FLOW OVER AN AIRFOIL (NACA 0017)
FLOW OVER AN AIRFOIL (NACA 0017)
AIM: To simulate the flow over an airfoil (NACA 0017) by varying the angle of attack number and to perform grid dependency test using SOLIDWORKS FLOWSIMULATION.
DESCRIPTION:
An airfoil is the cross-sectional shape of a wing, blade (of a propeller, rotor, or turbine), or sail (as seen in cross-section).
An airfoil-shaped body moving through a fluid produces an aerodynamic force.
The component of this force perpendicular to the direction of motion is called lift. The component parallel to the direction of motion is called drag.
The lift on an airfoil is primarily the result of its angle of attack. When oriented at a suitable angle, the airfoil deflects the oncoming air (for fixed-wing aircraft, a downward force), resulting in a force on the airfoil in the direction opposite to the deflection. This force is known as aerodynamic force and can be resolved into two components: lift and drag. Most foil shapes require a positive angle of attack to generate lift, but cambered airfoils can generate lift at zero angle of attack. This "turning" of the air in the vicinity of the airfoil creates curved streamlines, resulting in lower pressure on one side and higher pressure on the other. This pressure difference is accompanied by a velocity difference, via Bernoulli's principle, so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface. The lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of circulation and the Kutta–Joukowski theorem.
A fixed-wing aircraft's wings, horizontal, and vertical stabilizers are built with airfoil-shaped cross sections, as are helicopter rotor blades. Airfoils are also found in propellers, fans, compressors, and turbines. Sails are also airfoils, and the underwater surfaces of sailboats, such as the centerboard and keel, are similar in cross-section and operate on the same principles as airfoils. Swimming and flying creatures and even many plants and sessile organisms employ airfoils/hydrofoils: common examples being bird wings, the bodies of fish, and the shape of sand dollars. An airfoil-shaped wing can create a downforce on an automobile or other motor vehicle, improving traction.
AIRFOIL NOMENCLATURE:
The suction surface (a.k.a. upper surface) is generally associated with higher velocity and lower static pressure.
The pressure surface (a.k.a. lower surface) has a comparatively higher static pressure than the suction surface. The pressure gradient between these two surfaces contributes to the lift force generated for a given airfoil.
The geometry of the airfoil is described with a variety of terms:
The leading edge is the point at the front of the airfoil that has maximum curvature (minimum radius).
The trailing edge is defined similarly as the point of maximum curvature at the rear of the airfoil.
The chord line is the straight line connecting leading and trailing edges. The chord length, or simply chord, is the length of the chord line. That is the reference dimension of the airfoil section.
The shape of the airfoil is defined using the following geometrical parameters:
The mean camber line or mean line is the locus of points midway between the upper and lower surfaces. Its shape depends on the thickness distribution along the chord;
The thickness of an airfoil varies along the chord. It may be measured in either of two ways: Thickness measured perpendicular to the camber line. This is sometimes described as the "American convention";
Thickness measured perpendicular to the chord line. This is sometimes described as the "British convention".
Some important parameters to describe an airfoil's shape are its camber and its thickness. For example, an airfoil of the NACA 4- digit series such as the NACA 2415 (to be read as 2 – 4 – 15) describes an airfoil with a camber of 0.02 chord located at 0.40 chord, with 0.15 chord of maximum thickness.
Finally, important concepts used to describe the airfoil's behaviour when moving through a fluid are: The aerodynamic centre, which is the chord-wise length about which the pitching moment is independent of the lift coefficient and the angle of attack. The centre of pressure, which is the chord-wise location about which the pitching moment is zero.
OBJECTIVES:
1) To Simulate flow over an airfoil (NACA 0017) for the angle of attacks 0,2,4,8,10,12,14,16,18,20 degree
2) Compare the lift force, drag force, velocity, and pressure contours for different angle of attacks.
3) To perform a grid dependency test.
USER INPUTS:
GEOMETRY:
Dimensions of the Airfoil:
The text file containing the coordinates of the airfoil is downloaded and 0 is entered for z-axis for all the points, and
In Solidworks the coordinates are imported
Insert > curve > curve through x,y,z points.
And the curve is closed at rear end using line
And extruded by 0.2m to get the 3d model of airfoil
Dimensions of the Computational Domain/Wind tunnel:
Chord length = L = 0.001m
Length of the computational domain upstream = 5L=0.005m
Length of the computational domain downstream = 20L=0.02m
Height of the computational domain= 20L=0.02m
And 2D analysis is selected along XY plane.
General Settings:
Analysis Type: External
Transient state:
Transient state is where the time derivatives of the variables are also taken into account, and hence the magnitude of the values of the system can be monitored at any particular instant of time, but in steady state simulation only the initial values and steady state values are obtained.
