George S. Dulikravich

Three-Dimensional Aerodynamic Shape Optimization Using Genetic and Gradient Search Algorithms

This study introduces various gradient search methods as well as hybrid genetic techniques that achieve impressive convergence rates on constrained problems. These methods are applied to 3D shape optimization of ogive-shaped, star-shaped, and spiked projectiles and lifting bodies in a hypersonic flow. Flow-field analyses are performed using Newtonian flow theory and in certain cases verified using a parabolized Navier-Stokes (PNS) flow analysis algorithm. Three-dimensional geometrical rendering is achieved using a variety of techniques including beta-splines from the computer graphics industry. (Author)

Inverse and Optimization Problems in Heat Transfer

This paper presents basic concepts of inverse and optimization problems. Deterministic and stochastic minimization techniques in finite and infinite dimensional spaces are revised; advantages and disadvantages of each of them are discussed and a hybrid technique is introduced. Applications of the techniques discussed for inverse and optimization problems in heat transfer are presented. Keywords : Inverse problems, optimization, heat transfer

Inverse Determination of Steady Heat Convection Coefficient Distributions

An inverse Boundary Element Method (BEM) procedure has been used to determine unknown heat transfer coefficients on surfaces of arbitrarily shaped solids. The procedure is noniterative and cost effective, involving only a simple modification to any existing steady-state heat conduction BEM algorithm. Its main advantage is that this method does not require any knowledge of, or solution to, the fluid flow field. Thermal boundary conditions can be prescribed on only part of the boundary of the solid object, while the heat transfer coefficients on boundaries exposed to a moving fluid can be partially or entirely unknown. Over-specified boundary conditions or internal temperature measurements on other, more accessible boundaries are required in order to compensate for the unknown conditions. An ill-conditioned matrix results from the inverse BEM formulation, which must be properly inverted to obtain the solution to the ill-posed problem. Accuracy of numerical results has been demonstrated for several steady two-dimensional heat conduction problems including sensitivity of the algorithm to errors in the measurement data of surface temperatures and heat fluxes.

Aerodynamic shape design and optimization - Status and trends

A limited number of aerodynamic shape design concepts have been surveyed and an attempt has been made to classify them. Characteristics, both positive and negative, of the more prominent methods were outlined. Future research is expected to concentrate on the use of Navier-Stokes equations and applications to threedimensional configurations. Interdisciplinary constrained optimization is expected to play a more prominent role in the immediate future. Adjoint operator/control theory and its variations are the most promising concepts for interdisciplinary aerodynamic shape design which involves a large number of variables. This theory is expected to constitute the major development area in future research.

Inverse determination of boundary conditions and sources in steady heat conduction with heat generation

A Boundary Element Method (BEM) implementation for the solution of inverse or ill-posed two-dimensional Poisson problems of steady heat conduction with heat sources and sinks is proposed. The procedure is noniterative and cost effective, involving only a simple modification to any existing BEM algorithm. Thermal boundary conditions can be prescribed on only part of the boundary of the solid object while the heat sources can be partially or entirely unknown. Overspecified boundary conditions or internal temperature measurements are required in order to compensate for the unknown conditions. The weighted residual statement, inherent in the BEM formulation, replaces the more common iterative least-squares (L2) approach, which is typically used in this type of ill-posed problem. An ill-conditioned matrix results from the BEM formulation, which must be properly inverted to obtain the solution to the ill-posed steady heat conduction problem. A singular value decomposition (SVD) matrix solver was found to be more effective than Tikhonov regularization for inverting the matrix. Accurate results have been obtained for several steady two-dimensional heat conduction problems with arbitrary distributions of heat sources where the analytic solutions were available.

