Machine learning-accelerated aerodynamic inverse design

Inverse shape design in the context of fluid flow problems is commonly referred to the determination of the boundary shape corresponding to a given target surface pressure. Designers naturally turn to this class of problems whenever there are concerns regarding pressure-related phenomena such as cavitation, separation, shock waves, surface loading, etc. Numerical solution is often unavoidable and, therefore, three computational tools, i.e. a grid generator, a flow field solver and a shape updater, are required in an iterative solution procedure. In all existing iterative inverse design methods, the shape updater comes from separate mathematical or physical considerations that are not derived solely from the equations governing the flow field. In this paper, the currently used strategies to solve inverse shape design problems are categorized and reviewed, and then a truly physical-based iterative inverse shape design method is introduced in which the governing equations are not only used in the flow solver, but are also employed to update the shape. To explore the features of the proposed method, it is used to solve a number of shape design problems. The previously developed direct shape design method and a typical iterative solution approach are also explained and used for the solution of the same problems for the purpose of comparison. Computational results reveal that the proposed algorithm has a two to three times faster convergence rate as compared to the iterative algorithm. The convergence rate of the proposed algorithm usually stalls after three or two orders of magnitude reduction of the residual. For the test cases in this study, the direct design method is the fastest and most accurate method as compared to other algorithms. Both in-house developed computer codes and commercial software are used as a field solver to show the general applicability of the proposed method in its current state of development.

In this research, a novel inverse design algorithm called, Elastic Surface Algorithm (ESA), is developed for viscose and inviscid external flow regimes. ESA is a physically based iterative inverse design method that uses flow analysis code to estimate the pressure distribution on the solid structure, i.e. airfoil, and a 2D solid beam finite element code to calculate the deflections due to the difference between the calculated and target pressure distribution. The proposed method is validated through the inverse design of three different airfoils. In addition, two design examples are presented to prove the robustness of the method in various flow regimes. Also, the convergence rate of this method is compared with flexible membrane method (MGM) and Ball-Spine Algorithm (BSA) methods in inviscid flow regime. The results of this study showed that not only the ESA method is an effective method for inverse design of airfoils, but also it can considerably increase the convergence rate in transonic flow regimes.

Subsonic and transonic airfoil inverse design via Ball-Spine Algorithm

This paper deals with a vibration control experiment using an iterative identification and control design method. The purpose of this investigation is to suppress the natural vibrations of structures. The experimental device has three links behaves as a vibration system. The feature of this device is that the control system is not sensor / actuator collocated for practical use of an air jet actuator. In order to suppress natural vibrations, LQG control and Tb2 control are applied to the model, which is identified iteratively on the basis of the closed-loop experimental input / output data.The achieved performance is improved, moreover, by a change for the better of the designed control performance in each iteration. In control experiments, initial displacement responses and resonance signal responses are examined. It is shown that the iterative design method is useful to design vibration controlled systems and can perform better on suppressing the natural vibrations and disturbances than non-iterative design methods.

Development and validation of a hybrid aerodynamic design method for curved diffusers using genetic algorithm and ball-spine inverse design method

Elastic Surface Algorithm (ESA), which was proposed for the inverse design in external flows, substitutes the airfoil wall by an elastic curved beam that deforms due to a difference between the target and current pressure distributions. The original ESA, such as all inverse design methods, which use only pressure as the target parameter, cannot converge in separated flows because of an almost constant pressure inside the separated region. This study developed the ESA for the inverse design in external separated flows by considering a linear combination of normalized pressure and shear stress distribution as the target flow parameter. Removing the geometrical filtrations, the automatic determination of the beam elasticity modulus, and the definition of dynamic spines instead of the vertical spines were the other essential modifications to upgrade the ESA for separated flows. The method was verified for blunt-leading-edged airfoils in subsonic turbulent flow under different angles of attack, and different initially-guessed geometries. The method reduced the separation by modifying the wall shear stress along the separation region.

In this study, a new inverse design method called Elastic Surface Algorithm (ESA) is developed and enhanced for axial-flow compressor blade design in subsonic and transonic flow regimes with separation. ESA is a physically based iterative inverse design method that uses a 2D flow analysis code to estimate the pressure distribution on the solid structure, i.e. airfoil, and a 2D solid beam finite element code to calculate the deflections due to the difference between the calculated and target pressure distributions. In order to enhance the ESA, the wall shear stress distribution, besides pressure distribution, is applied to deflect the shape of the airfoil. The enhanced method is validated through the inverse design of the rotor blade of the first stage of an axial-flow compressor in transonic viscous flow regime. In addition, some design examples are presented to prove the effectiveness and robustness of the method. The results of this study show that the enhanced Elastic Surface Algorithm is an effective inverse design method in flow regimes with separation and normal shock.

