Local Entropy Generation Rate Research Articles

Local entropy generation optimization and thermodynamic irreversibility analysis of oval-shaped coaxial ground heat exchangers: A detailed numerical investigation

Optimizing the heat transfer and thermodynamic efficiency of Ground Heat Exchangers (GHE) is crucial for maximizing the energy efficiency of Ground-coupled Heat Pump (GCHP) systems utilized in building heating and cooling applications. This study pioneers an effective approach of both the first and second laws of thermodynamics of the newly oval-shaped coaxial GHEs (oval-CGHEs), assessing heat transfer, thermohydraulic performance, and local entropy generation rate to explore the optimum design and operational conditions for heat exchange maximization and entropy generation minimization. Utilizing a three-dimensional numerical model validated by experimental results, this study examines the trade-offs between heat transfer improvements and entropy generation rate intensification of the oval-CGHEs in comparison to the typical circular-shaped CGHE (circle-CGHE) further than exploring the effect of key operational and design parameters and performing sensitivity analysis. The results reveal that oval-CGHEs exhibit higher irreversibility as a penalty for their superior heat transfer capabilities compared to traditional circular-shaped CGHEs (circle-CGHE), which can be mitigated by optimizing the position of the inner tube. Moreover, the study underscores the criticality of maintaining a balance between enhanced heat transfer and the associated rise in irreversibility, particularly concerning the factors of mass flow rates and installation depths.

Assessment of thermohydraulic performance and entropy generation in an evacuated tube solar collector employing pure water and nanofluids as working fluids

This study conducts a numerical comparison of the thermal performance of three distinct working fluids (pure water, TiO2, and SiO2 water-based nanofluids) within an evacuated tube solar collector using Computational Fluid Dynamics. The study evaluates thermohydraulic performance alongside global and local entropy generation rates, while considering variations in solar radiation values and inlet mass flow rates. Results indicate that nanofluids demonstrate superior performance under low solar radiation, exhibiting higher outlet temperatures, velocities, thermal efficiency, and exergy efficiency compared to pure water. However, at the higher solar radiation level, the efficiency of SiO2 water-based nanofluid diminishes due to its impact on specific heat. Furthermore, the entropy generation analysis reveals significant reductions with TiO2 water-based nanofluid in all the phenomena considered (up to 79 %). The SiO2 nanofluid performance aligns closely with pure water under high radiation value. This investigation offers valuable insights into the utilization of nanofluids in solar collectors across diverse operating conditions, emphasizing their pivotal role in enhancing overall performance.

Energy distribution and chaotic pressure pulsation analysis of vortex ropes in Francis-99

Francis turbines, essential for stability in diverse operating conditions and variable-speed scenarios, encounter efficiency-compromising vortex rope formations in the draft tube, leading to substantial pressure fluctuations. This research delves into the analysis of energy loss and pressure fluctuations associated with these vortex ropes. Employing the local entropy generation rate (LEGR) method and chaos theory, we scrutinize the behaviour of vortex ropes and their resultant pressure fluctuations. Notably, vortex ropes exhibit maximum LEGR near the runner cone, with secondary vortices escalating instability downstream. In the elbow section, the collision of vortex ropes with the outer elbow amplifies LEGR, primarily driven by fluctuating velocities (approximately 90%). Leveraging the GWO-VMD algorithm, non-stationary signals are decomposed, unveiling a significant 1.6 Hz vortex rope frequency under partial load (PL) conditions and isolating external noise frequencies, such as the prominent 300 Hz. Following decomposition, chaos theory tools, including phase space reconstruction and phase trajectory graphs, unveil the chaotic nature of PL conditions attributed to spiral vortex ropes, resulting in profound pressure fluctuations. This study enhances our understanding of such systems and provides methodologies for improved noise reduction and optimization of turbine performance.

