**1. Wind Tunnel Fundamentals**

A wind tunnel is a tool used in aerodynamic research to study the effects of air moving past solid objects. A wind tunnel consists of a tubular passage with the object under test mounted in the middle. Air is made to move past the object by a powerful fan system or other means. The test object, often called a wind tunnel model is instrumented with suitable sensors to measure aerodynamic forces, pressure distribution, or other aerodynamic-related characteristics.Airfoil performance at low Reynolds numbers impacts the performance of a wide range of systems. Low Reynolds number aerodynamics of airfoils apply to a host of other applications such as wind turbines, motorsports, high altitude aircraft and propellers, natural flyers, and subscale testing of many full scale systems. Accurate measurements of low Reynolds number airfoil performance arekey to understanding and improving the efficiency of low Reynolds number systems. Most aerodynamic performance measurement techniques for airfoils rely on using balance systems or pressure systems, or a combination of both. The approach described here uses a force balance approach to obtain lift and moment data and the wake rake method to obtain drag.

**1.1 Types of wind tunnels**

Wind tunnels can be classified using four different criteria

Type I classification - Open vs closed circuit wind tunnel

In open-circuit (open-return) wind tunnel, the air is drawn directly from the surroundings into the wind tunnel and rejected back into the surroundings, the wind tunnel is said to have an open-air circuit.

Courtesy: http://www.grc.nasa.gov/

In closed-circuit, or closed-return, wind tunnel, the same air is being circulated in such a way that the wind tunnel does neither draw new air from the surrounding, nor returns it into the surroundings. The wind tunnel is said to have a closed-air circuit. It is conventional to call that a closed-circuit (closed-return ) wind tunnel.

Courtesy: http://www.grc.nasa.gov/

__Type II Classification- Subsonic vs Supersonic wind tunnel__

The criterion for classification is the maximum speed achieved by the wind tunnel. It is traditional to use the ratio of the speed of the fluid, or of any other object, and the speed of sound. That ratio is called the Mach number, named after Ernst Mach, the 19th century physicist. Schematic designs of subsonic and supersonic wind tunnels are shown in figure. If the maximum speed achieved by the wind tunnel is less than the speed of sound in air, it is called a subsonic wind tunnel. The speed of sound in air at room temperature is approximately 343 m/s and for this case Mach number is less than one (M<1).In case of supersonic wind tunnels, the maximum speed achieved by the wind tunnel is equal to or greater than the speed of sound in air hence Mach number is greater than 1(M>1).

Courtesy: http://www.grc.nasa.gov/

**Type III classification- Education vs research wind tunnel**

The criterion for classification is the purpose for which the wind tunnel is designed: research or education. If the wind tunnel is for research it is called a research wind tunnel. If however, it is designed to be used for education, then, it is called an educational wind tunnel.

__Type IV classification- Laminar vs turbulent wind tunnel__

The criterion for classification is the nature of the flow: laminar vs. turbulent flow. Boundary- layer wind tunnels are used to simulate turbulent flow near and around engineering and manmade structures.

__Amrita Wind Tunnel Specifications__

A view of the Amrita Wind Tunnel

* TYPE OF TUNNEL : Low speed, Open circuit suction type.

* TEST SECTION SIZE : 300 mm x 300 mm.

* CONTRACTION RATIO : 9 : 1

* DRIVE : Axial Flow fan driven by AC Motor (7.5 Hp) with AC Drive for Speed Controlling

* POWER REQUIREMENT : AC. 3 phase, 440 V, 32 Amps electrical supply

* MATERIAL OF CONSTRUCTION:

Effuser, Diffuser : FRP

Blower Frames &Supporting Frame: Mild Steel

EXPERIMENTAL CAPABILITIES:

* Study of Lift, Drag & Side Forces : Symmetric, Cambered on airfoils

* Study of Drag on : Wedge, Flat Disc, Bluff Bodies, Automobile models

* Study of Pressure Distribution : Symmetrical Airfoil, Unsymmetrical Airfoil, Smooth and Rough Cylinder

