• aerospace propulsion
• journal bearings
• mixed-flow impeller
• reduced-order model
• rocket engines
• splitter blades
• turbopumps

Turbopumps are the most weight-effective solution for liquid propellant feed systems of rocket engines for primary space propulsion. High power-density and affordable efficiency are required from these machines while still meeting their assigned specifications in flow rate, head, suction performance, and operational stability. In this dissertation, two reduced-order models are developed to design a turbopump mixed-flow impeller equipped with splitter blades and for the design of high-speed recessed journal bearings. Introducing the back-cut full blade called splitter blades in impeller could be a useful way to increase the pump performance with a negligible increase of its mass. Unfortunately, there are no established guidelines for splitter-blade design. To reduce cost, private companies and institutions have moved forward with reusing the entire propulsion system. To achieve this goal, replace the rolling bearings with lubricated journal bearings could represent a valuable way to increase bearing durability, reliability, maintainability, stiffness, rotordynamic damping, and extend shaft speed. Due to the high speed of the shaft and the low viscosity of lubricant liquid that coincides with the propellant itself, the bearing fluid film is manly turbulent. The turbulent flow must be considered to predict the bearing reaction and possible fluid cavitation in the bearing land. Moreover, the turbulent fluid film represents a challenge in the reduced-order modeling.
The key to reduced-order modeling is making assumptions and approximations such that the problem, although the simplifications, does not lose the relevant physics driving it. In this way, it is possible to obtain preliminary analytical results still handling the main physical phenomena. Therefore, the use of a reduced-order model capable of rapidly providing information on the pump geometry, performance, and flow field at an affordable computational cost is highly desirable. However, there is a lack of examples in the literature of fully-3D analytical models suitable for designing space propulsion turbopumps.
The reduced-order model of the mixed-flow impeller extends a model developed by professor d’Agostino and his colleagues. The model describes the velocity field of the impeller as the superposition of a 2D axial vorticity correction (slip flow) to a fully-guided forced-vortex flow. Then, integration of the turbulent boundary layers along the blade channels estimates the viscous effects (flow blockage, head losses, deviation, and other losses). In a series of water experiments under non-cavitating conditions, the model proved capable of successfully predicting the design pump performance of a reference machine called VAMPIRE.
The main research activities related to splitter blades are focused on the centrifugal impeller, and, on the other hand, there are no studies about the mixed flow impeller. Based on the state of the literature review performed in this work, no design guidelines have been drawn yet. Therefore, the lack of general design guidelines for selecting the best circumferential position and length of splitter blades could increase the turbomachinery design time. Thus, the present study aims to study the effects of splitter-blade length and circumferential position on impeller performance through a reduced-order model and numerical simulations. However, a fully deterministic analysis with two independent geometrical input parameters would imply a high computational cost. To overcome this limitation, in recent years, stochastic computational-fluid-dynamics approaches have been widely used. The reduced-order model with splitter blades has a pump-performance parabolic trend by changing both design parameters of splitter blades when introduced in the VAMPIRE impeller. These results applied to the polynomial chaos method led to selecting nine splitter-blade configurations for each design flow rate simulated. The obtained numerical simulation and reduced-order model results point out that adding splitters to the reference 6-impeller geometry reduces the pump performance. However, in addition to the innovative research method, this work reports that splitter blades and their geometry affect the impeller inlet flow leading to different stall blade scenarios. At the design flow rate, the impeller configuration with longer splitter blades reaches the higher head coefficient.
In contrast, at 80% and 120% of the design flow rate, a shorter splitter blade leads the alternate stall to a more symmetric configuration ensuring, for this reason, a mid-length splitter blade higher head coefficient. The splitter-blade length is the design parameter that mostly influences the interaction of the back-cut blades with the full-blade stall. On the other hand, the numerical simulation and reduced-order model confirm that the splitter-blade circumferential position is the design parameter that affects the head coefficient.
With his colleagues during the European Space Agency project “Long Life Journal Bearings for Turbopumps,” the author developed several reduced-order models for recessed journal bearings. In this work, one of these models is presented and modified to introduce the turbulent effects. Moreover, a finite difference model was developed to obtain a robust design tool for assessing journal bearing performance. After comparing experimental data found in the literature, the finite-difference model confirms a good accuracy for the bearing mass flow rate and reaction predictions as a function of shaft speed and eccentricity. On the other hand, the reduced-order model overpredicts the bearing mass flow rate and underpredicts the bearing reaction. Finally, a promising bearing geometry is proposed to be tested in the high-speed-journal-bearing test facility currently under development at the University of Pisa. This geometry should ensure the journal-bearing requirements for a liquid methane turbopump.