Entropy generation rate analysis of turbocharger radial flow compressor in range from surge to choke

This study compares the local losses of a radial compressor in the range from surge to choke considering shock phenomena, boundary layer separation, and mixing mechanisms. For this purpose, formulation of the local entropy generation rate (EGR) is added to the computational fluid dynamics (CFD) solver, which models the turbulent flow field of the compressor through the RANS approach. For validation, the numerical pressure rise curve of the compressor is compared with the experimental data. The results indicate that at the design point, the impeller, diffuser, and the volute account for approximately 50.8%, 30.0%, and 12.3% of the EGR, respectively, with approximately 5% in the impeller backspace, 1% in the diffuser cavity, and less than 0.5% in the inlet duct. Approaching the surge condition, local losses due to mixing and shock waves decline while boundary layer losses increase. Based on comprehensive analysis of the leading-edge boundary layer, the largest dead-air zone is found at the design point, resulting in a lower diffusion entrance loss and a higher mixing loss. Furthermore, the EGR variation in the diffuser channel is investigated by shedding light on mixing dynamics and classification of the channel flow regime into three different zones based on mixing ratio (MR). The outcomes show that the flow regime tends to mix more quickly at a higher MR, resulting in a slight decrease in EGR, which benefits compressor performance. We demonstrate that the mixing rate of flow regimes decreases in both the leading-edge boundary layer and the radial diffuser approaching the surge margin.

Performance Comparison of Different Flat Plate Solar Collectors by Means of the Entropy Generation Rate Using Computational Fluid Dynamics

In this work, a numerical analysis of three different flat plate solar collectors was conducted using their entropy generation rates. Specifically, the Computational Fluid Dynamics (CFD) technique was used to compare the detailed performance of conventional and zigzag tube geometries of flat plate solar collectors (FPCs) in terms of their entropy generation rates. The effects of fluid viscosity, heat transfer, and heat loss of the flat plate solar collectors were considered for the local and global entropy generation rate analyses. Variations on the inlet volumetric flow rate of the FPCs from 1.0 to 9.0 L/min were simulated under the average solar radiation for one year in the state of Guanajuato, Mexico. The results illustrate and discuss the temperatures, pressures, and global entropy generation rates for volumetric flow variations. The velocity, temperature, and pressure distributions and the maps of the local entropy generation rates inside the collectors are presented and analyzed for the case with a flow rate of 3.0 L/min. These results demonstrate that the zigzag geometries achieved higher outlet temperatures and greater entropy generation rates than the conventional geometry for all the volumetric flow rates considered.

Entropy generation analysis of a three-dimensional coal-fired furnace: A realistic study

An analysis of the entropy generation by radiative heat transfer in a three-dimensional virtual coal-fired furnace is performed. The gases, including CO2 and H2O, and particles, including soot, unburnt char and ash, are considered as a participating medium. The radiative transfer equation for a non-grey medium was solved by the discrete ordinate method, in which the radiative properties of the gases, soot, unburnt char and ash were obtained by using the statistical narrow-band correlated-k model, Rayleigh's theory, and Mie theory, respectively. The distributions of the local volumetric rate of entropy generation and the local rate of entropy generation at the wall are calculated. The contributions of various media in coal-burning furnaces to the radiative entropy generation rate (REGR) are evaluated, and the effects of several important factors, such as the oxidizer atmosphere, burnout rate, and the volume fraction of soot, unburnt char and ash on the REGR and dimensionless entropy generation were also investigated. The numerical results show that the irreversibility of the particle radiation contributes more than 80% of the volumetric radiative entropy generation. The concentration of particles also has an important effect on REGR, which decreases by 41% when the concentration of unburnt char and ash increases from 10 ppm to 50 ppm and decreases by 70% when the concentration of soot increases from 1 ppm to 6 ppm in a real-size furnace such as an optically thick furnace.

Quantitative investigation of the turbulence model effect on high-pressure-ratio centrifugal compressor performance prediction

The accuracy of centrifugal compressors performance and flow field prediction by Computational Fluid Dynamics (CFD) is a serious problem facing in the design and analysis process due to its complex flow feature inside. Different turbulence models choosing in the Reynolds-Averaged Navier-Stokes Equations (RANS) leads to different simulation results. In this paper, a high-pressure-ratio centrifugal compressor was used as the simulation object to discuss the effect of common turbulence models, including a one-equation model (Spalart-Allmaras model), a two-equation linear model (Shear Stress Transport model) and a two-equation nonlinear model (Explicit Algebraic RSM model), on performance prediction under design speed. By introducing the calculation method of local entropy generation rate, an improved method of dividing different types of loss in centrifugal compressors was proposed. After comparing with the experiment results, the effect of turbulence models on loss prediction inside the compressor was quantitative investigated. Further, the flow mechanism underlying was discussed. The results show that the secondary flow loss have the largest impact on the components' prediction performance, also, the reasons for different magnitudes of secondary flow loss inside the impeller and the diffuser are different. These comparisons hope to help designers choose an appropriate turbulence model in further compressor design process and may benefit future turbulence modelling development.

