scholarly journals Unsteady Volumetric Entropy Generation Rate in Laminar Boundary Layers

Entropy ◽  
2006 ◽  
Vol 8 (1) ◽  
pp. 25-30 ◽  
Author(s):  
E. Walsh ◽  
D. Hernon
Keyword(s):  
Boundary Layers ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Laminar Boundary Layers

An Entropic Minimization Technique for Turbine Blade Profiles

2002 ◽  
Author(s):  
Ed Walsh ◽  
Mark Davies ◽  
Roy Myose
Keyword(s):  
Boundary Layer ◽  
Velocity Distribution ◽  
Boundary Layers ◽  
Turbine Blade ◽  
Entropy Generation ◽  
Incompressible Flows ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Minimization Technique ◽  
Boundary Layer Edge

The optimization of the boundary layer edge velocity distribution may hold the key to the minimization of entropy generation in the boundary layers of turbomachinery blades. A preliminary optimization analysis in the laminar region of a non film cooled turbine blade is presented, which demonstrates the concept of how the entropy generation rate may be reduced by varying the boundary layer edge velocity distribution along the suction surface, whilst holding the work done by the blade constant. In the laminar region the analytical technique developed by Pohlhausen and others to predict the boundary layer momentum thickness in the presence of pressure gradients has been adopted to predict the entropy generated as described in other papers by the same authors. The result gives an expression for the entropy generation rate in terms of the boundary layer edge velocity distribution for incompressible flows. The boundary layer edge velocity distribution may then be represented as a polynomial with undefined variables. This allows a minimization technique to be used to minimize the entropy generation rate on these variables. Constraints are included to keep the work output constant and the diffusion low to avoid separation. In this analysis it is only the laminar region that is considered for minimization, thus it is necessary to ensure that the modified boundary layer edge velocity distribution does not undergo transition earlier than the baseline boundary layer edge velocity distribution. This is accomplished by considering transition and separation criteria available in the literature. The result of this analysis indicates that the entropy generation rate may be reduced in the laminar boundary layers by using this technique.

Predicting Entropy Generation Rates in Transitional Boundary Layers Based on Intermittency

2006 ◽  
Author(s):  
Kevin P. Nolan ◽  
Edmond J. Walsh ◽  
Donald M. McEligot ◽  
Ralph J. Volino
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Transition Region ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Time Averaging ◽  
Laminar And Turbulent Flow ◽  
Intermittency Factor

Prediction of thermodynamic loss in transitional boundary layers is typically based on time averaged data only. This approach effectively ignores the intermittent nature of the transition region. In this work laminar and turbulent conditionally-sampled boundary layer data for zero pressure gradient and accelerating transitional boundary layers have been analyzed to calculate the entropy generation rate in the transition region. By weighting the non-dimensional dissipation coefficient for the laminar conditioned data and turbulent conditioned data with the intermittency factor, the entropy generation rate in the transition region can be determined and compared to the time averaged data and correlations for laminar and turbulent flow. It is demonstrated that this method provides an accurate and detailed picture of the entropy generation rate during transition in contrast with simple time averaging. The data used in this paper have been taken from conditionally-sampled boundary layer measurements available in the literature for favorable pressure gradient flows. Based on these measurements a semi-empirical technique is developed to predict the entropy generation rate in a transitional boundary layer with promising results.

Predicting Entropy Generation Rates in Transitional Boundary Layers Based on Intermittency

2006 ◽  
Vol 129 (3) ◽  
pp. 512-517 ◽  
Author(s):  
Kevin P. Nolan ◽  
Edmond J. Walsh ◽  
Donald M. McEligot ◽  
Ralph J. Volino
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Transition Region ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Time Averaging ◽  
Laminar And Turbulent Flow ◽  
Intermittency Factor

Prediction of thermodynamic loss in transitional boundary layers is typically based on time-averaged data only. This approach effectively ignores the intermittent nature of the transition region. In this work laminar and turbulent conditionally sampled boundary layer data for zero pressure gradient and accelerating transitional boundary layers have been analyzed to calculate the entropy generation rate in the transition region. By weighting the nondimensional dissipation coefficient for the laminar conditioned data and turbulent conditioned data with the intermittency factor, the entropy generation rate in the transition region can be determined and compared to the time-averaged data and correlations for laminar and turbulent flow. It is demonstrated that this method provides an accurate and detailed picture of the entropy generation rate during transition in contrast with simple time averaging. The data used in this paper have been taken from conditionally sampled boundary layer measurements available in the literature for favorable pressure gradient flows. Based on these measurements, a semi-empirical technique is developed to predict the entropy generation rate in a transitional boundary layer with promising results.

