INTRODUCTION
Over the years rotorcraft have become increasingly more sophisticated with higher operational requirements resulting in the need for increased modeling accuracy and understanding. Areas where improved accuracy is especially needed include the prediction of rotorcraft aeromechanics and acoustics. From 2008–2018, NASA outlined a strategy to address the need for increased rotorcraft aerodynamic modeling accuracy by improving the capability of its high-fidelity computational fluid dynamics (CFD) codes. These improvements included mesh adaption for both off-body and on-body flow fields, higher-order numerical schemes with lower numerical dissipation, higher-order time schemes, improved turbulence modeling, development of boundary layer transition modeling, and general code performance improvements to reduce computational cost. As additional capabilities were added to the high-fidelity CFD codes, comparisons and validations were made against various wind tunnel experiments demonstrating their improved predictive capabilities. During 2016–2018, a rotor-blade multidisciplinary design optimization capability was developed and demonstrated using a high-fidelity unstructured CFD code and an adjoint-based optimization method. The improvements to the NASA CFD codes and validation activities are summarized in this chapter.
ADVANCED CFD DEVELOPMENT
This section highlights the improvements in capabilities made to NASA-developed high-fidelity CFD codes for increased accuracy and performance of rotorcraft simulations from 2008–2018. Most significant improvements have been in the areas of dynamic adaptive mesh refinement (AMR) and higher-order numerical methods. Combined, these two improved capabilities have significantly increased the fidelity of rotorcraft simulations resulting in increased aerodynamic accuracy.
Adaptive Mesh Refinement (AMR)
The state-of-the-art (SOA) survey for vertical lift technologies [Yamauchi and Young, 2009] recommended the development of AMR to allow for accurate simulation of the rotorcraft-wake system. One of the main barriers to capturing the rotor wakes has been the required grid resolution needed to accurately capture the vortical wake structures emanating from the rotor tips. This can be accomplished by using a very fine mesh over the entire rotor wake region, however this is typically prohibitively expensive. An alternative to uniform mesh refinement is to use dynamic mesh adaption and refine only the regions of the wake that require mesh
1 NASA Langley Research Center, 1A East Reid St., Hampton, VA 23681-2199. 2 NASA Ames Research Center, Moffett Field, CA 94035-1000.
refinement. The difficulty lies in how to best identify the regions that require adaption with the goal of achieving results similar to those obtained using uniform mesh refinement of the rotor wake.
The main focus of AMR for NASA vertical lift research over the last 10 years was to add dynamic mesh adaption capability to the structured Navier–Stokes flow solver, OVERFLOW2, initially for off-body mesh and then subsequently for near-body mesh. The mesh adaption approach was to develop a solution-adaptive capability using the existing chimera zonal grid framework in OVERFLOW2. While this is less rigorous than an adjoint-based approach as used in the unstructured Navier–Stokes flow solver, FUN3D [Park, 2011], the solution-based approach is much simpler to implement with a lower computational cost and is more conducive to dynamic mesh adaption for unsteady flow needed for rotor wakes.
Initial development of a solution-adaptive capability was performed by Holst and Pulliam [2009, 2010] for off-body Cartesian meshes where the mesh is divided into a series of uniform sub- regions. Each sub-region is evaluated for mesh refinement based on a sensor value of flow gradients such as a vortex core. The sub-regions matching the refinement criteria are uniformly refined. This research by Holst and Pulliam [2009, 2010] demonstrated that this dynamic local mesh refinement approach uses approximately five times less computational resources than a uniformly refined mesh. This work also demonstrated a significant improvement in the prediction of the vortex-core growth with wake age as compared to experiment, however, the vortex-core size for the CFD simulations were still larger than observed in the experiment. Calculations of the hover performance figure of merit (FM) matching a Tilt Rotor Aeroacoustics Model (TRAM) experiment showed improved prediction of FM from 0.73, about 6 percent below the experimental value of 0.75, to an FM of 0.75 for two levels of mesh refinement (~4 percent difference), and to an FM of 0.77 for three levels of refinement (~1.3 percent difference).
