Estimation of aerodynamic characteristics of un-symmetrically finned bodies of revolutions

Transcription

1 Estimation o aerodynami arateristis o un-symmetrially inned bodies o revolutions Praveen Gill, andeep Mali and Rajumar. Pant Graduate tudent, Aerospae Engineering Department, Indian Institute o Tenology Bombay ientist, Aerial Delivery Resear & Development Establisment, Agra, DRDO Assoiate Proessor, Aerospae Engineering Department, Indian Institute o Tenology Bombay Mumbai 476, India rpant@aero.iitb.a.in Fax: An existing semi-empirial steady state model o a inned axisymmetri body is suitably modiied to aount or un-symmetrial in arrangements su as inverted Y and V ins. Te modiied metod is applied to two aerostat onigurations, and te results obtained are ompared wit wind tunnel data and panel metod alulations. Good agreement is seen, wit minor variations due to ertain eets, wi are not taen into aount by te semi-empirial metod. Te metod was ten applied to estimate te position o neutral point. KEYWORD: Airsip, tability, Wind Tunnel, Panel Metod, emi Empirial Nomenlature Veile reerene lengt total ull lengt D Drag Fore I, I, J, J Geometrial integrals deined in text N Normal ore M Pit moment at nose nose Veile reerene area / (ull volume, Axial and lateral apparent mass oeiients q teady state dynami pressure ρu / η ull eiieny ator aounting or te eet o ins on ull η in-eiieny ator aounting or te eet o ull on te ins Fin ross low drag oeiient reerened to Hull ross low drag oeiient reerened to J Hull zero angle axial drag oeiient, reerened to Fin zero angle axial drag oeiient, reerened to (n Fin lit urve slope at ( t Fin leading edge sution oeiient reerened to ( l Distane rom nose to beginning o ull in intersetion ( l Distane rom te ull nose to in aerodynami entre ( l Distane rom te ull nose to in ross low drag entre Introdution Tis wor is based on te ross low analyti model or predition o aerodynami ores on airsips, proposed by Jones & DeLaurier []. Te sematis o te analyti model are represented in Fig.. Tis metod applies to te low speed regime, wen te low is attaed and no low separation as ourred over te airsip ull.

2 Estimation o Aerodynami oeiients Te equation or te normal ore is given as N q{( η I}sin( os( / + sin( sin( J + + [( n η (sin( / sin( sin( ]} Axial ore an be estimated using D q { [ + ]os ( I sin( sin( / ( t ( Moment about nose is estimated using M q [( η I sin( os( / nose + + η ( l + ( l ( n J sin( sin( (sin( / sin( sin( ]... ( }... (... ( Te integrals appearing in tese equations are deined as l l da da I dξ I ξ dξ dξ dξ J l l rdξ J rξdξ... (4 Te equations may be made dimensionless by te ollowing relations: N, D ( n, d q M mq I J Iˆ Jˆ ˆ ˆ,,, (,,, I, J ( Iˆ, Jˆ ( l,( l ((ˆ l,(ˆ l Te dimensionless oeiients as derived rom Equations -, assuming low or attaed low are given as: Lit oeiient: n [ J + + [( η Iˆ } +.5ˆ ˆ ( n ]sin( sin η ]sin( Moment oeiient: m [ ˆ ˆ J + (ˆ l ( d ]sin( sin [( ˆ.5 ˆ η I + η (ˆ l ( n ]sin( Drag oeiient: d d ˆ d ˆ [( + ( ]os ( ( Iˆ sin( sin( / ( t ˆ... (5... (6... (7 are sould be taen to ensure tat proper reerene parameters are osen to non-dimensionalize te geometrial parameters. For example or alulation o moment oeiient, one an use mean aerodynami ord o te in or te total ull lengt. imilarly veile reerene area is dierently taen as ull surae area or (ull volume /. Evaluation o te aerodynami oeiients disussed above requires nowledge o te aompanying unnowns in te respetive equations. Te next setion desribes ow te values o tese unnowns an be obtained. Estimation o Unnowns Involved in Aerodynami oeiients oeiients related to broad ategories o lit, drag and intererene are disussed individually in ollowing subsetions. Teir soures and related assumptions to estimate teir values are also stated. Fin Lit urve lope ( n ( n is alulated as per te ormula mentioned in Raymer [], werein lit urve slope or a in is π l AR tan Λ β η

3 ... (8 It must be noted tat in above ormula lit urve slope is or a in wi as zero diedral angle. I te in as a substantial diedral, ten te lit urve slope will ange on two aounts. Firstly or te at tat te projeted area o te in is redued by os(γ and seondly sine te angle o atta aed by te wing doesn t remain te same. For small, te eetive angle o atta beomes os(γ. Tereore ( n is given as os l ( Γ, i te entire in area is used. I, owever, te projeted area is taen into onsideration, tan one osine term an be dropped. Apparent Mass oeiient ( Te apparent mass term as a untion o l / d or streamline bodies is given in Perins & Hage [], te grap is regenerated ere, or te range o values relevant to te available wind tunnel results. urve itting was done to do away wit manual entry o tese oeiients. Hull Zero Angle ross Flow Drag oeiient is alulated using ormula provided by Hoerner [5] as d d l l... (9 Here d/l is te ratio o maximum diameter o ull to its lengt. Tis is used re... (, is available as a untion o Reynolds number in Hoerner [5]. Fin Zero Angle ross Flow Drag oeiient Fin axial drag oeiient is alulated as w re Were is obtained rom Hoerner [5], and w 6 t t ( Hull ross Flow Drag oeiient, (d From Hoerner [5], (d or te regime o operation o airsip is airly independent o ull sape and is taen as.. Fin ross Flow Drag oeiient, (d is a untion o te aspet ratio and te taper ratio o te in. It is provided in Wardlaw [4], as a grap or various taper ratios. For intermediate values o taper ratio, Λ te linear interpolation is used to get approximate value o (d. Fin and Hull Eiieny Fators, ( η, η Te value o η andη an be obtained by urve itting te available values o ull eiieny ators o nown airsips as suggested by Jones and DeLaurier []. omparison o Results Experimental results and panel metod preditions were available or two aerostat onigurations under development at ADRDE (Aerial Delivery Resear and Development Establisment, Agra. Data regarding in arrangement and ull sape was also available wi made it possible to validate te above metodology. Bot te aerostats were equipped wit an inverted Y in arrangement. Hene some minor adjustments were required in Jones and De Laurier s metod to aount or su nonsymmetrial in arrangement. One o te sapes was proposed by Pro. G.N.V. Rao o II, Bangalore and is ene named as GNVR sape. Te oter sape (named A, was developed by pae Appliation entre IRO, Amedabad.... (

