Interpolation in the overset domain connectivity information for a cell-centered CFD flow solver will typically use a least square procedure to determine the interpolation weights. The weights produced using the least square procedure are not bounded between zero and one. Thus the interpolation can be non-monotonic and introduce new extrema in the solution, which can cause difficulties with the CFD solution. Interpolation using a dual grid, which connects primal cell centers to form dual grid cells, can be used with tri-linear interpolation to produce weights bounded between zero and one. Forming the dual grid for a structured grid is trivial since the connectivity between cell centers is implicit. For an unstructured grid the dual grid connectivity must be generated. This paper investigates the use of tetrahedral meshing technology to form a tetrahedral unstructured dual grid. The first approach uses a global dual grid where a single grid connects all cell centers, which can be expensive to store. The second approach investigated uses a set of local dual grids where each primal grid element has an associated local dual grid that is independent of neighboring local duals. The local dual grid can reduce memory requirements by loading only the set of local dual grids required for interpolation. Compressible CFD solutions using the least square interpolation weights are compared with solutions using the global dual grid interpolation weights. These results show that the non-monotonic interpolation using the least square interpolation weights can cause solution instabilities. Clipping the interpolated values obtained by using the least square weights will force the interpolation to be monotonic and solution stability is preserved. The CFD solution is stable when using the dual grid interpolation weights as expected. For the configurations and conditions considered in this investigation the solution results using the dual grid interpolation and the clipped least square interpolation show only minor differences.

A methodology for the decomposition of the overset grid assembly problem is presented and evaluated. The method is based on identifying grid subsets of a computational domain for which each domain connectivity is calculated individually, and combined at run time to obtain the final complete solution. The proposed method is a framework for the partition of the problem based on the characteristics of the simulation and relies on the user's knowledge of the case, avoiding some of the pitfalls of automatic methods. The methodology was implemented in a computational fluid dynamics solver, allowing the scalable computation of very large simulations of moving bodies, with efficient use of the computational resources. Several examples illustrating the method and the performance improvements with respect to the standard assembly approach are presented.

High-order overset interpolation has been shown to increase solution accuracy in CFD calculations that utilize high order accurate inviscid flux discretization schemes. The purpose of this effort was to investigate the effect of high-order overset interpolation on the solution accuracy of vortex propagation within Overflow solutions. This was accomplished by adding the ability to compute high-order donor interpolation weights using Lagrangian polynomial to the Suggar++ overset grid assembly code. OVERFLOW 2.2 has been modified to accept these interpolants through the use of the DiRTlib library which can be linked to the code. Simple test cases are presented that demonstrate the operation of the new OVERFLOW 2.2/DiRTlib/Suggar++ system and reiterate the need for the use of high-order interpolants to maintain the intended order of accuracy. These cases are also constructed to demonstrate that standard tri-linear interpolation on increased number of fringe layers is not sufficient to maintain solution accuracy, and that the high-order interpolants are required.

This paper describes a computational fluid dynamic method used for modelling changes in aircraft geometry due to icing. While an aircraft undergoes icing, the accumulated ice results in a geometric alteration of the aerodynamic surfaces. In computational simulations for icing, it is necessary that the corresponding geometric change is taken into consideration. The method used, herein, for the representation of the geometric change due to icing is a non-cut cell Immersed Boundary Method (IBM). Computational cells that are in a body fitted grid of a clean aerodynamic geometry that are inside a predicted ice formation are identified. An IBM is then used to change these cells from being active computational cells to having properties of viscous solid bodies. This method has been implemented in the NASA developed node centered, finite volume computational fluid dynamics code, FUN3D. The presented capability is tested for two-dimensional airfoils including a clean airfoil, an iced airfoil, and an airfoil in harmonic pitching motion about its quarter chord. For these simulations velocity contours, pressure distributions, coefficients of lift, coefficients of drag, and coefficients of pitching moment about the airfoil's quarter chord are computed and used for comparison against experimental results, a higher order panel method code with viscous effects, XFOIL, and the results from FUN3D's original solution process. The results of the IBM simulations show that the accuracy of the IBM compares satisfactorily with the experimental results, XFOIL results, and the results from FUN3D's original solution process.

