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Airfoil Pressure Measurements: NACA 00121 Objective2 Materials and Equipment3 Background3.1 Airfoil Lift and Drag3.2 Governing Equations3.3 Similarity Parameters3.4 Pressure Coefficients3.5 Lift Coefficient3.6 Drag Coefficient4 Procedure4.1 Determination of the Lift Coefficient From Surface Pressure Measurements4.2 Determination of the Lift and Drag Coefficients From Wake Pressure Measurements5 Laboratory ReportReferencesMAE 200 – Aerodynamics LAB – DATA SHEETAirfoil DimensionsMAE 200 – Principles of Aeronautics & Astronautics Aerodynamics LabAIRFOIL PRESSURE MEASUREMENTS: NACA 00121 ObjectiveTo use pressure distribution to determine the aerodynamic lift and drag forces experienced by aNACA0012 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) Box3 Background3.1 Airfoil Lift and Drag We can determine the net fluid mechanic force acting on an immersed body using pressuremeasurements on the surface and in the viscous, separated wake. The net force can be resolved intotwo components: the lift component, which is normal to the freestream velocity vector; and the dragcomponent, which is parallel to the freestream velocity as shown on Figure 1.Figure 1 - Aerodynamic Force on an AirfoilWe often express these forces in non-dimensional coefficient form,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 EquationsIdeal Gas Law1/9LIFTDRAGU¥MAE 200 – Principles of Aeronautics & Astronautics Aerodynamics LabAt standard conditions, air behaves very much like an ideal gas (the intermolecular forces arenegligible). As a result, we can express relation between the pressure, p, the density, r, thetemperature, T, and a specific gas constant, R ( for air, R=287J/(kg K)), as.Sutherland's Viscosity CorrelationAt standard conditions, an empirical relationship between temperature and viscosity given by theSutherland correlation,where and .Bernoulli's EquationFor 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 thedirected motion of the fluid), and po, the total/stagnation pressure (pressure you would sense if thefluid flow was isentropically brought to rest), called Bernoulli's equation, can be derived asBernoulli's equation can be used to determine the velocity of an incompressible fluid flow.3.3 Similarity ParametersThe bodies tested in the wind tunnel are generally scale models of a full size prototype. As a result, wemust introduce similarity parameters that will allow us to perform a study of dimensional analysis andsimilitude.Reynolds NumberThe Reynolds number is the ratio of inertia forces to viscous forces. 'Low' Reynolds number flows tendto be dominated by viscosity and thus exhibit laminar boundary layers, while 'high' Reynolds numberflows 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 CoefficientsThe pressure coefficient can be expressed 2/9MAE 200 – Principles of Aeronautics & Astronautics Aerodynamics Lab.The pressure coefficient is thus the difference in the local pressure and a reference pressure divided bythe reference dynamic pressure. Typically, the freestream values far ahead of the body (denoted by thesubscript ‘¥’) are used for the reference conditions.3.5 Lift CoefficientConsider the pressure and shear stress distributions along the surface of an immersed body. We candivide 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 summingup these elemental contributions (i.e., integrating). Empirical results indicate that we can generallyneglect the shear stress contribution to the lift and only consider the contributions of pressure on theupper and lower body surfaces (as shown on Figure 2).Figure 2 - Pressure Distribution Around an AirfoilUsing this approach for a two-dimensional (or infinite span) body, a relatively simple equation for thelift coefficient can be derived,where a is the angle of attack, c is the body chord length, and the pressure coefficients (Cps)arefunctions of the normalized length x/c. Note that we use a lower case "l" to designate atwo-dimensional body or force per unit span.3.6 Drag CoefficientFor smooth streamlined bodies (such as an airfoil), the drag is predominantly due to shear stress. Thesurface 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 bycomparing 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 momentumintegral analysis (e.g., Chapter 3 of Ref 2). A Pitot-static probe can be traversed along vertical planesahead and behind the body to determine the profiles of local dynamic pressure and associated flowmomentum. In Ref. 3, an equation is derived for the drag of an immersed body based on this dynamicpressure profile in the separated wake. The resultant equation is given by3/9MAE 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, andY1 and Y2 are the beginning and ending coordinates of the vertical pressure probe traverse. Propervalues of q are only obtained if the wake has returned to the tunnel static pressure, p¥, and not the localstatic pressure near the body. Performing the pressure traverse several chord lengths behind the bodyrectifies this problem.4

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