Method For Steady-state Solutions Research Articles

Method for increasing upper limit of heat flux measurement of slug calorimeter in high enthalpy plasma jet

The temperature of the high-power inductively coupled plasma jet is very high, and its temperature is difficult to measure directly. The heat flux becomes a thermodynamic characteristic to measure the plasma jet. The existing heat flux calculation method is based on the temperature change rate after the response time. The slug is required to stay in the high enthalpy jet area for a longer time. With the slug temperature reaching the melting point as the upper limit, the shorter the residence time, the greater the upper limit of the measured heat flux. In this paper, the first-order transient solution is added to the steady-state solution of temperature (the calculation equation of the existing method), which can shorten the response time. The shortening of the response time can reduce the residence time of the slug in the jet region, and the reduction in the residence time can increase the upper limit of the calorimeter heat flux measurement. This paper uses numerical simulation and experimental methods to verify that the steady-state solution method and the first-order transient solution method can obtain consistent heat flux results. Using the first-order transient solution method can reduce the residence time of the slug calorimeter in the jet region. According to the shortening of the residence time, the method of using the first-order transient solution can increase the upper limit of the heat flux measurement by more than 25%.

A Steady State Solution Method for HIV/AIDS Model for the Assesment, Monitoring, Control and Evaluation of Confirmed Status with Vertical Transmission in Nigeria

HIV is a deadly virus transmitted either through having of unprotected sex, mother to child transmission, sharing of unsterilized objects that is capable of making cut or wounds on the body or blood or bodily fluid transmission. AIDS has no permanent cure but remedies that help in suppressing the power effect of the virus are available. Previous studies show that the epidemic claimed more lives via vertical transmission, mother-to-child transmission, blood transfusion, and sexual intercourse, injection drug users. The associated models were derived using diagnosis and treatments records of confirmed status of HIV/AIDS clients. A new model analyses were proposed that could handle cases of HIV/AIDS routes of transmission and treatments via vertical, mother-to-child, blood transfusion, sexual intercourse, injection drug users that were not considered in previous studies. The new model was solved using Steady state. The new model is a major contribution for optimal assessment, monitoring, evaluation, control and management of HIV/AIDS.

Progress in the development of an implicit steady state solution in the coupled code TRACE/PARCS

This paper describes the implementation of an implicit steady state solution method in the TRAC/RELAP Advanced Computational Engine (TRACE) thermal-hydraulics system code and Purdue Advanced Reactor Core Simulator (PARCS) code with the goal of improving solution stability and efficiency. The implicit steady state solution method has been implemented within the framework of the existing psuedo-transient solution method in TRACE and includes time-dependent thermal-hydraulic and heat transfer equations and time-independent neutron diffusion equations. The implicit solution method uses Newton's method to solve the thermal-hydraulic, heat transfer, and neutron diffusion equations during each psuedo-time step with an analytic construction of the Jacobian matrix. The linear system associated with each iteration of Newton's method is solved using a preexisting LU decomposition algorithm in TRACE. The implicit steady state solution was evaluated using two different meshes overlaid on a two-phase pipe model closely matching a boiling water reactor hydraulic channel. The implicit solution method reproduces the correct steady state solution for varying time step sizes for each mesh. An evaluation of the CPU runtime required to complete a steady state calculation using the implicit method shows that the well-developed and optimized explicit solution method currently requires less CPU runtime than the implicit solution method which has yet to be optimized. These results direct future development of the implicit solution method towards optimization strategies to reduce CPU runtime.

Free-Surface Viscous Flow Solution Methods for Ship Hydrodynamics

The simulation of viscous free-surface water flow is a subject that has reached a certain maturity and is nowadays used in industrial applications, like the simulation of the flow around ships. While almost all methods used are based on the Navier-Stokes equations, the discretisation methods for the water surface differ widely. Many of these highly different methods are being used with success. We review three of these methods, by describing in detail their implementation in one particular code that is being used in industrial practice. The descriptions concern the principle of the method, numerical details, and the method’s strengths and limitations. For each code, examples are given of its use. Finally, the methods are compared to determine the best field of application for each. The following surface descretisation methods are reviewed. First, surface fitting/mesh deformation in PARNASSOS, developed by MARIN; the description focuses on the efficient steady-state solution method of this code. Then surface capturing with Volume-of-Fluid in ISIS-CFD, developed by CNRS/Ecole Centrale de Nantes; the main topic of this review are the compressive flux discretisation schemes for the volume fraction that are used in this code. And finally, the Level Set method in SURF, developed by NMRI; this description contains a modified formulation of the Level Set method that is optimised for ship flow computation.

Three-Dimensional Discrete Ordinates Method in Transient Radiative Transfer

A complete transient three-dimensional discrete ordinates method is formulated for the e rst time to solve transient radiative transfer in a rectangular enclosure containing nonhomogeneous media that absorb, emit, and scatter. Twofold validation of the transient method is obtained: First, there is an excellent agreement between its results at long time stage with several steady-state solution methods. Second, the transient predictions of transmittance and ree ectance compare very well with Monte Carlo simulations. The sensitivity and accuracy of the transient method against the sizes of time increment and grid cell and angular discrete order are examined. The false radiation propagation and numerical diffusion associated with the differencing schemes are discussed. Calculations show the behavior of the wave nature of propagation of transient radiation. The transient behavior of radiation is found to be ine uenced by many parameters, such as the boundary conditions, the optical thickness of the medium, the scattering albedo, and the incident radiation pulse width. Duhamel’ s superposition theorem is also applied to obtain the transient response to different temporal input pulses.

定常解析法による変圧器の振動性過電圧現象の検討

定常解析法による変圧器の振動性過電圧現象の検討

Computation of wind flows around two tall buildings

Experimental results by Taniike [1] for wind flows around two tall buildings are compared with results from a computer simulation. The simulation uses a steady-state solution method with a k-ε model of turbulence. In the measured flow, the vortices shed from each building have a strong influence on pressures on and around the other building. This research examines the accuracy of steady-state solution methods in the prediction of mean pressures in such flows.

A computational study of annular cascade flows using aq-ω turbulence model with a wall function

A computational code has been developed for steady viscous flows in three dimensional annular cascades. This code solves a special form of the thin-layer Navier-Stokes equations with a two-equationq-ω turbulence model in curvilinear coordinates using a time asymptotic method for steady state solutions. It employs a scalar implicit approximate factorization in time and a finite volume formulation with second-order upwind-differencing in space. A wall function treatment is implemented at solid boundaries for turbulence equations instead of integration to the wall to relieve gridding requirements. In order to validate the effectiveness of this code, computational studies have been made to access modeling capability for complex turbulent flow fields in three dimensional annular cascade geometries which typically include laminar-turbulent boundary layer transition. The results have been compared with both the computational studies with integration to the wall and the experimental studies. The wall function treatment was found to be reliable by predicting secondary flows and loss contours reasonably well.

An Optimal Runge–Kutta Method for Steady-State Solutions of Hyperbolic Systems

An optimal two-stage Runge–Kutta time integration scheme is derived to compute steady-state approximations to hyperbolic equations. The analysis is general in the sense that it requires only that the eigenvalues of the derivative matrix lie in the right half of the complex plane. Thus it is applicable to spatial discretizations which do not have uniformly spaced points. As examples, the method is applied to two hyperbolic problems which have been discretized in space by Chebyshev spectral collocation.