Introductory Thoughts

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1 Flw Similarity By using the Buckingham pi therem, we have reduced the number f independent variables frm five t tw If we wish t run a series f wind-tunnel tests fr a given bdy at a given angle f attack, we need nly t vary the Reynlds and Mach numbers in rder t btain data fr the direct frmulatin f R thrugh With a small amunt f analysis, we have saved a huge amunt f effrt and wind-tunnel time Mre imprtantly, we have defined tw dimensinless parameters, Re and M, which gvern the flw. They are called similarity parameters 1

2 Flw Similarity Cnsider tw different flw fields ver tw different bdies. By definitin, different flws are dynamically similar if: The streamline patterns are gemetrically similar The distributins f V/V, p/p, T/T, etc., thrughut the flw field are the same when pltted against cmmn nn-dimensinal crdinates The frce cefficients are the same Observatin 3 is a cnsequence f bservatin 2; if the nn-dimensinal pressure and shear stress distributins ver different bdies are the same, then the nn-dimensinal frce cefficients will be the same 2

3 Flw Similarity Tw flws will be dynamically similar if: The bdies and any ther slid bundaries are gemetrically similar fr bth flws The similarity parameters are the same fr bth flws Fr many aerdynamic applicatins, Re and M are by far the dminant similarity parameters. Therefre, in a limited sense, but applicable t many prblems, we can say that flws ver gemetrically similar bdies at the same Mach and Reynlds numbers are dynamically similar, and hence the lift, drag, and mment cefficients will be identical fr the bdies This is a key pint in the validity f wind-tunnel testing. If a scale mdel f a flight vehicle is tested in a wind tunnel, the measured lift, drag, and mment cefficients will be the same as fr free flight as lng as the Mach and Reynlds numbers f the wind-tunnel test-sectin flw are the same as fr the freeflight case 3

4 Flw Similarity As we will see in subsequent chapters, this statement is nt quite precise because there are ther similarity parameters that influence the flw In additin, differences in freestream turbulence between the wind tunnel and free flight can have an imprtant effect n CD and the maximum value f CL Hwever, direct simulatin f the free-flight Re and M is the primary gal f many wind-tunnel tests 4

5 Flw Similarity 5

6 Flw Similarity 6

7 Flw Similarity Since the tw bdies are gemetrically similar and M and Re are the same, we have satisfied all the criteria; the tw flws are dynamically similar. In turn, as a cnsequence f being similar flws, we knw frm the definitin that The streamline patterns arund the tw cylinders are gemetrically similar 7

8 Flw Similarity Since the tw bdies are gemetrically similar and M and Re are the same, we have satisfied all the criteria; the tw flws are dynamically similar. In turn, as a cnsequence f being similar flws, we knw frm the definitin that The nn-dimensinal pressure, temperature, density, velcity, etc., distributins are the same arund tw cylinders. This is shwn schematically in the figure where the nn-dimensinal pressure distributin p/p is shwn as a functin f the nndimensinal surface distance s/d. It is the same curve fr bth bdies The drag cefficients fr the tw bdies are the same. Here, CD = D/q S, where S = πd2/4. As a result f the flw similarity, CD1 = CD2. We see that the lift n the cylinders is zer because the flw is symmetrical abut the hrizntal axis thrugh the center f the cylinder. The pressure distributin ver the tp is the same as ver the bttm, and they cancel each ther in the vertical directin 8

9 Scaled Flight Mdels One f the mre viable and valuable design tls since the advent f flight has been testing f subscale mdels Knwledgeable applicatins f these tls f the trade dramatically reduce risk and redesign, and increase the marketability and safety f new aerspace vehicles Mdels are nw rutinely used in many applicatins and rles, including aerdynamic data gathering in wind tunnel investigatins fr the analysis f full-scale aircraft designs prf-f-cncept demnstratrs fr radical aernautical cncepts prblem-slving exercises fr vehicles already in prductin 9

10 Scaled Flight Mdels These mdels have been used fr thusands f investigatins in a myriad f specialty areas ranging frm: Aerdynamic and hydrdynamic drag reductin High-lift systems Lads because f atmspheric gusts and landing impact Aircraft ditching Buffeting Prpulsive efficiency Cnfiguratin integratin Icing Effects Aerelasticity Assessments Of Stability And Cntrl Within these specialty areas, mdels can be further classified as static mdels r dynamic mdels 10

11 Rle f Dynamically Scaled Free-Flight Mdels In this representative cnventinal static wind tunnel test, a 2.7-percent scale mdel f the Being 777 airplane is munted t a sting supprt system fr testing at transnic speeds in the Natinal Transnic Facility at the NASA Langley Research Center The mdel cntains extensive instrumentatin and an internally munted electrnic strain-gauge balance fr measurements f aerdynamic data In static testing, data are taken at specific fixed cmbinatins f airspeed, mdel cnfiguratin, and mdel attitude as cntrlled by the test team 11

12 Rle f Dynamically Scaled Free-Flight Mdels Dynamic free-flight mdel tests f the X-29 advanced technlgy demnstratr were cnducted in the NASA Langley Full-Scale Tunnel t determine the cnfiguratin s dynamic stability and cntrl characteristics The phtgraph shws the mdel flying at a high angle f attack while researchers assess its behavir Nte the large nse-dwn deflectin f the canard surface, an indicatin f the inherent static instability f the cnfiguratin Active cntrls using data frm an angle-f-attack sensr n the nse bm prvided artificial stability 12

13 Rle f Dynamically Scaled Free-Flight Mdels Dynamic mdels have been used fr ver 50 years by the NACA and NASA t predict the spin entry and spin recvery behavir f highly maneuverable military aircraft A mdel f the F-15 fighter is shwn munted n a launching rig attached t a helicpter in preparatin fr an unpwered drp test, during which the unpwered mdel will be cntrlled by grund-based pilts in deliberate attempts t prmte spins As a result f extensive crrelatin f results with subsequent full-scale aircraft results, NASA has validated its testing prcedures 13

14 Rle f Dynamically Scaled Free-Flight Mdels Free-flying dynamically scaled mdels have evlved frm simple unpwered silk-span-cvered balsa replicas t highly sphisticated miniature aircraft with advanced materials, prpulsin units, cntrl systems, and instrumentatin This mdel f the X-48B blended wing-bdy cnfiguratin is typical f the current state f the art in dynamic mdel technlgy. 14

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