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References:This experiment showed that the potentialflow theory is invalid in real life due to the viscous nature of the flow.There tends to be a separation of laminar and turbulent boundary layersseparate at certain angular positions, leading to an increase in pressure drag.With an increase in the Reynolds number the boundary layer tends to transitfrom laminar to turbulent with the separation occurring towards the rear faceleading to a significant drop in the coefficient of frictionConclusion: · Presence of the pitot statictubes facing the oncoming flow adversely affects the flow.· Error due to blockage effects.The errors in reading tend to propagate even after ensuring corrective measuredto negate the blockage effects.b) Physical· Error in ensuring that the zerodegree tapping of the cylinder is towards the oncoming flow.
It was mandatoryto maintain the stillness of cylinder by hand.· Parallax error during readingof multitube manometer.a) Human:There were two classes of errorError Analysis: · It is applied to aircraftoperating in lower Reynolds numbers such as gliders. They make use of vortexgenerators to delay boundary layer separation by encouraging the boundary layerto transit from laminar to turbulent.
· This is the reason behind thedimples on golf balls, fluff on tennis balls and stitching on cricket balls toenhance their performance. In actuallife, due to the adverse pressure gradient acting on the boundary layer thelaminar layer tends to separate before the maximum thickness of the cylinder.Comparatively, the turbulent boundary layer is less susceptible to an adversepressure gradient. This means that the separation is delayed to the rearsurface of the cylinder.
By tripping the boundary layer, though the skinfriction is increased at higher Reynolds numbers, the pressure drag reductionsat the lower Reynolds numbers outweighs that concern. Applications of thisresult: Figure 13: Coefficient of drag on a circular cylinderas a function of Reynolds number.Figure 12: Measured pressure distributions on acircular cylinder compared with theoretical distribution calculated assumingideal flow. (From Bertin and Smith, 1989) Figure 11: Flow as visualised for a critical Reynolds number. Figure 10: Flow as visualised for a sub-criticalReynolds number.Results: xi. Conduct a series of tests todetermine the shape and form of the circular cylinder wake at a fixed Reynoldsnumber.
x. Conduct a series of tests todetermine the pressure distribution and drag coefficient on the circularcylinder at a fixed Reynolds number, and compare with inviscid theory. ix. Also note the reading of thestatic Pitot probe.viii. Using the manometer, measurethe pressures of corresponding to each pressure tap.
vii. Note the maximum speed of thetunnel. After sometime lower it to approximately half the maximum speed. vi. Secure all the items in tunneland turn on the facility and gradually change the speed. v.
Record the atmospheric airconditions and its properties. iv. Check for zero errors ofmanometers. iii. Determine the connectionsbetween the pressure taps on the cylinder surface, the cylinder angle and thetubes of the multitube manometer. ii. Do the same for the referencePitot static and also ensure that it is pointing in the right direction.
i. Record the dimensions andposition (x,y,z) of the cylinder model relative to the test section. ProcedureFigure 9: Smoke flow visualisation tunnelThe stagnation pressure can alsobe measured by the static Pitot probe. The stagnation pressure in inviscidsteady flow always remains constant and equal to its free stream value. Thestagnation pressure coefficient is 1 here. Due to viscous effects that can beencountered inside the edge of a turbulent wake, like that shed by thecylinder. the stagnation pressure tends to drop and hence, the stagnationpressure coefficient will always be less than 1.
This property of thestagnation pressure coefficient makes it a very good indicator of the edge andextent of a wake. . D. Instrumentation formeasuring the cylinder wake A two axis manual traverse gear is mounted towards the back of the wind tunneltest section.
In this gear, a Pitot-static probe is mounted. Tygon tubestransmit the pressures sensed by the Pitot-static to the manometer. Scalesattached to the horizontal and vertical axes of the traverse allow us to adjustthe relative position of thePitot probe in the cross plane A second Pitot-static probe is used to determinethe velocity distribution in the cylinder wake.
If po and p represent the Pitot and static pressure sensed by the probe thenthe ratio of the local velocity to the free stream velocity is given byC. Instrumentation formeasuring the pressure distribution on the cylinder surface The pressure coefficient is denoted as Cp with prepresenting the pressure at the cylinder surface. At its midspan, the circumferenceof the cylinder is embedded with 36 one-millimeter diameter pressure taps at 10degree intervals which sense the surface pressure p and transmit itthrough a series of Tygon tubes of 3 mm outside diameter. First is using the multitubemanometer. All the Tygon tubes are initially connected to it. The Tygon tubestransmit the pressure at each tap to the top of each water column in themanometer.