Thermodynamics second-law analysis in an unsteady conduction and radiation heat transfer system with internal heat source

This paper presents an improved thermodynamic analysis method used to evaluate the irreversibility and efficiency of a coupled conductive-radiative heat transfer process. The exergy analysis of the conductive-radiative process is developed based on the exergy balance equation. In the method, the local entropy generation rates due to the radiative heat transfer and heat conduction processes are calculated. Based on the entropy generation analysis, an exergy analysis is performed, the stored exergy of the system and the exergetic efficiency are determined, and the thermodynamic efficiency of the system is further evaluated. The results are verified by the principle of exergy balance and the exergy generation rate calculated by the method does not deviate from the theoretical value by more than 0.1%. Four heat source distributions are specified in the numerical analysis, which include completely uniform, partially uniform, and non-uniform heat source distributions in the numerical analysis. The effects of heat source distribution, conductive-radiative coefficient and total heat generation rate of medium on entropy generation and stored exergy of system are investigated. The numerical results show that the average temperatures and exergy storage rate of the systems with partially uniform heat source distribution are 5.1–79.7 K and 6.8–49.8% higher than the other distributions, and uniform and centralized heat generation in the internal region of the system is proposed. The total stored exergy of the systems has a tendency to first increase and then decrease, reaching its maximum at N = 1 as the conduction and radiation coefficients increase, and increasing as the total heat generation rate increases.

NUMERICAL ANALYSIS OF ENTROPY GENERATION IN A TWO-DIMENSIONAL POROUS HEAT RECOVERY SYSTEM

The main goal of this paper is the analysis of entropy generation in a two-dimensional porous heat recovery system. This system works based on the energy conversion between fluid enthalpy and thermal radiation. The fluid phase in this system is considered to be air assuming a non-radiative medium, whilst the solid phase is regarded as a gray radiating medium with emission, absorption, and isotropic scattering. These two phases are not in thermal equilibrium and the energy equation is separately analyzed for them. To solve the radiative equations in solid phase, the discrete ordinates method is employed. For a porous heat recovery system, the local entropy generation rate is obtained by summing the entropy generation rates due to the fluid friction and conductive and radiative heat transfer mechanisms. Besides, components of radiative entropy generation rates arise from the absorption-emission, scattering, and walls influences. However, influences of radiative parameters of optical thickness and scattering albedo on the entropy generation rates in this porous system are numerically investigated with full details. Results show that the best thermal performance of the porous heat recovery system occurs in a non-scattering medium with the highest magnitudes of optical thickness.

Heat transfer and entropy generation analysis of electroosmotic flows in curved rectangular nanochannels considering the influence of steric effects

The heat transfer characteristics and entropy generation of an electroosmotic flow in curved rectangular nanochannels under high zeta potential conditions are investigated numerically with consideration of the steric effects. The numerical solutions of the Nusselt number (Nu) and the local entropy generation rate (SG) are derived under constant wall heat flux assumption. The variation trends of Nu and SG with corresponding parameters, including the curvature ratio of the curved nanochannel (δ), the effective ionic size (a0) and the wall heat flux (qw) are investigated. Results reveal that, for small values of qw (qw < 10), the consideration of the steric effects (corresponding to a non zero assumption for a0) leads to a lower SG and an enhanced Nu simultaneously. In this case, to further reduce entropy generation, a curved nanochannel with a large curvature ratio δ is adopted. However, for relatively large values of qw, the steric effects will have a negative effect on entropy generation minimization, especially for a curved nanochannel with large curvature ratio. Our results may be useful in designing the efficient thermal nano-equipment.

