scholarly journals Efficient numerical analysis of transient heat transfer by Consecutive-Interpolation and Proper Orthogonal Decomposition

2019 ◽  
Vol 20 (K9) ◽  
pp. 5-14
Author(s):  
Nguyen Ngoc Minh ◽  
Nguyen Thanh Nha ◽  
Truong Tich Thien ◽  
Bui Quoc Tinh
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Proper Orthogonal Decomposition ◽  
Accurate Solution ◽  
Orthogonal Decomposition ◽  
Transient Heat Transfer ◽  
Computational Time ◽  
Gradient Fields ◽  
Order Increase ◽  
Proper Orthogonal

The consecutive-interpolation technique has been introduced as a tool enhanced into traditional finite element procedure to provide higher accurate solution. Furthermore, the gradient fields obtained by the proposed approach, namely consecutive-interpolation finite element method (CFEM), are smooth, instead of being discontinuous across nodes as in FEM. In this paper, the technique is applied to analyze transient heat transfer problems. In order increase time efficiency, a model- reduction technique, namely the proper orthogonal decomposition (POD), is employed. The idea is that a given large-size problem is projected into a small-size one which can be solved faster but still maintain the required accuracy. The optimal POD basis for projection is determined by mathematical operations. With the combination of the two novel techniques, i.e. consecutive-interpolation and proper orthogonal decomposition, the advantages of numerical solution obtained by CFEM are expected to be maintained, while computational time can be significantly saved.

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.

Reduced-Order Model of Unsteady Flows in a Turbomachinery Fan Modeled Using a Novel Proper Orthogonal Decomposition

2019 ◽  
Author(s):  
Elizabeth H. Krath ◽  
Forrest L. Carpenter ◽  
Paul G. A. Cizmas ◽  
David A. Johnston
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Reference Conditions ◽  
Stable Solution ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Computational Time ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Model Rotor

Abstract This paper presents a novel, more efficient reduced-order model based on the proper orthogonal decomposition (POD) for the prediction of flows in turbomachinery. To further reduce the computational time, the governing equations were written as a function of specific volume instead of density. This allowed for the pre-computation of the coefficients of the system of ordinary differential equations that describe the reduced-order model. A penalty method was developed to implement time-dependent boundary conditions and achieve a stable solution for the reduced-order model. Rotor 67 was used as a validation case for the reduced-order model, which was tested for both on- and off-reference conditions. This reduced-order model was shown to be more than 10,000 times faster than the full-order model.

Vibratory Parameters of Blades From Coordinate Measurement Machine (CMM) Data

2005 ◽  
Author(s):  
Alok Sinha ◽  
Benjamin Hall ◽  
Brice Cassenti ◽  
Gary Hilbert
Keyword(s):  
Finite Element ◽  
Proper Orthogonal Decomposition ◽  
Natural Frequencies ◽  
Orthogonal Decomposition ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of a procedure to model geometric variations of blades. Specifically, vibratory parameters of blades are extracted from CMM data on an integrally bladed rotor (IBR). The method is based on proper orthogonal decomposition (POD) of CMM data, solid modeling and finite element techniques. In addition to obtaining natural frequencies and mode shapes of each blade on an IBR, statistics of these modal parameters are also computed and characterized. Numerical results are validated by comparison with experimental results.

Systematic Characterization of Coupled Structural-Acoustic Systems With the Aid of Temporal and Spectral (Complex) Proper Orthogonal Decomposition

2008 ◽  
Author(s):  
Christos I. Papadopoulos ◽  
Ioannis T. Georgiou
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Proper Orthogonal Decomposition ◽  
Transient Response ◽  
Degrees Of Freedom ◽  
Sound Propagation ◽  
Orthogonal Decomposition ◽  
Pod Analysis ◽  
Proper Orthogonal ◽  
Spectral Complex

