Numerical and Experimental Study of Nose for LOx Floating Ring Seal in Turbopump

Abstract

Floating ring seals are widely used as a leakage control solution for turbomachines because they effectively operate with small clearances between the shaft and seal. The oxidizer pump of the 7 tonf liquid engine in the Korea Space Launch Vehicle II (KSLV-II) operates at high rotational speeds and under cryogenic conditions and has floating ring seals in the bearing cooling path to reduce leakages. In this study, we evaluated the frictional force acting on the nose of the floating ring in the oxidizer pump of the 7 tonf turbopump using numerical analysis, and we investigated the radial force on the floating ring induced by the vibration of the rotor and the flow characteristics around the floating ring seal. Through a comparison of the frictional and floating forces according to the change in the diameter of the floating ring noses, we also estimated the dynamic positioning of the floating ring. In addition, we examined the leakage of the floating ring seals with the rotational speed and gap size of the floating ring, and we used the results as data for designing a floating ring seal. Finally, we performed turbopump real-propellant tests with the floating ring seal of the high and the middle noses, finding that the test result was in good agreement with the results of numerical analysis.

1. Introduction

The Korea Space Launch Vehicle II (KSLV-II), which was developed by the Korea Aerospace Research Institute (KARI), is a three-stage rocket powered by liquid engines with open-cycle turbopump feed systems (Figure 1). It has four and one 75 tonf liquid engines used for the first and second stages, respectively, and a 7 tonf liquid engine used for the third stage [1]. The turbopump used in liquid engines is a fluid machinery that rotates at a high speed using centrifugal force to pressurize a low-pressure propellant and supply it to a combustor. The propellant that burns at a temperature above 3000 °C in the combustor is discharged as gas to obtain the necessary thrust during flight. Turbopump-type engines are lighter and more efficient than pressure-fed engines, thus it increases the payload limit [2]. The turbopump in the KSLV-II consists of an oxidizer pump (hereinafter referred to as a LOx pump) and a fuel pump that supply the oxidizer and fuel, a turbine that drives the pumps, and the shaft and seal systems with a rotor [3]. Turbopumps operate at a high rotating speed and high pressure under various environmental conditions with cryogenic media (liquid oxygen and liquid hydrogen), at room temperature (kerosene), and at high temperature (turbine gas) in liquid and gas states. Therefore, its design requirements are strict for the hydraulics, which must include thermal and structure analysis; seal design to control propellant leakage; consideration of axial thrust distribution; dynamic analysis of rotors to prevent bearing damage; and control of cavitation [2]. Because turbopumps operate at high pressures ranging from tens to hundreds of times of atmospheric pressure and under large temperature changes, the reliability of the bearings and seal systems that support the rotor for stable driving of the turbopump under such extreme operating environments must be maintained. Malfunction of these seal systems may cause not only performance degradation of the turbopump due to leakage, but also failure of the turbopump due to wear on the shaft or inflow of impurities. Under this background, many studies conducted on the turbo machinery used in the aerospace industry have focused on the development of bearing and seal elements.

The seals in the turbopump prevent the mixing of different fluids, such as propellant of pumps and combustion gas of a turbine or reduce the leakage of internal flow passage. Several types of seals widely used in turbopump are mechanical face seal (MFS), inter-propellant seal (IPS), floating ring seal, and labyrinth seal. Mechanical face seal is generally used as a seal unit between pump and turbine assemblies. Inter-propellant seal is a seal unit between fuel pump and LOx pump assemblies, and usually composed of annular rings and split carbon seals. The floating ring seal and labyrinth seal in the turbopump unit are mainly installed to control shaft thrust and the leakage of bearing cooling.

The floating ring seal is used to minimize leakage in rotating machinery because it effectively operates with small clearance between the shaft and seal. The floating ring seal in turbopumps, used to prevent leakage above and below the impeller, is a ring-shaped sealing device with a nose that generally floats in the fluid without being fixed to a shaft and controls leakage (Figure 2). Fluid forces acting on the floating ring are determined by size, shape, and nose of the floating ring. According to the strength of the compressive and radial forces on the floating ring, the floating ring can float in fluid and move freely or be fixed to the casing wall.

