Center for Turbulence ResearchAnnual Research Briefs 2007

73

Coupled URANS simulation for the MDARTrotor in forward flight

By S. Hahn, S. Ananthan†, G. Iaccarino, J. D. Baeder‡ AND P. Moin

1. Motivation and objectives

During Phase 1A (2004–2006) of the DARPA Helicopter Quieting Program, we havenewly developed and validated a coupled-simulation technique for rotorcraft analysis, inwhich fully compressible and incompressible CFD solvers are combined for near-bladeand wake/far-field regions, respectively (Hahn et al. 2005; Hahn et al. 2006). With thisoutcome, Phase 1B of the project has been recently launched. In Phase 1B, additionalvalidations are planned to be continued by further applying our tools to more exotic con-figurations in practice. Another main focus of Phase 1B is on exercising various elementsof our computational techniques systematically in the order of increasing sophisticationand complication: For example, first tackle the problem using a standalone comprehen-sive code with a simply modeled wake, next proceed to the wake-coupling approachwhich only involves CFD on a single blade, and ultimately pursue the full-scale wakecapturing which would require intensive computational costs but could provide morehigh-fidelity results (Sitaraman & Baeder 2006). This organized procedure will allow aclear identification of benefit and limitation in lower-order models.

With these techniques and procedures, we have chosen the MDART (McDonnell Dou-glas Advanced Rotor Technology) rotor as our first test case of Phase 1B. The MDARTrotor is a pre-production version of the MD-900 Explorer, a five-bladed bearingless ro-tor. With demands for detailed test data to validate the performance of a bearinglessrotor, a joint wind-tunnel test program was conducted by McDonnell Douglas and NASAAmes Research Center in 1994. The hardware details and measured data are documentedin Jacklin et al. (1994), Nguyen et al. (1993), Nguyen & Lau (1994), Nguyen, Lauzon& Anand (1994), Nguyen et al. (1994), Straub & Charles (2001), and Shen (2003). Inthis program, the MDART rotor was extensively tested over a wide range of operat-ing conditions, including the flight speed of up to 200kt (corresponding to the advanceratio of µ = 0.49) and thrusts over 10,000lbs (amounting to the thrust coefficient ofCT /σ = 0.13). Since this wind-tunnel test was intended to obtain various quantities forstate-of-the-art bearingless rotor systems, comprehensive measurements were conductedregarding diverse aspects of rotor design such as performance, loads, stability, acous-tics, and response to open-loop higher-harmonic control (HHC) input. Therefore, it isa proper test case for the purpose of tool validation. Furthermore, our next goal is toexplore the concept of smart rotor, such as investigated in Koratkar & Chopra (2002),using our computational tools. This issue will be addressed by analyzing the performanceof MDART rotor blades equipped with trailing-edge flaps. Hence, it is important for fur-ther progress of our study to first obtain firmly established computational data on thebaseline MDART rotor. In this paper, we describe the wake-capturing prediction for thebaseline MDART rotor using our coupling technique.

† Postdoctoral research fellow, University of Maryland.‡ Professor, University of Maryland.

74 S. Hahn et al.

2. Experimental condition and computational setup

The full-scale MDART rotor has five blades with the chord length and rotor radiusof c = 0.254m and R = 5.15m, respectively, leading to the aspect ratio of R/c = 20.3(figure 1). Among the various conditions covered in the experiment, we have chosen aforward-flight condition, where the flight velocity and angular speed of the rotor areV∞ = 63.4m/s (M∞ = 0.187) and Ω = 392rpm (41.05rad/s), respectively, yielding thetip Mach number Mt = 0.62 and the advance ratio µ ≡ V∞/(ΩR) = 0.3. In this case, thetip Reynolds number is Ret ≡ ΩRc/ν∞ = 3.7 × 106. On the other hand, the shaft angleis chosen to be αs = −9.1. In the Cartesian coordinate system of our computation, theforward flight is embodied by introducing a freestream velocity (0, V∞ cosαs, V∞ sinαs).

