Robins-Magnus Effect : A New Instability Mechanism & Role of Heuristics In Research

1. Robins-Magnus Effect: A New Instability Mechanism & Role of Heuristics In Research Tapan K. Sengupta* Department of Aerospace Engineering, IIT Kanpur *Others who contributed to this work are Dr. M.T. Nair, K. Gupta, Amit Kasliwal, Srikanth B. Talla & Anurag Dipankar.

2. Presentation Sequence • General Problem Definition • Historical Note • A New Mechanism • Current status vis-à-vis computing

3. What is Robins-Magnus Effect? • This is the lift force experienced due to side-slip or the sideforce due to cross-flow. • The major physical parameters for this problem are the Reynolds number and the non-dimensional rotation rate given by,

4. Lift * Velocity, Drag D weight X axis Y axis Z axis

5. At the beginning: Benjamin Robins (1707 – 1751) • Major Achievements: > Fellow of Royal Society at the age of 20. > Published Principles of Gunnery …. (1742). > Considered the father of Ballistics (introduced rifling/ importance of drag for trajectory estimation and transonic drag rise). > Started experimental fluid mechanics: developed whirling arm and ballistic pendulum. > First Engineer General of East India Company. Died in St. David, Madras in 1751. Posthumously, his works were published in Mathematical Tracts, vols. 1 and 2 by J. Nourse, London (1762)

6. Benjamin Robins’ Contribution to Experimental Fluid Mechanics: A Whirling Arm device designed by Robins – the progenitor of modern day wind-tunnels

7. Role of Heuristics : Robins-Magnus effect • Robins’ observation (1742) on this effect was disputed by Euler, who thought this was due to manufacturing defects of the model used. • Note that this was discussed in 1745, before Euler’s equation of hydrodynamics was enunciated in 1752 – the first mathematical model of fluid flow. • Euler Heuristically observed: A spinning body in side-slip (with top-down symmetry) cannot experience a lift force.

8. Role of Heuristics : Prandtl’s Role • The Robins- Magnus effect was explained by Prandtl (1926) based on a steady irrotational flow model of hydrodynamics. A typical set of results shown next.

9. Steady Irrotational Flow Model

10. Role of Heuristics : A maximum limit on lift by Prandtl • Based on STEADY IRROTATIONAL FLOW MODEL Prandtl proposed a maximum limit on lift experienced by the spinning cylinder. • It was reasoned that for spin rate beyond the critical value (figure (c)) the two distinct domain does not communicate with each other. • The location of the full saddle point at the lower-most point of the cylinder fixes the lift value to

11. Maximum Lift Principle • The maximum lift principle seemed inviolable, till Tokumaru & Dimotakis (JFM, vol. 255,1993) reported otherwise. • By indirect measurements they reported an excess of lift by 20% over the maximum limit for Re = 3800 and Ω = 10. • It was conjectured that diffusion, three- dimensionality and unsteadiness may be behind this violation.

12. Streamline and vorticity contour plots for real flow for Re = 3800 and Ω = 5.0

13. A New Mechanism of Instability • Computational results showing the flow instability were reported in: • Sengupta et al. (1998) Moving surface separation control for airfoil at high angles of attack. In the Proc. of IUTAM symposium on Mechanics of Passive and Active Flow Control held at Gottingen, Germany (Kluwer Academic) • Nair M.T. & Sengupta T.K. (1998) Magnus effect at high speed ratios. In the Proc. Of 3rd ACFD conference held at Bangalore. • Nair, Sengupta & Chauhan (1998) Flow past rotating cylinder at high Reynolds numbers using higher order upwind scheme. Computers & Fluids, vol. 27, 47-70. • Sengupta et al. (1999) Lift generation and limiting mechanism via unsteady flow development for Magnus-Robins effect. In the Proc. Of 8th ACFM held at Shenzhen (China). International Acad. Publishing, Beijing. • Sengupta et al. (2003) Temporal flow instability for Magnus-Robins effect at high rotation rates. J. Fluids & Structures, vol. 17, 941-953.

14. A New Instability Mechanism

15. The instability Mechanism • Was this instability seen before? • It was noted by H. Werle (1984) in: Hydrodynamic visualization of the flow around a streamlined cylinder with suction: Cousteau-Malavard turbine sail model. Recherché Aerospatiale, no. 1984-04 Who reported aperiodic instabilities for Re = 3300. • In a personal communication Prof. V.J. Modi (Univ. of British Columbia) have also confirmed observing instabilities while performing experiments with circulation control airfoils. (See the transcripts next.)

