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Special Issue "Entropy in Computational Fluid Dynamics"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (31 May 2017)

Special Issue Editor

Guest Editor
Priv.-Doz. Dr. Yan Jin

Hamburg University of Technology, Institute of Thermofluid Dynamics, Building K, Room 2542, D-21073 Hamburg, Germany
Website | E-Mail
Interests: fluid mechanics; heat/mass transfer; direct numerical simulation; turbulence modeling; optimization with the SLA; skin friction reduction

Special Issue Information

Dear Colleagues,

Losses in a flow and heat transfer process, from a thermodynamics point of view, are due to irreversible processes. In order to better understand the physics of these loss-producing mechanisms, fluid mechanic and heat transfer considerations might be complemented by some thermodynamic concepts with respect to the irreversible processes involved. Basically, these are concepts that assess energy by its value in terms of its convertibility from one form to another.

The second law analysis (SLA) is often used in thermodynamics in order to assess an irreversible process. According to the SLA, the quality of a flow and heat transfer process, and how reversible it is can only be assessed by the entropy generation rate. However, this concept is still not widely used to assess flow and heat transfer problems although they are often irreversible. The SLA may help to indicate where the losses occur and determine their strength, which is important for understanding a flow and heat transfer process. With the knowledge about the mechanisms of irreversibility, one may know how to reduce entropy generation, overall or locally, and thus improve the efficiency of a fluid machine.

Analysis of the irreversibility in flow or heat transfer processes, in particular for turbulent flows, is welcome. Papers about modelling the entropy generation due to turbulence are encouraged. Optimization of flow and heat transfer processes, e.g., reducing skin friction and enhancing heat transfer, with the SLA is of special interest.

Dr. Yan Jin
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

•    Entropy generation in a flow.
•    Entropy generation in a heat/mass transfer process.
•    Assessing the irreversibility with high accuracy methods, e.g., DNS.
•    Modeling the entropy generation due to turbulence.
•    Optimization with the second law of thermodynamics (SLA).
•    Skin friction reduction and heat transfer enhancement.

Published Papers (12 papers)

