1 Alexander A. Nikolsky Honorary LectureshipAnnual Forum, AHS International Montreal, Canada April 29, 2008 Alexander A. Nikolsky –1963

2 2008 Alexander Nikolsky LectureHow Dynamic Inflow Survives in the Competitive World of Rotorcraft Aerodynamics David A. Peters McDonnell Douglas Professor of Engineering Washington University in St. Louis 2008 Alexander Nikolsky Lecture

3 Acknowledgements Kurt HohenemserAlexander A. Nikolsky –1963

4 Acknowledgements Bob Ormiston [2015 Nikolsky]: “Dave, some day you will bring me a curve with a glitch, and I will ask you what it is. If you say, ‘I don’t know, that’s the way it came out of the computer,’ you’re fired.” Dewey Hodges [2014 Nikolsky]: “Structures and dynamics are the exact sciences, aerodynamics and thermodynamics are the inexact sciences.” Rose Brower: Design and production Debbie Peters: “The Love of my Life”

5 Ecological Niches of AerodynamicsCFD 2008 Alexander Nikolsky Lecture Free Wake Prescribed Wake Dynamic Wake

6 How Dynamic Wake Models Have SurvivedIs there still room for simple models in the competitive world of rotorcraft analysis? These models have been developed in response to pressing needs to explain physical phenomena found in experimental data. These models are physically intuitive. These models have been consistently based on engineering physics rather than on any heuristic mathematical fit of data. These models bring in just enough physics to explain the important behavior. These models are hierarchical so that each improvement includes all earlier versions and so that some version of the model can run in real time on any given computing platform. 2008 Alexander Nikolsky Lecture

7 What is a dynamic wake model?It is a model that—given the time history of blade loading—predicts the flow being pumped passed the rotor blades as a function of time, radius, and azimuth. It is a model that represents this evolution of inflow in first-order form in terms of a finite number of state variables. [M]{dvn/dt} + [C]{vn} = {Fm} It is a model that allows the number of states to vary with user needs. 2008 Alexander Nikolsky Lecture

8 2008 Alexander Nikolsky LectureFoundation 1950 – 1969 2008 Alexander Nikolsky Lecture

9 2008 Alexander Nikolsky LectureSeminal Conjecture Ken (1950) found that the measured roll damping of helicopters was roughly twice that predicted by the mathematical theories of his day. 2008 Alexander Nikolsky Lecture Ken Amer 1988 Nikolsky

10 2008 Alexander Nikolsky LectureAmer Conjecture “The discrepancy between the data and the theory appears to be due primarily to the changes in induced velocity which occur during rolling because of changes in the distribution of thrust around the rotor disk. These changes in induced velocity are not taken into account in the theoretical calculations because of the excessive labor that would be involved.” Ken Amer NACA TN October 1950, p.11. 2008 Alexander Nikolsky Lecture Figure 1: Source of damping in roll for a helicopter undergoing a rolling velocity.

11 2008 Alexander Nikolsky LectureG. J. Sissingh, 1952 2008 Alexander Nikolsky Lecture

12 2008 Alexander Nikolsky LectureG. J. Sissingh, 1952 Sissingh, in England, applied momentum theory to Ken Amer’s insight, but he applied it in a new way in terms of moments––in addition to thrust. Sissingh was able to obtain formulas for the gradient in inflow for the cases of hover and forward flight. 2008 Alexander Nikolsky Lecture

13 2008 Alexander Nikolsky LectureClassical Approach Bob Loewy (1955, 1957) realized that rotor inflow, unlike fixed-wing inflow, is dominated by the returning layers of vorticity below the rotor plane. Robert G. Loewy 1984 Nikolsky 2008 Alexander Nikolsky Lecture

14 2008 Alexander Nikolsky LectureWake Layers 2008 Alexander Nikolsky Lecture

15 2008 Alexander Nikolsky LectureLoewy Function 2008 Alexander Nikolsky Lecture

16 2008 Alexander Nikolsky LectureLessons Learned It is better not to use any Wake Model at all than to use Theodorsen Theory for a rotating wing. The buckets of the real part of the Loewy Function (including  = 0) are the identical lift deficiency that was found by Amer and Sissingh. The imaginary part of the Loewy function shows that there is a time lag in the development of that lift deficiency. 2008 Alexander Nikolsky Lecture