The engineering problem of airfoil design has been of great theoretical interest for almost a century and has led to hundreds of papers written and dozens of methods developed over the years. This interest stems from the practical implications of airfoil design. Airfoil selection significantly influences the application's aerodynamic performance. Tailoring an airfoil profile to its specific application can have great performance advantages. This includes considerations of the lift and drag characteristics, pitching moment, volume for fuel and structure, maximum lift coefficient, stall characteristics, as well as off-design performance. A common way to think about airfoil design is optimization, the process of taking an airfoil and modifying it to improve its performance. The classic design goal is to minimize drag subject to required lift and thickness values to meet aerodynamic and structural constraints. This is typically an expensive operation depending on the selected optimization technique because several flow solutions are often required in order to obtain an updated airfoil profile. The optimizer requires gradients of the design space for a gradient-based optimizer, fitness values of the members of the population for a genetic algorithm, etc. An alternative approach is to specify some desired performance and find the airfoil profile that achieves this performance. This is known as inverse airfoil design. Inverse design is more computationally efficient than direct optimization because changes in the geometry can be related to the required change in performance, thus requiring fewer flow solutions to obtain an updated profile. The desired performance for an inverse design method is specified as a pressure or velocity distribution over the airfoil at given flight conditions. The improved efficiency of inverse design comes at a cost. Designing a target pressure distribution is no trivial matter and has severe implications on the end performance. There is also no guarantee a specified pressure or velocity distribution can be achieved. However, if an obtainable pressure or velocity distribution can be created that reflects design goals and meets design constraints, inverse design becomes an attractive option over direct optimization. Many of the available inverse design methods are only valid for incompressible flow. Of those that are valid for compressible flow, many require modifications to the method if shocks are present in the flow. The convergence of the methods are also greatly slowed by the presence of shocks. This paper discusses a series of novel inverse design methods that do not depend on the freestream

In recent years, considerable research advancements have emerged in the application of inverse design methods to enhance the performance of electromagnetic (EM) metamaterials. Notably, the integration of deep learning (DL) technologies, with their robust capabilities in data analysis, categorization, and interpretation, has demonstrated revolutionary potential in optimization algorithms for improved efficiency. In this review, current inverse design methods for EM metamaterials are presented, including topology optimization (TO), evolutionary algorithms (EAs), and DL-based methods. Their application scopes, advantages and limitations, as well as the latest research developments are respectively discussed. The classical iterative inverse design methods categorized TO and EAs are discussed separately, for their fundamental role in solving inverse design problems. Also, attention is given on categories of DL-based inverse design methods, i.e. classifying into DL-assisted, direct DL, and physics-informed neural network methods. A variety of neural network architectures together accompanied by relevant application examples are highlighted, as well as the practical utility of these overviewed methods. Finally, this review provides perspectives on potential future research directions of EM metamaterials inverse design and integrated artificial intelligence methodologies.

This paper presents a novel iterative viscous inverse design method for turbomachinery blading. It is made up of two steps: the first one consists of an analysis by means of a Navier-Stokes solver; the second one is an inverse design by means of an Euler solver. The inverse design resorts to the concept of permeable wall, and recycles the ingredients of Demeulenaere’s inviscid inverse design method that was proven fast and robust. The re-design of the LS89 turbine nozzle blade, starting from different arbitrary profiles at subsonic and transonic flow regimes, demonstrates the merits of this approach. The method may result in more than one blade profile that meets the objective, i.e., that produces the viscous target pressure distribution. To select one particular solution among all candidates, a target mass flow is enforced by adjusting the outlet static pressure. The resulting profiles are smooth (oscillation-free). The design of turbine blades with arbitrary pressure distribution at transonic and supersonic outflow illustrates the correct behavior of the method for a large range of applications. The approach is flexible because only the pitch chord ratio is fixed and no limitations are imposed on the stagger angle.

This paper presents an iterative inverse design methodology based on proper orthogonal decomposition (POD) and its applications to the inverse design of turbomachinery blades. In the aerodynamic system with a number of snapshots, the aerodynamic performance with the corresponding aerodynamic shape within the design space can be described as a linear combination of a series of POD basis modes. In the present paper, the description ability of Gappy POD is evaluated firstly and the influence of different parametrization methods and different snapshot approaches are studied and compared in detail. In the POD-based inverse design, the aerodynamic shape can be obtained by only one design process. However, due to the error between the predicted aerodynamic performance by Gappy POD and that obtained from computational fluid dynamics, an iterative inverse design methodology is proposed herein based on the error correction to the target aerodynamic performance. Three inverse design studies of turbomachinery blades are performed. In the first two cases, the profiles of two-dimensional turbine blades are modified to approach the target pressure distributions on the blade surface in subsonic and transonic flow, respectively. In the third case, a three-dimensional supersonic turbine blade is restaggered along span to achieve a given loading distribution in the spanwise direction at the outlet. The design results are presented and compared in detail, demonstrating the effectiveness and improved accuracy of the POD-based iterative inverse design method.

