Viscous Transonic Flow Research Articles

[formula omitted]-adaptive discontinuous Galerkin solution of transonic viscous flows with variable time step-size

The discontinuous Galerkin methods demonstrated to be well suited for scale resolving simulations of complex configurations, characterized by different fluid dynamics phenomena, such as transition, separation, shock/boundary layer interaction. Unfortunately, solvers based on these methods cannot yet reach the computational efficiency of well-established standard solvers, e.g., based on finite volume methods. To reduce the computational cost and the memory footprint, while not spoiling the accuracy, different approaches were investigated, which act on the spatial or the temporal discretization, and on the linear algebra. The above approaches have been extensively investigated, but rarely considering their mutual interactions. In this work, a p-adaptation algorithm is coupled with a time step-size adaptation algorithm to mitigate robustness issues arising after each adaptation cycle, probably related to the projection of the old solution on the new polynomial orders distribution. Moreover, this strategy is able to control the transient phase before each adaptation cycle, and can handle also the presence of initial steady solution, when the mesh is too coarse and the polynomial degree has not yet compensated for the lack of spatial accuracy. The effectiveness and accuracy of the proposed algorithm are demonstrated on transonic viscous flows with shock-wave/boundary-layer interaction.

Recycling Krylov subspaces for efficient partitioned solution of aerostructural adjoint systems

Robust and efficient solvers for coupled-adjoint linear systems are crucial to successful aerostructural optimization. Monolithic and partitioned strategies can be applied. The monolithic approach is expected to offer better robustness and efficiency for strong fluid-structure interactions. However, it requires a higher implementation cost and convergence may depend on appropriate scaling and initialization strategies. On the other hand, the modularity of the partitioned method enables a straightforward implementation while its convergence may require relaxation. In addition, a partitioned solver often leads to a higher number of iterations to get the same level of convergence as the monolithic one.The objective of this paper is to accelerate the fluid-structure coupled-adjoint partitioned solver by considering techniques borrowed from approximate invariant subspace recycling strategies adapted to sequences of linear systems with varying right-hand sides. Indeed, in a partitioned framework, the structural source term attached to the fluid block of equations affects the right-hand side with the nice property of quickly converging to a constant value. For the fluid block of equations, we also consider deflation of approximate eigenvectors in conjunction with advanced inner-outer Krylov solvers.To demonstrate the effectiveness of our proposed recycling strategy, we compute the coupled derivatives for two emblematic problems in transonic viscous flow. The first one is an aeroelastic configuration of the ONERA-M6 fixed wing. For this exercise, the fluid grid was coupled to a structural model specifically designed to exhibit a high flexibility. The second one is a wing-body aeroelastic configuration of the Common Research Model. All computations are performed using a fully linearized one-equation Spalart-Allmaras turbulence model. Numerical simulations show up to 39% reduction in matrix-vector products for GCRO-DR and up to 25% for the nested FGCRO-DR solver.

Stability analysis of a uniform viscous transonic flow past a rotating circular cylinder

This work analyzes the transonic flow around a rotating circular cylinder. The combination of a uniform freestream flow and the flow due to the rotation of the cylinder (assuming clockwise rotation) generates a lift force (Robins-Magnus effect) that, for transonic flows, is conditioned by the presence of a shock wave on the upper side of the cylinder.Previous studies have focused primarily on incompressible flows, compressible flows at low Mach numbers, and hypersonic flows with detached shock waves. These works have barely considered the effect of the presence of the shock wave, its interaction with the wake of the cylinder and its impact in the aerodynamic coefficients.Two-dimensional numerical simulations have been carried out using the SU2 code. From these simulations, the value of the aerodynamic coefficients as a function of time and a set of snapshots of the fluid field have been obtained and analyzed using the POD and DMD techniques. This has allowed the identification of the dominant modes that characterize the time variations in the lift and drag coefficients acting on the circular cylinder for different values of the characteristic parameters of the problem.