17 2008 Alexander Nikolsky LectureClassical Approach Rene Miller of MIT (1964) added a three-dimensional correction. Rene Miller Nikolsky 2008 Alexander Nikolsky Lecture

18 2008 Alexander Nikolsky LectureDevelopment 1970 – 1989 2008 Alexander Nikolsky Lecture

19 H.C. “Pat” Curtiss, Jr. 2000 NikolskyPat Curtiss and Norm Shupe (1971) show that the Sissingh Lift Deficiency could be formally cast as an equivalent Lock number with the same lift deficiency as that of Loewy  = acR4/Iy a*/a = [1 + a/8V]-1 Curtiss also realized that it was sometimes necessary to put a time delay into the dynamic inflow 2008 Alexander Nikolsky Lecture

20 REXOR Had Dynamic InflowLockheed’s REXOR Program also had Sissingh’s inflow effect with a time constant 2008 Alexander Nikolsky Lecture

21 Appendix on Dynamic Wake

22 2008 Alexander Nikolsky LectureRobert A. Ormiston Ormiston [2015 Nikolsky] (1970) was analyzing data from the NASA 40x80 and 7x10 wind tunnels. He discovered large discrepancies and wondered if they might be due to elastic blade bending, reversed flow, higher harmonics, tip loss, or root cut-out. 2008 Alexander Nikolsky Lecture

23 2008 Alexander Nikolsky LectureNew Hire Dave Peters had just arrived at Ames and was given the job to create a code that would solve the blade flapping problem including all of the aforementioned effects. The results still showed large discrepancies with data; and Bob Ormiston postulated the effect reported by Amer, Sissingh, and Curtiss. 2008 Alexander Nikolsky Lecture David Peters 2008 Nikolsky

24 2008 Alexander Nikolsky LectureFirst Correlations The calculations showed that the inflow effect corrected steady results in hover but not forward flight and not unsteady results in either case. 2008 Alexander Nikolsky Lecture

25 2008 Alexander Nikolsky LectureApparent Mass Bob Ormiston postulated an apparent mass and inertia of the wake as posed by Carpenter and Fridovitch (1953) Simple potential flow theory gave the numbers. 2008 Alexander Nikolsky Lecture

26 Correlation was excellent in hover but lousy in forward flight2008 Alexander Nikolsky Lecture

27 Correlation was excellent in hover but lousy in forward flight2008 Alexander Nikolsky Lecture

28 2008 Alexander Nikolsky LectureKurt Hohenemser Independently, Kurt Hohenemser was trying to correlate some wind tunnel data taken by him and Sam Crews at Washington University. Hohenemser postulated a lift deficiency and phase lag of the inflow to explain the data and Dev Banerjee did parameter identification to find the gains and time constants. 2008 Alexander Nikolsky Lecture

29 Parameter IdentificationThe identified values were within 2% of the values used by Ormiston and Peters from the Sissingh theory and potential flow for apparent mass. 2008 Alexander Nikolsky Lecture

30 Anton J. “Jack” LandgrebeIn the meantime, efforts by Peters and Ormiston to find a forward flight version of dynamic inflow were fruitless. However, Vortex Lattice Models were coming into their own as computational speed and memory increased. 2008 Alexander Nikolsky Lecture

31 2008 Alexander Nikolsky LectureFree-Vortex Wake Trailing Tip Vortex Trailing Vortex Filaments Vortex Lattice Vortex Sheet 2008 Alexander Nikolsky Lecture Different types of vortex wake: vortex lattice, panel, and free

32 2008 Alexander Nikolsky LectureDale Pitt Dave Peters returned to Washington University in 1975 and Dale Pitt came as his first doctoral student in 1977. Pitt had a better idea and discovered Prandtl, Kinner and Mangler/Squire. 2008 Alexander Nikolsky Lecture

33 Circular Wing Theory Kinner Paper 2008 Alexander Nikolsky LectureWieslaw Z. “Steppy” Stepniewski 1981 Inaugural Nikolsky Recipient

34 2008 Alexander Nikolsky LecturePitt - Peters Model . 2008 Alexander Nikolsky Lecture

35 2008 Alexander Nikolsky LectureConnections By the way, Pitt ran Landgrebe, too, with the same results. 2008 Alexander Nikolsky Lecture

36 2008 Alexander Nikolsky LectureGopal Gaonkar 2008 Alexander Nikolsky Lecture Gaonkar helped with the correlations. IT WAS LIKE MAGIC!

