Generation Rate Distribution Research Articles

Entropy generation in developing laminar fluid flow through a circular pipe with variable properties

Entropy generation in a circular pipe is analyzed numerically. A two-dimensional solution for the velocity ant temperature profiles is obtained considering temperature dependent thenmophysical properties. Uniform wall heat flux case is considered as the thermal boundary condition. The distribution of the entropy generation rate is investigated throughout the volume of the fluid as it flows through the pipe. Engine oil is selected as the working fluid. In addition, ethylene glycol and air are used in a parametric study. The total entropy generation rate is calculated by integration over the various cross-sections as well as over the entire volume. The results are compared with those obtained for the constant viscosity case. A considerable discrepancy is found between the two cases since the viscosity of these fluids is highly sensitive to the temperature variation.

Numerical study on local entropy generation in a burner fueled with various fuels

This study considers numerical simulations of the combustions of hydrogen and various hydrocarbons with air, including 21% oxygen and 79% nitrogen, in a burner and the numerical solution of the local entropy generation rate due to the high temperature and velocity gradients in the combustion chamber. The combustion is simulated for the fuel mass flow rates providing the same heat transfer rate % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiqadg % fagaGaaiaacMcaaaa!3825! $$(\dot Q)$$ to the combustion chamber in the each fuel case. The effects of % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyuayaaca % aaaa!36CC! $$\dot Q$$ (only in the case of H2 fuel) and equivalence ratio (ϕ) on the combustion and entropy generation rate are investigated for the different % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyuayaaca % Gaae4Caaaa!37C2! $$\dot Q{\text{s}}$$ (from 5,000 to 10,000 W) and ϕs (from 0.5 to 1.0). The numerical calculation of combustion is performed individually for all cases with the help of the Fluent CFD code. Furthermore, a computer program has been developed to numerically calculate the volumetric entropy generation rate distributions and the other thermodynamic parameters by using the results of the calculations performed with the FLUENT code. The calculations bring out that the maximum reaction rates decrease with the increase of ϕ (or the decrease of λ). The large positive and negative temperature gradients occur in the axial direction, nonetheless, the increase of ϕ significantly reduces them. The calculations bring out also that with the increase of ϕ from 0.5 to 1.0, the volumetric local entropy generation rates decrease about 4% and that the merit numbers increase about 16%.

Design of a boiling water reactor core based on an integrated blanket–seed thorium–uranium concept

This paper is concerned with the design of a boiling water reactor (BWR) equilibrium core using thorium as a nuclear material in an integrated blanket–seed (BS) assembly. The integrated BS concept comes from the fact that the blanket and the seed rods are located in the same assembly, and are burned out in a once-through cycle. The idea behind the lattice design is to use the thorium conversion capability in a BWR spectrum, taking advantage of the 233U build-up. A core design was developed to achieve an equilibrium cycle of 365 effective full power days in a standard BWR with a reload of 104 fuel assemblies designed with an average 235U enrichment of 7.5 w/o in the seed sub-lattice. The main operating parameters, like power, linear heat generation rate and void distributions were obtained as well as the shutdown margin. It was observed that the analyzed parameters behave like those obtained in a standard BWR. The shutdown margin design criterion was fulfilled by addition of a burnable poison region in the fuel assembly.

Numerical calculation of local entropy generation in a methane–air burner

This study considers numerical simulation of the combustion of methane with air including 21% oxygen and 79% nitrogen in a burner and the numerical solution of the local entropy generation rate due to the high temperature and velocity gradients in the combustion chamber for various fuel flow rates (from 5 to 10 lpm). Swirling air flow is also used to burn the methane more efficiently. The effects of equivalence ratio ( ϕ ) and swirl number ( S ) on the combustion and entropy generation rate are investigated for different (consecutive) equivalence ratios (from 0.5 to 1.0) and swirl numbers (from 0 to 0.3). The numerical calculation of combustion is performed individually for these cases with the help of the Fluent CFD code. The volumetric entropy generation rate distributions and the other thermodynamic parameters are calculated numerically by using the results of the combustion calculations. The maximum values of the rates of reaction-1 and -2 decrease with the increase of ϕ . In the case of ϕ < 1, complete combustion occurs, and the combustion in the case of ϕ = 1 is very close to the complete combustion state. In the case of no swirl, the entropy generation rate decreases exponentially with the increase of ϕ in the cases of high Q f , whereas they have quadratic profiles having their minimum values in cases of low Q f . In terms of the entropy generation rates, the optimum equivalence ratios for Q f = 5, 6, 7, >7 lpm in the case of S = 0 and Q f = 10 lpm in the case of S = 0.3 are obtained as ϕ = 0.66, 0.8, 0.86, 1.0 and 0.92, respectively.

