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An aerodynamic shape optimization methodology based on a discrete adjoint solver for Navier-Stokes flows is described. The flow solver at the heart of this optimization process is a Reynolds-averaged Navier-Stokes code for multiblock structured grids. It uses Osher's approximate Riemann solver and the algebraic turbulence model of Baldwin-Lomax. A...
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The main purpose for the implementation of the optimization process into aerodynamics is to get a greater lift to drag value with some restraints that are put by other divisions of the airplane design such as stability, structure, propulsion and so on. In order to satisfy those constraints that are on the table and achieve the better values for aer...
An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations...
Aerodynamic shape optimization of a swept natural-laminar-flow wing in the transonic regime is still challenging. The difficulty is associated with reliable prediction of laminar–turbulence transition and reasonable compromise of viscous and wave drags. This paper proposes to use efficient global optimization based on surrogate models to address th...
The sensitivity analysis is a crucial step in algorithms for gradient-based aerody- namic shape optimization. The analysis involves computing the gradient of function- als such as drag, lift, or aerodynamic moments, with respect to the parameters of the design. Gradients are efficiently calculated by solving adjoints of the linearized flow equation...
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... In unsteady simulations, the adjustment of the active control device can be reg as surface deformation. The mesh is updated by a distance-based dynamic mesh rithm [33]. As shown in Figure 3, the mesh near the active surface maintains a good q and the far-field cells are largely unaffected. ...
... In unsteady simulations, the adjustment of the active control device can be regarded as surface deformation. The mesh is updated by a distance-based dynamic mesh algorithm [33]. As shown in Figure 3, the mesh near the active surface maintains a good quality and the far-field cells are largely unaffected. ...
At transonic flight conditions, the buffet caused by the shockwave/boundary-layer interaction can degrade aircraft performance and even threaten their safety. In this paper, a closed-loop control using an active shock control bump (SCB) has been proposed to suppress the buffet on a supercritical airfoil flying at transonic speeds. A closed-loop control law is designed by using the lift coefficient as the feedback signal and using the bump height as the control variable. The unsteady numerical simulations show that the buffet can be effectively suppressed by an optimal combination of the parameters of the control law, namely the gain and the delay time. Furthermore, the buffet control effectiveness is still acceptably constrained by a prescribed maximum bump height, which is believed to be practically important. In addition to being able to achieve both wave drag reduction and buffet alleviation, the active SCB is less sensitive to the parameters of the control law and has a shorter response time in comparison with the reference active trailing edge flap.
... The transition prediction method is incorporated into an in-house 3-D RANS solver [34,35]. The algebraic turbulence model of Baldwin-Lomax [36] is employed for turbulent boundary layers. ...
... The detailed differentiation of the equation can be found in LeMoigne and Qin [34] for the discrete adjoint RANS solver without transition models. Following the approach proposed by Rashad and ...
... The equation system is solved using the incremental iteration method [34] ...
At a transonic condition, the design of a natural laminar flow (NLF) wing is challenging because the extension of the laminar flow needs to be finely balanced with the potential wave drag increase. To achieve this balance, it is proposed to unlock the wing sweep and introduce a three-dimensional (3-D) contour shock-control bump (SCB) in the optimization of the NLF infinite swept wing aiming at total drag reduction. A 3-D Reynolds-averaged Navier–Stokes flow solver is extended to incorporate laminar–turbulent transition prediction due to streamwise and crossflow instabilities. The flow solver is integrated in a gradient-based optimization framework. The transition criteria including streamwise and crossflow instabilities are coupled in the sensitivity calculation using a discrete-adjoint solver. Transonic design optimization of the sectional profile and wing sweep angle is first conducted at a Mach number of 0.78. The optimization managed to alleviate the shock wave, reducing the pressure drag while it failed to extend the laminar flow. Furthermore, a combined optimization of the wing with a parameterized SCB at the same condition is carried out. The optimized wing with the SCB features a long favorable pressure gradient region and a low-sweep angle, which allows for a large proportion of laminar flow without significant pressure drag. The shock wave is controlled by the 3-D bump, and the SCB has little effect on the upstream flow.
