An Iterative Inverse Design Method of Turbomachinery Blades by Using Proper Orthogonal Decomposition

2015 ◽  
Author(s):  
Jiaqi Luo ◽  
Xiao Tang ◽  
Yanhui Duan ◽  
Feng Liu
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Design Methodology ◽  
Design Method ◽  
Aerodynamic Performance ◽  
Orthogonal Decomposition ◽  
Inverse Design ◽  
Turbomachinery Blades ◽  
Inverse Design Method ◽  
Proper Orthogonal ◽  
Gappy Pod

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.

Modeling and Inverse Design of Convective Heat Transfer in a Grooved Channel Using Proper Orthogonal Decomposition

2009 ◽  
Author(s):  
Hasan Gunes ◽  
Sertac Cadirci
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Proper Orthogonal Decomposition ◽  
Convective Heat Transfer ◽  
Orthogonal Decomposition ◽  
Inverse Design ◽  
Heat Sources ◽  
Design Problems ◽  
Proper Orthogonal

In this study we show that the POD can be used as a useful tool to solve inverse design problems in thermo-fluids. In this respect, we consider a forced convection problem of air flow in a grooved channel with periodically mounted constant heat-flux heat sources. It represents a cooling problem in electronic equipments where the coolant is air. The cooling of electronic equipments with constant periodic heat sources is an important problem in the industry such that the maximum operating temperature must be kept below a value specified by the manufacturer. Geometric design in conjunction with the improved convective heat transfer characteristics is important to achieve an effective cooling. We obtain a model based on the proper orthogonal decomposition for the convection optimization problem such that for a given channel geometry and heat flux on the chip surface, we search for the minimum Reynolds number (i.e., inlet flow speed) for a specified maximum surface temperature. For a given geometry (l = 3.0 cm and h = 2.3 cm), we obtain a proper orthogonal decomposition (POD) model for the flow and heat transfer for Reynolds number in the range 1 and 230. It is shown that the POD model can accurately predict the flow and temperature field for off-design conditions and can be used effectively for inverse design problems.

Inverse design of aircraft cabin environment using computational fluid dynamics-based proper orthogonal decomposition method

2017 ◽  
Vol 27 (10) ◽  
pp. 1379-1391 ◽  
Author(s):  
Jihong Wang ◽  
Tengfei (Tim) Zhang ◽  
Hongbiao Zhou ◽  
Shugang Wang
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Proper Orthogonal Decomposition ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Inverse Design ◽  
Air Supply ◽  
Spatial Modes ◽  
Cabin Environment ◽  
Proper Orthogonal

To design a comfortable aircraft cabin environment, designers conventionally follow an iterative guess-and-correction procedure to determine the air-supply parameters. The conventional method has an extremely low efficiency but does not guarantee an optimal design. This investigation proposed an inverse design method based on a proper orthogonal decomposition of the thermo-flow data provided by full computational fluid dynamics simulations. The orthogonal spatial modes of the thermo-flow fields and corresponding coefficients were firstly extracted. Then, a thermo-flow field was expressed into a linear combination of the spatial modes with their coefficients. The coefficients for each spatial mode are functions of air-supply parameters, which can be interpolated. With a quick map of the cause–effect relationship between the air-supply parameters and the exhibited thermo-flow fields, the optimal air-supply parameters were determined from specific design targets. By setting the percentage of dissatisfied and the predicted mean vote as design targets, the proposed method was implemented for inverse determination of air-supply parameters in two aircraft cabins. The results show that the inverse design using computational fluid dynamics-based proper orthogonal decomposition method is viable. Most of computing time lies in the construction of data samples of thermo-flow fields, while the proper orthogonal decomposition analysis and data interpolation is efficient.

An Improved Proper Orthogonal Decomposition Technique for the Solution of a 2-D Rotor Blade Inverse Design Problem Using the Entropy Generation Rate as the Objective Function

2007 ◽  
Author(s):  
G. Panzini ◽  
E. Sciubba ◽  
A. Zoli-Porroni
Keyword(s):  
Objective Function ◽  
Proper Orthogonal Decomposition ◽  
Entropy Generation ◽  
Design Problem ◽  
Fluid Dynamic ◽  
Orthogonal Decomposition ◽  
Inverse Design ◽  
Entropy Generation Rate ◽  
Cfd Simulations ◽  
Proper Orthogonal