Vx = 600 m/s
Total Length of the domain is 0.025m
And end time = 5sec
And time step= 1sec
Here the angle for attack is varied from 0 to 20 increment of 2 degree for different cases
Fluids:
Gas: Air
Since the initial temperature is T=293.2K and Pressure P=101325Pa
Density=1.204 kg/m^3
Dynamic viscosity=1.85e-5 Ns/m^2 (at 300K)
Flow Type= Laminar and Turbulent.
Wall conditions: Adiabatic Wall
Roughness: 0micrometer
Initial conditions:
Pressure: P=101325Pa
initial temperature is T=293.2K
GOALS:
Goals > Global goals > Force Fx and Force Fy
Goals > Global goals > friction force Fx and Fy
Goals > Surface Goals > SG force Fx and Fy
Rename SG Fx to Drag force since it’s the integrated force along x-direction
Rename SG Fy to Lift force since it’s the integrated force along y-direction
MESH:
Global Mesh
Initially a coarser mesh is used and after the grid dependency test the mesh is selected and that mesh is further used for analysis.
MATHEMATICAL MODEL:
1) Governing Equations
2) Boundary conditions.
1) Governing Equations:
Conservation of mass: This equation describes the time rate of change of the fluid density at a fixed point in space.
Conservation of momentum: Balance of Linear Momentum
Momentum balance along the x-axis:
Momentum balance along the y-axis:
Hit Run calculation
After solving we will get selected variables at selected points and from that, we can do Post-processing.
2) Boundary conditions:
Velocity boundary condition along the x-direction is applied at the inlet of the computational domain as 600m/s
And Initial conditions:
Pressure: P=101325Pa
the initial temperature is T=293.2K
GRID DEPENDENCY TEST:
This test is performed by taking the Case 1 when velocity is 600m/s and angle of attack is 0 degrees
Project name > New Parametric study
Input variables:
Local mesh is selected for variation > Level of refining fluid cells
Output Variables:
Various goal plots are selected
Scenario:
RESULTS AND PLOTS FORM GRID DEPENDECY TEST:
Results:
Maximum Values:
As seen from above values of drag and lift force (SG Fx and SG Fy) we would use the Mesh of design point 3 for further study as it is best in terms of the results and the less amount of computational time required.
VARIATION OF THE ANGLE OF ATTACK:
CASE 1 : ANGLE OF ATTACK = 0 degree
Velocity cutplot: maximum value=645.599m/s
Pressure cutplot: maximum value=449275Pa
Drag Force plot:
Lift force:
CASE 2 : ANGLE OF ATTACK = 2 degree
Velocity cutplot: maximum value= 655.616m/s
Pressure cutplot: maximum value= 448862.22Pa
Drag Force plot:
Lift Force plot:
CASE 3 : ANGLE OF ATTACK = 4 degree
Velocity cutplot: maximum value= 665.967m/s
Pressure cutplot: maximum value= 449397.92Pa
Drag Force plot:
Lift Force plot:
CASE 4 : ANGLE OF ATTACK = 6 degree
Velocity cutplot: maximum value= 677.317m/s
Pressure cutplot: maximum value= 451253.14Pa
Drag Force plot:
Lift Force plot:
CASE 5 : ANGLE OF ATTACK = 8 degree
Velocity cutplot: maximum value= 685.630m/s
Pressure cutplot: maximum value= 452893.40Pa
Drag Force plot:
Lift Force plot:
CASE 6 : ANGLE OF ATTACK = 10 degree
Velocity cutplot: maximum value= 693.910m/s
Pressure cutplot: maximum value= 452966.22Pa
Drag Force plot:
Lift Force plot:
CASE 7 : ANGLE OF ATTACK = 12 degree
Velocity cutplot: maximum value= 699.720m/s
Pressure cutplot: maximum value= 452966.22Pa
Drag Force plot:
Lift Force plot:
CASE 8 : ANGLE OF ATTACK = 14 degree
Velocity cutplot: maximum value= 704.292m/s
Pressure cutplot: maximum value= 451247.89Pa
Drag Force plot:
Lift Force plot:
CASE 9 : ANGLE OF ATTACK = 16 degree
Velocity cutplot: maximum value= 711.129m/s
Pressure cutplot: maximum value= 450477.55Pa
Drag Force plot:
Lift Force plot:
CASE 10 : ANGLE OF ATTACK = 18 degree
Velocity cutplot: maximum value= 716.495m/s
Pressure cutplot: maximum value= 442725.75Pa
Drag Force plot:
Lift Force plot:
CASE 11 : ANGLE OF ATTACK = 20 degree
Velocity cutplot: maximum value= 721.761m/s
Pressure cutplot: maximum value= 459812.75Pa
Drag Force plot:
Lift Force plot:
MATLAB COMPARISON PLOTS:
CODE:
%%%%%%%% Plotting of Graphs for Flow over an Airfoil %%%%%%%%%%%
%%%% MOHD AZHAR MERCHANT %%%%%%
%%%%%%%%%%%% Variation w.r.t Angle of Attack %%%%%%%%%%%%%%%%%%%
clc
clear all
close all
Angle_of_attack= [0 2 4 6 8 10 12 14 16 18 20]; %angle of attack in degrees
V_max=[645.599 655.616 665.967 677.317 685.630 693.910 699.720 704.292 711.129 716.495 721.61]; %maximum values of velocity in m/s
P_max=[449275 448862.22 449397.92 451253.14 452893.40 452966.22 452966.22 451247.89 450477.55 442725.75 459812.75]; %maximum values of pressure in Pa