In the late 1970s, Kirk et al. began the first detailed theoretical and experimental studies for floating ring seals used in industrial pumps [4,5,6], mainly studying the bearing system and rotor dynamics. Kirk et al. studied the dynamic response characteristics of floating rings and the external forces acting on floating rings. Suzuki and Nosaka et al. [7,8,9] conducted experiments on the characteristics of contacting and non-contacting seals in the turbopump mounted on liquid rockets H-1 and H-2 from the late 1980s, and examined the leakage and dynamic stabilities of the floating ring under extra-high pressure and the phenomenon of two-phase flow occurring in the gap between the seal and rotor. They conducted many studies on bearings and seals, especially under liquid hydrogen environments. Semanate et al. [10] proposed the fully developed bulk-flow model for low axial Reynolds numbers to predict the static and dynamic force response of a floating ring seal. They analyzed the laminar/turbulent flow in high pressure floating ring seal with surface roughness, variable seal clearances, fluid inertia and viscous loss effects. The bulk-flow model has the advantage of a relatively short analysis time, but it takes a lot of time to develop the code and has low accuracy for seals with complex shapes. Ha et al. and Lee et al. derived the governing equation of motion for a floating ring using the dynamic analysis method for the journal bearing, and investigated the leakage, rock-up position, and rotor dynamic coefficients of floating ring seals using experimental and analytical methods [11]. They especially tried to improve the performance of floating rings through various experiments. Ha et al. [12] designed a floating ring with circular holes on its surface to improve the leakage performance and dynamic stability of floating ring seals and found its leakage and rotor dynamic coefficients. Lee et al. [13] proposed a floating ring with a bump foil to reduce the eccentricity of the floating ring during operation. In addition, they conducted many tests to confirm the superior dynamic stability of the floating ring with bump foil. Duan et al. [14] improved Ha’s analysis method to calculate dynamic characteristics for the floating ring seal and validated the numerical analysis results by comparing with experimental data. With the development of computers, various computational fluid dynamics (CFD) method for solving the Navier–Stokes equation have been developed and applied to floating ring seal analysis. San Andres et al. [15] proposed a 2D CFD solution for eccentric smooth annular seals and showed that the analytical prediction had good agreement with the experimental results. Choi et al. [16] and Kim et al. [17] studied the change in pump efficiency for different gaps between the floating ring and rotor from the turbopump design viewpoint. Using CFD analysis and water tests, they found that the change in the gap of the floating ring seal considerably affects the suction and hydraulic performance of the turbopump. Mariot et al. and Arghir et al. [18,19] measured the eccentricity of floating ring seals owing to rotor vibration and traced the trajectory of the floating ring using a high-speed and high-resolution camera. From the results of the seal test, they confirmed that the vibration of the rotor and the motion of the floating ring are synchronized. Based on the experimental results, they evaluated the dynamic stability of the turbomachines related to the motion of the floating ring. Peng et al. [20,21] calculated the transient hydrodynamic force acting on the rotor and floating ring by improving the finite element method (FEM) and dynamic model for the whirling system, which have long been widely used. From the results, Peng et al. determined the dynamic characteristics of the rotor system, including those of the floating ring, by analyzing the change in the lock-up area of the floating ring with the nose and the correlation between the movement of the floating ring and the wheeling of the rotor. Bae et al. [22,23] experimentally investigated the frequency characteristics and instability of the floating ring seal with variations in the nose height and antirotating pin. Bae et al. confirmed that the antirotating floating ring seal is able to effectively reduce the unstable pressure fluctuations and the wear compared with a normal floating ring seal.

Researchers have mainly performed experimental, theoretical, or numerical analyses of the dynamic characteristics of floating ring seals under the normal rotating machinery operating conditions, studying the changes in the efficiency of fluid machines with floating rings, wear of floating ring seals, leakage through floating ring seal gaps, and rotor dynamic stability of total systems. However, a few studies discussed the unstable dynamic motions of the floating ring seal caused by the inappropriate design of the floating ring or by the abnormal vibration of the rotor system. In particular, the unstable dynamic characteristics of the floating ring seal, which can appear when the turbopump is driving, can cause the instability in the flow of the propellant at the outlet pipes of the turbopump and the malfunction of the turbopump due to the abrasion or damage of the floating ring seal [22].