This paper describes the addition of an overset grid capability to the DPLR flow solver for hypersonic flow in thermochemical nonequilibrium. Modifications to the preexisting flow solver were simplified through the use of DiRTlib, a “solver neutral” library of overset utilities. The new capability is demonstrated on a series of examples, including the Orion Crew Module and other reentry vehicles. For the overset grids used in these examples, the hole cutting and interpolation stencils were determined using SUGGAR, a generalized grid assembly code that can naturally accommodate both the three-dimensional and true two-dimensional cell-centered discretization schemes in DPLR. First a series of building-block examples are presented which highlight aspects of the new capability and assess the technique with comparisons to baseline, block-structured discretizations. The new capability is then exercised for the specific case of a tension tie geometry protruding from the Orion heatshield at both wind tunnel and flight conditions. The addition of overset capability to the DPLR flow solver is seen to be an essential feature for analyzing increasingly complex geometries in thermochemical nonequilibrium.

Unstructured mesh h-re nement replaces an existing element with a set of smaller child elements to improve the local resolution. A template can be used to create the child elements from the original nodes of the parent element and any new nodes that are introduced at edge, face, or element centers. Homogeneous re nement results when all the edges of the element are split and the child elements are typically of the same type as the parent. A transition re nement element is required to interface the homogeneously re ned element with the surrounding unre ned elements. The number of possible transition re nement templates is very large and typically only a fraction of the possible templates are implemented. The present e ort automates the process of generating the transition element templates through the use of metaprogramming: one program will generate the templates and write out software to be compiled into the actual mesh re nement code. The current approach is described in detail and demonstrated on three di erent test cases. The rst is re nement of all elements within a bounding box as might be used to improve local solution accuracy. The second case is re nement to eliminate orphans in an overset mesh system when the overlap between the meshes is insu cient to provide quality interpolation sources. The nal test case combines re nement to eliminate orphans with re nement to improve local solution accuracy. The current procedure generates over 900 unique templates that expands to over 12,000 possible combinations of transition re nement templates.

A computational fluid dynamics (CFD) method has been applied to gear configurations with and without shrouding. The goals of this work have been to validate the numerical and modeling approaches used for these applications and to develop physical understanding of the aerodynamics of gear windage loss. Several spur gear geometries are considered, for which experimental data are available. Various canonical shrouding configurations and free spinning (no shroud) cases are studied. Comparisons are made with experimental data from open literature, and data recently obtained in the NASA Glenn Research Center Gear Windage Test Facility, Cleveland, OH. The results show good agreement with the experiment. The parametric shroud configuration studies carried out in the Glenn experiments and the CFD analyses elucidate the physical mechanisms of windage losses as well as mitigation strategies due to shrouding and newly proposed tooth contour modifications.

In this paper we investigate phenomena associated with particle impingement on dynamic airfoils. Using an Eulerian based solver, a droplet velocity field is computed throughout the computational domain. This solver is used to scrutinize particular concepts, with the intent to save computation time, listed as follows: (i) The applicability of different time-averaging techniques to calculate an average local collection efficiency for dynamic simulations. (ii) Comparison between static and dynamic bodies undergoing particle surface interactions. (iii) The use of a numerically viscous solution to the Euler equations instead of a fully viscous solution to predict proper particle trajectories on dynamic airfoils. Guidance is provided herein, for the applicability of solution methods to reduce computational costs.

An efficient solver for the incompressible vorticity transport equations on adaptive Cartesian grids is coupled to an unstructured spectral volume solver for the conservative form of the compressible Euler equations using overset grid assembly and interpolation provided by SUGGAR and DiRTlib, respectively. Vortical flow structures originate at solid surfaces in near-body regions employing the Euler solver and are transported into the wake region that employs an Eulerian Vorticity Transport (EVT) solver. The excessive numerical dissipation common to most grid-based Navier-Stokes solvers is avoided in the wake region by solving the fluid dynamic equations in vorticity conservation form. In addition, the adaptive Cartesian mesh utilized in the wake region allows for efficient transport and preservation of vortical structures by means of localized adaptive mesh refinement and coarsening. Two different approaches for evaluating the EVT velocity field, one involving a fast summation technique based on the Cartesian Treecode method, and the other utilizing a multigrid Poisson approach, are presented and compared. The implementation of both the solution algorithm and overset coupling methodology is described in detail, and results for several different test cases are presented which demonstrate the effectiveness of the hybrid EVT-Euler simulation capability for accurately transporting vortical structures between a near-body compressible Euler solver and an off-body EVT solver.

