1 ,,---.-,. AIRCRAFT : Arrow 2 FILE NO: TITLE : - I A VRO AIRCR A FT LIM ITE D M ALT ON • ONTARIO TECHNICAL DEPARTMENJ (Aircraft) REPORT No!7 2 /Syst ems 2 2 ,/J l111 NO. OF SHEETS : ---~9~----- MODIFICATION OF THE fvIASS FLOW CONTROLLEH THEORY TO THE CONCEPT OF COMPLETE FLOW GU I DANCE BY THE ROTOR . \ PREPARED ,7J _.,JJ, CHECKED BY ~ • DATE April 1958 April 1958 DATE SUPERVISED BY DATE APPROVED BY ~~TE ISSUE NO, REVISION NO , REVISED BY APl!,ROVED BY DATE REMARKS < ----+-------+-----+---+'-------------------------- co ; "'1-------t-------+-----t-----'----+---+---------------'-------- < "' 0 "' > < AIRCRAFT: ii: ~it(" AVN0 AIRCRAFT LIM/TEO MALTON • ONTAR .10 REPORT No, 72/Systems 22/144 SHEET NO, __________ _ TECHNICAL DEPARTMENT Arrow 2 , PREPARED BY DATE MODIFICATION OF THEi { '1-----------+----- MASS FLOW CONTROLLER . J Dub bur THEORY Td THE CONCEPT CHECKED OF COMPLETE FLOW 1----------+------ INTRODUCTION If the rotor is built such that the flow leaves the rotor with a relative velocity paralle l to the blades ( as viewed from the blades) th~ri' the flow may be considered to be compl etely guided by themo That is the flow leaves the rotor with the same angul ar veloc;ty as the rotoro This results in a modificgtion to the theory given in Report Number 72/Systems 22/137 and to several useful improvements in the characteristics of the deviceo EK AVN(} A/F/ CNAFT LIM/TEO MALTQN • O NTARIO REPORT No. 72/Systems 22/144 TECHNICAL DE PARTMENT SHEET No. __ 2_-,--______ _ AIRCRAFT: ARROW 2 MODIFICATION OF THE MASS FLOW CONTROLLER PREPARED BY Jo Dubbur K"ril 1958 THEORY TO THE CONCEPT CHECKED BY ./-. DATE OF COMPLETE FLOW i--------_ 4 ...,_,;~,,..-+----- / ' Theory / Assuming the normal force curve slop ( d.¼--1 ft~) , / '/;() at approxima tel_y 27T and using the )lieory presented ' / in Report . Noo 72/Systems 22/13 7 ~ an / inconsistency becomes apparent when a rotor of high solidity is usedo For example ; if Nc= -12 inches S,_ .a 0384 Co:= · 003 ( Leo o< z:: . 3o5° based on J._~o<. z 2..,lr -t- = .lo75t~ then tlLe rotational outflow factor I.,- = lo 2657. Where. C. and -r- are the blade element chord & radi~s respectivelyo , J . and ~ _,..J__ Co are the blade element lift and drag coefficient respectively o Now it is obvious that Jr., ';f>l·O since this would correspond to the outflow rotating faster than the rotoro The reason: for the above anomaly becomes a_pparent when the characteristics of aerofoils in cascade are examinedo In "Aerodynamic Theory" by Durand section IV page 229 formula are quoted which give the behaviour of a cascade of flat plate aerofoils in potential flowo If a cascade is considered where the chord lines are. perpendicular to the line joining their leading edgesj then the following -for-mul~ re"Sl.11,te ,, ---~CD ;, E«: AVRO AIR CR AFT LIMITED REPORT No, 72/Systems 22/l 44 MALTQ N • C' N TARIO ' TECHNICAL DEPARTMENT SHEET NO. _ ____. _______ _ AIRCRAFT: ARROW 2 MOD IFICATION OF THE MASS FLOW CONTROLLER THEOnY TO THE CONCEPT PREPARED BY CHECKED BY CATE A ril 1958 CATE OF COMPLETE FL QW 1----------+----- Where = 2~1(f~ f-i"~;) S is the spacing of the { 2) blades oc is the incidence of the undisturbed st~eam s is the angl e through which the flow is deflected . Now as .$.. s Therefore and increases tanh ( 1!.S ) ~ 1.0 J... s Err~ ~ -#c --- (~\, 0) ~ ~ 1~0 --(4.0) Cl( If the simple a ssumpti on is made that the flow passing ✓ 1 ' through a c_ascade is deflected parallel to the aerofoils ( i.eo _i. = LO ) then f rom elementary considerations of 0( momentum a formula (consistent with(3)above ) eventuates. ..L el~ = _L..~ -- (5.0\ 1,_1T J _O( fr C / Now for appli cation to this spacing between the blades , particular jroblem, s= £JI:t N the Which substituted in (l )i(2 ) and (5) gives respectively, i Le:,, = .ft ~l/.lli) 2..1T J.o< Ne r, iJ i+ ~l 1.&-) l4~ .!,. = 2 tanhs ( N c -'r .;-- --(7.o) I+ Ji-;:I_ (~;) -1- J.c"' =-- 1:...r- _______ . (s. o\ 2.