In this study, we numerically and experimentally analyzed the nose design of a 7 tonf turbopump LOx floating ring by evaluating the performance of the floating ring seal with different nose positions under various operating conditions. We calculated the frictional forces acting on the nose of floating rings and the radial forces on the floating rings and investigated the flow characteristics around the floating ring seal. Through a comparison of the frictional and floating forces according to the change in the diameter of the floating ring nose, we compared the dynamic stability of floating rings with experiments. In addition, we examined the leakage of floating ring seals considering the rotational speed and gap size of the floating ring, and we tested the turbopump performance for floating ring seals with high and middle noses.

2. Floating Ring Seal Design

The floating ring in a fluid machine during driving is usually subjected to axial and the radial forces owing to the difference in the fluid pressure (Figure 3). The change in the clearance between the floating ring and rotor induced by the vibration of the rotor causes radial force acting on the floating ring seal. The opening force ($F_o$) created by the fluid, which flows through the small gap between the floating ring nose and casing wall, and the closing force ($F_c$) that appears in the high- to low-pressure direction are added to generate compressive force ($F_a$) in the axial direction, as shown in Equation (1). $P_1$ and $P_2$ are the high (upstream) and low (downstream) pressures before and after the floating ring, respectively; K is the pressure gradient factor, which represents the ratio of the average pressure between the floating ring and wall to the inlet pressure. In general, 0.5 and 0.667 are used for incompressible and compressible fluid, respectively [24]. $r_{ni}$, $r_{no}$, and $r_i$ are the inner radius of the floating ring nose, outer radius of the floating ring nose, and inner radius of the floating ring, respectively.

$$F_a=F_c-F_o=\pi \left(r_{ni}^2-r_i^2\right)(P_1-P_2)-\pi \left(r_{no}^2-r_{ni}^2\right)K{P}_1$$

(1)

Floating rings usually have a nose. This is because the compressive force acting on the floating ring is determined by the position of the contact surface where the floating ring is attached to the wall. In general, it is difficult for designers to estimate where the first contact surface of the floating ring without a nose with the wall is. If the floating ring has a nose, the compressive force of the floating ring can be well-controlled by appropriately designing the position and size of the nose. The frictional force ($F_f$) between the floating ring nose and casing wall is calculated by multiplying the axial force by the coefficient of friction ($f_{eq}$), which we measured in an experiment, as shown in Equation (2). The coefficient of friction is divided into the coefficient of static friction and the coefficient of kinetic friction according to the presence or absence of the relative motion of the body on the surface. Because a casing in contact with the floating ring nose is always vibrating when the turbopump is running, the coefficient of kinetic friction is used to calculate the frictional force. For steel with a smooth and lubricated surface in a cryogenic environment, the coefficient of kinetic friction is approximately 0.06 to 0.28 [25].

$$F_f=f_{eq} F_a$$

(2)

If the radial force acting on the floating ring by the vibration of the rotor is smaller than the frictional force between the floating ring and casing wall, the floating ring is fixed to the casing wall regardless of the rotor vibration. However, when the radial force acting on the floating ring is larger than the frictional force, the floating ring starts moving in contact with the wall.

Initially, the floating ring in the bearing cooling flow path is in contact with the rotor or casing of the turbopump owing to its own weight and starts to float in the fluid owing to the radial force generated when the rotor starts to rotate. At this time, the floating ring arbitrarily moves in the fluid owing to external forces such as frictional and viscous forces; when the lateral forces acting on the floating ring are balanced, the ring settles in an appropriate eccentric position [11]. When the rotational speed and the difference in pressure between the upstream and downstream sides of the floating ring increase, the floating ring attaches to the casing wall to control the leakage of the flow path. If the leakage of the bearing cooling path is large, the possibility of bearing damage due to overheating can be reduced, but the pump efficiency decreases. To find the optimal flow rate of the bearing cooling path, the floating ring should be designed considering various variables such as the shape and size of the floating ring, the size of the gap between the floating ring and rotor, and the position and height of the nose.

