A Comparative Investigation into Aerodynamic Performances of Two Set Finned Bodies with Circular and Non Circular Cross Sections

Transcription

1 A Comparatve Investgaton nto Aerodynamc Performances of Two Set Fnned Bodes wth Crcular and Non Crcular Cross Sectons MAHMOUD MANI and SHADI MAHJOOB Aerospace Engneerng Department Amrkabr Unversty of Technology Hafez St., Enghelab St., Tehran, IRAN Abstract: Accordng to the advantages of noncrcular bodes n storage and carrage purposes, these bodes have ganed substantal attenton by many researchers. In ths paper, two crcular and square (wth rounded corners) bodes, whch are attached to two fns, are studed n the free stream Mach number of The cross secton areas of bodes are the same. Ths work s done usng experment and CFD methods. In the CFD work, a three-dmensonal, compressble, statonary, vscous, turbulent flow s smulated usng FLUENT code wth the standard k-ε model and adaptve grds. The comparson of the results of experment and CFD smulaton shows that the results of CFD are enough accurate. The experment data n dfferent angles of attack ndcate that the square fn-body confguraton has hgher aerodynamc lft and drag coeffcents than the crcular one. Also, the results ndcate the same aerodynamc performance for both bodes. The results of CFD confrm the deducton obtaned from experment and also they explan the aerodynamc parameters of dfferent parts of fn-body confguratons (body alones, bases of bodes, and fns) whch are very consderable. The physcs of flow s also studed usng the pressure contours and velocty vectors. Key-Words: Aerodynamcs, Crcular and Non-Crcular Body Cross Sectons, Experment, Computatonal Flud Dynamcs Nomenclature CD Drag Coeffcent CL Lft Coeffcent L/D Aerodynamc Performance 1 Introducton In order to gan optmum aerodynamc performance and also to mprove the bodes for transportaton purposes, researcher's attentons have been towards the bodes wth non-crcular cross sectons. Jackson and Sawyer [1] have expermentally nvestgated bodes wth ellptcal cross-sectons and notced a consderable ncrease n aerodynamc effcency (L/D) for horzontal ellptcal cross-sectons (compared wth crcular cross-sectons). Also, the work of Graves [], whch was performed for a wde range of Mach numbers (from subsonc to supersonc) around ellptc and crcular cross-sectonal bodes showed smlar results. In famly of bodes wth non-crcular crosssectons, because of the storage and carrage purposes, the ones wth square or rectangular cross-sectons (wth round corners) are used more extensvely. In 1987, Sgal and Lapdot [3] performed an extensve expermental nvestgaton, n whch three famles of bodes wth same length and cross-sectonal areas were used. Ther results showed that C N was the hghest for the horzontal rectangular case and the second hghest for the square case. Of course, the problem wth the rectangular case s that, when the body rolls and ts cross-secton changes from horzontal rectangle to vertcal one, ts aerodynamc effcency drops drastcally (even to less than the crcular case). Note, ther results were consstent n both cases of a body wth and wthout fns. Mahoob and Man [4] studed the crcular and square body alones n a transonc flow usng experment, CFD, and sem-emprcal methods. The results of ther work ndcate that a change of the cross secton from crcular to square leads to the ncrease of the aerodynamc parameters (lft coeffcent, drag coeffcent, and aerodynamc performance). In addton, at low angles of attack, the change of the cross secton (from crcular to square) not only ncreases the lft coeffcent and aerodynamc performance very consderably, but also does not affect drag coeffcent very much. In fact, changng the cross secton from crcular to square n order to ncrease the aerodynamc performance s more successful and effectve at low angles of attack. Flow separaton effects are hghly related to the corners of the square or rectangular cross-sectons and cause unfavorable aerodynamc nstabltes [5]. Mahoob and Man [6] studed the effects of fn-body nterference n square and crcular bodes expermentally. The results ndcate that the fn-body nterference of crcular body s hgher than that of the square one. Models and Characterstcs Two dfferent bodes, one havng crcular cross secton and the other havng square cross secton wth rounded corners, are smulated n body-fn confguraton (Fg. 1). Both bodes have the same body length and cross secton area. The bodes have fneness-raton-3.5 ogve noses and cylndrcal after bodes, gvng overall fneness rato of The wngs have 47 sweepback angles, aspect ratos of 3.5, taper ratos of 0., and hexagonal sectons of 6% thckness, as showng n Fg.1. The fn span (the dstance between the tps of the fns) n both models of crcular and square s the same and the aerodynamc parameters n ths study s calculated based on the cross secton area whch s equal to m. The free stream Mach number s 0.83, the statc temperature s 66.86K, the statc pressure s 54400Pa, and the total pressure s 85000Pa.

