Application of an Inverse Design Method to Meet a Target Pressure in Axial-Flow Compressors

Madadi, Ali; Kermani, M.J.; Nili-Ahmadabadi, Mahdi

doi:10.1115/gt2011-46091

Cited by 6 publications

(4 citation statements)

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“…Here, the basis for the determination of this parameter is not discussed and interested readers may consult. [19][20][21][22] The flow chart of this algorithm is shown in Figure 4(a). In this algorithm, after solving the governing equation on the initial grid and calculating V 0 t , the boundary node coordinates are updated separately using Equation (14).…”

Section: A Typical Physical-based Shape Updatermentioning

confidence: 99%

“…In the flexible string algorithm, proposed by Nili-Ahmadabadi et al [16][17][18], the boundary is considered as an elastic string that deforms under the force due to the pressure mismatch. In another method, called the ball-spine Algorithm, [19][20][21][22] hypothetical balls are distributed along the boundary. These balls are allowed to move along specified directions, called spines, under the pressure mismatch force.…”

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confidence: 99%

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Inverse shape design via a new physical-based iterative solution strategy

Nikfar

Ashrafizadeh

Mayeli

2014

Inverse Problems in Science and Engineering

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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 inhouse 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.

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Section: A Typical Physical-based Shape Updatermentioning

confidence: 99%

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confidence: 99%

Inverse shape design via a new physical-based iterative solution strategy

Nikfar

Ashrafizadeh

Mayeli

2014

Inverse Problems in Science and Engineering

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“…Madadi et al [56] utilized the BSA for the quasi-3D inverse design of an S-shaped duct. In addition, they employed the BSA for the design of 2D cascade blades with sharp [57,58] and blunt [59] leading edges, and for the quasi-3D inverse design of the axialflow compressor rotor and stator blades [60]. They redesigned the rotor blade of an axial compressor with this method, so that the rotor loading coefficient was increased, which led to an increase of the compressor outlet pressure by 10%.…”

Section: Introductionmentioning

confidence: 99%

Aerodynamic Inverse Design of Transonic Compressor Cascades with Stabilizing Elastic Surface Algorithm

et al. 2021

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The upgraded elastic surface algorithm (UESA) is a physical inverse design method that was recently developed for a compressor cascade with double-circular-arc blades. In this method, the blade walls are modeled as elastic Timoshenko beams that smoothly deform because of the difference between the target and current pressure distributions. Nevertheless, the UESA is completely unstable for a compressor cascade with an intense normal shock, which causes a divergence due to the high pressure difference near the shock and the displacement of shock during the geometry corrections. In this study, the UESA was stabilized for the inverse design of a compressor cascade with normal shock, with no geometrical filtration. In the new version of this method, a distribution for the elastic modulus along the Timoshenko beam was chosen to increase its stiffness near the normal shock and to control the high deformations and oscillations in this region. Furthermore, to prevent surface oscillations, nodes need to be constrained to move perpendicularly to the chord line. With these modifications, the instability and oscillation were removed through the shape modification process. Two design cases were examined to evaluate the method for a transonic cascade with normal shock. The method was also capable of finding a physical pressure distribution that was nearest to the target one.

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“…They developed this method for quasi-3D design of meridional plane of centrifugal compressors (Nili et al 2013). In a recent paper, Madadi et al (2011) applied the ball-spine algorithm to 2D design of sharp leading edge airfoils.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Design of Axial Flow Compressor Blades Using the Ball-Spine Algorithm

Madadi¹,

Kermani

Nili³

2015

JAFM

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Recently a new inverse design algorithm has been developed for the design of ducts, called ball-spine (BS). In the BS algorithm, the duct walls are considered as a set of virtual balls that can freely move along some specified directions, called 'spines'. Initial geometry is guessed and the flow field is analyzed by a flow solver. Comparing the computed pressure distribution (CPD) with the target pressure distribution (TPD), new balls positions for the modified geometry are determined. This procedure is repeated until the target pressure is achieved. In the present work, the ball-spine algorithm is applied to three-dimensional design of axial compressor blades. The design procedure is tested on blades based on NACA65-410 and NACA65-610 profiles and the accuracy of the method is shown to be very good. As an application, the pressure distribution of the blade with NACA65-610 profiles is modified and the pressure gradient in the aft part of the blade is decreased and selected as target pressure distribution. The corresponding geometry which satisfies the target pressure is determined using the BS design algorithm.

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Application of an Inverse Design Method to Meet a Target Pressure in Axial-Flow Compressors

Cited by 6 publications

References 0 publications

Inverse shape design via a new physical-based iterative solution strategy

Inverse shape design via a new physical-based iterative solution strategy

Aerodynamic Inverse Design of Transonic Compressor Cascades with Stabilizing Elastic Surface Algorithm

Three-Dimensional Design of Axial Flow Compressor Blades Using the Ball-Spine Algorithm

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