Annual Forum, AHS International

Transcription

1 Alexander A. Nikolsky Alexander A. Nikolsky Honorary Lectureship Annual Forum, AHS International Montreal, Canada April 29, 2008

2 How Dynamic Inflow Survives in the Competitive World of Rotorcraft Aerodynamics David A. Peters McDonnell Douglas Professor of Engineering Washington University in St. Louis

3 Alexander A. Nikolsky Acknowledgements Kurt Hohenemser

4 Acknowledgements Bob Ormiston 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 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 Aerodynamics CFD Free Wake Prescribed Wake Dynamic Wake

6 How Dynamic Wake Models Have Survived Is there still room for simple models in the competitive world of rotorcraft analysis? 1. These models have been developed in response to pressing needs to explain physical phenomena found in experimental data. 2. These models are physically intuitive. 3. These models have been consistently based on engineering physics rather than on any heuristic mathematical fit of data. 4. These models bring in just enough physics to explain the important behavior. 5. 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.

7 What is a dynamic wake model? 1. 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. 2. It is a model that represents this evolution of inflow in first-order form in terms of a finite number of state variables. [M]{dv n /dt} + [C]{v n } = {F m } 3. It is a model that allows the number of states to vary with user needs.

8 Foundation

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

10 Amer 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 2136 October 1950, p.11. Figure 1: Source of damping in roll for a helicopter undergoing a rolling velocity.

11 G. J. Sissingh, 1952

12 G. 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.

13 Classical 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

14 Wake Layers

15 Loewy Function

16 Lessons Learned 1. It is better not to use any Wake Model at all than to use Theodorsen Theory for a rotating wing. 2. The buckets of the real part of the Loewy Function (including = 0) are the identical lift deficiency that was found by Amer and Sissingh. 3. The imaginary part of the Loewy function shows that there is a time lag in the development of that lift deficiency.

17 Classical Approach Rene Miller of MIT (1964) added a three-dimensional correction. Rene Miller 1983 Nikolsky

18 Development

19 H.C. Pat Curtiss, Jr Nikolsky Pat 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 = acr 4 /I y a*/a = [1 + a/8v] -1 Curtiss also realized that it was sometimes necessary to put a time delay into the dynamic inflow

20 REXOR Had Dynamic Inflow Lockheed s REXOR Program also had Sissingh s inflow effect with a time constant

21 Appendix on Dynamic Wake

22 Robert A. Ormiston Ormiston (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.

23 New 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. David Peters 2008 Nikolsky

24 First Correlations The calculations showed that the inflow effect corrected steady results in hover but not forward flight and not unsteady results in either case.

25 Apparent 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.

26 Correlation was excellent in hover but lousy in forward flight

27 Correlation was excellent in hover but lousy in forward flight

28 Kurt 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.

29 Parameter Identification The identified values were within 2% of the values used by Ormiston and Peters from the Sissingh theory and potential flow for apparent mass.

30 Anton J. Jack Landgrebe In 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.

31 Free-Vortex Wake x = - s 1 U t x t = G r G y Trailing Tip Vortex Trailing Vortex Filaments Vortex Lattice Vortex Sheet

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

33 Circular Wing Theory Kinner Paper Wieslaw Z. Steppy Stepniewski 1981 Inaugural Nikolsky Recipient

34 Pitt - Peters Model.

35 Connections By the way, Pitt ran Landgrebe, too, with the same results.

36 Gopal Gaonkar Gaonkar helped with the correlations. IT WAS LIKE MAGIC!

37 Bousman and Johnson William G. Bousman had taken some ground resonance data. Wayne Johnson tried to correlate it with his new comprehensive code, CAMRAD.

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

39 Peretz P. Friedmann As other aeroelasticians began to understand the importance of aerodynamics as states, Friedmann began to compare Loewy Theory and dynamic inflow theory and discovered what appeared to be a discrepancy.

40 Singularity 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.

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

42 Dynamic Flow Diagram

43 Time Constants at Harmonic Numbers Extension of Pitt Model: T = 0.75 / (1.5 + m) Loewy function at r = ¾: T = 0.75/m

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

45 Cheng 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.

46 Langley Wind Tunnel Data This was just in time for the Langley data. Why did dynamic wake out perform vortex lattice?

47 Hover Test Stand Data This was also just in time to correlate with hover test stand data taken by Komerath. Ay Su

48 Theory 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.)

49 Refinement 1990

50 Back to Washington University In 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.

51 Back to Washington University People 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.

52 Aviv Rosen Fig. 2 A graphic description of the wake distortion during a constant pitch rate.

53 Wake 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]. Pat Curtiss 2000 Nikolsky

54 Wake Distortion Parameters η + ν R χ Contraction V = η +2ν Skew X = tan(χ/2) Curvature К = 1/R

55 Generalized Dynamic Wake Model

56 Wake Curvature J.V.R. Prasad UH-60 Off-axis pitch to lateral stick doublet input (40 knots) 5 Zhao, Prasad and Peters No wake distortion effects Flight test data qb (deg/sec) 0 40knots, K Re = Time (sec)

57 Velocity Potential Model Jorge 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. Jorge Morillo Thus, the states imply all three components of flow everywhere in the flow field.

58 Jorge Morillo

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

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

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

62 So, 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.

63 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.

64 Will 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.

65 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

66 Finish ANY QUESTIONS?