The mesh adaption work by Holst and Pulliam [2009, 2010] was followed by an improved off- body solution adaption capability implemented in OVERFLOW2 by Buning and Pulliam [2011]. This new capability was based on the original work done by Meakin [1995] and provides for the automatic creation of multiple levels of finer Cartesian off-body meshes. The adaption capability was also coupled with load-balancing and an in-memory solution interpolation procedure, providing good performance for time-accurate simulations on parallel computer platforms. The work by Buning and Pulliam [2011] used a simple error estimation derived from the flow solution. The error estimation was calculated by the undivided second-difference of the primary flow variables of density, momentum, and stagnation energy per unit volume. This error estimation was shown by Buning and Pulliam [2011] to be effective for identifying both shock waves and vortices.
The new off-body AMR capability developed and implemented by Buning and Pulliam [2011] in OVERFLOW2 was used by Chaderjian and Buning [2011] to perform time-dependent CFD simulations of the highly resolved rotor wake of the TRAM rotor in hover. Figure 3.1 shows the highly resolved rotor wake using a two-level dynamic AMR grid system for the TRAM in hover. This work showed that the rotor performance in terms of the FM was more a function of the near-body rotor mesh resolution than the off-body rotor wake mesh. From this work Chaderjian
and Buning [2011] showed that using a Detached Eddy Simulation (DES) turbulence model, as opposed to a Reynolds-averaged Navier–Stokes (RANS) model, was crucial to accurately predicting the rotor FM. In addition to AMR, Chaderjian and Buning [2011] also used high-order spatial differencing developed by Pulliam [2011] to reduce numerical dissipation of rotor blade tip vortices and other wake flow structures. Chaderjian [2012b] followed this work by using AMR on an isolated UH-60A rotor in forward flight and demonstrating good agreement of the time-varying normal force and pitching moments with flight test data. He also showed good agreement of the vortex-core growth for the V22 (TRAM) hover case to experimental measurements.
Near-body mesh adaption capability was added to OVERFLOW2 by Buning and Pulliam [2016]. Near-body mesh adaption is a much more difficult problem to solve than off-body adaption because the off-body grids are Cartesian and straightforward to refine. Near-body grids are typically curvilinear since they are fitted to curved body surfaces and also include highly refined near-wall regions to resolve the boundary layers. The near-body mesh adaption capability in OVERFLOW was evaluated for a UH-60A rotor in forward flight by Chaderjian [2018]. Maintaining algorithm stability proved very difficult with the near-body adaption. This was mostly due to the Courant–Friedrichs–Lewy numbers becoming too high as the near-body grids were refined using an isotropic approach (grid is refined in all three dimensions). Using a non- isotropic approach would allow for refinement in the spanwise direction without increasing the
Figure 3.1. OVERFLOW two-level dynamic AMR grid system for the TRAM in hover with Mtip = 0.625, θ = 14°, and Re = 2.1 million. Vorticity magnitude sensor function (Fig. 6 of Chaderjian and Buning [2011]).
viscous clustering normal to the wall and should be considered for future work on improving near-body adaption. Chaderjian [2018] found that turning off the near-body adaption near the surface improved the algorithm stability and also significantly helped reduce the total number of grid points. Overall, the near-body adaption resulted in little change in the blade sectional airloads for up to two levels of adaption. OVERFLOW2 now has a near-body adaption capability, however further developmental and application work can be performed to improve its robustness and usability.
Higher-Order Schemes
Another area of research identified by the SOA survey for vertical lift technologies was the development and implementation of high-order spatial-differencing schemes, as well as higher- order time-stepping schemes including fully implicit multistage and compact schemes for OVERFLOW2. These improvements are required to help improve the performance and airloads accuracy for rotorcraft flows, as well as capturing the vortex wake system that includes wake- wake and blade-wake interactions for acoustics applications [Yamauchi and Young, 2009]. Two fifth-order spatial-weighted essentially non-oscillatory numerical schemes for the convective terms were added to OVERFLOW2 by Nichols et al. [2008]. These new schemes had much lower numerical dissipation/dispersion than the traditional third-order spatial monotone upstream-centered schemes. The reduced numerical dissipation allowed vortices to be propagated for much longer distances and was quickly adopted and demonstrated for rotor simulations by Boyd [2009].
Third- and fifth-order finite difference schemes for the convective terms of the Navier–Stokes equations were developed by Pulliam [2011] and implemented into OVERFLOW2. The third- order scheme uses a fourth-order central difference with third-order artificial dissipation, and the fifth-order scheme uses a sixth-order central difference with a fifth-order artificial dissipation. Pulliam [2011] showed how these new high-order schemes were able to improve the accuracy of a rotor wake using less grid resolution than lower-order schemes by comparing the vortex-core growth rate for the third- and fifth-order schemes for varying mesh sizes. The fifth-order-scheme results shown in Figure 3.2 have good agreement to the experimental results for 380 million grid points, whereas the third-order scheme would need 3 billion grid points, using uniform grid refinement, to achieve the same vortex growth rate.