The cylindrical coordinates, r =√

x2 + y2 and ψ = tan−1(−x/y), will be also used inthis paper.

To this problem, we have applied the same compressible–incompressible coupling tech-nique as was used in our earlier study (Hahn et al. 2005; Hahn et al. 2006). We use themulti-block, structured SUmb code (Van der Weide et al. 2006) and the unstructuredCDP solver (Ham & Iaccarino 2004) for compressible and incompressible flow solvers,respectively. Figure 1 shows the computational domain and grid system for each solver.The near-blade regions are solved by fully compressible SUmb (figure 1a), where thedomain extends approximately to 5c from each blade tip. On the other hand, the wakeand far-field regions are solved by incompressible CDP (figure 1b), where the extent ofcylindrical CDP domain is 0 < r/c < 40.6 and −20.3 < z/c < 14.2. After generating reg-ular structured-type hexahedral meshes in the CDP domain, inner holes were cut aroundfive blades (figure 1b) using the in-house software developed at University of Maryland,which forms overlap regions between SUmb and CDP domains (figure 1c). The SUmbmesh is based on the CO-type topology (figures 1d and e). The cross-sectional shapesof the MDART rotor blades are McDonnell Douglas HH-10 and HH-06 inboard andoutboard, respectively (figures 1f and g). The blade tips have a parabolic leading-edgesweep of 22 and 2:1 taper ratio (figure 1f). We have set up cylindrical meshes clusterednear the blade tip (figure 1h) in the CDP domain, while the core region is filled withtypical H-type meshes (figure 1i). We initially tried a CDP grid system with an innercylindrical hole and applied a slip boundary condition there. It resulted in spurious flowstructures near the inner cylindrical hole and was not successful. The v2–f turbulencemodel (Durbin 1995) is used for both flow solvers.

A uniform computational time step of ∆t = 2π/720Ω (i.e. 720 time steps per revo-lution) is used for both solvers in the present study. A free-stream boundary condition,(u, v, w) = (0, V∞ cosαs, V∞ sinαs), is imposed on the side and top boundaries of thecylindrical CDP domain, while the convective outflow condition is used at its bottomsurface. For the blade-hole interfaces in the CDP domain, all three velocity componentsand four turbulence variables (k, ǫ, v2, and f) are transferred from SUmb solutions tobe used as the interface condition. The same seven variables are also transferred fromCDP solutions to the outer surfaces of SUmb domain, where density is assumed to beconstant and pressure is extrapolated from the interior SUmb solutions. This interfacetreatment has shown a reasonably good performance in our earlier studies. The SUmb–CDP coupling is conducted in a tight manner: i.e. all data exchange between each solveris performed at every time step. All searches, interpolations, data transfers are exclusivelyhandled by CHIMPS (Alonso et al. 2006).

In regard to the CFD–CSD coupling, we use UMARC (University of Maryland Ro-torcraft Comprehensive Analysis Code) as a comprehensive CSD code. Contrary to the

Coupled URANS simulation for the MDART rotor 75

(a) (b) (c)

XY

Z

(d) (e) (f)

XY

Z

X

Y

Z X

Y

Z

(g) (h) (i)

Figure 1. Domain configuration and grid systems in the SUmb–CDP coupling for the MDARTrotor: (a) SUmb domain (dark and light regions for blades and interfaces, respectively); (b) CDPdomain (dark and light regions for inner holes and outer boundaries, respectively); (c) combinedview; (d) a C-mesh cross section in the SUmb domain; (e) an O-mesh cross section in the SUmbdomain; (f) blade-surface meshes near the tip; (g) blade-surface meshes near the rotor root; (h)CDP meshes (top view); (i) zoomed view of CDP meshes near the root.

SUmb–CDP coupling, this CFD–CSD coupling is conducted in a weak manner: i.e. air-load data and blade deformations are exchanged once per rotor revolution. Prior to thepresent coupled simulation, we first solved the same problem by weakly coupling UMARCand OVERTURNS (the overset-mesh version of TURNS; Srinivasan & Baeder 1993), andprovided the fully converged UMARC–OVERTURNS blade-deformation data as the ini-tial guess for the present coupled simulation. In this case, the flow quickly reached theperiodic state. The overall configuration and computational setup are similar to ourearlier experience on the UH-60A rotor (Hahn et al. 2006).

