NASA Technical Memorandum 102226 USAAVSCOM Technical Memorandum 89-A-001 

Correlation of Puma Airloads - 

Evaluation of CFD 

Prediction Methods 

Roger C. Strawn, Aeroflightdynamics Directorate, U.S. Army Aviation Research 

Andre Desopper, Office National d’Etudes et de Recherches Aerospatiales, Chatillon, France 

Judith Miller and Alan Jones, Royal Aerospace Establishment, Farnborough, England 

and Technology Activity, Ames Research Center, Moffett Field, California 

August 1989 

National Aeronautics and 

Space Administration SYSTEMS COMMAND 

Ames Research Center 

Moffett Field, California 94035 

AVIATION RESEARCH AND 

TECHNOLOGY ACTIVITY 

MOFFEl7 FIELD. CA 94305-1099 
CORRELATION OF PUMA AIRLOADS - EVALUATION OF 

CFD PREDICTION METHODS 

Roger C. Strawn 

U. S. Army Aeroflightdynamics Directorate 

Moffett Field, California, USA 

Andre Desopper 

Office National d’Etudes et de Recherches Aerospatiales 

Chatillon, France 

Judith Miller and Alan Jones 

Royal Aerospace Establishment 

Farnborough, England 

ABSTRACT 

A cooperative program has been undertaken by research organizations in England, 

France, Australia and the U. S. A. to study the capabilities of computational fluid 

dynamics codes (CFD) to predict the aerodynamic loading on helicopter rotor blades. 

The program goal is to compare predictions with experimental data for flight tests of a 

research Puma helicopter with rectangular and swept-tip blades. Two topics are studied 

in this paper. First, computed results from three CFD codes are compared for fiighttest cases where all three codes use the same partial inflow-angle boundary conditions. 

Second, one of the CFD codes (FPR) is iteratively coupled with the CAMRAD/JA 

helicopter performance code. These results are compared with experimental data and 

with an uncoupled CAMRAD/JA solution. The influence of flowfield unsteadiness 

is found to play an important role in the blade aerodynamics. Alternate boundary 

conditions are suggested in order to properly model this unsteadiness in the CFD 

codes. 

LIST OF SYMBOLS 

= rotor chord length 

= lift coefficient 

= pitching moment coefficient 

= pressure coefficient 

= ratio of rotor thrust coefficient to solidity 

= hover tip Mach number 

= spanwise distance along the rotor 

= radial distance to the rotor tip 

= time 

1 
X 

“P 

= chordwise distance along the rotor 

= partial angle of attack provided to the CFD codes 

P = rotor advance ratio 

1c, 

6 

= rotor azimuthal angle, deg. 

= blade cyclic pitch angle, deg. 

1. INTRODUCTION 

Accurate methods for flow prediction on helicopter rotors are an important part 

of the rotor design process. Examples of comprehensive helicopter prediction codes are 

given in Refs. 1-4. For these codes, typical aerodynamic models consist of lifting-line 

methods for the blade aerodynamic loads. Sectional lift, moment and drag are based 

on 2-D experimental airfoil data. Approximate methods are then used to correct for 

unsteady and three-dimensional effects near the blade tip. The rotor wake is modeled 

with discrete vortex segments that are tracked in a Lagrangian framework. Wakeinduced inflow to the rotor disc is computed with a Biot-Savart integration. The 

rotor-wake, aerodynamics and dynamics solutions are coupled together in an iterative 

trim solution in order to balance the forces for the entire helicopter. 

Alternatives to lifting-line models for blade aerodynamics are computational fluid 

dynamics schemes (CFD) that compute the full three-dimensional transonic flow around 

rotor blades. These methods typically solve the Navier-Stokes, Euler, or potential-flow 

equations. CFD methods have the advantage over other methods because they are 

designed to accurately model the three-dimensionality and the transonic flow nonlinearities that are associated with high-speed advancing rotors. The disadvantage of 

these methods is that computer speed and storage requirements limit the size of the 

computational domain. The complexities of resolving the rotor wake system and blade 

dynamics are typically beyond the capabilities of current CFD codes. 

To surmount these problems, hybrid approaches have been developed that replace 

the lifting-line aerodynamic models in rotor comprehensive codes with aerodynamic 

loads that are computed with CFD. The advantage is that the CFD-computed aerodynamic loads should more accurately model unsteady transonic effects and blade three 

dimensionality. In addition, the rotor-wake and dynamics can be modeled by simple 

boundary conditions to the CFD code. This type of hybrid coupling approach was first 

developed by Tung et al. [5] who iteratively coupled the CFD computed lift from a 

small-disturbance potential code to the CAMRAD comprehensive analysis [1,2]. 

Since then this same hybrid coupling procedure has been used with a number 

of different CFD methods and comprehensive rotorcraft codes [6-91. Typically these 

efforts have focused more on the development of the CFD methods than on the details 

of the comprehensive analyses and CFD coupling scheme. This makes it difficult to 

compare the various methods because comparisons between the CFD codes were not 

always made for the same cases and conditions. Also, it has typically been difficult 

to evaluate the different comprehensive rotorcraft codes since they too have not been 

tested for similar cases. Finally, it is always difficult to obtain accurate flight-test data 

to validate the various prediction methods. 

In order to resolve some of these issues, a cooperative research program has been 

undertaken between organizations in the United States, the United Kingdom, France, 

and Australia. The objective is to better understand the strengths and limitations of 

2 
various computational approaches for the prediction of rotor airloads. This was done 

by comparing the predictions from several computational schemes with airloads data 

obtained in the flight test of an AS 330 Puma with modified blade tips. 

The Puma mixed rotor system consists of both swept and rectangular tips as 

shown in Fig. 1. Pressure data were simultaneously recorded for both the swept and 

the rectangular-tip blades during the flight tests. These flight-test cases were chosen 

because the high-speed forward flight and blade three dimensionality provide challenging cases for aerodynamic prediction codes. More detailed descriptions of the Puma 

flight tests are given in Refs. 10 and 11. 

a NOT TO SCALE 

Fig. 1 Puma mixed bladed rotor configuration. 