Chemical Composition Design of Superalloys for Maximum Stress, Temperature, and Time-to-Rupture Using Self-Adapting Response Surface Optimization

ABSTRACT We have adapted an advanced semistochastic evolutionary algorithm for constrained multiobjective optimization and combined it with experimental testing and verification to determine optimum concentrations of alloying elements in heat-resistant austenitic stainless steel alloys and superalloys that will simultaneously maximize a number of the alloys mechanical properties. The optimization algorithm allows for a finite number of ingredients in the alloy to be optimized so that a finite number of physical properties of the alloy are either minimized or maximized, while satisfying a finite number of equality and inequality constraints. Alternatively, an inverse design method was developed, which uses the same optimization algorithm to determine chemical compositions of alloys that will be able to sustain a specified level of stress at a given temperature for a specified length of time. The main benefits of the self-adapting response surface optimization algorithm are its outstanding reliability in avoiding local minimums, its computational speed, ability to work with realistic nonsmooth variations of experimentally obtained data and for accurate interpolation of such data, and a significantly reduced number of required experimentally evaluated alloy samples compared with more traditional gradient-based and genetic optimization algorithms. Experimentally preparing samples of the optimized alloys and testing them have verified the superior performance of alloy compositions determined by this multiobjective optimization.

An inverse method for finding unknown surface tractions and deformations in elastostatics

We have developed a non-iterative algorithm for determining unknown deformations and tractions on surfaces of arbitrarily shaped solids where these quantities cannot be measured or evaluated. For this inverse boundary value technique to work, both deformations and tractions must be available and applied simultaneously on at least a part of the objects surface called an over-specified boundary. Our method is non-iterative only because it utilizes the boundary element method (BEM) to calculate deformations and tractions on surfaces where they are unavailable and simultaneously computes the stress and deformation field within the entire object. Inversely computed displacement and stress fields within simple solids and on their boundaries were in excellent agreement with the BEM analysis results and analytic solutions. Our algorithm is highly flexible in treating complex geometries and mixed elastostatics boundary conditions. The accuracy and reliability of this technique deteriorates when the known surface conditions are only slightly over-specified and far from the inaccessible surfaces.

Magnetic field suppression of melt flow in crystal growth

The p-version least-squares finite element method was used for prediction of solidification from a melt under the influence of an externally applied magnetic field. The computational results indicate significantly different flow-field patterns and thermal fields in the melt and the accrued solid in the cases of full gravity, reduced gravity, and an applied uniform magnetic field.

Finite-Element Simulation of Cooling of Realistic 3-D Human Head and Neck

Rapid cooling of the brain in the first minutes following the onset of cerebral ischemia is a potentially attractive preservation method. This computer modeling study was undertaken to examine brain-cooling profiles in response to various external cooling methods and protocols, in order to guide the development of cooling devices suitable for deployment on emergency medical vehicles. The criterion of successful cooling is taken to be the attainment of a 33 degrees C average brain temperature within 30 min of treatment. The transient cooling of an anatomically correct realistic 3-D head and neck with realistically varying local tissue properties was numerically simulated using the finite-element method (FEM). The simulations performed in this study consider ice packs applied to head and neck as well as using a head-cooling helmet. However, it was found that neither of these cooling approaches satisfies the 33 degrees C temperature within 30 min. This central conclusion of insubstantial cooling is supported by the modest enhancements reported in experimental investigations of externally applied cooling. The key problem is overcoming the protective effect of warm blood perfusion, which reaches the brain via the uncooled carotid arterial supply and effectively blocks the external cooling wave from advancing to the core of the brain. The results show that substantial cooling could be achieved in conjunction with neck cooling if the blood speed in the carotid artery is reduced from normal by a factor of 10. The results suggest that additional cooling means should be explored, such as cooling of other pertinent parts of the human anatomy.

Numerical simulation of laser induced plasma during pulsed laser deposition

A numerical study of the laser induced evaporation and ionization process during pulsed laser deposition is presented. The process is separated into three domains: (i) conduction inside the solid, (ii) a discontinuity layer between solid and vapor, and (iii) expansion of high temperature vapor/plasma. A quasi-one-dimensional model is solved to predict the temperature field inside the solid. Mass, momentum, and energy are conserved across the discontinuity layer. Equations of mass, momentum, and energy conservation are solved simultaneously to provide boundary conditions for the expansion process. Euler equations are used to model the expansion of high temperature vapor/plasma. The Euler equations are integrated numerically using a Runge–Kutta scheme combined with flux vector splitting. The density, pressure, temperature, and velocity contours of the vapor phase are calculated and the results are analyzed.