16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 26: Turbopumps

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1 6.5, Rocke Propulion Prof. Manuel Marinez-Sanchez Lecure 6: Turbopump Turbopump Componen The mechanical componen of he preurizaion cycle (pump and urbine) are nex o be conidered. An excellen recen urvey of hi area i given in Ref.40. A more comprehenive, bu older urvey i conained in a erie of NASA SP repor [4-43]. Pump and urbine will fir be dicued eparaely, and heir inegraion will hen be examined. (a) Pump Almo all exiing rocke have cenrifugal urbopump. Thee deliver more P per age han axial flow pump, wih only lighly le efficiency. Only if muliaging become neceary i here a poible incenive o go o axial pump; hi happen wih LH fuel, where, due o he low deniy, he P per age i limied by he aainable rim peed. In general, he deign aemp o maximize operaing peed, ince hi reduce he pump ize, and hence he weigh. Pump peed i limied by everal effec, mo imporanly caviaion a inle. Oher are cenrifugal ree (eiher a he impeller or in he driving urbine), limiing peripheral peed for bearing and eal, and avoidance of criical peed. Head rie i ued commonly inead of preure rie o expre he performance of pump. We can define head rie a he heigh o which one could raie one Kg of fluid wih he amoun of ideal work per Kg done by he pump: P dp H = h /g = P () ρg The rie i direcly relaed o he pump work, even if he fluid ha ignifican compreibiliy: Work/ma= gh h = () η p and hi i one of he advanage of i ue. Obviouly, if ρ = con., P H = Work P, = (3) ρ g ma ρη p 6.5, Rocke Propulion Lecure 6 Prof. Manuel Marinez-Sanchez Page of 8

2 The head rie i direcly o he peripheral peed of he impeller dik. The fluid ener axially near hey impeller hub, wih no angular momenum; i leave he impeller wih abolue angenial peed ωr V r an β, where β i he back-leaning blade angle a he rim Fig, and V r i he fluid radial exi velociy, relaed o he volume flow rae a Q = πr b V r (4) The orque needed o drive he impeller i he ne ouflow rae of angular momenum, and he work rae i hi, ime ω. Thu, i m R V an ω β ωr Power = ( ) r (5) and ince we alo have Power = i gh m, he head rie i η p ( R ) ω V =η anβ (6) r H p g ωr 6.5, Rocke Propulion Lecure 6 Prof. Manuel Marinez-Sanchez Page of 8

3 V r The quaniy ψ = ηp anβ ωr i omeime called he head coefficien. In erm of ψ, ( ω ) R H =ψ (7) g ψ i ypically beween 0. and 0.8. Value greaer han uniy could be obained if he blade were deigned o learn forward ( β < 0 ), bu hen P would increae wih Q (hrough he effec of V r ). Thi poiive lope of he P v. Q characeriic i known o produce inabiliie in he pumping yem [44]. Thee are generally dynamic in naure, and depend o ome exen on he characeriic of he re of he yem (free volume, hroling effec, ec), bu i i relaively eay o underand heir origin from a quaiaic argumen: if he pump emporarily deliver more flow han can be dipoed of in eady ae by he downream componen, ( P) and if i characeriic ha a poiive lope, he pump preure rie will alo Q be higher han normal. The downream preure will herefore end o increae for boh reaon, and a runaway iuaion enue. In addiion o hi yem inabiliy, here i alo a endency for flow maldiribuion analogou o roaing all, ince he flow i hen unable wih repec o ma inerchange beween parallel reamube [45]. Eq. (6) would predic a linear dependence of head on flow rae. In realiy varying he flow a a given peed will vary he inernal flow angle wih repec o blade, and will herefore reul in variaion of he lope H Q. Example of hi behavior are hown in Fig (Ref. 4), where he flow coefficien i defined a = R π Q ( ω ) R b (8) 6.5, Rocke Propulion Lecure 6 Prof. Manuel Marinez-Sanchez Page 3 of 8

4 The hroling range i defined by he poin of maximum head, below which operaion i unable. Similar (bu ronger) rericion apply o axial deign, uch a ha ued in he J- LH pump, and o hee deign end o be limied o applicaion which require very limied hroling. The pump i deigned o pecified head rie H or ( P) and volumeric flow Q. Thee quaniie can be ued o conruc he non dimenional quaniie called pecific diameer and pecific peed: 6.5, Rocke Propulion Lecure 6 Prof. Manuel Marinez-Sanchez Page 4 of 8