Fd=[0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.003 0.003 0.003 0.004] ; %values of Drag force in N
Fl=[7.524e-6 6.454e-4 0.001 0.002 0.003 0.003 0.004 0.004 0.005 0.006 0.006]; %values of Lift force in N
%%%plotting maximum velocity V/s Angle of Attack %%
figure(1)
plot(Angle_of_attack,V_max,'linewidth',3)
title('Maximum velocity V/s Angle of Attack')
ylabel('V(max) [m/s]')
xlabel('AoA [degree]')
figure(2)
plot(Angle_of_attack,P_max,'linewidth',3)
title('Maximum Pressure V/s Angle of Attack')
ylabel('P(max) [Pa]')
xlabel('AoA [degree]')
figure(3)
plot(Angle_of_attack,Fd,'linewidth',3)
title('Drag Force V/s Angle of Attack')
ylabel('F_d [N]')
xlabel('AoA [degree]')
figure(4)
plot(Angle_of_attack,Fl,'linewidth',3)
title('Lift Force V/s Angle of Attack')
ylabel('F_l [N]')
xlabel('AoA [degree]')
figure(5)
hold on
title('Drag Force & Lift Force comparison V/s Angle of Attack')
plot(Angle_of_attack,Fd,'linewidth',3)
plot(Angle_of_attack,Fl,'linewidth',3)
legend('Fd Drag Force','Fl Lift force')
ylabel('F_d & F_l [N]')
xlabel('AoA [degree]')
xlim([0 22])
ylim([0 7e-3])
hold offPLOTS:
Maximum Velocity V/s Angle of Attack:
Maximum Pressure V/s Angle of Attack:
Drag Force V/s Angle of Attack:
Lift Force V/s Angle of Attack:
Drag Force & Lift Force comparison V/s Angle of Attack:
CONCLUSION:
1) From the maximum values of velocities we can see that the values increases as the angle of attack increases.
1) From the velocity and pressure cut-plots we can see that at front region of the body the fluid particles stop and stagnation occurs pressure increases as velocity decreases in accordance with the Bernoulli equation. The relationship between pressure and velocity is nonlinear, i.e. pressure is proportional to the square of the velocity. This particular mathematical relationship may not be clearly evident by simple observation of the colours, but it is clear that the pressure hotspots coincide with the stagnation points where velocity is zero. At these two locations, fluid elements have given up all of their kinetic energy and pressure is at its highest.
Velocity cutplot for 14 degree angle of attack
Pressure cutplot for 14 degree angle of attack
This "turning" of the air in the vicinity of the Airfoil creates curved streamlines, resulting in lower pressure on one side and higher pressure on the other. This pressure difference is accompanied by a velocity difference, via Bernoulli's principle, so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface. The lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of circulation and the Kutta–Joukowski theorem.
A lift and drag curve obtained with varying the angle of attack is obtained above. With an increased angle of attack, lift increases. At about 18 degrees this airfoil stalls, and lift flattens off beyond that. The flatness in lift can be explained by the action of the upper-surface boundary layer, which separates and greatly thickens over the upper surface at and past the stall angle. The thickened boundary layer's displacement thickness changes the airfoil's effective shape, in particular, it reduces its effective camber, which modifies the overall flow field so as to reduce the circulation and the lift. The thicker boundary layer also causes a large increase in pressure drag, so that the overall drag increases sharply near and past the stall points.
REFERENCES:
[1] "...the effect of the wing is to give the air stream a downward velocity component. The reaction force of the deflected air mass must then act on the wing to give it an equal and opposite upward component." In: Halliday, David; Resnick, Robert, Fundamentals of Physics 3rd Edition, John Wiley & Sons, p. 378.
[2] "If the body is shaped, moved, or inclined in such a way as to produce a net deflection or turning of the flow, the local velocity is changed in magnitude, direction, or both. Changing the velocity creates a net force on the body" "Lift from Flow Turning" (https://web.archive.org/web/201107051 31653/http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html). NASA Glenn Research Center. Archived from the original (http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html) on 5 July 2011. Retrieved 2011-06-29.
[3] "The cause of the aerodynamic lifting force is the downward acceleration of air by the airfoil..." Weltner, Klaus; Ingelman-Sundberg, Martin, Physics of Flight – reviewed (https://web.archive.org/ web/20110719102847/http://user.uni-frankfurt.de/~weltner/Flight/PHYSIC4.htm), archived from the original (http://user.uni-frankfurt.de/~weltner/Flight/PHYSIC4.htm) on 2011-07-19
[4] https://krazytech.com/technical-papers/introduction-airfoil