76 S. Hahn et al.

0 100 200 300 400−2000

0

2000r/R=0.21

My (

lb−

in)

0 100 200 300 400−1000

0

1000r/R=0.34

0 100 200 300 400−1000

0

1000r/R=0.43

My (

lb−

in)

0 100 200 300 400−1000

0

1000r/R=0.59

0 100 200 300 400−1000

0

1000r/R=0.81

My (

lb−

in)

Azimuth, ψ (deg)0 100 200 300 400

−500

0

500r/R=0.89

Azimuth, ψ (deg)

Figure 2. Time histories of the mean-removed flapwise bending moment at different radial loca-tions: Standalone UMARC solution (red); UMARC–SUmb–PWAM solution (blue); experiment(symbol).

3. Results and discussion

As was described in Section 1, we first examined the performance of two rudimen-tary approaches for the MDART rotor case: A standalone comprehensive analysis usingUMARC and a wake-coupling approach where CFD on a single blade is coupled withfree-wake modeling. For the wake-coupling technique, we used UMARC, SUmb, andPWAM (Parallel Wake Analysis Module; Gopalan et al. 2006) for comprehensive, CFD,and free-wake-modeling solvers, respectively. Figures 2, 3, and 4 show comparisons ofmean-removed flapwise, torsional, and chordwise bending moments, respectively, amongstandalone UMARC, wake-coupling, and experimental results. Figure 2 indicates thatthe wake-coupling approach indeed shows better agreement with the experiment than thestandalone UMARC solution in flapwise bending-moment prediction. Especially notice-able is a positive bump around ψ = 180, shown at three inboard stations (r/R = 0.21,0.34, and 0.43) in the standalone UMARC solution, and its elimination by the wakecoupling. It results in better qualitative accordance with the experiment. Overall, thewake-coupled solution shows temporal behaviors much better correlated with the experi-ment, especially at two outboard stations (r/R = 0.81 and 0.89). On the other hand, theadvantage of wake coupling is not quantitatively prominent in torsional-moment predic-tions (figure 3). However, it is notable that the standalone UMARC and wake-coupledsolutions show mutually out-of-phase behaviors in 150 < ψ < 330 (most distinct atthe outboard location r/R = 0.75), and the phase information from the wake-couplingapproach is in general closer to the experiment. Meanwhile, neither of the standaloneUMARC and wake-coupled solutions shows a satisfactory prediction of the chordwise

Coupled URANS simulation for the MDART rotor 77

0 50 100 150 200 250 300 350 400−500

0

500r/R=0.25

Mx (

lb−

in)

0 50 100 150 200 250 300 350 400−500

0

500r/R=0.35

Mx (

lb−

in)

0 50 100 150 200 250 300 350 400−200

0

200r/R=0.75

Mx (

lb−

in)

Azimuth, ψ (deg)

Figure 3. Time histories of the mean-removed torsional moment at different radial locations.Legends are the same as in figure 2.

bending moment (figure 4). Most evident is the very good agreement between standaloneUMARC solution and experiment at r/R = 0.21, which leaves room for further investiga-tion. In general, the wake-coupled solution does not properly represent the high-frequencycontents and shows much smoother behaviors than the experiment, while the standaloneUMARC solution exhibits erroneous phase prediction. Therefore, a high-fidelity wake-capturing approach is believed to play an important role in the baseline MDART rotorprediction.

