scholarly journals A Comprehensive CFD Model for Dual-Phase Brass Indirect Extrusion Based on Constitutive Laws: Assessment of Hot-Zone Formation and Failure Prognosis

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 1043 ◽  
Author(s):  
George Pashos ◽  
George Pantazopoulos ◽  
Ioannis Contopoulos
Keyword(s):  
Stokes Equations ◽  
Metal Flow ◽  
Computational Cost ◽  
Constitutive Laws ◽  
Reduced Order Model ◽  
Preliminary Evaluation ◽  
Order Model ◽  
Zone Formation ◽  
Reduced Order ◽  
Prediction And Prevention

A numerical method for the precise calculation of temperature, velocity and pressure profiles of the α-β brass indirect hot extrusion process is presented. The method solves the Navier–Stokes equations for non-Newtonian liquids with strain-rate and temperature-dependent viscosity that is formulated using established constitutive laws based on the Zener–Hollomon type equation for plastic flow stress. The method can be implemented with standard computational fluid dynamics (CFD) software, has relatively low computational cost, and avoids the numerical artifacts associated with other methods commonly used for such processes. A response surface technique is also implemented, and it is thus possible to build a reduced order model that approximately maps the process with respect to all combinations of its parameters, including the extrusion speed and brass phase constitution. The reduced order model can be a very useful tool for production, because it instantaneously provides important quantities, such as the average pressure or the temperature of hot-spots that are formed due to the combined effect of die/billet friction and the generation of heat from plastic deformation (adiabatic shear deformation heating). This approach can assist in the preliminary evaluation of the metal flow pattern, and in the prediction and prevention of critical extrusion failures, thus leading to subsequent process and product quality improvements.

A Reduced-Order Model for Turbomachinery Flows Using Proper Orthogonal Decomposition

2013 ◽  
Author(s):  
Thomas A. Brenner ◽  
Forrest L. Carpenter ◽  
Brian A. Freno ◽  
Paul G. A. Cizmas
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Computational Cost ◽  
Wheel Speed ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Computational Time ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal

This paper presents the development of a reduced-order model based on the proper orthogonal decomposition (POD) method. The POD method has been developed to predict turbomachinery flows modeled by the Reynolds-averaged Navier–Stokes equations. The purpose of using a POD-based reduced-order model is to decrease the computational cost of turbomachinery flows. The POD model has been tested for two configurations: a canonical channel with a bump case and the transonic NASA Rotor 67 case. The Rotor 67 case has been simulated at design wheel speed and at three off-design conditions: 70, 80, and 90% of the wheel speed. The results of the POD-based reduced-order model where in excellent agreement with the full-order model results. The computational time of the reduced-order model was approximately one order of magnitude smaller than that of the full-order model.

Using Functional Gains for Optimal Sensor Placement in Fluid-Structure Interaction

2009 ◽  
Author(s):  
Imran Akhtar ◽  
Jeff Borggaard ◽  
John A. Burns ◽  
Lizette Zietsman
Keyword(s):  
Differential Equations ◽  
Stokes Equations ◽  
Reduced Order Model ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Mean Flow ◽  
Order Model ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Functional Gains

Functional gains are integral kernels of the standard feedback operator and are useful in control of partial differential equations (PDEs). These functional gains provide physical insight into how the control mechanism is operating. In some cases, these functional gains can provide information about the optimal placement of actuators and sensors. The study is motivated by fluid flow control and focuses on the computation of these functions. However, for practical purposes, one must be able to compute these functions for a wide variety of PDEs. For higher dimensional systems, computing these gains is at least as challenging as the original simulation problem. To reduce the complexity of the governing equations, reduced-order models are often developed by reducing the PDEs to ordinary-differential equations (ODEs). In this study, we use proper orthogonal decomposition (POD)-Galerkin based approach and develop a reduced-order model of a bluff body wake. We solve the incompressible Navier-Stokes equations, simulate the flow past a circular cylinder, and record the snapshots of the flow field. We compute the POD eigenfunctions and project the Navier-Stokes equations onto these few of these eigenfunctions to develop a reduced-order model. Later, we modify the model by introducing a control function simulating suction actuation on the cylinder surface. We linearize the model about the mean flow and apply feedback control to suppress vortex shedding. We then compute the functional gains for the applied control. We identify these gains at various stations in the wake region and suggest optimum locations for the sensors.

Computationally Efficient Approaches to Simulate the Dynamics of Microbeams Under Mechanical Shock

2006 ◽  
Author(s):  
Mohammad I. Younis ◽  
Danial Jordy ◽  
James M. Pitarresi
Keyword(s):  
Hybrid Approach ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Beam Model ◽  
Mechanical Shock ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Dynamic Loading Conditions

We present computationally efficient models and approaches and utilize them to investigate the dynamics of microbeams under mechanical shock. We explore using a hybrid approach utilizing a beam model combined with the shock spectrum of a spring-mass-damper model. We conclude that this approach is computationally efficient and yields accurate results in both quasi-static and dynamic loading conditions. We utilize a reduced-order model based on the nonlinear Euler-Bernoulli beam model. We demonstrate that this model is capable of capturing accurately the dynamic behavior of microbeams under shock pulses of various amplitudes (low-g and high-g), in various damping conditions, structural boundaries (clamped-clamped and clamped-free), and can capture both linear and nonlinear behavior. We investigate high-g loading cases. We report significant increase in the computational cost of simulations when using traditional nonlinear finite-element models because of the activation of higher-order modes. We demonstrate that the developed reduced-order model can be very efficient in such cases.