Entropy Generation in the Viscous Parts of Turbulent Boundary Layers

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Donald M. McEligot ◽  
Edmond J. Walsh ◽  
Eckart Laurien ◽  
Philippe R. Spalart
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Turbulent Boundary Layers ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Unit Surface Area ◽  
Pressure Gradients ◽  
Viscous Layer ◽  
Flat Plates

The local (pointwise) entropy generation rate per unit volume S‴ is a key to improving many energy processes and applications. Consequently, in the present study, the objectives are to examine the effects of Reynolds number and favorable streamwise pressure gradients on entropy generation rates across turbulent boundary layers on flat plates and—secondarily—to assess a popular approximate technique for their evaluation. About two-thirds or more of the entropy generation occurs in the viscous part, known as the viscous layer. Fundamental new results for entropy generation in turbulent boundary layers are provided by extending available direct numerical simulations. It was found that, with negligible pressure gradients, results presented in wall coordinates are predicted to be near “universal” in the viscous layer. This apparent universality disappears when a significant pressure gradient is applied; increasing the pressure gradient decreases the entropy generation rate. Within the viscous layer, the approximate evaluation of S‴ differs significantly from the “proper” value but its integral, the entropy generation rate per unit surface area Sap″, agrees within 5% at its edge.

Analysis of the Effects of Joule Heating and Viscous Dissipation on Combined Pressure-Driven and Electrokinetic Flows in a Two-Parallel Plate Channel with Unequal Constant Temperatures

2018 ◽  
Vol 233 (4) ◽  
pp. 871-879 ◽  
Author(s):  
Harshad Sanjay Gaikwad ◽  
Pranab Kumar Mondal ◽  
Dipankar Narayan Basu ◽  
Nares Chimres ◽  
Somchai Wongwises
Keyword(s):  
Viscous Dissipation ◽  
Entropy Generation ◽  
Joule Heating ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Local Entropy ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Local Entropy Generation

In this article, we perform an entropy generation analysis for the micro channel heat sink applications where the flow of fluid is actuated by combined influences of applied pressure gradient and electric field under electrical double layer phenomenon. The upper and lower walls of the channels are kept at different constant temperatures. The temperature-dependent viscosity of the fluid is considered and hence the momentum equation and energy equations are coupled in this study. Also, a hydrodynamic slip condition is employed on the viscous dissipation. For complete analysis of the entropy generation, we use a perturbation approach with lubrication approximation. In this study, we discuss the results depicting variations in the velocity and temperature distributions and their effect on local entropy generation rate and Bejan number in the system. It can be summarized from this analysis that the enhanced velocity gradients in the flow field due to combined effect of temperature-dependent viscosity and Joule heating and viscous dissipative effects, leads to an enhancement in the local entropy generation rate in the system.

Aerodynamic Optimization Design of Airfoil Shape Using Entropy Generation as an Objective

2018 ◽  
Vol 11 (2) ◽  
Author(s):  
Wei Wang ◽  
Jun Wang ◽  
Xiao-Pei Yang ◽  
Yan-Yan Ding
Keyword(s):  
Entropy Generation ◽  
Energy Cost ◽  
Optimization Design ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Aerodynamic Optimization ◽  
Analysis And Design ◽  
Constraint Model ◽  
The Impact ◽  
Drag Ratio

Abstract An entropy analysis and design optimization methodology is combined with airfoil shape optimization to demonstrate the impact of entropy generation on aerodynamics designs. In the work herein, the entropy generation rate is presented as an extra design objective along with lift-drag ratio, while the lift coefficient is the constraint. Model equation, which calculates the local entropy generation rate in turbulent flows, is derived by extending the Reynolds-averaging of entropy balance equation. The class-shape function transform (CST) parametric method is used to model the airfoil configuration and combine the radial basis functions (RBFs) based mesh deformation technique with flow solver to compute the quantities such as lift-drag ratio and entropy generation at the design condition. From the multi-objective solutions which represent the best trade-offs between the design objectives, one can select a set of airfoil shapes with a low relative energy cost and with improved aerodynamic performance. It can be concluded that the methodology of entropy generation analysis is an effective tool in the aerodynamic optimization design of airfoil shape with the capability of determining the amount of energy cost.