* Study of smoke pattern : Airfoil, Cylinder,

Sphere & Hemisphere

MAIN PARTS:

Honeycomb inlet mesh screen, Effuser, Blower unit with AC motor and thyristor controller three component lift, drag & Side force balance ,multi - tube manometer ,smoke generator constitute the complete tunnel

DESCRIPTION:

A. Inlet duct (effuser):

It is aerodynamically contoured section with contraction area ratio 9: 1. The inlet starts with dimension of 900mm x 900mm contoured to 300mm x 300mm. The axial and lateral turbulence are reduced and smooth flow of air entering the section is achieved by installing the Honey-combs and screens , for most effectiveness of the air inlet . The ratio of length to cell size of the Honey -comb is maintained as per the recommended standards . The wire mesh is also fixed to smoothen the flow further. This is particularly useful for obtaining laminar flow. The screen is made removable for possible cleaning. The duct is secured to the test section by flange. The provision is also made for easy removal of Effuser and diffuser for possible separation from the test section when required. It is also highly smoothened and painted.

B. Test section:

The central portion of the test section sandwiched between the inlet duct ( Effuser ) and the diffuser using flange. It has 300mm x 300mm cross section (inside ) and 550mm length. Fixed with transparent window on either side which facilitates fixing and viewing of the models. This houses smoke chest fixing points.

The traversing mechanism is fixed on its top of the movement of total pressure probe.The holes provided for holding the models for different studies and for taping out the pressure probes .

C. Diffuser :

The downstream portion of the tunnel is the diffuser .To the end of this is attached an axial flow fan . The diffuser starts with 300mm x 300mm square section at the test section end and enlarges to 900mm diameter round at the fan driven end . It is flanged and bolted to the test section.

D. Axial flowfan unit :

The fan unit is independent standalone type and does not require any foundation . It is housed in rounded casing which is secured to the diffuser . The bladed rotor is connected to AC motor directly coupled.

E. Control console:

The tunnel has two consoles, one for the air speed control ( AC motor Controller ) and the other for the indication of velocity head and forces . The console which houses thyristor speed controller connected to AC motor by 3 phase, 440 V, AC supply. All safety precaution for excessive electrical loading are provided.

F. Attachments:

( i )Strain gauge balance:

This is housed beneath the test section portion. The models are mounted on the vertical mechanical member called “String”. The lift drag & side forces are measured using this unit.

(ii)Multi bank manometer:

This manometer is used for studying the pressure distribution across the various models. This unit is mounted to the right of the test section

1.1.2 Fan RPM vs flow velocity curve

1.1.3 flow turbulence and losses (Wind Tunnel Corrections)

The flow field in a wind tunnel with confining walls is not the same as in free flight conditions. For traditional aerodynamic wind tunnels with solid walls, corrections have been developed over the years to make the wind tunnel measurements comparable to free flight. There are several types of corrections that need to be applied here: -

Solid blockage: the area of the tunnel test-section is effectively reduced by the presence of the model. Continuity and Bernoulli’s equations require that the flow velocity increases. The effects of solid blockage are functions of the model thickness (its maximum and its distribution) and the overall size, but not of the camber (Barlow et. al., 1999).

Wake blockage: the wake resulting from the shedding of the viscous layer from the model has inherently a lower mean velocity than the free stream. To maintain continuity, the flow outside of the wake must therefore have a mean velocity higher than the free stream to balance the momentum deficit of the wake.

Streamline curvature: In free flight conditions, the presence of a lifting body results in streamline deflections far away from the body itself. In the confined space of a test-section, this streamline displacement is limited by the presence of the walls (in our case the side walls). Due to this limitation, the body experiences a higher angle of attack than it is actually set at and therefore appears to have effectively more camber than it actually does. The increased camber results in higher lift and quarter chord moment.

Further description of the physical phenomena behind the blockage corrections can be found in Barlow et. al. (1999) and Allen and Vicenti (1947).

