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1 Copyright © 2012 by ASME

Proceedings of ASME Turbo Expo 2012 GT2012

June 11-15, 2012, Copenhagen, Denmark

GT2012-68700

NUMERICAL INVESTIGATION OF THE FLOW IN A HYDRODYNAMIC THRUST BEARING WITH FLOATING DISK

Magnus Fischer*, Andreas Mueller†, Benjamin Rembold, Bruno Ammann

ABB Turbo Systems AG Baden, Switzerland

* E-Mail: [email protected] † Current Address: Institute of Fluid Dynamics, ETH Zurich, Switzerland

ABSTRACT In this paper we present a novel method for the numerical

simulation of flow in a hydrodynamic thrust bearing with floating disk. Floating disks are commonly employed in turbochargers and are situated between the thrust collar, which is rotating at turbocharger speed, and the static casing. A floating disk reduces wear, improves the skew compensating capacity of the bearing and is freely movable in the axial direction.

The simulation model presented combines a commercial

flow solver (ANSYS CFX) with a control unit. Based on physical principles and a predefined axial thrust, the control unit automatically sets the rotational speed of the floating disk, the mass flow of the oil supply and the oil film thickness between the rotating disk and the casing wall and collar respectively. The only additional inputs required are the temperature and the pressure of the oil at the oil feed and the turbocharger speed. The width of the computational grid of the thin lubricating oil film in the gaps is adjusted using a mesh-morphing approach. The temperature-dependent variation in viscosity is included in the model. The calculated solution of the flow field in the domain, the oil film thickness and the resulting rotational velocity of the floating disk are validated against experimental data and demonstrate favorable agreement. The influence of uncertainties in the measurements

and the behavior of the systems are thoroughly investigated in parametric studies which reveal the key influencing factors. These are the temperature-dependent viscosity of the oil, the axial thrust and turbulence effects in the supply grooves and ducts of the floating disk. Using the model presented here, it is now possible to predict design variants for this type of bearing.

NOMENCLATURE

F Force (N)

h Lubricating film height (m)

k Proportional gain (-)

M Momentum (N m)

m Mass flow rate (kg s-1)

n Rotational speed (s-1)

p Pressure (Pa)

, ,r zφ Spatial coordinates (m,°,m)

zΔ Displacement of bearing wall (m)

ζ Pressure loss coefficient (-)


Θ Temperature (K)

μ Dynamic viscosity (kg m-1 s-1)

ρ Density (kg m-3)

FDω Angular velocity of Floating Disk (° s-1)

TCω Turbocharger speed (° s-1)

Subscripts

FD Floating Disk

TC Turbocharger

C Compressor side

T Turbine side

i Current iteration

Reservoir Conditions in the reservoir

Superscripts

0 Initial values

* Characteristic / nominal values

INTRODUCTION

Turbochargers for large medium-speed engines and for

low-speed engines are often driven by axial turbines. For the common flow arrangement, the compressor and turbine thrusts forces add up to a considerable net thrust at full load. In turbochargers this axial thrust is absorbed by a hydrodynamic tapered land thrust bearing. These types of bearings are widely-used for their compactness and for economic reasons. A conventional thrust bearing consists of one hydrodynamic oil-film between the thrust collar and the housing. By contrast, in a floating disk thrust bearing, two oil-films are established on each side of the floating disk. This disk rotates freely between the thrust collar and the housing. The concept of a floating disk thrust bearing corresponds to a full-floating journal bearing. The floating disk improves the skew compensating capacity of the bearing, reduces the bearing power losses and reduces wear due to lower relative velocities. However, the bearing size and the oil mass flow are larger than in a conventional thrust bearing of a comparable load capacity.

The dimensioning of turbocharger thrust bearings is usually based on the thermohydrodynamic (THD) theory, where the Reynolds equation and the energy equation are solved simultaneously. The Reynolds equations are derived from the Navier-Stokes equations by neglecting fluid inertia. Due to the high rotational speeds in conjunction with thermal dissipation the influence of temperature on the viscosity has to be taken into account by solving the energy equation. Examples

of the THD theory and its application can be found in [1-5]. Software based on the THD theory allows quick modeling and solving of conventional bearing geometries. Kucinischi et al. [6] applied the THD theory expanded to include the thermo-elastic equation for a three-dimensional analysis of a radially grooved thrust washer.

