Application of Irreversible Thermodynamics to Diffusion in Solids with Internal Surfaces

2020 ◽  
Vol 45 (4) ◽  
pp. 401-417
Author(s):  
Anna G. Knyazeva
Keyword(s):  
Thermodynamic Description ◽  
Stress Gradient ◽  
Thermodynamic System ◽  
Irreversible Thermodynamics ◽  
State Variables ◽  
Transfer Coefficients ◽  
State Equations ◽  
Diffusion In Solids ◽  
Internal Surfaces ◽  
Mass Transfer Mechanism

AbstractTwo types of additional variables were included in the set of state variables and were used for a thermodynamic description of diffusion in an ordinary thermodynamic system. Vacancies are included in the mass balance. Internal surfaces are massless but are characterized by some energy, which is included in the energy balance of the thermodynamic system. Fluxes of components, vacancies, and surfaces were expressed via two groups of thermodynamic constitutive equations of with cross effects. The first group follows from the Gibbs equation. These are state equations in a differential form. The second group relates generalized thermodynamic fluxes to generalized thermodynamic forces. It was shown for a binary system that only three of six transfer coefficients are independent even if the mass transfer mechanism caused by the stress gradient is taken into account.

Application of Meta-Heuristic Optimization Algorithms in Electric Power Systems

2015 ◽  
pp. 1292-1341
Author(s):  
N.I. Voropai ◽  
A. Z. Gamm ◽  
A. M. Glazunova ◽  
P. V. Etingov ◽  
I. N. Kolosok ◽  
...  
Keyword(s):  
Power Systems ◽  
Electric Power ◽  
Optimization Algorithms ◽  
Main Tool ◽  
Electric Power Systems ◽  
Heuristic Optimization ◽  
State Variables ◽  
State Equations ◽  
Electric Power Supply ◽  
Linear And Nonlinear Programming

Optimization of solutions on expansion of electric power systems (EPS) and their control plays a crucial part in ensuring efficiency of the power industry, reliability of electric power supply to consumers and power quality. Until recently, this goal was accomplished by applying classical and modern methods of linear and nonlinear programming. In some complicated cases, however, these methods turn out to be rather inefficient. Meta-heuristic optimization algorithms often make it possible to successfully cope with arising difficulties. State estimation (SE) is used to calculate current operating conditions of EPS using the SCADA measurements of state variables (voltages, currents etc.). To solve the SE problem, the Energy Systems Institute of Siberian Branch of Russian Academy of Sciences (ESI of SB RAS) has devised a method based on test equations (TE), i.e. on the steady state equations that contain only measured parameters. Here, a technique for EPS SE using genetic algorithms (GA) is suggested. SE is the main tool for EPS monitoring. The quality of SE results determines largely the EPS control efficiency. An algorithm for exclusion of wrong SE calculations is described. The algorithm using artificial neural networks (ANN) is based on the analysis of results of the calculation performed solving the SE problem with different combinations of constants. The proposed procedure is checked on real data.

Heat Transfer in a Rotating Two-Pass Rectangular Channel Featuring a Converging Tip Turn With Various 45 deg Rib Coverage Designs

2019 ◽  
Vol 11 (6) ◽  
Author(s):  
Andrew F Chen ◽  
Chao-Cheng Shiau ◽  
Je-Chin Han ◽  
Robert Krewinkel
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Rectangular Channel ◽  
Copper Plate ◽  
Internal Cooling ◽  
Transfer Coefficients ◽  
First Passage ◽  
Pressure Loss Coefficient ◽  
Internal Surfaces ◽  
Turbine Airfoils

