Application of STAR-CCM+ to Helicopter Rotors in Hover Lakshmi N. Sankar and Chong Zhou School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA Ritu Marpu Eschol CD-Adapco, Inc., Orlando, FL

Background Over the past several decades, engineers have used a variety of tools for modeling and improving rotor design. An engineering model called a “Lifting Line Model” with a look up of 2-D airfoil load characteristics look-up table is often used during early stages of design, with empirical corrections for compressibility, and sweep. During a second “preliminary” stage of design, hybrid CFD + Lifting Line methods would be used. During later “detailed design” stages, a more accurate CFD based model is used to refine the design. STAR-CCM+ is a valuable tool for this final detailed design. In this work, we show selected examples of three types of rotors, to see how a preliminary and detailed analysis may be done.

Overview Introduction Detailed Analysis/Design Tool (STAR-CCM+) Hybrid CFD Methodology (GT-Hybrid) Wake Model (Single Tip Vortex) Vortex Core Modeling Full Span Wake Model Performance Predictions and Validation Sikorsky S-76 Helicopter Rotor with swept Tip Helicopter Rotor with Swept Anhedral Tip Coaxial Rotor Concluding Remarks

Objectives Apply STAR-CCM+ Analysis Wake-capturing Models To S76 Rotors In Hover Validate The Analysis For S76 In Hover Compare Predictions With GT-Hybrid (Preliminary Design/Analysis Tool) Analyze The Effects Of The Anhedral Tip On The Inflow Distribution Explain Why The “efficiency” is Improved By The Anhedral Platform Analyze a Coaxial Rotor

STAR-CCM+ Computational Domain

y+ of first point off the wall Parameters for the S-76 Model Simulations Mach Number at the Tip 0.65 Reynolds Number 1.20E+06 Ds 1.60E-06 y+ of first point off the wall ~1 Rotor Radius 56 inches C 3.1inch Wake capturing model Unsteady simulations (7 to 20 revolutions) Time step : 1 Deg. Azimuth Sub-iterations: 10 to 15 per time step Physics Model Coupled Energy Ideal Gas K-Omega SST, fully turbulent flow

Mesh Overset Mesh Topology The mesh for the rotor region Background Mesh The mesh around the rotor blade Blade surface grid The cut plane of the rotor region

Refined Mesh Region

GT-Hybrid CFD Methodology (Preliminary Design Tool) Hybrid Methodology Reynolds Averaged Navier-Stokes (RANS) methodology for flow over blades. Lagrangian free wake to model far wake. The near wake is captured inherently in the Navier-Stokes analysis. The far wake and effect of other blades accounted for using wake model. Wake induced velocities are applied as boundary condition on Navier-Stokes domain. Schematic View of the Hybrid Method

Wake Model (Single Tip Vortex) Lagrangian Free Wake model Single concentrated tip vortex assumption Collection of piece-wise linear bound and trailed vorticities Strength of the vortex elements is set to be equal to the peak bound circulation Vortex shedding point based on centroid of trailed circulation between the tip and location of peak bound circulation Vortex trailed at discrete azimuthal intervals. Vortex elements convected through freestream velocities and wake induced velocities

Vortex Core Modeling Wake behind any lifting surface must be considered as a viscous phenomenon Velocity induced by a vortex with Vatistas (1991) core (n = 2) Vortex core growth using the Bhagwat – Leishman (2002) core growth model

Full Span Wake Model (FSWM) The baseline wake model assumes a single concentrated tip vortex trailing from a region near the blade tip. This assumption would be physically less accurate for rotors in low speed forward flight. Single tip vortex is replaced by user specified multiple vortex segments trailed from all the blades. FSWM is based on vorticity conservation laws.

Grid Used for Numerical Studies A C-H grid topology is used Allowing flexibility with grid density near surface Better orthogonality and smoothness of grid lines near blunt leading edge of typical rotor blade airfoils Baseline Grid Size 131 x 70 x 45 ~ 0.4 million grid points per blade Wall spacing 1*10-5 chords The far field boundary is located at 9 chords from surface

Baseline S-76 Rotor Characteristics Baseline Model Rotor Blade Baseline Blade Planform Number of blades 4 Radius 56.04” Nominal Chord 3.1” Equivalent Chord 3.035” Tip Taper 60% c Root Cutout 19% R Sweep (leading-edge) 35 degrees at 95% R Solidity 0.07043 Airfoil SC1013R8, SC1095R8, SC1095 Scale 1/4.71 Twist -10° linear twist Twist distribution Thickness distribution

