Week 9 - Mini project - Flow over an Airfoil

AIM:

Flow over an Airfoil

objectives:

Simulate flow over a 4 digit airfoil i.e NACA 2412 Airfoil.

• Drag co-efficient Vs Angle of Attack
• Lift co-efficient vs Angle of Attack
• Compare the effect of turbulence models on the above two results.
• Make sure that the inlet Reynolds number is 200,000
• Make sure you do above calculations for the following angle of attacks,
  • Angle of attack = 1º
  • Angle of attack = 5º
  • Angle of attack = 10º
  • Angle of attack = 15º

 

theory:

During the late 1920s and into the 1930s, the NACA(National Advisory Committee for Aeronautics airfoils) developed a series of thoroughly tested airfoils and devised a numerical designation for each airfoil — a four digit number that represented the airfoil section's critical geometric properties. By 1929, Langley had developed this system to the point where the numbering system was complemented by an airfoil cross-section, and the complete catalog of 78 airfoils appeared in the NACA's annual report for 1933. Engineers could quickly see the peculiarities of each airfoil shape, and the numerical designator ("NACA 2415," for instance) specified camber lines, maximum thickness, and special nose features. These figures and shapes transmitted the sort of information to engineers that allowed them to select specific airfoils for desired performance characteristics of specific aircraft.

                                                         

An aerofoil is the cross sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propellor, rotor or turbine. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. Airfoils designed for use at different speeds differ in their geometry: those for subsonic flight generally have a rounded leading edge, while those designed for supersonic flight tend to be slimmer with a sharp leading edge. All have a sharp trailing edge. foils of similar function designed with water as the working fluid are called hydrofoils.

                                                 

the main purpose of the aerofoil is to produce lift with minimum drag. this lift can be generated by reducing the pressure on the upper surface of the aeroil than the lower surface. this pressure difference can be achieved by using the asymmteric shape geometry as shown in the above figure. when air particles moves along the surface with constant velocity, the particle will attain the centrifugal force to move away from the surface of the geometry. but he air particles still attah the surface because of coanda effect. from this we can say that there is an external force balancing the centrifugal force so that the fluid particles remains attached to surface. this external force is obtained from the atmospheric pressure. so we can say that the pressure on the surface of the aerofoil is less than the atmospheric pressure. The Coanda Effect provides another important explanation for lift. While the shape of a wing (airfoil) is designed to create differences in air pressure, the Coanda Effect explains that a wing’s trailing edge must be sharp, and it must be aimed diagonally downward if it is to create lift. Both the upper and lower surfaces of the wing act to deflect the air. The upper surface deflects air downwards because the airflow “sticks” to the wing surface and follows the tilted wing down. This phenomena is also called Flow Attachment. After the wing has passed through the air, the air must remain flowing downwards for the lifting force to work.

 

geometry:

here i have taken the NACA 2412 aerofil. i have taken vertices of aerofoil from the NACA dat file. by using of vertices i have created the aerofoil geometry in the converge. 

                                              

now create a wind tunnel around the aerofoil so that we can measure the drag and lift coefficents by using wind tunnel test.  the chord length of the aerofoil is 1m. the lenght of the wind tunnelwe need to create is 50 times the chord length and the hight of the tunnel is 50 times the chord length. we need to make sure that the distance between the tunnel inlet and leading edge must be smaller than the distance between the tunnel outlet and trailing edge to visualize the vortices at the end of trailing edge.here i have scaled down the dimension to 0.1 so that the we gets the results faster. by scaling the dimensions there wont be any effect on the coefficent of drag. the below figure the final geometry that i have created.

                               

                now check the normals of all the faces are facing inside or not by using normal toggle tool and then buid case setup.then i have used boundary tool in the geometry.  here i have named the boundaries to the box. i have named the inlet and the outlet of the tunnel, the top and bottem surface of the tunnel as symmetry, the aerofoil as aerofoil wall and the front and back of the aerofoil as 2D  because the effects of primitive variables along the z direction is same. 