... The research activities cover several aspects of ASO. Le Moigne and Qin [77] presented a variable-fidelity ASO methodology based on a discrete adjoint solver for turbulent flows. The optimisation method was then employed for a systematic aerodynamic study of a BWB aircraft [78], including inverse design of the spanwise lift distribution [79], aerofoil and sweep optimisation [80], and deployment of shock control bumps [81]. ...
Computational fluid dynamics (CFD) has become the method of choice for aerodynamic shape optimisation of complex engineering problems. To date, however, the sensitivity of the optimal solution to numerical parameters has been largely underestimated. Meanwhile, aerodynamic shape optimisation based on high-fidelity CFD remains a computationally expensive task. The thesis consists of two research streams aimed at addressing each of the challenges identified, namely revisiting the optimal solution and developing an efficient optimisation framework. This work primarily focuses on the assessment of optimal design sensitivity and computational efficiency in gradient-based optimisation of aeronautical applications.
Two benchmark cases for NACA0012 and RAE2822 aerofoil optimisation are investigated using the open-source SU2 code. Hicks-Henne bump functions and free-form deformation are employed as geometry parameterisation methods. Gradients are computed by the continuous adjoint approach. The optimisation results of NACA0012 aerofoil exhibit strong dependence on virtually all numerical parameters investigated, whereas the optimal design of RAE2822 aerofoil is insensitive to those parameter settings. The degree of sensitivity reflects the difference in the design space, particularly of the local curvature on the optimised shape. The closure coefficients of Spalart-Allmaras model affect the final optimisation performance, raising the importance of quantifying uncertainty in turbulence modelling calibration. Non-unique flow solutions are found to exist for both cases, and hysteresis occurs in a narrow region near the design point.
Wing twist optimisations are conducted using two aerodynamic solvers of different levels of fidelity. A multi-fidelity aerodynamic approach is proposed, which contains three components: a linear vortex lattice method solver, an infinite swept wing solver, and a coupling algorithm. For reference, three-dimensional data are obtained using SU2. Two optimisation cases are considered, featuring inviscid flow around an unswept wing and viscous flow around a swept wing. A good agreement in terms of lift distribution and aerodynamic shape between the multi-fidelity solver and high-fidelity CFD is obtained. The numerical optimisation using the multi-fidelity approach is performed at a negligible computational cost compared to the full three-dimensional CFD solver, demonstrating the potential for use in early phases of aircraft design.
... The values of lift and drag coefficient for the Spalart-Allmaras, Wilcox k-ω and Menter SST turbulence models are shown in Table 3 together with numerical results from Le Moigne and Qin [29] and Nielsen and Anderson [30]. A maximum of nine lift counts deviation in the lift coefficient C L between the three turbulence models was observed. ...
... In addition, a maximum of 14 drag counts difference in the drag coefficient C D was computed, of which nine drag counts were due to the friction contribution to the drag coefficient. Furthermore, the present numerical results of lift and drag coefficients are in good agreement with numerical values by Le Moigne and Qin [29] and Nielsen and Anderson [30], who employed the Baldwin-Lomax and Spalart-Allmaras turbulence model, respectively. The pressure coefficient profiles C p at different sections across the wing span are depicted in Figure 8. ...
One of the key factors in simulating realistic wall-bounded flows at high Reynolds numbers is the selection of an appropriate turbulence model for the steady Reynolds Averaged Navier–Stokes equations (RANS) equations. In this investigation, the performance of several turbulence models was explored for the simulation of steady, compressible, turbulent flow on complex geometries (concave and convex surface curvatures) and unstructured grids. The turbulence models considered were the Spalart–Allmaras model, the Wilcox k- ω model and the Menter shear stress transport (SST) model. The FLITE3D flow solver was employed, which utilizes a stabilized finite volume method with discontinuity capturing. A numerical benchmarking of the different models was performed for classical Computational Fluid Dynamic (CFD) cases, such as supersonic flow over an isothermal flat plate, transonic flow over the RAE2822 airfoil, the ONERA M6 wing and a generic F15 aircraft configuration. Validation was performed by means of available experimental data from the literature as well as high spatial/temporal resolution Direct Numerical Simulation (DNS). For attached or mildly separated flows, the performance of all turbulence models was consistent. However, the contrary was observed in separated flows with recirculation zones. Particularly, the Menter SST model showed the best compromise between accurately describing the physics of the flow and numerical stability.
