Application of the HPCMP CREATETM-AV Kestrel to an Integrated Propeller Prediction

This article presents the results of a computational investigation of an integrated propeller test case using the HPCMP CREATETM-AV Kestrel simulation tools. There is a renewed interest in propeller-driven aircraft for unmanned aerial vehicles, electric aircraft, and flying taxies. Computational resources can significantly accelerate the generation of aerodynamic models for these vehicles and reduce the development cost if the prediction tools can accurately predict the aircraft/propeller aerodynamic interactions. Unfortunately, limited propeller experimental data are available to validate computational methods. An American Institute of Aeronautics and Astronautics (AIAA) workshop was therefore established to address this problem. The objective of this workshop was to generate an open access-powered wind tunnel test database for computational validation of propeller effects on the wing aerodynamics, specifically for wing-tip-mounted propellers. The propeller selected for the workshop has four blades and a diameter of 16.2 in. The wing has a root and tip chord of 11.6 and 8.6 in, respectively. Two different simulation approaches were used: one using a single grid including wind tunnel walls and the second using a subset grid overset to an adaptive Cartesian grid that fills the space between the near-body grid and wind tunnel walls. The predictions of both approaches have been compared with available experimental data from the Lockheed Martin low-speed wind tunnel to investigate the grid resolution required for accurate prediction of flowfield data. The results show a good agreement for all tested conditions. The measured and predicted data show that wing aerodynamic performance is improved by the spinning tip-mounted propeller.


Introduction
Recently, there has been a surge of interest in using propellers for small unmanned aerial vehicles, electric-powered vehicles, and urban air transportation concepts. In addition to the environmental benefits, Patterson et al. [1] mentioned up to a 90% reduction in the fuel consumption for an electric-powered aircraft compared with those using conventional internal combustion engines (ICE). Other advantages over ICE include increased efficiency, power independent of changes in altitude or flight speed, fewer parts, increased reliability, and reduced vibration as well as reduced noise [1]. However, a major drawback in the success of fully electric aircraft has been associated with the high weights of batteries. This issue should be overcome in the near future with advances in battery technologies to increase the battery specific energy levels (energy capacity per unit battery weight), but a short-term possible solution to this problem is improving the aerodynamic efficiency of an electric-powered aircraft.
propeller, the propeller prediction capability has not yet been validated for many integrated propeller configurations. The lack of experimental data for validating computational models of a distributed electric propulsion such as the X-57 Maxwell airplane has led to the establishment of the 1st American Institute of Aeronautics and Astronautics (AIAA) Workshop for Integrated Propeller Prediction (WIPP). However, it was decided to use a less complex configuration than the X-57 airplane for the first workshop, only considering a wing-tip-mounted propeller (Mod III without high-lift pylons). The objective of this workshop was to generate an open access-powered wind tunnel test database for computational validation of the effects of a wingtip-mounted propeller on the wing aerodynamics. This article specifically describes the use of the HPCMP CREATE TM -AV Kestrel simulation tools to investigate the propeller wing aerodynamic interaction of this novel configuration. Fully resolved geometry blades are modeled in Kestrel using two different solves of KCFD and KCFD/SAMAIR. KCFD uses a second-order ccurate cell-centered finite volume discretization, however, SAMAir utilizes a fifth-order finite volume discretization on Cartesian meshes and allows adaptive mesh refinement. This work establishes a validated computational framework for wing/propeller interaction predictions.

