kiran research summary

8/10/2019 Kiran Research Summary

1/18

Low-cost numericalmethods for unsteady

flowsKiran Ramesh


2/18

Features of unsteady flows Trailing-edge wakes

result in downwash on airfoil

Flow separation

loss in lift, pressure drag

Large added-mass

dominant force in high-frequency motions

Leading-edge vortices

increase lift and cause variation in pitchingmoment

Responsible for high-lift flight in insects

2


3/18

Overview of modelling approaches

My approach: Start with theoretical modelling - eliminate

assumptions, augment theory to account for viscous phenomena

Approach PROS CONS

Theoretical

fast, improve

understanding of

physics

limited by

assumptions such as

small-amplitudes,

attached flow

Experiment, CFDreliable, improve

understanding

expensive/slow,

unsuitable for real-time

simulation and design

Semi-empiricalfast, can be used forsimulation and design

depend on several

parameters, do notprovide insight into

physics

3


4/18

Large-angle unsteady thin-

airfoil theory Airfoil (body frame) starts at inertialframe and moves along any path

Airfoil vorticity is represented as a

Fourier series

Discrete-time method: at each time-

step, one vortex shed from trailing-edge

Assumptions: inviscid, incompressible

flow

Amplitudes, frequencies may be

arbitrarily large

4


5/18

Large-angle unsteady thin-

airfoil theory Time-stepping method: airfoil moves along any

arbitrary path

pitch

plunge

variation in freestream velocity

Solves for the vorticity on airfoil and trailing-edge vortex

Typical simulation of 500 time-steps: 3 sec

Large amplitudes, nonplanar wakes, added mass are modelled

Flow separation and LEV formation are not modelled5


6/18

Results from theory Motion (grey line, right axis): pitch up to

25 deg, hold, pitch down to zero

High pitch rate: typical of MAVs, insect

flight

Most important flowfeature : leading-edgevortex

Flow visualisation from experiment, CFD at four instants

Trailing-edge separationis negligible

Theory fails after point D

6


7/18

Criterion for LEV formation

Suction results at leading edge when airfoil

is at an angle of attack, because of flow

turning around the leading edge

A0(t)

Hypothesis - Start of LEV formation can be correlated with the

leading-edge suction exceeding a critical value

Suction at leading-edge from thin-airfoil theory: Proportional to

first Fourier coefficient

Leading Edge Suction Parameter (LESP) =

7


8/18

Verification of LESP

hypothesis SD7003 airfoil, Re=100,000

Start of LEV formation is

determined from CFD

LEV formation always occurs

when LESP > critical LESP (0.14),

so long as airfoil and Reynolds

number are same

8

Upper surface

LEV formation

Lower surface

LEV formation


9/18

Control of LEV occurrence using LESP

SD7003, Re=100,000 Baseline motion: pitch-up to 45 deg,

LEV forms on airfoil upper surface0 2 4

0

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(Baseline)

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No LEV formation

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9


10/18

LESP based discrete-vortex

method (LDVM) Vortex is shed from the leading-edgewhen LESP > critical LESP

Strength of vortex calculated

such that LESP = critical LESP

Typical run time for 500 time-steps: 25s

Salient feature: Models intermittent vortex shedding

Fortran code based on this model :

Available open-source at http://sourceforge.net/projects/unsflow

Outputs forces on airfoil and video of flow-visualisation as well asfundamental quantities such as pressure distribution, velocity and vorticity

on airfoil

10
http://sourceforge.net/projects/unsflow


11/18

Illustration of LDVMMotion (grey line): pitch up to 25 deg, hold, pitch down to zero; leading-edge pivot

Validation against CFD and experiment

LEV and vortex interactions are successfully modelled by LDVM

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12/18

Illustration of LDVMMotion (grey line): Smooth pitch-up to 90 degand pitch down to zero; trailing-edge pivot

Validation against CFD

3 instances of LEV formation

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13/18

Perching manoeuvresMotion : pitch-up to 45 deg, simultaneous deceleration to zero velocity

2 3 4 5 6 70

0.2

0.4

0.6

0.8

1

log10

(ReLE

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LESPcrit

Calibration data from CFD

Spline fit

Reynolds number is notconstant - critical LESP

changes

Critical LESP iscalibrated against Re atleading edge and usedin simulation

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CFD

13

CFD

LDVM


14/18

Hovering maneuvers

Freestream velocity is zero

Induced velocity at leading

edge is however not zero Critical LESP is calibrated

against Re at leading edge

and used in simulation

Motion : plunge up and down, zero freestream velocity

2 3 4 5 6 70

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15/18

Application to FSI - Flow

past a 2DOF airfoil Airfoil constrained by springs

Degrees of freedom - pitch, plunge

LESP based discrete-vortex

method is coupled with the

structural model

If freestream velocity is greater than

flutter velocity, airfoil extracts

energy from the freestream

15


16/18

Self-sustained limit-cycle

oscillations At speeds below flutter velocity: At speeds above flutter

velocity:

Divergent oscillations

bounded by LEVs

Limit-cycle oscillations

Structural and aerodynamic

parameters may be optimised

for small-scale power

generation

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17/18

Parametric studies of LCOs

E.g., Variation in LCO

characteristics with

freestream velocity

Each data point is a

simulation for 1200

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