Varying aspect ratio (AR) channels are found in modern gas turbine airfoils for internal cooling purposes. Corresponding experimental data are needed in understanding and assisting the design of advanced cooling systems. The present study features a two-pass rectangular channel with an AR = 4:1 in the first pass with the radial outward flow and an AR = 2:1 in the second pass with the radial inward flow after a 180 deg tip turn. Effects of rib coverage near the tip region are investigated using profiled 45 deg ribs (P/e = 10, e/Dh ≈ 0.11, parallel and in-line) with three different configurations: less coverage, medium coverage, and full coverage. The Reynolds number (Re) ranges from 10,000 to 70,000 in the first passage. The highest rotation number achieved was Ro = 0.39 in the first passage and 0.16 in the second passage. Heat transfer coefficients on the internal surfaces were obtained by the regionally averaged copper plate method. The results showed that the rotation effects on both heat transfer and pressure loss coefficient are reduced with an increased rib coverage in the tip turn region. Different rib coverage upstream of the tip turn significantly changes the heat transfer in the turn portion. Heat transfer reduction (up to −27%) on the tip wall was seen at lower Ro. Dependence on the Reynolds number can be seen for this particular design. The combined geometric, rib coverage, and rotation effects should be taken into consideration in the internal cooling design.

Heat Transfer in a Rotating Two-Pass Rectangular Channel Featuring Reduced Cross-Sectional Area After Tip Turn (Aspect Ratio = 4:1 to 2:1) With Profiled 60 deg Angled Ribs

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Andrew F Chen ◽  
Chao-Cheng Shiau ◽  
Je-Chin Han ◽  
Robert Krewinkel
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Direction ◽  
Rectangular Channel ◽  
Secondary Flows ◽  
Transfer Coefficients ◽  
First Passage ◽  
Cross Sectional ◽  
Internal Surfaces

The present study features a two-pass rectangular channel with an aspect ratio (AR) = 4:1 in the first pass and an AR = 2:1 in the second pass after a 180-deg tip turn. In addition to the smooth-wall case, ribs with a profiled cross section are placed at 60 deg to the flow direction on both the leading and trailing surfaces in both passages (P/e = 10, e/Dh ∼ 0.11, parallel and in-line). Regionally averaged heat transfer measurement method was used to obtain the heat transfer coefficients on all internal surfaces. The Reynolds number (Re) ranges from 10,000 to 70,000 in the first passage, and the rotational speed ranges from 0 to 400 rpm. Under pressurized condition (570 kPa), the highest rotation number achieved was Ro = 0.39 in the first passage and 0.16 in the second passage. The results showed that the turn-induced secondary flows are reduced in an accelerating flow. The effects of rotation on heat transfer are generally weakened in the ribbed case than the smooth case. Significant heat transfer reduction (∼30%) on the tip wall was seen in both the smooth and ribbed cases under rotating condition. Overall pressure penalty was reduced for the ribbed case under rotation. Reynolds number effect was found noticeable in the current study. The heat transfer and pressure drop characteristics are sensitive to the geometrical design of the channel and should be taken into account in the design process.

The Optimum Design of Spatial Frames Using the Method of Constrained Steepest Descent With State Equations

1971 ◽  
Vol 93 (4) ◽  
pp. 1261-1267 ◽  
Author(s):  
D. L. Bartel ◽  
E. J. Haug ◽  
Kwan Rim
Keyword(s):  
Nonlinear Programming ◽  
Mechanical Design ◽  
The State ◽  
Steepest Descent ◽  
Mathematical Programming Problem ◽  
State Variables ◽  
State Equations ◽  
Design Problems ◽  
Out Of Plane ◽  
Plane Frames

This paper considers the design of a class of spatial frames which occur frequently in mechanical systems: plane frames with out-of-plane loads. The design objective is to minimize the weight subject to constraints on stress and geometry. The method of constrained steepest descent with state equations is introduced to solve the resulting mathematical programming problem. This method differs from the usual methods of nonlinear programming in that the state variables and the state equations are used explicitly in the formulation. This results in a natural matching of the essential features of the design problem and the method used to obtain its solution. The method is effective and general in that it can be readily applied to a wide variety of design problems which occur in mechanical design.

scholarly journals Modelling of NO adsorption in fixed bed on activated carbon

2011 ◽  
Vol 32 (4) ◽  
pp. 367-377 ◽  
Author(s):  
Lenka Kuboňová ◽  
Lucie Obalová ◽  
Oldřich Vlach ◽  
Ivana Troppová ◽  
Jaroslav Kalousek
Keyword(s):  
Nitric Oxide ◽  
Mass Transfer ◽  
Activated Carbon ◽  
Fixed Bed ◽  
Breakthrough Curves ◽  
Force Model ◽  
Transfer Coefficients ◽  
No Adsorption ◽  
Response Curves ◽  
Mass Transfer Mechanism

