Sean Kamkar

Overview of the Helios Version 2.0 Computational Platform for Rotorcraft Simulations

This article summarizes the capabilities and development of the Helios version 2.0, or Shasta, software for rotary wing simulations. Specific capabilities enabled by Shasta include off-body adaptive mesh refinement and the ability to handle multiple interacting rotorcraft components such as the fuselage, rotors, flaps and stores. In addition, a new run-mode to handle maneuvering flight has been added. Fundamental changes of the Helios interfaces have been introduced to streamline the integration of these capabilities. Various modifications have also been carried out in the underlying modules for near-body solution, off-body solution, domain connectivity, rotor fluid structure interface and comprehensive analysis to accommodate these interfaces and to enhance operational robustness and efficiency. Results are presented to demonstrate the mesh adaptation features of the software for the NACA0015 wing, TRAM rotor in hover and the UH-60A in forward flight.

Automated Off-Body Cartesian Mesh Adaption for Rotorcraft Simulations

A new adaptive mesh refinement strategy is presented that couples feature-detection with local error-estimation. The goal is to guide refinement to key vortical features using feature detection, and to terminate refinement when a maximum acceptable error level has been reached. The feature detection scheme, which has been presented in previous related work, uses a special local normalization that allows it to properly identify regions of high vortical strength without tuning to a particular vorticity value. The newly introduced error estimation scheme applies a Richardson extrapolation-like procedure to detect local truncation error based on solutions from different grid levels. The error is then used the computed error to determine when to cut off further refinement. The paper presents a theoretical analysis of the scheme, applying it to computations of an isolated vortex and comparing to an exact solution. The scheme is implemented as part of the off-body Cartesian solver in the Helios code. Two practical cases are considered, resolution of the wake tip vortex from a NACA 0015 wing, and resolution of the wake structure of a quarter-scale V22 rotorcraft.

Automated Grid Refinement Using Feature Detection

We investigate feature detection schemes used to guide appropriate mesh resolution for CFD calculations with adaptive mesh refinement (AMR). Methods based on eigenvalues of the velocity gradient, difference between vorticity and strain rate magnitudes, and eigenvalues of the vorticity vector are investigated and compared to traditional vorticity-based detection schemes such as the Q-criterion. We are particularly interested in non-dimensional schemes that do not require the user to dial-in particular values of a quantity to refine to. Results are shown for a variety of analytic and practical test cases.

Combined Feature-Driven Richardson-Based Adaptive Mesh Refinement for Unsteady Vortical Flows

