Oktay Baysal

Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics

A new and efficient method is presented for aerodynamic design optimization, which is based on a computational fluid dynamics (CFD)-sensitivity analysis algorithm. The method is applied to design a simplified scramjet-afterbody configuration for an optimized axial thrust. The Euler equations are solved for the inviscid analysis of the flow, which provides the objective function and the constraints of the optimization problem. The CFD analysis is then coupled with the optimization procedure that used a constrained minimization method. The sensitivity coefficients, i.e., gradients of the objective function and the constraints, needed for the optimization are obtained using a quasi-analytic al method rather than the traditional finite difference approximations. During the one-dimensional search of the optimization procedure, an approximate flow analysis (predicted flow) based on a first-order Taylor series expansion is used to reduce the computational cost. Finally, the sensitivity of the optimum objective function to various flowfield problem parameters, such as the Mach number, which are kept constant during the optimization, is computed to predict new optimum solutions. The flow analysis of the demonstrative example are compared with the experimental data. It is shown that the method is more efficient than the traditional methods.

Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis

An aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three-dimensional geometries. The function of sensitivity analysis is to directly couple computational fluid dynamics (CFD) with numerical optimization techniques, which facilitates the construction of efficient direct-design methods. The development of a practical three-dimensional design procedures entails many challenges, such as: (1) the demand for significant efficiency improvements over current design methods; (2) a general and flexible three-dimensional surface representation; and (3) the efficient solution of very large systems of linear algebraic equations. It is demonstrated that each of these challenges is overcome by: (1) employing fully implicit (Newton) methods for the CFD analyses; (2) adopting a Bezier-Bernstein polynomial parameterization of two- and three-dimensional surfaces; and (3) using preconditioned conjugate gradient-like linear system solvers. Whereas each of these extensions independently yields an improvement in computational efficiency, the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficient design strategies in current use. The new aerodynamic shape optimization procedure is demonstrated in the design of both two- and three-dimensional inviscid aerodynamic problems including a two-dimensional supersonic internal/external nozzle, two-dimensional transonic airfoils (resulting in supercritical shapes), three-dimensional transport wings, and three-dimensional supersonic delta wings. Each design application results in realistic and useful optimized shapes.

Aerodynamic Sensitivity Analysis Methods for the Compressible Euler Equations

This study presents a mathematical formulation developed for aerodynamic sensitivity coefficients based on a discretized form of the compressible 2D Euler equations. A brief motivating introduction to the aerodynamic sensitivity analysis and the reasons behind an integrated flow/sensitivity analysis for design algorithms are presented. The finite difference approach and the quasi-analytical approach are used to determine the aerodynamic sensitivity coefficients. A new flow prediction concept, which is an outcome of the direct method in the quasi-analytical approach, is developed and illustrated with an example. Surface pressure coefficient distributions of a nozzle-afterbody configuration obtained from the predicted flowfield solution are compared successfully with their corresponding values obtained from a flowfield analysis code and the experimental data.

Airfoil Shape Optimization Using Sensitivity Analysis on Viscous Flow Equations

An aerodynamic shape optimization method has previously been developed by the authors using the Euler equations and has been applied to supersonic-hypersonic nozzle designs. This method has also included a flowfield extrapolation (or flow prediction) method based on the Taylor series expansion of an existing CFD solution. The present paper reports on the extension of this method to the thin-layer Navier-Stokes equations in order to account for the viscous effects. Also, to test the method under highly nonlinear conditions, it has been applied to the transonic flows. Initially, the success of the flow prediction method is tested. Then, the overall method is demonstrated by optimizing the shapes of two supercritical transonic airfoils at zero angle of attack. The first one is shape optimized to achieve a minimum drag while obtaining a lift above a specified value. Whereas, the second one is shape optimized for a maximum lift while attaining a drag below a specified value. The results of these two cases indicate that the present method can produce successfully optimized aerodynamic shapes.

Navier-Stokes Computations of Cavity Aeroacoustics with Suppression Devices

Effectiveness of two devices to suppress the cavity acoustics was computationally investigated. Two dimensional, computational simulations were performed for the transonic, turbulent flows past a cavity, which was first equipped with a rear face ramp and then with a spoiler. The Reynolds-averaged, unsteady, compressible, full Navier-Stokes equations were solved time accurately by a second-order accurate, implicit, upwind, finite-volume method. The effect of turbulence was included through the Baldwin-Lomax model with modifications for the multiple-wall effects and for the highly vortical flow with a shear layer. The results included instantaneous and time-averaged flow properties, and time-series analyses of the pressure inside the cavity, which compared favorably with the available experimental data. These results were also contrasted with the computed aeroacoustics of the same cavity (length-to-depth ratio of 4.5), but without a device, to demonstrate the suppression effectiveness.