We extend the application of temporal and spectral Proper Orthogonal Decomposition (POD) to study the sound propagation and sound-structure interaction of systems combined of acoustic and structural subsystems. We consider a prototypical system consisted of two adjacent rooms separated by a sound insulating plate. Approximation to the steady-state and transient response is obtained with the aid of the finite element method. We define the temporal (real) and spectral (complex) variations of POD to tackle acoustical and structural degrees of freedom. We apply the method to process the numerical databases of the finite element solutions. It is shown that the steady-state and transient response may be represented by a small number of dominant POD modes. The extracted frequencies and spatial shapes are evaluated and linked to the modal properties of the system. It is shown that POD analysis may provide significant insight on the properties of coupled structural-acoustic systems.

Analysis of Nonlinear Aeroelastic Panel Response Using Proper Orthogonal Decomposition

2004 ◽  
Vol 126 (3) ◽  
pp. 416-421 ◽  
Author(s):  
Sean A. Mortara ◽  
Joseph Slater ◽  
Philip Beran
Keyword(s):  
Differential Equations ◽  
Proper Orthogonal Decomposition ◽  
Model Reduction ◽  
State Space ◽  
Space Form ◽  
Reduction Technique ◽  
Orthogonal Decomposition ◽  
Computational Time ◽  
Model Reduction Technique ◽  
Proper Orthogonal

The nonlinear panel flutter problem solved by Dowell in 1966 is used to investigate the new application of the proper orthogonal decomposition model reduction technique to aeroelastic analysis. Emphasis is placed on the nonlinear structural dynamic equations with nonconservative forcing modeled assuming a supersonic, inviscid flow. Here the aeroelastic coupled equation is presented in discrete form using a finite difference approach, and subsequently in state space form, to be integrated as a set of first order differential equations. In this paper, a POD approach is developed for generalized second-order differential equations; however, the application of POD to the governing equations in state space form is also discussed. This study compares the results and effectiveness of the model reduction technique for integration of the full set of degrees of freedom. The solution is compared to Dowell’s classic results which forms the base reference for the model reduction study. The reduced order model is then created from the full simulation model. Accuracy of the solution, reduced computational time, limits of stability, and the strengths and weaknesses of the model reduction are investigated.

scholarly journals Direct synthesis of equivalent circuits from reduced FE models using proper orthogonal decomposition

2016 ◽  
Vol 35 (6) ◽  
pp. 2035-2044 ◽  
Author(s):  
Toshihito Shimotani ◽  
Yuki Sato ◽  
Hajime Igarashi
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fe Analysis ◽  
Electric Machines ◽  
Orthogonal Decomposition ◽  
Computational Time ◽  
Equivalent Circuits ◽  
Fe Model ◽  
Content Type ◽  
Electromagnetic Devices ◽  
Proper Orthogonal

Purpose The purpose of this paper is to propose a fast synthesis method of the equivalent circuits of electromagnetic devices using model order reduction. Finite element method (FEM) has been widely used to design electromagnetic devices. For FE analysis of these devices connected to control and deriving circuits, FE equations coupled with the circuit equations have to be solved for many times in their design processes. If the FE models are replaced by equivalent circuit models, computational time could be drastically reduced. Design/methodology/approach In the proposed method, a reduced FE model is obtained using proper orthogonal decomposition (POD) in which the size of FE equation is effectively reduced so that the computational time for FE analysis is shortened. Then, the equivalent circuits are directly synthesized from the admittance function of the reduced system. Findings Accuracy and computational efficiency of the proposed method are compared with those of another POD-based method in which the equivalent circuits are synthesized from fitting of frequency characteristics using optimization algorithm. There are no significant differences in the accuracy of both methods, while the speedup ratio of the former method is found larger than that for the latter method for the same sampling points. Originality/value The equivalent circuits of electric machines and devices have been synthesized on the basis of physical insight of engineers. This paper proposes a novel method by which the equivalent circuits are automatically synthesized from FE model of the electric machines and devices using POD.

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