Efficient Global Aerodynamic Shape Optimization of a Full Aircraft Configuration Considering Trimming

Most existing aerodynamic shape optimization (ASO) studies do not take the balanced pitching moment into account and thus the optimized configuration has to be trimmed to ensure zero pitching moment, which causes additional drag and reduces the benefit of ASO remarkably. This article proposes an efficient global ASO method that directly enforces a zero pitching moment constraint. A free-form deformation (FFD) parameterization combing Laplacian smoothing method is implemented to parameterize a full aircraft configuration and ensure sufficiently smooth aerodynamic shapes. Reynolds-averaged Navier–Stokes (RANS) equations are solved to simulate transonic viscous flows. A surrogate-based multi-round optimization strategy is used to drive ASO towards the global optimum. To verify the effectiveness of the proposed method, we adopt two design optimization strategies for the NASA Common Research Model (CRM) wing–body–tail configuration. The first strategy is to optimize the configuration without considering balance of pitching moment, and then manually trim the optimized configuration by deflecting the horizontal tail. The second one is to directly enforce the zero pitching moment constraint in the optimization model and take the deflection angle of the horizontal tail as an additional design variable. Results show that: (1) for the first strategy, about 4-count drag-reducing benefits would be lost when manually trimming the optimal configuration; (2) the second strategy can achieve 3.2-count more drag-reducing benefits than the first strategy; (3) compared with gradient-based optimization (GBO), surrogate-based optimization (SBO) is more efficient than GBO for ASO problems with around 80 design variables, and the benefit of ASO achieved by SBO is comparable to that obtained by GBO.

Oscillation quenching and physical explanation on freeplay-based aeroelastic airfoil in transonic viscous flow

Limit Cycle Oscillation (LCO) quenching of a supercritical airfoil (NLR 7301) considering freeplay is investigated in transonic viscous flow. Computational Fluid Dynamics (CFD) based on Navier-Stokes equations is implemented to calculate transonic aerodynamic forces. A loosely coupled scheme with steady CFD and an efficient graphic method are developed to obtain the aerodynamic preload. LCO quenching phenomenon is observed from the nonlinear dynamic aeroelastic response obtained by using time marching approach. As the airspeed increases, LCO appears then quenches, forming the first LCO branch. Following the quenching region, LCO occurs again and sustains until the divergence of the response, forming the second LCO branch. The quenching of LCOs was addressed physically based on the aerodynamic preload and the linear flutter characteristic. An “island” of stable region is observed in the flutter boundary, i.e. the flutter speed versus the mean Angle of Attack (AoA). The LCO quenches when the aerodynamic preload crosses this stable region with the increasing of airspeed. The LCO quenching of this model in transonic flow is essentially induced by destabilizing effect from aerodynamic preload, since the flutter speed is sensitive to AoA due to aerodynamic nonlinearity.

An efficient geometric constraint handling method for surrogate-based aerodynamic shape optimization

Handling a large number of geometric constraints brings a big challenge to the surrogate-based aerodynamic shape optimization (ASO) driven by computational fluid dynamics (CFD). It is not feasible to calculate the geometric constraint functions directly during the sub-optimization of a surrogate-based optimization, as the geometric constraint functions are to be evaluated thousands of times for each updating cycle and the total cost of a number of cycles can be prohibitive. This article proposes an efficient method of handling geometric constraints within the framework of a surrogate-based optimization to address this problem. The core idea is to use the Kreisselmeier-Steinhauser (KS) method to aggregate all geometric constraints into one that can be approximated by a cheap surrogate model, in order to avoid the large computational cost associated with tremendous calculation of geometric constraint values. The proposed method is verified by an analytical test case. Then, the proposed method is demonstrated and compared with the methods of building surrogate models of all geometric constraints and calculating all geometric constraints directly during each sub-optimization by drag minimizations of NACA0012 air foil and ONERA M6 wing in transonic flows. To investigate the ability of the proposed method for handling various geometric constraints, drag minimization of CRM wing in viscous transonic flow driven by CFD is performed. Results show that the proposed method can dramatically improve the optimization efficiency of ASO with the number of geometric constraints ranging from 15 to 1429 and the number of types of geometric constraints up to 3, which offers great potential for handling a larger number and more types of geometric constraints.