For complex geometries and when physical phenomena such as inertia, viscous forces and turbulence have to be considered without simplifying assumptions, CFD codes solving the Navier-Stokes equations have to be applied. The gain in accuracy in such a CFD approaches involves higher computational costs. Chen and Hahn [7] present a CFD analysis of hydrodynamic lubrication problems in various bearing geometries. In their study, they compare the CFD solution with results of Reynolds approximations, showing favorable agreement for the type of bearing investigated. Guo et al. [8] calculate hydrodynamic and hydrostatic journal bearings as well as squeeze film dampers with the commercial CFD Code TASCflow and compare the results with various standard lubrication theory numerical codes used in the industry, showing reasonable agreement.

The flow in a hydrodynamic thrust bearing with floating disk is characterized by the interplay of the pumping effect of the rotating floating disk, the absorption of axial thrust resulting in the adjustment of the lubricating film height and as a result, the varying mass flow rate of the lubricating oil. Due to the high relative velocities between the thrust collar, the floating disk (which is rotating at about half of the speed of the shaft) and the bearing housing (which is at rest) and the small height of the lubricating gaps, thermal dissipation due to viscous friction in the flow is very high. The lubricating oil heats up and in turn lowers the temperature-dependent viscosity. The system behavior is changed. The oil film thicknesses, the angular velocity of the floating disk and the oil flow rate through the system are, on the other hand, dependent on the turbocharger operating point.

The main objective of the present work is to understand these complex effects by introducing a tool to fully model the three dimensional flow and the varying lubricating film thicknesses. For a given axial thrust, turbocharger speed and supply pressure in the oil reservoir, the model should determine all other characteristic parameters of the thrust bearing. These are the rotational speed of the floating disk, the width of both lubricating gaps and the oil mass flow through the bearing. In order to calculate these parameters, the boundary conditions as well as the computational grid have to be adjusted automatically in a control unit. PHYSICAL MODEL

A schematic of the thrust bearing with floating disk is presented in Figure 1. It consists of a floating disk (2) which is arranged axially between the bearing housing (1) and the thrust collar (3). The thrust collar is mounted on the rotating shaft (4).


The floating disk is driven by the viscous friction in the gap between the thrust collar and the disk’s surface (h). Due to its rotary motion it is acting as an oil pump. From the oil reservoir (a) the lubricating oil is fed via two supply channels (b) into an annular plenum at the inlet of the bearing (c). At this point one part of the oil is driven along the lubricating groove on the compressor side (e). Another part of the oil is fed through a supply hole (d) to the lubricating groove on the turbine side (f). The remaining minority of the fluid passes through the journal bearing between the disk and the bearing collar (i). On both sides of the floating disk the oil is transported in the grooves radially outwards by the rotating motion of the floating disk and the thrust collar, respectively. It is pushed in circumferential direction into the wedge surface and the gaps between the floating disk and the walls (g, h). The wedges of the floating disk narrow in circumferential direction allowing the formation of a lubricating film and a pressure cushion, which absorbs the axial thrust. From there, the oil leaves the bearing into the plenum around the floating disk (k). A smaller oil flow exits the system through an annular gap (j) between the fixed bearing collar (5) and the rotating thrust collar.

Figure 1. Schematic of the thrust bearing and the floating disk. Solid parts are indicated by numbers: bearing housing (1); floating disk (2); thrust collar (3); shaft (4); bearing collar (5); Fluid regions are defined with letters as follows: oil reservoir (a); oil supply lines (b); annular plenum (c); supply hole (d); lubricating groove, compressor-side (e); lubricating groove, turbine-side (f); gap, compressor-side (g); gap, turbine-side (h); floating disk journal bearing (i); annular gap (j); plenum (k).

NUMERICAL MODEL Due to the periodicity of the geometry of the floating disk,

the system can be reduced to a 60 degree sector. For further simplification, the oil reservoir and the oil supply lines are not modeled either. Instead the conditions at the inlet of the computational domain are set according to the pressure drop in the oil supply line. The computational domain is indicated by the dotted red line in Figure 1. The domain is divided into several sub-domains, connected via fluid-fluid interfaces (full non-matching boundary conditions). With this approach design variants can thus be easily computed.