                                                             

in the above figure, sum represents the number of triangles selected at the each boundary. now use normal toggle tool. in the converge,the normals are aloways directed to outside of the box faces as a default. but here the fluid is inward flow. so eliminate them, click on transform in geometry and slect of triangle and click apply. to check whethere the geometry is correct or not(ie open edges errors, overlap errors), click on the diagnosis which is shown at the bottem left of the display and click findings. now buid the case setup.

case setup:

application type: time beased

materials: air

click on gas simulation as the air is gaseous state and click on species to calcuate how the mass fraction of N2 and O2 are changing along the flow.

                                                

species-

                             

 

simulation parameters:

run parameters-

i am running the simulation using transient state solver. because the transient solver gives the accurate results compared to steady state solver. 

                                       

simulation time parameters-

the reynods number of the flow i have taken is 200,000 and the fluid flowing over the aerofoil is air.

density of air = 1.225 kg/m^3

viscosity of air = 1.81 × 10^-5 kg/(m·s)

                                                                                               reynolds number, Re = `(rho.v.d)/mu`

where the d is charecterstic length which is the chord length of the aerofoil.

chord length after scaling is 0.1m

after solving the above equation, the velocity of the fluid is 29.55 m/s. the final velocity i have taken is 30 m/s

to calculate the end time of the simulation, we have the length the  wind tunn is 2.4m. so the final end time obtained is 2.4/30 = 0.08 s.

for the simulation we need to give simulation time must be greater than the end time.  

the maximum convection cfl number should always be less than or equal to 1. so that solution would converge otherwise solution gets blown up.

                                       

solver parameters-

                             

                              

initial conditions and events:

regions and initialization-

here i have named the entire box region as volumetric region. the initial pressure and temperature i have taken is room tamperature and atmospheric pressure. value of velocity should be same as that of Inlet velocity.

                                               

boundary conditions:

boundary-

• inlet- the inlet velocity of the fluid is 30 m/s.

                                                 

• outlet- the outlet pressure(static pressure) i have taken is atmospheric pressure

                                                  

• top and bottem - here the top and bottem are symmetric. so i have taken symmetry boudary condition.

                                                   

• front 2D- 

                                                    

• back 2D- 

                                                   

• aerofoil- as the flow is turbulent, so we have to take law of wall boundary condition

                                              

physical models:

turbulence modelling- here RNG K-epsilon model is taken

                                                                  

grid control:

base grid-

                                                                          

fixed embedding- 

i have enabled fixed embedding because to scale the cells at walls of the geometry that is aerofoil wall. it means to to capture the turbulence in the turbulence boundary layer region, we have to provide cells with small size at the walls of the boundary. embedded layers represents the number of layers of cells we are going to take.  scale represents how much the cell size is decreased from the base size. to calclulate the scale we have to use below formula

                                                                         first layer thickness = `(base size)/2^n`

where n represents the scale.

first layer thickness is obtained from the y+ value. for the k - epsilon models the value of y+ is in between the range of 30 to 300. so i have taken y+ value as 120. if the y+ values is in between 0 to 10, we can say that the flow is laminar. if the y+ value is in between 10 to 30, we can say that the flow is transient flow. by using of y+ calculator, we are going to find the first layer thickness. the first layer thickness obtained is 0.01247. so the obtained scale 'n' from the formulae is 3

                                                                 

output/post-processing:

post variable selection-

                                     

output- i have choosen 'boundaries only' wall output option to see the pressure forces along x and y direction.

                                         

          

                                     

 

solution:

now export all the input files in a folder. so from this we can see that converge is used to create the input files for the simulation. now insert the two application files from the converge folder to the folder where i have exported all the input files.