37 2008 Alexander Nikolsky LectureBousman and Johnson William G. Bousman took some ground resonance data [2011 Nikolsky] Wayne Johnson tried to correlate it with his new comprehensive code, CAMRAD. [2010 Nikolsky] 2008 Alexander Nikolsky Lecture

38 2008 Alexander Nikolsky LectureInflow Mode Wayne proved that there was an inflow mode. Soon every stability and handling qualities code had some form of dynamic inflow in it. 2008 Alexander Nikolsky Lecture

39 2008 Alexander Nikolsky LecturePeretz P. Friedmann As other aeroelasticians began to understand the importance of aero dynamics as states, Friedmann [2013 Nikolsky] began to compare Loewy Theory and dynamic inflow theory and discovered what appeared to be a discrepancy. 2008 Alexander Nikolsky Lecture

40 2008 Alexander Nikolsky LectureSingularity The discrepancy was simply that Loewy theory has a singularity for the collective mode at zero frequency. But looking at that got Dave Peters thinking. 2008 Alexander Nikolsky Lecture

41 2008 Alexander Nikolsky LecturePlea to NASA - Army In January 1985, Dave Peters pitched an idea to Bob Ormiston and Bill Warmbrodt that we could generalize the wake. 2008 Alexander Nikolsky Lecture

42 2008 Alexander Nikolsky LectureDynamic Flow Diagram 2008 Alexander Nikolsky Lecture

43 Time Constants at Harmonic NumbersExtension of Pitt Model: T = 0.75 / (1.5 + m) Loewy function at r = ¾: T = 0.75/m 2008 Alexander Nikolsky Lecture

44 2008 Alexander Nikolsky LectureGeorgia Tech In 1985, Dave Peters joined Georgia Tech 2008 Alexander Nikolsky Lecture Robin Gray 1991 Nikolsky Dan Schrage 1999 Nikolsky

45 2008 Alexander Nikolsky LectureCheng Jian He Cheng Jian He came as Dave Peter’s first Georgia Tech doctoral student (déjà vu all over again). He came up with closed-form matrices for all harmonics and distributions. 2008 Alexander Nikolsky Lecture

46 Langley Wind Tunnel DataThis was just in time for the Langley data. Why did dynamic wake out perform vortex lattice? 2008 Alexander Nikolsky Lecture

47 2008 Alexander Nikolsky LectureHover Test Stand Data This was also just in time to correlate with hover test stand data taken by Komerath. 2008 Alexander Nikolsky Lecture Ay Su

48 2008 Alexander Nikolsky LectureTheory and Experiment When the theory did not agree with the experiment, it turned out that Narayanan M. Komerath discovered a phasing error in the data extraction. (No one believes the theory except the one who derived it, and everyone believes the data except the one who took it.) 2008 Alexander Nikolsky Lecture

49 2008 Alexander Nikolsky LectureRefinement 1990 – 2008 Alexander Nikolsky Lecture

50 Back to Washington UniversityIn 1991 Dave Peters returned to Washington University. Cheng Jian He was now at Advanced Rotorcraft Technology (ART), and dynamic wake models were now being put into real-time flight simulations, including FLIGHTLAB. 2008 Alexander Nikolsky Lecture

51 Back to Washington UniversityPeople began to realize that these simulations were missing the off-axis coupling. Aviv Rosen postulated that, when in a pitching or rolling maneuver, the vortices piled up more densely on one side of the rotor than the other. 2008 Alexander Nikolsky Lecture

52 2008 Alexander Nikolsky LectureAviv Rosen 2008 Alexander Nikolsky Lecture Fig. 2 A graphic description of the wake distortion during a constant pitch rate.

