Lecture # 07: Laminar and Turbulent Flows

AerE 344 Lecture Notes

Dr. Hui Hu

Department of Aerospace Engineering Iowa State University Ames, Iowa 50011, U.S.A

DU Re  

• Laminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. Inflow dynamics laminar flow is a flow regime characterized by high momentum diffusion, low momentum convention, pressure and velocity almost independent from time. It is the opposite of turbulent flow. – In nonscientific terms laminar flow is "smooth," while turbulent flow is "rough."

• In fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum conversation, and rapid variation of pressure and velocity in space and time. – Flow that is not turbulent is called laminar flow

VD Re  

u  u  u'; v  v  v' w  w  w'

1 t0 T 1 t0 T 1 t0 T u  u(x, y, z,t)dt; v  v(x, y, z,t)dt; w  w(x, y, z,t)dt T  T  T  t0 t0 t0

u' 0; v'  0 w'  0 1 to T (u')2  (u')2 dt  0; (v')2  0 (w')2  0 T  t0

 u Laminar flows:   lam y     u'v' Turbulent flows: turb  u     u'v' lam turb y

A.laminar flow b.turbulent flow

D C  d 1 U 2 A 2 

DU Re  

1.0 )

 0.8

0.6

0.4

0.2 smooth-ball 0 rough-ball Centerline Velocity (U/U golf-ball Re=100,000 -0.2 -0.4 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Distance (X/D) Smooth ball Rough ball Golf ball

U m/s: -10 -5 0 5 10 15 20 25 30 35 40 2 U m/s: -10 -5 0 5 10 15 20 25 30 35 40 2 U m/s: -10 -5 0 5 10 15 20 25 30 35 40 2

1 1 1 /D /D /D Y Y Y 0 0 0

-1 -1 -1

Mercedes Boxfish Vortex generator above a Mitsubishi rear window

• Laminar flow airfoils are usually thinner than the conventional airfoil. • The leading edge is more pointed and its upper and lower surfaces are nearly symmetrical. • The major and most important difference between the two types of airfoil is this, the thickest part of a laminar wing occurs at 50% chord while in the conventional design the thickest part is at 25% chord. • Drag is considerably reduced since the laminar airfoil takes less energy to slide through the air. • Extensive laminar flow is usually only experienced over a very small range of angles-of-attack, on the order of 4 to 6 degrees. • Once you break out of that optimal angle range, the drag increases by as much as 40% depending on the airfoil

60 1.4 L C  40 1.2 l 1 V 2c 2  20

l 1.0 Airfoil stall

0.8 C*100 Before stall / GA(W)-1 airfoil Y -20

Lift Coefficient, C Coefficient, Lift 0.6 25 m/s C =2 shadow region L Experimental data -40 0.4

-60 vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 0.2 0 2 4 6 8 10 12 14 16 18 20 -40-200 20406080100120140 X/C*100 Angle of Attack (degrees) 60 0.40

0.35 40

0.30

d 20 0.25 Experimental data

0 0.20 C*100 / Y D GA(W)-1 airfoil After stall 0.15 Cd 

Drag Coefficient, C Coefficient, Drag 1 2 -20 V c 25 m/s 0.10 2 shadow region

-40 0.05 Airfoil stall vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

0 0 2 4 6 8 10 12 14 16 18 20 -20 0 20 40 60 80 100 120 X/C*100 Angle of Attack (degrees) Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved! Flow Separation and Transition on Low-Reynolds-number Airfoils

• Low-Reynolds-number airfoil (with Re<500,000) aerodynamics is important for both military and civilian applications, such as propellers, sailplanes, ultra-light man- carrying/man-powered aircraft, high-altitude vehicles, wind turbines, unmanned aerial vehicles (UAVs) and Micro-Air-Vehicles (MAVs). • Since laminar boundary layers are unable to withstand any significant adverse pressure gradient, laminar flow separation is usually found on low-Reynolds-number airfoils. Post- separation behavior of the laminar boundary layers would affect the aerodynamic performances of the low-Reynolds-number airfoils significantly • Separation bubbles are usually found to form on the upper surfaces of low-Reynolds-number airfoils . Separation bubble would burst suddenly to cause airfoil stall at high AOA when the adverse pressure gradient becoming too big.