                                        

for the simulation i have used cygwin64 terminal. in cygwin termpinal open the folder where you have pasted all the input and application files.

now for the simulation write mpiexec.exe -n 4 converge.exe restricted and click enter. here 4 represents the number of processors used at a time.

post processing of results:

                             

for this copy post convert application from converge folder to output folder which is generated in the input files folder. we are doing this because we are goingto convert all the output files into a vtk file which can be easily read by paraview software. toconvert the files we have to use post conver application as shown in the figure. there we can see the results that are obtained. now in cygwin open the output folder and write mpiexec.exe -n 4 post_convert.exe and click enter. now the below figure will appear

                            

after naming the case and choosing 10, hit enter. now click yes for boundary output surface. now all the output files will appear and then write 'all' to convert all the output files. now select 'all' at cell variable selection menu. now all the files gets converted into paraview vtk files.

 

now open paraview. in paraview, open file and select case name .. vtm file which is present in the output files. finally we see the geometry in the paraview. now choose slice tool to select the axis along which all the primitive variables are same. as we know that, along z axis the primitive varibles are equal. so select  axis and click apply. 

Result:

case 1- Angle of attack = 1º

pressure contour-

                                  

velocity contour-

                                 

animation of pressure-

                                               

animation of velocity-

                                               

 

 

case 2- Angle of attack = 5º

pressure contour-

                                    

velocity contour-

                                   

animation of pressure-

                                               

animation of velocity flow-

                                                 

 

 

case 3- Angle of attack = 10º

pressure contour-

                                     

velocity contour-

                                 

animation of pressure-

                                              

animation of velocity flow-

                                              

 

 

case 4- Angle of attack = 15º

pressure contour-

                                            

velocity contour-

                                            

animation of pressure-

                                                             

animation of velocity flow-

                                                          

 

 

plots at different angle of attacks:

drag force plot at different angle of attacks-

                              

lift force plot at different angle of attacks-

                              

y+ plot at different angle of attacks-

                               

 

to calclulate the drag and lift coefficents, we have to use below formulae

                                                                                     drag force = `1/2.C_d.A_1.rho.U^2`

                                                                                     lift force = `1/2.C_v.A_2.rho.U^2`

where Cd and Cv are drag and lift coefficents

A1 is the projected area of aerofoil perpendicular to lift drag force acting on aerofoil

A2 is the projected area of aerofoil perpendicular to lift lift force acting on aerofoil

 from the geometry of the aerofoil, we know that , A1 = 0.0121

                                                                          A2 = 0.1 

U is the free stream velocity = 30 m/s

rho is the density of air = 1.225 kg/m^3

take the averag drag and lift forces from the above plots.

by substituting the drag and lift forces in the above formulae, we will get drag and lift coefficents.

angle of attack	drag force(N)	lift force(N)	drag coefficent	lift coefficent
1	0.62	18.25	0.09	0.33
5	1.15	38.8	0.1124	0.7
10	4.3	50.1	0.644	0.9
15	11.7	37.5	1.754	0.68

 

angle of attack vs drag force plot-                                                                        angle of attack vs lift coefficent plot-

      

• to calclulate the drag forces oat different chord lengths, we can use the above drag and lift coefficent values. 

 

effect of turbulence models:

now i am going to use k-omega SST model with angle of attack 15 degrees

pressure contour-

                                                  

velocity contour-

                                                   

drag and lift force plots-

                                      

y+ plot-

                                         

 

conclusion:

• with increase of angle of attack, the drag and lift coefficents are increased upto angle of attacks 10 degrees.
• at the angle of attack 15 degrees, the lift coefficent got decreased and the drag coefficent is increased rapidly.
• at the angle of attack 15 degress, we have seen the vortex sheddings generated at the back of the aerofoil which creates more pressure drop at the end of the aerofoil. so that the pressure drag is going to increase.
• so from this we can say that with angles of attack less than or equal to 10 degress, there will be more lift with minimum drag coefficent.
• by taking the k - omega SST model, the fluctuations of y+ got reduced. so we can say that we can get the accurate results at the walls of the aerofoil using k-omega SST model compared to k- epsilon RNG model
• the drag and lift force values using both the turbulent models are almost same.