... There existing many successful geometric parameterization techniques of sectional airfoils. Among them, the following techniques are most popular: class/ shape transformation (CST) method (Kulfan and Bussoletti 2006), Hicks-Henne functions (Hicks and Henne 1978), NURBS curves (Wall et al. 2008), and Bezier or B-spline curves (Braibant and Fleury 1984;Moigne and Qin 2004). In this article, the Hicks-Henne parametrization is used to parametrize the airfoil geometry, which is illustrated in Fig. 1 with Hicks-Henne functions of ten control points. ...
In this paper, our newly proposed Nash-EGO algorithm is applied to real large-scale airfoil/wing optimizations. A finite wing is represented by mounting control airfoils parameterized with a set of design variables, which are manipulated to be increased gradually in purpose of enriching the searching space to accommodate possible more optimal solutions. The enriched design territory is technically split into small subsets to be assigned to the players of Nash-EGO. Doing this way, the performance of each efficient global optimization (EGO) player could be expected to keep at a high level due to EGO players now take care of only their own small-scale subsets instead of facing the large-scale problem directly. The algorithm is first applied to a constrained drag minimization of RAE 2822 airfoil with 14 to 54 design variables and two to eight Nash players to investigate the performance of Nash-EGO, particularly for having an understanding of the influences of the numbers of design variables and Nash players. Then, more challenging cases, sectional shape optimizations of DLR-F4 wing with up to 84 design variables, are conducted. The results show that, in comparison with the baselines, up to 47.5% drag reductions can be achieved by Nash-EGO optimizer; meanwhile, the CPU costs are greatly reduced (up to 366.8% speedup) as compared with the counterpart of the traditional EGO. The successful applications presented show the capability of Nash-EGO algorithm for solving real engineering optimizations with large scales.
... Another alternative is to combine low-and high-accuracy models in a so called multifidelity optimization loop in which most of the optimization is performed using a low-fidelity model reducing the overall computational time as presented by Le Moigne and Qin (2004). Low-fidelity data can be used as surrogate models for the solution of Partial Differential Equations (PDE)-constrained optimization problem. ...
We construct a multi-fidelity framework for statistical learning and global optimization that is capable of effectively synthesizing seakeeping predictions having two different levels of modeling fidelity, namely a strip theory and a boundary element method based on potential flow assumption. The objective of this work is to demonstrate that the multi-fidelity framework can be used efficiently to discover optimal small waterplane area twin hull shapes having superior seakeeping performance using a limited number of expensive high-fidelity simulations combined with a larger number of inexpensive low-fidelity simulations. Specifically, we employ multi-fidelity Gaussian process regression and Bayesian optimization to build probabilistic surrogate models and efficiently explore a 35-dimensional design space to optimize hull shapes that minimize wave-induced motions and accelerations, and satisfy specific requirements in terms of displacement and metacentric height. Our results demonstrate the superior characteristics of this optimization framework in constructing accurate surrogate models and identifying optimal designs with a significant reduction in the computational effort.
1. Introduction
During the past decades, estimating the seaworthiness of a ship in the early design stages has become a primary concern for naval architects. Increased requirements in terms of comfort and ergonomics have steered the research in developing innovative hull forms, with the specific target of decreasing motions in waves. From a safety point of view, extreme accelerations can exert harmful dynamic loads (on the vessel, cargo, or equipment), slamming, or green water effects that can severely damage the structural integrity of the vessel or lead to stability losses. When ship behavior in waves becomes a quantity of interest in the hull-form optimization process, seakeeping performance needs to be predicted with numerical models able to combine high fidelity and high computational efficiency.