The computational domain is rotating at the angular velocity of the floating disk, FDω . This velocity is not known a priori and is a result of the action of the control unit during the simulation as explained below. The wall of the bearing housing is at rest and the angular velocity of the wall of the thrust collar corresponds to the turbocharger speed TCω . For further simplification the axial position of the floating disk is fixed. The thickness of the lubricating films on both sides of the floating disk is, instead, adjusted by displacing the wall of the thrust collar and the bearing housing in axial direction. The computational grid is adjusted accordingly.

The walls of the domain are modeled as adiabatic, non-slip walls. At all outlets a pressure condition is set with the value of the ambient pressure. Periodic boundary conditions are set at the corresponding azimuthal ends of the 60° degree model. At the inlet of the computational domain, a mass flow condition is set. The mass flow at the inlet is not known a priori and is a result of an iterative process applying the control unit.

The oil is modeled as an incompressible Newtonian Fluid. Due to the high temperature variation within the thrust bearing the dependency of the viscosity on temperature cannot be neglected. The dynamic viscosity is modeled with a power law of the form, [9]:

( ) 00

l

μ μΘ

Θ =Θ

⎛ ⎞⎜ ⎟⎝ ⎠

(1)

Where 0μ is the viscosity at the temperature 0Θ . The coefficient l is a fitting parameter, smaller than zero. The heat capacity, density and thermal conductivity of the oil are modeled with constant values.


GOVERNING EQUATIONS The solution of the flow is obtained by applying a

commercial flow solver (ANSYS CFX). The steady-state velocity, pressure and temperature field are obtained by solving the Reynolds-averaged continuity, momentum and energy equation in a rotating reference frame. In the supply hole and the lubricating grooves high Reynolds numbers indicate the need for a turbulent model. The k-ω -SST model with automatic wall functions was applied [10]. In the lubricating gaps the fluid remains predominantly laminar.

The governing equations were discretized using a second order scheme and a first order upwind scheme for the turbulent quantities. Grid independence of the flow solution was ensured in parametric studies, resulting in an optimal number of about 1 million grid cells. In particular, the number of grid cells used in the lubricating gaps has a strong influence on the flow field. 13 evenly distributed cells ensure an adequate resolution to capture the physics correctly. This is shown in Figure 2, where the height of the lubricating film is plotted versus the number of grid cells.

Figure 2. Number of grid cells in the lubricating gaps on both sides of the floating disk vs. film height for a nominal operating point.

Besides the flow field, four additional equations have to be solved in order to determine the gap widths on the compressor and turbine side of the floating disk, Ch , Th , the angular velocity of the floating disk, FDω , and the mass flow at the inlet of the computational domain, m . The last variable is applied as a boundary condition at the inlet of the fluid domain. The four equations are derived in the following section.

The pressure in the oil reservoir Reservoirp is known and kept constant over the operational range. The pressure loss in the lubricating oil supply lines between the inlet boundary of the computational domain and the oil reservoir can be expressed in terms of the pressure loss coefficient

( )2

2

2 Reservoir InletA p pm

ρζ

−= , (2)

with the inlet Area A and the mass flow and density of the lubricating oil m and ρ , respectively.

The pressure loss coefficient of the lubricating lines upstream of the inlet of the present model, as a function of the pressure at the inlet Inletp was previously determined in additional CFD simulations. During an iteration of the computational run, the corresponding pressure in the oil reservoir *Resevoirp can be calculated at each time step during the simulation with the mass flow and pressure at the inlet

( ) 2*

22Inlet

Reservoir Inlet

p mp p

Aζ

ρ= + . (3)

The mass flow at the inlet is adjusted until *Resevoirp meets

the actual pressure in the oil reservoir, Reservoirp . The force-balance for the floating disk in a steady-state

operation yields the integral of pressure and friction forces on both walls (bearing housing and thrust collar side) has to be zero:

( ), 0FD z z

FD

F p n dA e∂

= − ⋅ ⋅ =∫ τ I , (4) where FD∂ is the surface of the floating disk and τ and p the shear stress and pressure. n is the normal to the surface FD∂ .