Modelling of NO adsorption in fixed bed on activated carbon Adsorption experiments of nitric oxide in nitrogen carrier gas were held on activated carbon in a fixed bed flow system. Breakthrough curves describing the dependence of exit concentrations of nitric oxide on time were matched with theoretical response curves calculated from the linear driving force model (LDF). The model assumes Langmuir adsorption isotherm for the description of non-linear equilibrium and overall mass transfer coefficient for mass transfer mechanism. Overall mass transfer coefficients were obtained by the method of least squares for fitting numerically modelled breakthrough curves with experimental breakthrough curves. It was found that LDF model fits all the breakthrough curves and it is a useful tool for modelling purposes.

scholarly journals Comparative Simulation Study on Synchronous Generators Sudden Short Circuits

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Lucian Lupşa-Tătaru
Keyword(s):  
Mathematical Model ◽  
Time Domain ◽  
Short Circuit ◽  
Structural Equations ◽  
Process Models ◽  
State Variables ◽  
Synchronous Generators ◽  
State Equations ◽  
Starting Point ◽  
Short Circuits

Although of a great extent in time, the research works directed at studying transients in synchronous generators have not yet provided fully sufficient comparative studies in respect to sudden short circuits of the machine. The present paper puts forward novel and comprehensive process models for dynamic simulation of short circuit faults of initially unloaded synchronous generators, using the generalizedd-q-0 mathematical model as starting point in derivation. Distinct from the time-domain analysis, the technique proposed here allows an effective comparative overview by employing a specialized procedure to perform repeated time-domain simulations accompanied by peak values recording for the various circumstances. The time consuming matrix numerical inversion at each step of integration, usually performed when selecting currents as state variables, is eliminated by advancing the process models in a convenient split matrix form that allows the symbolic processing. Also, the computational efficiency is being increased by introducing a set of auxiliary variables common to different state equations. The models derivation is carried out without altering the structural equations of the generalizedd-q-0 mathematical model of synchronous generators whilst the simulation results are both compared and discussed in detail.

Static Analysis of Thick Laminated Beams: Two-Dimensional Elasticity Solutions via Differential Quadrature

2005 ◽  
Vol 475-479 ◽  
pp. 1067-1072
Author(s):  
Chaofeng Lü ◽  
Ying Gao ◽  
W.Q. Chen
Keyword(s):  
Present Method ◽  
Matrix Theory ◽  
Laminated Composite ◽  
Static Problem ◽  
State Equation ◽  
Differential Quadrature ◽  
Two Dimensional ◽  
State Variables ◽  
State Equations ◽  
Elasticity Solutions

This paper intends to present two-dimensional elasticity solutions for static problem of thick laminated composite beams using a hybrid method of state-space-based differential quadrature. The technique of differential quadrature is employed to reduce the partial differential state equations into the ordinary differential ones at all arbitrary sampling points for each individual laminate. General solution to the assembled state equation is then obtained according to the matrix theory. Taking account of the continuity conditions at the interfaces of all the adjacent lamina, a relationship between state variables at the top and bottom surfaces of the beam is established through a global transfer matrix. After incorporating the boundary conditions at these two surfaces, an eigenvalue equation for static problem is then derived. Numerical examples are presented, through which the accuracy and convergence characteristics of the present method are investigated. It is shown that the present method is of excellent efficiency for laminated composite thick beams subjected to arbitrary end supporting conditions.