Nowadays, ship motion predictions mainly rely on three families of numerical models, here sorted by increasing level of fidelity: 2-D strip theories, 3-D boundary element methods (BEM), both developed under the assumption of potential flow, and unsteady fully viscous nonlinear 3-D methods in which ship motions are simulated in six Degrees of Freedom (DOF) for incident regular or irregular waves (see Fig. 5). In this article, we introduce a probabilistic method for constructing surrogate models using multi-fidelity training datasets that allows to increase the accuracy of the model with significant savings in computational resources. For the purpose of demonstration of the multi-fidelity framework, the training datasets used in this article are composed of classical 2-D and 3-D potential flow predictions; for this reason, we will refer to 2-D strip theories as low-fidelity models and a more accurate 3-D BEM as high-fidelity models. In the present study, our goal is to demonstrate the ability of the multi-fidelity framework in efficiently discovering hull forms with superior seakeeping characteristics by using simplified prediction models. Although in the present study, we do not include any viscous effects, the methodology is general and can combine any type of high-fidelity simulations or experimental data with low-fidelity simulations, experimental data, or even empirical correlations.
... N aerodynamic shape optimization, the discrete adjoint method is the useful tool to optimize the entire lifting surface with very large number of design variables [1,2]. An adjoint-based aerodynamic shape optimization involves the differentiation of the entire chain, i.e. flow, mesh and shape derivatives. ...
... By doing so, and assuming the shape has been parametrized, three types of sensitivity are needed, namely flow, grid and shape sensitivity. In this work, the flow adjoint is calculated using the discrete formulation where the discrete adjoint equation is derived after the discretisation of the governing equations [1,2]. This paper focuses on using non-consistent methods for both the mesh movement and grid sensitivity parts of the optimisation chain. ...
... Burgreen and Baysal [21] Le Moigne and Qin [2] Algebraic method Analytical Consistent ...
This paper presents an investigation of the influence of a nonconsistent approach in terms of mesh movement and mesh sensitivity calculation in a discrete adjoint-based optimization. Some mesh movement methods are more robust or of higher quality, whereas others can be more efficient for calculating mesh sensitivity. It is found that a nonconsistent approach gives comparable results when compared to a consistent approach. Therefore, an appropriate combination of nonconsistent approaches can be achieved for efficient adjoint optimization. This paper investigates and compares various consistent and nonconsistent combinations by using linear elasticity, Delaunay graph mapping, and radial basis function mesh movement methods. An investigation is presented, using a lift-constrained drag minimization, to assess which step of the chain introduces a deviation, if any, and to which degree this affects the final result.
... Another shortcoming of EGO is that it cannot be applied to problems where multiple models of differing accuracies are used. Using models of different accuracies and costs during optimization allows for significant analysis cost reductions without sacrificing accuracy in the neighborhood of the global optimum [19,[22][23][24][25][26]. This strategy is sometimes called variable-fidelity modeling. ...
... Models at multiple levels of accuracy can indeed enable design space exploration in a cost-effective manner, but an appropriate algorithm is required for managing the information obtained from each of the analysis models. Previous approaches to multiple accuracy modeling were often limited to only two analysis models, and moreover, did not explicitly account for the cost of the analyses used during the process [25,26,[32][33][34][35][36][37]. Therefore, what is needed is a method to combine predictions from any number of models of different accuracies so that all of the relevant information can be used and weighted according to its accuracy. ...