In this work we present a novel, generalized, multiscale physics, unstructured finite-volume, CFD approach for simulating ice accretion on aircraft. A multi-physics solver that evaluates the (1) air flow, (2) droplet trajectories, (3) surface-liquid flow, (4) solidification, and (5) computes the deformed ice shape, is presented. Initial results show promise in the developed methods and solvers, that are expected to later be extended for future rotorcraft ice-accretion analysis. Initial validation cases are presented for the various components of the solver, and compare reasonable well with LEWICE and experiments for simple geometries. This initial capability displays a capability that could be extended, in future efforts, with more detailed models and provide ice shapes of similar quality as the current methodologies, while providing a capability that extends to more complex configurations such as rotorcraft.

SUGGAR is a general overset grid assembly capability that is targeted at moving body simulations. DiRTlib is a library that encapsulates the functionality required to perform the overset interpolation and communications required in an overset composite grid solution. This paper describes enhancements that have been made to SUGGAR and DiRTlib to improve the performance and capability for moving body problems. A procedure to adapt the grids to overlap requirements is demonstrated and found effective in reducing or eliminating the orphans due to insufficient overlap. In addition, SUGGAR can also be linked into the flow solver as a library to provide a capability integral to the flow solver. The paper documents the library interface and discusses modifications required to the flow solver to utilize SUGGAR as a library. Finally, a new overset domain connectivity code, Suggar++, is being developed, and this paper briefly discusses the improvements it offers relative to SUGGAR.

The simulation of flow past bodies in relative motion is a challenging task due to the presence of complex flow features, moving grids, and rigid body movements under the action of external forces and moments. A generalized grid-based overset framework is presented for the simulation of this class of problems. The equations that govern the fluid flows are cast in an integral form and are solved using a cell-centered finite volume upwind scheme. The rigid body dynamics equations are formulated using quaternion and are solved using fourth-order Runge–Kutta (RK) time integration. The overset framework and the six degree of freedom (6-DOF) rigid body dynamics simulators are developed in a library form for easy incorporation into existing flow solvers. The details of the flow solver, the 6-DOF library, and the overset framework are presented in this paper along with the validation results of the developed system.

An unstructured overset moving mesh CFD method is adapted, validated and applied to spinning gear systems with emphasis on predicting windage losses. Several spur gears and a disc, spinning in air at rotation rates up to 1200 s−1 are studied. It is observed that the CFD simulations return good agreement with measured windage power loss, as determined by the deceleration of the gears due to torques exerted by viscous and pressure forces on the gear surfaces. Turbulence modeling choices, the relative importance of viscous and pressure torques with gear speed, and the physics of the complex 3D unsteady flow field in the vicinity of the gear teeth are studied. The capabilities and challenges associated with the overset mesh approach for enclosed gear train applications are demonstrated.

The overset, or chimera, grid methodology utilizes a set of overlapping grids to discretize the solution domain. The critical first step in the overset process is the hole cutting with many different approaches currently in use. The present paper investigates an approach that seeks to maximize automation and minimize user inputs. The method uses the surfaces of the grids that define geometry for the hole cutting and will cut a minimal hole, which is required for geometries with small gaps between geometry components. The method is demonstrated for twoand three-dimensional cases. The present procedure is found to be effective in cutting minimal holes around complex geometries including small gap regions.

The problem of surface ships free to pitch and heave in regular head waves is analyzed numerically with an unsteady Reynolds averaged Navier Stokes (URANS) approach. The unsteady single-phase level set method previously developed by the authors was extended to include six degrees of freedom (6DOF) motions. The method uses rigid overset grids that move with relative motion during the computation, and the interpolation coefficients between the grids are recomputed dynamically every time the grids move. The motions in each time step are integrated implicitly using a predictor–corrector approach. An earth-based reference system is used for the solution of the fluid flow, while a ship-based reference system is used to compute the rigid-body equations of motion. Predicted results for sinkage and trim and resistance at two Froude numbers (medium, Fr=0.28 and large, Fr=0.41) were compared against experimental data, showing good agreement. Pitch and heave motions were computed for near-resonant cases at Fr=0.28 and 0.41, with regular linear head waves with slope ak=0.025 and wavelength λ=1.5L, with L the ship length. The predicted motions compare favorably with existing experimental data. A solution for a large amplitude head wave case (ak=0.075) was also obtained, in which the transom wave breaks and extreme motions are observed. The medium Froude number case was subject to a verification and validation analysis. A problem with two ships pitching and heaving one behind the other is demonstrated.