Lecture 26: Turbopumps

16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 26: Turbopumps Turbopump Components The mechanical components of the pressurization cycle (pumps and turbines) are next to be considered. An excellent recent survey of this area is given in Ref.40. A more comprehensive, but older survey is contained in a series of NASA SP reports [41-43]. Pumps and turbines will first be discussed separately, and their integration will then be examined. (a) Pumps Almost all existing rockets have centrifugal turbopumps. These deliver more ∆ P per stage than axial flow pumps, with only slightly less efficiency. Only if multistaging becomes necessary is there a possible incentive to go to axial pumps; this happens with LH2 fuel, where, due to the low density, the ∆ P per stage is limited by the attainable rim speeds. In general, the design attempts to maximize operating speed, since this reduces the pump size, and hence the weight. Pump speed is limited by several effects, most importantly cavitation at inlet. Others are centrifugal stresses (either at the impeller or in the driving turbine), limiting peripheral speeds for bearing and seals, and avoidance of critical speeds. “Head rise” is used commonly instead of pressure rise to express the performance of pumps. We can define head rise as the height to which one could raise one Kg of fluid with the amount of ideal work per Kg done by the pump: H = ∆hs / g = ∫ P2 P1 dp ρg (1) The rise is directly related to the pump work, even if the fluid has significant compressibility: Work/mass= ∆h = gH ηp (2) and this is one of the advantages of its use. Obviously, if ρ = const., H= ∆P , ρg Work ∆P = mass ρ ηp (3) The head rise is directly to the peripheral speed of the impeller disk. The fluid enters axially near they impeller hub, with no angular momentum; it leaves the impeller with absolute tangential speed ωR2 – Vr2 tan β2, where β2 is the back-leaning blade angle at the rim Fig 1, and Vr2 is the fluid radial exit velocity, related to the volume flow rate as Q = 2πR2b2 Vr2 (4) The torque needed to drive the impeller is the net outflow rate of angular momentum, and the work rate is this, times ω. Thus, i ⎞ V 2 ⎛ Power = m ( ωR 2 ) ⎜1 − r2 tan β2 ⎟ ωR 2 ⎝ ⎠ i and since we also have Power = m ( ωR 2 ) 2 H = ηp g (5) gH , the head rise is ηp ⎛ ⎞ Vr2 tan β2 ⎟ ⎜1 − ωR 2 ⎝ ⎠ (6) ⎛ ⎞ V The quantity ψ = ηp ⎜1 − r2 tan β2 ⎟ is sometimes called the “head coefficient.” In R ω 2 ⎝ ⎠ terms of ψ , ( ωR2 ) 2 H=ψ (7) g ψ is typically between 0.2 and 0.8. Values greater than unity could be obtained if the blades were designed to learn forward ( β2 < 0 ), but then ∆ P would increase with Q (through the effect of Vr2). This positive slope of the ∆ P vs. Q characteristic is known to produce instabilities in the pumping system [44]. These are generally dynamic in nature, and depend to some extent on the characteristics of the rest of the system (free volume, throttling effects, etc), but it is relatively easy to understand their origin from a quasistatic argument: if the pump temporarily delivers more flow than can be disposed of in steady state by the downstream components, ∂ ( ∆P ) and if its characteristic has a positive slope , the pump pressure rise will also ∂Q be higher than normal. The downstream pressure will therefore tend to increase for both reasons, and a runaway situation ensues. In addition to this system instability, there is also a tendency for flow maldistribution analogous to rotating stall, since the flow is then unstable with respect to mass interchange between parallel streamtubes [45]. Eq. (6) would predict a linear dependence of head on flow rate. In reality varying the flow at a given speed will vary the internal flow angles with respect to blades, and will therefore result in variations of the slope ∂ H ∂ Q . Examples of this behavior are shown in Fig 2 (Ref. 41), where the flow coefficient is defined as ∅2 = Q 2π R2 b2 ( ωR 2 ) (8) The throttling range is defined by the point of maximum head, below which operation is unstable. Similar (but stronger) restrictions apply to axial designs, such as that used in the J-2 LH pump, and so these designs tend to be limited to applications which require very limited throttling. The pump is designed to specified head rise H or ( ∆ P) and volumetric flow Q. These quantities can be used to construct the non dimensional quantities called specific diameter and specific speed: 1 ds = D(gH) Q 1 1 ns = ωQ 4 (9) 2 2 (10) 3 ( gH) 4 In the U.S. literature, D is expressed in feet, Q in gpm and ω in rpm, and g is omitted. This procedure, of questionable practically, result in related parameters Ds, Ns given By Ns= 2728 ns, Ds = 0.01985ds. Notice that ns ds = ωD 1 ( gH) 2 (11) and hence, from (7), nsds = 2 ψ (12) or, in English units, NsDs = 108.3 ψ . Since for centrifugal pumps, we found ψ <1, we can see that their domain is a ( ns , ds ) map is ns ds >2 (or NsDs > 108 ). The considerable