5 d 4 D(gH) = (9) Q n ωq = (0) ( gh) 3 4 In he U.S. lieraure, D i expreed in fee, Q in gpm and ω in rpm, and g i omied. Thi procedure, of queionable pracically, reul in relaed parameer D, N given By N = 78 n, D = d. Noice ha nd and hence, from (7), ωd = () ( gh) nd = () ψ or, in Englih uni, ND = 08.3 ψ. Since for cenrifugal pump, we found ψ <, we can ee ha heir domain i a ( n,d ) map i nd > (or ND > 08 ). The coniderable empirical evidence on pump performance ha been diilled (Ref.46) by conrucing ( n,d ) map on which favorable region are hown for variou ype of machine. A very generalized example (aken from Ref. 4) i hown in Fig. 3, where line of conan peak efficiency are hown for a wide variey of pump. Thee ue a e of clearance, olerance, roughne, ec. facor, and are o be aken only a indicaive, ince acual deign may depar from adoped value. We noice in Fig. 3 he line ND 00, denoed a he limi for dynamic pump, in accordance o our dicuion above. Radial and axial pump deign nearly merge, alhough he axial ype i indicaed for he highe pecific peed, which a Eq. 0 how, may be imply a reflecion of low head rie, a for example, in he inducer age feaured commonly a he inle of cenrifugal pump for caviaion uppreion. Table give he feaure of he high preure SSME pump, and he reuling ( N, D ) poin are included in Fig 3, where hey are een o lie roughly on he η = 0.8 line. 6.5, Rocke Propulion Lecure 6 Prof. Manuel Marinez-Sanchez Page 5 of 8

6 6.5, Rocke Propulion Lecure 6 Prof. Manuel Marinez-Sanchez Page 6 of 8

7 The pump mu be deigned o a o avoid caviaion, which boh, degrade performance, and caue damage o reuable aricle. Caviaion rik exi a he pump inle, where he liquid preure i lowe, and i increae wih boh, he fluid velociy and he peed of he pump inducer blade meeing he fluid. The inducer diameer need o be large enough o reduce he inle fluid dynamic head ρ C m o ome fracion of he exce inle preure over auraion P -P a,. Thi la quaniy i called he Ne Poiive Sucion Preure (NPSP), and i uually given a a ucion head NPSH= NPS/( ρg ). Hydrogen Pump Oxygen Pump P (N/m ) (per age) H (m) 0,000,930 Q (m 3 /ec) (per ide) ω (rad/ec) D (m) n (N ) (050) (90) d (D ) 6.6 (0.03) 435 (0.0866) Table. Characeriic of he SSME high-preure fuel and oxidizer pump The raio: ( NPSP ) ( NPSP ) σ= = C / ρ C m m g (3) i called he Thoma parameer, and empirical evidence [40,4] indicae ha i hould be graer han for LH, for LOX and 3 for waer and orable propellan. The more favorable iuaion for hydrogen appear o be relaed o a greaer vapor uppreion effec due o evaporae chilling when bubble ar o form. Several oher parameric repreenaion of caviaion daa exi. Thu, Ref [40] and [4] ue a ucion pecific peed S defined a in Eq (0), bu wih H replaced by he NPSH, and wih correcion for flow blockage by he hub. Thi parameer can be hown o be relaed o Thoma parameer σ and o = c / ω R (R= inducer radiu) by.98 S = (4) 3 σ 4 m In Englih uni, he numerical facor i 83. The daa on caviaion one for a variey of liquid how ha σ remain approximaely conan for each, a noed above. Independenly, Ref. 47 how caviaion reul in he form τ= f( Z ) (5) 6.5, Rocke Propulion Lecure 6 Prof. Manuel Marinez-Sanchez Page 7 of 8

8 where τ= NPSP ρ ω ( R ) ; Z in ϑ = + coϑ (6) and ϑ i he inducer leading edge blade angle, which, a deign condiion, i cloe τ = 3Z. Wih mall 0 o an and i ypically The daa lie cloe o he line angle approximaion for ϑ and, hi can be hown o be equivalen o σ= 3, inermediae beween Sangeland recommendaion [40] for LH and LOX. Wih he inducer diameer choen from he above crieria, he haf peed i limied [40] o a o keep he inducer ip peed below 70 m/ec (LOX) or 340 m/ec (LH). Thi i done in order o conrol caviaion in he blade-ip leakage vorex [40]. Thi peed limiaion may conflic wih he deire o place he ( r, d poin on a ) favorable po in he efficiency map. In ha cae, he NPSH mu be raied, eiher by parial preurizaion of he ank, or, a in he SSME, by he ue of eparae lowpreure booer pump. Thee are only rough guideline, and, he precie allowable limi depend upon deailed deign of he inducer. Progre in inducer deign ha been a pacing iem in allowing urbopump peed o increae, hu reducing weigh (a well a increaing life). Reference cied: 40. M. L. Joe Sangeland. Turbopump for Liquid Rocke Engine. Ninh Cliff Garre Turbomachinery Award Lecure, April 7, 99. SAE/SP-9/ Turbopump Syem for Liquid Rocke Engine, NASA SP-807, Aug Liquid Rocke Engine Turbine, NASA SP-80, Jan Liquid Rocke Engine Cenrifugal Flow Turbopump, NASA SP-809, Dec E.M. Greizer, The Sabiliy of Pumping Syem, ASME, Tranacion, Jl. of Fluid Engineering 03 (98), pp J.L.Kerrebrock, Aircraf Engine and Ga Turbine, MIT pre. 99 (Sec.5-7). 46. O.E. Balje, Turbomachine: A Guide o Deign, Selecion and Theory, J. Wiley & Son, New York, L.B. Sripling, Caviaion in Turbopump, p., Tran. ASME, Serie D, J. Of Baic Engineering (96): , Rocke Propulion Lecure 6 Prof. Manuel Marinez-Sanchez Page 8 of 8