If the floating ring nose is properly designed and the vibration of the rotor is excessively large during the operation of the turbopump, the radial force acting on the inner surface of the floating ring, which is produced by the vibration of the rotor, synchronizes the motion of the rotor and floating ring. At this time, because the nose of the floating ring is in contact with the casing of the pump, the nose surface may wear due to friction, but the floating ring is synchronized with the vibration of the rotor and stably settles to control leakage. However, if the contact force between the floating ring nose and casing is excessively large, the radial force on the floating ring cannot overcome the frictional force between the nose and casing wall, or the floating ring slowly responds to the movement of the rotor. Then, the floating ring can be damaged through collision with the rotor. For this reason, in the case of a large high-speed pump with strong vibration, the floating ring nose is designed so that the floating ring easily synchronizes with the movement of the rotor for stable pump operation. Conversely, because the vibration of the rotor is sufficiently weak in a small low-speed pump, the floating ring is designed to easily attach to the casing owing to the fluid pressure and to increase the pump efficiency by minimizing the leakage flow rate.

The floating ring seal in a turbopump acts as a contacting seal during normal operation, but transition region exists in which normal pressure is not formed at the start and end of pump operation, so damage of floating ring seal frequently occurs. Friction and wear of a floating ring seal exposed to an oxidizer (LOx) can cause failure and explosion of the turbopump, so the appropriate floating ring seal design and materials are required to resist ignition in LOx environments.

3. Numerical Method and Validation

The fluid force acting on a floating ring widely varies depending on the design of the floating ring and operating conditions, such as the position of the nose, gap size between the floating ring and rotor, pressure before and after the floating ring, or rotating speed of the rotor. In particular, the positioning of the nose is a crucial factor in the design of a floating ring because it determines the magnitude of the axial force acting on the floating ring. However, it is costly and time-consuming to measure the positioning experimentally because a test rig that can measure the force acting on the floating ring must be designed and built, and various floating rings with different nose diameters must be manufactured. Therefore, if the operating conditions of the floating ring and fluid force acting on the floating ring for different nose diameters can be appropriately simulated by numerical analysis, the time and cost for designing a floating ring can be considerably reduced.

For numerical analysis, first, the boundary of the flow field including the main body should be defined and the grid system should be constructed. Figure 4 and Figure 5 show the schematics and the grid system of the simplified LOx rear floating ring and the bearing cooling flow path of a 7 tonf turbopump, respectively. For the convergence of CFD analysis and convenience of grid generation, we assumed that the inside of the bearing was a simplified resistor, and we created the grid as a multiblock structured grid using Pointwise, which is commercial grid-generation code. The total number of grids was about 900,000, and we adjusted the size of the first grid on the wall so that the dimensionless wall distance y⁺ was maintained between 30 and 200 to enable the use of a wall function that could reduce numerical costs and increase the calculation convergence.

We performed numerical analysis using the pressure-based, steady, incompressible Reynolds-averaged Navier–Stokes (RANS) equation with the realizable k-ε turbulence model in ANSYS FLUENT, commercial CFD code. Similar to the experiment, the material and boundary conditions included a total pressure of 63 barA at the inlet and a static pressure of 12 barA at the outlet of liquid oxygen. We applied a moving reference frame (MRF) method to analyze the rotating body. The MRF method, which described rotating effect without moving the grid by applying a virtual centrifugal force to the external force term of the RANS equation, is fast and converges well, but it is less accurate than the sliding mesh method and struggles to analyze unsteady flow conditions. However, we applied the MRF method in this case because the floating ring is axis-symmetric in steady flow.