Entropy Generation in Laminar Fluid Flow through a Circular Pipe

A numerical solution to the entropy generation in a circular pipe is made. Radial and axial variations are considered. Navier-Stokes equations in cylindrical coordinates are used to solve the velocity and temperature fields. Uniform wall heat flux is considered as the thermal boundary condition. The distribution of the entropy generation rate is investigated throughout the volume of the fluid as it flows through the pipe. Engine oil is selected as the working fluid. In addition, water and Freon are used in a parametric study. The total entropy generation rate is calculated by integration over the various cross-sections as well as over the entire volume.

Generation of Droplets in Slag-Metal Emulsions through Top Gas Blowing

The behavior of metal droplets in a slag-metal-gas emulsion through impinging gas blowing was investigated experimentally using a cast iron-slag-nitrogen gas system at high temperatures. A mathematical model of the emulsification process for determining the generation rate, size distribution, and residence time of metal droplets has been developed and successfully validated using experimental data. From the present work, it was found that the generation rate and size distribution of metal droplets is strongly influenced by the ratio of the inertial force of blown gas to the surface tension and buoyancy forces of the liquid metal. A new dimensionless number, i.e. blowing number, which represents the ratio of inertial to surface tension and buoyancy forces and also the departure of the system from its stable condition defined by the Kelvin-Helmholtz criterion, is proposed. A functional relationship of generation rate and size distribution of metal droplets with the blowing number is proposed.

Cutting Fluid Aerosol Generation due to Spin-off in Turning Operation: Analysis for Environmentally Conscious Machining

This paper presents an analytical model for the prediction of shop floor aerosol generation rate and particulate size distribution due to the spin-off motion of cutting fluid from a rotational workpiece in a turning operation. Based on the theory of atomization and principles of fluid motion, the model analyzes the generation of cutting fluid aerosol associated with the formation of rotating cylindrical peripheral disk and liquid sheet on the workpiece surface. In coupling with fluid flow rate analysis and Rosin and Rammler distribution model, the airborne particulate generation rate and size distribution are expressed in terms of fluid properties, fluid application condition, and machining process parameters. Experiments were performed with the use of the light scattering particle measurement devices to calibrate and verify the analytical models. Under various fluid flow rates and workpiece rotational speeds, experimental data have shown reasonable agreement with model predictions. The predictive models developed in this paper can be used as a basis for human exposure and health hazard analysis. It can also facilitate the control and optimization of the use of cutting fluids in achieving a balanced consideration of process productivity and environmental consciousness.

Analysis of Urea Nitrogen and Creatinine Kinetics in Hemodialysis: Comparison of a Variable-Volume Two-Compartment Model with a Regional Blood Flow Model and Investigation of an Appropriate Solute Kinetics Model for Clinical Application

To investigate an appropriate solute kinetics model for clinical application, we analyzed urea nitrogen (UN) and creatinine (Cr) kinetics by a variable-volume two-compartmental model (2CM) and a regional blood flow model (RBF) in 44 hemodialysis patients with varying proportions of first compartmental volume and regional volume (p₁). Solute kinetics could not be solved in some of the patients with higher p₁ values, and there were more solution failures by the RBF than by the 2CM. The solute generation rate (g) and solute distribution volume in the dry state (V_D) increased with increases in p₁ in both models, but there were some differences between the two models. When g was normalized by V_D, it became relatively constant, irrespective of the p₁ value or model used (0.133 ± 0.029 mg/min/l by the 2CM and 0.132 ± 0.029 mg/min/l by the RBF for UN; 0.0200 ± 0.0049 mg/min/l by the 2CM and 0.0198 ± 0.0048 mg/min/l by the RBF for Cr). The intercompartmental mass transfer coefficient (K_c; liters/min) calculated by the 2CM decreased as p₁ increased (K_c = –1.77·p₁ + 1.16, p < 0.0001, R = 0.999 for UN; K_c = –0.847·p₁ + 0.556, p < 0.0001, R = 1.000 for Cr). The systemic blood flow (Q_sys; liters/min) calculated by the RBF also decreased as p₁ increased (Q_sys = –11.1·p₁ + 6.21, p < 0.0005, R = 1.000 for UN; Q_sys = –5.22·p₁ + 2.90, p < 0.001, R = 0.999 for Cr). Since the RBF more frequently failed to solve the solute kinetics and since there was a difference in its Q_sys values for UN and Cr, the 2CM was considered to be a superior model. When p₁ was extremely low, the 2CM could be transformed into a modified variable-volume one-compartment model (1CM) which presented a similar g/V_D (0.133 ± 0.029 for UN; 0.0200 ± 0.0048 for Cr). This modified 1CM was considered to satisfy appropriate conditions for clinical application, since it is simpler than the 2CM and provides useful information on the dialysis dose.