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Research

Open AccessArticle Thermodynamic Analysis for Buoyancy-Induced Couple Stress Nanofluid Flow with Constant Heat Flux
Entropy 2017, 19(11), 580; doi:10.3390/e19110580
Received: 20 September 2017 / Revised: 14 October 2017 / Accepted: 17 October 2017 / Published: 29 October 2017
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Abstract
This paper addresses entropy generation in the flow of an electrically-conducting couple stress nanofluid through a vertical porous channel subjected to constant heat flux. By using the Buongiorno model, equations for momentum, energy, and nanofluid concentration are modelled, solved using homotopy analysis and
[...] Read more.
This paper addresses entropy generation in the flow of an electrically-conducting couple stress nanofluid through a vertical porous channel subjected to constant heat flux. By using the Buongiorno model, equations for momentum, energy, and nanofluid concentration are modelled, solved using homotopy analysis and furthermore, solved numerically. The variations of significant fluid parameters with respect to fluid velocity, temperature, nanofluid concentration, entropy generation, and irreversibility ratio are investigated, presented graphically, and discussed based on physical laws. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessArticle Second Law Analysis for Couple Stress Fluid Flow through a Porous Medium with Constant Heat Flux
Entropy 2017, 19(9), 498; doi:10.3390/e19090498
Received: 16 August 2017 / Revised: 4 September 2017 / Accepted: 11 September 2017 / Published: 18 September 2017
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Abstract
In the present work, entropy generation in the flow and heat transfer of couple stress fluid through an infinite inclined channel embedded in a saturated porous medium is presented. Due to the channel geometry, the asymmetrical slip conditions are imposed on the channel
[...] Read more.
In the present work, entropy generation in the flow and heat transfer of couple stress fluid through an infinite inclined channel embedded in a saturated porous medium is presented. Due to the channel geometry, the asymmetrical slip conditions are imposed on the channel walls. The upper wall of the channel is subjected to a constant heat flux while the lower wall is insulated. The equations governing the fluid flow are formulated, non-dimensionalized and solved by using the Adomian decomposition method. The Adomian series solutions for the velocity and temperature fields are then used to compute the entropy generation rate and inherent heat irreversibility in the flow domain. The effects of various fluid parameters are presented graphically and discussed extensively. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessFeature PaperArticle Second-Law Analysis of Irreversible Losses in Gas Turbines
Entropy 2017, 19(9), 470; doi:10.3390/e19090470
Received: 26 July 2017 / Revised: 29 August 2017 / Accepted: 31 August 2017 / Published: 4 September 2017
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Abstract
Several fundamental concepts with respect to the second-law analysis (SLA) of the turbulent flows in gas turbines are discussed in this study. Entropy and exergy equations for compressible/incompressible flows in a rotating/non-rotating frame have been derived. The exergy transformation efficiency of a gas
[...] Read more.
Several fundamental concepts with respect to the second-law analysis (SLA) of the turbulent flows in gas turbines are discussed in this study. Entropy and exergy equations for compressible/incompressible flows in a rotating/non-rotating frame have been derived. The exergy transformation efficiency of a gas turbine as well as the exergy transformation number for a single process step have been proposed. The exergy transformation number will indicate the overall performance of a single process in a gas turbine, including the local irreversible losses in it and its contribution to the exergy obtained the combustion chamber. A more general formula for calculating local entropy generation rate densities is suggested. A test case of a compressor cascade has been employed to demonstrate the application of the developed concepts. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessArticle A Numerical Study on Entropy Generation in Two-Dimensional Rayleigh-Bénard Convection at Different Prandtl Number
Entropy 2017, 19(9), 443; doi:10.3390/e19090443
Received: 2 July 2017 / Revised: 16 August 2017 / Accepted: 21 August 2017 / Published: 30 August 2017
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Abstract
Entropy generation in two-dimensional Rayleigh-Bénard convection at different Prandtl number (Pr) are investigated in the present paper by using the lattice Boltzmann Method. The major concern of the present paper is to explore the effects of Pr on the detailed information
[...] Read more.
Entropy generation in two-dimensional Rayleigh-Bénard convection at different Prandtl number (Pr) are investigated in the present paper by using the lattice Boltzmann Method. The major concern of the present paper is to explore the effects of Pr on the detailed information of local distributions of entropy generation in virtue of frictional and heat transfer irreversibility and the overall entropy generation in the whole flow field. The results of this work indicate that the significant viscous entropy generation rates (Su) gradually expand to bulk contributions of cavity with the increase of Pr, thermal entropy generation rates (Sθ) and total entropy generation rates (S) mainly concentrate in the steepest temperature gradient, the entropy generation in the flow is dominated by heat transfer irreversibility and for the same Rayleigh number, the amplitudes of Su, Sθ and S decrease with increasing Pr. It is found that that the amplitudes of the horizontally averaged viscous entropy generation rates, thermal entropy generation rates and total entropy generation rates decrease with increasing Pr. The probability density functions of Su, Sθ and S also indicate that a much thinner tail while the tails for large entropy generation values seem to fit the log-normal curve well with increasing Pr. The distribution and the departure from log-normality become robust with decreasing Pr. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessArticle Entropy Analysis of the Interaction between the Corner Separation and Wakes in a Compressor Cascade