Vorticity and Q-criterion Distribution swept-tapered S-76 Planform, at CT/σ=0.09 Near wake is well captured, including the inner wake. Far field wake is smeared due to numerical diffusion because of the coarser grid “Starting vortex” is also seen

Results for the Baseline Tip Case CT: Wake Capture Model Matches Well with the Experimental Data CQ: Works Better at High Collective Pitch Angle

Results for the Baseline Tip Case

Parametric Studies

Results for the Anhedral Tip Case

Wake Vortex Trajectory (CT/σ = 0.09) Vertical location No test data available Vertical location Matches Well with OVERFLOW Good correlation could only be achieved for the first revolution (360 degrees of vortex age At higher vortex age, factors such as numerical diffusion, grid density, etc begin to cause deviations among the various methods. Radial location Over Predict the tip vortex contraction rate compare with other solvers Acceptable: Matches well with OVERFLOW Radial location

S-76 Baseline Rotor (Inflow is non-uniform) Induced Velocity (at the Rotor Disk), at 9.5 Degrees Pitch Angle

Rotor with Anhedral Tip has a more uniform inflow Induced Velocity (at the Rotor Disk), at 9.5 Degrees Pitch Angle

Results and Discussion for the coaxial rotor

Harrington Rotor Characteristics Blade Planform Harrington “Rotor 1” Harrington “Rotor 2” Tested inside a full-scale wind tunnel at NACA Langley Research Center Reference: Harrington, R.D., “Full-Scale-Tunnel Investigation of the Static Thrust Performance of a Coaxial Helicopter Rotor,” NACA TN 2318, Mar. 1951

Hover Performance

Contributions: Upper & Lower Rotor to Thrust

Upper vs Lower Rotor Figure of Merit

Effect of Number of Wake Filaments

Tip Vortex Structures (STAR-CCM+)

Comparison of Tip Vortex Descent Rate

Comparison of Tip Vortex Contraction Rate

Summary The aerodynamic behavior of a conventional rotors, anhedral rotors, and coaxial rotors has been studied using two approaches – a hybrid Navier-Stokes-free wake solver, and a full wake-capturing approach Comparisons with test data have been done. Anhedral tips produce a more uniform induced velocity. This leads to a more efficient rotor. Coaxial rotors are compact, have reduced swirl losses, and eliminate the need for tail rotor. The performance of upper and lower rotors, for equal and opposite torque, was examined Comparisons of the predicted vortex descent rate and radial contraction rate were also examined

Conclusions At lower thrust settings, both methods give good agreement with test data As the thrust level increases, the hybrid method tends to underestimate the power required, and overestimate the figure of merit We are in the process of improving the hybrid results using vortex particle methods, improved tip cap grids, and improved treatment of root regions

Conclusions (Continued) In terms of computational time, the hybrid method is very efficient, requiring 4 to 6 hours of CPU time on a Linux cluster with 72 cores of CPU The wake capturing method is considerably more expensive. For this reason, the hybrid method is well suited for initial design studies where the rotor geometry is parametrically varied, and quick reasonably accurate solutions are essential Once a few promising configurations have been identified, more accurate (but computationally expensive) wake capturing simulations may be done to refine the design.

Related Prior Work Hariharan, N., Egolf, T. A., and Sankar, L. N., “Simulation of Rotor in Hover: Current State, Challenges and Standardized Evaluation,” AIAA 2014-0041. Lorber, P.F., et al., “A Comprehensive Hover Test of the Airloads and Airflow of an Extensively Instrumented Model Helicopter Rotor,” Proceedings of the 45th Annual Forum, American Helicopter Society, May 1989, pp 281-295. Balch, D. T., “Experimental Study of Main Rotor Tip Geometry and Tail Rotor Interactions in Hover, Volume 2, Run Log and Tabulated Data,” NASA CR 177336, 1985. Marpu, R., Sankar, L. N., Egolf, T. A., and Hariharan, N., “Simulation of S- 76 Rotor in Hover Using a Hybrid Methodology,” AIAA-2014-0210, SciTech 2014, January 2014. Baeder, J., Medida, S., “OVERTURNS Simulation of S-76 Rotor in Hover,” AIAA-2014-0045, SciTech 2014, National Harbor, MD, January 2014.