Double-sweep LF-CV technique for generation rate determination in MOS capacitors

A novel technique for determining the generation rate in MOS structures based on the measurement of two independent gate current sweeps in non-equilibrium, non-steady state is presented. The described method allows the selfconsistent evaluation of the generation rate distribution in the bulk of inhomogeneously doped MOS capacitors without requiring knowledge of the doping profile. Experimental results are compared with the related double sweep HF-CV technique and the standard Zerbst HF-C(t) technique.

Sensitivity analysis for estimating urea kinetics parameters during hemodialysis

In this paper a time-varying volume, double-pool urea kinetics model is considered and a sensitivity analysis is carried out to determine those patient parameters that have greater influence on the time course of blood urea nitrogen concentration (BUN) during and between dialysis treatment. The model parameters include the urea generation rate, the initial distribution volume of the urea, the ratio between intracellular and extracellular volumes, and the mass transfer coefficient between the two pools. The analysis demonstrates that BUN is highly sensitive to the urea generation rate and total distribution volume whereas it is influenced by the remaining parameters to a much lesser extent. In addition, the location of the absolute maxima of BUN sensitivity functions suggests the rational placement of a reduced number of blood samples that may still allow sufficiently accurate estimates for the parameters of clinical interest, such as the urea generation rate, total distribution volume, and the ratio between intracellular and extracellular volumes. This conclusion has been confirmed by simulation studies where parameter estimation has been performed with a varying number of observation points.

LO‐Phonon Generation with Energy Collision Broadening in Polar Semiconductors

AbstractThe generation of LO‐phonons in the process of the hot electron cooling in polar semiconductors is studied theoretically. The generation rate formula is derived in the frame of the theory of the nonequilibrium statistical operator. The electron energy collision broadening is included in an approximation which meets the requirements of the elementary thermodynamics. Numerical results giving the generation rate and quasi‐steady state LO‐phonon distribution function in some materials are presented. The generalization of the generation rate formula to the case of the nonthermalized electronic system is also given.

A two-dimensional model for predicting substrate current in submicrometer MOSFETs

The authors present a more rigorous hydrodynamic postprocessing approach than that implemented by J.W. Slotboom et al. (1991). The proposed model is 2-D and is based on the 1-D form of energy equation described by R.K. Cook et al. (1982), implemented into the 2-D drift-diffusion simulator PISCES as a postprocessor to calculate substrate current. This new approach involves the determination of the average energy along many current contours using the 1-D energy conservation equation and the local electric fields calculated by PISCES along each current path. The impact ionization rates are calculated using an energy parameterized form of the Chynoweth law. These coefficients along with the current densities calculated by PISCES are then used to determine the 2-D distribution of generation rates, and the generation rates are integrated over the entire 2-D device structure to calculate the substrate current. The authors have demonstrated very good agreement with substrate current characteristics measured on a broad range of LDD (lightly doped drain) NMOSFET devices with varying channel lengths, gate biases, and drain biases.

A study on hybrid modeling of electrical phenomena in contacts

The effect of microcontacts (size of the microcontact interface, space angle of the microcontact, etc.) on the potential and joule heat generation rate distribution of the contact device is analyzed using a hybrid finite-element model. In this model, the analytical solution of constriction resistance for single line contacts is adopted to consider the effect of microcontacts on calculating the potential distribution of the contact device using the finite-element method. The microcontact was treated as a one-dimensional element, which has only a resistance characteristic. The results of calculations revealed that the effect of microcontacts on the potential and joule heat generation rate distribution in the conducting bodies is substantial and consequently should be considered when simulating the thermal response of contact devices. >

Current density and heat generation rate in the neighborhood of a single-line contact with various space angles

Using the fact that the electric potential at any point and the current flowing through a segment in a conducting body are not changed by geometrical transformations, the distribution of heat generation rate in a neighborhood about a single-line contact was calculated for various space angles by applying a conformal mapping. It is shown that the space angle of a single-line contact has a large influence on the distribution of the Joule heating rate in the conducting body and hence must be considered for accurate prediction of the thermal response of contact devices, especially when the space angle is approaching pi radians. The heat generation rate under a constant electrical resistivity is extremely high in the region near the contact line, especially at positions near the edge of the line contact, which will cause thermal damage in that area. >

Development of a Four-Equation Reactor Coolant System Model for Pressurized Water Reactor Simulation

A four-equation drift-flux reactor coolant system (RCS) model REVOT-HKU has been developed by the University of Hong Kong for pressurized water reactor simulators. Models have also been developed to simulate the thermal hydraulics of the RCS as well as the vapor generation rate and void distribution. Comparisons with the FRIGG loop experimental data and the Westinghouse advanced model were made. The results have demonstrated that the present model is satisfactory in predicting void distribution in a boiling channel and RCS dynamics during a loss-of-pumping power transient.