Entropy 2017, 19(7), 324; doi:10.3390/e19070324
Received: 27 May 2017 / Revised: 27 June 2017 / Accepted: 27 June 2017 / Published: 30 June 2017
Cited by 1 | PDF Full-text (34674 KB) | HTML Full-text | XML Full-text
Abstract
The corner separation in the high-loaded compressors deteriorates the aerodynamics and reduces the stable operating range. The flow pattern is further complicated with the interaction between the aperiodic corner separation and the periodically wake-shedding vortices. Accurate prediction of the corner separation is a
[...] Read more.
The corner separation in the high-loaded compressors deteriorates the aerodynamics and reduces the stable operating range. The flow pattern is further complicated with the interaction between the aperiodic corner separation and the periodically wake-shedding vortices. Accurate prediction of the corner separation is a challenge for the Reynolds-Averaged Navier–Stokes (RANS) method, which is based on the linear eddy-viscosity formulation. In the current work, the corner separation is investigated with the Delayed Detached Eddy Simulation (DDES) approach. DDES results agree well with the experiment and are systematically better than the RANS results, especially in the corner region where massive separation occurs. The accurate results from DDES provide a solid foundation for mechanism study. The flow structures and the distribution of Reynolds stress help reveal the process of corner separation and its interaction with the wake vortices. Before massive corner separation occurs, the hairpin-like vortex develops. The appearance of the hairpin-like vortex could be a signal of large-scale corner separation. The strong interaction between corner separation and wake vortices significantly enhances the turbulence intensity. Based on these analyses, entropy analysis is conducted from two aspects to study the losses. One aspect is the time-averaged entropy analysis, and the other is the instantaneous entropy analysis. It is found that the interaction between the passage vortex and wake vortex yields remarkable viscous losses over the 0–12% span when the corner separation has not yet been triggered; however, when the corner separation occurs, an enlarged region covering the 0–30% span is affected, and it is due to the interaction between the corner separation and wake vortices. The detailed coherent structures, local losses information and turbulence characteristics presented can provide guidance for the corner separation control and better design. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessArticle Entropy Generation Rates through the Dissipation of Ordered Regions in Helium Boundary-Layer Flows
Entropy 2017, 19(6), 278; doi:10.3390/e19060278
Received: 23 March 2017 / Revised: 9 June 2017 / Accepted: 12 June 2017 / Published: 15 June 2017
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Abstract
The results of the computation of entropy generation rates through the dissipation of ordered regions within selected helium boundary layer flows are presented. Entropy generation rates in helium boundary layer flows for five cases of increasing temperature and pressure are considered. The basic
[...] Read more.
The results of the computation of entropy generation rates through the dissipation of ordered regions within selected helium boundary layer flows are presented. Entropy generation rates in helium boundary layer flows for five cases of increasing temperature and pressure are considered. The basic format of a turbulent spot is used as the flow model. Statistical processing of the time-dependent series solutions of the nonlinear, coupled Lorenz-type differential equations for the spectral velocity wave components in the three-dimensional boundary layer configuration yields the local volumetric entropy generation rates. Extension of the computational method to the transition from laminar to fully turbulent flow is discussed. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessArticle Application of Entropy Generation to Improve Heat Transfer of Heat Sinks in Electric Machines
Entropy 2017, 19(6), 255; doi:10.3390/e19060255
Received: 15 April 2017 / Revised: 24 May 2017 / Accepted: 26 May 2017 / Published: 2 June 2017
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Abstract
To intensify heat transfer within the complex three-dimensional flow field found in technical devices, all relevant transport phenomena have to be taken into account. In this work, a generic procedure based on a detailed analysis of entropy generation is developed to improve heat
[...] Read more.
To intensify heat transfer within the complex three-dimensional flow field found in technical devices, all relevant transport phenomena have to be taken into account. In this work, a generic procedure based on a detailed analysis of entropy generation is developed to improve heat sinks found in electric machines. It enables a simultaneous consideration of temperature and velocity distributions, lumped into a single, scalar value, which can be used to directly identify regions with a high potential for heat transfer improvement. By analyzing the resulting entropy fields, it is demonstrated that the improved design obtained by this procedure is noticeably better, compared to those obtained with a classical analysis considering separately temperature and velocity distributions. This opens the door for an efficient, computer-based optimization of heat transfer in real applications. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessArticle Entropy Generation of Double Diffusive Forced Convection in Porous Channels with Thick Walls and Soret Effect