This paper discusses the optimization of a 2D rotor profile attained via a novel inverse-design approach that uses the entropy generation rate as the objective function. A fundamental methodological novelty of the proposed procedure is that it does not require the generation of the fluid-dynamic fields at each iteration step of the optimisation, because the objective function is computed by a functional extrapolation based on the Proper Orthogonal Decomposition (POD) method. With this new method, the (often excessively taxing) computational cost for repeated numerical CFD simulations of incrementally different geometries is substantially decreased by reducing much of it to easy-to-perform matrix-multiplications: CFD simulations are used only to calculate the basis of the POD interpolation and to validate (i.e., extend) the results. As the accuracy of a POD expansion critically depends on the allowable number of CFD simulations, our methodology is still rather computationally intensive: but, as successfully demonstrated in the paper for an airfoil profile design problem, the idea that, given a certain number of necessary initial CFD simulations, additional full simulations are performed only in the “right direction” indicated by the gradient of the objective function in the solution space leads to a successful strategy, and substantially decreases the computational intensity of the solution. This “economy” with respect to other classical “optimization” methods is basically due to the reduction of the complete CFD simulations needed for the generation of the fluid-dynamic fields on which the objective function is calculated.

Development of an (Adaptive) Unstructured 2-D Inverse Design Method for Turbomachinery Blades

2002 ◽  
Author(s):  
Benjamin M. F. Choo ◽  
Mehrdad Zangeneh
Keyword(s):  
Shock Waves ◽  
Design Method ◽  
Inverse Design ◽  
Pressure Jump ◽  
Triangular Meshes ◽  
Pressure Loading ◽  
Trailing Edge ◽  
Turbomachinery Blades ◽  
Inverse Design Method ◽  
Blade Geometry

An aerodynamics inverse design method for turbomachinery blades using fully (adaptive) unstructured meshes is presented. In this design method, the pressure loading (i.e. pressure jump across the blades) and thickness distribution are prescribed. The design method then computes the blade shape that would accomplish this loading. This inverse design method is implemented using a cell-centred finite volume method which solves the Euler equations on Delaunay unstructured triangular meshes using upwind flux vector splitting scheme. The analysis/direct Euler solver first is validated against some test cases of cascades flow. Computational grid and solution adaptation is performed to capture any flow behaviors such as shock waves using some error indicators. In the inverse design method, blade geometry is updated at the end of each design iteration process. A flexible and fast remeshing process based on a classical ‘spring’ methodology is adopted. An improved spring smoothing methodology for large changes of blades geometry is also presented. This flexible remeshing method can be used in designing a real blade (i.e. round leading and trailing edge) and also ‘fat’ turbine blades with blunt leading and trailing edge. The inverse design method using unstructured triangular meshes is validated by regeneration of a generic compressor rotor blade geometry subjected to a specified pressure loading and blade thickness. Finally, the method is applied to the design of the tip section of Nasa Rotor 67. The result shows that the design method is very useful in controlling shock waves.

scholarly journals On 3D Inverse Design of Centrifugal Compressor Impellers With Splitter Blades

1998 ◽  
Author(s):  
M. Zangeneh
Keyword(s):  
Centrifugal Compressor ◽  
Design Methodology ◽  
Design Method ◽  
Leading Edge ◽  
Inverse Design ◽  
Conventional Design ◽  
Blade Shape ◽  
Edge Location ◽  
Stacking Condition ◽  
Inverse Design Method

In the design of centrifugal compressor impellers with splitter blades it is quite common to use the same blade shapes on the full and splitter blades with the splitters placed at the mid-pitch location. However, recent results using conventional design methodology have indicated that by moving the pitchwise location of the leading edge of the splitter it is possible to improve splitter performance. In this paper a 3D inverse design method is developed for the design of compressor impellers with splitters. In this design method the blades are designed subject to a specified distribution of the circulation on the full and splitter blades. The paper describes the choice of loading (or derivative of circulation with respect to meridional distance) and stacking condition to limit the complexity of the blade shape. Two different generic impellers are designed with different splitter leading edge location. The performance of these inverse designed impellers is then compared with the corresponding conventional impellers by using a 3D viscous code at design and off-design conditions.

AN INVERSE DESIGN METHOD FOR A WING IN FULL CRUISING CONFIGURATION OF A REGIONAL AIRCRAFT VIA RANS APPROACH

2020 ◽  
Vol 51 (1) ◽  
pp. 1-13
Author(s):  
Anatoliy Longinovich Bolsunovsky ◽  
Nikolay Petrovich Buzoverya ◽  
Nikita Aleksandrovich Pushchin
Keyword(s):  
Design Method ◽  
Inverse Design ◽  
Inverse Design Method
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