Curvilinear Body-fitted Grids Research Articles

On the coupling of wall-model immersed boundary conditions and curvilinear body-fitted grids for the simulation of complex geometries

One of the main limitations in computational aerodynamics lies in the ability of CFD solvers to handle complex geometries while maintaining their accuracy. Among the currently available strategies, the Zonal Immersed Boundary Conditions (ZIBC) has shown its capability to introduce complex geometrical details for the simulations of high Reynolds turbulent flows. In this context, this work aims to extend the ZIBC framework, initially adapted to reproduce blockage effects, to take into account configurations where the influence of spatially developing boundary layers has to be accurately predicted. For this purpose, a compact sharp interface immersed boundary method has been developed for curvilinear grids. Moreover, a Thin Boundary Layer Equations (TBLE) wall model based on one-dimensional RANS Spalart-Allmaras equations is coupled with the IBC to model the inner part of compressible turbulent boundary layers. The coupling with the Zonal Detached Eddy Simulation (ZDES) approach is improved and permits to simulate turbulent flows capturing accurately the wall-normal gradients with a limited grid resolution. This strategy is applied to the simulation of a generic missile configuration (FG5) with an angle of attack of 10∘ using RANS and ZDES approaches. For the first time, wall quantities such as unsteady loads, including the viscous contribution, are accuratly reproduced on surfaces modelled with IBC using hybrid RANS/LES (ZDES) computations and for a realistic configuration at high Reynolds number. Such a reconstruction of physical quantities at the wall is achieved thanks to a precise reconstruction procedure using a TBLE wall model.

Efficient three-equation two-phase model for free surface and water impact flows on a general curvilinear body-fitted grid

In this work, a simple and efficient three-equation two-phase model is transformed to a multi-dimensional general curvilinear coordinate system for simulation of free surface and water impact flows on curvilinear body-fitted grids. The two-phase model is a reduced version of the Baer–Nunziato model for compressible multiphase flows, in which the governing equations for only the liquid phase are active, whereas those for the air phase are neglected. The CPU cost is significantly reduced by solving the equation system only in the liquid regions, instead of solving the entire computational domain as in classical Euler approaches. The physical system is formulated in a hyperbolic vector form in a curvilinear coordinate system and solved using a monotonic upstream-centered scheme for conservation laws (MUSCL)/Godunov-type finite volume scheme. Compressive MUSCL limiters combined with the high-order finite volume approach result in a sharp interface solution. Validations with numerical grid refinement and convergence studies on dam-break and water impact problems are addressed, and the capability and robustness of the present model for accurate simulation of free surface and water impact flows are demonstrated. The implementation of the present system on a curvilinear body-fitted grid and the use of the Tait equation of state for water for the closure of the compressible system allow the method to solve water impact flow problems with both low-speed and high-speed complex geometries in industry and engineering.

Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability, the convective derivatives in the free-surface boundary conditions are treated using an upwind-biased stencil. Instead of solving for the radiation impulse response functions, a pseudo-impulsive Gaussian type displacement is employed in order to tailor the frequency-content to the discrete spatial resolution. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth-order convergence of the calculations on simple geometries is demonstrated, along with a nearly linear scaling of the solution effort with increasing grid resolution. The code is validated by comparison with analytical and semi-analytical solutions using submerged and floating closed-form geometries. Calculations are also made for a modern bulk carrier, and good agreement is found with experimental measurements.