CFD Solver
Kestrel is the fixed-wing product of the CREATE TM -AV program funded by the DoD High Performance Computing Modernization Program (HPCMP). The objective of the CREATE TM program is to improve the Department of Defense acquisition time, cost, and performance using state-of-art computational tools for design and analysis of ships, aircraft and antenna. Kestrel is specifically developed for multidisciplinary fixed-wing aircraft simulations incorporating components for aerodynamics, jet propulsion integration, structural dynamics, kinematics, and kinetics [19]. The code has a Python-based infrastructure that integrates Python, C, C++, or Fortran written components [20]. Kestrel 10.4.1 is the latest release and used in this work. The code has been extensively tested and a variety of validation documents have been reported.
Kestrel CFD solvers include KCFD [21], COFFE [22], and KCFD/SAMAir [23]. The KCFD flow solver and the dual mesh KCFD/SAMAir are used in this study. KCFD uses a second-order accurate cell-centered finite volume discretization, however, SAMAir utilizes a fifth-order finite volume discretization on Cartesian meshes [24]. In more detail, the KCFD flow solver discretizes the Reynolds averaged Navier-Stokes (RANS) equations into a second-order cell-centered finite-volume form. The code then solves the unsteady, three-dimensional, compressible RANS equations on hybrid unstructured grids [25]. The KCFD flow solver uses the method of lines (MOL) to separate temporal and spatial integration schemes from each other [21]. The spatial residual is computed via a Godunov type scheme [26]. Second-order spatial accuracy is obtained through a least squares reconstruction. The numerical fluxes at each element face are computed using various exact and approximate Riemann schemes with a default method based on the HLLE++ scheme [27]. In addition, the code uses a subiterative, point-implicit method (a typical Gauss-Seidel technique) to improve the temporal accuracy. Some of the turbulence models available within Kestrel include Spalart-Allmaras (SA) [28], Spalart-Allmaras with rotational/curvature correction (SARC) [29], Menter's SST [30], and delayed detached Eddy simulation (DDES) with SARC [31].
Kestrel can include fully resolved blades, however, the propeller grid should be individually generated. The propeller flow-field can be simulated using a sliding interface approach for a non-spinning propeller or using an overset grid approach for spinning propellers. In addition, the code allows a thin actuator disk approach with uniform and non-uniform load distributions. A non-uniform case requires a given radial position for maximum thrust force. The loading profile is assumed to be linear with a zero thrust at the inner blade radius and then increases until the radial position of maximum thrust, then decreases to zero at the rotor tip. The blade element momentum modeling has been recently included in Kestrel version 11.0.
The Kestrel's off-body Cartesian flow solver, SAMAir, can capture higher fidelity flow features (e.g., wakes) away from the primary body. SAMAir uses an overset grid approach in which the "near-body" grid is overset to the "off-body" Cartesian grid. The near-body grid can be generated from an existing grid using the subset mesh manipulation method. This subset grid should include the prism layers on the no-slip surfaces, i.e., the off-body grid should not be used to capture the boundary layer at these surfaces. The off-body grid, on the other hand, fills the computational space between the near-body and far-field boundary. An overset fringe is used where these two grids overlap. Using adaptive mesh refinement (AMR), the Cartesian solver can automatically refine the mesh around the regions of interest, and therefore, increase the solution accuracy where it is needed. The code only needs the extent of far-field boundary and the maximum number of grid refinement levels.

Test Case
The configuration used in the 1st AIAA Workshop for Integrated Propeller Prediction consists of a wing and a wingtip-mounted propeller resembling a 40.5% model scale of the X-57 airplane. The geometry details are given in Figure 1. The wing has a leading-edge sweep angle of 1.9 deg, a tip chord of 8.6 in, a root chord of 11.6 in, an aspect ratio of 6.7, and a mean aerodynamic chord of 10.15 in. The 10%-scale C-130 4-blade propeller with a diameter of 16.2 inches has been used and mounted on a pylon at the wing tip. The pylon length and maximum diameter measure 24.15 and 4.75 inches, respectively. The propeller blade angle was set at 37.5 deg to provide representative thrust and advance ratio values at tested airspeeds. Test cases include an isolated wing with spinner geometry and the wing with propeller blades. The isolated wing was used to establish a baseline to investigate the propeller effects. All models contain a splitter plate fairing at the wing root which was 17.25 inches long and 6.0 inches wide. This splitter plate is attached to a fused deposition modeling fairing, which allows the splitter plate to be 6.4 inches from the tunnel floor. Hooker et al. [32] provide more details of tested geometries.  Six spanwise positions were selected for pressure tap measurements, including two behind the propeller disk. The configuration was mounted vertically on the wind tunnel floor and a boundary layer diverter was used to eliminate the effects of boundary layer formed at the tunnel lower wall on the wing aerodynamic performance. Notice that in Figure 1a, blue-colored surfaces are only used to account for forces/moments imposed on the wing surface. The red-colored surfaces are used to measure propeller thrust and torque. In denoting forces and moments, the term "TC" shows thrust corrected, i.e., thrust has been removed from the total forces/moments measured at the load balance. The moment reference point is located at (2.99, 0.28, 6.35) inches and is highlighted in Figure 1b

