Proper orthogonal decomposition assisted inverse design optimisation method for the compressor cascade airfoil

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.

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

Indoor and Built Environment ◽

10.1177/1420326x17718053 ◽

2017 ◽

Vol 27 (10) ◽

pp. 1379-1391 ◽

Cited By ~ 4

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.

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Comparative Study on Modal Decomposition Methods of Unsteady Separated Flow in Compressor Cascade

Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University ◽

10.1051/jnwpu/20203810121 ◽

2020 ◽

Vol 38 (1) ◽

pp. 121-129

Author(s):

Jiawei Hu ◽

Yangang Wang ◽

Hanru Liu ◽

Weixiong Chen ◽

Yong Xu

Keyword(s):

Proper Orthogonal Decomposition ◽

Separated Flow ◽

Decomposition Methods ◽

High Load ◽

Orthogonal Decomposition ◽

Single Frequency ◽

Compressor Cascade ◽

Modal Decomposition ◽

Cascade Flow ◽

Proper Orthogonal

The present work investigated the vortex structure and fluctuation frequency characteristics generated by boundary layer separation of a high-load compressor cascade using modal decomposition methods. The dominant modes and dynamic behaviors of unsteady flow in the cascade were obtained, and the differences of three modal decomposition methods (Proper Orthogonal Decomposition, Dynamic Mode Decomposition and Spectral Proper Orthogonal Decomposition) in feature recognition of cascade flow were discussed. The results show that:(1) The POD method can accurately extract the dominant spatial structure of the flow field, but the modal coefficients are multi-frequency coupled, which makes the dominant modal characteristics of cascade flow unclear. (2) The standard DMD method can obtain the spatial-temporal single frequency mode of cascade flow, as well as their growth rates and frequencies. However, this method is likely to capture the suboptimal mode of large amplitude with large attenuation rate, and fails to obtain the high-frequency coherent structure, which makes it impossible to obtain the dominant feature with limited mode number. (3) The SPOD method, based on spectral characteristics, can obtain spatial and temporal single frequency modes, and there is no modal screening problem. The use of spectral estimation method (SPOD) reduces the sensitivity to numerical noise. This method can obtain the low-rank behavior of cascade flow, which is helpful to understand cascade flow mechanisms. Therefore, SPOD method is more advantageous for the modal analysis of unsteady separated flow in high-load compressor cascade.

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Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition

AIAA Journal ◽

10.2514/1.2159 ◽

2004 ◽

Vol 42 (8) ◽

pp. 1505-1516 ◽

Cited By ~ 248

Author(s):

T. Bui-Thanh ◽

M. Damodaran ◽

K. Willcox

Keyword(s):

Proper Orthogonal Decomposition ◽

Orthogonal Decomposition ◽

Inverse Design ◽

Data Reconstruction ◽

Proper Orthogonal

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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

Volume 8: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A and B ◽

10.1115/imece2007-43461 ◽

2007 ◽

Cited By ~ 1

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.

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

Volume 2B: Turbomachinery ◽

10.1115/gt2015-42876 ◽

2015 ◽

Cited By ~ 1

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.

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