A workshop was held at RAE-Farnborough in May 1988 to compare the CFD and 

comprehensive lifting-line aerodynamic predictions for the Puma flight-test cases and 

to assess the relative strengths and limitations of each. This paper and its companion 

paper “Correlation of Puma Airloads - Lifting-Line and Wake Calculation” will examine the major questions that resulted from the workshop and summarize the substantial 

work that has been done subsequent to the workshop. The purpose of these papers is 

to address the following questions. 

. 

1. 

2. 

3. 

4. 

5. 

How good are the experimental data? Are they suitable for validation purposes? 

How well do the lifting-line/wake methods predict the airloads measured on the 

Puma? Can limitations in modeling capabilities be identified? 

Independent of the CFD predictive capability with respect to the experimental 

data, how well do they compare with each other? What advantages are obtained 

as the analysis sophistication increases from the quasi-steady small-disturbance 

theory to the unsteady small-disturbance theory to the full-potential model? 

How satisfactory are the methods used to calculate the inflow for the CFD methods? How important are the differences between simply prescribing the inflow 

(uncoupled) and iterating between the lifting-line/wake and CFD methods (coupled)? 

How satisfactory are the CFD methods for airloads prediction? Despite their 

dependence upon the lifting-line/wake methods for the correct modeling of the 

inflow can they provide useful physical insight? 

3 
This paper will primarily address questions 3 through 5 while the companion paper 

will examine questions 1 and 2. Specifically, this paper will first compare results from 

three CFD methods for several of the Puma flight-test cases. The same prescribed 

inflow boundary conditions will be used for each code. The objective will be to answer 

question 3 in the above list. Next, the paper will take one of the CFD codes and 

iteratively couple its computed lift to the CAMRAD/JA comprehensive helicopter code 

[12]. Results will be presented and compared to the Puma flight-test data. The iterative 

coupling procedure and its influence on the final set of results will be examined in detail. 

Results from this study will address questions 4 and 5 in the list above. 

2. DESCRIPTION OF THE CFD CODES 

RAE TSP Method 

The RAE Transonic Small Perturbation code (TSP) solves the three-dimensional 

quasi-steady small-disturbance potential equation for helicopter rotor blades. The 

equation is written in nonconservative form and discretized with the streamwise derivatives switched from central to upwind differences in regions of supersonic flow. The 

wake is assumed to be a plane vortex sheet skewed in the direction of the resultant 

free-stream flow. Jump conditions on the velocity potential are imposed across the 

vortex sheet. Boundary conditions at the far field are set to free-stream values. 

The difference equations are solved by an iterative relaxation technique with sweeps 

in each of the coordinate directions at each iteration step. A grid sequencing method 

using both coarse and fine grid solutions is used to speed up convergence. Further 

details of the code and early computed results can be found in Ref. 13. More recent 

work has been concerned with improvements in the grid, and inclusion of some of the 

terms in the differential equation which were originally considered negligible. 

The grid for the Puma cases is generated algebraically and a total of 105,600 grid 

points are used: 60 in the chordwise direction, 44 radially, and 40 vertically. On the 

blade surface there are 31 points in the chordwise direction, 31 and 35 in the spanwise 

direction for the rectangular and swept-tip cases respectively. The outer boundaries of 

the computational region are at infinity. For the forward-flight Puma cases, a separate 

quasi-steady calculation was performed at each azimuthal station required. A total 

quasi-steady calculation consisting of grid generation, 150 iterations on the coarse grid, 

and 150 iterations on the fine grid requires about 170 CPU minutes on a DEC VAX 

111780. 

ONERA TSD Method 

The unsteady transonic small-disturbances method (TSD) was developed ten years 

ago in a cooperative effort by the Office National d'Etudes et de Recherches Aerospatiales (ONERA) and the U. S. Army Aeroflightdynamics Directorate (AFDD) at Ames 

Research Center. The computer code solves a conservative form of the unsteady, threedimensional transonic small disturbance potential equation for rotor blades of nearly 

arbitrary planform. 

The TSD code originally solved a form of the small-disturbance potential equation 

that was obtained by neglecting some of the spanwise terms in the equation since 

they are typically small, especially in cases with transonic flow near $ = 90" azimuth. 

Details of the method are given in Refs. 14 and 15. 

4 
Significant improvements to the original TSD code gre described by Desopper [16]. 

This improved version of the code now includes all of the terms in the spanwise direction 

with no approximations. These modifications have improved both the stability of the 

method and also the computed results for non-rectangular blades. 

For the Puma cases, the total number of mesh points used was 48300;.70 chordwise, 

23 spanwise (16 on the blade) and 30 in the vertical direction. The outer boundaries 

of the computational domain were 9 chords upstream and 6 chords downstream, from 

0.5 R to 1.5 R in the spanwise direction and 6 chords above and below the blade. The 

solution moved forward 1" of rotor azimuth per time step and the computing time on 

a CRAY XMP machine for a full 360" cycle was 850 CPU seconds. 

U. S. Army FPR Method 

The Full-Potential Rotor code (FPR) solves the unsteady, three-dimensional, fullpotential equation in strong conservation form. The code employs a finite-difference 

scheme with first-order backward differencing in time and second-order central differencing in space. The temporal density derivative is locally linearized about the old 

time levels in a manner that preserves the conservative form. Stability in regions of 

supersonic flow is obtained by biasing the density calculation in the upwind direction. 

A spanwise series of parallel 0-grids are used for the basic grid system. Rotor flows 

are computed by assigning an appropriate rotational coordinate velocity to each grid 

point. As a result, the rotor and the attached finite-difference grid move through still 

air. On the surface of the blade, a transpiration velocity condition is used to simulate 

angle-of-attack conditions (including wake-induced inflow angles). At the outer radial 

boundary of the 0-grid, a nonreflection boundary condition is used to prevent the 

accumulation of numerical disturbances. 

Typical grid sizes for the calculations used for the Puma calculations are 80 points 

in the chordwise direction, 25 in the spanwise direction and 25 in the direction normal 

to the rotor surface. Figure 2 shows a top view of the FPR grid for the swept-tip Puma 

Fig. 2 Top view of the FPR grid for the swept-tip Puma calculation. 