18. Computational Evidences: Apart from us, Mittal & Kumar (2003) talk about an instability for low Reynolds number of 200.

19. For the same Reynolds number, we obtain the following results for lift, drag and pitching moment coefficients.

20. What is this Instability, after all? • In MK (2003) any time periodicity is construed as instability! It is not the same that was reported in Werle (1984) or seen by Modi (1998). • It was not explained why there is a narrow window of rotation rate for instability at Re = 200. • There was no instability seen for Re = 3800. • The lift calculated for Re = 200 and Re = 3800 are of the same order. This is highly improbable!

21. Results from Mittal (2001) • Naturally, the question arises, which of these results are correct? • We can resolve this by looking closely at the numerical methods.

22. Analysis of Numerical Methods • This is following the method developed by Sengupta et al. (JCP, 2003) and in Fundamentals of CFD (Sengupta, 2004), where a spectral method is developed for analysis of any discrete computational method. • We look at (a) the spectral resolution, (b) added numerical dissipation and (c) Dispersion Relation Preservation (DRP) property. • We compare our Compact Difference Scheme (FDM) with the Streamline Upwind Petrov- Galerkin (SUPG- FEM) scheme to check their effectiveness for DNS.

23. Spectral ResolutionSUPG-FEM <--<--|  Compact-FDM

24. Added Numerical DissipationSUPG-FEM <--<-- | Compact-FDM

25. Solution of 1D wave equation bySUPG-FEM <-- <-- |   Compact-FDM

26. Animation of streamlines

27. Animation of Streamlines

28. Vorticity Animation (Total field)

29. Vorticity Animation (Near field)

30. On Abuse of Numerical Simulations • Environmental problems are often managed by specialists in “simulations”, that is to say, people whose competence is more in the area of computer programming than in interpreting scientific data. Large computers can produce predictions that look quite credible even though the numerical outputs may be deficient. That is one great evils of our time. … The strength of numbers bolstered by the power of images is enough to sustain in the public an irrational, quasi-mystical mind-set. • Pierre-Giles de Gennes & Jacques Badoz (in Fragile Objects, 1996)

31. The Physical Instability Mechanism • The instability seen in this flow-field is due to interaction of vortices at large distances of separation- as clearly evidenced in the vorticity animation. • The theory behind this phenomenon has been reported in Sengupta et al. (2003): Vortex-induced instability of an incompressible wall-bounded shear layer (JFM, 493, pp 277-286) based on some experiments performed at NUS (to appear in Expts. in Fluids (2004)). • We developed an energy based instability equation.

32. The Instability Mechanism • Starting from the governing Navier-Stokes equation, one can look at the rotational part of the flow field and obtain an equation for the instantaneous distribution of disturbance energy as given below:

33. The Instability Mechanism • The right hand side of the Poisson equation represents either source/ sink of energy. A negative right hand side implies instability (growth of disturbance energy). • Thus, it is instructive to look at the evolution of the right hand side with time to look for instability. • We show a short animation of r.h.s. of the Poisson equation next.

34. Contour Plot of R.H.S.

35. Quo Vadis ? • A new instability shows that a spinning body experiences discontinuous aerodynamic loads. • For a spinning projectile or sports ball this may explain the subtle variation of trajectories- specially when the net force and moment change abruptly. • For example, for the rotating cylinder at a Reynolds number of 200 the variation in the direction of the net force is shown next.

36. Deviation of Aerodynamic Force Direction with Time During Instability

37. Trajectories of Projectiles and Sports Balls • We have only discussed the motion past cylindrical bodies. Hence, these results directly apply to motion of projectiles in the cross flow plane. The parameter ranges are relevant for this to occur in real life. • However, the physical mechanism is one of vortex-induced instability- that might be present for spherical bodies as well. This has not been done, so far. • Specially, for sports balls, the relevant Reynolds numbers are rather large (roughly 1000 per kmph speed) and the corresponding flow will be turbulent where the likelihood of vortex-induced instability is more pronounced.

38. Future work • We are interested in flow control of bluff-bodies using different strategies. • We are starting work on drag reduction for bluff-body flows using GA as a viable tool with KanGAL. • The vortex-induced instability phenomenon- being a by-pass transition depends sensitively on back-ground disturbance environment- an aspect not investigated properly. We plan to start some preliminary experiments to verify and characterize the presented results.