28TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES
INTGRATED DESIGN METHOD OF A ROCKET ENGINE TURBOPUMP SUB-SYSTEM FOR SUPPRESSING ROTOR LATERAL VIBRATION
Masaharu Uchiumi*, Mitsuru Shimagaki*, Satoshi Kawasaki*, Yoshiki Yoshida* and Kazuhiko Adachi** *Japan Aerospace Exploration Agency, **Kobe University [email protected]; [email protected]
Keywords: Turbopump, Rotor Lateral Vibration, Rotordynamics, Design of Morphology
Abstract is generally considered that the rotor vibration characteristic depends on the bearing A rocket turbopump is the high-speed and high- characteristics sustaining the rotor, which is power turbomachinery that raise the pressure of especially dominant in the case of stiffness of cryogenic fluid to higher than the combustion ball bearing. However, in order to meet the chamber pressure. Various rotor vibration demands of the high efficiency and performance problems had occurred caused by rotation in the for the rocket turbopump, the clearance between development phase of the turbopumps for the the rotating part and stationary part is very Japanese rocket engines. In order to suppress narrow. Therefore, it is required consideration of the rotor instability vibrations, rotordynamic how the small clearance area will affect the rotor. fluid forces induced by the turbomachinery Rotordynamic fluid forces (hereafter components should be taken account in the termed “RD fluid forces”) with a frequency rotordynamics analysis. The design method is a dependence, which are generated in wetted or kind of multi-disciplinary optimum design and is gas surface areas (i.e., such as an impeller, an formed in two steps. inducer, a shaft seal, a balance piston), have a This paper presents a new the integrated large effect on rotor vibration. Especially, design method concept developed to provide tangential fluid force which foster a good stability for rotor lateral vibration while destabilizing action, may lead to self-excited rotating at all operation range. vibration (destabilizing vibration). Establishment of an integrated design method consisting of three turbopump sub- 1 Introduction systems, i.e., a pump system, a turbine system A rocket turbopump is often described the heart and a rotor system, is expected to suppress rotor of an engine as an indication of its importance. vibration. The design method consists of As a human heart pumps blood through the body, “multidisciplinary optimum design” and “design a turbopump feeds high-pressure propellant to of morphology” considering RD fluid forces the combustion chamber. The rocket turbopump and rotordynamics. This paper presents a is high-speed, high-power turbomachinery. In concept of the new integrated design method the development phase of the turbopumps for which is developed to provide stability for rotor Japanese rocket engines, various rotor vibration lateral vibration in the whole operational range. problems caused by the increase in energy density have occurred [1-3]. Such problems are 2 Dynamics Design for Turbopumps the result of the interaction between excitation and damping, and remain unresolved without reference to dynamics, e.g., the frequency 2.1 Rotordynamic Fluid Forces and characteristic, the axial mode shape and so on. It Rotordynamics
1 Masaharu Uchiumi, Mitsuru Shimagaki
A cross section of a hydrogen turbopump for a the tangential direction (Ft) and the radial LE-7 engine is shown in Fig. 1. The sources of direction (F n ) as shown in Fig. 3. The RD fluid force acting on the rotor exist at destabilizing action is strongly affected by the locations where the inducer, the impeller, the tangential fluid force with the same whirling seals, the bearings and the turbine have small direction as the rotor spin direction, and is clearance area filled with fluid. Typical fluid generated at each small clearance area in the forces which should be considered in turbopump. It has a negative effect on the rotordynamics analysis are as follows. damping ratio of the rotor system. The damping 1. Mechanical excitation force caused by ratio is the real part of the complex eigenvalue residual mass unbalance or misalignment. given by the rotordynamics analysis. Occurrence 2. Fluid-dynamic unbalance force. of the self-excited vibration is decided by the 3. Bearing reaction force. damping ratio of the rotor system (i.e. in case of 4. Internal damping into rotors (negative negative for the real part, the system is stable). damping at over-critical speed). Therefore, it is necessary to individually obtain 5. Destabilizing force caused by shaft seals. the RD fluid forces of major components and the 6. RD fluid force due to impellers. elements which are sensitive for swirl. 