Numerical analysis of the thermo-hydraulic performance and entropy generation rate of a water-in-glass evacuated tube solar collector using TiO2 water-based nanofluid and only water as working fluids

A thermo-hydraulic performance and entropy generation rate comparison of a water-in-glass evacuated tube solar collector using TiO2 water-based nanofluid and water as working fluids is carried out by means of Computational Fluid Dynamics. A complete 3D geometry with variations of the solar radiation and inlet mass flow rates as operating conditions is considered. It was found that, the evacuated tube solar collector had a better performance in terms of outlet temperature and velocity using the nanofluid than using only water as working fluid. Also, the thermal and the exergy efficiencies are increased with the use of the nanofluid. The phenomena of viscous effects, heat transfer and heat loss in a global and local form are considered in the formulation of the entropy generation rate. The results of the local entropy generation rate due to the viscous effects and heat transfer are illustrated. Also, it was obtained that, using nanofluid as working fluid leads to a maximum reduction of the entropy generation rate of 87.5%, 65.5% and 14.71% due to viscous effects, heat transfer and heat loss, respectively. Finally, an improvement of the performance of the water-in-glass evacuated tube solar collector can be observed by using water-based nanofluid as working fluid.

Local entropy generation model for numerical CFD analysis of fluid flows through porous media, under laminar and turbulent regimes

Porous media structures have been proposed as an interesting solution on the design of high-temperature volumetric heat exchangers and sensible thermal energy storage devices. The wide exchange area between the solid matrix and the fluid offers the possibility to reach higher conversion efficiencies, particularly on applications of high-temperature (∼1000°C) gases. Nevertheless, the presence of the solid matrix increases the hydrodynamic resistance on the flow, and consequently, generates irreversibilities. The entropy generation can assess in the same figure of merit the different irreversibilities generation mechanisms. In this context, this work presents a physical and mathematical model to determine the local entropy generation (LEG) rate and recognizes its different generation mechanisms for porous media. The proposed model defines a useful expression to determine the LEG as a post-process variable from the usual CFD scalar and vectorial results (temperature, velocity, TKE, and ), without the necessity of solving an additional entropy transport equation. A numerical experiment was implemented showing inflection points where the porous hydrodynamic resistance forces exceed the heat transfer in the LEG rate. The Forchheimer hydrodynamic resistance effect can domine the LEG in comparison to the volumetric heat transfer for high porous Reynolds regimes (>100) when the porosity is under 0.6.

Entropy generation rate minimization for sulfur trioxide decomposition membrane reactor

Sulfuric acid decomposition is the critical reaction in sulfur-iodide thermochemical cycle to produce oxygen. Sulfuric acid can decompose spontaneously into sulfur trioxide (SO3) and water, and SO3 continues to decompose into oxygen and sulfur dioxide. The application of membrane reactor can effectively improve the conversion rate of SO3 and thermal efficiency of sulfur-iodide cycle. The decomposition of SO3 requires the absorption of a large amount of heat due to its highly endothermic properties, and there are many irreversible processes such as heat transfer, mass transfer, chemical reaction and friction flow in the SO3 membrane reactor. Therefore, it is necessary to conduct thermodynamic analysis and optimization of the decomposition process to reduce the irreversible loss of the membrane reactor system. In this paper, a finite time thermodynamic model of SO3 decomposition membrane reactor is established, and the kinetic parameters of decomposition reaction are deduced and calculated based on experimental data. Firstly, the membrane reactor heated by hot helium gas is solved and used as reference reactor. Secondly, optimal control theory is used to optimize the reference reactor under fixed reactant inlet conditions and outlet conversion rate with total entropy generation rate minimization as optimization objective. The total entropy generation rate of Opt-1 reactor is reduced by 32.7% compared with the reference value. For variable reactor length, the total entropy generation rate of Opt-2 reactor is quadratic optimum at L=0.72 m, which is 34.7% less than the reference value. It is found that the reduction of total entropy generation rate in optimal reactors is mainly achieved by minimizing the entropy generation rate in heat transfer process. The distribution of local entropy generation rate is relatively uniform in the middle position, approximately consistent with the principle of equalization of entropy production rate. The conclusions obtained herein can provide guidelines for the energy-saving design of SO3 decomposition membrane reactors.