5 
blade. The finite-difference grid extends approximately 7 chords inward from the rotor 

tip and two chords outward from the tip in the spanwise direction. The outer radial 

boundary of the 0-grid is located 5 chords from the surface of the blade. Constant 

time steps were used corresponding to 0.25" of rotor azimuthal angle per time step. 

Unsteady calculations for a complete 360" of rotor azimuth required approximately 

1800 CPU seconds on a CRAY XMP computer system. 

A more complete description of the Full-Potential Rotor Code can be found in 

Refs. 17 and 18. Significant improvements to the differencing algorithm in FPR have 

recently been made and these are detailed in Ref. 19. This improvements increase the 

accuracy and stability of the solution algorithm and have been used for all of the Puma 

computations. Also discussed in Ref. 19 are the inclusion of viscous effects in the code 

and the calculation of rotor drag, torque and power. 

3. TEST CASES FOR THE CFD METHODS 

The three CFD prediction schemes can be compared to each other by examining 

the computed results from five test cases in detail. For the first three test cases the 

RAE supplied partial inflow angles to the CFD codes using the RAE/WHL rotor loads 

analysis code [3]. These partial inflow angles are implemented as an effective twist 

distribution at each blade azimuth that represents the influence of the far-wake and 

rotor dynamics. Further details on this partial inflow angle boundary condition are 

given in Section 5 of this paper. The important thing to keep in mind is that all three 

codes are compared with consistent partial inflow angle boundary conditions. 

The five computed test cases can be described as follows. 

1. Rectangular blade - Baseline rectangular blade case, MT = 0.6225, p = 0.3761, 

CT/U = 0.0798, partial inflow angles provided by the RAE/WHL rotor loads 

analysis code. 

2. Swept-tip blade - Swept-tip Puma blade with the same flight conditions as the 

rectangular blade case number 1. Partial inflow angles are provided by the 

RAE/WHL analysis. 

3. Swept-tip blade - A swept-tip blade with slightly different flight conditions than 

cases 1 and 2. In this case, MT = 0.6244, p = 0.3813, and CT/U = 0.0799. This 

case differs from case 2 in that all four rotor blades have swept tips. Flight-test 

cases 1 and 2 used a mixed combination of rectangular and swept blades. Once 

again, partial inflow angles were provided by the RAE/WHL analysis. 

4. Swept-tip blade - This case is identical to flight-test case 2 except that the 

specified inflow angles are replaced by a uniform 2" angle of attack along the 

blade. 

5. Rectangular-tip blade - This case is identical to flight-test case 1 except that 

the specified inflow angles are replaced by a uniform 2" angle of attack along 

the blade. 

Initially, cases two and three were proposed because it was suspected that the 

analysis would show significant differences between a flight-test with only one swepttip blade and a case where all four blades are swept. This turned out not to be the case 

however and the RAE /WHL performance analysis showed little difference between 

the two cases, and this was confirmed by the experimental data. As a result, all of the 

CFD predictions for case two are very similar to those for case three. This discussion 

will therefore not include case three in the detailed study of CFD-computed results. 

6 
In cases 1, 2 and 3 the CFD methods predicted the sectional lift to be significantly 

lower than the experimental data. These lift discrepancies are caused by low partial 

inflow angles that were provided to the codes from the RAE/WHL performance analysis. This result led to subsequent development of both the RAE/WHL and CAMRAD 

models for the PUMA to the improved standard reported in Ref. 20, which also includes a detailed discussion of the partial inflow calculations. These low partial inflow 

angles mean that it is not particularly useful to compare the CFD results directly to 

experimental data. All three of the CFD methods have been run with the same partial 

angles however, so it is still useful to compare them to each other. 

As a consequence of the low partial inflow angles input to the codes, the first three 

computed cases do not show the strong shocks on the advancing side of the rotor that 

are seen in the experiment. Since the ability of the CFD codes to predict unsteady 

shock motion was an important issue in these comparisons, cases four and five were 

added to the list of computations. Although these cases do not represent any real 

flight conditions, they give an opportunity to compare the different CFD codes where 

significant shocks are present on the advancing side of the rotor disk. 

The next part of this paper will present a selected portion of the results from the 

various CFD methods. Rather than go through the results for each case, representative 

figures will be shown that highlight important issues for the CFD codes. A more 

complete collection of the computed results is contained in the Final Report from the 

May 1988 workshop, currently in preparation. 

FPR 

TSD CASE 1 . . . . . . . . . . . . . . . 

.15- -.-.- TSP (RECTANGULAR) 

4. CFD RESULTS AND DISCUSSION 

CASE 2 *. * . . *. 

- . : -. * (SWEPT) 

Figure 3 shows predicted sectional lift results for cases 1 and 2. The computed results from the three CFD codes show good agreement, particularly for the rectangulartip case 1. This agreement in lift between the codes is encouraging since lift is a major 

quantity of engineering importance. The largest discrepencies between the three predictions is seen for the swept-tip at 95% radius. Here the TSP code shows lower lift in 

the first and fourth azimuthal quadrants than either the FPR or TSD results. All three 

codes show good agreement in the second azimuthal quadrant and the TSD code shows 

higher lift in the third quadrant than either the TSP or FPR codes. The disturbance 

in the TSD and FPR results near ?,b = 280" is due to a slope discontinuity in the partial 

Fig. 3 Time histories for lift for test cases 1 and 2, r/R = 0.95. 

7 
inflow angles corresponding to a blade-vortex interaction predicted by the RAE/ WHL 

performance code. This disturbance does not appear in the TSP results because they 

were computed at individual discrete azimuthal angles. 

The results shown in Fig. 3 are fairly typical of the comparisons that are seen for 

lift in all five of the test cases. The rectangular cases show good agreement between all 

of the codes while some discrepancies are seen in comparisons between the swept-tip 

cases. In general, the lift comparisons are the least sensitive measure of differences 

between the three CFD codes. 

The issues of planform three dimensionality and transonic flow are addressed in 

Fig. 4. Here Mach contours are shown for the swept-tip case 4 at 90" azimuthal angle. 

All three codes show a strong shock inboard of the tip with a decrease in shock strength 

at the start of the forward sweep. They also show about the same area and shape of 

the supercritical flow region. The only significant difference between the three contour 

plots is in the supercritical region just outboard from the start of the forward sweep. 