-n-~ Ne. -~ I Equations (6) and (8} are shown plotted in Figure l and (7) in Fig.ure 2. ' From the above equations the followin g conclusions may be made§ : (i) 'Phat ~ -<< 2,,r for all practical rotor configurationso EC AVN(J A IRCRAFT LIM/TEO MALTQN - O N TARIO REPORT No, 72 /Systems / 144 TECHNICAL DEPARTMENT SHEET No. _ ___:;r__ _______ _ AIRCRAFT: MOD IFICATI ON OF THE PREPARED ev DATE Arrow 2 SS FLOW C.uNTKOLLER J o Dubbury A ril 1958 THEORY TO THE CONCEPT CHECKED ev DATE OF COMPLETE FLOW 1----------+----- (2 ) That the blade spacing required to give nearly complet e guidance ( ¾.. _. f·O) i s quite easi l y built i nto a practi cal rotoro ( e og o ..t:1e :z 2·5' gives~ 2·.993\ 4-r- e;,<.. '/ ( 3 ) Tha t due to the rapid decline in J ~ /J« . with increasing solidity the normal force coefficients on the blades of h igh sol i dity rotors will be lower and their stalling much delayedo It would further seem l ikely that even with stalled blades of close spacing. the flow mus t leave the rotor subst1rttially., par allel to the bladeso , The char ac t eristics of a rotor ach:Le.ving complete flow guidanc e In thi s case the angular velocity of the outflow is equal to that of th e rotor so that from angular momentum considerations Then it -. 2,'lT f t..J V-,- 3 - Where Fis the 1density downs t ream of the rotor ~ lJ is the angular veloa}ty of the rotor (and theref ore also of the outflow) ~ V is the axial velocity component of the flow downs t ream of the rotoro -r- is t he r adius of the blade element~ Q is the tor que on the rotoro EC AVR0 A/R t RAFT LIM/TEO MALTC> N • O N TARIO REPORT No. 72/Systems 22/1~4 TECHNICAL DEPARTMENT SHEET No. ----"-5 _______ _ AIRCRAFT: ARROW 2 MOD IFICATION OF THE MASS FLOW CONTROLLER PREPARED BY DATE Jo D,ubburv Apri l 1958 THEORY TO THE CONCEP Tl-__ c_H_E_c_K_E_D __ a_v __ --'-__ D_A_T_E __ OF COMPLETE FLOW Assuming Then Now GU lLJAl\Jv~ n Y '1'Hl0 .tfOTUrt V and P. to be independent of radius o G'( : 2:rr P V w f_,-t-~ 3 J.,.. . -t; : f f V t.J (-t{r - -t-,f) -"M....., -- A Where A is the duct area ~ and -t-2.. are the root a.nd tip radi i respectively Thus q = ~ (--fi '-+- -t; i) ]_ Advantages of complete flow guidance ' It may be concluded that , given compl ete guidance of the flow by the rotor the fol lowi ng advantages may be obtainedo (1) Low flows involving hi gh relative incidences . on the rotor are acceptableo (11 ) The Mach Number of the incident flow is of no significanc eo (111) The flow of solid particles ( such as sand) could be measuredo _Typic.al._rotor .design t6 _a chiev:e . nearl.y: co.mpl..et.e . . gui.dance . Consider a rotor of 1n root radius and 2n tip radiuso Let sixteen blades have a chord of 1n eacho Then Ns. = 4 00 at root 4 -r-- - 2,~17 at mean radius %, . 2 o0 at tip J EK AVRO AIR CRA FT LIM/TEI) MA LTQ N • , N T ARIO TECHNICAL DEPARTMENT REP.ORT No. 72/Systems 22 /144 SHEET NO. ____ 6 ______ _ PREPARED ev DATE AIRCRAFT: 0DI FI CATION OF THE r I ARROW 2 Thus ]_ = o( . -- = SS FLOW CONTROLLER HEORY TO THE CONCEPT F COMPLETE FLOW 09997 at root 09952 at mean radius 09817 at tip CHECKED BY Whi ½.h is obviously very cl ose to comple te guidanceo The ~t-0rque characteristics of such a r otor are shown i n Figure 3 o - ✓ DATE • • If r---, I ,------...., ~ti. fq1 ~ ,-'-f iPH-1-S,'FF-.:J~i-=-'7?-,-j-=:=-;-J=.l:f+R'fm_:..r, ::.!,/'.C:.::J;;+!, ff-= -:,fi-O~~Jii;z+ic+++H+;:J7;L~--"!--ffi t4I;~ i Q :· ,:'. ~j~j <" •r:..; ; l -r ; ·::·~~ ~ ;) '•: '_ . ·- - :-1 :: j ~--1 ! I ~I-.- , .:ti:~L; l J· '-i, . · , ' · ; • \ ;--, 1e· • I , ,=l~ ·; q:_ '/ •IOQQ. 1 • I , .,, =-", { ·1 -i_o ' ' '-'·'-'-'----'----'-'-'--''-'-'-' ' """'!.P'+Ffi- trpcl=, "'."°_']:C':: ~:• ;~,~+< ' ~ ,±;-i.,;h ":.J • -, -- T .'-;i.,. a ! _: __ . ~ ~-.;:.:Cf,-..:.;,JJ,-_: , ·~ •- - f1 -_'" J, ~ t' --.YJ t I~:J±EfJ:i W-J-'--W......W...L'-L~ ...L~ ..L.=.LLC.:....il..-ll-..U.~.C.•1..-C-'' -- '--'' ,c:c_ ·..1...._'l-.-'.' .C:-1c,•.:;_• _.:' ..c' '--..L:.:=U: 7• ,-H I ,·; : • t •• l , ===D..!-"l C...J_C.:..'.J.C=:C•===L.:.CC,:J...:t:±f:t!lil J. DtJBBL/RY APl

Modification of the Mass Flow Controller theory to the concept of complete flow guidance by the rotor

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