In this paper; reduced order modeling (ROM) of unsteady two-phase flows is performed based upon two-fluid models and a Proper-Orthogonal Decomposition (POD) method. The four-equation two-phase flow model is used as a mathematical model to describe physics of the problem. After presenting the governing equations, direct numerical solution of the problem is introduced using AUSMDV* method. Then, the POD method is introduced as a mathematical tool to reduce computational time of the transient problems. In the present research, an equation free/Galerkine free POD method is used for ROM of the unsteady two-phase flows. In this approach, the singular value Decomposition (SVD) method is used to compute the base vectors of the reduced space. A shock tube and water-air separation two-phase problems are solved using the present ROM method. Results show that this approach can reduce computational time of unsteady simulations about 35%. Reduction of the computational time directly depends on the size of the computational gird. The results also indicate that application of POD method on the fine grids is more efficient than on the coarse grids.

The occurrence and development of the dominant unsteady flow structures in a vanless centrifugal pump impeller are revealed by the Proper Orthogonal Decomposition (POD) method. The pressure and velocity data of four radial surfaces is selected as the variables of Decomposition. The results show that this method is beneficial to the analysis of flow field when there is no strong interaction of flow structures. When the flow rate starts to decrease from the design flow rate, unstable flow phenomenon such as flow separation and wake begin to appear and develop in the impeller. The POD analysis reveals the influence of the main unsteady structures on the flow field when there is no mixed or have little interaction among flow structures. It outlines the development of flow separation near the suction side of impeller and the wake near the trailing edge as the flow rate changes. However, the flow field inside the impeller becomes more and more complex as the operation condition is far away from the design condition, which needs to be combined with other methods to better analyze the flow field.

This paper investigates the performance of a non-symmetric airfoil in a perturbed flow for a low Reynolds number by creating small vortical structures. A newly designed two-dimensional numerical tool is used to examine the interaction between the NACA 23015 airfoil and the vortex shedding from a square cylinder. Different airfoil position ratios are numerically simulated concerning the square cylinder G/D (D: square cylinder diameter), the channel centerline T/d (d=D/2), and the vortices scale size D/c (c: airfoil chord length). Results show that the maximum values of the lift and drag aerodynamic coefficients are influenced by the airfoil’s lateral and longitudinal positions. The Proper Orthogonal Decomposition (POD) method is used to identify the most energetic flow structures. For all simulated scenarios, it was found that the first two modes reflect the dominating coherent structures in the flow field. The results also show that a leading-edge vortex is formed over the airfoil. The observed phenomena of symmetric and antisymmetric shedding vortex mechanisms essentially depend on the lateral distance of the airfoil T/d and the vortex scale size D/c. However, the spectral analysis demonstrates that the shedding frequency mainly depends on the gap distance G/D.

Determining the modal characteristics of structures such as natural frequencies and damping ratios is one of the most important issues in structural engineering. In this regard, providing a low-cost and robust experimental method against all types of noises is very important. In the present paper, a new algorithm for determining the natural frequencies and damping ratios of structures under impact loads using the Proper Orthogonal Decomposition technique is presented. This method uses the vibrational response of the structure to impact loads, without the need to calculate the impact magnitude. One of the strength points of the proposed methodology is the accumulation of laboratory noises in the latest modes. In other words, in the process of calculating the frequencies related to the first few modes, laboratory noise does not enter the calculations and will be aggregated in higher modes that are less important. The feasibility and efficiency of the new method was evaluated using numerical simulations as well as laboratory validation. In this research, four pure numerical models were used to evaluate and validate the accuracy of the proposed algorithm. These models include a simply supported beam, a two-dimensional portal frame, a three-dimensional truss and a clambed-clambed beam. The natural frequencies and damping ratios of the mentioned models were calculated using the new method, then the results were compared with those that obtained from the finite element method. Very good agreement was observed between the results of the two methods. For further investigation, various states such as the effect of the noise on the results, the effect of multiple impact loads and the effect of the number of sensors were also studied. The results of these numerical studies showed that the proposed method is very stable and robust against laboratory noises and has small errors. Acceptable results can be obtained in using a few numbers of sensors (even one sensor) and repetition of the test. Also, the results for multiple impact loads are almost similar to the results obtained from the excited state with a simple impulse load. In this study, in order to further investigate the efficiency of the POD based method, a small-scale laboratory model developed at Shahid Rajaee Teacher Training University and whose modal information has already been calculated using the closed image processing method, was studied. Good agreement was observed between the results of the two methods, so it can be another reason for the efficiency and capability of the new method. Based on various studies, it was concluded that for structures with low damping, the proposed method has acceptable accuracy and with increasing damping, the accuracy of the results gradually decreases. Since conventional structures have a relatively low attenuation, the proposed algorithm is very suitable for determining their modal information. The proposed method due to the availability, cheapness and no need for complex experimental tools can be used as a useful algorithm to determine the modal information of a structure as well as control the results obtained from other experimental methods.

