An efficient grid assembling method in unsteady dynamic motion simulation using overset grid

https://doi.org/10.1016/j.ast.2020.106450Get rights and content

Abstract

The overset grid method may be a competitive choice of structured grid to discretize the progressively complicated aerodynamic shapes. Grid assembling process is a unique process for the overset grid method, which should be done repeatedly followed by any occurrence of grid motion in unsteady dynamic motion simulation. In this work, a simplified grid assembling method for the unsteady dynamic overset grid method is devised and validated. The grid motion information, generally including the position or the speed of the solid body, could be viewed as an additional information. The difference of the grid position indicates the change of the relative position of the grid points. The relative position of a grid point is very critical in the corresponding grid assembling process. The traditional grid assembling method usually omits the additional grid motion information. The proposed method utilizes the difference value of the grid position and the specially designed grid system to simplify the traditional grid assembling method. Three test cases including a 2D airfoil with different motion types and a 3D commercial airplane with pitching motion are implemented to demonstrate the high efficiency of the proposed method while the accuracy is kept. According to the results, the proposed method saves more than 85% of the computational time spent on the grid assembling process. This method is potentially a better candidate for the unsteady motion simulation using overset grid.

Introduction

Overset grid method [1] is generally employed in todays' Computational Fluid Dynamics (CFD). The application of overset grid method contains some common fields such as the fixed wing aircraft [2], [3], the rotorcraft [4], [5] and the aerodynamic 6-DoF (Degrees of Freedom) simulations [6], [7], etc. From the first AIAA (American Institute of Aeronautics and Astronautics) CFD drag prediction workshop (DPW) to the latest sixth DPW, the overset grid is always officially provided as a choice among many standard grids from the committee. The same situation occurs in every session of the AIAA CFD high lift prediction workshop (HiLiftPW). A special notice is that the overset grid is the only option of structured grid for the JAXA (Japan Aerospace Exploration Agency) standard model (JSM) which seems to be a very complicated configuration in the 3rd HiLiftPW [8], [9]. It indicates that, for the more and more complicated aircraft configurations, the overset grid method may be a better choice among the structured grid method by virtue of grid generation flexibility. Compared to other methods, overset grid method combined with Arbitrary Lagrangian-Eulerian approach (ALE) has some inherent advantages on the rotorcraft simulations and 6-DOF simulations with the flexible grid assemble capacity. The flexible grid assemble capacity maintains the initial grid quality throughout the any grid motion if the surface deformation is not considered and a rigid grid motion is employed.

Fig. 1 briefly shows the flowchart for the overset grid method. Generally, computational grids in the overset grid method can be classified into two types: the near-body grid and the background off-body grid. The near-body grid contains many body-fitted grid-blocks which are overlapped with each other. The off-body grid is a series of Cartesian grids with different spacing in general. Fig. 2 presents a typical overset grid typology for a commercial airplane model.

The grid assembling process is a special and unique process to distinguish the overset grid method from others. Domain connectivity [10] is another name of this process in some papers. Two steps are included in grid assembling process. One is the hole cutting step, another is the interpolation searching step. In the hole cutting step, the grid points inside the aircraft solid body are identified and tagged out. The interpolation searching step provides the reasonable interpolation coefficients for the overset boundary grid points. The overset boundary grid points contain the boundary points around the hole and those without any physical or special computational boundary condition. The special computational boundary conditions are periodic plane, axial line, and symmetric plane in general. Fig. 3 gives a detailed description of these overset boundary grid points for a NACA 0012 airfoil. The number of the layers for the overset boundary grid points are determined by the orders of the spatial discretization method. The tagged-out hole points and the overset grid boundary points are excluded from the iterative calculation of the flow field. The flow field information is interpolated from other grid cells for the overset grid boundary points.

The main purpose is to determine the location of the overset boundary grid points in the interpolation searching step. The details of this step will be illustrated in the next section. The result is the interpolation coefficients for the overset boundary grid points. The flowfield information is transferred through the overlapped region between different grid blocks by these interpolation coefficients.

In the static simulation, the grid assembling process only needs to be performed at the beginning. As for the dynamic motion simulation, the grid moves with time. The grid assembling process should be repeatedly performed followed by each time when the grid motion appears. The computational time of the grid assembling process is proportional to the number of overset boundary grid points, which directly depends the total grid points number in the simulation. With the development of CFD, the grid density increases rapidly with the demand to resolve more detailed turbulent flow structures. The new methods to solve the turbulent flow such as hybrid RANS/LES (Reynolds Averaged Navier-Stokes/Large Eddy Simulation) method [11], wall modeled LES method [12], LES method [13] and DNS (Direct Numerical Simulation) method [14] essentially demand a finer grid than RANS method to get a more physical flow solution. As a result, the grid assembling process becomes a time-consuming process considering a large total number of the grid points.