Here, all three codes predict slightly different shapes in the supercritical Mach number 

contours. Once the backward sweep begins to take effect, the three results look very 

similar. 

More detailed differences between the three codes in regions of transonic flow are 

seen in Fig. 5. This is a rectangular-tip case with the strongest shocks in all cases. In 

fact, not much difference was seen in the transonic flow modeling of the codes until the 

advancing-side shock became this strong. At $ = 90" the TSP result shows a shock 

wave that is further forward than either of the other codes. This is probably due to a 

lack of conservation in the TSP algorithm. The FPR and TSD codes show excellent 

TSP FPR TSD 

Fig. 4 Upper surface Mach contours at .tc, = 90" for test case 4. 

8 
-.75r FPR 

TSP -.-.- 

JI = goo 

-25 .50I 1 I 

.75 

0 

1 

.2 .4 .6 .8 1 

CHORD LOCATION, x/c 

0 .2 .4 .6 .8 1 

CHORD LOCATION, x/c 

Fig. 5 Transonic surface pressures at T/R = 0.95 for test case 5. 

agreement on upper surface shock location and strength. The lower-surface pressure 

for the TSD code shows more leading edge expansion than either the FPR or TSP 

results. 

At t,6 = 120" in Fig. 5, significant transonic unsteadiness is present as the shock 

weakens in the second quadrant. Here, the maximum discrepancies are seen between 

all three predictions. The TSP calculation shows a shock wave that is further forward 

than either of the other codes, primarily because the TSP algorithm is quasi-steady. 

The unsteady effect on shock motion is to delay the decay of the shock wave in the 

second quadrant of the rotor disc. A quasi-steady code cannot model this phenomenon 

and is expected to show a more rapid shock decay. The FPR and TSD results again 

show good agreement on shock location but the FPR code shows less expansion near 

the leading edge of the blade. There is good agreement in the leading edge expansion 

region between the FPR and TSP results. 

One of the important issues for the CFD codes is their ability to compute highlift solutions on the retreating side of the rotor disk. Fig. 6 shows high-lift chordwise 

pressure distributions at II, = 270" for both the rectangular and swept tip (cases 1 and 

2). The discrepancies between the codes in the leading edge region are consistent with 

the approximations in the small-disturbance potential equation. These approximations 

lead to an underestimation of the flow expansion around the leading edge of an airfoil 

in low-speed, high-lift conditions. 

This trend is confirmed for the retreating-side results in Fig. 6 which show both 

small-disturbance codes with lower leading-edge lift than the FPR code. It is surprising 

that the TSP code shows more leading edge expansion than the TSD code at II, = 270" 

while the reverse was true on the advancing side in Fig. 5. This seems to rule out a 

difference in leading edge grid resolution as a cause for the differences in leading edge 

expansion for the TSD and TSP codes. The TSD result shows less lift at the leading 

edge than either the TSP or FPR codes but more lift at the trailing edge. This will tend 

to balance out when calculating integrated lift for the blade. It has more significant 

9 
CASE 2 

(SWEPT) 

-.010 - 

-.015 - (RECTANGULAR) 

CASE 1 

-.4 - 

TSD CASE 1 . . . . . . . . . . . . . . 

-.-.- TSP (RECTANGULAR) 

Q 

0 

N 

E 

- 

CASE 2 ’-.* 

- (SWEPT) ’* .. .. .. ’*..* 

.L ~~ 

0 .2 .4 .6 .8 10 .2 .4 .6 .8 1 

CHORD LOCATION, x/c CHORD LOCATION, x/c 

Fig. 6 Retreating side high-lift surface pressures for test cases 1 and 2, T/R = 0.95, 

11, = 270”. 

effects on the moment calculation however, tending to give the TSD result a larger 

nose-down moment than either of the other two codes. 

Moment comparisons for the three codes are shown in Fig. 7. As discussed above, 

the TSD result shows lower moment values (more nose down) on the retreating side 

than either the FPR or TSD code. This is particularly true for the swept-tip case 

2. The FPR code shows higher moment values than either of the other two codes for 

all azimuthal angles. In general there is poor agreement between the three codes for 

pitching moment predictions. This is not too surprising since the pitching moment is a 

difficult and sensitive quantity to predict accurately and subtle differences in chordwise 

surface pressure distributions can lead to large differences in the integrated pitching 

moments . One of the major questions to be addressed in this paper is, “What level of CFD 

modeling is required to accurately compute transonic three-dimensional rotor geometries?” The answer to this question is not clear-cut. It is difficult to determine whether 

I I I I I I I 1 I 

90 180 270 360 0 90 180 270 360 

1 

BLADE AZIMUTH, deg 

0 

-.020 

BLADE AZIMUTH, deg 

Fig. 7 Time histories for moment for test cases 1 and 2, T/R = 0.95. 

10 
any calculation method is superior since none of the computations showed good agreement with the experimental data. However it is possible to draw some conclusions from 

the comparison of the three methods to each other. 

All three of the codes showed good agreement on sectional lift coefficients and 

the qualitative effects of three-dimensional blade-tip shapes. If computed sectional lift 

coefficients are the only desired output from the CFD codes, then they all give similar 

results for the various test cases. This is because the pressure integration process for 

lift smooths out individual differences in the surface pressures. 

On the other hand, if drag, pitching moments or detailed surface pressures for 

acoustics are required, then significant individual differences exist between the three 

CFD analyses. These differences are difficult to generalize and seem to be dependent 

on the particular test case. In general however, errors in shock location will show up as 

large discrepancies in inviscid wave drag and advancing-side torque. Errors in leading 

or trailing edge pressures will show up in both the the drag and moment predictions. 

The full-potential equation in the FPR code is the most rigorous theoretical model 

out of the three methods, and should give more accurate results than the smalldisturbance codes. This is particularly true near the rotor leading edge where high 

gradients exist in geometry and surface pressures. One would expect to see these effects on the retreating side of the rotor disk where high inflow angles cause large suction 

peaks near the rotor leading edge. 

