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Chapter 1
1.
INTRODUCTION
In space transportation systems, turbopumps are crucial components of all primary propulsion concepts based on liquid propellant rocket engines. In this context dynamic stability considerations often impose limitations that can prevent from reaching the extreme suction and pumping performance needed in high power density systems. In these components, a minor gain in efficiency and performance will affect the entire engine. As a consequence of a displacement of the rotation axis, fluid induced rotordynamic forces arise, leading to a secondary motion of the shaft axis here referred as whirl motion. This precession of the shaft can be both unstable or stable depending on the direction of the rotordynamic force with respect to the whirl orbit characteristics. Rotordynamic forces and flow instabilities, along with cavitation phenomena, are of great concern in turbopumps for space applications. Their most dangerous effect consists in the development of vibrations that can lead to unwanted behavior of the flow, producing additional unsteady forces that can adversely affect the impeller, the bearings, and the seals. Up to date the investigation on rotordynamic forces acting on centrifugal pump impellers has been extensively studied, whereas the effect of cavitation on these forces is not yet well understood. Experimental campaigns focused on the investigation of rotordynamic forces on cavitating inducers and centrifugal turbopump impellers have been mainly carried out at the California Institute of Technology, Pasadena, California, USA, by Bhattacharyya and by the Chemical Propulsion Team at Alta, Pisa, Italy. The most critical aspect of rotordynamic instability is the inception of a self-sustained lateral whirl motions of the impeller as a consequence of fluid induced forces resulting from the interaction of axial misalignments due to elastic deformations, mounting errors, degrading structure, etc.. The combined effects of this motion with cavitation creates additional forces that should be taken into account in the design of a turbopumps for space applications, as they significantly affect the critical speeds of the machine. Given the importance of the topic, Alta’s Cavitating Pump Rotordynamic Test Facility (CPRTF), originally set-up under ASI (Italian Space Agency) and ESA (European Space Agency) funding, is one of the few experimental test benches in the world and the first openly documented facility in Europe capable of carrying out the direct measurement of the unsteady rotordynamic fluid forces on cavitating or noncavitating turbopump impellers. Recently, an ESA-sponsored experimental campaign has been carried in this facility on a three bladed, tapered-hub, variable-pitch inducer entirely designed by means of a reduced order model previously developed at Alta. The aim of this campaign has been the investigation of the effects of cavitation, flow rate, and flow temperature on the rotordynamic forces acting on the impeller as a consequence of an imposed whirl motion with constant eccentricity and angular velocity. In this
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chapter the basis about the most important aspects about cavitating turbopumps and rotordynamics will be presented.
1.1.
CAVITATION
“The word cavitation refers to the formation of vapor bubbles in regions of low pressure within the flow field of a liquid”. The result of this phenomena is the same as the boiling, except that the latter is an effect of a temperature increase whereas the former is a result of a pressure decrease.
Figure 1.1 Typical phase diagrams. Brennen [2]
In boiling process it is virtually impossible to transfer heat to the liquid uniformly but what happens is that the temperature increases at the boundary, where a solid wall is present, and the heat is transported away by convection. This situation usually takes place in a pot in which the hot and less-dense water on the bottom layer moves upwards, and the cool and more less-dense water near the top moves to the bottom.
On the other hand a uniform and rapid change in liquid pressure is possible and is commonplace. Looking at the phase change diagram (Figure 1.1), when a pure liquid at the state A is depressurized at constant temperature two different scenario can occur if the pressure is reduced below that of point B (saturated liquid pressure). If sufficient numbers of nucleation sites are present, the liquid undergoes the transition to vapor following the straight line from B to C. Otherwise, if there aren’t any nucleation sites a certain metastable state D can be reached. The pressure difference between B and D is the magnitude of tension at which D is.
Therefore a liquid subjected to a decreasing pressure, p, which falls below the saturated vapor pressure, pv, will have a tension of ∆p = (pv-p). When the tensile strength of the liquid, ∆pC, is reached,
rupture occurs and vapor bubbles occurs which will present an interface with a certain surface tension. This process is usually malevolent and dangerous for the correct operation of the turbomachine. The deleterious consequences can be divided in three categories.