For pressures lower than atmospheric, the colored water moves up thetube. If the pressure is higher the level of the colored water subsides. Thechange in height of the fluid column is used to infer the pressure p(relative to atmospheric) using the hydrostatic equation. The principleadvantage of the multi-tube manometer is that it provides an easily understoodway of simultaneously visualizing the pressure distribution on the entirecircumference of the circular surface. The disadvantage of this system is thatit is difficult to read the change in fluid heights with much accuracy,particularly at lower free stream speeds. A reference probe monitors thevelocity and pressure of the free stream. The probe has two pressureconnections to it.
One on the axis is connected to the Pitot, or stagnation portand thus registers the stagnation pressure of the free stream po. i.e, thepressure produced due to choking of flow halt at the mouth of the tube. Theconnection on the other side of the probe is connected to the static ports onthe side of the probe which registers the actual pressure of the freestream p.
The difference in these pressures is relatedto the free stream velocity. To sense this pressure difference and the freestream velocity the probe, through two Tygon tubes, is connected to a digitalmanometer, that can measure pressures in kPa or inches of water column. Tubecarrying the static pressure from the reference probe has a T connector in it.With the tunnel off the manometer should read zero.
A multitube manometer capable of measuring upto 40 pressures simultaneously is available for use with the open jet windtunnel. The manometer is filled with water. All the manometer tubes areconnected at one end to a reservoir of fluid (ref. fig.
7) which is open toatmosphere. At the other end each tube is connected to the pressure to bemeasured. The manometer is thus sensitive to pressures relative to atmospheric.The inside and outside temperatures of thetunnel is monitored by a digital thermometer fixed to the side of the tunneldownstream of the test section. The accuracy being 0.1 degrees.
Ambient(atmospheric) pressure is measured by a barometer attached to the right handside of the wind-tunnel control panel. The probes can be moved horizontally andvertically across the test section using a traversing gear. A lead screw,covered with a shroud of airfoil cross-section moves the probe horizontally. Theprobe can be moved vertically by a rack, pinion and ratchet system mountedoutside the flow in steps of 5.7mm. Figure 8: Errors due to misalignment in velocitymeasurement made with a Pitot-static probe. Figure 7: Diagram showing connection of a single tubeof the multi-tube manometer.
A 3 mm diameter Pitot-static probe monitors theflow speed in the test section. An inclined manometer is connected to the Pitot-staticprobe. It measures the speed of flow at the upstream end of the test sectionwhere it is assumed to be not affected by the presence of a model. But, placinga large model in the test section might artificially increase the velocitysensed by the probe. The manometer has an accuracy of about ±0.
02 inches ofwater. Figure 6: Mean velocity distribution across an emptytest section of the wind tunnel. B. Open jetwind-tunnel model and circular cylinder model The experiment is performed in a 3-foot subsonic wind tunnel.
The cylindermodel is mounted in the wind tunnel. The model is preferably made of Plexiglas.The radius of the cylinder is 70 mm and it has a span of 462 mm. Circular endplates of radius 152.
5 mm minimize the flow around the ends of the cylinder.These plates tend to make the flow more two dimensional. The cylinder model ismounted spanwise across the test section. The mount is such that it allows thecylinder to be rotated about its axis by a measured angle which is indicated byan attached protractor. This setup, hence, also allows the cylinder to beplaced at different streamwise positions. T is in Kelvin. m =1.
4578 × 10-6 × T 1.5The temperature is used to inferthe dynamic viscosity of the air using Sutherland’s relation. For SI units, Figure 5: Setup to test air properties.
A. Instrumentationfor measuring the properties of the air. The open jet wind tunnel used laboratory atmosphere as the working fluid. Theproperties of the air in the lab are dependent on the weather, the mostimportant properties being its density and viscosity. Instead of measuring densitydirectly, for accuracy reasons, it is obtained by measuring pressure andtemperature and then using the equation of state for a perfect gas.
An aneroidbarometer for measuring atmospheric pressure is provided on the side of theopen-jet wind tunnel control panel. A digital thermometer for measuringatmospheric temperature is located on the side of the open-jet tunnel adjacentto the test section. Pressure output is in milibar and the thermometer outputi.e, Celsius or Fahrenheit is setting dependent. The gas constant R inthe equation of state for a perfect gas (p =rRT) is 287 J/kg/K. Experimentation apparatus, instrumentationand methods It is not included in the formula givenfor the calculation of drag above. CD should bedetermined for smooth cylinders for different values of U.