We validated the numerical analysis for the floating ring seal by comparing the calculation and experimental results at the rated rotational speed of 27,000 rpm. In the real-propellant tests of the turbopump, the outlet pressure of the impeller gradually changes depending on the test conditions. Therefore, to accurately determine the effect of the floating ring on the fluid, we compared the differences between the impeller outlet static pressure ($P_1$) and rear static pressure of the floating ring ($P_2$) that we measured by four repeated experiments and calculated by the numerical analysis (Figure 6). The differences between the results of the four experiments and the numerical analysis showed an error of approximately −2.4% to −7.8%. Considering the changes in the operating environment that occurred during the test, we evaluated the results of the numerical analysis and experiments as being similar. Therefore, we determined that the flow analysis in the bearing cooling path including the floating ring and bearing was adequately simulated by the grid system and the numerical methods we applied in this study.

4. Results and Discussion

4.1. Performance of Floating Ring Seal with Variations in Rotating Speed

We performed a numerical analysis of a floating ring with a medium-diameter nose (hereinafter referred to as “middle nose”) to calculate the flow rate through the gap of the floating ring, external force acting on the floating ring, and pressure and velocity around the floating ring when the rotating speed changes. The distance between the ring and rotor was set to 170 μm in the rotational direction, which is the same as the average design gap between the actual floating ring and rotor. When the rotor is stationary, the pressure and velocity distributions around the floating ring is shown in Figure 7. Passing the floating ring, the static pressure decreased from 56 to 20 barA, and we calculated the maximum flow velocity through the gap between the floating ring and rotor to be approximately 80 m/s. Figure 8 shows the pressure and velocity around the floating ring when the rotor drives at the rated rotating speed of 27,000 rpm. When the rotor rapidly rotates, the centrifugal force by the rotation is transferred to the fluid, and the pressure behind the floating ring rises. Therefore, the pressure passing the floating ring decreases from 56 to 31 barA, which is less of a reduction compared with the case where it does not rotate. As the pressure difference between the front and rear of the floating ring decreases, the maximum velocity through the floating ring gap decreases to approximately 66 m/s, and the leakage decreases.

Figure 9, Figure 10 and Figure 11 show the changes in dynamic pressure, static pressure, and flow velocity with streamlines, respectively, in the bearing cooling path including the floating ring when the rotational speed increases from 0 to 36,000 rpm. As the rotational speed of the rotor increases, the dynamic pressure in the chamber behind the floating ring increases due to the transfer of rotational kinetic energy by the fluid on the surface of the rotor. When the rotational speed exceeds 27,000 rpm, the dynamic pressure in the chamber behind the floating ring becomes higher than the jet flow from the gap between the floating ring and the rotor. At this time, we calculated the dynamic pressure around the rotor at 27,000 rpm to be approximately 41 bar.

As the rotational speed of the rotor increases, the static pressure in the chamber behind the floating ring increases in the radial direction due to centrifugal force. When the rotational speed exceeds 27,000 rpm, the static pressure in the chamber behind the floating ring, which occupies a large space in the flow path, has a difference with more than 30 bar in the radial direction, as shown in Figure 10. This increases the static pressure in the region behind the floating ring, so that the flow rate and velocity through the gap of the floating ring considerably decrease.

Figure 11 shows the flow velocity and streamline distribution in the bearing cooling path according to the increase in rotational speed. As the rotational speed increases, the jet flow in the gap of the floating ring caused by the pressure difference before and after the floating ring weakens, and the rotational velocity along the entire flow path due to the rotation of the rotor substantially increases. Under operating conditions above the rated rotational speed, the centrifugal force, mainly due to the rotation of the rotor, has a stronger effect on the flow in the flow path than the pressure difference between the inlet and outlet. In addition, complex flow phenomena, such as a strong vortex flow inside the chamber, occur when the rotational flow meets the jet flow passing through the floating ring gap. The vortex flow gradually decreases as the jet flow weakens as the rotational speed increases.

4.2. Performance of Floating Ring Seal with Variations in Nose Diameter

To examine the flow characteristics in the bearing cooling path with the change in the position of the floating ring nose, we conducted CFD analysis for three floating rings with a large-diameter nose (hereinafter referred to as “high nose”), a middle nose, and a small-diameter nose (hereinafter referred to as “low nose”), as shown in

Table 1. Specifications of floating ring seal with 3 types of noses.