In the dynamic motion simulations, a complicated grid motion can be deemed as the combination of several 1-DoF motions. The translation and rotation motions are two basic types for 1-DoF motions. The unsteady simulation of a rotor, a propeller, a pitching motion are three classical examples for the rotation motion. The unsteady simulation of a plunging motion is a representative one for the translation motion.

In the rotor and propeller simulation, people always care about the development and the structure of the wake, which is fully obtained after several revolutions of the rotor or the propeller. The physical time step is usually small to get a better numerical stability. In Ref. [4], 720 physical time steps were contained in one rotor revolution. These two factors lead to a great number of the total physical time steps (normally tens of thousands) for the rotor and propeller simulation.

The simulation of a pitching and plunging motion can be used in many application fields including the unsteady aerodynamic modeling [15], the aerodynamic shape optimization [16] and the calculation of the dynamic derivatives [17], [18], etc. The number of physical steps simulated in these applications is usually huge to get enough information. Mehdi et al. [19] provided a framework to approximate the nonlinear unsteady aerodynamics using a Radial Basis Function Neural Network (RBFNN). In their research, 60 thousand physical steps were employed to train the RBFNN. Wang et al. [20] used the gradient-based SQP (Sequence Quadratic Programming) method to optimize a rotor airfoil shape. They used the sinusoidal pitching motion to evaluate the aerodynamic performance of the rotor airfoil. The total calling times of CFD simulations equaled 40 at least in their research. In Ref. [21] they validated the CFD code using a similar airfoil pitching case. Three cycles of airfoil pitching are simulated in the validation case. 200 physical steps are included in one cycle of pitching motion. As a result, at least 24 thousand total steps were needed to optimize the rotor airfoil using their method. The total steps will increase significantly for a global optimization method, which usually needs a larger number of samples than the gradient-based local optimization method.

With the demand of the finer grid density as well as the large number of total physical time steps, the computational time grows rapidly, which limits the development of these applications. The computational time mainly contains two parts: the time of the grid assembling process and the time of the flowfield calculation process. To reduce the computational time of the flowfield calculation process, high order methods [22], [23], [24], [25] are proposed to reduce the grid points as well as the number of physical time steps mentioned above.

As for the computational time of the grid assemble process, it can be largely reduced using the additional information provided by the grid motion in the unsteady motion simulation. However, the traditional grid assembling method omits this grid motion information in the unsteady motion simulation, which causes a considering time-wasting when the total number of grid points is extremely large. In this paper, an efficient grid assembling method is proposed based on the additional information and the special designed grid systems in unsteady dynamic motion simulation using structured overset grid method. The computational time of the grid assemble process is extremely reduced by the proposed method.

The rest of this paper is organized as follows. Section 2 describes the details of the proposed method. Section 3 illustrates three numerical examples including a 2D airfoil with different motion types as well as a 3D commercial airplane with pitching motion. Section 4 shows and analyzes the results of these three test cases. Finally, section 5 summarizes the proposed method.

Section snippets

Methodology

The grid assembling process distinguishes the overset grid method from others. In the traditional overset grid method, hole cutting step and interpolation searching step are two essential steps in the grid assembling process. Hole cutting step identifies and blanks out the grid points which are inside the solid body surfaces. After the hole cutting step, the overset boundary grid points can be fully determined as shown in Fig. 3. In some existing methods [10], the hole surface is optimized by

Test cases

In this section, three test cases are employed to check the accuracy and efficiency of the proposed method. The first two cases use 2D airfoil with pitching motion and combined motion, respectively. The last one employs a 3D commercial airplane with pitching motion. The motions in all cases are defined as a sinusoidal form. To validate the accuracy and efficiency of the proposed method, the simulations are performed using both the traditional grid assembling method and the simplified grid

2D airfoil with pitching motion

The normal force coefficients and the pitching moment coefficients obtained by from the experiment the traditional and the proposed grid assembling method are plotted in Fig. 18 for comparison. The results of two different grid assembling methods coincide with each other, which differ slightly from the experimental data. The force and moment coefficients are integrated from the surface grid, which is the same in two different grid assembling methods. Hence, it is reasonable that two results

Conclusions

In this paper, a simplified grid assembling method is established for the dynamic motion simulation using overset grid. The hole-cutting step and the interpolation searching step in the traditional grid assembling method have been substituted by the “local grid freezing”, the special designed buffer grid, the special designed off-body grid, and the global interpolation coordinates. The complicated traversal and iterative operations are replaced by some simple algebraic operations.