Entropy 2017, 19(4), 171; doi:10.3390/e19040171
Received: 14 March 2017 / Revised: 13 April 2017 / Accepted: 13 April 2017 / Published: 15 April 2017
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Abstract
The second law performance of double diffusive forced convection in a horizontal porous channel with thick walls was considered. The Soret effect is included in the concentration equation and the first order chemical reaction was chosen for the concentration boundary conditions at the
[...] Read more.
The second law performance of double diffusive forced convection in a horizontal porous channel with thick walls was considered. The Soret effect is included in the concentration equation and the first order chemical reaction was chosen for the concentration boundary conditions at the porous-solid walls interfaces. This investigation is focused on two principal types of boundary conditions. The first assumes a constant temperature condition at the outer surfaces of the solid walls, and the second assumes a constant heat flux at the lower wall and convection heat transfer at the upper wall. After obtaining the velocity, temperature and concentration distributions, the local and total entropy generation formulations were used to visualize the second law performance of the two cases. The results indicate that the total entropy generation rate is directly related to the lower wall thickness. Interestingly, it was observed that the total entropy generation rate for the second case reaches a minimum value, if the upper and lower wall thicknesses are chosen correctly. However, this observation was not true for the first case. These analyses can be useful for the design of microreactors and microcombustor systems when the second law analysis is taken into account. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessArticle Entropy Generation Analysis and Performance Evaluation of Turbulent Forced Convective Heat Transfer to Nanofluids
Entropy 2017, 19(3), 108; doi:10.3390/e19030108
Received: 21 January 2017 / Revised: 26 February 2017 / Accepted: 8 March 2017 / Published: 11 March 2017
Cited by 1 | PDF Full-text (2486 KB) | HTML Full-text | XML Full-text
Abstract
The entropy generation analysis of fully turbulent convective heat transfer to nanofluids in a circular tube is investigated numerically using the Reynolds Averaged Navier–Stokes (RANS) model. The nanofluids with particle concentration of 0%, 1%, 2%, 4% and 6% are treated as single phases
[...] Read more.
The entropy generation analysis of fully turbulent convective heat transfer to nanofluids in a circular tube is investigated numerically using the Reynolds Averaged Navier–Stokes (RANS) model. The nanofluids with particle concentration of 0%, 1%, 2%, 4% and 6% are treated as single phases of effective properties. The uniform heat flux is enforced at the tube wall. To confirm the validity of the numerical approach, the results have been compared with empirical correlations and analytical formula. The self-similarity profiles of local entropy generation are also studied, in which the peak values of entropy generation by direct dissipation, turbulent dissipation, mean temperature gradients and fluctuating temperature gradients for different Reynolds number as well as different particle concentration are observed. In addition, the effects of Reynolds number, volume fraction of nanoparticles and heat flux on total entropy generation and Bejan number are discussed. In the results, the intersection points of total entropy generation for water and four nanofluids are observed, when the entropy generation decrease before the intersection and increase after the intersection as the particle concentration increases. Finally, by definition of Ep, which combines the first law and second law of thermodynamics and attributed to evaluate the real performance of heat transfer processes, the optimal Reynolds number Reop corresponding to the best performance and the advisable Reynolds number Read providing the appropriate Reynolds number range for nanofluids in convective heat transfer can be determined. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessArticle An Entropy-Assisted Shielding Function in DDES Formulation for the SST Turbulence Model
Entropy 2017, 19(3), 93; doi:10.3390/e19030093
Received: 12 November 2016 / Revised: 7 February 2017 / Accepted: 23 February 2017 / Published: 27 February 2017
Cited by 1 | PDF Full-text (5212 KB) | HTML Full-text | XML Full-text
Abstract
The intent of shielding functions in delayed detached-eddy simulation methods (DDES) is to preserve the wall boundary layers as Reynolds-averaged Navier–Strokes (RANS) mode, avoiding possible modeled stress depletion (MSD) or even unphysical separation due to grid refinement. An entropy function fs is
[...] Read more.