The Local Distribution of Temperatures and Entropy Generation Rate in an Ideal Counterflow Heat Exchanger

The process of heat exchange between two fluids of different temperatures and separated by a solid wall occurs in many engineering applications. Log mean temperature difference and effectiveness-NTU methods are widely used to assist in the design of heat exchangers. However, the two methods focus on overall analysis and cannot show the local temperature distributions. This paper obtains the mathematical solutions to the temperature profiles in an ideal counterflow heat exchanger. The aim of this research is to explain the phenomenon called the “entropy generation paradox”, which indicates a discrepancy between effectiveness and optimal entropy generation. The theoretical analysis reveals that the temperature curves are exponential functions when the heat capacity rates of the two streams are different; otherwise, the curves are linear functions. A heat exchanger is demonstrated to draw the temperature profiles under different working conditions. Local entropy generation rates are determined by the ratio of local stream temperatures in the form of a hook function. To realize a certain heat duty, there are many stream flow rate couples, and each couple results in a different entropy generation profile and obtains a corresponding total entropy generation. The helical steam generator of a high-temperature gas-cooled reactor is analyzed in this article and the principle of equipartition of entropy generation is confirmed. This principle indicates that, among the many working conditions to achieve a certain heat duty, a heat exchanger characterized by a nearly constant entropy production gives the best second law efficiency possible in order to achieve the best energy conversion.

Entropy generation minimization analysis of two immiscible fluids

The entropy generation of two immiscible fluids is investigated in a conjugate heat transfer system. The velocity and temperature fields are analytically obtained by solving the momentum and energy conservation equations. These analytical solutions are used to calculate the local and total entropy generation rates. Based on the entropy generation minimization (EGM), the total entropy generation of two-layer thermal flow system can be minimized by using the method of single variable optimization. Compared with the classical single-layer thermal flow system, the effects of viscosity ratio, thermal conductivity ratio and density ratio between upper and bottom fluids on the total entropy generation have been given special attention. Result shows that the total entropy generation can be minimized for the specific values of physical parameter ratio when the other parameters keep constant. Besides, it is also found that the total entropy generation of two immiscible fluids can be smaller than that of single fluid. This implies that the irreversible losses can be reduced in the present two-layer thermal flow system. And this reduction of irreversible losses can be helpful in improving the thermal performance of system. The present study is aimed at achieving a theoretical prediction to choose beforehand the appropriate types and heights of two immiscible fluids.

DNS Of entropy generation rates for turbulent flows subjected to high temperature gradients

Direct Numerical Simulations are performed to analyze the influence of key boundary conditions and flow characteristics on entropy generation rate statistics in a highly anisothermal forced convective turbulent channel flow of a thermo-dependent fluid submitted to asymmetrical heating. Each parameter is varied separately to quantify its influence compared to a reference simulation, the hot to cold wall temperature ratio from 1.5 to 3, the mean friction Reynolds number from 150 to 210, the mean thermodynamic pressure from 1bar to 3bar. Two thermal boundary condition types are also compared (fixed temperatures vs. fixed heat flux density at the walls). For each parameter that is varied, the evolution of the entropy generation rate mean, root-mean-square and correlations with the temperature and the streamwise or wall-normal velocity components are presented and discussed. All simulations have in common the thermal asymmetry and the highly non-isothermal nature of the flow: beyond the changes induced by the variation of each parameter, the common characteristics of the statistical quantity profiles are also analyzed. This work establishes how the spatial distribution of the local entropy generation rate is modified by the parameters studied, in which direction and with which sensitivity. It demonstrates the significant influence of the thermal boundary condition type on the entropy generation rate fluctuations near the walls.