According to the conservation of angular momentum the momentum imposed on the floating disk has to be zero in order to ensure a stationary operation. It follows:

( ), 0FD z

FD

M p n dAξ∂

= − ⋅ × =⎡ ⎤⎣ ⎦∫ τ I . (5) In Equation (5) the vector ξ denotes the distance to the

axis of rotation. The fourth expression equates the force exerted on the wall of the thrust collar to the axial thrust of the turbocharger:

( ),TC z z Thrust

TC

F p n dA e F∂

= − ⋅ ⋅ =∫ τ I . (6) CONTROL UNIT

With Equations (3)-(6) the set of the four unknown

variables Ch , Th , FDω and m can be iteratively adjusted during a computational run. This is done by executing a control unit. The angular velocity of the floating disk is corrected with a simple P-controller according to the following equation:

( )1 1, ,i i iFD FD FD z FD zk M Mωω ω − −= + − , (7)


where iFDω is the adjusted angular velocity of the current

iteration, and 1−iFDω is the angular velocity of the previous iteration. ωk is the proportional gain. The term in brackets denotes the error between the calculated momentum of the floating disk (process variable) and the target momentum,

, 0FD zM = (set point). For the other unknowns similar controllers can be set up:

( )1 1, ,i i iC C hC FD z FD zh h k F F− −= + − , (8) with , 0FD zF = ,

( )1 1, ,i i iT T hT TC z TC zh h k F F− −= + − , (9) with ,TC z ThrustF F= and with the oil reservoir pressure, obtained from Equation (3):

( )1 * 1i i iv Resevoir Resevoirm m k p p− −= + − . (10) Based on a simplified analytical model an initial guess for

the gain values was obtained. Based on experience (convergence speed vs. stability) these values were adapted to 2×10-8 m N-1 for hCk , 5×10

-9 m N-1 for hTk , 5×10-8 kg (Pas)-1

for vk and 3 (Nms) -1 for ωk .

The controller is set up such that the variables are controlled based on the dominant dependency on the process variable. The film height on the turbine side depends predominantly on the force at the thrust collar wall. The film height on the side of the compressor is predominantly dependent on the force at the floating disk. Angular speed and axial momentum of the floating disk show a major dependency. Corrective action in one of the four variables leads to a change in all process variables. However, the change of the variables due to the crossover dependency is reduced by the iterative and alternate adjustment of all four variables. After an adjustment of a variable, only the flow field is solved for a few iterations, to enable the flow field to adjust to the new settings.

MESH MORPHING TECHNIQUE

Not only the boundary conditions are adjusted during the

control loop but also the geometry of the computational domain: the width of the lubricating gap on the compressor and the turbine side is either diminished or enlarged. As the axial position of the floating disk is fixed, the walls of the bearing housing and the thrust collar are adjusted such that the required gap widths of the control unit, iTh and

iCh , are met. The

modification of the gap size is relatively small. Thus a mesh morphing method can be applied. In this method only the axial position of the grid nodes is changed. In order to keep the grid quality at an adequate level, the mesh morphing method requires that the angles of the grid cells are almost orthogonal. At the beginning of a computational run the coordinates of all

grid nodes { }000 ,, zr φ in both gaps, as well as the initial axial gap width for both gaps, 0Th and

0Ch , are stored. Those

variables are available at any iteration. The displacement of the wall (bearing housing and thrust collar) is determined by using the result of the control unit, Equations. (8) and (9):

0i iC C Cz h hΔ = − , (11) 0i iT T Tz h hΔ = − . (12) In every iteration the new axial position of all nodes in the

gaps is calculated as: ( )0 0 ,i iT Tz z z zξ= + Δ , (13)

( )0 0 ,i iC Cz z z zξ= + Δ . (14) The displacement function ξ is modeled using a linear

approach, as it is exemplarily shown in Figure 3 for the lubricating gap on the compressor side.

Figure 3 The linear displacement function ξ for the gap on the compressor side.

SOLUTION PROCEDURE

The steady state flow field and operational parameters of

the thrust bearing are calculated in an iterative manner. At the beginning of a computational run, an initial guess for the four controlled variables and the flow field is read in. The mesh of the lubricating gaps, which is adjusted during the calculation, is initially sized for a nominal operation point. Every iteration consists of three sub steps in which the control unit, the mesh morpher and the flow solver are executed. This procedure is conducted in the following order:

1. Control unit: In the first step the control unit updates the

boundary and operational conditions. The new gap width at the compressor and turbine side, the new mass flow boundary condition at the inlet and the new rotational speed of the floating disk are determined using the four P-Controllers, Equations. (6)-(10).