The intent of shielding functions in delayed detached-eddy simulation methods (DDES) is to preserve the wall boundary layers as Reynolds-averaged Navier–Strokes (RANS) mode, avoiding possible modeled stress depletion (MSD) or even unphysical separation due to grid refinement. An entropy function fs is introduced to construct a DDES formulation for the k-ω shear stress transport (SST) model, whose performance is extensively examined on a range of attached and separated flows (flat-plate flow, circular cylinder flow, and supersonic cavity-ramp flow). Two more forms of shielding functions are also included for comparison: one that uses the blending function F2 of SST, the other which adopts the recalibrated shielding function fd_cor of the DDES version based on the Spalart-Allmaras (SA) model. In general, all of the shielding functions do not impair the vortex in fully separated flows. However, for flows including attached boundary layer, both F2 and the recalibrated fd_cor are found to be too conservative to resolve the unsteady flow content. On the other side, fs is proposed on the theory of energy dissipation and independent on from any particular turbulence model, showing the generic priority by properly balancing the need of reserving the RANS modeled regions for wall boundary layers and generating the unsteady turbulent structures in detached areas. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessArticle Local Entropy Generation in Compressible Flow through a High Pressure Turbine with Delayed Detached Eddy Simulation
Entropy 2017, 19(1), 29; doi:10.3390/e19010029
Received: 11 November 2016 / Revised: 3 January 2017 / Accepted: 9 January 2017 / Published: 11 January 2017
Cited by 3 | PDF Full-text (26076 KB) | HTML Full-text | XML Full-text
Abstract
Gas turbines are important energy-converting equipment in many industries. The flow inside gas turbines is very complicated and the knowledge about the flow loss mechanism is critical to the advanced design. The current design system heavily relies on empirical formulas or Reynolds Averaged
[...] Read more.
Gas turbines are important energy-converting equipment in many industries. The flow inside gas turbines is very complicated and the knowledge about the flow loss mechanism is critical to the advanced design. The current design system heavily relies on empirical formulas or Reynolds Averaged Navier–Stokes (RANS), which faces big challenges in dealing with highly unsteady complex flow and accurately predicting flow losses. Further improving the efficiency needs more insights into the loss generation in gas turbines. Conventional Unsteady Reynolds Averaged Simulation (URANS) methods have defects in modeling multi-frequency, multi-length, highly unsteady flow, especially when mixing or separation occurs, while Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are too costly for the high-Reynolds number flow. In this work, the Delayed Detached Eddy Simulation (DDES) method is used with a low-dissipation numerical scheme to capture the detailed flow structures of the complicated flow in a high pressure turbine guide vane. DDES accurately predicts the wake vortex behavior and produces much more details than RANS and URANS. The experimental findings of the wake vortex length characteristics, which RANS and URANS fail to predict, are successfully captured by DDES. Accurate flow simulation builds up a solid foundation for accurate losses prediction. Based on the detailed DDES results, loss analysis in terms of entropy generation rate is conducted from two aspects. The first aspect is to apportion losses by its physical resources: viscous irreversibility and heat transfer irreversibility. The viscous irreversibility is found to be much stronger than the heat transfer irreversibility in the flow. The second aspect is weighing the contributions of steady effects and unsteady effects. Losses due to unsteady effects account for a large part of total losses. Effects of unsteadiness should not be neglected in the flow physics study and design process. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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Open AccessArticle Determining the Optimum Inner Diameter of Condenser Tubes Based on Thermodynamic Objective Functions and an Economic Analysis
Entropy 2016, 18(12), 444; doi:10.3390/e18120444
Received: 1 October 2016 / Revised: 3 December 2016 / Accepted: 6 December 2016 / Published: 10 December 2016
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Abstract
The diameter and configuration of tubes are important design parameters of power condensers. If a proper tube diameter is applied during the design of a power unit, a high energy efficiency of the condenser itself can be achieved and the performance of the
[...] Read more.
The diameter and configuration of tubes are important design parameters of power condensers. If a proper tube diameter is applied during the design of a power unit, a high energy efficiency of the condenser itself can be achieved and the performance of the whole power generation unit can be improved. If a tube assembly is to be replaced, one should verify whether the chosen condenser tube diameter is correct. Using a diameter that is too large increases the heat transfer area, leading to over-dimensioning and higher costs of building the condenser. On the other hand, if the diameter is too small, water flows faster through the tubes, which results in larger flow resistance and larger pumping power of the cooling-water pump. Both simple and complex methods can be applied to determine the condenser tube diameter. The paper proposes a method of technical and economic optimisation taking into account the performance of a condenser, the low-pressure (LP) part of a turbine, and a cooling-water pump as well as the profit from electric power generation and costs of building the condenser and pumping cooling water. The results obtained by this method were compared with those provided by the following simpler methods: minimization of the entropy generation rate per unit length of a condenser tube (considering entropy generation due to heat transfer and resistance of cooling-water flow), minimization of the total entropy generation rate (considering entropy generation for the system comprising the LP part of the turbine, the condenser, and the cooling-water pump), and maximization of the power unit’s output. The proposed methods were used to verify diameters of tubes in power condensers in a200-MW and a 500-MW power units. Full article
(This article belongs to the Special Issue Entropy in Computational Fluid Dynamics)
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