7. Fluid force caused by cavitation and When the rotordynamics analysis is carried out rotating stall. f 8. Unbalance torque caused by axial turbines. f f f Typical RD fluid forces acting on the rotor for a rocket turbopump are shown in Fig. 2. M is K K additional mass matrix, K is stiffness matrix, C M C C M M M is damping matrix and f represents RD fluid K M K K K C K force. Each matrix is used for the linearly C C C expressed RD fluid forces. The matrix of each C element consists of direct action and cross- Fig. 2 Rotordynamic fluid forces acting on a coupled action by a diagonal term and a non- rotor. diagonal term respectively. Most of the rotorvibrations induced by the action of the fluid forces is self-excited vibration. So the state of the vibration is decided by the stability of the rotor. This vibration occurs at each natural Casing center Ft frequency of fluid phenomena [4] and at a wider range of rotational speed than the resonance Shaft center frequency. RD fluid forces are decomposed in F Sealing elements Inducer, Impellers and Turbine n
Rotordynamic force effect at 0
Fn 0 ： inertia effect
Fn 0 ： restoring effect
Ft 0 ： destabilizing effect F 0 ： damping effect t
Fig. 3 Schematic of the RD fluid forces acting Bearings on an impeller whirling in a circular orbit. Fig. 1 LE-7 Fuel turbopump
2 INTGRATED DESIGN METHOD OF A ROCKET ENGINE TURBOPUMP SUB-SYSTEM FOR SUPPRESSING ROTOR LATERAL VIBRATION by using the finite element modeling, the rotor decompose the RD fluid forces into additional behavior can be expressed by the equation of mass, damping and stiffness matrices according motion as follows. to:
n m m 2 Fn Ft x R xx xy x R m ij x j (t ) c ij x j (t ) k ij x j (t ) f i (t ) m m 2 j 1 Ft Fn y R xy xx y R (i 1, 2, , n) (1) cxx cxy x R cxy cxx y R where mij is the mass coefficient, cij is the damping coefficient, k is the stiffness k xx k xy x R ij coefficient between the nodes i and j, f (t) is the k k y R i xy xx (6) excitation force. And x‥( t), x･ (t), x (t), n are the i i i displacement, velocity, acceleration for “i” and Equation (6) means the RD fluid forces can the number of node respectively. These are be expressed as quadratic function of whirl ratio expressed by using matrices as follows: “/”. Thus the non-dimensional RD fluid
forces are written by: [m ] = M, [c ] = C, [k ] = K (2) ij ij ij 2 If the displacement depends on linear fn = mxx(/) – cxy(/) – kxx (7) vibration system, the following equalities are 2 true. ft = – myy(/) – cxx(/) + kxy (8)
[M] = [M]T, [C] = [C]T, [K] = [K]T (3) According to the expressions (7) and (8), the RD fluid forces are dealt with as six where exponent T means transposed matrix. By rotordynamics coefficients for the using the relational expressions (4), the equation rotordynamics analysis, therefore the effect of of motion (1) is easily stated as equation (5): the RD fluid forces on the rotor vibration can be estimated. As an example, well-known rotordynamic expressions of unbalanced torque n n force (Thomas force) acting on a rocket turbine x j (t) x(t) , f j (t) F(t) (4) j1 j1 is described below. Thomas force is explained by the [M]{x(t)}+[C]{x(t)}+[K]{x(t)} = {F(t)} (5) unbalanced torque which results from the different leakage at the clearance between the On the other hand, RD fluid forces which act tip of the turbine and the casing. This force acts on the mechanical element of the turbopump are as the destabilizing action which decreases the expressed by the linearized rotordynamics damping ratio of the rotor system. Thomas model is used for turbine-rotordynamic- coefficient (i.e., mxx and mxy are additional mass coefficient calculation as follows. coefficients, cxx and cxy are the damping coefficients, and k and k are stiffness xx xy T T T coefficients). Also, RD fluid forces in the 0 1 0 Ft 1 cos cos rotordynamic analysis are entered as matrices R T0 into the node corresponding to the locations 2 1 T T T acting on the RD fluid forces. In case of the 0 1 1 0 cos cos d 0 rotor is whirling at the condition of a circular 2 R T0 whirl motion of eccentricity and whirl angular Ttotal T1 T0 velocity , so that displacement x(t) = cost 2R T0 and y(t) = sint, it is conventional to (9)
