Entropy Generation Distribution Research Articles

Influence of Maximum Airfoil Camber Position on Hydrofoil Cavitation Performance

Abstract This study’s primary goal is to investigate how various airfoils’ maximum camber positions affect hydrofoil cavitation performance. Through numerical simulation, the cavitation low properties of hydrofoils with various maximum camber positions are compared. The accuracy of the modi ied turbulence viscosity and SST k-ω turbulence model on the temporal and spatial evolution characteristics of cavitation near the hydrofoil is evaluated by combining it with the model test. Analysis is done on the cavitation low ield of four airfoils at two distinct design angles of attack (+4° and +6°) with varying maximum camber locations (fmax = 35%C, 40%C, 50%C, and 60%C). The indings indicate that at 35%C, the hydrofoil’s maximum camber position has improved cavitation performance. The hydrofoil’s cloud cavitation evolution time is shorter than that of the original hydrofoil, and during the same time period, more cavitation is generated. The lift-to-drag ratio and lift coef icient of the cavitation low ield are signi icantly improved at both angles of attack. At the same time, the vorticity distribution and entropy generation distribution can be effectively reduced under the design angle of attack and high angle of attack cavitation, and the hydraulic loss in the cavitation low ield can be reduced. This research can serve as a guide for optimizing the hydrofoil’s cavitation performance and designing the impeller of the axial low pump that follows.

Numerical study of the porous cavity with different square size vanes with a high focus on Nusselt number

This study extensively analyzes various regular and irregular vanes in pipe porous cavities on natural convection, thermal entropy generation, stream function, and temperature distribution in fluid and solid phases. The finite element method (FEM) is employed to study stream function, temperature distribution in the fluid phase and solid phase, and various γ for Nuf, ave and Nus, ave in SR, TR, SIR, and TIR. In the present study, a significant contribution of this research is the investigation into the effects of regular versus irregular vanes in the context of enclosures formed by pipe porous cavities that the SIR specimen has the most influence on stream function and thermal effect in the fluid phase and solid phase that aims to enhance system performance and optimize energy efficiency. In addition, the significant influence of geometrical parameters constitutes many heated obstacles in the middle of SIR, various heated vanes in the left of SIR, and employed Ra and ε in the analysis of Nuf, ave and Nus, ave in SIR are carried out to investigate the percentage discrepancies obtained, notably 89.35 % and 89.72 %, respectively. In validation, the calculation in results was adapted accurately to the finite element method's stream function, the temperature distribution in the fluid phase and solid phase, and various γ for Nuf, ave and Nus, ave which means that the percentage differences in obtaining results reached under 1 %. Numerical results revealed that the Hartman number has a significant influence in Shtf, ave, Shts, ave, Tyave, Nuf, ave and Nus, ave in TR, SR, TIR, and SIR.

Local Entropy Generation Analysis of the Counter-Flow Dew-Point Evaporative Coolers

Abstract A comfortable indoor working circumstance can be accomplished by a ventilation and air conditioning system. There are several factors influencing the quality of indoor air, with the insufficiency of ventilation accounting for over 50% of the overall considerations. While traditional air conditioner is able to fulfill the needs of ventilation and indoor temperature control, low-efficiency and high energy consumption no longer align with the current sustainable and energy-efficiency goals. Thus, the development of energy-saving and high-efficiency air conditioning systems is crucial for realizing green and efficient building practices. Evaporative cooling technology, specifically dew-point evaporative cooling, has garnered extensive attention as an efficient cooling method and a candidate for environmentally friendly and high-performance alternatives to traditional air conditioning systems. This article investigates the thermodynamic losses involved in a dew-point evaporative cooling system using the counter-flow design. Detailed mathematical models for the evaporative cooler along with the entropy generation in the channels are developed. The model facilitates calculations of (1) the entropy generation distribution in different layers within the system and (2) the entropy generation of each layer and the whole system under various input conditions. Approaching the system from the second law of thermodynamics perspective, this model serves as a guide for selecting the optimal operating conditions, thus promoting the widespread application and commercialization of dew-point evaporative cooling systems with the counter-flow structure.