Separation point

Turbulence transition -3.0 AOA = 06 deg AOA = 08 deg Reattachment point -2.5 AOA = 09 deg AOA = 10 deg -2.0 AOA = 11 deg AOA = 12 deg -1.5 AOA = 14 deg

P -1.0 C -0.5 0 0.5 1.0 Typical surface pressure distribution when a laminar 1.5 separation bubble is formed (Russell, 1979) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 X / C 0.15 12.0 0.10 Transition 0.05 11.5 Reattachm ent Separation 11.0 Y/C 0 -0.05 10.5 -0.10 10.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 9.5 AOA (degree) AOA X/C 9.0 GA (W)-1 airfoil 8.5

(also labeled as NASA LS(1)-0417 ) 8.0

10 10

C*100 5 / C*100 Y 10 m/s / GA (W)-1 airfoil Y separation reattachment 0 Spawise GA (W)-1 airfoil vorticity 0 -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0 10.0 14.0 18.0 U m/s: 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 -5 0 5 10 15 20 25 30 35 X/C*100 -5 0 5 10 15 20 25 30 35 X/C*100 Instantaneous flow field Ensemble-averaged flow field 11 11 10 10 9 9 8 8 7 7 Y/C*100 6 Y/C*100 6

5 5 Reattachment 10 m/s Spanwise 10 m/s 4 Vorticity 4 3 (1/s * 10 ) -25.0 -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0 Um/s: 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 3 3 18 20 22 24 26 28 30 32 34 18 20 22 24 26 28 30 32 34 X/C*100 X/C*100 PIV measurement results at AOA = 10 deg, Re=68,000

• Stall hysteresis, a phenomenon where stall inception and stall recovery do not occur at the same angle of attack, has been found to be relatively common in low-Reynolds-number airfoils. • When stall hysteresis occurs, the coefficients of lift, drag, and moment of the airfoil are found to be multiple- valued rather than single-valued functions of the angle of attack. • Stall hysteresis is of practical importance because it produces widely different values of lift coefficient and lift-to-drag ratio for a given airfoil at a given angle of attack. It could also affect the recovery from stall and/or spin flight conditions. Lift coefficient

Lift coefficient Increasing AOA Increasing AOA decreasing AOA decreasing AOA

AOA – Angle of Attack AOA – Angle of Attack Lift coefficient curve of a “typical” airfoil Lift coefficient curve with stall hysteresis Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved! Measured airfoil lift and drag coefficient profiles

1.6 0.40

1.4 0.35

1.2 0.30 d

l 1.0 0.25 AOA increasing AOA decreasing 0.8 Hysteresis loop 0.20 0.6 0.15 Hysteresis Lift Coefficient, C Coefficient, Lift Drag Coefficient, C Coefficient, Drag 0.4 AOA increasing loop AOA decreasing 0.10 0.2 0.05 0

-0.2 0 -4 -2 0 2 4 6 8 10 12 14 16 18 20 -4 -2 0 2 4 6 8 10 12 14 16 18 20

Angle of Attack (degree) Angle of Attack (degree)

GA(W)-1 airfoil, ReC = 160,000 • The hysteresis loop was found to be clockwise in the lift coefficient profiles, and counter-clockwise in the drag coefficient profiles.

• The aerodynamic hysteresis resulted in significant variations of lift coefficient, Cl, and lift-to-drag ratio, l/d, for the airfoil at a given angle of attack.

• The lift coefficient and lift-to-drag ratio at AOA = 14.0 degrees were found to be Cl = 1.33 and l/d = 23.5 when the angle is at the increasing angle branch of the hysteresis loop.

