A Comparison of Strong and Weak Coupling Schemes for Computational Aeroelasticity in OpenFOAM

2018 ◽  
Author(s):  
Sabet Seraj ◽  
Amin Fereidooni ◽  
Anant Grewal
Keyword(s):  
Rigid Body ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Body Motion ◽  
Coupling Scheme ◽  
Lower Sensitivity ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Structure Interaction

Two coupling schemes for fluid-structure interaction using the OpenFOAM structural solver sixDoF Rigid Body Motion are developed. The first scheme is developed by modifying the baseline leapfrog weak coupling scheme to minimize the lag between the fluid and structural solvers. The second is a strong coupling scheme based on the Crank-Nicolson method. The two newly implemented schemes and the baseline are compared through the aeroelastic simulation of a NACA 64A010 airfoil and the Benchmark Supercritical Wing. The aeroelastic solutions obtained using the newly implemented schemes exhibit significantly lower sensitivity to changes in time step size compared to the baseline weak coupling scheme. The modified weak coupling and strong coupling schemes perform comparably for the cases studied.

scholarly journals Partitioned Strong Coupling of Discrete Elements with Large Deformation Structural Finite Elements to Model Impact on Highly Flexible Tension Structures

2020 ◽  
Vol 2020 ◽  
pp. 1-28
Author(s):  
Klaus Bernd Sautter ◽  
Tobias Teschemacher ◽  
Miguel Ángel Celigueta ◽  
Philipp Bucher ◽  
Kai-Uwe Bletzinger ◽  
...  
Keyword(s):  
Finite Elements ◽  
Strong Coupling ◽  
Particle Methods ◽  
Coupling Scheme ◽  
Step Size ◽  
Time Step ◽  
Solution Quality ◽  
Time Step Size ◽  
Tension Structures ◽  
Element Method

This article presents a staggered approach to couple the interaction of very flexible tension structures with large deformations, described with the finite element method (FEM), and objects undergoing large, complex, and arbitrary motions discretized with particle methods, in this case the discrete element method (DEM). The quantitative solution quality and convergence rate of this partitioned approach is highly time step dependent. Thus, the strong coupling approach is presented here, where the convergence is achieved in an iterative manner within each time step. This approach helps increase the time step size significantly, decreases the overall computational costs, and improves the numerical stability. Moreover, the proposed algorithm enables the application of two independent, standalone codes for simulating DEM and structural FEM as blackbox solvers. Systematic evaluations of the newly proposed iterative coupling scheme with respect to accuracy, robustness, and efficiency as well as cross comparisons between strong and weak FEM-DEM coupling approaches are performed. Additionally, the approach is validated against the rest position of an impacting object, and further examples with objects impacting highly flexible protection structures are presented. Here, the protection nets are described with nonlinear structural finite elements and the impacting objects as DEM elements. To allow the interested reader to independently reproduce the results, detailed code and algorithm descriptions are included in the appendix.

Adaptive Semi-Implicit Integrator for Articulated Rigid-Body Systems

2016 ◽  
Author(s):  
Joe Hewlett ◽  
Laszlo Kovacs ◽  
Alfonso Callejo ◽  
Paul G. Kry ◽  
József Kövecses ◽  
...  
Keyword(s):  
Rigid Body ◽  
Adaptive Method ◽  
Point Of View ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Geometric Stiffness ◽  
Starting Point ◽  
The Stability ◽  
Mechanical Dissipation

This paper concerns the dynamic simulation of constrained rigid-body systems in the context of real-time applications and stable integrators. The goal is to adaptively find a balance between the stability of an over-damped implicit scheme and the energetic consistency of the symplectic, semi-implicit Euler scheme. As a starting point, we investigate in detail the properties of a new time stepping scheme proposed by Tournier et al., “Stable constrained dynamics”, ACM transactions on Graphics, 2015, which approximates a full non-linear implicit solution with a single linear system without compromising stability. This introduces a geometric stiffness term that improves numerical stability up to a certain time step size, at the cost of large mechanical dissipation compared to the traditional formulation. Dissipation is sometimes undesirable from a mechanical point of view, especially if the dissipation is not quantified. In this paper, we propose to use an additional control parameter to regulate how “implicit” the Jacobian matrix is, and change the degree to which the geometric stiffness term contributes. For the selection of this parameter, adaptive schemes will be proposed based on the monitoring of energy drift. The proposed adaptive method is verified through the simulation of chain-like systems.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