Interrelationships of entropy production and turbulence kinetic energy associated with simple angle and compound angle full coverage film cooling

The present paper compares experimentally-measured distributions of entropy generation with numerically-predicted distributions of streamwise vorticity, turbulence kinetic energy, and production of turbulence kinetic energy. These comparisons are provided for two full-coverage film cooling environments which are designed to model the thermal management arrangements employed for combustor liners within gas turbine engines. One of these arrangements includes alternating compound angle values of +30° in one row of holes, followed by −30° in the next row of holes. The other arrangement includes simple angle holes with a zero degree compound angle value. The associated full-coverage film cooled boundary layers are investigated within a double-wall cooling test facility wherein the air for each full-coverage film cooling arrangement is provided by an impingement jet array. Experimentally-measured entropy generation values are obtained from film cooled boundary layer measurements of local total pressure variations, obtained in isothermal flow, relative to the freestream values outside of the boundary layer. The resulting entropy generation values quantify second law losses, which are associated with aerodynamic gains. To obtain the associated numerical-prediction results for a steady-state, three-dimensional flow field, employed is the ANSYS FLUENT Version 2022 R2 computational code with a SST k–ω turbulence closure model. The resulting comparisons of entropy generation, streamwise vorticity, turbulence kinetic energy, and production of turbulence kinetic energy are provided for a blowing ratio BR of 2.9 for simple angle film cooling with a main flow Reynolds number Rems of 138,000, and for compound angle film cooling with a main flow Reynolds number Rems of 142,000. Overall, evidence is provided of strong relationships between local turbulence kinetic energy and local entropy production since the two quantities are highly correlated with each other over s substantial range of experimental conditions and configurations. For example, ratio of turbulence kinetic energy to entropy generation data collapse for Z/de values from 0 to 3.5 for Y/de = 0.5, Y/de = 1.5, and both film cooling arrangements. Here, the value of the TKE/Sgen ratio is approximately constant for these conditions, which evidences direct and simple dependences of local turbulence kinetic energy upon local entropy generation, even for lower magnitudes of Z/de. The direct and simple dependences of local turbulence kinetic energy upon local entropy generation are further illustrated by the simplicity of linear correlation equations, which represent physical behavior for different conditions and configurations. These correlation equations are developed for three arrangements, which are associated with X/de = 54.54.

The Differential Entropy Generation Rate as a Unified Measure for Both the Stability and Efficiency of an Axial Compressor

Stability and efficiency are the two most important performance indicators of highly loaded aviation axial compressors; however, they often cannot be achieved simultaneously. As an effective means of stability expansion, casing treatment usually damages the peak efficiency. In this study, the differential entropy generation rate was used as a unified measure of stall margin and efficiency, so that both stability enhancement and efficiency improvement could be considered at the initial casing treatment design stage. NASA Rotor 67 was selected, and two single circumferential grooves at two different axial positions were applied, which served as a test case to check how entropy generation rates in the flow field vary with changes in peak efficiency and stall margin. The distribution of entropy generation and differential entropy generation rate were compared with that of the solid casing. The correlation between differential entropy generation rate and the peak efficiency was analyzed, and how the flow mechanism of casing treatments affects entropy generation was determined. Methods for measuring and comparing the impact of different casing treatments on peak efficiency are proposed. At the same time, the distributions of differential entropy generation rate in the near stall were explored, and the relationships between the differential entropy generation rate and the flow structures are detailed. A comparison of the influence of different casing treatment on stability is given with respect to the contours of the differential entropy generation rates. It is demonstrated that the differential entropy generation rate is a unified measure to balance the tradeoffs between the stability and the peak efficiency for different casing treatments for the same compressor.

