Computations of high‐speed compressible flows with adaptive cell‐centered finite element method

Abstract

An upwind cell‐centered finite element formulation is combined with an adaptive meshing technique to solve Navier‐Stokes equations for high‐speed inviscid and viscous compressible flows. The finite element formulation and the computational procedure are described. An adaptive meshing technique is applied to increase the analysis solution accuracy, as well as to minimize the computational time and the computer memory requirement. The efficiency of the combined method is evaluated by the examples of Mach 2.6 inviscid flow in a channel with compression and expansion ramps, Mach 6.47 inviscid and viscous flows past a cylinder, and Mach 4 viscous flow over a flat plate.     

The Design and Implementation of a Self-Healing Database System

In this paper, we present the design and implementation of ITDB, a self-healing or intrusion-tolerant database prototype system. While traditional secure database systems rely on preventive controls and are very limited in surviving malicious attacks, ITDB can detect intrusions, isolate attacks, contain, assess, and repair the damage caused by intrusions in a timely manner such that sustained, self-stabilized levels of data integrity and availability can be provided to applications in the face of attacks. ITDB is implemented on top of a COTS DBMS. We have evaluated the cost-effectiveness of ITDB using several micro-benchmarks. Preliminary testing measurements suggest that when the accuracy of intrusion detection is satisfactory, ITDB can effectively locate and repair the damage on-the-fly with reasonable (database) performance penalty.     

Properties of Extract from Okara by Its Subcritical Water Treatment

Okara was treated with subcritical water at temperatures ranging from 170 to 260°C for various times. After clarification, the extracts were analyzed for their protein and carbohydrate contents, DPPH radical scavenging activity, and antioxidative activity. The carbohydrate content significantly decreased with the increasing treatment temperature and time. The protein content, however, increased with the increasing treatment temperature and slightly decreased with a heating time longer than 10 min. The extract obtained from the subcritical water treatment at 240°C for 5 min, which would be used to evaluate the antioxidative activity, provided the relatively highest radical scavenging activity and the activity tended to decrease with the prolonging heating time and temperature. The extract also exhibited a suppressive activity to the autoxidation of linoleic acid with the increasing weight ratio of the extract to linoleic acid. The results clearly showed okara still contained highly valuable substances for human consumption.     

Flux‐difference splitting scheme with modified multidimensional dissipation on unstructured meshes

Abstract

A flux‐difference splitting scheme with a modified multidimensional dissipation for high‐speed compressible flow analysis on unstructured meshes is presented. The scheme eliminates unphysical flow behaviors such as a spurious bump of the carbuncle phenomenon that occurs on the bow shock from flow over a blunt body, and the expansion shock generated from flow over a forward facing step. The switching function suggested by Quirk is implemented as a choice to detect the vicinity of strong shock. The proposed scheme is further extended to obtain higher‐order spatial and temporal solution accuracy. The scheme is, in addition, combined with an adaptive meshing technique that generates unstructured triangular meshes to resemble the flow phenomena for reducing computational effort. The entire procedure is evaluated by solving several benchmarks as well as steady‐state and transient high‐speed compressible flow problems.     

Combined finite volume and finite element method for convection-diffusion-reaction equation

A combined finite volume and finite element method is presented for solving the unsteady scalar convection-diffusion-reaction equation in two dimensions. The finite volume method is used to discretize the convection-diffusion-reaction equation. The higher-order reconstruction of unknown quantities at the cell faces is determined by Taylor’s series expansion. To arrive at an explicit scheme, the temporal derivative term is estimated by employing the idea of local expansion of unknown along the characteristics. The concept of the finite element technique is applied to determine the gradient quantities at the cell faces. Robustness and accuracy of the method are evaluated by using available analytical and numerical solutions of the two-dimensional pure-convection, convection-diffusion and convection-diffusion-reaction problems. Numerical test cases have shown that the method does not require any artificial diffusion to improve the solution stability. This paper was recommended for publication in revised form by Associate Editor Dongshin Shin Pramote Dechaumphai received his B.S. degree in Industrial Engineering from Khon-Kaen University, Thailand, in 1974, M.S. degree in Mechanical Engineering from Youngstown State University, USA in 1977, and Ph.D. in Mechanical Engineering from Old Dominion University, USA in 1982. He is currently a Professor of Mechanical Engineering at Chulalongkorn University, Bangkok, Thailand. His research interests are numerical methods, finite element method for thermal stress and computational fluid dynamics analysis. Sutthisak Phongthanapanich received his B.S. degree in Mechanical Engineering from Chiangmai University, Thailand in 1990. He then received his M.S., and Ph.D. degrees in Mechanical Engineering from Chulalongkorn University, Thailand in 2002, and 2006, respectively. He is a Lecturer of Mechanical Engineering Technology at King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand. His research interests are finite element method, finite volume method, mesh generation and adaptation, and shock wave dynamics.     

Decomposition kinetics of monoacyl glycerol and fatty acid in subcritical water under temperature-programmed heating conditions

The decompositions of monocaprylin, monocaprin, monolaurin and their corresponding fatty acids in subcritical water were measured under temperature-programmed heating conditions where the reaction temperature was linearly increased from room temperature to 350 °C at specified rates to estimate the activation energies E_i and the frequency factors k_i0 for the decompositions. The decompositions of both monoacyl glycerol and fatty acid obeyed first-order kinetics, and the decomposition of a monoacyl glycerol proceeded consecutively to form its constituent fatty acid and then further decomposition compounds. There was a tendency for both the E_i and k_i0 values for a monoacyl glycerol or fatty acid with a longer acyl chain to be smaller, and it was shown that the enthalpy–entropy compensation held for the decompositions of monoacyl glycerols and fatty acids as well as for those of fatty acid esters with various acyl and alkyl chains in subcritical water.     

Interaction of high-speed compressible viscous flow and structure by adaptive finite element method

Interaction behaviors of high-speed compressible viscous flow and thermal-structural response of structure are presented. The compressible viscous laminar flow behavior based on the Navier-Stokes equations is predicted by using an adaptive cell-centered finite-element method. The energy equation and the quasi-static structural equations for aerodynamically heated structures are solved by applying the Galerkin finite-element method. The finite-element formulation and computational procedure are described. The performance of the combined method is evaluated by solving Mach 4 flow past a flat plate and comparing with the solution from the finite different method. To demonstrate their interaction, the highspeed flow, structural heat transfer, and deformation phenomena are studied by applying the present method to Mach 10 flow past a flat plate.     

Nodeless variables finite element method and adaptive meshing teghnique for viscous flow analysis

A nodeless variables finite element method for analysis of two-dimensional, steady-state viscous incompressible flow is presented. The finite element equations are derived from the governing Navier-Stokes differential equations and a corresponding computer program is developed. The proposed method is evaluated by solving the examples of the lubricant flow in journal bearing and the flow in the lid-driven cavity. An adaptive meshing technique is incorporated to improve the solution accuracy and, at the same time, to reduce the analysis computational time. The efficiency of the combined adaptive meshing technique and the nodeless variables finite element method is illustrated by using the example of the flow past two fences in a channel.