	Floating Ring w/Low Nose	Floating Ring w/Middle Nose	Floating Ring w/High Nose
Floating ring length/ Floating ring outer diameter (%)	10.0
Nose height/ Floating ring outer diameter (%)	0.43
Nose outer diameter/ Floating ring outer diameter (%)	93.45	94.79	96.30
Nose inner diameter/ Floating ring outer diameter (%)	96.30	97.64	99.15

, at a rotational speed 27,000 rpm. Figure 12 and Figure 13 show the static pressure and flow velocity distribution with the change in nose height, respectively.

The axial forces of the floating ring with changes in the nose widely vary as the areas of low and high pressure change according to the change in the upper and lower parts of the nose. However, the radial force on the floating ring and the pressure distribution before and after the floating ring are similar regardless of nose height. Figure 13 shows that the flow rate and the velocity through the gap of the floating ring barely differ with changes in the position of the floating ring nose. Therefore, the positioning of the floating ring nose can control the compressive and frictional forces acting on the floating ring independent of other design variables. When the nose is properly designed, the external forces such as frictional and floating forces on the floating ring are well-balanced with each other, so that the dynamic positioning of the floating ring can be controlled according to the design intent.

4.3. Performance of Floating Ring Seal with Variations in Gap Size

We performed numerical analysis for a floating ring with a middle nose by changing the gap between the floating ring and rotor in the radial direction to 0%, ±12.5%, ±25%, ±37.5%, ±50%, and ±62.5% compared with the average gap size (170 μm) at a rotational speed 27,000 rpm. Figure 14 and Figure 15 show the static pressure and flow velocity distribution, respectively, calculated through the numerical analysis when the change in the gap size is 0% and ±62.5%.

If the gap size of the floating ring does not change, the flow passing through the gap between the floating ring and rotor has the same velocity distribution in the rotational direction, and the pressure in the gap also has an axisymmetric distribution. Therefore, radial force on the floating ring is barely generated, and the maximum velocity of the jet flow through the gap is approximately 66.5 m/s regardless of the rotational direction.

When the floating ring is ±62.5% of the average size of the gap, the maximum flow velocities passing through the gap with the change in the channel width are distributed from approximately 63.7 to 69.7 m/s according to the rotational direction, as shown in Figure 15. At this time, the gap size and fluid velocity in the gap are proportional. If the gap size of the channel increases, so does the fluid velocity due to the influence of the boundary layer inside the gap. As the fluid velocity in the gap increases, the static pressure decreases according to Bernoulli’s law, and the radial fluid force acts on the floating ring in the direction of the larger to the smaller gap. As a result, when the rotor vibrates, if the effect of damping by the fluid is weak, the floating ring also moves in the direction in which the rotor moves. That is, the floating ring is synchronized with the movement of the rotor. We estimated the radial force acting on the floating ring by the difference of the gap size to be approximately 271.35 N.

From the results of the numerical analysis, we found that as the gap size between the floating ring and rotor increases in the rotational direction, the change in the flow velocity distribution in the gap increases; then, the difference in static pressure around the gap of the floating ring also increases. Eventually, the restoring force acts on the floating ring in the direction where the gap of the floating ring is balanced. In this process, a properly designed floating ring is not damaged by the vibration of the rotor and operates well in synchronization with the rotor.

We calculated the change in mass flow rate for gap size variations of the floating ring with a middle nose, and the changes in mass flow rate and rotational force acting on the floating ring by the rotational speed change for three floating rings with a high, middle, and low nose using the numerical analysis. The results are shown in Figure 16.

Predicting the mass flow rate passing through the floating ring is difficult due to various reasons such as axial misalignment, face roughness, phase change owing to the surface temperature in the gap, viscosity change by cavitation, and transition between laminar and turbulent flow. Therefore, we performed these calculations assuming an ideal single-phase turbulent flow without temperature change to ensure stable convergence and a convenient numerical analysis. The leakage flow rate due to the change in the size of the gap between the floating ring and rotor is shown in Figure 16 (left).

