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

In this research, an optimal aerodynamic design of an axe-symmetric diffuser is performed via combination of a developed boundary layer numerical code, BSA inverse design Algorithm and genetic optimization algorithm. To do this, developed numerical boundary layer code is incorporated into the genetic algorithm to reach to an optimum pressure distribution on the wall in such a way that the maximum pressure recovery is obtained without separation. To validate the developed boundary layer code, the calculated quantities are compared with Blasius and Howart’s analytical results. Then, the optimized pressure distribution will be the candidate “target pressure distribution” for the inverse design algorithm to find out the relevant optimum geometry. Geometry modification takes place based on the combination of Ball-Spine algorithm and fluent software as the flow field solver. Implementation of this combination is completed through User Defined Function (UDF) feature of Fluent. Fluent advantageous provides the capabilities for extension of the proposed method to turbulent flows, complicated geometries and employment of both structured and unstructured grids. To show the true performance of the proposed method of inverse design, several issues have been investigated for different initial guess. To validate the effect of the presented method, increased pressure coefficient for an optimized diffuser is illustrated.

The midspan section of Rotor 67 is redesigned simultaneously at two different design points using a new inverse blade design method where the blade walls move with a virtual velocity distribution derived from the difference between the current and the target pressure distributions on the blade surfaces. This inverse method is fully consistent with the viscous flow assumption and is implemented into the time accurate solution of the Reynolds-Averaged Navier-Stokes equations that are expressed in an arbitrary Lagrangian-Eulerian (ALE) form to account for mesh movement. A cell-vertex finite volume method of the Jameson type is used to discretize the equations in space; time accurate integration is obtained using dual time stepping. An algebraic Baldwin-Lomax turbulence model is used for turbulence closure. The CFD analysis provides the initial blade pressure distributions at both operating points, e.g. at two different back pressures and/or blade speeds. At each operating point, a target pressure distribution that results in a performance improvement, is prescribed. The inverse design method is then used to reach the prescribed target pressure distributions at both operating points, simultaneously. This is done by using a weighted average of the difference between the target and current pressure distributions at the two operating points, to modify the airfoil profile. The results show that by carefully tailoring the target pressure loadings at the two design points, some performance improvement can be achieved over the entire range between the two operating points.

In this study, a new inverse design method is proposed for the full 3-D inverse design of S-ducts using curvature-based dimensionless pressure distribution as a target function. The wall pressure distribution in a 3-D curved duct is a function of the centerline curvature and the cross-sectional profile and area. A dimensionless pressure parameter was obtained as a function of the duct curvature and height of the cross-sections based on the normal pressure gradient equation. The dimensionless pressure parameter was used to eliminate the effect of the cross-sectional area on the wall pressure distribution. Full 3-D inverse design of an S-shaped duct was carried out by substituting the 3-D duct with a large number of 2-D planar ducts. The ball-spine inverse design method with vertical spins was coupled with the dimensionless pressure parameter as a target function for the design of the planar ducts. The inverse design process was performed in two steps. First, the height of each cross-section was considered constant, and only the duct centerline was allowed to be deformed by applying the difference between the dimensionless pressure on the upper and lower lines of symmetry plane. Then, a constant curvature was considered for each centerline in the equation, and the difference between the current and the target dimensionless pressure was applied to each upper and lower line of the planar sections to correct the heights of the 2-D planar sections, separately. The method was validated by choosing a straight duct as an initial guess, which converges to the target S-shaped duct. The results showed that the method is an efficient physical-based residual-correction method with low computational cost and good convergence rate. The 3-D wall pressure distribution of a high-deflected 3-D S-shaped diffuser was modified to eliminate the separation, secondary flow, and outlet distortion. Finally, the geometry corresponding to the modified pressure was obtained by the proposed 3-D inverse design method, which revealed higher pressure recovery, lower total pressure loss, and lower outlet flow distortion and swirl angle.

Application of constrained target pressure specification to takanashi's inverse design method

A new dual-point inverse blade design method was developed and applied to the redesign of a highly loaded transonic vane, the VKI-LS89, and the first 2.5 stages of a low speed subsonic turbine, the E/TU-4 4-stage turbine that is built and tested at the university of Hannover, Germany. In this inverse method, the blade walls move with a virtual velocity distribution derived from the difference between the current and the target pressure distributions on the blade surfaces at both operating points. This new inverse method is fully consistent with the viscous flow assumption and is implemented into the time accurate solution of the Reynolds-Averaged Navier-Stokes equations. An algebraic Baldwin-Lomax turbulence model is used for turbulence closure. The mixing plane approach is used to couple the stator and rotor regions. The dual-point inverse design method is then used to explore the effect of different choices of the pressure distributions on the suction surface of one or more rotor/stator on the blade/stage performance. The results show that single point inverse design resulted in a local performance improvement whereas the dual point design method allowed for improving the performance of both VKI-LS89 vane and E/TU-4 2.5 stage turbines over a wide range of operation.