Experimental Apparatus
Hooker et al. [32] detail the conducted experiments. In summary, the WIPP configuration was tested in the lockheed Martin low speed wind tunnel, which is a conventional single return, atmospheric pressure, closed test section facility. Test section size measures as 16.25 × 23.25 × 43 ft with a 9000 HP (6700 kw) motor. The tunnel top speed is 90 m/s. The WIPP model was positioned vertically in this tunnel, Figure 2a, over a turnable plate. Experiments include isolated wing (no propeller blades), prop-off, and prop-on tests at different Mach numbers and angles of attack. The measurements include wing integrated forces and moments, pressure tap data at six spanwise locations, and a wake survey taken at several locations aft of the propeller. The pressure tap positions can be seen in Figure 2a where the leading edge paint is colored white at tap positions. The vertical and horizontal wake survey measurements can be seen in Figure 2a,b. The rake was moved to 5 locations behind the propeller and flow parameters, which were measured at every 0.2 in along wake strip.
Power-on conditions were tested at thrust coefficients of 0.04, 0.2, and 0.4, where the thrust coefficient is defined as: where T is the propeller thrust, q ∞ = 0.5ρV 2 is the free-stream dynamic pressure, and S re f is the wing planform area of 675.6 in 2 .
Tunnel conditions were set to Mach numbers of 0.08 and 0.11 at sea-level conditions. The angles of attack tested include [0, 5,7,9,11,13,15,17] deg. Table 1 summarizes the simulation cases of this study. (a) Vertical rake (b) Horizontal rake

Computational Grids
Two different computational grids have been tested: grids with farfield boundaries that match the wind tunnel walls and subset grids that overset to a background Cartesian grid. These grids have been used to investigate the grid resolution required for accurate prediction of flowfield data. Computational grids including the wind tunnel walls are referred to as "RANS" grids in this article.
Wing and propeller grids were generated individually; the propeller grid was then overset to the wing grid. Figure 3 shows the wing geometry relative to the walls in the RANS grids. The overset boundary is shown in this figure as well. In this work, all wing and propeller surfaces were modelled as no-slip walls. The tunnel floor was modeled as a slip wall to eliminate the need for generating prism layers to capture the boundary layer. All other tunnel walls were modeled as far-field. In more detail, computational grids were generated in Pointwise version 18.0. The surface grid cells are mostly structured quadrilaterally, but anywhere that these cell types are not possible to make, triangular surface cells are used. The interface between structured and unstructured mesh uses the surface T-rex technique, which ensures high quality transition between the structured and unstructured surface meshes. The main motivation for using the quadrilateral mesh is to have very good grid resolution on the blade leading and trailing edges and at the blade tips. A part of the hub is covered with patches of structured meshes as well. The volume mesh is fully unstructured with 50 prism layer on the propeller surface. The growth ratio of the prism layer is 1.25 and the growth is terminated when the transition between the prism layer and the tetrahedral mesh is smooth.
The wing grid including the tunnel volume has around 83 million cells. The propeller grid has an overset boundary with a diameter of about 1.5 times of blade diameter. This grid has around 19 million cells. Some grid images are given in Figure 4.
For Kestrel simulations, subset grids of the wing and propeller were generated. The subset grids are clipped at a normalized distance of 4 inches from the walls. The subset grid should include the prism layers to capture the boundary layer formed over the no-slip walls. The subset grids are shown in Figure 5a,b. The wing and propeller subset grids contain about 23.2 and 18.3 million cells, respectively. These subset grids are overset to a background Cartesian grid with 200-inches distance in front, back, and above the model. The sides have a distance of 138 inches. The lower surface is at the wind tunnel floor. All sides were assumed to be a farfield, but the bottom side was assumed to be a slip wall. A refinement region was defined around and behind the propeller. The Cartesian grid extent and the refinement region can be seen in Figure 5c. Seven tap locations were defined to match the wake survey measurements in the wind tunnel. These tap positions are shown in Figure 5d.