The measurement of static pressure distribution isdone relative to the tunnel static pressure ptunnel prevailing at that location. As The coefficient of drag can be given as Using the knowledge of p(R,q), form drag per unit length acting on thecylinder can be calculated as Figure 4: Measurement of pressure over cylindersurface. Time-averaged values of forces arediscussed. Hence, the measurements of pressure and velocity are alsotime-averages. A single pitot tube is embedded within a circular cylindermeasures pressure distribution p(R, q) (static pressure as a function of q at r= R, at the cylinder surface) where R is the radius of thecylinder and ? is the angular location on the surface of the cylinder.Angle q is varied byturning the position of the cylinder relative to the main flow. In the figure 4 shown below, OA is the Pitot tube, which senses the local surfacestatic pressure. Figure 3: Inviscid and real pressure distributionaround a circular cylinder.
For potential flow, coefficient ofpressure is given as: The total drag in separated flow consistsof both the drags i.e, form drag and viscous drag but the former is greater inproportion. An asymmetric distribution of the surface pressure on the forwardand rear halves of the cylinder leads to form drag which hence can be measured.It constitutes a representative value for the total drag. 6. In the final regime, theboundary layer on the forward face transits to turbulent and the point ofseparation starts to creep back across the rear face and back onto the frontface. This coupled with the increase in skin friction and wake size againincreases the coefficient of drag.5.
A sharp drop in drag is notedas the Reynolds number approximately reaches 400,000. This is observed due to asmaller pressure drop which occurs due to the transition of the boundary layer fromlaminar to turbulent and reattaching with the cylinder on the rear face.4. As Reynolds number reaches theorder of 103 the laminar boundary layer separated from the frontface of the cylinder and the shear layer starts its transition towardsturbulent form leading to the formation of wake. At this point the dragcoefficient is stable and is approximately equal to one.3. A loss of stability is observedwith further increase of Reynolds number which gives rise to the phenomenon ofvon Karman street i.e, alternative shedding of vortices.
2. This viscosity tends to affectthe flow at the surface forcing the flow to separate into two separatevortices. 1.
At very low Reynolds numbersbalance between the inertial and viscous forces exists in the expression ofReynolds number. This is called as the Stokes flow whose characteristics arealmost perfect symmetrical streamlines but due to domination of viscous forces,a lot of drag is experienced.From figure 2 we can observe that many differentregimes exist. These can be explained as: Figure 2: Coefficient of drag against Reynolds numberfor a circular cylinder. From vectorcalculus, it is shown that the curl of a gradient is equal to zero, therefore. This also means that the vorticity, or the curl of thevelocity field is zero, i.e. .
Hence, potential flow is given by the fact that thevelocity field is equal to the gradient of the velocity potential,. The inviscid assumption gives rise to the d’Alambertparadox which, hence, results in a cylinder with zero drag. Real flow is viscidwhich was a correct observation of Sir Prandtl has a boundary layer whichseparates causing drag due to adverse pressure gradient. Therefore, theReynolds number affects the drag and the coefficient of drag, CD, asit is the factor which determines the boundary layer transition.
3. Incompressible flow.2.
Irrotational flow, and,1. Inviscid flow,Potentialflow is dictated by three assumptions: Theory Additionally, the solution to d’Alambertparadox via Prandtl’s viscous effects idea will also be determined bycalculating the lift and drag coefficients of the body while accounting for theeffects of blockages. Figure 1: Smoke tunnel visualisation of flow past acircular cylinder at high order Reynolds number. d) Correlate thepressure distribution with flow visualization images recorded.
c) To identify thepoint of boundary-layer separation and, b) To calculate formdrag and form drag coefficient by integration. a) To determine the variation ofpressure over the cylinder in a dimensionless form for a chosen range ifReynolds number. The objectivesof the experiment are: Introduction This experimentdepicts that the potential flow theory is invalid for flow around a circularcylinder and it help to determine the effects on drag due to a change in theReynold’s number. The mean and fluctuating pressure distributions were measuredfor long smooth and rough surfaced cylinders. The presence of free streamturbulence at Reynolds number of order 105 suppressed the coherentvertex on the smooth cylinder and led to the formation of a complex field ofpressure in which the mean pressure distribution was almost found to beindependent of the Reynolds number whereas in the case of rough surfacedcylinders the pressure distribution was different in the laminar and turbulentstreams. But when the Reynolds number was increased to the order of 107 thepressure distributions for both the cylinders i.e, smooth and rough surfaced,was found to be the same. Abstract Sr.
No. Content Page Number 1. Abstract 2 2. Introduction 2 3.
Theory 3 4. Experimentation apparatus, instrumentation and methods 6 5. Procedure 11 6. Results 11 7. Error Analysis 14 8.
Conclusion 14 9. References 14 Tableof Contents