MAE 200 Principles of Aeronautics Astronautics Aerodynamics Lab AIRFOIL PRESSURE MEASUREMENTS NACA 0012 1 Objective To use pressure distribution to determine the aerodynamic lift and drag forces experienced by a NACA 0012 airfoil placed in a uniform free stream velocity 2 Materials and Equipment UAH 1 ft x 1 ft open circuit wind tunnel Traversing mechanism Pitot static probe Molded epoxy NACA 0012 airfoil section with a 4 inch chord and an array of 9 pressure taps along its upper surface Digital pressure transducer Data Acquisition DAQ Box Background 3 3 1 Airfoil Lift and Drag We can determine the net fluid mechanic force acting on an immersed body using pressure measurements on the surface and in the viscous separated wake The net force can be resolved into two components the lift component which is normal to the freestream velocity vector and the drag component which is parallel to the freestream velocity as shown on Figure 1 U LIFT DRAG We often express these forces in non dimensional coefficient form Figure 1 Aerodynamic Force on an Airfoil where F can be the lift L or drag D force and AREF is a specified reference area For two dimensional bodies the force is per unit span or width or the area is determined with a unit span 3 2 Governing Equations Ideal Gas Law 1 9 MAE 200 Principles of Aeronautics Astronautics Aerodynamics Lab At standard conditions air behaves very much like an ideal gas the intermolecular forces are negligible As a result we can express relation between the pressure p the density r the temperature T and a specific gas constant R for air R 287 J kg K as Sutherland s Viscosity Correlation At standard conditions an empirical relationship between temperature and viscosity given by the Sutherland correlation where and Bernoulli s Equation For a steady incompressible inviscid irrotational fluid flow a relation between p the static pressure due to random molecular motion of the fluid molecules the dynamic pressure due to the directed motion of the fluid and po the total stagnation pressure pressure you would sense if the fluid flow was isentropically brought to rest called Bernoulli s equation can be derived as Bernoulli s equation can be used to determine the velocity of an incompressible fluid flow 3 3 Similarity Parameters The bodies tested in the wind tunnel are generally scale models of a full size prototype As a result we must introduce similarity parameters that will allow us to perform a study of dimensional analysis and similitude Reynolds Number The Reynolds number is the ratio of inertia forces to viscous forces Low Reynolds number flows tend to be dominated by viscosity and thus exhibit laminar boundary layers while high Reynolds number flows tend to exhibit turbulent boundary layers The Reynolds number can be expressed as where r and m are respectively the density and the viscosity of the fluid V is the flow velocity and c is a characteristic dimension of the body 3 4 Pressure Coefficients The pressure coefficient can be expressed 2 9 MAE 200 Principles of Aeronautics Astronautics Aerodynamics Lab The pressure coefficient is thus the difference in the local pressure and a reference pressure divided by the reference dynamic pressure Typically the freestream values far ahead of the body denoted by the subscript are used for the reference conditions 3 5 Lift Coefficient Consider the pressure and shear stress distributions along the surface of an immersed body We can divide the surface into small elemental areas and resolve the contributions to lift and drag on each area see Figs 1 15 1 16 1 17 and 1 18 of Ref 1 The net lift and drag forces are obtained by summing up these elemental contributions i e integrating Empirical results indicate that we can generally neglect the shear stress contribution to the lift and only consider the contributions of pressure on the upper and lower body surfaces as shown on Figure 2 Figure 2 Pressure Distribution Around an Airfoil Using this approach for a two dimensional or infinite span body a relatively simple equation for the lift coefficient can be derived where a is the angle of attack c is the body chord length and the pressure coefficients Cps are functions of the normalized length x c Note that we use a lower case l to designate a two dimensional body or force per unit span 3 6 Drag Coefficient For smooth streamlined bodies such as an airfoil the drag is predominantly due to shear stress The surface integration technique requires knowledge of the shear stress distribution along the surface which may be difficult to obtain experimentally In this case we can estimate the drag of the body by comparing the momentum in the air ahead of the body to the momentum behind the body The total momentum loss can be equated to the drag of the body by application of a momentum integral analysis e g Chapter 3 of Ref 2 A Pitot static probe can be traversed along vertical planes ahead and behind the body to determine the profiles of local dynamic pressure and associated flow momentum In Ref 3 an equation is derived for the drag of an immersed body based on this dynamic pressure profile in the separated wake The resultant equation is given by 3 9 MAE 200 Principles of Aeronautics Astronautics Aerodynamics Lab where q and q are the local and freestream values of dynamic pressure d is the cylinder diameter and Y1 and Y2 are the beginning and ending coordinates of the vertical pressure probe traverse Proper values of q are only obtained if the wake has returned to the tunnel static pressure p and not the local static pressure near the body Performing the pressure traverse several chord lengths behind the body rectifies this problem 4 Procedure 4 1 Determination of the Lift Coefficient From Surface Pressure Measurements The coefficient of lift can be obtained by integrating the measured pressure profile around the airfoil using Eq 7 The test model is a molded epoxy NACA 0012 airfoil section with a 4 inch chord and an array of 9 pressure taps along its upper surface The airfoil spans the test section width i e infinite span and can be set at various angles of attack to the flow The airfoil pressure tap locations are provided in table 1 Table 1 Airfoil static pressure tap locations Distance Along the Chord From Leading Edge mm 4 10 20 30 40 50 60 70 80 Port 1 2 3 4 5 6 7 8 9 The following procedure is used to determine the surface pressure distribution 1 Turn on the data acquisition box DAQ and allow approximately ten minutes for the