Extended Radial Basis Functions for Metamodeling: A Comparative Study

Economic competitiveness is driving industry to new frontiers of engineering design. Robustness and reliability based design, multidisciplinary simulation based design, increased complexity and sophistication of our design, and optimization aided design are four such areas, which are seriously challenging our ability to keep pace with the need to adequately model the systems we seek to design – in spite of the exponential growth of computing power. An emerging consensus within the community is that the effective development of computationally benign models (metamodels) will help us navigate the challenging road ahead. The process of constructing metamodels for computationally expensive models, such as finite element, aerodynamic, and heat transfer models, is representative of the tasks we must address. Among the available metamodeling techniques, Radial Basis Functions (RBFs) have recently generated much interest for their effectiveness and versatility. Radial basis functions offer numerous advantages over traditional the Response Surface Methodology (RSM), including their ability to effectively generate multidimensional interpolative approximations. This paper, however, shows how the typical RBF approach lacks the critical flexibility required to handle the wide variety of complex models arising from the use of advanced techniques, such as uncertainty handling and multiobjective optimization, often encountered in modern design. Further, in this paper, we propose a powerful new approach – the Extended Radial Basis Function (E-RBF) approach – that provides the designer with significant flexibility and freedom in the metamodeling process, compared to conventional RBFs. Examples are provided that demonstrate the effectiveness of the new approach, and explore its potential superiority over traditional RBF and response surface methodologies. Initial investigation indicates that the E-RBF possesses unique and novel properties not available in any other single method.

An integrated computational fluid dynamics (CFD) and computational structural dynamics (CSD) method is developed here for the calculation and analysis of wing flutter in the time domain. The CFD solver is based on an unsteady multi-grid finite-volume algorithm for the Euler/Navier—Stokes equations on a multi-block structured grid. The CSD solver adopts a linear multi-step method to integrate the aeroelastic governing equations expressed in the modal space. A grid deformation method employing a radial basis function approach is introduced here to generate a dynamically moving grid. The solving procedure of an aeroelastic system is implemented with a predictor—corrector scheme in the physical time. By extrapolating the aerodynamic force, the hybrid predictor—corrector scheme is introduced to save the flow calculation right before the correcting step. The coupled CFD—CSD method is used to simulate wing flutter problems in the time domain in order to predict the stability of an aeroelastic system, which, in this paper, is fulfilled by finding the flutter boundaries. The calculation of the Isogai wing finds an S-shaped flutter boundary, which has been predicted by other studies. The obtained flutter boundary of the AGARD 445.6 wing shows a distinct transonic dip, which agrees well with the experiment result. Computational efficiency and accuracy using two predictor—corrector algorithms and a strong coupling algorithm are also compared.

CFD (Computational Fluids Dynamics) simulations of HRSGs (Heat Recovery Steam Generators) can improve and optimize the performance of combined cycle power plants. For example CFD results can help to analyze the effect that different working conditions such as changes in power or fuel quality can have on the uniformity of the flow. A uniform flow is important because the tubes inside the HRSG are more susceptible to corrosion and rupture when the flow distribution is strongly nonuniform. An accurate modeling of the flow and heat transfer characteristics is paramount in order to obtain a realistic representation of the process. However, a big problem in CFD modeling of HRSGs, or any equipment with tube-and-shell heat exchangers, is the different length scales of the equipment, which vary from a few centimeters for the tubes diameter to tens of meters for the HRSG vertical height. The problem is that these different length scales would require a very large computational mesh and consequently a very expensive simulation. To overcome this problem, a common approach in CFD simulations of HRSG has been to model the tube banks following a porous media approach, where the tubes are represented by a volume with a porosity factor which gives the volume fraction of fluid within the porous region. Using this model a pressure drop and the total heat absorbed due to the presence of the solid tubes is calculated. However, due to the recent advances and relatively lower prices of computer equipment it is now possible in a relatively economical way to explicitly include the tube banks in the CFD models of HRSGs. In this study a CFD model of a HRSG is presented where the tube banks are included in the geometric model. Results using this model show the fluid flow and heat transfer between the numerous tubes. A further advantage, in contrast to the porous media model, is that the flow inside the tubes is also modeled which gives a more realistic representation of the phenomena inside the tubes.

Performance analysis and design optimization of a novel Trombe wall system using CFD and response surface method

In this article, we describe a hybrid optimizer based on a highly accurate response surface method, which uses several radial basis functions and polynomials as interpolants. The response surface is capable to interpolate linear as well as highly non-linear functions in multi-dimensional spaces having up to 500 dimensions. The accuracy, robustness, efficiency, transparency and conceptual simplicity are discussed. Based on the extensive testing performed on 296 test functions, the radial basis functions (RBFs) approach seems computationally easy to implement and results are superior, requiring small computing time. The performance of the RBF approximation is compared with wavelets neural networks for several selected test cases and the optimizer is compared with other hybrid optimizers, as well as with the IOSO commercial code.