A face-based immersed boundary method for compressible flows using a uniform interpolation stencil

In this study, an immersed boundary method developed for compressible viscous flows (Ramakrishnan, R., Girdhar, A., & Ghosh, S. (2016). Immersed Boundary Methods for Compressible Laminar Flows) is modified to improve their stability and robustness. The embedded object is represented as a set of line segments in two dimensions with their outward unit normal vectors specified. A forcing method that leverages the finite volume approach is used, wherein the solution at the cell interfaces that lie near the boundaries of the embedded solid is reconstructed to implicitly satisfy boundary conditions at the immersed surface. The proposed immersed boundary method is validated for transonic inviscid flow past a bump in a channel, supersonic flow past a circular cylinder, transonic viscous flow past a NACA0012 airfoil, and supersonic viscous flow past a circular cylinder. The results are compared with simulations from the literature using contours of flow properties, surface pressure, or Mach number plots and show good agreement.

Influence of Fluid Viscosity and Compressibility on Nonlinearities in Generalized Aerodynamic Forces for T-Tail Flutter

The numerical assessment of T-tail flutter requires a nonlinear description of the structural deformations when the unsteady aerodynamic forces comprise terms from lifting surface roll motion. For linear flutter, a linear deformation description of the vertical tail plane (VTP) out-of-plane bending results in a spurious stiffening proportional to the steady lift forces, which is corrected by incorporating second-order deformation terms in the equations of motion. While the effect of these nonlinear deformation components on the stiffness of the VTP out-of-plane bending mode shape is known from the literature, their impact on the aerodynamic coupling terms involved in T-tail flutter has not been studied so far, especially regarding amplitude-dependent characteristics. This term affects numerical results targeting common flutter analysis, as well as the study of amplitude-dependent dynamic aeroelastic stability phenomena, e.g., Limit Cycle Oscillations (LCOs). As LCOs might occur below the linear flutter boundary, fundamental knowledge about the structural and aerodynamic nonlinearities occurring in the dynamical system is essential. This paper gives an insight into the aerodynamic nonlinearities for representative structural deformations usually encountered in T-tail flutter mechanisms using a CFD approach in the time domain. It further outlines the impact of geometrically nonlinear deformations on the aerodynamic nonlinearities. For this, the horizontal tail plane (HTP) is considered in isolated form to exclude aerodynamic interference effects from the studies and subjected to rigid body roll and yaw motion as an approximation to the structural mode shapes. The complexity of the aerodynamics is increased successively from subsonic inviscid flow to transonic viscous flow. At a subsonic Mach number, a distinct aerodynamic nonlinearity in stiffness and damping in the aerodynamic coupling term HTP roll on yaw is shown. Geometric nonlinearities result in an almost entire cancellation of the stiffness nonlinearity and an increase in damping nonlinearity. The viscous forces result in a stiffness offset with respect to the inviscid results, but do not alter the observed nonlinearities, as well as the impact of geometric nonlinearities. At a transonic Mach number, the aerodynamic stiffness nonlinearity is amplified further and the damping nonlinearity is reduced considerably. Here, the geometrically nonlinear motion description reduces the aerodynamic stiffness nonlinearity as well, but does not cancel it.

A Modified Fifth-Order WENO-HLLC Riemann Solver for Transonic Viscous Flows around Helicopter Rotor in Hover

This paper presents a modified fifth-order WENO-HLLC Riemann solver for the transonic compressible viscous flows around the helicopter rotor in hover. The HLLC approximate Riemann solver is proposed to discrete the convection term involving grid velocity of the Navier-Stokes equations. In order to solve the interface flow accurately, a modified fifth-order WENO scheme is presented by designing the smoothness indicators based on L 1 norm measurement. The improved WENO scheme can provide the optimal approximation order even at critical points. Numerical accuracy and robustness are validated by several benchmark inviscid flow problems. Then the numerical properties of the WENO-HLLC solver in conjunction with the implicit LU-SGS time integration method with high efficiency are further validated by simulating transonic viscous flows over RAE2822 airfoil and ONERA-M6 wing. The results show that the accuracy of calculating shock, discontinuity, and the vortex is significantly improved. Finally, the method is developed to compute the transonic vortex flow around the helicopter rotor with a domain discretized by overset grids. The results indicate that the proposed method is very robust and effective in acquiring high resolution for vortex wake.