3 Masaharu Uchiumi, Mitsuru Shimagaki
where R is the turbine radius, T0 is torque at the We JAXA are now studying the above- mean clearance, T1 is torque at the maximum mentioned optimization method. It is the design clearance, Ttotal is the entire torque of the turbine, method of optimal rotor system by using and = t. Furthermore the cross-coupled multidisciplinary optimization due to integration stiffness coefficient definition is: of the subsystems of the turbopump (e.g. pump, turbine and rotor). Herein, the each subsystem Kxy = T β／Dm L (10) is discussed as a discipline. Because the rotor vibration is the result of the interaction between Where β is defined as “the change in excitation and damping, knowledge and insight thermodynamic efficiency per unit of rotor obtained by the "Dynamics" point of view are displacement”, Dm is the mean blade diameter, L essential. Therefore, this design method is is the turbine blade height, T is the torque. As approached by “Dynamics”, and its key words explained above, Thomas force is expressed as are “Dynamics design”, “Multidisciplinary the cross-coupled stiffness, therefore only the optimal design” and “Design of morphology”. destabilizing action is generated. (1) The dynamics design This design takes the motion and the response 2.2 Multidisciplinary Optimal Design and (e.g., the unsteadiness, the disturbance, the Design of Morphology [5] mutual interference and the stability) into For realizing a next generation flagship launch consideration, that is, the phenomena of time vehicle, a manned launch vehicle and a reusable and frequency domains are focused. In contrast, space transportation system, higher reliability, “static design” is the method of focusing higher robustness, higher energy density, and performance, efficiency, constant and non- longer operating life for the rocket engines will interactive phenomena. be more and more required. In order to figure out appropriate solutions for a wide variety of (2) Multidisciplinary optimal design requirements from the rocket engine system, The optimal solution for the rotor system is largeness and depth of the design flexibility and pursued to stabilize the rotor at the upper level expandability of the turbopumps is very hierarchy. The dynamics characteristics, e.g., important. Although the shortage of RD coefficient, from each rotational element at performance and efficiency of the turbopump the lower level are input into the upper level decreases a rocket engine power and hierarchy. The subsystems are designed and also performance, it doesn't result in the catastrophic optimized to increase stability at a discrete area. failure and functional damage. However, rotor vibration of the turbopump may cause the (3) Design of morphology functional failures of the rocket engine and “Morphology design” method does not pursue eventually mission failure. Therefore, it is not each element shape such as the detailed blade too much to say that one factor which threatens profile, but determines the location and/or the the reliability of rocket engines and launchers is layout and/or permutation of the subsystems as rotor vibration in the turbopump. Thus, the the system form first. design flexibility of the rotordynamics in the turbopump has a possibility of becoming a The selection of the rotor form (layout, primary constraint condition during the permutation of the rotating elements) is located development of a future rocket engine. Now the as the upper level hierarchy in the design inverse design method and the multi-objective optimization problem. The optimization of each optimization are applicable as a useful tool for the pump subsystem, the turbine subsystem and designing the blade profiles, establishing the rotor subsystem which includes seals and “design of morphology” optimization technique bearings are located as the lower level hierarchy. of the rotor system is eagerly expected in the While each subsystem is optimized according to purpose of suppressing rotor vibration. some independent objective functions in the 4 INTGRATED DESIGN METHOD OF A ROCKET ENGINE TURBOPUMP SUB-SYSTEM FOR SUPPRESSING ROTOR LATERAL VIBRATION