Initial Steady-state Conditions Research Articles

Compressor Station Recycle System Dynamics During Emergency Shutdown

Transient phenomena associated with gas recycling during compressor emergency shutdown (ESD) have been studied both experimentally and numerically. A scaled-down laboratory test rig has been constructed to study the influence of various underlying parameters on ESD operation. Three different configurations representing different design scenarios were tested. The first configuration has a long recycle system with a volume capacitance representing an air-cooled heat exchanger in the recycle loop, and the recycle valve located close to the discharge side. The second one is the same as the first except the recycle valve is placed close to the suction side. In the third configuration, the cooler capacitance was removed from the recycle loop and the piping capacitance on the discharge side was further reduced. Shutdown tests were carried out from different steady-state initial conditions varying the recycle valve opening time, and the synchronization time between the compressor ESD signal and valve opening signal. Numerical simulations based on the solution of the full one-dimensional conservation equations using the method of characteristics were also conducted for the above configurations. Good agreement was obtained between measurements and simulation results. Numerical simulations were used to analyze other cases, which were not investigated experimentally, to further investigate the interaction between equipment and flow parameters. Results indicate that the valve prestroke time is more crucial than the stroke time and that it should be made short to avoid surging the compressor during ESD. Locating the recycle valve as close as possible to the suction or discharge of the compressor helps reduce unit surge during shutdown.

The Kinetic Factors That Determine the Affinity and Selectivity for Slow Binding Inhibition of Human Prostaglandin H Synthase 1 and 2 by Indomethacin and Flurbiprofen

We present here for the first time a method for determining the rate constants associated with slow binding inhibition of prostaglandin H synthase (PGHS). The rate constants were determined by a method using initial steady-state conditions, which minimize the impact of catalytic autoinactivation of the enzyme. The currently available methods for determining the kinetic constants associated with slow binding enzyme inhibition do not distinguish between rate decreases due to enzyme inhibition or due to autoinactivation of the enzyme. A mathematical model was derived assuming a rapid reversible formation of an initial enzyme-inhibitor complex (EI) followed by a slow reversible formation of a second enzyme-inhibitor complex (EI*). The two enzyme inhibitor complexes are assumed to be in slow equilibrium. This method was used to evaluate the kinetic parameters associated with the binding and selectivity of the nonsteroidal antinflammatory drugs (NSAIDs), flurbiprofen and indomethacin. The KI values associated with the formation of the first reversible complex (EI) for flurbiprofen with PGHS1 and PGHS2 were 0.53 +/- 0. 06 and 0.61 +/- 0.08 microM, respectively; the rate constants for the forward isomerization, k2, into the second reversible complex (EI*) were 0.97 +/- 0.99 and 0.11 +/- 0.01 s-1, respectively, and rates of the reverse isomerization from EI*, k-2, were 0.031 +/- 0.004 and 0.0082 +/- 0.0008 s-1, respectively. Indomethacin was estimated to form the EI complex with the same affinity for both PGHS1 and PGHS2, 10.0 +/- 2.8 microM and 11.2 +/- 2.0 microM, respectively, and dissociate from EI* at approximately the same rate 0.0011 +/- 0.0002 s-1 and 0.0031 +/- 0.0003 s-1, respectively. However, the rate of isomerization into EI* from EI was much greater for PGHS1 than PGHS2, 0.33 +/- 0.08 s-1 as compared with 0.034 +/- 0.004 s-1. These results show that the overall affinity for the inhibition of PGHS1 versus PGHS2 was 30-fold greater for indomethacin (KI* = 0.032 +/- 0.005 and 1.02 +/- 0.08 microM, respectively) and 3-fold greater for flurbiprofen (KI* = 0.017 +/- 0.002 and 0.045 +/- 0.004 microM, respectively). The results also show that for both PGHS1 and PGHS2, flurbiprofen was bound tighter to the initial EI complex than indomethacin; however, the rate of dissociation from EI* was slower for indomethacin than flurbiprofen. The rate of the forward isomerization to EI* is primarily responsible for the selectivity of both NSAIDs for PGHS1. This analysis shows the quantitative importance of the different kinetic parameters upon the overall binding affinity of these NSAIDs and should greatly assist in our understanding of the structural interactions that promote enzyme-inhibitor binding.