Adjoint-based aerodynamic drag minimisation with trim penalty

AbstractThe aerodynamic performance of conventional aircraft configurations are mainly affected by the wing and horizontal tail. Drag reduction by shape optimisation of the wing, while taking into account the aircraft trimmed constraint, has more benefit than focusing solely on the wing. So in order to evaluate this approach, the following study presents results of a single and multipoint aerodynamic shape optimisation of the wing-body-tail configuration, defined by the Aerodynamic Design Discussion Group (ADODG). Most of the aerodynamic shape optimisation problems published in the last years are focused mainly on the wing as the main driver for performance improvement, with no trim constraint and/or excess drag obtained from the fuselage, fins or other parts. This work partially fills this gap by an investigation of RANS-based aerodynamic optimisation for transonic trimmed flight. Mesh warping and geometry parametrisation is accomplished by fitting the multi-block structured grid to a B-spline volumes and performing the mesh movement by using surface control points embedded within the free-form deformation (FFD) volumes. A gradient-based optimisation algorithm is used with an adjoint method in order to compute the derivatives of the objective and constraint functions with respect to the design variables. In this work the aerodynamic shape optimisation of the CRM wing-body-tail configuration is investigated, including a trim constraint that is satisfied by rotating the horizontal tail. The shape optimisation is driven by 432 design variables that envelope the wing surface, and 120 shape variables for the tail, as well as the angle of attack and tail rotation angles. The constraints are the lift coefficient, wing’s thickness controlled by 1,000 control points, and the wing’s volume. For the untrimmed configuration the drag coefficient is reduced by 5.76%. Optimising the wing with a trim condition by tail rotation results in shock-free design with a considerably improved drag, even better than the untrimmed-optimised case. The second optimisation problem studied is a single and multi-point lift constraint drag minimisation of a gliding configuration wing in transonic viscous flow. The shock is eliminated, reducing the drag of the untrimmed configuration by more than 60%, using 192 design variables. Further robustness is achieved through a multi-point optimisation with more than 45% drag reduction.

On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization—Part II: Viscous Flows

This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization) to viscous transonic flows. In this work, we showed that the same procedure to derive an explicit expression for an exact step length βexact in a gradient-based optimization method for inviscid transonic flows can be employed for viscous transonic flows. The extended numerical method was evaluated for the viscous flows over the transonic RAE 2822 airfoil at two common flow conditions in the transonic regime. To do so, the RAE 2822 airfoil was reconstructed by a Bezier curve of degree 16. The numerical solution of the transonic turbulent flow over the airfoil was performed using the solver ANSYS Fluent (using the Spalart–Allmaras turbulence model). Using the proposed step length, a gradient-based optimization method was employed to minimize the drag-to-lift ratio of the airfoil. The gradient of the objective function with respect to design variables was calculated by the finite-difference method. Efficiency and accuracy of the proposed method were investigated through two test cases.

Single- and Multipoint Aerodynamic Shape Optimization Using Multifidelity Models and Manifold Mapping

In this paper, a computationally efficient multifidelity local search algorithm for aerodynamic design optimization is presented. In this paper’s approach, direct optimization of a computationally expensive model is replaced by an iterative updating and reoptimization of a fast multifidelity model constructed using a low-fidelity model adapted locally using manifold mapping (MM) to become a reliable representation of the high-fidelity one during the optimization process. Only one high-fidelity model evaluation is needed per design iteration, and no gradient information is used. The proposed method is validated and characterized by applying it to a few single- and multipoint optimization problems involving inviscid and viscous transonic flows. The proposed method is compared with the sequential least-squares programming (SLSQP) gradient-based approach with the gradients calculated based on adjoint sensitivities. In the inviscid single-point test case, a drag reduction of 410.8 counts was achieved by the MM algorithm while requiring approximately 1469 min on a high performance computing (HPC) with 32 processors. SLSQP with adjoints achieved a drag reduction of 425.9 counts, while requiring approximately 1536 min under the same HPC setup. For the viscous single-point test case, a 83.2 drag count reduction was reported for the MM compared to 83.4 for SLSQP with adjoints. In that case, the MM algorithm was around eight times faster in terms of computing time. In the multipoint design test case, the MM algorithm was computationally cheaper by at least an order of magnitude compared to SLSQP with adjoints, although the objective function value was around three drag counts higher. Furthermore, it was found that in the multipoint cases the MM algorithm scales favorably with the number of operational conditions considered compared to SLSQP with adjoints.