The most critical step in designing a turbomachine is to design the blades. In this study, an axial turbine blade is designed using an inverse design method called Ball-Spine Algorithm. In some cases, the target pressure distribution is not specified in the inverse design process, and it has to be determined arbitrarily by the designer. This study is conducted in order to compute the optimal target pressure distribution by maximizing the cascade blade efficiency. Optimization is carried out using the Genetic Algorithm. Two commercial software packages, ANSYS and MATLAB, are used in this research. Since inverse design is an iterative process, these software packages are linked together to execute the whole procedure automatically. Validation of the approach is accomplished by redesigning an existing blade. Then the optimization method is applied, and the desired blade is inversely designed. Results show that the cascade blade efficiency increases by about 9% on average for this blade.

Fourier series solution for inverse design of aerodynamic shapes

An aerodynamic inverse design method is developed for the simulation of three-dimensional viscous flow over blades, it is implemented into a commercial CFD program, namely ANSYS-CFX, and it is applied to the design of a transonic compressor stage. The implementation is validated for Rotor 37; it is then assessed in the redesign of Stage 67 stator. One set of design choices is to prescribe a target blade pressure loading and blade thickness distributions and a stacking line from hub to tip. The blade walls are assumed to be moving with a virtual velocity that would asymptotically drive the blade to the shape that would correspond to the specified target pressure distribution. This virtual velocity distribution is computed from the difference between the computed and the target pressure distributions. This inverse design approach is fully consistent with the viscous flow assumption and is independent of the CFD approach taken. The Arbitrary Lagrangian-Eulerian formulation of the unsteady Reynolds-Averaged Navier Stokes equations is solved in a time accurate fashion with the blade motion being the source of unsteadiness. At each time step, the blade shape is modified and dynamic meshing is used to remesh the fluid flow domain. To demonstrate the ability of this approach, it is applied to redesign the stator of a transonic axial fan, Stage 67, to improve its performance.

Three-dimensional aerodynamic shape inverse design based on ISOMAP

An inverse airfoil design process is presented that makes use of the CST parameterization method. The CST method is very powerful in that it can easily represent any airfoil shape within the entire design space of smooth airfoils. This makes it an ideal modeling technique for an inverse design process because accurate airfoil geometry treatment is required. The downfall of some inverse design processes is that they do not accurately handle the leading edge region due to large ow gradients and high curvature distributions. One way to account for this is by representing airfoils with smooth analytic functions, such as the CST method. The inverse airfoil design process presented is based on the relation between pressure residuals and the required airfoil shape change. The pressure residuals give the sign of the normal vector with which to modify the airfoil shape. The CST method is then used as the smoothing algorithm. The inverse design method is simple, accurate, and ecient. It is shown to accurately determine the airfoil geometry in both subsonic and transonic ows. Since this method simply examines pressure distributions to modify the airfoil shape, the ow solver can be kept separate from the inverse design process, allowing any delity ow solver to be used.

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

Double-decoupled inverse design of natural laminar flow nacelle under transonic conditions

A parameterized-loading driven inverse design and multi-objective coupling optimization method for turbine blade based on deep learning

Aerodynamic design of cascade airfoil using Genetic Algorithms with single objective and multiple objectives has been presented in this paper. Both inverse and direct design problems are faced. In the first part of this work, Genetic Algorithms based on Boltzmann selection are applied to turbine cascade inverse design through minimizing difference between target pressure distribution and computed pressure distribution. The result shows that the pressure distribution of obtained cascade airfoil is well agreement with the target pressure distribution and so is the geometry shape. In the second part of this work, based on the multi-branch Boltzmann selection and Pareto criteria method, multiobjective Genetic Algorithms have been developed and used for compressor cascade airfoil design. Goal of the compressor cascade design is to search higher pressure rise and lower total pressure loss on the basis of Controlled Diffusion Airfoil(CDA) at the given flow condition. Pareto solution of multiobjective design can supply many design plans for decision maker to select. The cascade with higher pressure rise and lower total pressure loss can be considered to have higher aerodynamic performance than the existed CDA. The optimization results also confirm that the feasibility and robustness of the present Genetic Algorithms based on Boltzmann selection.

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.