On the Influence of Inflow Model Selection for Time-Domain Tiltrotor Aeroelastic Analysis

2021 ◽  
Author(s):  
Ethan Corle ◽  
Matthew Floros ◽  
Sven Schmitz
Keyword(s):  
Experimental Data ◽  
Particle Method ◽  
Comprehensive Analysis ◽  
Solution Stability ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Vortex Particle Method ◽  
Whirl Flutter ◽  
Vortex Particle

The methods of using the viscous vortex particle method, dynamic inflow, and uniform inflow to conduct whirl-flutter stability analysis are evaluated on a four-bladed, soft-inplane tiltrotor model using the Rotorcraft Comprehensive Analysis System. For the first time, coupled transient simulations between comprehensive analysis and a vortex particle method inflow model are used to predict whirl-flutter stability. Resolution studies are performed for both spatial and temporal resolution in the transient solution. Stability in transient analysis is noted to be influenced by both. As the particle resolution is refined, a reduction in simulation time-step size must also be performed. An azimuthal time step size of 0.3 deg is used to consider a range of particle resolutions to understand the influence on whirl-flutter stability predictions. Comparisons are made between uniform inflow, dynamic inflow, and the vortex particle method with respect to prediction capabilities when compared to wing beam-bending frequency and damping experimental data. Challenges in assessing the most accurate inflow model are noted due to uncertainty in experimental data; however, a consistent trend of increasing damping with additional levels of fidelity in the inflow model is observed. Excellent correlation is observed between the dynamic inflow predictions and the vortex particle method predictions in which the wing is not part of the inflow model, indicating that the dynamic inflow model is adequate for capturing damping due to the induced velocity on the rotor disk. Additional damping is noted in the full vortex particle method model, with the wing included, which is attributed to either an interactional aerodynamic effect between the rotor and the wing or a more accurate representation of the unsteady loading on the wing due to induced velocities.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

1997 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Stiff Systems ◽  
Step Size ◽  
Step Method ◽  
Integral Of Motion ◽  
Time Step ◽  
Time Step Size ◽  
Variable Time ◽  
Numerical Integrator

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

Numerical Simulation of Proppant Transport in Hydraulically Fractured Reservoirs

2021 ◽  
Author(s):  
Seyhan Emre Gorucu ◽  
Vijay Shrivastava ◽  
Long X. Nghiem
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Fractured Reservoirs ◽  
Injection Timing ◽  
Fracture Permeability ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Proppant Transport ◽  
Fracture Closure

Abstract An existing equation-of-state compositional simulator is extended to include proppant transport. The simulator determines the final location of the proppant after fracture closure, which allows the computation of the permeability along the hydraulic fracture. The simulation then continues until the end of the production. During hydraulic fracturing, proppant is injected in the reservoir along with water and additives like polymers. Hydraulic fracture gets created due to change in stress caused by the high injection pressure. Once the fracture opens, the bulk slurry moves along the hydraulic fracture. Proppant moves at a different speed than the bulk slurry and sinks down by gravity. While the proppant flows along the fracture, some of the slurry leaks off into the matrix. As the fracture closes after injection stops, the proppant becomes immobile. The immobilized proppant prevents the fracture from closing and thus keeps the permeability of the fracture high. All the above phenomena are modelled effectively in this new implementation. Coupled geomechanics simulation is used to model opening and closure of the fracture following geomechanics criteria. Proppant retardation, gravitational settling and fluid leak-off are modeled with the appropriate equations. The propped fracture permeability is a function of the concentration of immobilized proppant. The developed proppant simulation feature is computationally stable and efficient. The time step size during the settling adapts to the settling velocity of the proppants. It is found that the final location of the proppants is highly dependent on its volumetric concentration and slurry viscosity due to retardation and settling effects. As the location and the concentration of the proppants determine the final fracture permeability, the additional feature is expected to correctly identify the stimulated region. In this paper, the theory and the model formulation are presented along with a few key examples. The simulation can be used to design and optimize the amount of proppant and additives, injection timing, pressure, and well parameters required for successful hydraulic fracturing.