Overset Methods for Unstructured Mesh
An unstructured overset mesh capability was added to FUN3D by Biedron and Thomas [2009] extending the mesh motion capabilities. Previously, FUN3D only allowed rigid mesh motion of the entire domain, which limited the range of applications [Biedron and Thomas, 2009]. Rotorcraft applications are particularly challenging for mesh motion since the rotor blades undergo large rotational and pitch motions, as well as aeroelastic deformations. These large rotor motions in the presence of a fuselage without overset grids would require remeshing, which is not only costly but also not easily compatible with the backward-time integration schemes.
Figure 3.2. Growth rate of vortex core with wake age for third- and fifth-order schemes for the baseline small (13.7 million), medium (58.4 million), large (379.8 million), and huge (3.087 billion) grids (Fig. 9 of Pulliam [2011]).
The overset unstructured mesh methodology has a set of overlapping meshes that require the computation of the domain connectivity information to establish how the overset meshes exchange information between each other. In order to maintain the parallel scalability, the computation of the overset domain connectivity needs to also be parallel and have sufficient scalability when using a large number of computer nodes in order to keep the entire flow solver scalable. Noack et al. [2009] developed a new code called Suggar++. It was developed from scratch using C++ and had the same general capability as an existing overset mesh assembly code called SUGGAR, but it was more efficient and had improved serial and parallel execution performance because of efficient hole cutting and grid partitioning methods.
Multigrid Methods
To improve the efficiency of a three-dimensional (3D) unsteady compressible Navier–Stokes flow solver, research on improving multigrid methods was performed by Diskin et al. [2007] and Liao et al. [2008]. They were able to demonstrate “textbook” multigrid efficiency, which is the optimal efficiency of a multigrid method, for the unsteady subsonic compressible Navier–Stokes equations in three dimensions, for an implicit discretization that was second-order accurate in time and space. The multigrid method was shown to have optimal efficiency at high Reynolds numbers and for large time steps. The application was for a domain with periodic boundary conditions, with future work for more general inflow, outflow, and no-slip boundary conditions.
Turbulence Modeling
The influence of turbulence modeling on the vortical wake of rotorcraft simulations was conducted by Potsdam and Pulliam [2008]. They showed that some turbulence model formulations, like the Spalart–Allmaras model, were observed to produce too much turbulent eddy viscosity if the production was based on the vorticity field of a vortex-dominated rotor wake. As a result of excessive turbulent eddy viscosity in the rotor wake, and its subsequent convection and diffusion, the wall-bounded viscous flow was modified. To remedy this, the turbulence model production source terms were turned off in the rotor wake, demonstrating an improvement in the solution accuracy for hover and forward flight.
A computational study on the parameters affecting Large Eddy Simulations (LES) for bluff body flows was investigated by Mankbadi and Georgiadis [2014]. This investigation examined the numerical sensitivities of the mesh size, time step, and sample frequency, as well as the extent of the spanwise domain on the prediction of the flow over a square cylinder. This study showed that an insufficient spanwise extent results in an overprediction of the streamwise and transverse turbulent intensities. This research was followed by a comparison between high- and low-order methods for LES simulations of a compressible shear layer [Mankbadi et al., 2015]. This investigation showed that the low- and high-order methods had similar results on a fine mesh but that the high-order method could achieve the same results on a coarse mesh.
Flow Visualization
Unsteady-flow visualization is required to understand complex flow fields, especially because of the large amounts of data from rotorcraft CFD simulations [Yamauchi and Young, 2009]. Of particular interest is the tracking of rotor tip vortices and their properties like vortex-core size and cross-flow velocity profiles. Kao and Chaderjian [2010] developed an automated approach that extracts vortex-core trajectories as well as cross-flow velocity profiles from a CFD solution. This was an improvement over a previous vortex-core detection algorithm that extracted noncontinuous vortex-core line segments. The approach was improved by Kao [2011] to generate contiguous vortex-core line segments that can span multiple grid zones. This work was then followed up by improvements of the vortex-core properties for a UH-60A application [Kao et al., 2015] and vortex-core growth rate for an isolated V22 TRAM rotor in hover [Kao et al., 2018]. Figure 3.3 shows the blade tip vortices tracked from a fine-grid CFD case.