Numerical study on the physical and chemical processes in n-decane spray ignition

Core-mounted target-type thrust reverser (CMTTTR) design was proposed by NASA in the second half of the 90 s. NASA carried out several experiments at static conditions, and their acquired results suggested that the performance characteristics of the CMTTTR design fall short to comply with the mandatory thrust reverser (TR) performance criteria, and were therefore regarded as an infeasible design. However, the authors of this paper believe that the results presented by NASA for the CMTTTR design require further exploration to facilitate the complete understanding of its true performance potential. This part 2 paper is a continuation from Part 1 (reverser stowed configuration) and presents a comprehensive three-dimensional (3D) computational fluid dynamics (CFD) analyses of the CMTTTR in deployed configuration. The acquired results are extensively analyzed for aforementioned TR configuration operating under the static operating conditions at sea level, i.e., sea-level static, International Standard Atmosphere (ISA); the analyses at forward flight conditions will be covered in part 3. The key objectives of this paper are: First, to validate the acquired CFD results with the experimental data provided by NASA; this is achieved by measuring the static pressure values on various surfaces of the deployed CMTTTR model. The second objective is to estimate the performance characteristics of the CMTTTR design and corroborate the results with experimental data. The third objective is to estimate the pressure thrust (i.e., axial thrust generated due to the pressure difference across various reverser surfaces) and discuss its significance for formulating the performance of any TR design. The fourth objective is to investigate the influence of kicker plate installation on overall TR performance. The fifth and final objective is to examine and discuss the overall flow physics associated with the thrust reverse under deployed configuration.

Coupling dynamics and chemistry in the air pollution modelling of street canyons: A review

Wind profile prediction at different scales plays a crucial role for efficient operation of wind turbines and wind power prediction. This problem can be approached in two different ways: one is based on statistical signal processing techniques and both linear and nonlinear models can be employed either separately or combined together for profile prediction; on the other hand, wind/atmospheric flow analysis is a classical problem in computational fluid dynamics (CFD) in applied mathematics, which employs various numerical methods and algorithms, although it is an extremely time-consuming process with high computational complexity. In this work, a new method is proposed based on synergy's between the signal processing approach and the CFD approach, by alternating the operations of a quaternion-valued least mean square (QLMS) algorithm and the large eddy simulation (LES) in CFD. As demonstrated by simulation results, the proposed method has a much lower computational complexity while maintaining a comparable prediction result.

Computational fluid dynamics for chemical reactor engineering

Through a systematic optimization study using high-fidelity finite-element (FE) models, torque capability of three common synchronous machine technologies, namely a permanent magnet (PM) synchronous machine (PMSM) with V-shaped rare-earth (RE) rotor magnets, a PMSM with deep V-shaped ferrite rotor magnets, and a synchronous reluctance machine (SynRM) with four layers of conforming flux barriers are compared for an application in a 48-V mild hybrid electric car. The optimization of the deep V-shaped ferrite PMSM automatically resulted in a spoke-type PM layout for maximum torque production. Yet, an optimized SynRM with conforming flux barriers was achieved that could produce a higher torque than ferrite PMSM. One machine technology is selected and is subsequently subjected to a large-scale FE model-based drive-cycle design optimization. Various pole-slot combinations are methodically compared in terms of drive-cycle losses, active material cost, torque ripple, and PM demagnetization level. More than 20,000 designs were analyzed over ten energy-centric torque-speed points to identify an optimal design solution. The results of multi-physics analysis incorporating electromagnetics, computational fluid dynamics (CFD), and structural analyses are provided, including a study on two different water jacket concepts. A final design is prototyped and initial experimental results are provided.

Computational fluid dynamics (CFD) simulation of a single stage, dry-feed entrained flow gasifier is carried out to predict several physical and chemical processes within the gasifier. The model is developed using a commercial software package FLUENT. The CFD model is based on an Eulerian-Lagrangian framework, where the continuous fluid phase is modeled in Eulerian approach and the particle flow trajectory is simulated in Lagrangian frame. The two phases are coupled by appropriate source terms in the conservation equations. The gasification process can be divided into the following sub-processes, which are inert heating, moisture release, coal devolatilization, char gasification and gas phase reactions. Discrete Phase Model (DPM) is used to model the coal particles and coupled with heterogeneous particle surface reactions in Species Transport module. The interaction between reaction chemistry and turbulence is described by Finite-rate/Eddy dissipation model. The simulation provides detailed information of temperature field and species concentration profile inside the gasifier. The temperature distribution clearly indicates the three different reaction zones for devolatilization, gasification and reduction. Steady state model predictions are compared with benchmark experimental data from literature. The trend of the predicted species mole fraction distribution is in good agreement within error bound of the experiment. The model thus provides a validated set of model parameters along with an insight to the underlying flow physics and chemical reactions of gasification process that can be employed to improve design of experiments. This study also develops the basis to achieve further accuracy incorporating complex effects such as detailed reaction kinetic mechanisms, proper devolatilization models, effect of ash-slag transition and particle deposition.

Tabulated chemical kinetics for efficient and detailed simulations of diesel engine combustion

Breast imaging via microwave tomography involves estimating the distribution of dielectric properties within the patient's breast on a discrete mesh. The number of unknowns in the discrete mesh can be very large for 3-D imaging, and this results in computational challenges. We propose a new approach where the discrete mesh is replaced with a relatively small number of smooth basis functions. The dimension of the tomography problem is reduced by estimating the coefficients of the basis functions instead of the dielectric properties at each element in the discrete mesh. The basis functions are constructed using knowledge of the location of the breast surface. The number of functions used in the basis can be varied to balance resolution and computational complexity. The reduced dimension of the inverse problem enables application of a computationally efficient, multiple-frequency inverse scattering algorithm in 3-D. The efficacy of the proposed approach is verified using two 3-D anatomically realistic numerical breast phantoms. It is shown for the case of single-frequency microwave tomography that the imaging accuracy is comparable to that obtained when the original discrete mesh is used, despite the reduction of the dimension of the inverse problem. Results are also shown for a multiple-frequency algorithm where it is computationally challenging to use the original discrete mesh.

A novel interactive preferential evolutionary method for controller tuning in chemical processes