Figure 5 shows airload contours on the rotor disk obtained from the coupled SUmb–CDP simulation, where the mean airload is removed as was done in Sitarman & Baeder(2006) and Hahn et al. (2006). The overall trend is similar to what was observed in theUH-60A rotor for the high-speed forward-flight condition (C8534): i.e. negative normalforce and pitching moment on the advancing side (90 < ψ < 180) and strongly positivenormal force near ψ = 360. The inboard normal-force distribution also shows a similarbehavior to that in the UH-60A C8534 condition. Currently, no experimental data areavailable about normal/chordwise force components and pitching moment. Therefore, asan alternative to validate the present computation, we compared the results of coupledSUmb–CDP simulation with those from OVERTURNS computation. Figures 6, 7, and8 show comparisons of normal and chordwise force components and pitching moment,respectively, between two different simulations. In general, the extent of agreement isvery good in all three airload components. In particular, the accordance shown in thenormal and chordwise force components is almost perfect at all radial locations, eventhough different turbulence models are used for each solver (Spalart–Allmaras and v2–f for OVERTURNS and SUmb–CDP coupling, respectively), which again confirms the

78 S. Hahn et al.

0 100 200 300 400−4000

−2000

0

2000

4000r/R=0.21

Mz (

lb−

in)

0 100 200 300 400−5000

0

5000r/R=0.34

0 100 200 300 400−3000

−2000

−1000

0

1000

2000r/R=0.59

Mz (

lb−

in)

Azimuth, ψ (deg)0 100 200 300 400

−2000

−1000

0

1000

2000r/R=0.81

Azimuth, ψ (deg)

Figure 4. Time histories of the mean-removed chordwise bending moment at different radiallocations. Legends are the same as in figure 2.

0.05000.04470.03950.03420.02890.02370.01840.01320.00790.0026

-0.0026-0.0079-0.0132-0.0184-0.0237-0.0289-0.0342-0.0395-0.0447-0.0500

0.01200.01070.00950.00820.00690.00570.00440.00320.00190.0006

-0.0006-0.0019-0.0032-0.0044-0.0057-0.0069-0.0082-0.0095-0.0107-0.0120

0.00150.00130.00120.00100.00090.00070.00060.00040.00020.0001

-0.0001-0.0002-0.0004-0.0006-0.0007-0.0009-0.0010-0.0012-0.0013-0.0015

Figure 5. Mean-removed airload distribution on the rotor disk: Normal (left) and chordwide(middle) force components and pitching moment (right). Arrows denote the flight direction.

suitability of our compressible–incompressible coupling technique for rotorcraft applica-tions.

Figure 9 shows instantaneous vortical structures represented by iso-surfaces of q2 ≡

−∂ui/∂xj × ∂uj/∂xi. Most of the typical flow features in high-speed forward flight arewell captured in the present simulation. The most dominant flow feature is the long trailof tip vortices observed on the retreating side, whereas small-size vortices are also foundto be shed near the rotor root. Thin vortex sheets formed along the entire blade spanare also evident especially on the retreating side.

Coupled URANS simulation for the MDART rotor 79

r/R=0.23

ψ

CnM

2

0 120 240 360

0

0.1

0.2 r/R=0.40

ψ

CnM

2

0 120 240 360

0

0.1

0.2 r/R=0.55

ψ

CnM

2

0 120 240 360

0

0.1

0.2

r/R=0.67

ψ

CnM

2

0 120 240 360

0

0.1

0.2 r/R=0.77

ψ

CnM

2

0 120 240 360

0

0.1

0.2 r/R=0.86

ψ

CnM

2

0 120 240 360

0

0.1

0.2

r/R=0.92

ψ

CnM

2

0 120 240 360

0

0.1

0.2 r/R=0.96

ψ

CnM

2

0 120 240 360

0

0.1

0.2 r/R=0.99

ψ

CnM

2

0 120 240 360

0

0.1

0.2

Figure 6. Time histories of the normal force component Cn: , SUmb–CDP coupling;, OVERTURNS.

Acknowledgments

This work is supported by the Defense Advanced Research Projects Agency (DARPA)of the United States Department of Defense.

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r/R=0.23

ψ

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ψ

CmM

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0 120 240 360-0.005

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CmM

2

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0

0.005

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V∞

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Figure 9. Iso-surfaces of q2 at Ωt/2π = 4.

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