Results and Discussions
Only the Mach 0.08 case was considered in this study. Kestrel-KCFD and Kestrel-SAMAir flow solvers with the DDES-SARC turbulence model were used. First results correspond to the validation of propeller thrust and torque with available measured data at thrust coefficients of 0.04, 0.2, and 0.4. For validation purposes, the wing and propeller cases were run with different propeller spin rates ranging from 2000 to 7000 rpm. The RANS grid with five Newton sub-iterations was used. A time step of 0.0001 s and a temporal damping coefficient of 0.01 were used in all these simulations. The simulations were run for 5500 time steps with the propeller beginning to spin at t = 0.05 s. For each case, the thrust and torque applied to the propeller blades (red surfaces in Figure 1a) were calculated in Kestrel. These data were compared with experimental data at three spin rates and are shown in Figure 6. Good agreement was found between CFD and experimental data. Note that there is no thrust force for spin rates below 2800 rpm. The force generated by the propeller at these low spin rates is an additional drag force on the whole configuration.  The following results are focused on the isolated wing (no propeller blades). Kestrel was run in an unsteady mode (second-order accuracy in time) with a time step of 0.001 s and three Newton sub-iterations. Only RANS grids were used. Simulations were run for 5500 iterations, including 500 start-up iterations. The start-up iterations are usually helpful to have a robust startup capability before a motion begins, e.g., propeller spin or control surface deflection. Note that physical time will be held fixed at zero during these iterations. Temporal damping coefficient was set to 0.01 as well. The solutions for the final two seconds were time averaged. Simulations were run for angles of attack of [0, 5,7,9,11,15,17] degrees. Figure 7 compares the predicted drag polar and pitch moment values with measured data for an isolated wing. Figure 7 shows that CFD data agree well with experimental data up to nine degrees angle of attack. At higher angles, CFD predicts larger drag values and a steeper pitch moment curve slope. In addition, CFD data predict slightly larger lift values for angles between 7 and 9 degrees.   Next, the wing with a powered-off propeller is simulated using RANS and SAMAir grids. The powered-off propeller is denoted as CT = 0. These simulations were run for 7500 time steps. The mesh refinement begins at iteration 3600 with refinement at every 250 iterations based on the scaled Q-Criterion. Time step is 0.001 s. Off-body temporal damping coefficient was set to 0.025. Three Newton sub-iterations were used. Figure 9 compares the isolated wing predictions with wing/propeller predictions using RANS and SAMAir grids. Note that the blade forces and moments were included in the shown integrated forces and moments. The non-spinning propeller will increase the drag force compared with the isolated wing. At small angles of attack, the lift is slightly smaller than for the isolated wing as well. Both RANS and SAMAir predictions agree well with each other up to 9 degrees angle of attack.
At larger angles, the SAMAir data have drag coefficients similar to the isolated wing (decreasing lift at these angles), but the RANS grid shows increasing lift at large angles of attack.  In more detail, Figures 10-12 compare the wing surface pressure data of an isolated wing with a wing/propeller with CT = 0 using RANS and SAMAir grids. At small angles of attack, the propeller has no effect on the pressure data at Tap Figure 13 compares the flow solution of wing and powered-off propeller simulations using RANS and SAMAir grids at angles of attack of 0, 5, and 15 degrees. Contours of pressure coefficient and iso-surfaces of zero x-velocity are shown. Figure 13 shows that both RANS and SAMAir grids have similar pressure coefficient data at angles of 0 and 5 degrees. At 15 degrees angle of attack, there are different pressure values at the wing's upper surface at the wing's root and mid-sections. The SAMAir simulations show smaller pressure regions near the trailing edge. SAMAir simulations also show a larger separated flow region at the wing's trailing edge than the RANS grid. Finally, for angles of 0 and 5 degrees, both grids show similar separated flow regions, however, SAMAir shows more details of the eddies formed in the separated region than RANS grid. In the final simulations, the propeller rotates at different rates to match thrust coefficients of 0.04, 0.2, and 0.4. Simulations are again run with RANS and SAMAir grids. Five Newton sub-iteraions with a time step of 0.00005 s were used. Refinement frequency was set to every five time step. Figure 14 compares the drag polar plots of the isolated wing with wing/propeller at three different thrust settings. Note that in Figure 14a, the thrust force was included in the shown forces but it has been removed in the plots of Figure 14b. Figure 14a shows that CFD data predicted with RANS and SAMAir grids match well with each other and experimental data at all thrust settings, though for the highest CT value the discrepancy between predictions and experimental data was higher than for the other CT values. Figure 14b shows that a wingtip-mounted propeller will improve the wing aerodynamic performance as less drag and larger lift values are predicted compared with a no-propeller case.  Figure 15 shows the effects of the propeller at different thrust coefficients on the wing pressure distribution. No pressure differences can be seen between the isolated wing and integrated wing/propeller at pressure taps located far from the propeller disk. Closer to the propeller disk, the pressure differences between upper and lower surfaces become larger with increasing thrust coefficient. This is due to increased dynamic pressure behind the propeller and the changes in local angle of attack due to propeller rotation. This means that the wing will experience higher local lift at these locations. In more detail, Figure 16 shows the propeller slipstream for thrust coefficients of 0.04, 0.2 and 0.4. The slipstream becomes stronger with increasing thrust coefficient, as shown in this figure. Notice the highly reduced pressure regions formed over the wing upper surface due to the spinning propeller. The pressure becomes smaller as the propeller spins at higher rates.