2. Mesh solver: In the second step, the mesh in the gaps is adjusted according to Eqs. (13) and (14).

3. Flow solver: Finally the flow field (temperature, pressure, velocity, turbulent quantities) is solved.


The three steps are executed until a converged solution is obtained. An example of the convergence history is given in Figure 4. At the beginning of a computational run the flow is solved applying a constant mass flux at the inlet. After 12 iterations the angular velocity of the thrust collar wall is gradually increased until turbocharger speed is reached (Phase A). At the same time the control unit for the angular velocity of the floating disk, Equation (7), is activated. As a result, the floating disk, and thus the domain, start to rotate in order to eliminate the angular momentum induced by the flow. To prevent instability of the flow solution and an eventual crash of the computation, the control unit is only switched on every 10 iterations. After the thrust collar has reached turbocharger speed, the system is stabilized for some more iterations (Phase B). The residuals of the flow solver drop. In Phase C the control unit for the lubricating gap on the compressor side, Equation (8) is switched on, followed by the control unit for the turbine sided gap in Phase D, Eq. (9). From these phases on the width of the lubricating gaps on the compressor and turbine side are adjusted. The initially equally sized gaps are changed until a converged gap width is reached on both sides. The gap size control units are executed typically every 10 iterations. The mass flow control unit, Eq. (10) , is switched on in Phase E.

Figure 4 Typical convergence history during a computational run.

RESULTING FLOW FIELD In the following section a detailed description of the flow

field in the hydrodynamic thrust bearing is presented for an operating point at part load.

From the annular plenum at the inlet of the thrust bearing one part of the oil is feed into the lubricating groove at the compressor side. Due to the rotary motion of the floating disk the oil is accelerated in circumferential direction and pushed into the wedged surface and the gap between the bearing housing and the floating disk. The upper part of Figure 5 shows the pressure on both walls of the lubricating gap - the wall of the bearing housing and the wall of the floating disk. An oval pressure cell is established (red region in the figure). This cell absorbs the axial thrust of the turbocharger. At the side where the fluid enters the axial gap the pressure cell is tapered in circumferential direction. The shape of the oval cell flattens at the end of the wedge. At this position the gap has its minimal width; the maximum pressure is reached. The pressure cells are similar in shape and magnitude on both walls of the lubricating gap, indicating a constant pressure field over the gap width. In radial direction, the pressure in the gap is limited by the pressure at the inlet and the outlet of the bearing. The radial distribution of the pressure is balanced out over the floating disk showing the maximum at the middle. For small and medium radii the pressure in the lubricating groove is smaller than in the gaps. However it increases towards a maximum value at the end of the groove at a stagnation point. This pressure maximum is still smaller than the highest pressure in the cell.

Figure 5 Pressure and temperature field on the walls of the gap at the compressor side. Left: wall of the turbine housing. Right: wall of the floating disk. Top: pressure field. Bottom: temperature field.

The temperature field for both walls is shown in the lower

part of Figure 5. The temperature at the wall of the floating disk is significantly lower than on the bearing housing wall. One reason for this difference is that the fresh oil from the lubricating grooves first stays at the wall of the floating disk. On the other side, the bearing housing wall, the exposure time


is long enough to heat it up. The temperature increase in the gap is caused by thermal dissipation due to high velocity gradients in the gap. The oil enters the gap with the circumferential velocity of the floating disk. It is decelerated to zero at the bearing housing wall. At the outer edge of the floating disk a small band of cold fluid is flowing from the end of the lubricating groove towards the outlet. This can be clearly seen on the wall of the bearing housing.

Figure 6 Pressure, temperature and velocity field on a cutting plane through the gap on the compressor side on a medium radius. At the bottom the radial velocity field is shown; vectors indicate the circumferential relative velocity.

In Figure 6 the pressure, temperature and radial velocity

distribution in the compressor side gap at a medium radius are depicted. The pressure field is constant in axial direction, confirming the assumption, usually made when deriving the Reynolds-Equations for the calculation of thrust bearings. Throughout the groove (45-55°) the pressure is lower, slightly increasing to the right side, where the trailing wall is pushing the fluid into the gap.

The strong temperature gradient over the gap can also be observed in Figure 6. This emphasizes the necessity to consider the temperature dependent viscosity of the oil in the fluid model. The temperature at the wall of the bearing housing is at a very high level whereas the fluid at the wall of the floating disk stays at lower temperatures. The oil temperature rises when the gap size decreases between the angular positions 35° and 45°. In the lower graph of Figure 6, the radial velocity field is depicted. Arrows indicate the tangential relative velocities. The radial velocity is positive throughout the gap where the oil is flowing outwards. In the lubricating groove (45-55°) the fluid displays the pumping effect; it is also flowing radially outwards. However, a dark blue color indicates that the fluid entering the gap is being pushed radially inwards by the radial pressure gradient.