As the change in the gap size of the floating ring is larger, the leakage flow rate gradually increases due to the change in the wall boundary layer thickness, even though the cross-section area of the gap and the average size of the gap do not substantially differ. The fluid force (Figure 16, middle) in the rotational direction acting on the floating ring increases as the rotational speed increases, but the magnitude is not as large as that of the fluid force in the radial direction.

Conversely, when the rotational speed increases, the mass flow rate (Figure 16, right) through the gap of the floating ring decreases due to a decrease in the pressure difference between the front and rear of the floating ring. In addition, we confirmed that the rotational fluid force acting on the floating ring and leakage in the gap are almost independent of nose height.

4.4. Experiment with Floating Ring Seal with Variations in Nose Diameter

We measured the acceleration of the LOx pump casing in a real-propellant test with the 7 tonf turbopump to which a floating ring with a middle nose was applied. The velocity and displacement calculated by time integration are shown in Figure 17. We calculated the range of the frequency-filtered acceleration between 10 and 10,000 Hz to be approximately ±800 m/s², the range of the velocity was approximately ±5 cm/s, the range of the displacement was approximately ±0.06–0.08 mm, and the displacement corresponded to approximately 35–47% of the average gap size (0.17 mm) of the floating ring. Figure 18 shows the acceleration, velocity, and displacement measured in the real-propellant test of the 7 tonf turbopump with a floating ring with a high nose. The range of the acceleration was calculated to be approximately ±700 m/s², the velocity was approximately ±4.5 cm/s, and the displacement was approximately ±0.05–0.07 mm. The results of the test with the two floating ring seals did not differ much.

Because the rotor is directly connected to the casing by the bearings and the vibration of the casing comes from the vibration of the rotor, we assumed that the vibrational displacement of the rotor had a phase difference with the displacement of the casing measured in the test, but their magnitude was similar.

We calculated the axial forces acting on three floating rings with a high, middle, and low nose for different rotating speeds by numerical analysis. The results are shown in the left of Figure 19. The right side of Figure 19 shows the radial forces with the change in the gap size of the floating ring that we calculated by numerical analysis and the frictional forces with the change in the nose position that are induced by the axial forces acting on the floating rings. To estimate the frictional force inferred from the axial force calculated through CFD analysis, we used a coefficient of kinetic friction of 0.15, which is the average value measured in the ball-on-disk tests in a cryogenic environment [25]. Figure 19 (right) shows the actual radial force (gray region) on the floating ring calculated by a comparison of the radial force curve according to the gap size of the floating ring with the vibrational displacement (gray region) of the LOx pump measured in the test at the rated rotation speed.

Due to the vibration of the rotor, the gap between the rotor and floating ring continuously changes, and the change in the gap size causes a change in the mass flow rate through the gap to generate floating force in the radial direction of the floating ring. The radial fluid force due to the change in the gap of the floating ring is independent of the position of the nose. When the radial force is stronger than the frictional force acting on the floating ring, the floating ring periodically moves in synchronization with the vibration of the rotor. Regardless of the nose position of the floating ring, if the rotational speed of the rotor increases, the static pressure behind the floating ring increases, and the pressure difference before and after the floating ring decreases. As such, the compressive and frictional forces between the floating ring nose and the casing wall also decrease.

By comparing the frictional force on the floating ring calculated through CFD analysis and the radial fluid force (gray region) on the floating ring estimated from the vibration displacement (gray region) measured in the real-propellant test, as shown in Figure 19, we evaluated the dynamic positioning of the floating ring with changes in the nose position. From Figure 19 (right), we found that the frictional force (210.0 N) of the floating ring with a high nose is larger than the range (119–175 N) of the radial fluid force on the floating ring produced by the vibrational displacement of the rotor. This means that a floating ring with a high nose experiences minimal dynamic displacement in the radial direction. In the case of a floating ring with a middle nose, we found that the floating ring may weakly move according to the oscillating displacement of the rotor because the frictional force (161.3 N) falls within the range of the radial fluid force of the floating ring. In the case of a floating ring with a low nose, the radial fluid force is stronger than the frictional force (105.3 N), so it can easily synchronize with the vibration of the rotor.