Development of a New Algorithm for Modeling Viscous Transonic Flow on Unstructured Grids at High Reynolds Numbers

Abstract This study investigates a new algorithm for modeling viscous transonic flow at high Reynolds number cases suitable for unstructured grids. The challenge of modeling viscous transonic flow around airfoils becomes intense at high Reynolds number cases due to a variety of flow regimes encountered, such as boundary layer growth and the shockwave/turbulent boundary-layer interaction, accompanied by large separation bubble. Therefore, it is highly demanded to develop robust and efficient models that can capture the shock-induced problems of turbulent flows for aircraft design purposes. The new model is essentially a hybrid algorithm to address the conflict between turbulence modeling and shock-capturing requirements. A skew-symmetric form of a collocated finite volume scheme with minimum aliasing errors was implemented to model the turbulent region in the combination of a semidiscrete, central difference scheme to capture discontinuities with adequately low numerical dissipation for the minimal effect on turbulent flows. To evaluate the effectiveness of the model, it was tested in three conventional cases. The computational results are close to measured data for predicting the shock locations. This implies that the model is able to predict the scale of the separation bubble and the main characteristics of turbulent transonic flow adequately.

Box Wing and Induced Drag: Compressibility Effects in Subsonic and Transonic Regimes

Prandtl introduced the best wing system or Box Wing a century ago and showed its exceptional lift-induced drag performance with respect to wing systems having the same wingspan and lift (Prandtl, L., “Induced Drag of Multiplanes,” NACA TN-182, 1924.). In this work, and for the first time, their superior induced drag properties are verified in compressible and transonic regimes. The aerodynamic forces are obtained by analyzing computational fluid dynamics data, and the drag is subdivided in induced, viscous, and wave contributions. This decomposition is provided by a recently introduced aerodynamic force breakdown technique based on the vortex-force theory and allows an unambiguous definition of the lift-induced drag. The methodology is applicable to incompressible, compressible, and transonic flows. This paper will address whether the Best Wing system provides interesting induced drag performance also in transonic viscous flow.

A high-order accurate unstructured spectral difference lattice Boltzmann method for computing inviscid and viscous compressible flows

In the present work, the spectral difference lattice Boltzmann method (SDLBM) is implemented on unstructured meshes for the solution methodology to be capable of accurately simulating the compressible flows over complex geometries. Both the inviscid and viscous compressible flows are computed by applying the unstructured SDLBM. The compressible form of the discrete Boltzmann–BGK equation with the Watari model is considered and the solution of the resulting system of equations is obtained by applying the spectral difference method on arbitrary quadrilateral meshes. The accuracy and robustness of the unstructured SDLBM for simulating the compressible flows are demonstrated by simulating four problems that are steady inviscid supersonic flow past a bump, steady inviscid subsonic flow over the two-element NACA 4412-4415 airfoil with and without the ground effect, steady viscous transonic flow around the NACA 0012 airfoil and unsteady viscous subsonic flow past two side-by-side cylinders. The results obtained by applying the unstructured SDLBM are in good agreement with those of the available high-order accurate Euler/Navier-Stokes solvers and also the experimental data. The present study introduces the unstructured SDLBM as an appropriate inviscid and viscous compressible LBM flow solver for accurately simulating fluid flows over practical problems.

Solid wall and open boundary conditions in hybrid recursive regularized lattice Boltzmann method for compressible flows

Complex geometries and open boundaries have been intensively studied in the nearly incompressible lattice Boltzmann method (LBM) framework. Therefore, only few boundary conditions for the high speed fully compressible LBM have been proposed. This paper deals with the definition of efficient boundary conditions for the compressible LBM methods, with the emphasis put on the newly proposed hybrid recursive regularized D3Q19 LBM (HRR-LBM) with applications to compressible aerodynamics. The straightforward simple extrapolation-based far-field boundary conditions, the characteristic boundary conditions, and the absorbing sponge layer approach are extended and estimated in the HRR-LBM for the choice of open boundaries. Moreover, a cut-cell type approach to handle the immersed solid is proposed to model both slip and no-slip wall boundary conditions with either isothermal or adiabatic behavior. The proposed implementations are assessed considering the simulation of (i) isentropic vortex convection with subsonic to supersonic inflow and outflow conditions, (ii) two-dimensional (2D) compressible mixing layer, (iii) steady inviscid transonic flow over a National Advisory Committee for Aeronautics (NACA) 0012 airfoil, (iv) unsteady viscous transonic flow over a NACA 0012 airfoil, and (v) three-dimensional (3D) transonic flows over a German Aerospace Center (DLR) F6 full aircraft configuration.