1.1.4 flow similarity and non-dimensional coefficients

The forces and moment depend on a large number of geometric and flow parameters. When we look at absolute aerodynamic quantities like the lift force or the pitching moment, we find that those quantities depend on a large number of fluid parameters like the density, viscosity and temperature and additionally on the flow speed and model size. That makes it very difficult to apply experimental results to applications. A much better way is to non-dimensionalize the aerodynamic quantities with flow speed and model size and to look at similarity parameters rather than fluid parameters. In our example we are interested in the time average of the lift coefficient for low speed flow (i.e. Mach number smaller than 0.3). It turns out that those coefficients only depend on one single similarity parameter, the Reynolds number, and the angle between free stream velocity and chord line, the angle of attack.

It is often advantageous to work with non-dimensionalized forces and moment, for which most of these parameter dependencies are scaled out. For this purpose we define the following reference parameters:

**Physical parameters**

A large number of physical parameters determine aerodynamic forces and moments. Specifically, the following parameters are involved in the production of lift.

The distribution of the pressure coefficient integrated along the airfoil section contour yields the lift and moment coefficient.

By integration the surface pressure coefficient distribution, one can obtain the lift, pressure drag, and pitching moment coefficients. The lift force is the force acting on the airfoil section perpendicular to the mean flow direction. The pitch moment is the moment about the quarter chord point, positive when nose up. We measure aerodynamic quantities in the middle of the airfoil section and assume that the flow is approximately two-dimensional. In this special case it is convenient to look at the force and moment per unit span.

The choices for S and Lare arbitrary, and depend on the type of body involved. For aircraft, traditional choices are the wing area for S, and the wing chord or wing span for ℓ and the dynamic pressure for q∞ .The non-dimensional lift, pressure drag and moment coefficients are respectively defined as :

With L the lift force per unit span, D the drag force per unit span and M the pitch moment per unit span.

The lift coefficient

The lift coefficient is a number that aerodynamicists use to model all of the complex dependencies of shape, inclination, and some flow conditions on lift. The lift coefficient expresses the ratio of the lift force to the force produced by the dynamic pressure (q∞) times the area. By knowing the lift coefficient, we can predict the lift that will be produced under a different set of velocity, density (altitude), and area conditions using the lift equation. For given air conditions, shape, and inclination of the object, we have to determine a value for C_{L} to determine the lift.

Where L is the lift force, ρ is air density, Ʋ is the true air speed, A is the planform area (projected area of the wing) and CL is the lift coefficient.

The Drag coefficient

The drag coefficient is a number used to model all of the complex dependencies of shape, inclination, and flow conditions on aircraft drag. The drag coefficient expresses the ratio of the drag force to the force produced by the dynamic pressure times the area. In a controlled environment (wind tunnel) we can set the velocity, density, and area and measure the drag produced. Through division we arrive at a value for the drag coefficient. As pointed out on the drag equation slide, the choice of reference area (wing area) will affect the actual numerical value of the drag coefficient that is calculated. We can predict the drag that will be produced under a different set of velocity, density (altitude), and area conditions using the drag equation.

For given air conditions, shape, and inclination of the object, we must determine a value for CD to determine drag. Determining the value of the drag coefficient is more difficult than determining the lift coefficient because of the multiple sources of drag. The drag coefficient given above includes form drag, skin friction drag, wave drag, and induced drag components.

Where FD is the drag force, is the mass density of the fluid, is the velocity of the object relative to the fluid, A is the reference area, and CD is the drag coefficient.

For 2-D bodies such as airfoils, the appropriate reference area/span is simply the chord c, and the reference length is the chord as well. The local coefficients are then defined as follows.

These local coefficients are defined for each span wise location on a wing, and may vary acrossthe span. In contrast, the C_{L}, C_{D}, C_{M} are single numbers which apply to the whole wing.

__1.2 Wind tunnel measurements__

1.2.1 pressure distribution

This is used for studying pressure distribution across various models such as Airfoil, cylinder, special purpose shapes . It contains 13 Nos. Of tubes mounted on board with adjustable inclination. Bottom of all tubes are interconnected and in turn to the balancing reservoir filled with coloured water . While the last tube is left open to atmosphere for reference , all other 12 tubes are connected at their top to pipe / tube bundles of the model. The required model is held in the test section between holes provided front and back side Perspex windows. The pressure tapings ( tube outlets ) are connected to the glass limbs of the respective Serial Number . The required degree of angle of inclination can be given to the tube bundle and angle measured with respect to the horizontal .