The other clear difference between the three codes is that the TSP method is 

quasi-steady while the FPR and TSD codes are fully unsteady. The assumption of 

quasi-steady flow in the TSP code breaks down when there is significant unsteady 

transonic flow over the rotor. This often occurs in the second quadrant of the rotor 

disk. Outside of this region however, the flowfield unsteadiness does not seem to cause 

major differences between the three codes in the Puma test cases. 

5. FPR AND CAMRAD/JA COUPLED SOLUTION METHOD 

In order to examine more closely the role of the CFD methods in the prediction of 

helicopter flight-test data a fully coupled solution was performed between the CAMRAD/JA performance code [12] and the U.S. Army FPR code. The CAMRAD/JA 

and FPR codes were chosen as representative performance and CFD codes because the 

first author of this paper had easy access to both codes. Puma flight-test case 3 was 

chosen for the solution because we wanted to study the iterative coupling scheme for 

a swept-tip blade and also because the uncoupled CAMRAD/JA results for this case 

were in good agreement with the experimental data (see Ref. 20). 

The iterative coupling scheme between the two codes was developed by Tung et 

al. [5] and is shown in the diagram in Fig. 8. An initial solution with CAMRAD/JA 

is performed and partial inflow angles (ap) are provided to the CFD code. The partial 

inflow angles are functions of both span and blade azimuthal angle. They represent the 

inflow to the blade due to cyclic pitch, blade flapping and dynamics, and rotor wake. 

They are called partial angles because the inflow effects of the near-wake, contained in 

the CFD domain, have been removed. An example of this near-wake region is shown by 

the FPR grid in Fig. 2. The reason that the CAMRAD/JA wake effects are removed 

in this region is because the near-wake is also calculated by the CFD code. Its effect 

would be redundant if it were included in both CAMRAD/JA and the FPR code. 

11 
CAMRADJA 

INITIAL SOLUTION 

FPR CODE 

CALCULATE CL (FPR) 

.c ffP 

CL = CL (FPR) + ACL (2-D TABLE) 

CL = CL + CL (UNSTEADY) 

ffP 

CALCULATE c~p 

ACI (2-D TABLE) = 0 ~~ ~ t YES 

1 DONE I 

Fig. 8 Iterative coupling scheme between CAMRAD/JA and FPR. 

Given the partial inflow angles from the CAMRAD/JA analysis, the FPR code 

computes the unsteady lift values as functions of span and azimuthal angle. These lift 

values are then provided to the CAMRAD/JA analysis and used in its trim solution. 

Note that the FPR code sits outside of the CAMRAD/JA trim loop. Because the 

CAMRAD/JA code must dynamically update its CI values many times throughout the 

trim loop, it would be impractical to run the CFD solution at every trim iteration. 

Instead, the ACI values that are required in the CAMRAD/JA trim loop are provided 

by computationally-fast two-dimensional tables of experimental data. Once the global 

iteration between CAMRAD/JA and FPR has converged, the AC1 values from the 2-D 

airfoil data go to zero and the lift values used for the CAMRAD/JA aerodynamic loads 

are completely provided by the three-dimensional unsteady CFD code. At this point, 

the calculation is considered to be fully converged and the CAMRAD/JA airfoil tables 

have been replaced by Ci values computed with the FPR code. 

Note that after the FPR Ci values are brought into the CAMRAD/JA trim loop, 

they are modified with an unsteady correction that is derived from thin airfoil theory. 

The pitching moments, computed from 2-D airfoil tables, are also modified with a 

similar unsteady correction. These unsteady corrections are described in Ref. 12. The 

unsteady correction to Ci, was originally thought to be small and its effects on the CFD 

lift negligible. In this paper it will be shown that this is not necessarily the case for the 

Puma flight-test cases. The unsteady correction for moment is much more important 

and will also be examined in this paper. 

For the Puma flight-test case 3, the iteration between CAMRAD/JA and FPR 

was considered converged after four runs with the CAMRAD/JA code and three runs 

with the FPR code. The results in the next section will investigate the effects of the 

iterative FPR coupling on the CAMRAD/JA solution. 

Note that the airfoil sections used for the modified Puma blades are very similar 

to NACA 0012 sections but they are slightly thinner. Since no experimental airfoil 

data exists for these blades, the performance codes used NACA 0012 airfoil tables for 

their sectional aerodynamics. The CFD codes used the actual airfoil geometries in 

their calculations. The effects of this discrepancy are thought to be small and will be 

investigated further in follow-on work. 

12 
6. RESULTS AND DISCUSSION FOR THE COUPLED SOLUTION 

.3 

.2 

-I 

NU .1 

5 

0- 

-.l 

Figure 9 shows some of the positive effects that the FPR computed lift has on the 

aerodynamic solution. Here the iteratively coupled FPR solution is compared with the 

initial uncoupled CAMRAD/JA solution and with the experimental data. The effects 

on the spanwise lift distribution are most clearly seen at 0" and 210". At 0" there is a 

large spanwise flow toward the blade tip. Because of the large amount of blade sweep, 

this tends to make the area near the tip act like the trailing edge of an airfoil. Thus the 

lift drops abruptly near the tip as the pressure tries to reach stagnation. At 210" blade 

azimuth, the combined effects of blade sweep and spanwise flow tend to make the area 

near the blade tip act like the leading edge of an airfoil. Thus the flow expands along 

the upper surface and the lift is increased near the tip. This is clearly shown in the 

FPR solution and in the experimental data. The uncoupled CAMRAD/JA solution is 

based on two-dimensional airfoil tables with a tip-loss factor that always makes the lift 

go to zero at the blade tip. Thus the CAMRAD/JA solution cannot correctly model 

the three-dimensional lift increase at the blade tip near 180" azimuth. 

The effects of the CFD coupling on the computed lift are shown in Fig. 10. Here the 

experimental data is shown as a heavy solid line in the figure. The initial CAMRAD/JA 

uncoupled solution is shown as a dotted line. The agreement is quite good with the 

experimental data. The 

agreement with experimental data is not as good as for the uncoupled CAMRAD/JA 

solution particularly at 0" and 180" blade azimuth. This was initially discouraging 

because one would think that the CFD lift should improve the solution. Finally it was 

discovered that the CAMRAD/JA code was taking the FPR lift solution and adding an 

unsteady correction factor to it as shown in the diagram in Fig. 8. This corrected value 

of lift is then used to compute the blade aerodynamic forces in the trim loop. This 

unsteady correction, based on thin airfoil theory, is not small as originally assumed. 