Three test

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by Yangtze River Delta Research Institute of Northwestern Polytechnical University.

References (37)

  • W.M. Chan

    Overset grid technology development at NASA Ames Research Center

    Comput. Fluids

    (2009)
  • W. Jiang et al.

    Numerical simulations of complex aircraft configurations using structured overset grids with implicit hole-cutting

    Aerosp. Sci. Technol.

    (2019)
  • T. Liu et al.

    A three-dimensional aircraft ice accretion model based on the numerical solution of the unsteady Stefan problem

    Aerosp. Sci. Technol.

    (2019)
  • H. Qi et al.

    A study of coaxial rotor aerodynamic interaction mechanism in hover with high-efficient trim model

    Aerosp. Sci. Technol.

    (2019)
  • J.Y. Hwang et al.

    Assessment of S-76 rotor hover performance in ground effect using an unstructured mixed mesh method

    Aerosp. Sci. Technol.

    (2019)
  • R. Koomullil et al.

    Moving-body simulations using overset framework with rigid body dynamics

    Math. Comput. Simul.

    (2008)
  • W.J. Horne et al.

    A massively-parallel, unstructured overset method to simulate moving bodies in turbulent flows

    J. Comput. Phys.

    (2019)
  • C.L. Rumsey et al.

    Overview and summary of the Third AIAA High Lift Prediction Workshop

    J. Aircr.

    (2018)
  • J.G. Coder et al.

    Contributions to HiLiftPW-3 using structured, overset grid methods

  • S.E. Rogers et al.

    PEGASUS 5: an automated preprocessor for overset-grid computational fluid dynamics

    AIAA J.

    (2003)
  • J. Fröhlich et al.

    Hybrid LES/RANS methods for the simulation of turbulent flows

    Prog. Aerosp. Sci.

    (2008)
  • M. Terracol et al.

    Wall-resolved large-eddy simulation of a three-element high-lift airfoil

    AIAA J.

    (2020)
  • C.J. Barnes et al.

    High-fidelity LES simulations of self-sustained pitching oscillations on a NACA0012 airfoil at transitional Reynolds numbers

  • A.R. Koblitz et al.

    Direct numerical simulation of particulate flows with an overset grid method

    J. Comput. Phys.

    (2017)
  • Q. Wang et al.

    Unsteady aerodynamic modeling at high angles of attack using support vector machines

    Chin. J. Aeronaut.

    (2015)
  • Y. Zuo et al.

    Rotor airfoil design optimization based on unsteady flow

    Trans. Jpn. Soc. Aeronaut. Space Sci.

    (2017)
  • B. Mi et al.

    Review of numerical simulations on aircraft dynamic stability derivatives

    Arch. Comput. Methods Eng.

    (2019)
  • M. Tatar et al.

    Investigation of pitch damping derivatives for the standard dynamic model at high angles of attack using neural network

    Aerosp. Sci. Technol.

    (2019)
  • Cited by (11)

    • An efficient Cartesian mesh generation strategy for complex geometries

      2024, Computer Methods in Applied Mechanics and Engineering
    • A new overset grid assembly strategy for dynamic grid systems

      2023, Mathematics and Computers in Simulation
    • Theoretical and numerical analysis of effects of sudden expansion and contraction on compressible flow phenomena in Hyperloop system

      2022, Aerospace Science and Technology
      Citation Excerpt :

      The overset mesh method for a dynamic mesh was applied to the computational grid. This method has been widely adopted for a moving object owing to several advantages [41–44]. The overset mesh consists of a background and component mesh.

    • Application of immersed boundary method to the simulation of transient flow in solid rocket motors

      2021, Aerospace Science and Technology
      Citation Excerpt :

      The burning surface regression leads to the motion and deformation of flow-filed boundaries. The dynamic grid method is commonly used to compute the flow field on the body-fitted grid with boundary motion and deformation, and it is divided into three main categories [3]: deformed grid method [4,5], overset grid method [6–9], and re-meshing method [10–12]. The deformed grid method is applied to the small boundary deformation.

    • Investigations on high-fidelity low-dissipation scheme for unsteady turbulent separated flows

      2021, Aerospace Science and Technology
      Citation Excerpt :

      All numerical simulations are conducted with the in-house finite volume solver involving various numerical schemes. The reliability of the code has been validated and verified by a series of numerical simulations [8,17,18,27–31]. The equations are numerically solved by discretizing time and space terms independently.

    View all citing articles on Scopus
    View full text