Bioconvective surface-catalyzed Casson hybrid nanofluid flow analysis by using thermodynamics heat transfer law on a vertical cone

The main finding of this research is to describe the numerical analysis of MHD bioconvective base Casson nanomaterials (hybrid nanofluid) flow via a non-Darcy permeable medium confined in a vertical cone with homogeneous-heterogeneous reactions. Feature of hybrid nanofluid which containing nanoparticles like Ag and MgO with water as a working fluid is discussed. Viscous dissipation, thermal stratification, and non-uniform heat source/sink are also investigated as heat transport mechanisms. The 2nd law of thermodynamics is used to determine a total entropy rate, which is based on three different forms of irreversibility’s heat transfer, fluid friction, and the Darcy-Forchheimer relation. To get numerical solutions of the flow model is transformed into system of couple nonlinear equations, which is solved by implementing shooting approach. The influence of the evolving parameters on non-dimensional velocity, temperature, concentration, microorganism, and entropy generation distribution is graphically examined. It is worth interesting to see that a stronger value of Casson fluid parameters improves the fluid velocity, whereas fluid velocity reduces by the growth of porosity parameter, the reason behind the reduction of velocity is that greater porosity parameter, contained more nanoparticles, which produce more resistance to the fluid velocity. Further, it is observed that higher estimation of local Rayleigh number improves the entropy generation, because heat production boosts up due to strong values of Rayleigh number.

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

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

Numerical studies for effect of geometrical parameters on water jet pump performance via entropy generation analysis

This paper presented an implementation of entropy generation analysis in the main flow field of a water jet pump via the CFD method. This study aimed to identify the inefficient location of energy conversion and to analyse entropy generation sources in each region of the water jet pump. The 2D-axisymmetric model and realisable k-ε (RKE) turbulence model at steady-state conditions were performed to validate jet pump performance and to assess the entropy generation. Likewise, the effects of the projection ratio and throat-aspect ratio as independent parameters were investigated. As a result, the throat is the most inefficient part due to the high total entropy generation rate, following by diffuser part. Also, the entropy generation rate was assessed dominant than viscous dissipation due to the turbulent dissipation, which was caused by a turbulent shear stress layer of mixing the streams. In conclusion, the projection ratio influenced the growth of the shear stress layer as well as the entropy generation. Further, the throat-aspect ratio affected the distribution of entropy generation in the throat section. An appropriate combination of both parameters has an impact on the jet pump performance improvements reducing the entropy generation rate in the future.

Thermodynamic assessment and optimization on louver fin with non-uniform arrangement at different tube rows by desirability approach

The parametric study explores the thermodynamic performance of louver fin with non-uniform arrangement at different tube rows based on three factors: Reynolds number (Re), number of slotted at first tube row (Ns1), and number of slotted at second tube row (Ns2). The distributions of local entropy generation are displayed and analyzed in detail. Thermal entropy generation is mainly concentrated in the first row, but the viscous entropy generation of the first row is roughly the same to the second row. Compared with plate fin, the louver fins can effectively reduce thermal entropy generation, but also bring greater viscous entropy generation at variable Re. The thermal entropy generation and viscous entropy generation increase, but the thermal entropy generation per unit mass flow decreases and the viscous entropy generation per unit mass flow increases as the increasing Re. It is found that the increase in Ns1 will lead to a far greater improvement in thermal performance than the increase in Ns2. However, the increase in resistance caused by the increase in Ns1 is approximately equal to the increase in resistance caused by the increase in Ns2. Meanwhile, the correlations of the thermal performance and resistance are given, which facilitates the design of the heat exchanger. The non-uniform arrangement is quantitatively optimized using the desirability approach, and the arrangement of first-dense-then-sparse at Re = 900, Ns1 = 8, Ns2 = 4 is given. The arrangement of first-dense-then-sparse can reduce the resistance without reducing the thermal performance evidently.

Effects of incident angle of sealing ring clearance on internal flow and cavitation of centrifugal pump