Size and Generation Rate of Sidestream Cigarette Smoke Particles

Sidestream cigarette smoke generated using an automatic smoking machine (SEM-II) and Kentucky 2R1 reference cigarettes was analyzed for particle generation rate and size distribution. Part of the sidestream smoke was sampled with an Andersen Cascade Impactor, following dilution with about 29 to 54 liters/min of laboratory air. The remaining sidestream smoke was further diluted 1,000-fold with vapor phase from filtered sidestream smoke before analysis with an Electrical Aerosol Analyzer and Condensation Nuclei Counter. The smoking parameters of primary dilution ratio and puff pressure were varied in the experiments. The number median diameter of sidestream cigarette smoke was about 0.10 μm, and the mass median diameter was typically 0.16 μm, about half the size of fresh mainstream smoke. Additionally, the size distribution of sidestream smoke was significantly broader than that of mainstream smoke. The particle generation rate of sidestream smoke depended on smoking conditions and varied from 1.4 × 109 to ...

Electrical Charging of Macroscopic Particles Using a Beta Source and Electric and Magnetic Fields

A theoretical and experimental study of an aerosol particle charging apparatus that utilizes a 407-MBq (11-mCi) /sup 90/Sr--/sup 90/Y beta source and electric and magnetic fields has been performed. Fluid models of electron trajectories in the presence of the magnetic field, ion generation due to electron energy deposition, and particle charge acquisition due to ion transport are developed and applied to the experimental apparatus. Calculated average axial ion generation rates on the order of 10/sup 14//m/sup 3/ s are confirmed by experimental measurements, and calculated radial profiles are in good agreement with experiments. Calculated and experimental charging rates agree within 30% for 50- to 100-..mu..m-dia glass spheres in an electric field of 100 kV/m and a magnetic field of 0.141 T. It is found that both the magnitude and spatial distribution of the ion generation rate play important roles in determining the rate of charge acquisition by an aerosol particle in a partially ionized gas subjected to an external electric field.

A small signal theory of FM electroluminescent diodes

Under simplifying assumptions the theory of FM spontaneous mode electro luminescent diodes of flat geometry is presented. Derived expressions for area and edge emitted photon flux follow from the analysis of the photon generation rate distribution and of radiation losses. The origin of subcarrier signal phase shift in the pattern is discussed.

Nitric Oxide Formation in Recirculating Flows

Abstract Nitric oxide generation rate and concentration distribution in combustors containing regions of recirculating flow are calculated using a computer program developed for two-dimensional elliptic compressible flows. Two special techniques have been incorporated in the computer program to evaluate nitric oxide. One is the flame finding procedure by which the peak temperature lines, near which most of the nitric oxide is formed and which generally straddle the grid points of a numerical network, are located by double interpolation through local enthalpy and fuel-air composition. The other is the evaluation of nitric oxide formation in a grid volume by considering the temperature variations as well as the average temperature in the volume element. The chemical compositions, except nitric oxide, are assumed to be at local equilibrium. Methane-air equilibrium combustion tables, relating temperature and chemical species such as water vapor, carbon dioxide, and molecular oxygen to fuel-air ratio and enthalpy, are employed. Sample results for the profiles of stream function, swirl velocity, fuel mass fraction, temperature, nitric oxide formation rate, and nitric oxide concentration are presented.

The distribution of cell generation times.

ABSTRACTTwo different distributions of generation times, log‐normal and reciprocal normal, were compared by fitting them to experimental generation time distributions for bacteria, yeast, protozoa, and mammalian cells. In every case, the reciprocal normal distribution gave better agreement, whether the original frequency distributions or their cumulatives were compared. the log‐normal distribution failed to give significant agreement for three of the original distributions. It is concluded that the reciprocal normal distribution of generation times, or more precisely, the truncated normal distribution of generation rates, is consistent with the published data for steady state populations of all kinds of cells that divide by regular binary fission. A model is suggested for this distribution of generation times, associating it with control of transport of materials into the cell, and with linear cell growth.