Conclusions
This article applies the Kestrel simulation tools to the test cases of the 1st AIAA Workshop for Integrated Propeller Prediction (WIPP). Two computational approaches were used: Kestrel-KCFD using a grid that models wind tunnel walls and Kestrel-SAMAir that uses subset grids overset to a background Cartesian grid. Simulations include an isolated wing, wing with a powered-off propeller, and wing-propeller at different thrust coefficients. The predictions were compared with the available experimental data. The results show good agreement with experiments in most cases, specifically at low angles of attack. The effects of powered-on and powered-off propellers on the wing aerodynamic performance were discussed. The spinning propeller (tested in this work) will generate reduced pressure regions on the wing upper surface behind the propeller disk. This is due to the increased local angle of attack and increased dynamic pressure behind the propeller. This leads to a better aerodynamic performance, i.e., higher lift values compared with an isolated wing. Results show good agreement between predictions from RANS and SAMAir grids as well.

Acknowledgments:
The authors would like to thank Rick Hooker of Heldon Aerospace for providing the geometries and experimental data. Computer, software, and help-desk resources of the DoD HPCMP and CREATE TM -AV teams were instrumental in making this research possible. This work was supported in part by a grant of computer time from the DOD High Performance Computing Modernization Program on the Onyx supercomputer at the ERDC DoD Supercomputing Resource center. This material is based in part on research sponsored by the US Air Force Academy under agreement numbers of FA7000-16-2-0010 and FA7000-17-2-0007. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the organizations involved with this research or the U.S. Government. This work has been approved for public release: distribution unlimited (Public release approval PA#:USAFA-DF-2020-351).

Conflicts of Interest:
The authors declare no conflict of interest.