2 3 Expermental Facltes The expermental test has been done n a mult purposed ST- wnd tunnel. The tunnel s desgned and calbrated for subsonc, transonc, and supersonc regmes for Mach numbers of 0.4 to.. The test secton s 60Cm 60Cm. Its nozzle s flat and controllable and the nozzle s geometry can be changed durng the test. Ths s done by seven double handle and electrcal acks. Tunnel s power s produced by a turbofan engne wth the power of KW whose control s done by remote control electro mechancally. The range of angle of attack s from - to 16. The accuracy of models' manufacturng s about 0.01 mm. 4 Computatonal Methodology The FLUENT CFD code [7], whch uses a cell centered fnte volume method and has been proven to work well for dfferent flow regmes around bodes, s used n ths study. The explct method mplemented uses a coupled soluton method. Note, all the schemes used here are second order. The SIMPLE algorthm wth underrelaxaton coeffcents s used n the overall dscretzaton of the equatons. In order to reduce the dsperson errors (and also to ncrease the speed of the computatons), the mult-grd approach s also used. Because of the complexty of geometry of models, exstence of transonc flow, and also solvng full Naver Stocks equatons, wth consderng vscosty and turbulence, t took more than 10,000 teratons for convergence. So that the resduals are lower than Also, each of teratons took a lot of tme. In order to ncrease the accuracy of the results, adaptve grds were used. 4.1 Governng Equatons and Physcal Propertes The Reynolds averaged governng equatons nclude contnuty, momentum, and energy whch are as follows: ( ρu ) = 0 x x x where τ x x T = K + u x x p ( ρ u u ) = + + ρ g + F ( ρ u h ) + τ, u u τ µ = eff + µ eff x x 3 p x l u x u µ l eff = µ + µ δ ; T. x The flow consdered here s three-dmensonal, compressble, statonary, sngle-phase, vscous and turbulent that the standard κ-ε model s used for turbulence modelng. The flud s ar, for whch the vscosty s obtaned usng Sutherland relaton and densty s obtaned usng deal gas relaton. The turbulence ntensty s 1%, the characterstc length scale (the body s dameter of cross-secton) s 0.04m Turbulence Modelng The standard k ε model wth the standard wall functons [8] s used n ths study. Recall that, n k ε model, the averaged Reynolds stresses are taken proportonal to the averaged velocty gradents and the proportonalty constant (µ T ) s found from k and ε equatons. The turbulent knetc energy, k, and ts rate of dsspaton, ε, are obtaned from the followng transport equatons: Dk µ t k + Gk YM Dt x +, ρ = µ ρε σk x and Dε ρ = Dt µ t ε ε µ + C1 ε x + σ ε x k ( G ) k ε C ε ρ k In addton, the standard wall functons, based on the work of Launder and Spaldng were used [9]. 4. Geometrc Modelng In Fg. 1, the bodes' geometry and cross sectons are presented. The computatonal doman around bodes, s assumed to be a cylnder whose dameter s 1 tmes half of the span of the bodes (Fg.). The other outer boundares are assumed to be 5 body lengths at the front and 5 body lengths behnd the bodes (Fg. ). Ths sze of the doman s shown to be optmal usng numercal expermentaton. Note, due to the symmetrc assumpton used, only half of the doman s consdered here. Our computatonal results ndcate that ths assumpton does not affect the results consderably. 4.3 Computatonal Grd A blocked structured, body ftted, and non-unform grd s used n ths study (Fgs. 3 and 4). The grd was clustered around the bodes and fns and also n senstve regon (wth hgh pressure and velocty gradents). Because of the complexty of body geometres and the exstence of sweepback fns, 31 blocked were created. After grd resoluton study, a 364,000 cells grd s chosen as the basc grd (Fgs. 3 and 4). To nsure grd nsenstvty, adaptons are made on Y + and pressure gradents. 4.4 Boundary Condtons Dfferent boundares of the physcal doman are used n ths work (Fg.). The wall of the body and fns are assumed to be adabatc (A). The free stream pressure s assumed at the nlet (B) and outlet (C) of the doman. In the pressure outlet boundary condton, only the statc pressure s specfed and all other flow quanttes are extrapolated from the flow n the nteror. The far feld pressure condton s also used (D).Ths boundary condton s often called a characterstc boundary condton because t uses characterstc nformaton (Reman nvarants) to determne the flow varables at the boundares. At the symmetrc plane, the symmetrc boundary condton s mplemented (E) and the axs boundary s used at two axs of front and behnd body (F). 5 Results In ths work, the aerodynamc parameters of square and crcular fn-body cross sectons have been compared

