Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
R. Maffulli ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Time Derivative ◽  
Computational Cost ◽  
Strong Impact ◽  
Time Step ◽  
Time Stepping ◽  
Adaptive Time ◽  
Fully Coupled ◽  
Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

2018 ◽  
Author(s):  
R. Maffulli ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Time Derivative ◽  
Computational Cost ◽  
Strong Impact ◽  
Time Step ◽  
Time Stepping ◽  
Adaptive Time ◽  
Fully Coupled ◽  
Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully-coupled time-accurate unsteady Conjugate Heat Transfer (CHT) results under these conditions would require to march in both domains using the time step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that removes these requirements through a source-term based modelling approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

AN ADAPTIVE TIME-STEPPING PROCEDURE BASED ON THE SCALED BOUNDARY FINITE ELEMENT METHOD FOR ELASTODYNAMICS

2012 ◽  
Vol 09 (01) ◽  
pp. 1240007 ◽  
Author(s):  
Z. H. ZHANG ◽  
Z. J. YANG ◽  
GUOHUA LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Local Error ◽  
Error Estimator ◽  
Time Step ◽  
Time Stepping ◽  
Time Increment ◽  
Adaptive Time ◽  
Adaptive Time Stepping ◽  
Scaled Boundary Finite Element

This study develops an adaptive time-stepping procedure of Newmark integration scheme for transient elastodynamic problems, based on the semi-analytical scaled boundary finite element method (SBFEM). In each time step, a posteriori local error estimator based on the linear distributed acceleration is employed to estimate the error caused by the time discretization. The total energy of the domain, consisting of the kinetic energy and the strain energy, is calculated semi-analytically. The time increment is automatically adjusted according to a simple criterion. Three examples with stress wave propagation were modeled. The numerical results show that the developed method is capable of limiting the local error estimator within specified targets by using an optimal time increment in each time step.

Parameter-Free Time Adaptivity Based on Energy Evolution for the Cahn-Hilliard Equation

2016 ◽  
Vol 19 (5) ◽  
pp. 1542-1563 ◽  
Author(s):  
Fuesheng Luo ◽  
Tao Tang ◽  
Hehu Xie
Keyword(s):  
Large Time ◽  
Main Idea ◽  
Energy Evolution ◽  
Time Step ◽  
Time Stepping ◽  
Hilliard Equation ◽  
Phase Field Models ◽  
Adaptive Time ◽  
Cahn Hilliard Equation ◽  
Adaptive Time Stepping

AbstractIt is known that large time-stepping method are useful for simulating phase field models. In this work, an adaptive time-stepping strategy is proposed based on numerical energy stability and equi-distribution principle. The main idea is to use the energy variation as an indicator to update the time step, so that the resulting algorithm is free of user-defined parameters, which is different from several existing approaches. Some numerical experiments are presented to illustrate the effectiveness of the algorithms.

scholarly journals Development of a Balanced Adaptive Time-Stepping Strategy Based on an Implicit JFNK-DG Compressible Flow Solver

2021 ◽  
Author(s):  
Yu Pan ◽  
Zhen-Guo Yan ◽  
Joaquim Peiró ◽  
Spencer J. Sherwin
Keyword(s):  
High Efficiency ◽  
Total Error ◽  
Steady State Flow ◽  
Time Step ◽  
Spatial Error ◽  
Flow Solver ◽  
Time Stepping ◽  
Adaptive Time ◽  
Temporal And Spatial ◽  
Adaptive Time Stepping

AbstractA balanced adaptive time-stepping strategy is implemented in an implicit discontinuous Galerkin solver to guarantee the temporal accuracy of unsteady simulations. A proper relation between the spatial, temporal and iterative errors generated within one time step is constructed. With an estimate of temporal and spatial error using an embedded Runge-Kutta scheme and a higher order spatial discretization, an adaptive time-stepping strategy is proposed based on the idea that the time step should be the maximum without obviously influencing the total error of the discretization. The designed adaptive time-stepping strategy is then tested in various types of problems including isentropic vortex convection, steady-state flow past a flat plate, Taylor-Green vortex and turbulent flow over a circular cylinder at $${Re}=3\,900$$ Re = 3 900 . The results indicate that the adaptive time-stepping strategy can maintain that the discretization error is dominated by the spatial error and relatively high efficiency is obtained for unsteady and steady, well-resolved and under-resolved simulations.

Towards developing an adaptive time stepping for compressible unsteady flows

2019 ◽  
Vol 29 (2) ◽  
pp. 487-503 ◽  
Author(s):  
Nikhil Kalkote ◽  
Ashwani Assam ◽  
Vinayak Eswaran
Keyword(s):  
Error Control ◽  
Transient Flow ◽  
Stokes Equations ◽  
Local Error ◽  
Time Step ◽  
Content Type ◽  
Time Stepping ◽  
Adaptive Time ◽  
Time Accuracy ◽  
Adaptive Time Stepping