In fact, a fourth curve in Fig. 10, given by the dashed line, shows the lift values that 

the coupled CAMRAD/JA solution uses after it makes the unsteady lift correction. 

This line is very close to the initial uncoupled CAMRAD/JA solution and is in good 

agreement with the experimental data. 

An obvious question regarding this situation is, "Why not simply remove the 

unsteady lift correction to the CFD code?" After all, the CFD codes should should 

Next, the coupled FPR lift is shown as a dot-dash line. 

- 

- FLIGHT TEST 

FPR (COUPLED) 

CAMRADJA (UNCOUPLED) ............. 

...... $ = 210" 

- 

$ = 0" - 

...... .... 5.. *- ......... ......... 

I I I 1 I I I I I I 

Fig. 9 Spanwise lift distributions at two azimuthal angles for the swept-tip Puma case 

3. 

13 
FLIGHT TEST 

FPR (COUPLED) 

CAMRADJA (COUPLED) 

. . . . . . . . . . . . . CAMRADJA (UNCOUPLED) .3 

e. L. -.-____ 

I 1 I 1 1 1 I I I I I 1 1 I I I 

0 90 180 270 360 0 90 180 270 360 

BLADE AZIMUTH, deg BLADE AZIMUTH, deg 

Fig. 10 A comparison of experimental and computed lift distributions for Puma flighttest case 3. 

be able to correctly model any flowfield unsteadiness. It turns out that there are 

several problems with this line of reasoning, First, when the switch is used to turn off 

the unsteady lift correction in the CAMRAD/JA code, it also turns off the unsteady 

correction to the pitching moment. The unsteady correction for the pitching moment 

is very important for this Puma flight-test case and removing it would adversely affect 

the blade dynamics and trim. 

The remaining problems with removing the unsteady lift correction in CAMRAD/JA are much more fundamental. If the unsteadiness has such an important effect 

on lift, then the CAMRAD/JA partial inflow angles do not convey adequate information to compute the unsteady effects. The CAMRAD/JA partial inflow angles lump 

together the unsteady effects of the rotor cyclic pitch, blade dynamics and wake inflow 

into a single inflow angle. The sum of the unsteadiness due to each of these separate 

unsteady mechanisms is different than the unsteadiness due to a single lumped partial 

angle. In other words, the correct boundary conditions for computing unsteady blade 

aerodynamics should include each of the blade lift mechanisms separately to the CFD 

code. The combined effects of cyclic pitch and torsion should be modeled as a local 

pitch effect. Blade flapping and bending should be treated as plunge, and the unsteady 

wake should be treated as a gust with distributed inflow over the blade surface. Separate tabular outputs for each of these effects need to be written by the performance 

codes and incorporated into the CFD boundary conditions. 

A final point concerns the implementation of the boundary condition for pitch in 

the FPR code. The FPR code generates a grid about a zero angle-of-attack rotor section 

and then varies the sectional inflow angles with a transpiration boundary condition. 

This boundary condition is based on a quasi-steady assumption that says that the 

entire airfoil “sees” the same angle of attack at any given instant in time. It is not 

completely accurate for an unsteady pitching airfoil. Because the airfoil is pitching 

about the quarter chord, there is an unsteady effect that makes different chordwise 

sections of the airfoil experience slightly different angles of attack due to the unsteady 

pitch rate. For instance, if the airfoil is pitching nose-up, then the leading edge of 

the airfoil “sees” an additional negative inflow angle due to the unsteady motion and 

the trailing edge “sees” an additional positive angle of attack. Thus the FPR solution 

is time-accurate in the flowfield quantities and for plunge (this is still important for 

14 
transonic shock motion), but at present, the transpiration boundary condition does not 

accurately describe an unsteady pitching motion. 

When the CFD codes were first coupled to CAMRAD by Tung et al. [5], the idea 

was mainly to include three-dimensional lift effects and unsteady transonics. Both of 

these can be adequately modeled with the current coupling scheme. They assumed that 

the low-speed unsteady effects were small because the reduced frequencies are typically 

low. For the Puma cases, the CAMRAD/JA solution says that the low-speed unsteady 

effects are important. If this is true, then the low-speed unsteady effects for lift and 

moment must be included properly in the CFD codes. It is relatively straightforward to 

put a rigorous unsteady surface boundary condition into the FPR code and we plan to 

do this as soon as possible. Guruswamy has already done this with a small-disturbance 

code and an Euler code in Refs. 21 and 22. 

An illustration of how the unsteady effects of pitch are important is given in Fig. 11. 

The dominant term in the CAMRAD/JA unsteady lift and moment corrections is due 

to the blade cyclic pitching rate, d. Fig. 11 shows that the local cyclic pitch rate at 

T/R = 0.95 is a maximum near 45" and 180" blade azimuth, roughly where the largest 

unsteady lift corrections are seen in Fig. 10. Also shown in Fig. 11 is the partial inflow 

angle that is provided as a boundary condition to the CFD code. The rate of change 

of the partial inflow angle is substantially less than that of the blade cyclic-pitch angle, 

particularly at 180" azimuthal angle. This illustrates the problem that the unsteadiness 

due to the sum of the lumped partial inflow angles will be different than the sum of each 

of the unsteady motion mechanisms. It also illustrates the second problem with the 

coupling scheme, that the FPR code does not contain the proper boundary condition 

to accurately include the unsteady pitching effects, even for the partial angles. 

Even though the 

CAMRAD/JA and FPR codes are coupled by the computed lift, there is no coupling 

between the two codes for pitching moment. Thus it is expected that the two codes 

will have different results for pitching moment, especially since the FPR solution has 

Figure 12 shows the computed results for pitching moment. 

BLADE PITCH 

CFD PARTIAL ANGLE 

20- - 

----- 

15 - 

0 90 180 270 360 

BLADE AZIMUTH, deg 

Fig. 11 Cyclic pitch and CAMRAD/JA partial angles of attack for Puma case 3 at 

r/R = 0.95. 