This paper presents a novel iterative viscous inverse method for turbomachinery blading design. It is made up of two steps: The first one consists of an analysis by means of a Navier-Stokes solver, the second one is an inverse design by means of an Euler solver. The inverse design resorts to the concept of permeable wall, and recycles the ingredients of Demeulenaere’s inviscid inverse design method that was proven fast and robust. The re-design of the LS89 turbine nozzle blade, starting from different arbitrary profiles at subsonic and transonic flow regimes, demonstrates the merits of this approach. The method may result in more than one blade profile that meets the objective, i.e. that produces the viscous target pressure distribution. To select one particular solution among all candidates, a target mass flow is enforced by adjusting the outlet static pressure. The resulting profiles are smooth (oscillation-free). The design of turbine blades with arbitrary pressure distribution at transonic and supersonic outflow illustrates the correct behavior of the method for a large range of applications. The approach is flexible because only the pitch chord ratio is fixed and no limitations are imposed on the stagger angle.

An aerodynamic design optimization method is presented that generates an airfoil, producing a specified surface pressure distribution at a transonic speed. The design procedure is based on the coupled Euler and boundary-layer technology to include the rotational viscous physics which characterizes transonic flows. A leastsquare optimization technique is used to minimize pressure discrepancies between the target and designed airfoils. The method is demonstrated with several examples at transonic speeds. The design optimization process converges quickly, that makes the method attractive for practical engineering applications. I. Introduction I N recent years, computational fluid dynamics (CFD) has become a valuable engineering tool in the aircraft industry. CFD plays a complementary role, not a replacement, to experiments in practical design communities. Rubbert1 showed some good examples of the use of CFD and experiment, in combination, for transonic design. A major strength of CFD is the ability to produce detailed insights into complex flow phenomena. The process of decomposition and parameterization can help identify the cause of weak aerodynamic performance, and the microscopic understanding of the flow can lead to improved design. Continuing advances in computer hardware and simulation techniques provide an unprecedented opportunity for CFD. Now simulations of more complete configurations with more complex physics can be performed at an affordable cost. Accuracy and reliability of the computation have been continuously improved. The use of high-level flow models and large-size refined grids enables one to analyze flows with complicated structures and various length scales. Compared to the remarkable advances in analysis capability, however, relatively few advances have been made in design technology. Conventional design practices, therefore, often depend on analysis methods through iterative cut-and-try approaches. A unique advantage of CFD is the capability of inverse design. Inverse design directly determines the airfoil geometry that produces the pressure distribution specified by a designer. Many existing inverse design methods are based on the potential flow assumption due to its simplicity. Volpe and Melnik2 employed an inverse design method using the nonlinear full potential formulation. Bauer and colleagues3 used the hodograph method that solves the full potential equation in the hodograph plane where the equations are linear. The potential flow model, however, cannot properly represent transonic features such as embedded shock waves and shock-boundarylayer interactions. An accurate analytic capability is a prerequisite for a successful design, because the quality of the design depends on the quality of the method used to predict the flowfield. Several inverse design methods were demonstrated using the Euler formulations by Giles and Drela,4 and Mani.5 Instead of achieving the prescribed pressure distribution, some design methods use a constrained optimization process

The duct inverse design in fluid flow problems usually involves finding the wall shape associated with a prescribed distribution of wall pressure or velocity. In this investigation, an iterative inverse design method for 2-D subsonic ducts is presented. In the proposed method, the duct walls shape is changed under a novel algorithm based on the deformation of a virtual flexible string in flow. The deformation of the string due to the local flow conditions resulting from changes in wall geometry is observed until the target shape satisfying the prescribed wall's pressure distribution is reached. The flow field at each step is analysed using Euler equations and the advection upstream splitting method method. Some validation test cases and a design example are presented here which show the robustness and flexibility of the method in handling complex geometries. The method is a physical and quick converging approach and can efficiently utilize commercial flow analysis software.

Pressure‐based inverse design (ID) cannot converge in flow regimes with ultralow Reynolds numbers (Res). This study proposes a shear‐stress‐based ID method for airfoil design at Re = 1000 at the optimal angle of attack (AOA) in the presence of a laminar separation bubble. The proposed method applies the difference between the existing and target shear stress distributions (SSDs) to a deformable surface. The Navier–Stokes equations are solved to calculate the wall SSD during each iteration of the ID process. This process modifies the airfoil geometry until the abovementioned difference becomes negligible, achieving convergence to the target geometry. Achieving the maximum lift‐to‐drag ratio by manually correcting the wall SSD involves extensive trial and error, making it almost impossible. Thus, in the second part of this research, we trained Gaussian process regression and an ensemble of trees deep learning (DL) models using data generated during ID at the optimal AOA to predict lift and drag coefficients, respectively. The SSD was optimized throughout the ID process by coupling the DL models with a genetic algorithm (GA). Optimization was performed in several consecutive cycles, with the DL models becoming more accurate and updated as more data were gathered, helping the GA obtain the optimal SSD and geometry precisely. Finally, the performance curves of different geometries obtained through the optimization cycles were evaluated and compared using the Fluent solver. The results demonstrated a 22.42% increase in the lift‐to‐drag ratio relative to the initial population at the optimal AOA.