4 Figure 8- sow te omparison amongst te semi empirial metod, wind tunnel testing and panel metod or te A oniguration. Aerodynami oeiients or te A sape were available bot troug wind tunnel testing, undaram [6], and panel metod, Narayana [7]. For te GNVR sape owever te wind tunnel results were not available. Figure & sows omparison o semi empirial metod and panel metod or te GNVR oniguration. It an be seen tat results obtained by te modiied semi-empirial metod results in good o-relation wit te panel metod alulations or te lit, drag and moment urve or te A sape. As ar as omparison wit te wind-tunnel data is onerned, only te trends are similar, but te values, espeially or te Drag urve are not mating well. Te drag urve is unsymmetrial due to te sielding o two ins at negative angle o attas, wile at positive angle o attas only one in is sielded. Furter at low angle o attas te drag value is iger as te wind tunnel model ad orrugated ins. Reasonably good o-relation is also seen or lit and moment oeiient wit te panel metod or GNVR sape. alulation o Neutral Point From te m vs L urve te pit stability oeiient d m / d L an be obtained. One te slope o m vs L urve is nown, it is possible to estimate te position o te neutral point using te ollowing equation rom Perins and Hage []. d d m L X nose X L NP... ( Neutral point loation elps in deiding at.g. limits, and ene governs loation o various strutures lie ballonet, gondola and power plant. Figure 4 & 5 present travel o neutral point as a untion o stabiliser area or te A and GNVR sapes. It an be observed rom te graps tat or low stabiliser area te neutral point sits quily to at positions wit small inrease in area. However, tis ast sit is not sustained or long. A saturation o neutral point position around 55% is observed at stabiliser area approaing 5% o ullted area. onlusions It an be onluded tat te modiied semiempirial metod an be a useul tool or qui estimation o te aerodynamis arateristis o bodies o revolution wit un-symmetrial in geometries, or wi te original metod annot be diretly applied. Te metod an also be applied to determine te rear limit o te loation o enter o gravity, by estimating te position o te neutral point. Reerenes [] Jones,. P. and DeLaurier, J. D., 98, Aerodynami Estimation Teniques or Airsips and Aerostats, Journal o Airrat, Vol., No.. [] Raymer, D. P., 989, Airrat Design: A oneptual Approa, AIAA, pp 64. [] Perins,. D. and Hage, R. E., 96, Airplane Perormane tability and ontrol, Jon Wiley & ons, pp. 6. [4] Wardlaw, A. B., Jr., Hig-Angle-o-Atta Missile Aerodynamis AGARD Leture eries No. 98, February 979, Tenial Editing and Reprodution Ltd., London, pp. 5-6 to 5-9. [5] Hoerner. F., 965, Fluid Dynami Drag, Hoerner Fluid Dynamis, Britown, N.J., 965, pp -6. [6] undaram, 999, Wind Tunnel Test on :7 and :8 ale Aerostat Models, PD EA 995, NAL Bangalore [7] Narayana. L., 998, FD Analysis o Aerostat onigurations, Interim Report on BLI, NAL Bangalore

5 NBB (N (N M nose D T D U o l i l i+ l (l (l Fig. ematis o Airsip Geometry, Fores and Moments (d 6 Λ 4 Λ ½ Λ Aspet Ratio Figure Deinition o Fin Areas Figure 4 Fin ross Flow Drag oeiient η l/d 7 / Figure 5 Fin Eiieny Fator Figure Lateral and Axial Apparent Mass oeiient

6 emi Empirial Metod Wind Tunnel Panel Metod η.. m os (Γ/J Figure 6 Hull Eiieny Fator GNVR ape A ape Figure 7 Hull apes or GNVR and A onigurations (only top al sown m Figure Moment urve or A ape emi Empirial Metod -.5 Panel Metod -. Figure Moment urve omparison or GNVR ape L emi Empirial Metod Wind Tunnel Panel Figure 8 Lit urve omparison or A sape.8 L.6 D emi Empirial Metod Panel Metod -.4 Figure Lit urve or GNVR ape.4 emi Empirial Metod Wind Tunnel Panel Metod Figure 9 Drag urve or A ape

7 . m L m emi Empirial Metod -. L Figure Pit tability oeiient alulation rom emi Empirial metod results or GNVR ape NP Loation (% Hull Lengt tabiliser Area (% Hull Area Figure 4 Neutral Point Travel Due To ange in Fin Area (For A ape 65 NP Loation (% o Hull Lengt tabiliser Area (% Hull Wetted Area Figure 5 Neutral Point Travel Due To ange in Fin Area (For GNV ape