The temperature and pressure at the wall of the thrust collar and the floating disk in the gap on the turbine side are shown in Figure 7. A similar, oval shaped pressure cell is established in the gap on the side of the thrust collar. It is again tapered towards the lubricating groove, where the fluid is

entering the gap and flattens on the side where the gap narrows. The pressure in the lubricating groove increases towards the outlet, however the maximum pressure at the end of the groove is less prominent than in the groove on the compressor side (Figure 5) as the area on this side is slightly smaller. The temperature at the wall of the floating disk is considerably lower than the temperature at the wall of the thrust collar. As previously stated, this can be explained by the residence time and the inertia of the oil. It is entering the zone at a low temperature. The wall temperature of the floating disk is increasing with the increasing residence time of the oil and the reduction of the gap width in circumferential direction. The cooling effect of the oil arriving from the supply hole can be observed by the band of decreased temperature on the wall of the thrust collar (green region). From there the temperature rises in a radial direction and exhibits its maximum at the outer edge of the wall.

Figure 7 Pressure and temperature field on the walls of the gap at the turbine side. Left: wall of the thrust collar. Right: wall of the floating disk. Top: pressure field. Bottom: temperature field.

The flow variables in the gap on the compressor side at a

medium radius are depicted in Figure 8. The pressure field does not experience any gradients in axial direction. The pressure cell situated in the wedged surface with its maximum near the smallest gap size (5°) can be clearly seen. The gradients in temperature are nearly as high as in the gap on the compressor side. The maximum temperature is reached at the wall of the thrust collar. The circumferential velocity (vectors) and the radial velocity field are shown in the lower part of the figure. The circumferential velocity reaches its maximum at the wall of the thrust collar (which is rotating at turbocharger speed) and decreases towards the floating disk. The radial velocity is positive with higher velocities in the middle of the gap and in the lubricating groove.


Figure 8 Pressure, temperature and velocity field on a cutting plane through the gap on the turbine side on a medium radius. The radial velocity field is shown at the bottom; vectors indicate the circumferential relative velocity.

Figure 9 Pressure and velocity field in cutting planes at the supply hole. At the top the axial velocity field is shown; vectors indicate the in plane velocity.

Results of the flow field in the supply hole are given in

Figure 9, where the velocity and pressure field on different cutting planes are depicted. The flow in the supply hole is highly three dimensional and turbulent. This is a result of the complex geometry, larger length scales and the rotational motion of the floating disk. At the beginning of the supply hole, the fluid has to be accelerated in the circumferential direction to meet the speed of the floating disk. The pressure field depicted in Figure 9 shows maximal values at the trailing wall of the borehole (Plane 1). During the passage through the supply hole this maximum propagates to the top of the hole and the leading wall (Plane 2 and 3). This is a result of centrifugal forces, which impose an angular momentum. The twisting movement of the fluid particles during their passage through the supply hole can be seen at the velocity profiles, as depicted in the upper part of the figure. The axial velocity field exhibits

its maximum at the trailing wall. This region of high velocities also propagates to the top of the hole. In the middle of the cutting planes, backflow regions with negative velocity can be observed.

VAILDATION AGAINST MEASSUREMENT DATA In the following section results for different operating

points of an ABB Turbocharger are shown and validated against measurements. Measurements have been conducted on a combustion chamber test rig. During the measurements, data was obtained for the rotating speed of the floating disk, the gap width on the compressor side as well as temperatures at various positions.

Table 1 Boundary conditions of the three operating points. */ nnTC

*/ FFThrust */ pp ervoirRes

*/ΘΘReservoir

OP1 0.80 0.38 1.00 1.00 OP2 1.00 1.00 1.00 1.00 OP3 1.35 2.28 1.00 1.00

Results have been calculated for three operating points at

three different turbocharger speeds: one at the nominal rotational speed *n , one at reduced speed and one at nearly maximum speed, *0.8n and *1.35n . The values listed in Table 1 are normalized with the nominal rotational speed and force,

*n and *F , a characteristic pressure *p and a temperature

difference *Θ . The thermodynamic conditions of the oil reservoir (pressure and temperature) were kept constant for all operating points, whereas the axial thrust varies over the operational range.

