SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL ENGINEERING HYDRAULICS 2 LABORATORY EXERCISE. Forces on Two-Dimensional Bodies in a Wind Tunnel

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1 Objet SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL ENGINEERING HYDRAULICS LABORATORY EXERCISE Fores on Two-Dimensional Bodies in a Wind Tnnel To ompare drag oeffiients made by diret measrement on a drag balane with those obtained by indiret measrements: () for a blff body (ylinder), by integrating the pressre distribtion; () for a streamlined body (aerofoil) by sing the wake traverse method. PART I. FORCES ON A CYLINDER BY INTEGRATING PRESSURE Apparats A ylinder is monted in a drag balane. The ylinder has only one pressre tapping bt it an be rotated to measre the pressre at any point on the irmferene of a 63.5 mm diameter irle. The wind tnnel is provided with a Pitot tbe and a stati tapping in the wall pstream of the model to enable the free-stream onditions to be determined. A manometer, set in its vertial position, is sed for all pressre measrements. Measrements () Read the laboratory barometer and thermometer. Dede air density from p RT T is the absolte temperatre in Kelvin. R an be taken as 87 J kg K for air. Dede the air visosity from Stherland s law (given in yor Topi notes). () Mont the ylinder in the drag balane so that it swings freely and tighten the srews in the monting plates to prevent the plates being sked onto the wind tnnel sides. With both fans rnning, take the erene Pitot pressre (p 0, ) and stati pressre (p ) in the free stream. Note that these pressres are gage pressres and are negative (i.e., less than atmospheri). Dede the free-stream dynami pressre p p Hene, ompte the free-stream veloity and the Reynolds nmber: Re D where D is the diameter of the ylinder. (3) Measre the drag fore F on the ylinder sing the drag balane. Sine the ratio of arm lengths on the drag balane is :3, the added weight is.5 times the drag. 0, (4) Free the srews in the monting plates and take a reading of stati pressre at a nmber of angles for a omplete (360 ) revoltion of the ylinder. Hydralis Wind Tnnel - David Apsley

2 Callations Reslts are presented in dimensionless form and in a way that makes it nneessary to onvert pressre measrements into different nits. (i) Pressre Coeffiient Pressre is sally made dimensionless by sbtrating the erene pressre and dividing by the free-stream dynami pressre. The pressre oeffiient P is defined by: p p p p P p p Plot P against (in degrees), where is the angle measred from the pstream stagnation point see the diagram below). Mark the stagnation and the separation points. On the same graph plot the reslt for an ideal (i.e. invisid) flid: P 4sin (ii) Drag Coeffiient Diret Measrement From the Drag Balane Fores are made dimensionless by dividing by the prodt of free-stream dynami pressre and a erene area. For a blff body the latter is onventionally the ross-setional area normal to the stream; i.e. A D b, where D is the diameter of the ylinder and b the span (i.e., width of the wind tnnel). The drag oeffiient, D is defined by: F D A F is the total drag (i.e., fore omponent parallel to the approah flow). Callate a diret vale of the drag oeffiient from the fores on the drag balane. 0, (iii) Drag Coeffiient Indiret Measrement by Integrating Pressre The pressre fore on an ar with length r d is pressre area p( br d ) where b is the span of the model. This fore is toward the entre of the ylinder. The omponent in the streamwise (x) diretion is ( pbr d )os Smming over all elements (noting that a onstant bakgrond erene pressre makes no net ontribtion) the total drag is: F ( p p ) br os 0 Finally, divide by A ( p0, p )( rb ) to obtain: D P os d P d(sin ) ½ area enlosed by a P vs sin graph; 0 ( simply means an integral rond a losed path, here orresponding to from 0 to ). d flow diretion p(br d θ) dθ θ Hydralis Wind Tnnel - David Apsley

3 Plot a graph of P against sin and hene, by graphial integration (onting sqares) or otherwise, dede the drag oeffiient D. Yo will need to think abot whether the varios areas enlosed make a negative or positive ontribtion to the fore oeffiient; i.e., as yo traverse the rve from 0 to is the prodt of the hange d(sin ) and the pressre oeffiient p positive or negative? Compare the drag oeffiient obtained by diret means (measring the fore on a drag balane) to that obtained by indiret means (integrating the pressre distribtion). Note that the latter method yields the form drag (i.e., that de to pressre fores alone), whereas the drag balane measres total drag (i.e., inlding the additional effet of visos fores). Comparisons Find from a textbook or other reptable sore (whih shold be indiated) a typial vale of D expeted for a ylinder at the Reynolds nmber in yor experiment. Yor Sbmission Yor sbmission for Part I shold ontain ONLY the following: () Data and allations handwritten on the reslts sheet issed dring the laboratory session. () Graphs, as desribed above, of: p vs p vs sin These shold be adeqately labelled and stapled to the reslts sheet. Hydralis Wind Tnnel - 3 David Apsley