15 
.010 

Fig. 12 A comparison of experimental and computed pitching moments for Puma 

’ flight-test case 3. 

.............. CAMRADJA (UNCOUPLED) 

FPR (COUPLED) 

------- CAM R ADJA (COUPLED) 

- -.- 

- 

not included the viscous boundary-layer effects. This is indeed the case in Fig. 12. 

The coupled and uncoupled CAMRAD/JA results are very similar as was the case 

with the computed lift. They show reasonable agreement with the data, particularly 

at T/R = 0.92, but there is some phase lag at T/R = 0.95. 

The FPR-computed moment is very different from the experimental data and 

also from the two CAMRAD/JA solutions. Rather than dismiss the FPR moments 

prediction as a poor calculation, it is useful to look at the influence of unsteady effects on 

the moment calculations. Figure 13 shows the same FPR and CAMRAD/JA moment 

results that are given in Fig. 12. A third result in Fig. 13 shows the CAMRAD/JA 

pitching moment that comes from the 2-D airfoil tables. The 2-D airfoil table result 

shows zero moment for most of the blade azimuth. It is only when it receives the 

unsteady correction in CAMRAD/JA that it takes on the large negative value in the 

second azimuthal quadrant and comes into better agreement with the experiment. 

Since it has already been stated that the boundary condition to the FPR code does 

not adequately convey the flowfield unsteadiness, then one cannot expect the CFDcomputed pitching moment to agree with either the experimental data or the final 

- 

- - I I I I I I 1 1 I I I I 1 I I I 

P 

0 

H 

N 

CAMRADJA (2-D TABLES) ............. FPR (COUPLED) 

CAMRADJA (COUPLED) -.- .005 

0 

-.005 

I L’ 

I I I I I I I 

0 90 180 270 360 

BLADE AZIMUTH, deg 

-.010 ‘ I 

Fig. 13 A comparison of computed pitching moments for Puma flight-test case 3 at 

T/R = 0.95. 

16 
CAMRAD/JA result. In fact, the FPR pitching moment agrees better with the 2-D 

steady airfoil table result than it does with either the unsteady CAMRAD/JA result 

or the experimental data. 

6. SUMMARY 

A number of conclusions can be drawn from the coupled CAMRAD/JA and FPR 

results for this Puma swept-tip flight test. First, it is clear that the CFD coupling 

process is far from routine and that a meaningful solution must pay attention to the 

details of 1) the CFD solution, 2) the helicopter performance code, and 3) the coupling 

boundary condition between the two. The results in this paper have pointed out the 

need for a more accurate boundary condition between the helicopter performance codes 

and the CFD methods. The importance of accurately conveying unsteady information 

to the CFD codes is even more important if the CFD-computed drag and pitching 

moments are to be coupled to the performance codes. 

The role of unsteadiness in the modeling of these flight-test cases casts a different 

light on some of the CFD results shown earlier in this paper. If the flowfield unsteadiness 

is important for lift and moment calculations, then the quasi-steady TSP code may not 

be suitable for coupled CFD and performance code calculations. Also, the disagreement 

of the three CFD codes on moment predictions is discouraging because the inclusion 

of significant flowfield unsteadiness will simply make these calculations more difficult. 

In spite of these problems, it is clear that the CFD solutions offer details about the 

blade aerodynamics that cannot be provided by conventional helicopter performance 

codes. These details can be used in evaluating the relative effects of planform shape 

and airfoil section in rotor design. An example of this type of study is given by Scott 

et al. [23]. Also, the CFD aerodynamics makes the solution independent from the need 

for experimental 2-D airfoil tables. This paper has pointed out that there remains 

significant work to be done to accurately integrate the CFD codes into helicopter performance predictions. Hopefully it has also shown that a great deal of progress in CFD 

rotor predictions has been made to date and that this is expected to continue into the 

future. 

7. ACKNOWLEDGEMENTS 

The authors would like to thank Mr. John Bridgeman and Dr. Frank Caradonna 

of the U. S. Army Aeroflightdynamics Directorate (AFDD) for their helpful comments 

and discussion of this paper. Also, the efforts of Mr. William Bousman, also from 

the U. S. Army AFDD, are appreciated for developing a computer database for the 

computational and experimental data. 

17 
8. REFERENCES 

1. Wayne Johnson, Development of a Comprehensive Analysis for Rotorcraft - I. Rotor 

Model and Wake Analysis, Verticu, vol. 5, 1981, pp. 99-130. 

2. Wayne Johnson, Development of a Comprehensive Analysis for Rotorcraft - 11. Aircraft Model, Solution Procedure and Applications, Vertica, vol. 5, 1981, pp. 185- 

216. 

3. C. Young, “Development of the Vortex Ring Wake Model and Its Influence on the 

Prediction of Rotor Loads,” AGARD Conference Proceedings No. 934, May 1982. 

4. J. R. Van Gaasbeek, T. T. McLarty, and S. G. Sadler, “Rotorcraft Flight Simulation, 

Computer Program C81, Volume I - Engineer’s Manual,” USARTL TR77-54A, 

1979. 

5. C. Tung, F. X. Caradonna and W. Johnson, The Prediction of Transonic Flows on 

Advancing Rotors,” J. Am. Hel. SOC., Vol. 31, July, 1986, pp. 4-9. 

6. G. K. Yamauchi, R. M. Heffernan, and M. Gaubert, “Correlation of SA349/2 Helicopter Flight Test DATA with a Comprehensive Rotorcraft Model,” NASA TM 

88951 Feb. 1987. 

7. R. C. Strawn and C. Tung, “Prediction of Unsteady Transonic Rotor Loads with a 

Full-Potential Rotor Code,” Presented at the 49rd Annual Forum of the American 

Helicopter Society, May 18-20, 1987, St. Louis, MO. 

8. I-Chung Chang, and C. Tung, “Numerical Solutions of the Full- Potential Equation 

for Rotors and Oblique Wings using a New Wake Model,” AIAA Paper 85-0268, 

Jan. 1985. 