3 usng expermental and computatonal methods. The results are presented as follows. 5.1 Expermental Results: Fg. 5 whch shows the lft coeffcent of bodes ndcates that changng the cross secton from crcular to square ncreases the lft coeffcent. Fgure 6 shows the drag coeffcent of bodes. Ths fgure ndcates that at all angles of attack, the body wth square cross secton has more drag coeffcent than the crcular one. Snce the ncrease percentage of lft and drag coeffcents are somehow the same, the aerodynamc performance (L/D) of crcular and square bodes are very smlar (Fg.7). 5. Computatonal Results In order to study the effects of cross secton on the aerodynamc parameters of dfferent parts of fn-bodes (such as body alones and fns separately) and also to study the physcs of flow whch could not be acheved by expermental data, two crcular and square fn bodes are smulated usng computatonal methods. In addton to study the effects of changng the angle of attack on the physcs of flow, the crcular body s also smulated at 16.7 angle of attack. At frst, to valdate the computatonal results, the expermental and computatonal results are compared and then the aerodynamc parameters of bodes and the physcs of flow (usng total pressure contours and velocty vectors at dfferent stuatons) are studed Code Valdaton Study Comparson of expermental and computatonal data shows a good agreement and accuracy. In CFD results, at zero angle of attack, the lft coeffcent of bodes are zero whch s completely true because the bodes are symmetrc. As t s shown at table 1, the drag coeffcent obtaned from experment and CFD are very close to each other and the dfference at zero angle of attack s under 1%. The error of lft and drag coeffcents obtaned from CFD for crcular body at 16.7 angle of attack s under 5%. One of the man reasons of errors especally at low angles of attack s related to the base drag. In fact, n expermental test, the bases of the bodes are attached to the after body so ts setup s dfferent from CFD smulaton where flow can move behnd the bodes and create the wake and so ncrease the base drag. Although, the drag obtaned from the base surface of the bodes are reduced from the CFD results for valdaton study, there are stll some effects of flow physcs behnd the body on the area around the bodes whch can affect the aerodynamc parameters. It s also notceable that because of lack of drer system or flter n the wnd tunnel, the results can have a lttle error. It happens especally at hgh speed (supersonc regmes) that the ar flow reaches the two phase flow stuaton. 5.. Effects of Cross Secton on Aerodynamc Parameters In ths work, the pressure and frcton drags caused by dfferent parts of the crcular and square fn-body confguratons are studed. In the crcular body at zero angle of attack, about 54.68% of drag s belonged to the pressure drag and 45.3% of drag s belonged to the frcton drag. 9.1% of the drag s caused by the fns n whch 10% of the drag s belonged to the pressure drag of fns and 19.1% of the drag s belonged to the frcton drag of fns. In addton, 33.1% of drag s belonged to the base drag. The rest, 37.8% of drag s caused by the body alone (wthout consderng fns and bases). In fact, 11.56% of the drag s belonged to the pressure drag and 6.4% of the drag s belonged to the frcton drag. In the square body at zero angle of attack, about 5.6% of drag s belonged to the pressure drag and 47.4% of drag s belonged to the