First of all it can cause a damage of the surfaces in contact with the collapsing bubbles that are created during the process as they are convected into regions of higher pressure (see Figure 1.2 and Figure 1.3). Since it is practically impossible to eliminate the effect of cavitation, the efforts must be redirected in minimizing its effects beforehand. In Figure 1.4 it can be seen the damages presented by
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a turbine operating in presence of cavitation. The second effect of cavitation is the degradation of the turbomachine performance. In pumps, there is a level of inlet pressure that leads to cavitation breakdown at which the performance will decline dramatically. To optimize the performance in cavitating conditions, an inducer is usually adopted upstream of the main impeller in order to pressurize the flow in such a way that the centrifugal impeller will not operate under cavitating condition, whereas the inducer operates under controlled cavitation.. The third adverse effect is due to the fact that it affects also the dynamic response of the flow and leads to instabilities (rotating cavitation, auto-oscillation, etc.) that can give rise to oscillating flow rates and pressure.
Figure 1.2 Tip vortex cavitation. Brennen [2]
Figure 1.3 Photographs of bubble collapse. A. Ellis [4]
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Two different forms of nucleation can typically occur. The homogeneous nucleation is the process in which the thermal motions within the liquid tend to form microscopic voids that can constitute the nuclei. However the major weaknesses occur at the boundary of the solid wall or at small particles suspended in the liquid. In the latter case it is termed heterogeneous nucleation and it is commoner to find it in practical engineering situations.
1.2.
TYPES OF CAVITATION
When the density of cavitation becomes large, the cavitating bubbles may start to interact each other in a significant manner. Indeed an increasingly amount of bubble in a region can alter the environment in such a way that an increasingly smaller nuclei may be activated.
Different type of cavitation may be observed and it is useful to divide them in an arbitrary classification, bearing in mind that different forms may occur which not fall within this classification system. In Figure 1.5 it is possible to notice some of the forms of cavitation that can occur in an unshrouded axial flow impeller.
In many practical situations the first large-scale structure observed, as the pressure is lowered, is the vortex cavitation. It is commonplace that a flow present a region of concentrated vorticity where the pressure in the core is significantly smaller than in the peripheral flow. This is what happens, for example, in a swirling flow. Therefore cavitation inception often takes place in these vortices and the entire core may be filled with vapor. This type of cavitation can occur at the tip vortex of the impeller’s blades and it can create a stable flow structure with a continuous tip vortex cavity that can persist for a long distance downstream of the propeller, as shown in Figure 1.2. The tip vortex cavitation occurs as a consequence of the pressure difference set by the rotor blade that tend to create a backflow vortex at the tip clearance.
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Bubble cavitation. Nuclei that are present in the inlet flow tend to grow in dimensions passing through low pressure region at the impeller blades, collapsing as they reach regions with higher pressure.
A separated flow or a wake can be filled with vapor. This form of cavitation is termed sheet cavitation and in the pump field it is known as blade cavitation. Bluff bodies often exhibit a transition between bubble cavitation and sheet cavitation as the pressure is lowered, as can be seen in Figure 1.6. In blade cavitation, the attached cavity may close on the suction surface of the foil (partial cavitation) or downstream of the trailing edge (supercavitation) if the inlet pressure is still lowered. These two particular forms are sketched in Figure 1.9. The supercavitation results to be less dangerous than partial cavitation. This is a consequence of the cavity closure that in partial case can lead to local damaging due to fatigue failure.
Figure 1.6 The picture on the left shows bubble cavitation whereas on the right the fully developed cavity is visible. Brennen [1]
Another form of cavitation, known as backflow cavitation, occurs when a turbomachine operates at flow rates lower than that of the design. This phenomena consists of cavitating bubbles and vortices which arise in the annular region of backflow upstream with respect to the inlet plane. The increase in the pressure rise across the pump yields to the upstream penetration of the tip clearance flow, generating a backflow that can reach distances of many diameters. It is important to note that this form of cavitation is supported by the presence of a relatively high clearance.