9. Ki-Chung Kim and Inderjit Chopra, “Effects of Three-Dimensional Aeorodynamics 

on Blade Response and Loads,” AIAA Paper 89-1285, April, 1989. 

10. M. J. Riley and Judith V. Miller, “Pressure Distributions on a Helicopter Swept Tip 

from Flight Tests and from Calculations,” Paper No. 9, Presented ut the Ninth 

European Rotorcraft Forum, Sep 1983. 

11. M. J. Riley, “Measurements of the Performance of a Helicopter Swept Tip Rotor in 

Flight,” Paper No. 35, Presented at the Twelfth European Rotorcraft Forum, Sep 

1986. 

12. W. Johnson, “CAMRAD/ JA; A Comprehensive Analytical Model of Rotorcraft 

Aerodynamics and Dynamics; Johnson Aeronautics Version; Volume I, Theory 

Manual,” Johnson Aeronautics, Palo Alto, California, 1988. 

13. J. Grant, “The Prediction of Supercritical Pressure Distributions on Blade Tips of 

Arbitrary Shape Over a Range of Advancing Blade Azimuth Angles,” Vertica, 3, 

14. F. X. Caradonna, and M. P. Isom, “Numerical Calculation of Unsteady Transonic 

Flow over Helicopter Rotor Blades,” AIAA J. No. 4, April 1976. 

15. J. J. Chattot, “Calculation of Three-Dimensional Unsteady Transonic Flow Past 

Helicopter Blades,” NASA TP 1721, also AVRADCOM TR 80-A-2 (AM), 1980. 

16. A. Desopper, “Study of the Unsteady Transonic Flow on Rotor Blades with Different 

Tip Shapes,” Vertica, Vol. 9, 1985. 

17. J. 0. Bridgeman, J. L. Steger, and F. X. Caradonna, “A Conservative FiniteDifference Algorithm for the Unsteady Transonic Potential Equation in Generalized Coordinates,” AIAA Paper No. 82-1388, August, 1982. 

18. R. C. Strawn, and F. X. Caradonna, “Conservative Full-Potential Model for Unsteady Transonic Rotor Flows,” AIAA Journal Vol. 25, No. 2, Feb. 1987, pp. 193- 

198. 

1979, pp. 275-292. 

18 
19. J. 0. Bridgeman, R. C. Strawn and F. X. Caradonna, “Advanced Rotor Compu20. 

21. 

22. 

23. 

tations wi-th a Corrected Potential Method,” Presented at the 45th Annual Forum 

of the American Helicopter Society, May 22-24, Boston, MA. 

W. G. Bousman, C. Young, N. Gilbert, F. Toulmay, W. Johnson, and M. J. Riley, 

“Correlation of Puma Airloads - Lifting-Line and Wake Calculations,” Presented 

at the 15th European Rotorcraft Forum, Amsterdam, The Netherlands, 12-15 Sept., 

1989. 

G. Guruswamy and T. Y. Yang, “Aeroelastic Time Response Analysis of Thin Airfoils by Transonic Code LTRAN2,” Computers and Fluids, Vol. 9, No. 4, pp. 409- 

425. 

G. Guruswamy, “Interaction of Fluids and Structures for Aircraft Applications,” 

Computers and Structures, Vol. 30, No. 112, pp. 1-13, 1988 

M. Scott, D. Sigl, and R. Strawn, “Computational and Experimental Evaluation 

of Helicopter Rotor Tips for High-speed Forward Flight,” AIAA paper 1845, Presented at the AIAA 20th Fluid Dynamics, Plasma Dynamics and Lasers Conference, Buffalo, New York, 12-14 June, 1989. 

19 
NASA 

1. Report No. 

NASA TM-102226 

USAAVSCOM TM-89-A-001 

Report Documentation Page 

2. Government Accession No. 

17. Key Words (Suggested by Author@)) 

7. Author(s) 

Roger C. SUawn, Andre Desopper (Office National d'Etudes et de Recherches 

Aerospatiales, Chatillon, France), Judith Miller and Alan Jones (Royal Aerospace Establishment, Famborough, England) 

9. Performing Organization Name and Address 

Aeroflightdynamics Directorate, U.S . Army Aviation 

Research and Technology Activity, Ames Research Center, 

Moffett Field, CA 94035-1099 

18. Distribution Statement 

12.ponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

19. Security Classif. (of this report) 20. Security Classif. (of this page) 

Unclassified Unclassified 

15. Supplementary Notes 

21. No. of Pages 22. Price 

20 A02 

3. Recipient's Catalog No. 

5. Report Date 

August 1989 

6. Performing Organization Code 

8. Performing Organization Report No. 

A-89223 

10. Work Unit No. 

992-21-01 

1 1. Contract or Grant No. 

13. Type of Report and Period Covered 

Technical Memorandum 

14. Sponsoring Agency Code 

Point of Contact: Roger C. Strawn, Ames Research Center, MS 215-1, Moffett Field, CA 94035 

(415) 694-4050 or FTS 464-4050 

Report to be presented at the Fifteenth European Rotorcraft Forum, Sept. 12-15, 1989, Amsterdam 

16. Abstract 

A cooperative program has been undertaken by research organizations in England, France, Australia and the U. S. A. to 

study the capabilities of computational fluid dynamics codes (CFD) to predict the aerodynamic loading on helicopter rotor 

blades. The program goal is to compare predictions with experimental data for flight tests of a research Puma helicopter 

with rectangular and swept-tip blades. Two topics are studied in this paper. First, computed results from three CFD codes 

are compared for flight-test cases where all three codes use the same partial inflow-angle boundary conditions. Second, 

one of the CFD codes (FPR) is iteratively coupled with the CAMRAD/JA helicopter performance code. These results are 

compared with experimental data and with an uncoupled CAMRADDA solution. The influence of flowfield unsteadiness 

is found to play an important role in the blade aerodynamics. Alternate boundary conditions are suggested in order to 

properly model this unsteadiness in the CFD codes. 

Helicopter aerodynamics 

Computational fluid dynamics 

Helicopter performance prediction 

Unclassified-Unlimited 

Subject Category - 02 

NASA FORM 1626 OCT 86 

For sale by the National Technical Information Service. Springfield, Virginia 22161 

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