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Transient Heat Transfer Effects from a Flapping Wing
Behrouz AbedianRobert Lind Tuesday, October 25, 2005
Azuma, p26
Presented at the COMSOL Multiphysics User's Conference 2005 Boston
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Numerical Experimentation with a 2D Model
Subject: Warm wing flapping in cold air flying forward with speed U.
Purpose: Investigate heat transfer effects using:
The trailing temperature field.The rate of heat transfer.
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Results to Date: Established the Numerical Model of a Flapping Wing
We demonstrate the heat transfer from a flapping wing Vary the wings flapping frequency, , and its forward speed, U: Generate various flow regimes and heat flows. Examples of temperature fields from two trial runs:
Future: Quantitative assessment of the heat transfer.
(2, 3200) (1, 1100)
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Research Inspiration: Birds, Insects and FishFlapping wings and fanning tails
Wings for lift & thrust Tails for thrust only
Alexander
Azuma, p194
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Flapping Wings: Focus on Birds
Symmetrical flapping: produces no net thrustDownstroke forward thrust.Upstroke reverse thrust.Exactly cancels !
Azuma, p28
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Biomechanical Research Parameters
ULK =Reduced frequency:
Flapping wing parameters:
Reynolds frequency:
Length of wing, LAir viscosity Flapping angular frequency, Wing forward speed, U
2Re Lf =
Angular speedForward speed
Inertia forcesViscous forces
kUL fReRe ==
U
L
Dimensionless numbers used to scale and organize the wing motion
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Dimensionless Numbers Categorize the Wing Motion of Flying Creatures
Parameters Small Wasp Locust Pigeon
Wing Length, L 0.0006 m 0.04 m 0.25 m
Angular frequency, 400 rads/s 20 rads/s 5 rads/s
Forward velocity, U 1 m/s 4 m/s 5 m/s
Reduced frequencyk= L/U 0.24 0.20 0.25
Reynolds frequencyRef= L2/ 10 2,300 22,500
Biomechanical dimensionless numbers are used to determine the wing angular frequencies, , and forward speeds U, in the numerical mode.
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Model the Flapping Wing with Femlab
Femlabs multiphysics package:Fluid Dynamics Module: Incompressible Transient Analysis
Navier-Stokes equation: momentumHeat Transfer Module: Convection & Conduction Transient Analysis
Energy Equation for temperature field
Model assumptionsWing: Rigid wing, L=0.1m
Sinusoidal motion, (t)=(/2)sin(t)Forward speed, U=0.4Temperature, T = 275 K
Air: IncompressibleTemperature, T = 255 KViscosity, = 13.91e-6 m/s2
Flow: Laminar flow only
(t)=(/2)sin(t)
0.1m
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Fluid Dynamics: Develop the Flapping Wing Motion Equations
jtvitudttdP )()()( +=
s ( ) ( )( ) ( )( )[ ]jtitLtP sincos +=( ) ( ) ( )tst sin2=
( )20 sLA =
( ) ( ) ( )[ ] ( )ttsAtu cossin2sin0 =( ) ( ) ( )[ ] ( )ttsAtv cossin2cos0 =
Velocity components of the flapping wing for the Navier-Stokes equation.
u(t) Horzontal velocity v(t) verticle velocity
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Fluid Dynamics: Modify the Upstroke Horizontal Velocity
( ) ( ) ( )[ ] ( )ttsAtu cossin2sin0 =
Solution: Apply an on/off function to the horizontal velocity. A 7-term Fourier Series cancels the upstroke horizontal velocity.
Problem: Cancel the reverse thrust:
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Fluid Dynamics: Apply the Motion Equations The wing is fixed in place
To simulate wing motion:The Equations of motion are applied to the fluid, at wing surface: Horizontal velocity, u(t) and Vertical velocity, v(t)
L
v(t)
u(t)
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Heat Transfer: Apply the Energy Equation
+
=yTv
xTucQ p
Issue: Heat is convected from the wing (275 K) to the air (255 K) and is swept away downstream ~ a trailing temperature field.
Density, 1.265 kg/m3
Kinematic viscosity, 13.91e-6 m/s2
Specific heat, cp 1008 J/kg-K
Thermal conductivity, k 0.0255 W/m-K
Approach: 1st solve the Navier-Stokes fluid flow solution in the model.2nd apply the 2D heat conduction equation, (Convection is not specified)
Thermal properties of air at 255 K and atmospheric pressure.
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Summary: The Model Geometry and Boundary Conditions
1.0m
0.5m
Fixed line as wingLength, L=0.1m, Temperature, T=275 K
Bulk fluid: AirVelocity, U= L/kTemperature, T=255 K
Outlet Pressure, p=0
Solving the model: 1st solve the fluid field. 2nd solve the heat field, using the flow field results.
The completed multiphysics model is ready for solving(Fluid dynamic subdomain and heat transfer subdomain)
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Trial Runs: Numerical Experiments
K U
1.5 0
2 1.5 0.075
1 1.5 0.150
0.25 1.5 0.600
K U
4.5 0
2 4.5 0.225
1 4.5 0.450
0.25 * 3.1 1.240
Heat is transferred for various flow regimes.Vary flapping frequency, , and forward speed U,Trials organized by dimensionless parameters K and Ref
Dimensionless Parameters:k=L/U Ref= L2/
Results of Trial Set 2: Ref = 3200. K = , 2, 1, 0.25Videos of solutions, 12 seconds with output 0.05 seconds per frame.
Trial Set 1: Ref = 1100 Trial Set 2: Ref = 3200
* Ref = 2200 maximum attained
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Biological Observations Can be Quantified with Modeling
Observed in 3D
Modeled in 2D
Alexander
(1, 3200)
Trailing Flow of a slow gait:
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The Next Steps
Ongoing Research: Analyze the wing surface data: Viscous drag on wing: Skin friction No, Cf = /(1/2)U2L Heat convection from wing: Nusselt No, Nu = qL/k(Tw-Ta)
Correlate with: Reduced frequency k = L/UReynolds frequency Ref = L2/
(2, 1100) (1, 1100) (0.25, 1100)
Trials produced ranges of heat transference and temperature fields
(, 1100)
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Key Issues for Ongoing Research
Post processing data acquisitionIntegrate data along length of wing, L, and over one cycle, T. Viscous forces, , and heat convection, Q.
Wing was modeled as a single lineThe net heat flux on top and bottom surfaces is combined.We need to separate the top and bottom surface heat fluxes.
Model a compliant wingFemlabs fluid structure interaction technique
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Citations
1. Alexander, David E. Natures flyers: Birds, insects, and the biomechanics of flight. The John Hopkins University Press. (2002).
2. Azuma, Akira. The Biokinetics of flying and swimming. Springer-Verlag, Tokyo. (1994).
3. Comsols Femlab Multiphysics.Tufts School of Engineering.
Transient Heat Transfer Effects from a Flapping WingNumerical Experimentation with a 2D ModelResults to Date: Established the Numerical Model of a Flapping WingResearch Inspiration: Birds, Insects and FishFlapping Wings: Focus on BirdsBiomechanical Research ParametersDimensionless Numbers Categorize the Wing Motion of Flying Creatures Model the Flapping Wing with FemlabFluid Dynamics: Develop the Flapping Wing Motion EquationsFluid Dynamics: Modify the Upstroke Horizontal VelocityFluid Dynamics: Apply the Motion EquationsHeat Transfer: Apply the Energy EquationSummary: The Model Geometry and Boundary ConditionsTrial Runs: Numerical ExperimentsBiological Observations Can be Quantified with ModelingThe Next StepsKey Issues for Ongoing ResearchCitations