Development of Analysis Program for Incompressible Looped Flow Network Using Constitutive Topologic Matrix Equation

Abstract

Flow network which consists of a number of flow paths and their junctions is popularly used in analysis of flow and pressure distribution for complicated pipe or channel flow structure. In order to analyze flow network, it is required to resolve mass conservation equation at each junction and energy conservation equation on all independent closed loops of the flow network. Topologic matrix which reflects characteristics of network connectivity simply transforms continuity equations into linear algebraic equations. However, typical solving procedure based on topologic matrix and linear analysis includes complicated algorithm to retrieve basic closed loop for energy conservation equations. It must confront the problem of nondeterministic polynomial completion. To resolve the problem of typical flow network analysis, the theory of constitutive topologic matrix equation is known to be effective. This paper describes a program algorithm of flow network analysis based on constitutive topological matrix theory and shows user interface of the program. Additionally, comparing analysis results of developed program with commercial software is provided to prove accuracy and reliability of developed program.

Optimization Based on Product and Desirability Functions for Flow Distribution in Multi-Channel Cooling Systems of Power Inverters in Electric Vehicles

“…The constraint condition for the objective functions in Equations (10) and (11) is the constant total flow rate, which can be expressed as follows:…”

“…Thus, Equations (10) and (11) are functions that represent the characteristics of the cooling system. Furthermore, a multi-response objective function can be constructed by combining Equations (10) and (11) along with each response.…”

“…Thus, Equations (10) and (11) are functions that represent the characteristics of the cooling system. Furthermore, a multi-response objective function can be constructed by combining Equations (10) and (11) along with each response. The optimization algorithm for the multi-response object function can be defined by applying the response surface methodology using the desirability function, i.e., for the multi-response objective function, based on the direct response (R i ) in Equations (10) and (11), optimization can be achieved using the following desirability objective function [23,26]:…”

“…The analytical model was constructed in accordance with the experiment sequence, and CFD analysis was performed using the commercial software ANSYS Fluent 8.0. Based on the simulation results, the response values of the response (R i ) and system characteristic equations, i.e., Equations (10) and (11), were calculated; these are listed in Table 4.…”

“…Brkić and Praks proposed the hardy cross method for calculating channel network flow distribution [8,9]. Also, Kim, Yoo, and Cho analyzed incompressible looped flow networks using constitutive topologic matrix equations [10]. Furthermore, water distribution networks were analyzed by Niazkar and Afzali using MATLAB and Excel spreadsheets [11,12].…”