High-energy fluid at the outlet of the impeller might get access to the impeller inlet via the sealing ring clearance of the centrifugal pump with shrouded impeller. In this case, the great velocity and energy differences between the fluid at the inlet and outlet of the impeller might trigger unsteady flows during the collision with large energy loss produced. As a result, the flow status of the impeller inlet can be exacerbated; causing that the centrifugal pump is susceptible to cavitation. A centrifugal pump with a low specific speed was studied in this paper. To begin with, five incident angles, that is the original angle (90°), 75°, 60°, 45°, and 30° were formed between the incident section of the sealing ring clearance and the inlet circumference of the impeller through changing the front cover of the impeller and the outer contour of the centrifugal pump. Then, the accuracy of the calculation results of the prototype pump (90°) was verified experimentally with analyses on the entropy generation, velocity streamline, backflow at the inlet section, internal entropy generation distribution of the centrifugal pump, and distribution of cavitation in specific conditions at the incidence of clearance of the centrifugal pump with different incident angles of sealing ring clearance. As can be seen from the results, changing the incident angle of the sealing ring clearance exerts a certain influence on the external characteristics of the centrifugal pump. To be specific, the sealing ring clearance with a small incident angle can lower the flow loss in the front cavity flow area and the impeller flow area of the centrifugal pump as well as can restrain the backflow prewhirl at the inlet section of the centrifugal pump and the cavitation inside the centrifugal pump.

Entropy generation in an opposed-flow laminar non-premixed flame—Effects of using reduced and global chemical mechanisms for methane–air and syngas–air combustion

The distribution of entropy generation is calculated with the aim of comparing second-law results for reduced and global mechanisms against a detailed mechanism. For methane, the DRM19 mechanism and a global, one-step irreversible mechanism are used for comparison with GRI3.0. For an equimolar CO/H2 mixture, the Davis et al. mechanism and a global mechanism are compared with GRI3.0 for flames at 1, 10 and 20 atm. Conduction is the largest contributor to entropy generation, followed by mass diffusion and chemical reactions. For the conduction and mass-diffusion components, the reduced mechanisms give results close to the full mechanism. The global mechanisms have some deviations due to, among other things, inaccurate prediction of flame position and temperature. Overall, entropy generation by chemical reactions of the reduced mechanisms correspond to full mechanism reasonably well, in spite of larger deviations between the individual reactions included in both mechanisms. When reactions are left out in mechanism reduction, their effects are compensated by adjustments in the remaining reactions. These are clearly made with objectives other than entropy generation. Reaction-by-reaction comparison shows that the importance with respect to entropy generation can be very different to that of heat release. Some simplified models are also investigated.

Study on external performance and internal flow characteristics in a centrifugal pump under different degrees of cavitation

Cavitation as a form of unsteady flow within centrifugal pumps can cause the reduced performance of pumps, disordered internal flow regimes, and flow loss. The present criterion used for determining the occurrence of cavitation is a 3% head drop. However, in most cases, pump cavitation already occurs with less than a 1%–2% head drop due to significant changes in the internal flow status. To examine changing patterns in internal flow characteristics as the degree of cavitation deepens in the early stage of cavitation in centrifugal pumps when the head curve does not show significant fluctuation, this paper focuses on a low specific speed centrifugal pump to analyze distributions of total internal pressure, speed, bubble volume, vortex structure, and entropy generation across different degrees of cavitation and obtain internal flow characteristics and flow loss patterns of pumps, with an aim of providing preferences for anti-cavitation hydraulic design of centrifugal pumps.

Analysis of NO Formation and Entropy Generation in a Reactive Flow

A comprehensive investigation of turbulent combustion is accomplished to study the relationship between nitrogen oxide (NO) formation and entropy generation distribution in a non-premixed propane combustion. The radiation heat transfer and combustion are simulated, employing the discrete ordinates model and laminar flamelet model, respectively. A post processing model is employed to estimate the NO formation rate. The present results of NO species formation, mean temperature and velocity are compared with the existing experimental data, and good agreements are obtained. It is shown that the main region of total entropy generation rate and NO formation rate is at the same axial position. The entropy generation distribution may be defined as an index by which the combustion region and main region of NO formation are predicted. However, total entropy generation rate is more sensitive to high temperature (1500–1930 K) than that of NO formation rate. With an increase of 28.7% in temperature, the entropy generation and NO formation rates rise by 900% and 127%, respectively. The occurrence of chemical reactions plays the major role in the generation of entropy.