• The values were found to become Cl = 0.8 and l/d = 3.66 for the same AOA=14.0 degrees when the angle is at the deceasing angle branch of the hysteresis loop

60 60

40 40

20 20 0 0

1 0 * C

/ 0 GA(W)-1 airfoil C *100 / separation bubble Y Y -20 GA(W)-1 airfoil

25 m/s -20 shadow region 25 m/s -40 shadow region 1.5 -40 vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 -60 1.4 vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

-40 -20 0 20 40 60 80 100 1201.3 140 X/C *100 -20 0 20 40 60 80 100 120 X/C *100 l 1.2

1.1

1.0

0.9

0.8 Lift Coefficient, C Coefficient, Lift 60 0.7 AOA decreasing 40 40 0.6 AOA increasing

0.5 20 8 9 10 11 12 13 14 15 16 17 18 19 20 20

Angle of Attack (degree) 0 GA(W)-1 airfoil 0 C *100 C *100 / / Y

Y -20 GA(W)-1 airfoil 25 m/s -20 shadow region 25 m/s -40 shadow region

-40 -60 vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

-20 0 20 40 60 80 100 120 -40 -20 0 20 40 60 80 100 120 140 X/C *100 X/C*100 Copyright(Hu, Yang, © by Dr.Igarashi, Hui Hu Journal@ Iowa St ofate Aircraft, University. Vol. All 44.Rights No. Reserved! 6 , 2007) Refined PIV Measurement Results

20 20

15 15

10 10 C*100 / C *100

/ 5 5 Y Y

0 0 25 m/s 25 m/s GA(W)-1 airfoil GA(W)-1 airfoil 1.5 -5 -5 -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0 vort: -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0 1.4 -10 1.3 -5 0 5 10 15 20 25 30 35 -5 0 5 10 15 20 25 30 35 X/C*100

X/C*100 l 1.2

1.1

1.0

0.9

0.8 25 C Coefficient, Lift 20 0.7 AOA decreasing 20 0.6 AOA increasing 15

15 0.5 8 9 10 11 12 13 14 15 16 17 18 19 20 10 10 Angle of Attack (degree)

C*100 5 / C *100 5 / Y Y

0 0 GA(W)-1 airfoil GA(W)-1 airfoil 25 m/s 25 m/s

-5 -5 vort: -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0 vort: -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0

-10 -10 -5 0 5 10 15 20 25 30 35 X/C *100 -5 0 5 10 15 20 25 30 35 X/C *100 Copyright(Hu, Yang, © by Dr.Igarashi, Hui Hu Journal@ Iowa St ofate Aircraft, University. Vol. All 44.Rights No. Reserved! 6 , 2007) Lab 6: Airfoil Wake Measurements and Hotwire Anemometer Calibration

F  D  ( pnˆdA)  X  X CS  D  p dA  p(y)dA  up  1 2 y Since pup  p; p(y)  p

  FX  D x 2 U (y) U (y)  F  D  U  [ ( 1)]dA  X  2  2 U  U 

2 U (y) U (y)  D  U  [ (1 )]dA  U U 2  2  

2 U (y) U (y)  U  [ (1 )]dA D  U U 2 C   2   D 1 1 U 2C U 2C 2  2  2 U (y) U (y)  C  [ (1 )]dy D  C 2 U  U  • Compared with the drag coefficients obtained based on airfoil surface pressure measurements at the same angles of attack!

Pressure rake with 41 total pressure probes y (the distance between the probes d=2mm)

x 80 mm

Flow Field

Current flow through wire

dTw 2 mc  i Rw  q(V ,Tw ) dt • Constant-temperature anemometry

CTA hotwire probe

• To quantify the relationship between the flow velocity and voltage output from the CTA probe

18 y=a+bx+cx2+d*x3+e*x4 max dev:0.166, r2=1.00 a=10.8, b=3.77, c=-26.6, d=13.2 16 14

12 Curve fitting 10 Experimental data 8

Flow velocity (m/s) Flow velocity 6 4 2 0 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2

voltage (V)

Required Plots:

• Cp distribution in the wake (for each angle of attack) for the airfoil wake measurements

• Cd vs angle of attack (do your values look reasonable?) based on the airfoil wake measurements

• Your hot wire anemometer calibration curve: Velocity versus voltage output of hotwire anemometer (including a 4th order polynomial fit)

Please briefly describe the following details:

• How you calculated your drag—you should show your drag calculations

• How these drag calculations compared with the drag calculations you made in the previous experiment.

• Reynolds number of tests and the incoming flow velocity