Development of a MELCOR Self-Initialization Algorithm for Boiling Water Reactors

The MELCOR code, developed by Sandia National Laboratories, is suitable for calculating source terms and simulating severe accident phenomena of nuclear power plants. Prior to simulating a severe accident transient with MELCOR, the initial steady-state conditions must be generated in advance. The current MELCOR users` manuals do not provide a self-initialization procedure; this is the reason users have to adjust the initial conditions by themselves through a trial-and-error approach. A MELCOR self-initialization algorithm for boiling water reactor plants has been developed, which eliminates the tedious trial-and-error procedures and improves the simulation accuracy. This algorithm adjusts the important plant variable such as the dome pressure, downcomer level, and core flow rate to the desired conditions automatically. It is implemented through input with control functions provided in MELCOR. The reactor power and feedwater temperature are fed as input data. The initialization work of full-power conditions of the Kuosheng nuclear power station is cited as an example. These initial conditions are generated successfully with the developed algorithm. The generated initial conditions can be stored in a restart file and used for transient analysis. The methodology in this study improves the accuracy and consistency of transient calculations. Meanwhile, the algorithm provides all MELCOR usersmore » an easy and correct method for establishing the initial conditions.« less

Self-Initialization Algorithm of the Kuosheng Plant Analyzer

A plant analyzer was developed for the Kuosheng power station, based on the AD-100 peripheral processor system. To analyze a transient from partial power conditions, the initial steady-state conditions must be generated in advance. A self-initialization algorithm for generating the initial partial power conditions has been developed. The initialization of the rated power conditions is performed first. The self-initialization algorithm then simultaneously adjusts important plant variables, such as the reactor power, dome pressure, downcomer level, feed-water temperature, and core flow, to the desired partial power conditions form the rated conditions with the aid of existing plant control systems and four extra control loops. This algorithm was developed and encoded in the Kuosheng plant analyzer. The initialization for a recirculation pump trip test at 68% of rated power demonstrates the success of this algorithm. The initial conditions generated can be saved and used for transient analysis. Tedious and time-consuming trial-and-error initialization procedures are eliminated. This methodology improves the accuracy and consistency of transient calculations for partial power conditions.

Kinetic mechanism of beef heart ubiquinol:cytochrome c oxidoreductase.

The electron transfer from ubiquinol-2 to ferricytochrome c mediated by ubiquinol:cytochrome c oxidoreductase [E.C. 1.10.2.2] purified from beef heart mitochondria, which contained one equivalent of ubiquinone-10 (Q10), was investigated under initial steady-state conditions. The Q10-depleted enzyme was as active as the Q10-containing one. Double reciprocal plots for the initial steady-state rate versus one of the two substrates at various fixed levels of the other substrate gave parallel straight lines in the absence of any product. Intersecting straight lines were obtained in the presence of a constant level of one of the products, ferrocytochrome c. The other product, ubiquinone-2, did not show any significant effect on the enzymic reaction. Ferrocytochrome c non-competitively inhibited the enzymic reaction against either ubiquinol-2 or ferricytochrome c. These results indicate a Hexa-Uni ping-pong mechanism with one ubiquinol-2 and two ferricytochrome c molecules as the substrates, which involves the irreversible release of ubiquinone-2 as the first product and the irreversible isomerization between the release of the first ferrocytochrome c and the binding of the second ferricytochrome c. Considering the cyclic electron transfer reaction mechanism, this scheme suggests that the binding of quinone or quinol to the enzyme and electron transfer between the iron-sulfur center and cytochrome c1 are rigorously controlled by the electron distribution within the enzyme.

Meizothrombin formation during factor Xa-catalyzed prothrombin activation. Formation in a purified system and in plasma.