empirical evidence on pump performance has been distilled (Ref.46) by constructing ( ns , ds ) maps on which favorable regions are shown for various types of machine. A very generalized example (taken from Ref. 41) is shown in Fig. 3, where lines of constant peak efficiency are shown for a wide variety of pumps. These use a set of clearance, tolerance, roughness, etc. factors, and are to be taken only as indicative, since actual design may depart from adopted values. We notice in Fig. 3 the line Ns Ds ∼ 100 , denoted as the “limit for dynamic pumps”, in accordance to our discussion above. Radial and axial pump designs nearly merge, although the axial type is indicated for the highest specific speed, which as Eq. 10 shows, may be simply a reflection of low head rise, as for example, in the inducer stages featured commonly at the inlet of centrifugal pumps for cavitation suppression. Table 1 gives the features of the high pressure SSME pumps, and the resulting ( Ns , Ds ) points are included in Fig 3, where they are seen to lie roughly on the η = 0.8 line. The pumps must be designed so as to avoid cavitation, which both, degrades performance, and causes damage to reusable articles. Cavitation risk exists at the pump inlet, where the liquid pressure is lowest, and it increases with both, the fluid velocity and the speed of the pump inducer blades meeting the fluid. The inducer 1 diameter needs to be large enough to reduce the inlet fluid dynamic head ρ C m2 to 2 some fraction of the excess inlet pressure over saturation P1-Psat, 1. This last quantity is called the Net Positive Suction Pressure (NPSP), and is usually given as a suction head NPSH= NPS/(ρg) . ∆ P (N/m2) H (m) Q (m3/sec) ω (rad/sec) D (m) ns (Ns) ds (Ds) Hydrogen Pump Oxygen Pump 1.38 × 107 (per stage) 20,000 0.96 3674 0.308 0.386 (1050) 6.61 (0.0131) 3.30 × 107 2,930 0.229 (per side) 3246 0.16 0.703 (1920) 435 (0.0866) Table 1. Characteristics of the SSME high-pressure fuel and oxidizer pumps The ratio: σ= ( NPSP ) 1 2 ρ Cm 2 = ( NPSP ) 2 / 2g Cm (13) is called the Thoma parameter, and empirical evidence [40,41] indicates that it should be grater than 1 for LH, 2 for LOX and 3 for water and storable propellants. The more favorable situation for hydrogen appears to be related to a greater vapor suppression effect due to evaporate chilling when bubbles start to form. Several other parametric representations of cavitation data exist. Thus, Refs [40] and [41] use a “suction specific speed” Ss defined as in Eq (10), but with H replaced by the NPSH, and with correction for flow blockage by the hub. This parameter can be shown to be related to Thoma’s parameter σ and to ∅t = cm / ωR1 (R1= inducer radius) by Ss = 2.981 3 σ 4 ∅t (14) In English units, the numerical factor is 8132. The data on cavitations onset for a variety of liquids show that σ remains approximately constant for each, as noted above. Independently, Ref. 47 shows cavitations results in the form τ = f (Zt ) (15) where τ= NPSP 2 1 ρ ( ωR1 ) 2 ; Zt = sin ϑ ∅t 1 + cos ϑ (16) and ϑ is the inducer leading edge blade angle, which, at design conditions, is close to tan−1 ∅t and is typically 50 − 100 . The data lies close to the line τ = 3Zt . With small angle approximations for ϑ and ∅t , this can be shown to be equivalent to σ = 3 2 , intermediate between Stangeland’s recommendations [40] for LH and LOX. With the inducer diameter chosen from the above criteria, the shaft speed is limited [40] so as to keep the inducer tip speed below 170 m/sec (LOX) or 340 m/sec (LH). This is done in order to control cavitation in the blade-tip leakage vortex [40]. This speed limitation may conflict with the desire to place the (rs , ds ) point on a favorable spot in the efficiency maps. In that case, the NPSH must be raised, either by partial pressurization of the tanks, or, as in the SSME, by the use of separate lowpressure booster pumps. These are only rough guidelines, and, the precise allowable limits depend upon detailed design of the inducer. Progress in inducer design has been a pacing item in allowing turbopump speed to increase, thus reducing weight (as well as increasing life). References cited: 40. M. L. Joe Stangeland. “Turbopumps for Liquid Rockets Engines”. Ninth Cliff Garrett Turbomachinery’ Award Lecture, April 7, 1992. SAE/SP-92/924. 41. Turbopump Systems for Liquid Rocket Engines, NASA SP-8107, Aug. 1974. 42. Liquid Rocket Engine Turbines, NASA SP-8110, Jan 1974. 43. Liquid Rocket Engines Centrifugal Flow Turbopumps, NASA SP-8109, Dec. 1973. 44. E.M. Greitzer, “The Stability of Pumping Systems”, ASME, Transactions, Jl. of Fluids Engineering 103 (1981), pp.193-242. 45. J.L.Kerrebrock, Aircraft Engines and Gas Turbines, MIT press. 1992 (Sec.57). 46. O.E. Balje, Turbomachines: A Guide to Design, Selection and Theory, J. Wiley & Sons, New York, 1981. 47. L.B. Stripling, “Cavitation in Turbopumps”, pt. 2, Trans. ASME, Series D, J. Of Basic Engineering (1962): 339.