Study on the Hydraulic and Energy Loss Characteristics of the Agricultural Pumping Station Caused by Hydraulic Structures

The pumping station is an important part of the agricultural irrigation and drainage system. The sump is one of the common water inlet types of agricultural pumping stations. In the sump, to facilitate the installation and maintenance of equipment, some hydraulic structures, such as pump beams, maintenance platforms and chest walls, are added to the sump. At present, the impact of hydraulic structures in the sump on the hydraulic performance of the pump device is not clear, so this paper focused on the impact of hydraulic structures on the hydraulic characteristics and entropy generation characteristics of the pump device by using numerical simulation methods. The results showed that the installation of hydraulic structures in the sump has the greatest impact on the efficiency of the pump device. The efficiency coefficient increased after adding a pump beam in the sump and decreased by about 2% after adding a maintenance platform and a water retaining chest wall. Results also showed that the installation of hydraulic structures in the sump will lead to uneven distribution of entropy generation in the sump, especially in the vicinity of the hydraulic structures. The installation of the maintenance platform and chest wall will lead to the increase of the total entropy generation in the sump, which also means that the hydraulic loss in the sump will increase accordingly. Hence, in addition to the pump beam, other structures should be avoided in the sump.

Analysis of a falling film H2O/LiBr absorber at local scale based on entropy generation

A solution of laminar H2O/LiBr falling film flowing under the effect of gravity on a vertical plate heated by a heat transfer fluid was studied to determine the local temperature, concentration and velocity fields from a numerical resolution. In order to investigate a real absorber case, the heat transfer fluid was assumed to flow counter-current to the falling film. Different heat transfer fluid flow regimes were studied and compared with the limit cases: adiabatic and isothermal walls. A local entropy generation formulation was performed to identify the different sources of irreversibility with the aim of locating and quantifying them. The results enabled analysis of the distribution of entropy generation in the entire absorber, namely, the heat transfer fluid, the wall and the falling film. The analysis shows that an increase in the driving force generated at the film interface and of the heat transfer fluid velocity leads to an increase in the absorbed mass flow rate, but this increase is associated with higher irreversibility. Thermal entropy generation dominates near the wall for both fluids while mass entropy generation dominates at the film interface. Total entropy generation per width of absorber is mainly due to heat transfer irreversibilities through the film – more than 35% – while the irreversibilities due to mass transfer represent less than 15% under the assumptions considered.

Numerical Study on Entropy Generation of the Multi-Stage Centrifugal Pump.

The energy loss of the multi-stage centrifugal pump was investigated by numerical analysis using the entropy generation method with the RNG k-ε turbulence model. Entropy generation due to time-averaged motion and velocity fluctuation was mainly considered. It was found that the entropy generation of guide vanes and impellers account for 71.2% and 23.3% of the total entropy generation under the designed flow condition. The guide vanes are the main hydraulic loss domains and their entropy generation is about 9 W/K, followed by impellers. There are vortices at the tongue of the guide vane inlet as well as flow separations in the impellers, which lead to entropy generation. The fluid impacts the outer surface of the guide vanes, resulting in the increase in entropy generation. There are refluxes near the guide vane tongues which also increase the entropy generation of this part. The entropy generation distribution of the guide vanes and impellers was investigated, which found that the positive guide vane has more entropy generation compared with the reverse guide. The entropy generation of the blade suction surface is higher compared with the pressure surface. This study indicated that the entropy generation method has distinct advantages in the assessment of hydraulic loss.

Prediction of hybrid nanofluids behavior and entropy generation during the cooling of an electronic chip using the Lagrangian–Eulerian approach

AbstractA numerical study is performed to predict the behavior of hybrid nanofluids and entropy generation in a cooling application problem using the Lagrangian–Eulerian approach. The equations governing the continuous phase (base fluid) were solved using the finite volume technique, while the discrete phase (nanoparticles) was tracked using the force balance equation of particles. The interaction between the base fluid and the nanoparticles was considered. Brownian motion and the thermophoresis effect have been included in the solver specifications. In the first step, the numerical procedure using the discrete phase model (DPM) has been thoroughly validated with previous published numerical data, and a good agreement has been achieved. After that, various parameters are adopted by varying nanoparticles' diameter (dp), volume fraction (ϕ), and Reynolds number (Re). Their imprints have been highlighted on isotherms, streamlines, Nusselt numbers, entropy generations (Sg), and Bejan numbers (Be). It is found that the entropy generation is more pronounced at the electronic chip corners. Heat transfer is enhanced, and entropy generation increases when the solid volume fraction and Reynolds number grow. However, the Nusselt number and irreversibility decrease when increasing the nanoparticle diameter. In addition, the results substantiate that the thermal entropy generation prevails over the friction entropy generation, resulting in high values of the Bejan number. Finally, variations in the distribution of isotherms, streamlines, and local entropy generation are noted between the DPM and single‐phase model (SPM) approaches. Also, the average Nusselt number is higher in SPM than in the DPM approach, but the opposite is observed for the entropy generation and the Bejan number.