Meizothrombin and thrombin formation were quantitated during factor Xa-catalyzed activation of human prothrombin in reaction systems containing purified proteins and in plasma. In the purified system considerable amounts of meizothrombin accumulated when prothrombin was activated by factor Xa (with or without accessory components) under initial steady state conditions. The ratio of the rates of meizothrombin and thrombin formation was not influenced by variation of the pH, temperature, or ionic strength of the reaction medium. When 2 microM prothrombin was activated by the complete prothrombinase complex (factor Xa, factor Va, Ca2+, and phospholipid) 80-90% of the initially formed reaction product was meizothrombin. Lowering the prothrombin concentration from 2 to 0.03 microM caused a gradual decrease in the ratio of meizothrombin/thrombin formation from 5 to 0.6. When the phosphatidylserine content of the phospholipid vesicles was varied between 20 and 1 mol % and prothrombin activation was analyzed at 2 microM prothrombin the relative amount of meizothrombin formed decreased from 85 to 55%. With platelets, cephalin, or thromboplastin as procoagulant lipid, thrombin was the major reaction product and only 30-40% of the activation product was meizothrombin. We also analyzed complete time courses of prothrombin activation both with purified proteins and in plasma. In reaction systems with purified proteins substantial amounts of meizothrombin accumulated under a wide variety of experimental conditions. However, little or no meizothrombin was detected in plasma in which coagulation was initiated via the extrinsic pathway with thromboplastin or via the intrinsic pathway with kaolin plus phospholipid (cephalin, platelets, or phosphatidylserine-containing vesicles). Thus, thrombin was the only active prothrombin activation product that accumulated during ex vivo coagulation experiments in plasma.

Fast steady-state technique for harmonic analysis

The authors describe an alternative method for harmonic analysis in electric networks. The steady state solution is found in the time domain using an interactive Newton algorithm, and a Fourier analysis is applied on the magnitudes of interest. The search for the steady state solution is as follows: first, one or several cycles are simulated in the time domain beginning from arbitrary initial conditions; then, the periodicity condition is checked. If it is not satisfied, the Newton algorithm is applied, and new initial conditions are found, from which a new period of integration begins. After several iterations, steady state initial conditions should be found and steady state waveforms obtained. Finally, a Fourier analysis is carried out and the harmonic spectra of the variables of interest calculated. This method has been implemented in the program FASST.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The stability of the plasma-sheath with secondary emission

The potential and charge particle distributions are calculated for a collisionless sheath bounding a plasma adjacent to a wall which emits secondary electrons under both floating and current-carrying conditions. The corresponding conditions at the sheath-plasma boundary are determined in terms of the parameters secondary electron beam density/plasma density and beam velocity/plasma electron thermal speed. This 'steady state initial condition' is then examined for instability to excitation of the beam-plasma instability using particle-in-cell computer simulations. Results are given and summarized in the appropriate parameter space showing when the instability can be classified as weak, strong, or violent. The work is related to other work on the beam-plasma instability-theoretical, computational and experimental- and on large amplitude electron plasma waves.

A new method for the analysis and design of the class E power amplifier taking into account the&amp;lt;tex&amp;gt;Q_L&amp;lt;/tex&amp;gt;factor

Most previous papers on class E power amplifier are based on an analysis method proposed by Raab in which it is assumed that the Q_L factor of the series-tuned circuit is high enough that the output current is essentially a sinusoid at the carrier frequency. In this paper, a new method for the analysis and design of a class E amplifier is presented and implemented for the case of the series-tuned, shunt-capacitor class E configuration, in which the assumption of infinite Q_L is eliminated. The amplifier performance equations are obtained by finding the steady-state initial conditions of the load-network state variables. The design requirements are then imposed on the resulting equations. This leads to a nonlinear system of design equations which is solved for the design values using numerical optimization methods. For values of Q_L less than 15, the differences between the design values obtained using this method and those given by Raab become gradually more significant. The performance curves given in this paper show clearly that the overall amplifier performance is strongly affected by Q_L . Therefore, this method of analysis and design is useful because it provides accurate design values which ensure optimum and safe performance for the class E amplifier even in cases of low Q_L , it provides quantitative criteria for the usual tradeoffs concerning Q_L , and it makes the amplifier performance more predictable.

Modeling of Unsteady‐Flow Water Temperatures

A mathematical model is presented to simulate water temperatures of one‐dimensional unsteady flows in a river‐lake system having time‐varying lateral inflows and several cross‐sectional changes along its length. In the hydraulic part initial steady state conditions are computed by numerically integrating the gradually‐varied flow equation using the fourth‐order Runge‐Kutta method and the unsteady flow conditions by integrating the one‐dimensional Saint Venant equations using an implicit finite difference method. An upwind implicit finite difference scheme is used to solve the partial differential equation governing the water temperature of unsteady flows. Comparison of the computed water temperatures with those measured on the Columbia and Kootenay Rivers show good agreement.