Figure 10 Calculated and experimentally obtained rotational speed of the floating disk vs. turbocharger speed.


Figure 10 shows the measured and calculated speed of the floating disk. The floating disk rotates at around 40% of the turbocharger speed for all operating points. Both the calculated data and the measurements show the trend of increasing speed of the floating disk with turbocharger speed. All calculations show an offset towards a higher speed. However, for the low and nominal operating point the error is less than 10%. At the high operating point the calculated speed of the floating disk differs by 20%. This discrepancy is attributed to the fact that the heat fluxes through the walls in the bearing are neglected. As a result, the calculated temperature in the film between the floating disk and the bearing housing are calculated too high (Figure 12), leading to an over prediction of the viscosity. In turn the calculated shear forces in the film are too low. This effect is predominant at high rotational speeds, where viscous dissipation is strong.

Figure 11. Oil film thickness on the turbine and compressor side of the thrust bearing vs. turbocharger speed.

The oil film thickness was only measured on the side of the compressor. Measurements were conducted with three eddy current sensors mounted in the bearing housing. Measuring the distance to floating disk, the sensors detect the floating disk profile consisting of taper, land and groove. The minimum film thickness is evaluated for each sensor. The data presented show the arithmetic average of the three sensors. The measurement error is in the range of ±10%. The calculated width of the lubricating gap at the turbine side and the measured data are compared in Figure 11. Both the gap at the turbine and the compressor sides of the floating disk decrease with increasing turbocharger speed. For the operation point at reduced speed, the gap is predicted too wide in the numerical simulation. This can be explained by a under estimation of the axial thrust. For low turbocharger speeds, the height of the lubricating film is very sensitive to changes in axial thrust, as explained below (Figure 16). For the nominal and the higher operating points measurements and calculations agree very well. For all

operating points the gap on the compressor side is wider than on the turbine side. This difference decreases with higher turbocharger speed and hence axial thrust.

Figure 12 Comparison between measured and calculated temperatures in the lubricating gap on the turbine side. Results are plotted for the three different operating points.

The temperature of the bearing housing was measured by thermocouples mounted close to the oil film (g) at three different radial positions. The experimentally obtained results are compared to the calculations in Figure 12. All data show a similar trend; the temperatures increase with higher turbocharger speed. The highest temperatures are measured and calculated at the position 1 at the medium radius. The temperatures at the inlet and outlet of the oil film are nearly equal (positions 2 and 3). As a result of the over-prediction of the gap size for the operating point with reduced turbocharger speed, the calculated temperatures are too low for this point. For both the other operating points, the temperatures are calculated too high. As previously mentioned, this discrepancy is caused by the adiabatic conditions at the bearing housing wall. In reality a heat flux towards the bearing housing reduces the temperature of the lubricating film. When comparing the experiments and calculations, it has to be kept in mind that the temperatures are measured in a region where large gradients are present.

Results of the calculated mean lubricant temperature at the outlets of turbine and compressor side gap and the supply hole are presented in Figure 13. The temperature in the supply hole is nearly the same as the temperature at the inlet of the computational domain. This indicates that the fluid is flowing directly into the supply hole. The temperature in the hole increases slightly with turbocharger speed. Compared to the increase at the other measurement positions this increase is insignificant. Both the temperature at the outlet of the turbine and compressor-side gap of the floating disk exhibit a higher temperature which increases with higher turbocharger speed.


The temperature at the outlet of the gap on the turbine side is higher than on the compressor side. This is a result of higher axial velocity gradients due to a higher velocity difference between the floating disk and the wall of the thrust collar as well as a smaller gap size (Figure 11).

Figure 13 Calculated mean lubricant temperature at the outlets of the lubricating gaps and the supply hole vs. turbocharger speed.

The lubricant mass flow through the axial bearing is shown in Figure 14 (red line). It decreases with turbocharger speed and exhibits a non-linear behavior. This can be explained by two major effects. On the one hand, the pumping effect of the floating disk increases with its rotational speed. On the other hand the gap widths are reduced by the increasing thrust due to turbocharger speed. The second outbalances the pumping effect of the floating disk. As the pressure at the oil reservoir is kept at a constant level, mass flow reduces.