scholarly journals Development of a Reduced Order Model for Fuel Burnup Analysis

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 890 ◽  
Author(s):  
Christian Castagna ◽  
Manuele Aufiero ◽  
Stefano Lorenzi ◽  
Guglielmo Lomonaco ◽  
Antonio Cammi
Keyword(s):  
Methodological Approach ◽  
Computational Cost ◽  
Reaction Rates ◽  
Reduced Order Model ◽  
Fuel Burnup ◽  
Order Model ◽  
Reduced Order ◽  
Solution Accuracy ◽  
Proper Orthogonal ◽  
Over Time

Fuel burnup analysis requires a high computational cost for full core calculations, due to the amount of the information processed for the total reaction rates in many burnup regions. Indeed, they reach the order of millions or more by a subdivision into radial and axial regions in a pin-by-pin description. In addition, if multi-physics approaches are adopted to consider the effects of temperature and density fields on fuel consumption, the computational load grows further. In this way, the need to find a compromise between computational cost and solution accuracy is a crucial issue in burnup analysis. To overcome this problem, the present work aims to develop a methodological approach to implement a Reduced Order Model (ROM), based on Proper Orthogonal Decomposition (POD), in fuel burnup analysis. We verify the approach on 4 years of burnup of the TMI-1 unit cell benchmark, by reconstructing fuel materials and burnup matrices over time with different levels of approximation. The results show that the modeling approach is able to reproduce reactivity and nuclide densities over time, where the accuracy increases with the number of basis functions employed.

Projection-based and neural-net reduced order model for nonlinear Navier–Stokes equations

2021 ◽  
Vol 89 ◽  
pp. 1294-1315
Author(s):  
My Ha Dao ◽  
Hoang Huy Nguyen ◽  
Chin Chun Ooi ◽  
Quang Tuyen Le
Keyword(s):  
Stokes Equations ◽  
Reduced Order Model ◽  
Navier Stokes ◽  
Neural Net ◽  
Order Model ◽  
Navier Stokes Equations ◽  
Reduced Order

scholarly journals Time Stable Reduced Order Modeling by an Enhanced Reduced Order Basis of the Turbulent and Incompressible 3D Navier–Stokes Equations

2019 ◽  
Vol 24 (2) ◽  
pp. 45 ◽  
Author(s):  
Nissrine Akkari ◽  
Fabien Casenave ◽  
Vincent Moureau
Keyword(s):  
Stokes Equations ◽  
A Priori ◽  
Order Reduction ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Navier Stokes ◽  
Reduced Basis ◽  
Order Model ◽  
Navier Stokes Equations ◽  
Reduced Order

In the following paper, we consider the problem of constructing a time stable reduced order model of the 3D turbulent and incompressible Navier–Stokes equations. The lack of stability associated with the order reduction methods of the Navier–Stokes equations is a well-known problem and, in general, it is very difficult to account for different scales of a turbulent flow in the same reduced space. To remedy this problem, we propose a new stabilization technique based on an a priori enrichment of the classical proper orthogonal decomposition (POD) modes with dissipative modes associated with the gradient of the velocity fields. The main idea is to be able to do an a priori analysis of different modes in order to arrange a POD basis in a different way, which is defined by the enforcement of the energetic dissipative modes within the first orders of the reduced order basis. This enables us to model the production and the dissipation of the turbulent kinetic energy (TKE) in a separate fashion within the high ranked new velocity modes, hence to ensure good stability of the reduced order model. We show the importance of this a priori enrichment of the reduced basis, on a typical aeronautical injector with Reynolds number of 45,000. We demonstrate the capacity of this order reduction technique to recover large scale features for very long integration times (25 ms in our case). Moreover, the reduced order modeling (ROM) exhibits periodic fluctuations with a period of 2 . 2 ms corresponding to the time scale of the precessing vortex core (PVC) associated with this test case. We will end this paper by giving some prospects on the use of this stable reduced model in order to perform time extrapolation, that could be a strategy to study the limit cycle of the PVC.

A Nonlinear Reduced-Order Model for Electrostatic MEMS

2003 ◽  
Author(s):  
Eihab M. Abdel-Rahman ◽  
Mohammad I. Younis ◽  
Ali H. Nayfeh
Keyword(s):  
Equations Of Motion ◽  
Computational Cost ◽  
Design Tool ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Design Parameters ◽  
Mems Devices ◽  
Order Model ◽  
Reduced Order ◽  
Galerkin Procedure

We present an analytical approach and a reduced-order model (macromodel) to investigate the behavior of electrically actuated microbeam-based MEMS. The macromodel provides an effective and accurate design tool for this class of MEMS devices. The macromodel is obtained by discretizing the distributed-parameter system using a Galerkin procedure into a finite-degree-of-freedom system consisting of ordinary-differential equations in time. The macromodel accounts for moderately large deflections, dynamic loads, and the coupling between the mechanical and electrical forces. It accounts for linear and nonlinear elastic restoring forces and the nonlinear electric forces generated by the capacitors. A new technique is developed to represent the electric force in the equations of motion. The new approach allows the use of few linear-undamped mode shapes of a microbeam in its straight position as basis functions in a Galerkin procedure. The macromodel is validated by comparing its results with experimental results and finiteelement solutions available in the literature. Our approach shows attractive features compared to finite-element softwares used in the literature. It is robust over the whole device operation range up to the instability limit of the device (i.e., pull-in). Moreover, it has low computational cost and allows for an easier understanding of the influence of the various design parameters. As a result, it can be of significant benefit to the development of MEMS design software.

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