Modeling and simulation are useful tools to optimize and analyze the dynamic behavior of leadacid batteries. One of the main problems is that the governing equations of lead-acid batteries are highly coupled, which significantly increases the computational time of numerical methods in simulations. Using reduced order models (ROM) is one of the best ways to overcome this difficulty. In the present study, the one-dimensional electrochemical governing equations of leadacid battery are solved using model order reduction based on Proper Orthogonal Decomposition (POD). To show the capability of this method, the governing equations including conservation of charge in solid and liquid phases and conservation of species are solved simultaneously for a leadacid cell during discharge, rest and charge process. The results of reduced order model including cell voltage, acid concentration and state of charge (SoC) are compared to the results of finite volume method (FVM). The obtained numerical results show that not only does the POD-based ROM of lead-acid battery significantly decrease the computational time (speed-up factor of 15), but also there is excellent agreement with the results of previous computational fluid dynamic (CFD) models.

This study deals with inverse approach for damage detection in a double-beam system. A double-beam system made of two parallel beams connected through an elastic layer. Degradation in stiffness of beams element, crack occurrence and partly destruction of inner layer has been considered as different types of damage. The time domain acceleration response of the system measured and Proper Orthogonal Decomposition has been applied to the collected data in order to derive the Proper Orthogonal values (POV) and Proper Orthogonal modes (POM) of the system. Effect of single damage in different locations on the POV has been analyzed and an objective function has been defined using the dominant POV and POM of each beam separately. In order to increase robustness of the method against noise, the objective function enriched by adding statistical Property of time domain response. The teaching-learning based optimization algorithm has been employed to solve optimization problem. Efficiency of the proposed method for detecting single and multiple damages in the system demonstrated with and without noise. Simulation results show good accuracy of the proposed method for detection single and multiple damages of different types in the system.

The radiative transfer equation models the thermal radiation in a participating medium. Except in specified cases, there is no analytical solution for this equation. Solving the radiative transfer equation with numerical methods is usually time-consuming. This work presents a fast method based on Proper Orthogonal Decomposition to solve the radiative transfer equation. Some variables are selected as independent parameters. The radiative transfer equation for the specified value of these parameters is solved using the discrete ordinates method, and the system responses form the snapshot matrix. The matrix is decomposed singular value Decomposition as a product of three matrices. Due to the magnitude of singular values, only a few first columns of these matrices are selected. As a result, the degrees of freedom of the original system are decreased, and a reduced-order model is created. Employing the radial basis functions, the system response, corresponding to any arbitrary input vector (independent parameters), can be approximated with high speed. The results show that the reduced-order method has high accuracy compared to the numerical solution. The complexities of the system do not affect the reduced-order method. Regardless of the characteristics of the medium (the value of independent parameters), the solution time is the order of 0.02 seconds.

Background and Objective: Dams play an important role in development of countries by drinking and agricultural water supply, flood control, hydropower energy supply and recreational purposes. Constructing a dam and making an artificial lake has an important effect on surrounding environment, so being able to forecast the inflow to the dam is an important issue for water resource management. Method: In this study artificial neural network (ANN) was applied to forecast the monthly inflow from Soofichai River to Alavian Dam. Regarding the huge amount of input data to ANN model and for optimizing its application, Proper Orthogonal Decomposition (POD) was used in order to determine the best inputs for ANN model. Finally, the application of ANN and POD-ANN models was evaluated by determination coefficient (R2), mean absolute error (MAE) and average of absolute relative error (AARE). Findings: Results of ANN and POD-ANN models indicated that although ANN output is close to the observed values of inflow to the dam, but it has significant errors. POD-ANN model showed better results than ANN model for high values of inflow. In generall, comparing R2, MAE and AARE values of two models revealed that POD-ANN model had better performance in both calibration and verification steps in comparison with ANN model. R2, MAE and AARE in verification step of PODANN model were 0. 93, 0. 79, and 0. 54, respectively. Discussion and Conclusion: Preprocessing data contributes to better performance of POD-ANN than ANN model, especially in high values of inflow. Therefore, it can be concluded that applying data preprocessing and reducing inputs to ANN model enhances its performance.

This paper presents the Large-Eddy-Simulation (LES) of two-phase turbulent thermo-magnetic convection of ferrofluid (water-Fe3O4) within a cubic cavity. The current two-phase model considers Brownian, thermophoresis, magnetophoresis, and eddy diffusions in the dispersion of ferromagnetic particles. Two parallel electrical wires influence ferrofluid flow. The numerical computations are performed by utilizing the finite volume method for three different magnetic numbers (i.e. Mnf=0, 1.4×1010 and 1.4×1010). For all numerical calculations, particle volume fraction and Rayleigh are held constant at 0.04 and 108, respectively. Based on the heat transfer analysis, a magnetic field with a strength of 5.6×1010 enhances the Nusselt number by 16.67%. Observed increases in heat transfer can probably be attributed to the Kelvin force induced by the magnetic field, which affects the coherent structures of the flow. Using the Proper Orthogonal Decomposition (POD) method, coherent structures are extracted from velocity and pressure fluctuations. Further, the time coefficients of the first three modes are extracted for the pressure fluctuation. According to the results, the applied magnetic field reduces the cumulative energy of modes and increases the number of modes required to reconstruct a given amount of flow. The coherent structures also change from plane to spanwise roll structures with increasing magnetic number. The energy content of the first three modes decreases from 98.7% to 73% as the magnetic field increases from Mnf=0 to 1.4×1010.