frcton drag. 30.3% of the drag s caused by the fns n whch 9.8% of the drag s belonged to the pressure drag of fns and 0.5% of the drag s belonged to the frcton drag of fns. In addton, 3.4% of drag s belonged to the base drag. The rest, 37.3% of drag s caused by the body alone (wthout consderng fns and bases). In fact, 10.4% of the drag s belonged to the pressure drag and 6.9% of the drag s belonged to the frcton drag. The above percentages show that the drag dstrbuton s very smlar n both crcular and square bodes. However, there are some nterestng dfferences between these two bodes. At zero angle of attack, the drag coeffcent of square fn-body s a bt hgher than that of the crcular fn-body. The comparson of the drag coeffcents of crcular and square body alones (wthout consderng the bases) ndcates that the pressure drag of square body alone s lower than that of the crcular body alone. Whle, the frcton drag of square body alone s hgher than that of the crcular one. Ths s because, although the areas of crcular and square cross sectons are equal, the permeter of square cross secton s more than that of the crcular one so the area of the square body alone s more than that of the crcular body alone. Totally, the drags of both body alones are somehow the same. Snce the span of fns (dstance between the tps of fns) s the base for crcular and square body-fn confguratons, and regardng to smaller wdth of square cross secton than that of crcular one, the fns attached to the square body are larger than those of the crcular body so the frcton drag of fns attached to the square body s hgher than that of the crcular body whch results n a bt hgher drag coeffcent for square fn-body confguraton. At zero angle of attack, because of the symmetry of fn-bodes, the lft coeffcents of both fn-bodes s equal to zero Physcs of Flow Fgures 8 and 9 ndcate the total pressure contour at crcular and square fn-body confguratons at zero angle of attack. At both fgures, the stagnaton regon s located around the nose of the bodes. Also, the least pressure s located at the bases of the bodes. The study of maxmum and mnmum pressure show that the maxmum pressure of the crcular body s hgher than

4 that of the square body and the mnmum pressure of the crcular body s lower than that of the square body. Therefore, the pressure dfference between the front and behnd the bodes, whch makes the pressure drag, n crcular fn-body confguraton s hgher than that of the square one. Ths deducton s also presented n Table. The study of Fgs. 8 and 9 also shows a hgh pressure at the leadng edge of fns. The effects of fn-body nteractons are also seen at these fgures whch are accompaned wth the decrease of the total pressure. In Fg. 10, the total pressure contour at crcular fnbody confguratons at 16.7 angle of attack s presented. Accordng to Fgs 8 and 10, by ncreasng the angle of attack, the stagnaton regon s moved to under the body and a pressure dfference s created between the above and below the body whch resulted n lft force. The study of total pressure contour over and below the fns s also notceable. Increasng the angle of attack (Fg.10) decreases the pressure over the fns consderably, especally near the leadng edge, whch results n a hgh pressure dfference between over and below the fns and so a consderable lft force. Comparng Fgs 8 and 10 whch shows the effects of changng the angle of attack ndcates that at zero angle of attack, total pressure contours over and below the body are smlar and symmetry that results n zero lft coeffcent. However, at 16.7 angle of attack, the dstrbuton of pressure contours over and below the body s very dfferent. In addton, study of the maxmum and mnmum pressure of crcular fn-body confguraton (Fgs. 8 and 10) ndcates that by ncreasng the angle of attack, the pressure dfference ncrease very consderably whch results n hgher pressure drag. It s notceable that at 16.7 angle of attack (Fg.10), the mnmum pressure over the leadng edge of the fns s even less than that of the wake regon 9behnd the