It can be often observed a structure that is termed cloud cavitation (Figure 1.7) which consists in a periodic formation and collapse of a cloud of cavitation bubbles. Such a structure may occur for the shedding of cavitating vortices or as a result of a periodic disturbance imposed on the flow such as the interaction rotor/stator. This form of cavitation is a primary concern as the collapsing cloud can cause an intense noise and lead to a potential damage. This form of cavitation can actually be seen as a consequence of partial cavitation since cloud cavitation occurs when a partial cavity oscillates in length releasing clouds periodically.
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Figure 1.7 From left to right: formation, separation and collapse of a cavitation cloud on the suction surface of a hydrofoil. The flow is from left to right. Brennen [2]
1.3.
TURBOMACHINERY INSTABILITIES
Even in the absence of cavitation, many types of fluid structure interactions can lead to structural failure. These kind of interactions may be divided in three different kinds of flow oscillations: global flow oscillations, local flow oscillations, radial and rotordynamic forces.
For global flow oscillations are meant a number of identified vibration problems involving large scale oscillations of the flow. One of the main types of large scale oscillations is the rotating cavitation which occurs when a turbomachine rotates at high value of incidence angle close to the one at which the blades may stall. It is commonplace that a small adjacent number of blades manifest cavitation that will propagate circumferentially at some fraction of the main impeller rotation speed.
Figure 1.8 Cascade under rotating cavitation conditions. Brennen [1]
In a turbomachine that is required to operate at positive slope of the curve head rise/flow rate, surge can manifest. This axial system instability involves all the systems such as inlet and feed lines. Oscillation of pressure and flow rate throughout the system are the consequences of this kind of instability. In the presence of cavitation it may arises at negative slope too.
Partial and supercavitation can cause oscillations of cavity length if the cavity collapses in the region of the trailing edge, which leads to violent oscillations.
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Figure 1.9 Cascade presenting partial cavitation (left) and supercavitation (right). Brennen [1]
In partial cavities, the cavity closure reattaches to the blade by dividing the flow in two components:
• a re-entrant jet that travels upstream inside the cavity, • the outer flow which reattaches to the wall.
In thin cavities the liquid counterflow is small enough to be re-entrained by the outer flow but in the case of thick cavities it becomes important and it may reach the leading edge, at the cavity front section. This configuration is clearly not steady and the process is repeated periodically leading to the separation of part of the cavity that is then entrained by the main flow and due to the circulation that arises around this structure it is separated in multiple bubbles or cavitating vortices that will collapse downstream (see Figure 1.10).
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Auto oscillations occur when a pump cavitates and the head rise across the pump is consequently affected. This kind of instability sets violent oscillations in pressure and flow rate in the whole system and can cause radial forces on the shaft that can reach 20% of the axial thrust. It can occur if the slope of the pump head rise/flow rate curve is highly negative and it happens readily at lower flow coefficients. These are conditions in which backflow manifests and therefore it has been noted that the backflow is connected to the dynamics of auto-oscillations.
Line resonance is associated with pressure oscillation which may cause substantial damage and it occurs when the blade passing frequency coincides with one of the acoustic mode of the inlet or discharge line.
POGO instabilities are a particular type of global flow oscillations in which it is involved the vibration of that machine as a whole. A simple example can be the thrust that the propulsive system provides to the rocket.
Local flow oscillations involve phenomenon as blade flutter of an individual blade, blade excitation due to rotor-stator interaction (wakes from the upstream blade can cause a significant vibration for the downstream blades) and blade excitation due to vortex shedding or cavitation oscillations.
Radial forces are global forces perpendicular to the axis of rotation caused by circumferential nonuniformities of the inlet flow, casing or volute.
As a consequence of a displacement of the rotation axis, fluid induced rotordynamic forces arise, leading to a secondary motion of the shaft axis here referred as whirl motion. This precession of the shaft can be both unstable or stable depending on the direction of the rotordynamic force with respect to the whirl orbit characteristics.