A DAPTIVE mesh refinement (AMR) is a useful approach for computational fluid dynamic (CFD) simulations that contain isolated relevant features like shocks or tip vortices, which are small in size with respect to the surface geometry but have a profound impact on the resulting flowfield. The fixed-wing aerodynamics community has used adaptively refined grids for high-fidelity solutions of transonic and supersonic flows [1–3]. In addition to shocks, trailing tip vortices occur in fixed-wing flight but are of greater interest for rotorcraft flight, in which the vortices shed from the blade tips can dominate the unsteady dynamics of the turbulent wake and can significantly impact vehicle performance, vibration, and noise. Accurate wake resolution can therefore lead to improvements in the prediction of rotor performance metrics [4], such as the figure of merit, a nondimensional parameter that represents the efficiency of a rotor in hover. Additionally, wake modeling is important because rotorcraft fly in their own wake, which may become entrained during hover and interact with the fuselage during forward flight [5]. However, despite the need to accurately resolve tip vortices, the rotorcraft community has not exercised AMR to the degree that the fixed-wing community has to model shocks, mainly due to the complexities in the unsteadiness of rotary-wing problems. Similar to shock modeling for fixed-wing cases, the spatial scales of trailing vortices are relatively smaller than the chord distance, thereby requiring relatively fine meshes and making the use of uniformly fine grids largely impractical [5]. Therefore, in this work, we develop an unsteady AMR strategy that targets vortical features with the goal of enhancing the resolution for both fixedand rotarywing problems. In particular for rotorcraft, complexities involving the inherently unsteady flowfield and the relative motion between the rotor and the fuselage make the implementation of efficient adaptive schemes especially challenging. Moreover, high-fidelity rotorcraft CFD are highly unsteady and require time-accurate simulations. Adjointbased AMR has shown promise for steady CFD applications [1,6,7], but time accurate solutions require the adjoint problem to be fully solved backwards in time, which is intractable for large-scale rotorcraft simulations that can involve 10 to 10 time-steps. Therefore, in this work we seek an alternative error-based refinement approach that specifically targets the vortex cores in a local manner without having to solve the full adjoint. Our approach first identifies the vortex cores using feature detection, and then the level of mesh resolution is set according to local solution error. In our earlier work [8,9], we developed four locally normalized methods that appropriately guided the AMR process based upon popular methods by the feature detection community [10–13]. A major goal of this development was to eliminate the parameter tuning that is required for common (dimensional) approaches, e.g., vorticity-based. Whereas dimensional approaches require highly tuned thresholds to select regions for refinement, the normalized schemes are able to mark regions with key vortical features using a fixed threshold, regardless of vortical strength, size, and/or resolution. However, while these nondimensional schemes effectively deal with the issue of identifying regions for refinement, the degree of mesh resolution still needs to be specified by the user. To reduce user dependency and improve computational efficiency, in this study, we examine a method of automatically setting the degree of mesh resolution by using the solution error as a guide. The objective of the current paper is to develop a solution-based error estimator that can be coupled with the nondimensional featurebased AMR. The error estimator is used to limit the amount of applied grid resolution so that additional refinement will be halted once the solution error is sufficiently low. Similar to a global functional, which is commonly used by adjoint approaches, our approach uses a local functional that is based upon quantities of interest to vortical motion. In effect, we aim to reduce the local error estimate through additional mesh refinement. Moreover, the Richardson estimator is quite practical because it is relatively simple to implement and efficient to execute. The remainder of the paper is organized as follows. A description of the adaptive overset grid-based CFD approach used for the present work is presented first in Sec. II. Thereafter, Sec. III briefly reviews the nondimensional feature-based approach, which is used to identify candidate regions for mesh refinement. Section IV offers a theoretical analysis of the Richardson error estimator, along with spatial accuracy validation tests. Then, the coupled AMR strategy that combines the feature identification with the Richardson Presented at the 49th AIAA Aerosciences Conference, Orlando, FL, January 4–7, 2011; received 14 October 2011; revision received 30 April 2012; accepted for publication 7 May 2012. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Copies of this paper may be made for personal or internal use, on condition that the copier pay the

An Automated Adaptive Mesh Refinement Scheme for Unsteady Aerodynamic Wakes

10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0001-1452/12 and

Using Feature Detection and Richardson Extrapolation to Guide Adaptive Mesh Refinement for Vortex-Dominated Flows

10.00 in correspondence with the CCC. ∗Post-Doctoral Researcher; skamkar@merlin.arc.nasa.gov. AIAAMember. Aerospace Engineer; andrew.m.wissink@us.army.mil. AIAA Member. Aerospace Engineer; vsankaran@merlin.arc.nasa.gov. AIAA Member. Professor; jameson@baboon.stanford.edu. AIAA Fellow. AIAA JOURNAL Vol. 50, No. 12, December 2012

Cartesian Adaptive Mesh Refinement for Rotorcraft Wake Resolution

A non-dimensional feature detection approach is employed to control adaptive mesh refinement for unsteady aerodynamic simulations in which the wake experiences highly unsteady vortical structures. The scheme identifies vortical flow features, independent of types, size, and strength, and thereby provides a means to refine the mesh in an automated fashion without the need for case-specific tuning and user intervention. The feature-based scheme can also be coupled with Richardson Extrapolation error estimation to control mesh resolution requirements. High-order numerics are applied together with localized mesh refinement improve far-field resolution of vortical structures. Test cases include an advecting theoretical ring vortex, vortex shedding over a cylinder, and hovering rotor wake flow. In all cases, the scheme demonstrates the ability to automatically control mesh refinement without user intervention.

Feature-driven Cartesian adaptive mesh refinement for vortex-dominated flows

The article describes a Cartesian-based adaptive mesh refinement approach applied to vortex-dominated flows. Several distinct feature-detection methods are investigated to furnish a means for tagging cells for refinement. In each case, appropriate normalization is defined so that the process is automated for a range of operating conditions. Richardson extrapolation is proposed to assess the local error and terminate the mesh refinement once adequate error reduction is achieved.