluation in this paper, and the dehumidifier main operating parameters are investigated experimentally to identify their influences and internal air temperature variations, including inlet air relative humidity (RH), inlet solution concentration and temperature, heat capacity rate ratio (Cr*) and number of heat transfer units (NTU). It is found that both the inlet air RH and solution temperature have the negative influences on the dehumidifier effectiveness, while the desiccant solution concentration has little positive influence; the air moisture removal rate rises sharply with the inlet air RH and solution concentration. The highest sensible, latent and total effectiveness achieved in this study are 0.823, 0.802 and 0.810 respectively when both Cr* and NTU are equal to 12. However the operating condition with NTU = 8 and Cr* = 6 is recommended with the corresponding sensible, latent and total effectiveness of 0.758, 0.71 and 0.728 respectively.

A graphical method for the determination of optimum operating parameters in a humidification-dehumidification desalination system

Humidification–dehumidification (HDH) technology is an innovative desalination technology which has received considerable attention from researchers in recent years. In this study, the effects of mass flow rate ratio and pinch point temperature difference (PPTD) on the energy consumption of the HDH system are investigated by pinch analysis. A new parameter, pinch point heat capacity rate ratio (PHCR), is introduced to normalise the optimum point for energy consumption. It is found that the specific energy consumption of the system is minimised when the PHCR of the dehumidifier equals to unity. The value of GIR can be achieved 3.978 when the PHCR of dehumidifier equals to unity, at the inlet temperature of the solution in the humidifier equals to 65 °C and PPTD of the humidifier and dehumidifier equals to 1 °C. Based on this discovery, the regression equations are used to predict the optimum value of the mass flow rate ratio at different operating parameters. Combining the regression equations with the evaporation rate contour plots, an efficient graphical method is proposed for the determination of optimum operating parameters of the HDH system. It can be used to determine the operating parameters efficiently according to the performance requirements of the system.

Theoretical analysis for heat exchange performance of transcritical nitrogen evaporator used for liquid air energy storage

In view of violent changes of thermo-physical properties, the segmental design method is adopted to explore the heat exchange performances of the transcritical nitrogen (T-N2) evaporator used for liquid air energy storage, in which cold N2 is heated up successively by hot propane and methanol in two wide temperature sections. The local heat capacity rate ratio between cold and hot fluids has crucial effects on the local heat exchange performance of evaporator, such as local effectiveness, local entransy dissipation, and local required heat conductance or local heat transfer rate. They have extremums near the positions where the local heat capacity rate ratio equals one, but their optimal values need to be determined by combining the changing trend of the local heat capacity rate ratio. The total heat exchange performance of evaporator is evaluated using total entransy dissipation and total exergy efficiency. When the heat load is fixed, the total performance is improved with the decrease in the mass flow rate of methanol, but at the expense of the required total heat conductance; The total performance can be optimized by precisely tailoring the heat load ratios between the two temperature sections. When the heat conductance is given, the optimum total performance can be obtained by adjusting the mass flow rate of hot fluids at a fixed heat conductance ratio; Increasing the heat conductance ratio of the low temperature section can further elevate the optimum total performance whereas the affordable heat load or the outlet temperature of N2 is notably decreased. Increasing N2 pressure elevates the total performance of evaporator but diminishes the extractable cold amount from the liquid N2 in the same temperature rise. This work is beneficial for selection of key parameters to achieve optimal operation of the T-N2 evaporator.

Performance Analysis of Printed Circuit Heat Exchanger for Supercritical Carbon Dioxide

A printed circuit heat exchanger (PCHE) was selected as the recuperator of supercritical carbon dioxide (S-CO2) Brayton cycle, and the segmental design method was employed to accommodate the rapid variations of properties of S-CO2. The local heat capacity rate ratio has crucial influences on the local thermal performance of PCHE, while having small influences on the frictional entropy generation. The heat transfer entropy generation is far larger than the frictional entropy generation, and the total entropy generation mainly depends on the heat transfer entropy generation. The axial conduction worsens the thermal performance of PCHE, which becomes more and more obvious with the increase of the thickness and thermal conductivity of plate. The evaluation criteria, material, and size of plate have to be selected carefully in the design of PCHE. The present work may provide a practical guidance on the design and optimization of PCHE when S-CO2 is employed as working fluid.