Simulation of transonic low-Reynolds jets using quasi-gas dynamics equations

In this paper application of the OpenFOAM solver QGDFoam for numerical simulation of transonic viscous flows is considered. The developed solver, which implements regularized or quasi- gas dynamics (QGD) algorithms, is validated using the transonic low-Re jet flow case (Ma=0.9, Re=3600). The conducted numerical simulations allow the assessing applicability of the solver for modelling hydrodynamic instabilities and their interaction with transonic flow. Results of the numerical simulations are compared with experimental observations and Navier-Stokes-based code simulation. Results of the present study formulate a guideline for choosing (values of) QGD-algorithm tuning parameters.

Unsteady Forces in LP Last Stage 380 MW Steam Turbine Rotating and Non-vibrating Rotor Blades with Exhaust Hood

Cracks were found in the roots of the last stage rotor blades. Tip-timing measurements showed high vibration amplitudes in certain working conditions. The aim of this paper is to analyse unsteady forces acting in such working conditions on the last stage of rotor blades, taking into account unsteady flow in the exhaust hood. Using ANSYS CFX, this paper examines unsteady forces in a low pressure steam turbine last stage with an exhaust hood. A sliding mesh model was used for interaction between the stator-rotor blades and the rotor blade- exhaust hood. The study included a 3D transonic viscous flow. The CFD mesh included all the last stage stator, rotor blades. The rotor blades vibrated but do not rotate. Numerical static pressure and temperature values in selected exhaust hood crosssections were compared with experimental ones. Unsteady rotor blade forces and moments were analysed along the lengths of the blades. This study has shown that interaction with the exhaust hood causes the non-symmetrical pressure and temperature along and behind the rotor blades. The low frequency unsteady harmonic is higher towards the tip of the blade. The greatest low component of unsteady forces was 50 Hz, which is far below the natural frequency and therefore irrelevant to rotor blade vibration. The second harmonic, 100 Hz, is much more dangerous, because is relatively close the natural frequency of the blade.

Benchmark aerodynamic shape optimization with the POD-based CST airfoil parametric method

This paper conducts a benchmark aerodynamic shape optimization with the developed POD-based CST airfoil parametric method. The POD analysis transforms the basis functions of the CST parametric method into reduced orthogonal POD basis functions which are used to describe the geometric variation of the aerodynamic shape. A benchmark aerodynamic shape optimization for drag minimization of RAE2822 airfoil in transonic viscous flow provided by AIAA aerodynamic design optimization discussion group is used to verify the optimization effect of the developed parametric method. The optimized results indicate that developed parametric method can maintain almost the same ability to cover potential airfoils with much fewer parameters as the original high-dimensional CST method does, which can overcome the contradiction of high-dimensionality of design parameters and increase of optimization difficulty well. Moreover, the benchmark optimized results verify the optimization effect of the developed method by comparing with benchmark results optimized by other international counterparts in the field of aerodynamic shape optimization.

Global optimization of benchmark aerodynamic cases using physics-based surrogate models

The paper proposes the combination of physics-based surrogate models, adaptive sampling of the design space and evolutionary optimization towards the solution of aerodynamic design problems. The Proper Orthogonal Decomposition is used to extract the main features of the flow field and Radial Basis Function networks allow the surrogate model to predict the target response over the entire design space. In order to train accurate and usable surrogates, ad hoc in-fill criteria are provided which smartly rank and select new samples to enrich the model database. The solution of two aerodynamic benchmark problems is proposed within the framework of the AIAA Aerodynamic Design Optimization Discussion Group. The two benchmark problems consist respectively in the drag minimization of the RAE 2822 airfoil in transonic viscous flow and of the NACA 0012 airfoil in transonic inviscid flow. The shape parameterization approach is based on the Class-Shape Transformation (CST) method with a sufficient degree of Bernstein polynomials to cover a wide range of shapes. Mesh convergence is demonstrated on single-block C-grid structured meshes. The in-house ZEN flow solver is used for Euler/RANS aerodynamic solution. Results show that, thanks to the combined usage of surrogate models and adaptive training in an evolutionary optimization framework, optimal candidates may be located even with limited computational resources with respect to plain evolutionary approaches and similar standard methodologies.