Begell House Inc.
Hybrid Methods in Engineering
HME
1099-2391
2
1
2000
A TURBULENCE MODEL FOR COMPUTING THE FLOW OF POWER-LAW FLUIDS WITHIN CIRCULAR TUBES
13
D. O. A.
Cruz
Mechanical Engineering Department, Federal University of Rio de Janeiro, Av. Moniz de Aragao 420, 21945-972 Rio de Janeiro, Brazil
C. E.
Maneschy
Mechanical Engineering Department, Universidade Federal do Para—UFPA, Campus Universitdrio do Guamd, Belem, Parti, Brasil
Emanuel N.
Macedo
Mechanical Engineering Department, Chemical Engineering Department, Universidade Federal do Para-UFPA, Campus Universitario do Guama, RuaAugusto Correa, 01, 66075-900 -Belem, PA, Brazil
Joao N. N.
Quaresma
School of Chemical Engineering, Universidade Federal do Para, FEQ/UFPA, Campus Universitario do Guama, 66075-110, Belem, PA, Brazil
The purpose of this work is to analyze the problem of the turbulence modeling of non-Newtonian fluids. First, the Kolmogorov characteristic parameters for the case of power-law fluids is obtained. The characteristic dissipation length is showed to be a function of the power-law index (n) and reduces to the Newtonian case when n = l. In addition, an algebraic turbulence model is proposed, in which an extension of the Van Driest damping function for power-law fluids is developed. A numerical solution to the hydrodynamically developed turbulent equation of motion flow in circular tubes is obtained. Comparisons with experimental data and with those from an empirical correlation for turbulent flow of non-Newtonian power-law fluids are made, showing good agreement.
SCALAR TRANSPORT IN HETEROGENEOUS MEDIA: A SIMPLIFIED GREEN ELEMENT APPROACH
15
Okey Oseloka
Onyejekwe
Department of Civil Engineering, University of Durban, Westvill, Durban, South Africa
Modeling techniques that apply only to homogeneous systems are often too restricted to accurately describe real-life problems. For adequate and more realistic treatment, media heterogeneity should be taken into account by relaxing the general theory describing mass flow and transport in a conducting medium. In this study we use the Green element method (GEM) to study the influence of heterogeneity on scalar transport. GEM is a hybrid finite-element, boundary-element solution procedure that implements the singular boundary integral theory efficiently. Not only is the resulting coefficient matrix banded and easier to handle numerically, but heterogeneity, which poses computational problems for the classical boundary element method (BEM), is handled straightforwardly and with relative ease. The GEM computational procedure described herein, achieves the integral representation of the governing partial differential equation by the application of Green's second identity, and the resulting integral equation is represented on each element of the problem domain. To complete the methodology, the integral equations are then solved by a typical finite-element procedure to give the dependent variables of interest. All the results obtained in this study, when tested against those in the literature, were found to be close and in agreement with physics.
ASYMPTOTIC SOLUTIONS FOR THE FREE CONVECTION BOUNDARY-LAYER FLOW ALONG A VERTICAL SURFACE IN A POROUS MEDIUM WITH NEWTONIAN HEATING
10
Ioan
Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
Daniel
Lesnic
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Derek B.
Ingham
Centre for CFD, Department of Applied Mathematical Studies, The University of Leeds, Leeds, LS2 9JT, UK; Energy-2050, Faculty of Engineering, University of Sheffield, Sheffield, S10 2TN, UK
In this article the steady, free-convection boundary-layer flow along a vertical surface embedded in a porous medium with Newtonian heating is investigated. The mathematical problem reduces to a pair of coupled partial differential equations for the temperature and the streamfunction, and asymptotic solutions are obtained for small and large values of the coordinate along the plate, x. Furthermore, a simple expression for the temperature on the plate which matches the small and large solutions is derived.
NUMERICAL AND ANALYTICAL MODELS FOR THE ANALYSIS OF AGITATION STATES AND RESONANCE PROBLEMS IN HARBORS
20
M. A. Vaz
dos Santos
Departamento de Materials e Construcao, Fundacao Universidade Federal do Rio Grande, Rio Grande, Brasil
D. C.
Cuchiara
Fundacao Universidade Federal do Rio Grande, Rio Grande, Brasil
Armando M.