lower level hierarchy, matching between the subsystem. The obtained each rough size upper and the lower level hierarchies must be information and data of the RD fluid force adjusted. In parallel, the rotor form is optimized estimated by the rough size are taken in the in the upper level hierarchy. So, changing from platform to control the optimization system and the conventional design method, in which the programs. Also, the platform administers data fluid performance is the first priority, to the from each subsystem and manages the interfaces improved design method, in which the rotor between the subsystems. The optimized rotor stability is the first priority, makes the reliability forms given by integration of the elements are and robustness of turbopump higher. finally obtained from the complex eigenvalue The design flow concept of the improved analysis of the rotordynamics program [6]. In design method is shown in Fig. 4. This process the first step, the unique technique is adopted to for achieving to the optimized design solution is get the appropriate solution within a suitable divided into two steps. time. Table.1 shows the samples of the selection The first step is the important process for rules used in the morphology design process. In figuring out some initial optimal forms as shown this task, improbable forms as the turbopumps at the left side in Fig. 4. After the turbopump is are screened by the rules of morphology design. given the required design specifications from the The second step is the optimization process engine system, rough physical size of the for determining the distance from the axial front mechanical elements with the discrete rotational edge to each elements and shaft diameter at each speed parameter are calculated for each element with regard to some excellent solutions
STEP:1 DesignDesign of of form morphology STEP2: Design of physical constitution START Selection of the layout, element permutation Selection of detailed diameter and length for the elements
Design parameter Models of each element Matching between Subsystems optimizations
・Subsystems ・System and subsystem
Inducer Impeller Turbine
RD fluid forces
Required design spec. spec. Required design Bearing Rotating-shaft seal Rough physical size Selected solutions by step1Selected by solutions
“DesignMorphology of form” optimization optimization ex. Internal flow network Axial thrust, ・・・ Optimized by ・Selection rules “Shaft geometry” optimization ・Constraints Optimized by ・Object functions ・Stabilities ・Natural frequencies ・Weight ・・・, etc
etc. Complex eigenvalue analyses Various layouts and permutations Superior No Solutions Yes Yes Solution END Another solution No
Fig. 4 Concept of the dynamic design.
5 Masaharu Uchiumi, Mitsuru Shimagaki
Table.1 Selection rules for morphology design.
No. The selection rules for the form design Reasons In case of bilateral symmetry for two permutations, one of two is Avoid of geometric multiple. 1 calculated. In case of two pairs of bearings adjoins, a spacer is located at Meaningless alignments. 2 between two pairs. There is a pair of bearings or nothing at between a inducer and first Avoid of a complicated flow path. 3 impeller. Another element cannot locate at there. 4 A seal is not located at a end of a shaft. Meaningless alignments. 5-1 A turbine is located on right hand of a seal. Avoid of a complicated structure. An inducer, first impeller and second impeller are located on left hand Constraint of shaft length. 5-2 of a seal. 5-3 A seal orientation is remained unchanged by roles (5-1) and (5-2). Meaningless alignments. No.2 bearings (a pair of bearings) is located on right hand of No.1 Avoid of geometric multiple. 6 bearings (a pair of bearings). 7 Flow direction of an inducer, No.1 impeller and No.2 impeller are Avoid of a complicated flow path. No.1 impellor is located at downstream of an inducer. No.2 impeller is Avoid of a complicated flow path. 8 located downstream of No.1 impeller. 9 In case of a seal is located at downstream of No.2 impeller, 9-1 ⇒a spacer is located at between a No.2 impeller and seal. Keep a depressurization area. ⇒when No.2 impeller, No.1 bearings and No.2 bearings form a line, a Meaningless alignments. 