Figure 20 shows photos of the exterior shape and enlarged photos around the nose and the inner surface of two floating ring seals obtained after the real-propellant tests with the 7 tonf turbopump equipped with a floating ring for both a middle and high nose. The floating ring of the middle nose mainly showed scratches and severe wear on the nose surface in contact with the casing wall, and weak frictional marks on the inner surface of the floating ring. In the case of the floating ring with a high nose, weak scratches were observed on the nose surface of the floating ring, and strong metal oxidation occurred over the entire circumference on the inner surface of the floating ring in the nose direction. This means that the floating ring with a middle nose synchronized with the movement of the rotor and wear mainly occurred on the nose surface in contact with the casing rather than the inner surface. In the case of the floating ring with a high nose, the inner surface of the floating ring and the rotor were mainly rubbed while the floating ring was fixed to the casing wall. These frictional characteristics of the floating ring with the change in the nose diameter in the experiments are similar to those of the numerical analysis of the dynamic positioning of the floating ring related to the frictional force on the nose surface (Figure 19).

From the results of the numerical analysis and the experiment, we find that a floating ring with a middle nose has difficulty positioning on the wall due to the vibration of the rotor, but has the superior wear resistance. Because a floating ring with a high nose has a relatively large frictional force, it quickly fixes to the pump casing. However, the risks of metal oxidation and ignition are high due to friction and wear with the shaft. These phenomena are more likely to occur as the vibration of the rotor increases with the rotational speed; the possibility of failures and accidents during the operation of the turbopump with liquid oxygen, which is a fire-hazardous propellant, also increases. Therefore, the floating ring nose must be designed considering the operational stability as the top priority rather than the leakage performance with stable positioning.

5. Conclusions

In this study, to confirm the principle of the operation of a floating ring seal that controls the cooling flow of the bearing in a turbopump and to determine the optimal position of the floating ring nose, we conducted a numerical analysis to investigate the fluid forces acting on the floating ring and the amount of leakage through the gap in the floating ring with changes in the rotational speed of the rotor, the position of the floating ring nose, and the gap size of the floating ring. We evaluated the dynamic positioning of the floating ring seal with the three nose designs by comparing the frictional force on the noses with the floating force induced from the vibrational displacement of the LOx pump measured in a real-propellant test. In addition, to validate the findings regarding the dynamic positioning of the floating ring seal with changes in the nose position, we conducted the real-propellant tests with the turbopump with a floating ring seal with high and middle noses, and we visually inspected the two floating rings after the tests. The results are summarized as follows:

• Based on the results of numerical analysis, we found that as the nose diameter of the floating ring increases, the compressive force acting on the floating ring and the frictional force on the nose increase, but they do not affect the leakage.
• When the variation of the gap size between the floating ring and rotor owing to the vibration of the rotor is larger, the radial fluid force, which is proportional to the difference in the flow velocity inside the gap, also increases, and the synchronization between the floating ring and the rotor increases.
• As the diameter of the floating ring nose increases, the dynamic positioning of the floating ring owing to the vibration of the rotor becomes relatively weak, and the floating ring quickly attaches to the casing wall and stably controls leakage. However, the risk of wear and damage caused by vibration of the rotor increases.
• We designed an evaluation method that can predict the dynamic positioning of a floating ring seal by combining the radial and the frictional forces acting on the floating ring calculated from the numerical analysis and the vibration displacement measured from the turbopump experiment. The results were in good agreement with those obtained from real-propellant tests with the turbopump.

In this study, we determined the dynamic positioning of a floating ring for different nose positions based on a numerical analysis and vibration measurement. However, the results do not specifically represent the interaction between the floating ring and the rotor when the turbopump is running, and we could not accurately simulate the dynamic motion of the floating ring that causes turbopump instability. Therefore, additional studies should be conducted on the actual motion trajectory of the floating ring, the interaction between the floating ring and rotor during turbopump operation, and the creation of an experimental method to verify the results.