Reduced-order steady-state and dynamic models for separation processes. Part II. Application to nonlinear multicomponent systems

AIChE Journal ◽  
1983 ◽  
Vol 29 (2) ◽  
pp. 270-276 ◽  
Author(s):  
Y. S. Cho ◽  
B. Joseph
Keyword(s):  
Steady State ◽  
Dynamic Models ◽  
Multicomponent Systems ◽  
Separation Processes ◽  
Reduced Order

scholarly journals Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 266
Author(s):  
Péter German ◽  
Mauricio E. Tano ◽  
Carlo Fiorina ◽  
Jean C. Ragusa
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Data Driven ◽  
Reduced Order ◽  
Medium Formulation ◽  
Flow Resistances

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

Cyclic Breathing Simulations in Large Scale Models of the Lung Airway From the Oronasal Opening to the Terminal Bronchioles

2012 ◽  
Author(s):  
D. Keith Walters ◽  
Greg W. Burgreen ◽  
Robert L. Hester ◽  
David S. Thompson ◽  
David M. Lavallee ◽  
...  
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Large Scale ◽  
Whole Body ◽  
Patient Specific ◽  
Cfd Simulations ◽  
Reduced Order ◽  
Scale Models ◽  
Steady State Simulation ◽  
Conducting Zone

Computational fluid dynamics (CFD) simulations were performed for unsteady periodic breathing conditions, using large-scale models of the human lung airway. The computational domain included fully coupled representations of the orotracheal region and large conducting zone up to generation four (G4) obtained from patient-specific CT data, and the small conducting zone (to G16) obtained from a stochastically generated airway tree with statistically realistic geometrical characteristics. A reduced-order geometry was used, in which several airway branches in each generation were truncated, and only select flow paths were retained to G16. The inlet and outlet flow boundaries corresponded to the oronasal opening (superior), the inlet/outlet planes in terminal bronchioles (distal), and the unresolved airway boundaries arising from the truncation procedure (intermediate). The cyclic flow was specified according to the predicted ventilation patterns for a healthy adult male at three different activity levels, supplied by the whole-body modeling software HumMod. The CFD simulations were performed using Ansys FLUENT. The mass flow distribution at the distal boundaries was prescribed using a previously documented methodology, in which the percentage of the total flow for each boundary was first determined from a steady-state simulation with an applied flow rate equal to the average during the inhalation phase of the breathing cycle. The distal pressure boundary conditions for the steady-state simulation were set using a stochastic coupling procedure to ensure physiologically realistic flow conditions. The results show that: 1) physiologically realistic flow is obtained in the model, in terms of cyclic mass conservation and approximately uniform pressure distribution in the distal airways; 2) the predicted alveolar pressure is in good agreement with previously documented values; and 3) the use of reduced-order geometry modeling allows accurate and efficient simulation of large-scale breathing lung flow, provided care is taken to use a physiologically realistic geometry and to properly address the unsteady boundary conditions.

Reduced-order steady-state descriptor Kalman fuser weighted by block-diagonal matrices

2008 ◽  
Vol 9 (2) ◽  
pp. 300-309 ◽  
Author(s):  
Zi-Li Deng ◽  
Yuan Gao ◽  
Gui-Li Tao
Keyword(s):  
Steady State ◽  
Reduced Order ◽  
Block Diagonal

Analysis and Control of Torque Split in Hybrid Electric Vehicles by Incorporating Powertrain Dynamics

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Mehran Bidarvatan ◽  
Mahdi Shahbakhti
Keyword(s):  
Steady State ◽  
Energy Consumption ◽  
Energy Management ◽  
Control Strategy ◽  
Hybrid Electric Vehicle ◽  
Internal Combustion Engines ◽  
Dynamic Models ◽  
Management Control ◽  
Drive Cycle ◽  
Hybrid Electric

Hybrid electric vehicle (HEV) energy management strategies usually ignore the effects from dynamics of internal combustion engines (ICEs). They usually rely on steady-state maps to determine the required ICE torque and energy conversion efficiency. It is important to investigate how ignoring these dynamics influences energy consumption in HEVs. This shortcoming is addressed in this paper by studying effects of engine and clutch dynamics on a parallel HEV control strategy for torque split. To this end, a detailed HEV model including clutch and ICE dynamic models is utilized in this study. Transient and steady-state experiments are used to verify the fidelity of the dynamic ICE model. The HEV model is used as a testbed to implement the torque split control strategy. Based on the simulation results, the ICE and clutch dynamics in the HEV can degrade the control strategy performance during the vehicle transient periods of operation by around 8% in urban dynamometer driving schedule (UDDS) drive cycle. Conventional torque split control strategies in HEVs often overlook this fuel penalty. A new model predictive torque split control strategy is designed that incorporates effects of the studied powertrain dynamics. Results show that the new energy management control strategy can improve the HEV total energy consumption by more than 4% for UDDS drive cycle.

Comparison of two model reduction approaches of an industrial drying process

2021 ◽  
Vol 69 (8) ◽  
pp. 667-682
Author(s):  
Marc Oliver Berner ◽  
Martin Mönnigmann
Keyword(s):  
Dynamic Models ◽  
Orthogonal Decomposition ◽  
Wood Chips ◽  
Residual Water ◽  
Balanced Truncation ◽  
Reduced Order Models ◽  
Drying Process ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Many Particles

Abstract Dynamic models have proven to be helpful for determining the residual water content in combustible biomass. However, these models often require partial differential equations, which render simulations impracticable when several thousand particles need to be considered, such as in the drying of wood chips. Reduced-order models help to overcome this problem. We compare proper orthogonal decomposition (POD) based to balanced truncation based reduced-order models. Both reduced models are lean enough for an application to systems with many particles, but the model based on balanced truncation shows more accurate results.

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