Aerodynamic study of aerofoil and wing in simulated rain environment via a two-way coupled Eulerian-Lagrangian approach

AbstractAerodynamic performance degradation has been considered a critical hazard to aircraft due to flying in heavy rain. In this work, a two-way momentum coupled Eulerian-Lagrangian approach is developed to study the aerodynamic performance of a two-dimensional (2D) transport-type NACA 64-210 cruise and landing configuration aerofoil as well as a three-dimensional (3D) NACA 64-210 cruise configuration rectangular wing in heavy rain environment. Raindrop impacts, splashback and formed water film are modeled. The steady-state incompressible air flow field and the raindrop trajectory are calculated alternately by incorporating an interphase momentum coupling term through a curvilinear body-fitted grid surrounding the aerofoil/wing. Our simulation results agree well with the experimental results and show significant aerodynamic penalties for all the test cases in heavy rain. Rain-induced premature boundary-layer transition and separation are observed and details of the raindrop splashback effect on the boundary layer are examined. A 1° rain-induced decrease in stall angle-of-attack is predicted. An uneven water film upon the wing surface is observed and its effect on the wing surface roughness is also examined.

HIGH-ORDER CURVILINEAR SIMULATIONS OF FLOWS AROUND NON-CARTESIAN BODIES

The current work describes the application of high-order numerical techniques to single or multiple overset curvilinear body-fitted grids, demonstrating the feasibility of direct computations of noise radiated by flows around complex non-Cartesian bodies. Flows of both physical and industrial interest can be investigated with this approach. We first rapidly describe the numerical techniques implemented in our curvilinear simulations. The explicit high-order differencing and filtering schemes are presented, as well as their application to the curvilinear Navier–Stokes equations. We then present brief results of various 2-D acoustic simulations. First the flow around a cylinder, and the associated acoustic field, are described. The diameter-based Reynolds number Re D = 150 is under the critical Reynolds number of the onset of 3-D phenomena in the vortex-shedding. Simulation results can thus be meaningfully compared to experimental measurements. A case of acoustic scattering is then examined. A non-compact monopolar source is placed half way between two differently sized cylinders. A complex diffraction pattern is created, and resulting RMS pressure data are compared to the analytical solution. Finally the noise generated by a low Reynolds number laminar flow around a NACA 0012 airfoil is presented.

중첩격자계와 접합격자계를 이용한 적응격자 기법

중첩격자계와 접합격자계를 이용한 적응격자 기법이 개발되었다. 유동장은 물체와 근접한 영역과 떨어진 영역으로 구분된다. 근접한 영역은 곡선 격자계로 채워지며 중첩격자기법으로 영역이 연결되고 떨어진 영역은 다양한 적응 단계를 가진 직교 격자계로 채워지며 접합격자기법으로 연결된다. 본 적응격자기법은 격자생성에 있어서의 유연성과 효과적인 격자적응 기능을 보여준다. 2차원 스토어 분리 해석을 포함하는 몇 가지 수치해석을 통해 본 적응격자기법의 성능을 검증하였다. A grid adaptation method within systems of chimera and patched grids is presented. Problem domains are divided into near-body and off-body fields. Near-body field is filled with curvilinear body-fitted grids that extend only a short distance from body surfaces and connected to other grid systems via chimera domain connectivity method. Off-body field is filled with patched uniform cartesian grids of varying levels of refinement. This method gives flexibility in grid generation and efficient adaptation capability. Several numerical experiments including 2D store separation were performed to show the performance of the proposed adaptation method.

Comparative study between two Navier-Stokes algorithms for transonicairfoils

A critical examination of several aspects of the numerical simulation of high Reynolds number transonic airfoil flows is presented. Subcritical and supercritical flowfields about an aft-cambered airfoil were generated by solving the mass-averaged Navier-Stokes equations with turbulence incorporated through an algebraic eddy viscosity model. The governing equations were solved on curvilinear body-fitted grids utilizing two different algorithms, i.e., MacCormack's explicit and Beam-Warming implicit. The numerical uncertainties associated with different schemes, grid resolution, artificial viscosity, and far-field boundary placement were investigated and found to be of the same order of magnitude or less than the corresponding uncertainties in the available experimental data. Comparison of computed and experimental results showed good prediction of all the essential flow features. However, detailed comparison of velocity profiles pointed out deficiencies of the turbulence model downstream of the shock-wave boundary-layer interaction, in the airfoil cove and in the near wake. Thinlayer and Navier-Stokes computed results were found to be in excellent agreement with each other.