The Role of Fin Geometry in Heat Sink Performance

2006 ◽  
Vol 128 (4) ◽  
pp. 324-330 ◽  
Author(s):  
W. A. Khan ◽  
J. R. Culham ◽  
M. M. Yovanovich
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Entropy Generation ◽  
Heat Sink ◽  
Control Volume ◽  
Generation Rate ◽  
Heat Transfer Fluid ◽  
Entropy Generation Rate ◽  
Minimum Entropy ◽  
Axis Ratio

The following study will examine the effect on overall thermal/fluid performance associated with different fin geometries, including, rectangular plate fins as well as square, circular, and elliptical pin fins. The use of entropy generation minimization, EGM, allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general dimensionless expression for the entropy generation rate is obtained by considering a control volume around the pin fin including base plate and applying the conservations equations for mass and energy with the entropy balance. The formulation for the dimensionless entropy generation rate is developed in terms of dimensionless variables, including the aspect ratio, Reynolds number, Nusselt number, and the drag coefficient. Selected fin geometries are examined for the heat transfer, fluid friction, and the minimum entropy generation rate corresponding to different parameters including axis ratio, aspect ratio, and Reynolds number. The results clearly indicate that the preferred fin profile is very dependent on these parameters.

Second-Law Analysis on Wavy Plate Fin-and-Tube Heat Exchangers

1998 ◽  
Vol 120 (3) ◽  
pp. 797-800 ◽  
Author(s):  
W. W. Lin ◽  
D. J. Lee
Keyword(s):  
Entropy Generation ◽  
Operating Conditions ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Second Law ◽  
Spanwise Direction ◽  
Minimum Entropy ◽  
Tube Heat Exchanger ◽  
Second Law Analysis ◽  
Minimum Entropy Generation

Second-law analysis on the herringbone wavy plate fin-and-tube heat exchanger was conducted on the basis of correlations of Nusselt number and friction factor proposed by Kim et al. (1997), from which the entropy generation rate was evaluated. Optimum Reynolds number and minimum entropy generation rate were found over different operating conditions. At a fixed heat duty, the in-line layout with a large tube spacing along streamwise direction was recommended. Furthermore, within the valid range of Kim et al.’s correlation, effects of the fin spacing and the tube spacing along spanwise direction on the second-law performance are insignificant.

scholarly journals Entropy Generation Rates in Two-Dimensional Rayleigh–Taylor Turbulence Mixing

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 738 ◽  
Author(s):  
Xinyu Yang ◽  
Haijiang He ◽  
Jun Xu ◽  
Yikun Wei ◽  
Hua Zhang
Keyword(s):  
Time Evolution ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Two Dimensional ◽  
Spatial Averaging ◽  
Mixing Process ◽  
Thermal Entropy ◽  
Large Gradient ◽  
Turbulence Mixing

Entropy generation rates in two-dimensional Rayleigh–Taylor (RT) turbulence mixing are investigated by numerical calculation. We mainly focus on the behavior of thermal entropy generation and viscous entropy generation of global quantities with time evolution in Rayleigh–Taylor turbulence mixing. Our results mainly indicate that, with time evolution, the intense viscous entropy generation rate s u and the intense thermal entropy generation rate S θ occur in the large gradient of velocity and interfaces between hot and cold fluids in the RT mixing process. Furthermore, it is also noted that the mixed changing gradient of two quantities from the center of the region to both sides decrease as time evolves, and that the viscous entropy generation rate ⟨ S u ⟩ V and thermal entropy generation rate ⟨ S θ ⟩ V constantly increase with time evolution; the thermal entropy generation rate ⟨ S θ ⟩ V with time evolution always dominates in the entropy generation of the RT mixing region. It is further found that a “smooth” function ⟨ S u ⟩ V ∼ t 1 / 2 and a linear function ⟨ S θ ⟩ V ∼ t are achieved in the spatial averaging entropy generation of RT mixing process, respectively.

Sign in / Sign up

Export Citation Format

Share Document