4 PART II. FORCES ON AN AEROFOIL BY THE WAKE-TRAVERSE METHOD Apparats An aerofoil (hord 0.5 m; span b 0.30 m; NACA 00 setion) is monted in a drag balane. A omb of Pitot and stati tbes is monted downstream of the aerofoil. Tbes nmbered 5,, and 8 measre stati pressre, while the rest measre Pitot (stagnation) pressre. The tbes are onneted to a mlti-tbe manometer, leaving for spare manometer tbes (33-36). A Pitot-stati tbe is provided pstream of the model to measre free-stream onditions and its two onnetions shold be onneted to two of the spare manometer tbes. The manometer shold be set at a low inlination (0º to the horizontal). Note that the manometer is gradated in entimetres and ontains flid of speifi gravity Measrements () As in Part I, read the laboratory barometer and thermometer to determine the air density and visosity. () With the wind tnnel rnning at maximm speed (both fans on), take the erene pitot pressre (p 0, ) and stati pressre (p ) pstream and onvert the differene from mm to Pa, noting the sign! Dede the free-stream dynami pressre: p p and Reynolds nmber based on hord: Re 0, (3) Note all the inlined-manometer readings. (4) Make a diret measrement of drag from the weight (mg) added to the drag balane. In this instane the ratio of arm lengths on the drag balane is :, so that the added weight is eqal to the drag. Callations Appliation of the momentm priniple to a ontrol volme onsisting of the working setion between free-stream measrements and downstream rake gives (see yor notes for T): F ( ) bdy downstream This form is onvenient as the veloity integral need not be taken right to the tnnel walls. The drag fore F an be non-dimensionalised by A where, in this instane, the relevant erene area is A span hord b (sine most of the drag is visos drag on pper and lower srfaes). Then the drag oeffiient is D F b wake ( ) dy (*) Hydralis Wind Tnnel - 4 David Apsley

5 The veloity ratio / is easily established from the ratio of pressre differenes (pressres an be left in mm, bease the nits and signs will anel): p0 p p0, p Sbsript 0 indiates total (Pitot) pressre; sbsript indiates pstream erene onditions. The downstream stati pressre p is nearly niform and may be taken as eqal to the mean p of the for downstream stati-pressre measrements. Find the drag oeffiient by integrating (*) graphially over the height of the wind tnnel. (Plot the integrand as a fntion of y and find the area between the rve and the baseline level in the free stream. This baseline may not be preisely zero otside the wake bease the free-stream veloity downstream is slightly different to the erene veloity pstream; yo may like to think why.) Find the drag oeffiient also from the diret measrement of drag. / Comparisons (i) Wake traverse vs diret measrement. Compare the drag oeffiients D obtained indiretly by a wake traverse and diretly from a drag balane. (ii) Aerofoil vs flat plate of similar plan area. Compare with drag oeffiients for a smooth flat plate of the same plan area, in the two flow regimes sing the following formlae (White, Chapter 7; the fator aonts for sides): (a) laminar: D.33 Re / ; (b) trblent: D 0.03 Re /7. (iii) Streamlined body vs blff body. To ompare like with like, hange yor aerofoil drag oeffiient to one based on frontal area not plan area (the thikness of a NACA 00 aerofoil is % of its hord) and ompare with that in Part for the ylinder. Yor Sbmission Yor sbmission for Part II shold ontain ONLY the following: () Data and allations handwritten on the reslts sheet issed dring the laboratory session. () Graph of integrand vs y for the integral (*) as desribed above. This shold be adeqately labelled and stapled to the reslts sheet. Hydralis Wind Tnnel - 5 David Apsley

The Simple Solutions of Four Actual Problems. of General Theory of Relativity.

The Simple Solutions of Four Actual Problems. of General Theory of Relativity. The Simple Soltions of For Atal Problems of General Theory of Relativity. H Changwei Room 81, No.17,Lane 1769, Pdong Wlian Road, 19 Shanghai China,1-8818, hhangwei5@yahoo.om.n Abstrat: It is qite ompliated