In this paper, a value-based global optimization (VGO) algorithm is introduced. The algorithm uses kriging-like surrogate models and a sequential sampling strategy based on value of information (VoI) to optimize an objective characterized by multiple analysis models with different accuracies. VGO builds on two main contributions. The first contribution is a novel surrogate modeling method that accommodates data from any number of different analysis models with varying accuracy and cost. Rather than interpolating, it fits a model to the data, giving more weight to more accurate data. The second contribution is the use of VoI as a new metric for guiding the sequential sampling process for global optimization. Based on information about the cost and accuracy of each available model, predictions from the current surrogate model are used to determine where to sample next and with what level of accuracy. The cost of further analysis is explicitly taken into account during the optimization process, and no further analysis occurs if the expected value of the new information is negative. In this paper, we present the details of the VGO algorithm and, using a suite of randomly generated test cases, compare its performance with the performance of the efficient global optimization (EGO) algorithm (Jones, D. R., Matthias, S., and Welch, W. J., 1998, “Efficient Global Optimization of Expensive Black-Box Functions,” J. Global Optim., 13(4), pp. 455–492). Results indicate that the VGO algorithm performs better than EGO in terms of overall expected utility—on average, the same quality solution is achieved at a lower cost, or a better solution is achieved at the same cost.
... The particular test considered is the well-studied ONERA M6 wing [92]. This geometry has been studied by numerous authors [93,94,95,96,97,10,12] due to the simple, well defined geometry and the availability of experimental data. ...
... A four-objective optimization of wing shape and planform were presented using 72 design variables, subject to thickness and planform shape constraints. Moigne and Qin [96] studied aerodynamic shape optimization based on a discrete adjoint of a Reynolds-averaged Navier-Stokes (RANS) solver. A variable-fidelity optimization method combining low-and highfidelity models was used. ...
With increasing fidelity and efficiency of numerical simulations, it becomes possible to rely on computational simulations and optimization to achieve a better aircraft design. One of the most computationally intensive disciplines is the aircraft external aerodynamic design. Computational fluid dynamics based on Reynold-averaged Navier--Stokes equations is necessary to accurately resolve the flow field in order to achieve a practical design. High-fidelity CFD poses difficulties to numerical optimization due to its high computational cost, especially when large number of shape design variables are used. This thesis presents an approach to compute the gradients of Reynold-averaged Navier--Stokes equation equations with a Spalart--Allmaras turbulence model using a combination of the adjoint method and automatic differentiation algorithms, for use in gradient-based aerodynamic shape optimization. The resulting gradients are accurate, robust, and efficient.
With this state-of-the-art Reynolds-averaged Navier--Stokes adjoint and aerodynamic shape optimization framework, we performed three high-fidelity aerodynamic design optimization studies in this thesis. The wing of a Boeing 777-sized aircraft is optimized for single and multiple flight conditions. The drag coefficient is minimized with respect to 720 shape design variables, subject to lift, pitching moment, and geometric constraints, using grids with up to 28.8M cells. Drag coefficient of the optimized design was reduced by 8.5% relative to the initial design. The second application is to optimize the aerodynamics of a near-term aircraft retrofit modification: a wing with morphing trailing edge. A drag reduction in the order of 1% is achieved for on-design conditions, and reductions up to 5% were achieved for off-design conditions. Finally, we extend the aerodynamic shape optimization studies to design an unconventional configuration, the blended-wing-body aircraft. The best compromise between performance and stability was achieved by enforcing a small static margin that can be tolerated in a commercial airplane (1%) and including the center of gravity position as a design variable. This resulted in a trimmed configuration that exhibits a nearly elliptical lift distribution and the lowest drag among the trimmed stable designs. This was achieved by a combination of optimized washout and reflex airfoils.
... The technique employed to update the grid is taken from ref. [11]. The deformation of the grid is considering individually every grid line. ...
Shock control bumps are a promising technique in reducing wave drag of civil transport aircraft flying at transonic speeds. This paper investigates the optimization of 3D shock control bumps on a supercritical wing with a sweep angle of 16A degrees at the 1/4 chord. A similar supercritical wing with a higher sweep angle of 24.5A degrees at the 1/4 chord has been adopted as a baseline for the study. Numerical results show that the drag coefficient of the low sweep wing with the optimized 3D shock control bumps is reduced below that for the high sweep wing, indicating shock control bumps can be used as an effective means to reduce the wave drag caused by reducing the wing sweep angle. From the point of view of the wing structure design, lower sweep angle will also bring the benefits of weight reduction, resulting in further fuel reduction.