body). In Fgs. 11 and 1, velocty vectors at the bases of the crcular and square bodes and the symmetry plane are presented at zero angle of attack. Behnd the bodes, there are two symmetry wakes whose centers are located at a quarter of cross sectons' wdth from the center of cross sectons. In these fgures, the symmetry of wakes on the bases of bodes and the symmetry plane of doman are presented. The length of the vectors shows the velocty magntudes, whch are very small n the wake regon, and shows the small or zero velocty magntudes. Fgs. 11 and 13 ndcate that ncreasng the angle of attack, damages the symmetry of flow streamlnes and wakes. In addton, ncreasng the angle of attack (Fg. 13) decreases the wake regon area whch s destroyed by the man-flow more rapdly than the smaller angles of attack. References: [1] Jackson, C.M. and Sawyer, W.C., Bodes wth Non- Crcular Cross-Sectons and Bank-to-Turn Mssles, Progress n Astronautcs and Aeronautcs, Vol. 141, pp , [] Graves, E.B., Aerodynamc Characterstcs of a Mono- Planar Mssle Concept wth Bodes of Crcular and Ellptcal Cross-Sectons, NASA TM-74079, Dec [3] Sgal, A. and Lapdot, E., The Aerodynamc Characterstcs of Confguratons Havng Bodes wth Square, Rectangular, and Crcular Cross-Sectons at a Mach Number of 0.75, AIAA, Inc., [4] Mahoob, S. and Man, M., The Ablty of CFD Methods to Study Noncrcular Bodes, Presented and Publshed n the Proceedngs of ICCMSE 004, Internatonal Conference of Computatonal Methods n Scences and Engneerng, Greece, November 004. [5] Nelsen, J.N., Problems Assocated wth the Aerodynamc Desgn of Mssle Shapes, Proceedngs of the Second Symposum on Numercal and Physcal Aspects of Aerodynamc Flows, CA, Jan [6] Mahoob, S., Man, M., Ebnoldn, H., Haghr, A., Aerodynamc Study of Bodes wth Non-Crcular Cross Secton Usng Expermental Method, Publshed n the Proceedngs of The 8 th Inter. Conf. of Iranan Socety of Mechancal Engneers, Tehran, Iran, May 004. [7] FLUENT 5 User s Gude, FLUENT Incorporated, [8] Launder, B.E. and Spaldng, D.B. Lectures n Mathematcal Models of Turbulence, Academc Press, London, England, 197. [9] Launder, B. E., and Spaldng, D. B., The Numercal Computaton of Turbulent Flows, Journal of Computer Methods n Appled Mechancs and Engneerng, Vol. 3, 1974, pp Table 1: Drag Coeffcents of crcular and square fn-body confguratons. Drag Coeffcent Crcular, 0 angle of attack Square, 0 angle of attack Crcular, 16.7 angle of attack Experment CFD (wthout bodes' base drag) CD CD pr (Pressure) Table : Drag Coeffcents of dfferent parts of the bodes at zero angle of attack. CD F (Frcton) CD B (Base) CD Fns CD Fns,Pr (Pressure) CD Fns,F (Frcton) CD Body (Body Alone Wthout Bases) CD Body,Pr (Pressure) Crcular Square CD Body,F (Frcton)

5 Fg1. The geometry of body and cross sectons, crcular and square wth rounded corners. E B F A C D Fg.. The computatonal doman and boundary condtons. Fg. 3. The computatonal grd at the symmetry plane of the doman (before adapton). CL Lft Coeffcent Alpha (deg) Square Secton Crcular Secton Fg. 4. The computatonal grd at the symmetry plane, the body and the fn (before adapton). Fg.5. Lft coeffcent of crcular and square fnbodes obtaned from expermental test. CD Drag Coeffcent Square Secton Alpha (deg) Crcular Secton Fg.6. Drag coeffcent of crcular and square fnbodes obtaned from expermental test L/D 4 Aerodynamc Performance Square Secton Alpha (deg) Crcular Secton Fg.7. Aerodynamc performance of crcular and square fn-bodes obtaned from expermental test.

6 Fg.8. Total pressure contour at crcular fnbody at 0 angle of attack. Fg.9. Total pressure contour at square fnbody at 0 angle of attack. Fg.10. Total pressure contour at crcular fnbody at 16.7 angle of attack. Fg. 11. Velocty vectors at the base of crcular fnbody and the symmetry plane of the doman at 0 angle of attack. Fg. 1. Velocty vectors at the base of square fnbody and the symmetry plane of the doman at 0 angle of attack. Fg. 13. Velocty vectors at the base of crcular fnbody and the symmetry plane of the doman at 16.7 angle of attack.