Robins-Magnus Effect: A New Instability Mechanism

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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.

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Presentation Sequence

• General Problem Definition
• Historical Note
• A New Mechanism
• Current status vis-à-vis computing

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What is Robins-Magnus Effect?

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

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X axis
Y axis
Z axis
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At the beginning Benjamin Robins (1707 1751)

• Major Achievements
• gt Fellow of Royal Society at the age of 20.
• gt Published Principles of Gunnery . (1742).
• gt Considered the father of Ballistics
  (introduced rifling/ importance of
  drag for trajectory estimation
• and transonic drag rise).
• gt Started experimental fluid mechanics
  developed whirling arm and ballistic
  pendulum.
• gt 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)

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

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Role of Heuristics Prandtls 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.

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Steady Irrotational Flow Model
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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

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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 O 10.
• It was conjectured that diffusion, three-
  dimensionality and unsteadiness may be behind
  this violation.

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Streamline and vorticity contour plots for real
flow for Re 3800 and O 5.0
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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.

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A New Instability Mechanism
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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.)

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Computational Evidences Apart from us, Mittal
Kumar (2003) talk about an instability for low
Reynolds number of 200.
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For the same Reynolds number, we obtain the
following results for lift, drag and pitching
moment coefficients.
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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!

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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.

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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.

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Spectral Resolution SUPG-FEM lt--lt-- ??
Compact-FDM
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Added Numerical Dissipation SUPG-FEM
lt--lt-- ?? Compact-FDM
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Solution of 1D wave equation bySUPG-FEM
lt-- lt-- ? ? Compact-FDM
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Animation of streamlines
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Animation of Streamlines
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Vorticity Animation (Total field)
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Vorticity Animation (Near field)
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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)

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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.

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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

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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.

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Contour Plot of R.H.S.
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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.

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Deviation of Aerodynamic Force Direction with
Time During Instability
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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.

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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.