53 2008 Alexander Nikolsky LectureWake Curvature Soon, Pat Curtiss had shown that this could also be predicted by momentum-theory dynamic inflow with the pitch rate as a new forcing function. Prasad and his students at Georgia Tech showed that, just as Pitt had added wake skew, one could add wake curvature as a new parameter effecting [L]. 2008 Alexander Nikolsky Lecture Pat Curtiss 2000 Nikolsky

54 Wake Distortion Parametersη + ν χ R Contraction V = η +2ν Skew X = tan(χ/2) Curvature К = 1/R 2008 Alexander Nikolsky Lecture

55 Generalized Dynamic Wake Model2008 Alexander Nikolsky Lecture

56 Wake Curvature J.V.R. PrasadUH-60 Off-axis pitch to lateral stick doublet input (40 knots) 2008 Alexander Nikolsky Lecture

57 Velocity Potential ModelJorge Morillo, Ke Yu, and Antonio Hsieh worked together to show that the entire inflow theory could be derived by application of a Galerkin Method to the potential flow equations with the states being coefficients of velocity potentials. Thus, the states imply all three components of flow everywhere in the flow field. 2008 Alexander Nikolsky Lecture Jorge Morillo

58 2008 Alexander Nikolsky LectureJorge Morillo 2008 Alexander Nikolsky Lecture

59 2008 Alexander Nikolsky LectureSteven Makinen Makinen showed how swirl correction could give results of Goldstein/ Prandtl at high inflow. This gave answer to Frank Harris. 2008 Alexander Nikolsky Lecture Frank Harris 2006 Nikolsky

60 Effect of Wake Rotation2008 Alexander Nikolsky Lecture Circulation at any blade radial location for Prandtl, Goldstein, and using Finite-State methods.

61 Effect of Wake Rotation2008 Alexander Nikolsky Lecture Circulation at any blade radial location for Prandtl, Goldstein, and using Finite-State methods.

62 Most Recent Additions Zhongyang Fei and Jianzhe Huang now have shown how to get the flow below the disk (including inside of the wake) by the Adjoint Theorem. They also have modified the modle to have complete nonlinearities and wake curvature.

63 2008 Alexander Nikolsky LectureSo, how have dynamic wake models survived in the competitive world of aerodynamic models? They are founded in responses to experimental data. They have just enough texture to explain the desired phenomena and no more. They are hierarchical so that each new model is easily put into the old slot and so that the user can truncate at just the fidelity needed. What they lack in modeling detail, they make up in efficient computation. 2008 Alexander Nikolsky Lecture

64 Will models like this ever be obsolete?I don’t think so. No matter how fast computers become, they will never be able to solve every molecule in real time, and lower fidelity models will be needed. There will always be a need for real-time simulation. These models give physical insight into behavior that is helpful in the design process beyond just the numbers of the calculation. 2008 Alexander Nikolsky Lecture

65 2008 Alexander Nikolsky LectureWill CFD, Vortex lattice and comprehensive codes ever be replaced by simple models? Absolutely not. These analysis tools are indispensable; and, as computers become faster, these tools will take over more and more of the ecological niches now dominated by simple codes. There will always, however, be niches in which the big predators cannot compete as effectively as the simple, closed-form methods. 2008 Alexander Nikolsky Lecture

66 Conclusions “There are more things in heaven and earth, Horatio, than are even dreamt of in your philosophy.” Shakespeare “Life consisteth not in the abundance of things which a man possesseth.” Jesus of Nazareth “The purpose of computing is insight, not numbers.” Hamming “Don’t ever say, ‘That’s the way it came out of the computer.’” Ormiston 2008 Alexander Nikolsky Lecture

67 2008 Alexander Nikolsky LectureFinis. ANY QUESTIONS? 2008 Alexander Nikolsky Lecture

68 Most Recent Additions Zhongyang Fei and Jianzhe Huang now have shown how to get the flow below the disk with complete nonlinearities.

69 2008 Alexander Nikolsky LectureLoewy Function 2008 Alexander Nikolsky Lecture

70 2008 Alexander Nikolsky LectureLoewy Function 2008 Alexander Nikolsky Lecture

71 Velocity Potential ModelMost recently, data taken in partial ground effect by the Japanese show the importance of having all three components of inflow everywhere in the flow field. Since the He model is from potential flow theory, it seemed logical that, given one component of the velocity, one could find a velocity potential and, thus, all three components. 2008 Alexander Nikolsky Lecture

72 Wake Curvature J.V.R. Prasad2008 Alexander Nikolsky Lecture