Purpose The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive time-stepping (ATS)-based local error control instead of CFL-based time-stepping technique. Also, an all-speed flow algorithm is implemented with simple low dissipation AUSM convective scheme, which can be computed without preconditioning which in general destroys the time accuracy. Design/methodology/approach In transient flow computations, the time-step is generally determined from the CFL condition. In this paper, the authors demonstrate the usefulness of ATS based on local time-stepping previously used extensively in ordinary differential equations (ODE) integration. This method is implemented in an implicit framework to ensure the numerical domain of dependence always contains the physical domain of dependence. Findings In this paper, the authors limit their focus to capture the unsteady physics for three cases: Sod’s shock-tube problem, Stokes’ second problem and a circular cylinder. The use of ATS with local truncation error control enables the solver to use the maximum allowable time-step, for the prescribed tolerance of error. The algorithm is also capable of converging very rapidly to the steady state (if there is any) after the initial transient phase. The authors present here only the first-order time-stepping scheme. An algorithmic comparison is made between the proposed adaptive time-stepping method and the commonly used dual time-stepping approach that indicates the former will be more efficient. Originality/value The original method of ATS based on local error control is used extensively in ODE integration, whereas, this method is not so popular in the computational fluid dynamics (CFD) community. In this paper, the authors investigate its use in the unsteady CFD computations. The authors hope that it would provide CFD researchers with an algorithm based on an adaptive time-stepping approach for unsteady calculations.

scholarly journals An error-controlled adaptive time-stepping method for particle advancement in coupled CFD-DEM simulations

2021 ◽  
Vol 379 ◽  
pp. 203-216
Author(s):  
Hariswaran Sitaraman ◽  
Deepthi Vaidhynathan ◽  
Ray Grout ◽  
Thomas Hauser ◽  
Christine M. Hrenya ◽  
...  
Keyword(s):  
Time Stepping ◽  
Dem Simulations ◽  
Adaptive Time ◽  
Adaptive Time Stepping

Unsteady Conjugate Heat Transfer Investigation of a Multistage Steam Turbine in Warm-Keeping Operation With Hot Air

2018 ◽  
Author(s):  
Piotr Łuczyński ◽  
Dennis Toebben ◽  
Manfred Wirsum ◽  
Wolfgang F. D. Mohr ◽  
Klaus Helbig
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Flow Patterns ◽  
Operating Conditions ◽  
Angle Of Incidence ◽  
Time Step ◽  
Hot Air ◽  
Wide Range ◽  
Vortex Systems ◽  
Operating Points

In recent decades, the rising share of commonly subsidized renewable energy especially affects the operational strategy of conventional power plants. In pursuit of flexibility improvements, extension of life cycle, in addition to a reduction in start-up time, General Electric has developed a product to warm-keep high/intermediate pressure steam turbines using hot air. In order to optimize the warm-keeping operation and to gain knowledge about the dominant heat transfer phenomena and flow structures, detailed numerical investigations are required. Considering specific warm-keeping operating conditions characterized by high turbulent flows, it is required to conduct calculations based on time-consuming unsteady conjugate heat transfer (CHT) simulations. In order to investigate the warm-keeping process as found in the presented research, single and multistage numerical turbine models were developed. Furthermore, an innovative calculation approach called the Equalized Timescales Method (ET) was applied for the modeling of unsteady conjugate heat transfer (CHT). The unsteady approach improves the accuracy of the stationary simulations and enables the determination of the multistage turbine models. In the course of the research, two particular input variables of the ET approach — speed up factor (SF) and time step (TS) — have been additionally investigated with regard to their high impact on the calculation time and the quality of the results. Using the ET method, the mass flow rate and the rotational speed were varied to generate a database of warm-keeping operating points. The main goal of this work is to provide a comprehensive knowledge of the flow field and heat transfer in a wide range of turbine warm-keeping operations and to characterize the flow patterns observed at these operating points. For varying values of flow coefficient and angle of incidence, the secondary flow phenomena change from well-known vortex systems occurring in design operation (such as passage, horseshoe and corner vortices) to effects typical for windage, like patterns of alternating vortices and strong backflows. Furthermore, the identified flow patterns have been compared to vortex systems described in cited literature and summarized in the so-called blade vortex diagram. The comparison of heat transfer in the form of charts showing the variation of the Nusselt-numbers with respect to changes in angle of incidence and flow coefficients at specific operating points is additionally provided.

An Adaptive Time Stepping Method for Transient Dynamic Response Analysis

2016 ◽  
Vol 6 (2) ◽  
pp. 152-170
Author(s):  
Jianguo Huang ◽  
Huashan Sheng
Keyword(s):  
Dynamic Response ◽  
Response Analysis ◽  
Dynamic Response Analysis ◽  
Transient Dynamic ◽  
Time Stepping ◽  
Adaptive Time ◽  
Spatial Discretisation ◽  
Transient Dynamic Response ◽  
Adaptive Time Stepping ◽  
Reduced Problem

AbstractAn efficient adaptive time stepping method is proposed for transient dynamic response analysis, which is frequently encountered in civil engineering and elsewhere. The reduced problem following the spatial discretisation can be discretised in the time by a C0-continuous discontinuous Galerkin method, and the adaptive time stepping strategy is based on optimal a posteriori error estimates developed using the energy method. Some numerical experiments demonstrate the effectiveness of our approach.

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