The coefficient of pressure is obtained by

1.2.2 velocity measurement. Pitot probe

One very important use of wind tunnels is to visualize flow patterns and measure the pressure at a selected point in the flow field and compute the corresponding speed of air. The equation relates the speed of the fluid at a point to both the mass density of the fluid and the pressures at the same point in the flow field. For steady flow of an incompressible fluid for which viscosity can be neglected, the fundamental equation has the form

Where V is the speed of the fluid, P0 is the total, also called the stagnation, pressure at that point of measurement, and p is the static pressure at the same point. This equation comes from the application of Bernoulli’s equation for the steady flow of an incompressible and inviscid fluid along a streamline. Bernoulli’s equation is typically obtained by integrating Euler’s equations along a streamline. It will be recalled that Euler’s equations are a special case of the Navier -Stokes equations, when the viscosity of the fluid has been neglected. The Navier-Stokes equations, in turn, are obtained from Newton’s second law when it is applied to a fluid for which the shear deformation follows Newton’s law of viscosity

1.2.3 force coefficients from pressure distribution

By integration the surface pressure coefficient distribution, one can obtain the lift, pressure drag, and pitchining moment coefficients. The lift force is the force acting on the airfoil section perpendicular to the mean flow direction. The pitch moment is the moment about the quarter chord point, positive when nose up. We measure aerodynamic quantities in the middle of the airfoil section and assume that the flow is approximately two-dimensional. In this special case it is convenient to look at the force and moment per unit span. The section lift, pressure drag and moment coefficients are respectively defined as

With L the lift force per unit span, dp the drag force per unit span and m the pitch moment per unit span and c is the chord length.

1.2.4 forces from strain gauge load cells

a) WIND TUNNEL BALANCE :

The tunnel balance is three component type ( three forces ) designed using the electrical strain gauges to indicate separately on the digital indicator. The balance is intended for indicating the lift , drag & side force in case of airfoils, and drag force only in case of bluff bodies,Viz., spherical, Hemi - spherical, Flat disc. These models are mounted on the string (Vertical square rod) situated exactly beneath the test section. The output from the lift, drag & side forces (strain gauges) are connected to the respective multi - pin sockets provided at control panel.

View of the Load cell balance (Wind tunnel) at Amrita Virtual Lab

**2. Aerodynamics fundamental**

**2.1 Generation of lift and drag on a turbine blades**

Lift and drag forces are related to stress distributions on a body through integration. Consider the stress acting on the airfoil shown in figure. There is a pressure distribution and a shear stress distribution. To relate the stress to force, select a differential area as shown in figure below. The magnitude of the pressure force is dF_{p} = pdA and the magnitude of the viscous force is dF_{v} = ΓdA. The differential lift force is normal to the free stream direction

dF_{L = } - p dAsinθ – Γ dAcosθ

and the differential drag is parallel to the free stream direction

dF_{D} = -p dAcosθ + Γ dA sin θ

Integration over the surface of the airfoil gives the lift force (F_{L}) and drag force (f_{D})

F_{L }= ∫ (-p sinθ – Γ cosθ) dA

F_{D} = ∫ (-p cosθ + Γ sinθ) dA

This equations of F_{D}and F_{L} show that the lift and drag are related to pressure distributions through integration.

**The drag force Equation**

The drag force F_{D} is found by using the drag equation

F_{D} = C_{D} A (ρ V^{2})/2

Where C_{D} is the coefficient of Drag. A is the reference area of the body, ρ is the fluid density and V_{0} is the free stream velocity measured relative to the body.

The above equation shows that Drag force drag force is related to four variables. Drag is related to the shape of anobject because shape is characterized by the value of *CD*. Drag is related to the size of the object because size ischaracterized by the reference area. Drag is related to the density of ambient fluid. Finally, drag is related to thespeed of the fluid squared.