Aerodynamic shape optimization using preconditioned conjugate gradient methods

In an effort to further improve upon the latest advancements made in aerodynamic shape optimization procedures, a systematic study is performed to examine several current solution methodologies as applied to various aspects of the optimization procedure. It is demonstrated that preconditioned conjugate gradient-like methodologies dramatically decrease the computational efforts required for such procedures. The design problem investigated is the shape optimization of the upper and lower surfaces of an initially symmetric (NACA 0012) airfoil in inviscid transonic flow and at zero degrees angle of attack. The complete surface shape is represented using a Bezier-Bernstein polynomial

Computational and experimental investigation of cavity flowfields

This paper presents a computational and experimental investigation of supersonic flow past a cavity in a flat plate. The source of the particular interest in this problem is the ongoing study of the aerodynamic interference effects between a separating store and its bay in the parent body. An upwind relaxation scheme, utilizing flux vector splitting and line-Gauss-Seidel iterations, is used to solve Reynolds-averaged Navier-Stokes equations. Spatial discretizations of this two-dimensional analysis are based on implicit and finite-volume methods. Turbulence is modeled and shocks are captured. The flowfield of the symmetry plane at the half-width is computationally visualized and all flow properties are computed. Experimental tests are conducted in the Langley Unitary Plan Wind Tunnel to measure wall pressures and to capture schlieren photographs. Qualitative as well as quantitative data of computations and experiments agree very well. These two vehicles of investigation are merged to show open, closed and transitional cavity flow behaviors.

Improving the Efficiency of Aerodynamic Shape Optimization

The computational efficiency of an aerodynamic shape optimization procedure that is based on discrete sensitivity analysis is increased through the implementation of two improvements. The first improvement involves replacing a grid-point-based approach for surface representation with a Bezier-Bernstein polynomial parameterization of the surface. Explicit analytical expressions for the grid sensitivity terms are developed for both approaches. The second improvement proposes the use of Newtons method in lieu of an alternating direction implicit methodology to calculate the highly converged flow solutions that are required to compute the sensitivity coefficients

A low-voltage nano-porous electroosmotic pump

A low-voltage electroosmotic (EO) micropump based on an anodic aluminum oxide (AAO) nano-porous membrane with platinum electrodes coated on both sides has been designed, fabricated, tested, and analyzed. The maximum flow rate of 0.074 ml min(-1) V(-1) cm(-2) for a membrane with porosity of 0.65 was obtained. A theoretical model, considering the head loss along the entire EO micropump system and the finite electrical double layer (EDL) effect on the flow rate, is developed for the first time to analyze the performance of the EO micropump. The theoretical and experimental results are in good agreement. It is revealed that the major head loss could remarkably decrease the flow rate, which thus should be taken into account for the applications of the EO micropump in various Lab-on-a-chip (LOC) devices. However, the effect of the minor head loss on the flow rate is negligible. The resulting flow rate increases with increasing porosity of the porous membrane and kappaa, the ratio of the radius of the nanopore to the Debye length.

Diffusiophoretic motion of a charged spherical particle in a nanopore.

The diffusiophoretic motion of a charged spherical particle in a nanopore, subjected to an axial electrolyte concentration gradient, is investigated using a continuum theory, which consists of the ionic mass conservation equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equations for the hydrodynamic field. With the concentration gradient imposed, the particle motion is induced by two different mechanisms: an electrophoresis generated by the induced electric field arising from the difference of ionic diffusivities and the double layer polarization (DLP) and a chemiphoresis by the resulting osmotic pressure gradient induced by the solute gradient in the electrical double layer around the particle. The particle diffusiophoretic velocity along the axis of the nanopore is computed as functions of the ratio of the particle size to the thickness of the electrical double layer, the ratio of the nanopore size to the particle size, the particle surface charge density, and the properties of the salt solution. The diffusiophoretic behavior of a particle comparable to the nanopore size is governed predominantly by the induced electrophoresis generated by the DLP-induced electric field, caused by the imposed concentration gradient and the double layer compression due to the presence of the impervious nanopore wall.