scholarly journals Studying Inertia Effects in Open Channel Flow Using Saint-Venant Equations

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1652
Author(s):  
Dong-Sin Shih ◽  
Gour-Tsyh Yeh
Keyword(s):  
Stokes Equations ◽  
Field Application ◽  
Benchmark Problems ◽  
Algebraic Equations ◽  
Step Size ◽  
Time Step ◽  
Cross Sectional ◽  
Inertia Effects ◽  
Time Step Size ◽  
Saint Venant Equations

One-dimensional (1D) Saint-Venant equations, which originated from the Navier–Stokes equations, are usually applied to express the transient stream flow. The governing equation is based on the mass continuity and momentum equivalence. Its momentum equation, partially comprising the inertia, pressure, gravity, and friction-induced momentum loss terms, can be expressed as kinematic wave (KIW), diffusion wave (DIW), and fully dynamic wave (DYW) flow. In this study, the method of characteristics (MOCs) is used for solving the diagonalized Saint-Venant equations. A computer model, CAMP1DF, including KIW, DIW, and DYW approximations, is developed. Benchmark problems from MacDonald et al. (1997) are examined to study the accuracy of the CAMP1DF model. The simulations revealed that CAMP1DF can simulate almost identical results that are valid for various fluvial conditions. The proposed scheme that not only allows a large time step size but also solves half of the simultaneous algebraic equations. Simulations of accuracy and efficiency are both improved. Based on the physical relevance, the simulations clearly showed that the DYW approximation has the best performance, whereas the KIW approximation results in the largest errors. Moreover, the field non-prismatic case of the Zhuoshui River in central Taiwan is studied. The simulations indicate that the DYW approach does not ensure achievement of a better simulation result than the other two approximations. The investigated cross-sectional geometries play an important role in stream routing. Because of the consideration of the acceleration terms, the simulated hydrograph of a DYW reveals more physical characteristics, particularly regarding the raising and recession of limbs. Note that the KIW does not require assignment of a downstream boundary condition, making it more convenient for field application.

scholarly journals CFD Simulation and Experimental Study on Coupled Motion Response of Ship with Tank in Beam Waves

2022 ◽  
Vol 10 (1) ◽  
pp. 113
Author(s):  
Tao He ◽  
Dakui Feng ◽  
Liwei Liu ◽  
Xianzhou Wang ◽  
Hua Jiang
Keyword(s):  
Working Conditions ◽  
Large Scale ◽  
Cfd Simulation ◽  
Stokes Equations ◽  
Body Motion ◽  
Time Step ◽  
Coupled Motion ◽  
Motion Response ◽  
Time Step Size ◽  
Tank Sloshing

Tank sloshing is widely present in many engineering fields, especially in the field of marine. Due to the trend of large-scale liquid cargo ships, it is of great significance to study the coupled motion response of ships with tanks in beam waves. In this study, the CFD (Computational Fluid Dynamics) method and experiments are used to study the response of a ship with/without a tank in beam waves. All the computations are performed by an in-house CFD solver, which is used to solve RANS (Reynold Average Navier-Stokes) equations coupled with six degrees-of-freedom solid-body motion equations. The Level Set Method is used to solve the free surface. Verification work on the grid number and time step size has been conducted. The simulation results agree with the experimental results well, which shows that the numerical method is accurate enough. In this paper, several different working conditions are set up, and the effects of the liquid height in the tank, the size of the tank and the wavelength ratio of the incident wave on the ship’s motion are studied. The results show the effect of tank sloshing on the ship’s motion in different working conditions.

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