In the design process, the axial thrust of a turbine can be estimated within a confidence interval of ±10%. The influence of a 10% higher and 10% lower axial thrust is investigated in the following section. All other operating conditions were kept unchanged for these calculations. In Figure 14 the mass flow for both cases (0.9 FThrust and 1.1 FThrust) is plotted. Due to increasing gap widths (Figure 16), the mass flow through the axial bearing increases when the thrust is reduced. In the case of increased thrust, the mass flow drops. The change is higher for the lower operating point and less pronounced for higher turbocharger speeds. Here, the counteracting pumping effect of the floating disk is higher.

Figure 14 Mass flow through the thrust bearing for different operating points and a thrust variation.

The sensitivity of the speed of the floating disk to a thrust variation is relatively small, as shown in Figure 15. However, at the nominal operating point the speed of the floating disk exhibits an abnormal dip. This can be explained by an abnormally high temperature in the film on the side of the bearing collar. Compared to the other operating points, the temperature of the film is almost the same as for nominal thrust. The abnormally high temperature of the film reduces the viscosity of the fluid and, in turn, the rotational speed of the floating disk drops.

Figure 15 Floating disk speed for different axial thrust vs. turbocharger speed.

Figure 16 reveals the influence of the axial thrust on the

gap widths. The bearing has to absorb the increase in thrust by a higher pressure in the lubricating film. As the pressure in the oil reservoir is kept at a constant value, this pressure rise can only be established by reducing the film height. The gap width


reduces with increasing thrust. For all operating points this change is more pronounced on the side of the bearing housing. At low turbocharger speeds, the gap width is very sensitive to changes in axial thrust: when increasing the thrust by 10% the gap at the compressor side is reduced by 8.7%, while the gap on the turbine side is reduced by 5.7%. When the thrust is increased by 10% the gap widths increase by 9.4% and 6.0% respectively .

Figure 16 Width of the lubricating gaps on the turbine and compressor side of the floating disk for the three different operating points with a variation of the axial thrust.

Figure 17 Mean lubricant temperature at the outlet of the lubricating gaps vs. turbocharger speed for different axial thrusts. With increasing thrust, the gap widths reduce and, as the speed of the floating disk barely changes, the velocity gradient in axial direction increases. An increase in the velocity gradients leads to higher viscous dissipation and the oil-temperature

rises. Figure 17 shows that higher temperatures are clearly seen at the outlets of both gaps for high turbocharger speeds. Here the temperature rises by 3.6% on the compressor side and 3.9% at the turbine side. When decreasing the axial thrust, the temperature decreases accordingly by 3.8% and 4.5% respectively. At low turbocharger speeds these temperature changes are less pronounced and in the range of 0.7%-2.8%.

CONCLUSIONS A comprehensive model has been established to investigate

the three dimensional flow in a hydrodynamic thrust bearing with floating disk. The model was set up such that it adapts automatically when the operating conditions change. The latter are the supply pressure and temperature in the oil reservoir, axial thrust and turbocharger speed. The resulting lubricating film thicknesses, rotational speed of the floating disk and the mass flow are adjusted by applying an automated control unit.

The results confirm the existence of pressure cells in both lubricating gaps which absorb the axial thrust. It was demonstrated that the pressure in both gaps does not change in the axial direction. The velocity field in the lubricating film is dominated by the circumferential velocity. The axial velocity gradients induced by the rotational motion of the walls are the reason for high thermal dissipation in the bearing. With increasing exposure time, the oil temperature rises. Large local temperature differences and strong axial gradients emphasize the importance of the thermal modeling and the need for a temperature dependent viscosity model.

The flow in the lubricating grooves and the supply hole is turbulent, showing regions of highly three dimensional flow with recirculation zones.

The results obtained in the present study were compared to experimental data and showed good agreement. Excessive rotational speeds in the floating disk, especially for the high operating point, can be explained by the fact that the heat fluxes through the walls of the bearing have been neglected. The over-prediction of the turbine-side gap size, as well as the lower calculated film temperatures for this operating point, can be explained by the uncertainty regarding axial thrust.

In a parametric study where the axial thrust was varied, it was shown that not all aspects of the behavior of the system are intuitively predictable. A small variation in axial thrust changed the system behavior. An increase in axial thrust leads to smaller gap sizes and a smaller oil mass flow through the bearing. The decreased lubricating film height results in higher velocity gradients which cause an increase in thermal dissipation and, combined with larger exposure time, an increase in oil temperature. This effect lowers the viscosity of the oil, which in turn changes the system behavior. Lower thrust leads to larger gap sizes, increased oil flow and reduced temperatures.


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