9-2 spacer is located between No.1 and No.2 bearings. ⇒when No.2 impeller, No.1 bearing and a seal form a line, a spacer is Keep a depressurization area. 9-3 located downstream of No.1 bearings. ⇒when No.2 impeller, No.2 bearings and a seal form a line, a spacer is Keep a depressurization area. 9-4 located upstream of No.2 bearings. In case of a top of inducer face in a turbine, a spacer is located ahead Avoid of a complicated flow path and structure. 10 of a top of inducer. In case of No.1 and No2. impeller adjoin, a spacer is located between Avoid of a complicated flow path and structure. 11 impellers. obtained by the first step. In this step, an the constraints, the performance indexes and the example of the performance indexes are the real design parameters. While solving the part (stability) and the imaginary part (natural optimization problem for the layout and frequencies) of the complex eigenvalue analysis permutation of the elements, the sizes of the in the rotordynamics program. rotating elements are fixed. Also in contrast, The optimization in the first step is given a while solving the optimum problem for the rotor variety of equality constraints and inequality geometry and shape (shaft diameter and distance constraints from the subsystems. For example, from the front edge to the elements), the layout these are the upper limit of the DN value for the and permutation of the elements are fixed. The bearings, the upper limit of the differential optimization of the shapes such as the blade pressure of the shaft seals, the shaft power of the profile etc., in the subsystems will be carried out turbines (equality constraint), the upper limit of by using an inverse design method or the multi- the tip-circumferential velocity of the impellers objective optimization under the given and the turbines, the criterion apart from the constraints after the completion of the critical speeds, the upper limit of the whirl optimization as the rotor system by the amplitude at each node corresponding to the morphology design method. mode shape, and so on. Therefore, the most important thing for the development of the 3 Conclusion morphology design method will be how to set
6 INTGRATED DESIGN METHOD OF A ROCKET ENGINE TURBOPUMP SUB-SYSTEM FOR SUPPRESSING ROTOR LATERAL VIBRATION
New concept regarding the morphology design give permission, or have obtained permission from the method for suppressing the rotor lateral copyright holder of this paper, for the publication and distribution of this paper as part of the ICAS2012 vibration for the rocket engine turbopumps is proceedings or as individual off-prints from the presented in this paper. This design method proceedings. takes into account the RD fluid force generated from the rotating elements. Although it is not easy to obtain data of the RD forces by CFD or EFD, but need of the fluid forces will be higher with the increase in the energy density of the turbomachinery. In addition, in order to suppress rotor vibration, deep knowledge and insight about the RD fluid forces and rotordynamics is needed. The rotor vibration problem for the rocket engine turbopumps is directly related to the reliability of rocket engines, therefore the development of this design method is expected strongly and widely.
References
[1] Motoi, H., Kitamura, A., Sakazume, N., Uchiumi, M., Uchida, M., Sakai, K., Nozaki, M., and Iwatsubo, T., Sub-synchronous Whirl in the LE-7A Rocket Engine Fuel Turbopump, ISORMA-2, Gdansk, 2003. [2] Yamada, H., and Uchiumi, M., Flow-Induced Vibrations of Rocket Turbopumps (in Japanese), Turbomachinery Society of Japan, Vol.36 (2), 2008, pp. 67-73. [3] Okayasu. A., Ohta. T., Azuma. T., Fujita. T, and Aoki. H., Vibration Problem in the LE-7 LH2 Turbopump, AIAA/SAE/ASME/ASEE 26th Joint Propulsion Conference, Orlando, 1990. [4] Eguchi, M., Vibrations of Centrifugal Pumps -Flow Phenomena and Rotordynamics-, (in Japanese), EBARA JIHOU, No.221, Vol.10, 2008. [5] Uchiumi, M., Yoshida, Y., and Iwatsubo, T., Dynamics Design for Suppression of Rotor Whirl on Rocket Turbopumps (in Japanese), Proceedings of the 51st Conference on Aerocraft Engine and Space Propulsion, JSASS-2011-0007, Hiroshima, 2011. [6] Adachi, K., Uchiumi, M., and Inoue, T., Linear Vibration Modeling for Formed design of Rocket Turbopump (in Japanese), Proceedings of 66th Conference on Turbomachinery, Turbomachinery Society of Japan, Miyazaki 2011-9, pp.291-296.
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