The present thesis will focus on the problem of fluid induced rotordynamic forces and the consequences that these forces have on turbomachinery.
1.4.
ROTORDYNAMIC FORCES
As previously seen, these kind of forces are recognized as the most dangerous sources of vibrations for impeller, bearings and all other components of a turbomachine.
The trend of the current state of art is to increase the rotational speed of the shaft and to decrease the weight of the turbomachine. This means that the trend is to use supercritical turbomachines.
The most dangerous rotordynamic instability is the inception of a motion perpendicular to the axis of rotation that can become self-sustained. This whirl motion is a precession of the shaft axis that can follow a complex path and can operate in an unstable equilibrium if the forces are such that the displacement radius (termed eccentricity in the present context) or the whirl rotation speed tends to increase.
The reasons for which the whirl is set can be classified in two groups depending on the origin: Mechanical. Unbalance mass can be a consequence of the wrong alignment of the center of
mass with the axis of rotation. This can be seen as a static unbalance but if the axis of rotation is not a principal axis of inertia the whirl can manifest as a dynamic response. Fluid dynamic. This kind of origin involves flow asymmetries, leakage flow or
recirculation.
As soon as whirl motion is set, it is strongly coupled with the flow which generates destabilizing rotordynamic forces on the shaft of the impeller. In general the cavitation may play an important role in affecting these forces because of their destabilizing effect on the precession motion.
Indicating with ω the whirl speed and with Ω the angular velocity of the impeller there can be three different situations:
9 • Subsynchronous: |ω| < |Ω|
• Synchronus: |ω| = |Ω| • Supersynchronous: |ω| > |Ω|
Figure 1.11 Schematic representation of whirl motion.
The two motions can also be concordant or discordant, depending on the sign of ω and Ω. In particular the counterclockwise rotation will be defined as a positive rotation.
The speed ratio between ω and Ω, the cavitation, the flow rate and operating conditions are all parameters that affect the rotordynamic forces.
1.5.
THESIS OBJECTIVES
Recently, an ESA-sponsored experimental campaign has been carried out in the Cavitating Pump Rotordynamic Test Facility (CPRTF) at ALTA S.p.A., on a three bladed, tapered-hub, variable-pitch inducer (named DAPROT3) and on a radial pump (named VAMPIRE) both entirely designed by means of a reduced order model previously developed at Alta. The aim of this campaign has been the investigation of the effects of cavitation, flow rate, and flow temperature on the rotordynamic forces acting on the impeller as a consequence of an imposed whirl motion with constant eccentricity and angular velocity. The experimental campaign is based on three different configurations:
1. DAPROT3, 2. VAMPIRE,
3. DAPROT3+VAMPIRE (named VAMPDAP).
These configurations have been tested under different operating conditions: • Flow temperature of 20 °C and 70 °C;
• Three different flow rates;
• Three different values of the inlet pressure;
• Eight values of ω/Ω = -0.7, -0.5, -0.3, -0.1, 0.1, 0.3, 0.5, 0.7;
• The cavitating performance has been obtained, fixing all parameters except inlet pressure which has been linearly lowered during a single test. The same test has been performed at different whirl frequency ratios;
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• The noncavitating performance has been obtained from tests at different values of flow rate, fixing all other parameters. The curves in terms of hydraulic efficiency and total pressure rise have been obtained both for centered and whirling tests.
Nevertheless, in the present work only the relevant results on rotordynamic forces and hydraulic efficiency are presented about DAPROT3 and VAMPDAP pump, along with their cavitating/noncavitating performance. The software developed will be available in appendix A, B, and C to provide the omitted results obtained from the tests performed during the overall experimental campaign.
1.6.
REFERENCES
[1] C.E. Brennen, Hydrodynamics of Pumps, Oxford University Press, 1994
[2] C.E. Brennen, Cavitation and Bubble Dynamics, Oxford University Press, 1995.
[3] J.P. Franc, J.M. Michel, Fundamentals of cavitation, Kluwer Academic Publishers, 2004 [4] A.T. Ellis, Observations on Cavitation Bubble Collapse, Caltech, 1952