Kao et al. [2013] also explored other flow visualization techniques that examined clipping of iso- surfaces to reduce the visual clutter of traditional iso-surfaces, and a flow texture mapping technique to provide an efficient way to depict flow patterns on cutting planes and aerodynamic surfaces. Figure 3.4 shows a comparison between a traditional streamline flow visualization, where the streamlines are restricted to the blade surface, and the texture map technique. The textured map technique has the advantage of not being dependent on the seed location (as in the streamline visualization) thus helping to quickly identify flow features of interest.
Figure 3.3. Blade tip vortices tracked from three blades using a fine-grid CFD case (Fig. 17 of Kao et al. [2018]).
Figure 3.4. Comparison of upper surface flow patterns using two different approaches at 90° azimuth (Fig. 9 of Kao et al. [2013]).
Computational Structural Dynamics
Work was done by Guruswamy [2008, 2009, 2010] to couple a beam-finite-element-based structure solver with a Navier–Stokes flow solver, OVERFLOW, for time-accurate, tight coupling for rotor blade simulations. Calculations for a nonrotating blade, rotating rigid blade, and rotating elastic blade were made and compared to experiments. Overall the dynamic aeroelastic responses compared well in both magnitude and phase to the experimental data. In 2012, Guruswamy [2012a] used the above tight-coupling approach to predict and compare results to the HART-II wind tunnel data. Figure 3.5 shows the time-accurate tight-coupling sectional normal force results comparted to the HART-II wind tunnel data for = 0.14, a shaft angle of 4 degrees, and a blade rotation of 1,020 RPM. The rotor blade collective and cyclic inputs from the experiment were used in the coupled simulation.
Figure 3.5. Comparison of sectional normal forces at 87% radial station for the HART-II for
= 0.14, 4 shaft angle, and 1,020 RPM blade rotation (Fig. 7 of Guruswamy [2012a]).
Guruswamy [2012b] performed a procedure to compute the bending-torsion flutter boundaries for a rotating blade using unsteady aerodynamic data from a time-accurate Navier–Stokes flow solution. The flutter speeds were computed by solving the eigenvalues equations that determine the system damping to identify the flutter point. The approach was compared to nonrotating blade experimental data. A flutter analysis was performed for a typical rotating blade case to demonstrate the approach.
Additional Research
A multi-code Python-based infrastructure that uses different gridding paradigms was demonstrated by Wissink et al. [2008]. The main advantage of this approach is to couple well- established, documented CFD codes that capture near-wall viscous turbulent flows together with structured cartesian grids away from the wall that have automatic grid generation with high-order numerical accuracy and time-dependent automatic mesh refinement. The focus of this research is the design of the infrastructure and mechanisms needed to turn existing standalone codes into modules that may be used in the infrastructure. The infrastructure was demonstrated using an unstructured near-body solver, NSU3D, with a structured off-body solver, SAMRAI, on an isolated V-22 rotor case [Wissink et al., 2008].
Jain et al., [2016] reported on a collaborative effort between the U.S. Army Aeroflightdynamics Directorate (AFDD) and NASA to integrate FUN3D as a near-body unstructured grid solver into the Helicopter Overset Simulation (Helios) tool, a high-fidelity computational framework for rotorcraft modeling supported by the U.S. Department of Defense High Performance Computing Modernization Program (HPCMP) Office and the U.S. Army. To demonstrate the integration of FUN3D into Helios, the following cases were tested: an isolated TRAM rotor in hover for performance and airloads; an isolated UH-60A rotor in high-speed forward flight for airloads and CFD/computational structural dynamics (CSD) coupling; the HART-II rotor-fuselage for blade-
vortex interaction (BVI) load, wake predictions, and combined rotor-fuselage modeling; dual counter-rotating UH-60A rotors for airloads; and a tandem rotor H-47 full aircraft for multiple near-body solvers, CFD/CSD coupling, and free-flight trim.
A hybrid CFD approach for rotorcraft simulations was developed by Anusonti-Inthra and Floros [2008] where a RANS flow solver was fully coupled with a Particle-based Vorticity Transport Method (PVTM). The approach divides the flow field into two regions, near-body and off-body, and uses an appropriate flow solver according to the dominate flow physics of that region. The near-body flow contains the solid surfaces, is dominated by boundary layer and viscous effects, and is best solved by a compressible RANS solver. The off-body regions are dominated by