Numerical study on the biomimetic trailing edge in the environment of a high-pressure turbine stage

In this study, the whisker structure of a harbor seal is applied to the trailing edge of a high-pressure turbine stage to reduce energy loss. The method to produce biomimetic geometry is provided. Two cases are studied in this paper including a prototype of a high-pressure turbine stage and this stage with the biomimetic trailing edge. The delayed detached-eddy simulation (DDES) method is used to simulate the flow of the stages. The energy loss coefficient of the turbine stage with the biomimetic trailing edge is significantly reduced. The analysis of the local entropy generation rate shows that the wake loss of the biomimetic stage and the loss in the blade passage are greatly reduced. Two reasons for the widening of the wake of the prototype vane during the downstream movement are analyzed. For the biomimetic stage, the Karman vortices are completely suppressed and transformed into small vortices with strong three-dimensional motion. The wake width of the biomimetic trailing edge is narrowed and the speed recovery becomes faster. This leads to the reduction of the wake loss and the interaction between the wake of the vane and the downstream blade.

Accurate Prediction of Loss Using High Fidelity Methods

Abstract Further improvements in aero-engine efficiencies require accurate prediction of flow physics and incurred loss. Currently, the computational requirements for capturing these are not known leading to inconsistent loss predictions even for scale-resolving simulations depending on the chosen convergence criteria. This work investigates two aspects of loss generation using high-fidelity simulation. In the first case study, we look at the effect of resolution on capturing entropy generation rate by simulating a Taylor-Green vortex canonical flow. The second case study focuses on the effect of resolution on flow physics and loss generation and uses a compressor cascade subjected to freestream turbulence. The results show that both resolving local entropy generation rate and capturing the inception and growth of instabilities are critical to accuracy of loss prediction. In particular, the interaction of free-stream turbulence at the leading-edge and development of instabilities in the laminar region of the boundary layer are critical to capturing loss.

Non-Newtonian effect on heat transfer and entropy generation of natural convection nanofluid flow inside a vertical wavy porous cavity

A numerical study on heat transfer and entropy generation in natural convection of non-Newtonian nanofluid flow has been explored within a differentially heated two-dimensional wavy porous cavity. In the present study, copper (Cu)–water nanofluid is considered for the investigation where the specific behavior of Cu nanoparticles in water is considered to behave as non-Newtonian based on previously established experimental results. The power-law model and the Brinkman-extended Darcy model has been used to characterize the non-Newtonian porous medium. The governing equations of the flow are solved using the finite volume method with the collocated grid arrangement. Numerical results are presented through streamlines, isotherms, local Nusselt number and entropy generation rate to study the effects of a range of Darcy number (Da), volume fractions (ϕ) of nanofluids, Rayleigh numbers (Ra), and the power-law index (n). Results show that the rate of heat transfer from the wavy wall to the medium becomes enhanced by decreasing the power-law index but increasing the volume fraction of nanoparticles. Increase of porosity level and buoyancy forces of the medium augments flow strength and results in a thinner boundary layer within the cavity. At negligible porosity level of the enclosure, effect of volume fraction of nanoparticles over thermal conductivity of the nanofluids is imperceptible. Interestingly, when the Darcy–Rayleigh number Ra^*gg 10, the power-law effect becomes more significant than the volume fraction effect in the augmentation of the convective heat transfer process. The local entropy generation is highly dominated by heat transfer irreversibility within the porous enclosure for all conditions of the flow medium. The particular wavy shape of the cavity strongly influences the heat transfer flow pattern and local entropy generation. Interestingly, contour graphs of local entropy generation and local Bejan number show a rotationally symmetric pattern of order two about the center of the wavy cavity.

Analysis on Energy Loss Characteristic of a Bidirectional Tubular Turbine Based on Entropy Generation Theory

To obtain the external characteristic parameters and the distribution of hydraulic loss, ANSYS CFX code is used to for numerical simulations of a tidal bidirectional tubular turbine under positive and reverse conditions. The method of entropy generation analysis is used to obtain the energy loss in the unit and its local entropy generation rate. Besides, the influence of the shaft inclination in the guide vane on the tubular turbine is explored. The results show that there is a certain connection between the traditional hydraulic loss analysis and entropy generation analysis. Entropy generation could be adopted for the measurement of hydraulic loss with its distribution. The total entropy production is dominated by the runner under positive optimal condition, while the ones in the runner and the intake are the highest under reverse optimal condition. In addition, the greater the shaft inclination angle of the guide vane, the larger the total entropy production on the blade surface of the runner under the positive condition.