Modelling Entropy in Magnetized Flow of Eyring-Powell Nanofluid through Nonlinear Stretching Surface with Chemical Reaction: A Finite Element Method Approach.

The present paper explores the two-dimensional (2D) incompressible mixed-convection flow of magneto-hydrodynamic Eyring–Powell nanofluid through a nonlinear stretching surface in the occurrence of a chemical reaction, entropy generation, and Bejan number effects. The main focus is on the quantity of energy that is lost during any irreversible process of entropy generation. The system of entropy generation was examined with energy efficiency. The set of higher-order non-linear partial differential equations are transformed by utilizing non-dimensional parameters into a set of dimensionless ordinary differential equations. The set of ordinary differential equations are solved numerically with the help of the finite element method (FEM). The illustrative set of computational results of Eyring–Powell (E–P) flow on entropy generation, Bejan number, velocity, temperature, and concentration distributions, as well as physical quantities are influenced by several dimensionless physical parameters that are also presented graphically and in table-form and discussed in detail. It is shown that the Schemit number increases alongside an increase in temperature, but the opposite trend occurs in the Prandtl number. Bejan number and entropy generation decline with the effect of the concentration diffusion parameter, and the results are shown in graphs.

Local Entropy Generation Analysis for Cavitation Flow Within a Centrifugal Pump

Abstract Local entropy generation is derived from the second law of thermodynamics, which can directly identify the source of irreversible dissipation and learn more about the physical mechanism of performance degradation. Zwart cavitation model is modified to clarify the rapid head drop of a cavitation flow within a test centrifugal pump, and it is used to simulate the cavitation flow. Local entropy generation method is used to analyze the cavitation flow with varying net positive suction head. The magnitude of entropy generation in different types and regions is compared. Spatial distribution of turbulent and near-wall entropy generation are analyzed. Results show that the modified Zwart cavitation model can better capture the cavity morphology and its evolution. Turbulent and near-wall entropy generations, which mainly concentrate on the impeller, have a large proportion of total entropy generation. The rapid increase in fluctuating velocity entropy generation near the impeller blade pressure side and near-wall entropy generation near the trailing edge of the impeller blade are the main reasons for the rapid head drop within a test centrifugal pump. The sources of turbulent and near-wall entropy generation are vortex and shear stress, respectively.

Entropy generation on magnetohydrodynamic laminar boundary‐layer Casson CNT‐based nanofluid flow across a wedge by using the homotopy analysis method

AbstractThe purpose of the study is to scrutinize the entropy generation analysis on magnetohydrodynamic heat transfer flow from Casson single‐walled carbon nanotube on a wedge with Joule heating and viscous dissipation. Kerosene oil is considered as base fluid because of its exclusive features, advanced thermal conductivity, application, and unique behavior. Using similarity variables, the regulating equations are modified into nonlinear coupled, ordinary differential equations, which are then tackled using homotopy analysis method. Impacts of emerging parameters on entropy generation, temperature, velocity, and Bejan number distributions are discussed and shown graphically. The Nusselt number and skin‐friction coefficient values are shown in a table. The results reveal that velocity enhances due to increasing magnetic and Casson parameters. It was inspected that entropy production enhances due to increasing wedge angle and magnetic parameter and decays with Casson parameter. Also, it is examined that the Bejan number upsurges due to larger Casson and wedge angle parameters but a reverse trend can be observed with increasing values of a magnetic parameter. The present results have been endorsed by comparing with the available data in the literature, it was discovered that they are in excellent agreement.