The Calculation of the Void Fraction by Slip Ratio Correlations: A General Method

A useful simplification in the analysis of the motion of boiling coolant in a channel is slip hypothesis. Unfortunately, many complex empirical slip ratio correlations make the solution of two-phase flow problems quite difficult. A suitable fitting for all these correlations is proposed in this work, thus reducing the problem to one of elementary quadratures. A short analysis is performed about the steady-state initial condition concept, and a more correct definition of it in time-dependent initial value problems is suggested.

Modeling of Solid Rotor Turbogenerators Part II: Example of Model Derivation and Use in Digital Simulation

This paper uses the techniques discussed in Part I to derive a variety of direct-and quadrature-axis models of a small laboratory generator. The predictions of these models in computer simulations are compared to measured performance. Based upon these results, the models and modeling techniques are evaluated and discussed. The need for further study of saturation effects is highlighted by the inability of the models to predict initial steady state conditions and the consequent effects upon the results of transient simulations.

The Pt—O + H 2 reaction from initial steady-state potentiostatic conditions

H 2 reactivity with steady-state formed Pt—O is far slower and more complex than H 2 reactivity with transient formed Pt—O ad. Under steady state, dermasorbed oxygen, adsorbed sulphate ions, and the uncertainty in the types and total quantities of associated oxygen make the relationship between the concentration of oxygen and time, or potential, too complex for direct kinetic evaluation. The early, diffusion-independent, open-circuit potential decay from steady state, however, can be described using a model of two capacitive discharges. One process is a double-layer capacitance discharge plus complex adsorption/desorption effects, while the second is the chemical removal of Pt—O by reaction with H 2.

Digital simulation of nonlinear electromagnetic circuits

Magnetic devices are well known for their inherent ruggedness, economy, and reliability. However, design of nonlinear electromagnetic circuits is difficult and, if done improperly, prevents the realization of the full benefits of magnetic devices. This paper describes a digital simulation technique which enables accurate performance prediction of circuits containing saturable magnetic devices and nonlinear electronic devices such as diodes, transistors, 4-layer diodes, silicon-controlled rectifiers, field-effect transistors, tunnel diodes, etc. More specifically, a computer program is described which was developed for a large scientific digital computer such as the IBM 7094 or equivalent. This computer program is user oriented ; it only requires topological input data describing the interconnections of the various circuit elements; and, in turn, produces graphical output plots similar to visual representations obtained in a laboratory from an oscilloscope. The heart of the computer program is the built-in transient solution procedure. From the input data describing the circuit topology the computer program writes its own internal equations, solves for steady-state initial conditions using an iterative Newton-Raphson technique and solves for the transient or time-history response using a combination time step integration and Newton-Raphson technique. The paper describes the digital simulation technique in further detail. It presents some of the mathematical models stored in the program, and illustrates the use of the technique by means of a practical circuit problem, namely the magnetic pulse-width modulator.

Design of a versatile liquid-fluorineliquid- hydrogen upper stage

obtained have been checked against known solutions and a limited number of photoelastic and experimental test models. In all instances adequate correlation was achieved. In the particular case of environmental conditioning propellant grains, maximum stresses and strains invariably occur at the initial or final steady-state condition. This does not eliminate these systems from consideration, however, because not all loadings are maintained until steady-state temperatures are achieved as in the first example problem. Although the failure criteria used in this analysis do not include timeor path-dependent characteristics, some propellants possibly may exhibit such properties. If such phenomena are anticipated, a critical condition could exist at an intermediate temperature, and a transient analysis would be required. This study has been oriented specifically toward propellantgrain problems, but no such limitation is inherent in the techniques described. The computer program can be applied without modification to other axisymmetric components such as nozzles, nose cones, and turbine rotors. Loads other than thermal stresses can also be analyzed because the formulation includes surface pressure, shears, and body forces generated by either axial or rotational accelerations. Experimental data for these problems are not very extensive, however, and the analysis must be used with caution until adequate substantiating data become available.