The reference area *A *depends on the type of body. One common reference area, called *projected area *and given by the symbol *Ap*, is the silhouetted area that would be seen by a person looking at the body from the direction offlow. The referencearea for an airplane wing is the planform area, which is the area observed when the wing is viewed from above. The coefficient of drag C_{D} is the parameter that characterize the drag force associated with a given body shape. The value of C_{D }is usually found out by experiments. The drag force can be measured by a force balance using a wind tunnel. Then C_{D}can be calculated by the following equation

For this calculation, speed of the air in the wind tunnel *V*0 can be measured using a Pitot-static tube or similar device and air density can be calculated by applying the ideal gas law using measured values of temperature andpressure.

**2.2 Types of drag**

** 2.2.1 Form drag**

Form drag is the portion of the total drag force that is associated with the pressure distribution. Friction drag isthe portion of the total drag force that is associated with the viscous shear-stress distribution. The drag force onanybody is the sum of form drag and friction drag. The drag equation can be written as sum of two terms.

F_{D} = ∫ ( -p cos θ + Γ sin θ) dA

F_{D} = ∫ ( -p cos θ ) dA + ∫ ( Γ sin θ) dA

Ie, (Total drag force) = (form drag) + (friction drag)

** 2.2.2 Theory of lift –The Circulation theory**

Circulation is a characteristic of a flow field which gives a measure of the average rate of rotation of fluid particles that are situated in an area that is bounded by a closed curve. The circulation is defined by the path integral as shown in figure below.Along any differential segment of the path, the velocity can be resolved into components that are tangent and normal to the path. Signify the tangential component of velocity as V_{L}. On integrating the V_{L}dL around the curve, the resulting quantity that we get is circulation (Γ).

Sign convention dictates that in applying above equation, one uses tangential velocity vectors that have a counterclockwise sense around the curve as negative and take those that have a clockwise direction as having a positive contribution. For the circulation for an irrotational vortex, the tangentialvelocity at any radius is *C/r*, where a positive *C *means a clockwise rotation. Therefore, if circulation is evaluatedabout a curve with radius *r*, the differential circulation is

** dΓ = V**_{L}dL = (C_{1}/r_{1})r_{1}dθ = C dθ

Integral around entire circle :

Lift is a result of circulation in the flow produced by the airfoil. Consider flow of an ideal flow (nonviscous and incompressible) past an airfoil as shown in Figure below. Here, as for irrotational flow past a cylinder, the lift anddrag are zero. There is a stagnation point on the bottom side near the leading edge, and another on the top sidenear the trailing edge of the foil. In the real flow (viscous fluid) case, the flow pattern around the upstream halfof the foil is plausible. However, the flow pattern in the region of the trailing edge cannot occur. A stagnation point on the upper side of the foil indicates that fluid must flow from the lower sidearound the trailing edge and then toward the stagnation point. Such a flow pattern implies an infinite accelerationof the fluid particles as they turn the corner around the trailing edge of the wing. This is a physical impossibility, and the separation occurs at the sharp edge. As a consequence of the separation, the upstream stagnation point moves to the trailing edge. Flow from both the top and bottomsides of the airfoil in the vicinity of the trailing edge then leaves the airfoil smoothly andessentially parallel tothese surfaces at the trailing edge.

To bring theory into line with the physically observed phenomenon, it was hypothesized that a circulationaround the airfoil must be induced in just the right amount so that the downstream stagnation point is moved allthe way back to the trailing edge of the airfoil, thus allowing the flow to leave the airfoil smoothly at the trailing edge. This is called the Kutta condition. When analyses aremade with this simple assumption concerning the magnitude of the circulation, very good agreement occursbetween theory and experiment for the flow pattern and the pressure distribution, as well as for the lift on atwo-dimensional airfoil section (no end effects). Ideal flow theory then shows that the magnitude of thecirculation required to maintain the rear stagnation point at the trailing edge (the Kutta condition) of a symmetricairfoil with a small angle of attack is given by