The Analysis and Design of Saturators for Power Generation Cycles: Part 2 — Heat and Mass Transfer

2003 ◽  
Author(s):  
A. Aramayo-Prudencio ◽  
J. B. Young
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Control Volume ◽  
Numerical Procedure ◽  
Saturation Temperature ◽  
Irreversible Thermodynamics ◽  
Interface Temperature ◽  
Specific Work ◽  
Transfer Coefficients ◽  
Analysis And Design

The introduction of water into a gas turbine circuit is known to provide benefits of increased efficiency and specific work output. There are several methods of humidification but the use of a pressurised saturator in an evaporative cycle offers many attractive features. This two-part paper presents an in-depth study of the saturator, in Part 1 via a thermodynamic approach and in Part 2 via a detailed heat and mass transfer analysis. The analysis in Part 2 starts from a rigorous control volume formulation and includes a derivation of the entropy production equation in keeping with the theory of irreversible thermodynamics. The specification of the heat and mass transfer coefficients is discussed and an analytical expression derived for the liquid-gas interface temperature. A novel numerical procedure for solving the equations is then presented which provides more flexibility than the traditional method of solution. After a discussion on the possibility of occurrence of supersaturated vapour states, results are presented showing the effects of variation of saturator height. The limiting condition when the water exit temperature falls to the inlet vapour adiabatic saturation temperature is also discussed.

Yucca Mountain Project Preclosure Ventilation Heat Transfer Analysis: Determining the Mixed Convection Heat Transfer Coefficients

2004 ◽  
Author(s):  
Sandra Dalvit Dunn ◽  
Stephen W. Webb ◽  
Robert Walsh ◽  
Veraun Chipman
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Outer Cylinder ◽  
Convection Heat Transfer ◽  
Heat Transfer Analysis ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Mass Transfer Mechanism ◽  
Convection Model ◽  
Experimental Values

Mixed convection is an important heat and mass transfer mechanism in the YMP drifts prior to the repository closure. There is little information in the literature on mixed turbulent convection for a similar horizontal annulus configuration. A model was developed using the Morgan approach, combining forced and natural convection models. A rigorous uncertainty analysis was performed. Comparisons between the mixed convection model and experimental values showed agreement for the inner cylinder. The model consistently under-predicted heat transfer from the outer cylinder. The methodology was later employed in the analysis to predict the heat transfer associated with a full scale ventilated emplacement drift.

scholarly journals Thermodynamics and Kinetics of Glycolytic Reactions. Part II: Influence of Cytosolic Conditions on Thermodynamic State Variables and Kinetic Parameters

2020 ◽  
Vol 21 (21) ◽  
pp. 7921 ◽  
Author(s):  
Kristina Vogel ◽  
Thorsten Greinert ◽  
Monique Reichard ◽  
Christoph Held ◽  
Hauke Harms ◽  
...  
Keyword(s):  
Kinetic Parameters ◽  
Kinetic Models ◽  
Ph Value ◽  
Irreversible Thermodynamics ◽  
Force Model ◽  
State Variables ◽  
Kinetic And Thermodynamic Parameters ◽  
Reliable Quantification ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions

For systems biology, it is important to describe the kinetic and thermodynamic properties of enzyme-catalyzed reactions and reaction cascades quantitatively under conditions prevailing in the cytoplasm. While in part I kinetic models based on irreversible thermodynamics were tested, here in part II, the influence of the presumably most important cytosolic factors was investigated using two glycolytic reactions (i.e., the phosphoglucose isomerase reaction (PGI) with a uni-uni-mechanism and the enolase reaction with an uni-bi-mechanism) as examples. Crowding by macromolecules was simulated using polyethylene glycol (PEG) and bovine serum albumin (BSA). The reactions were monitored calorimetrically and the equilibrium concentrations were evaluated using the equation of state ePC-SAFT. The pH and the crowding agents had the greatest influence on the reaction enthalpy change. Two kinetic models based on irreversible thermodynamics (i.e., single parameter flux-force and two-parameter Noor model) were applied to investigate the influence of cytosolic conditions. The flux-force model describes the influence of cytosolic conditions on reaction kinetics best. Concentrations of magnesium ions and crowding agents had the greatest influence, while temperature and pH-value had a medium influence on the kinetic parameters. With this contribution, we show that the interplay of thermodynamic modeling and calorimetric process monitoring allows a fast and reliable quantification of the influence of cytosolic conditions on kinetic and thermodynamic parameters.

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