Awruch
Graduate Program in Civil Engineering (PPGEC),
Federal University of Rio Grande do Sul (UFRGS)
99 Osvaldo Aranha Ave. 3rd floor, 90035-190, Porto Alegre, RS, Brazil
The formulation and computational implementation of a mathematical model to analyze agitation states and resonance problems in harbors using the finite element method are presented in this work. This study intends to aid and to guide in choosing suitable technical and economical solutions for problems related to the action of waves on anchored and moored ships, to designing sailing channels, and to maneuvering ships in ports. The finite-element model was applied to harbors of regular form and compared with analytical solutions or experimental results.
ROBUST ADAPTIVE CONTROL OF SISO DYNAMIC HYBRID SYSTEMS
37
M.
de la Sen
Departamento de Electricidad y Electrónica, Facultad de Ciencias, Universidad del Pais Vasco, Leioa (Bizkaia), Bilbao, Spain
This article deals with the problem of synthesizing a robust adaptive controller for a class of single-input, single-output (SISO), time-invariant hybrid plant that can operate under bounded disturbances and/or unmodeled dynamics. The hybrid plant dealt with is composed of two coupled subsystems, one being of continuous-time type while the other is digital. The estimation algorithm is of a continuous-time nature, because the plant parameter estimates are updated for all times. The adaptive scheme is pole-placement-based and of indirect type, because the controller parameters are reupdated at all times based on the calculated plant parameter estimates. An input-output model is first derived which involves filtered signals for the hybrid plant from an initial state-space description. Such a model is simultaneously driven by the standard continuous-time input plus an extra signal. The extra input is composed for all times of a signal that involves the contribution of the input and output over a finite number of previous sampling instants plus a signal which involves the contribution of the weighted integral of the continuous-time input on a set of preceding sampling intervals. The last driving signal is due to the existing couplings between the continuous-time and digital substates of the hybrid plant. A relative adaptation dead zone is used in the parameter estimation scheme whose role is robust adaptive stabilization in the presence of uncertainties. The hybrid nature of the system becomes apparent, because the plant is simultaneously driven by the continuous time input plus its samples at sampling instants. As a result, its input-output differential equation has forcing terms generated by the system description at sampling instants.
MATHEMATICAL AND PHYSICAL ASPECTS IN CONSTRUCTING NUMERICAL SCHEMES FOR SOLVING THE ADVECTION EQUATION
11
The article addresses stability limits and accuracy of methods of advancing the solution of a system of ordinary differential equations (ODEs) in time by the Runge-Kutta (RK) and Taylor series (TS) methods. This system of ODEs arises as a result of discretizing the advection equation (a partial differential equation, PDE) spatially. Symbolic manipulation is used in the stability analysis. The Von Neumann linear stability method is illustrated with the aid of symbolic programming. The program is general and can be extended easily to analyze the stability of higher-order advection and advection-diffusion schemes. It is found that the RK and TS methods produce identical results as far as accuracy and stability limit are concerned. The TS method requires less memory storage than the RK method. Also, an explicit scheme based on the physics of the problem is constructed. The scheme is unconditionally stable and accurate for all values of Courant parameter.
A NUMERICAL STUDY OF TWO-DIMENSIONAL SOLUTE TRANSPORT IN A GROUNDWATER PATHWAY VIA THE INTEGRAL TRANSFORM METHOD
20
Marco A.
Leal
Laboratório de Transmissão e Tecnologia do Calor - LTTC, Mechanical Engineering Dept. - Universidade Federal do Rio de Janeiro, EE/COPPE/UFRJ, Cidade Universitária - Cx. Postal 68503 - Rio de Janeiro - RJ - 21945.970 - Brazil
Nerbe J.
Ruperti, Jr.
Brazilian Nuclear Energy Commission, Waste Management Department, COREJ/CNEN, Rua General Severiano 90-22294-900 Botafogo, Rio de Janeiro RJ, Brazil
A hybrid solution is developed for a two-dimensional screening transport model in a homogeneous aquifer with a steady uniform groundwater flow. The source is assumed to be located at the top of the aquifer, and a constant-flux boundary condition is investigated. The generalized integral transform technique (GITT) is utilized to provide the proposed hybrid numerical-analytical solution. Two numerical procedures are presented in order to reach fast and accurate results. The results obtained in the present work are compared against previously reported exact solutions.