Analysis of Flow in the Lock-up Clutch of an Automotive Torque Converter

131 Analysis of Flow in the Lock-up Clutch of an Automotive Torque Converter Eiji EJIRI The flow through the single-plate lock-up clutch in an automotive torque converter with a 250-mm nominal diameter was numerically investigated using a CFD code. The flow was computed under various clearances between the lock-up piston and the torque converter cover. The stable location of the lock-up piston was determined so that the thrust acting on it became zero. The computation results showed that the fluid flowed outwards in the narrow channel between the lock-up clutch facing and the converter cover, whereas the flow reversed inwards near the lock-up piston surface upstream and downstream of the narrow channel in most cases. Along the outer surface of the axial flow channel near the exit, the flow also reversed far upstream of the channel. The computation results well predicted the stable position of the lock-up piston. It is noteworthy that the sharp increase in clearance in the coupling range can be clearly captured with this method. Key Words: Axisymmetric Flow, Boundary Layer, Computational Fluid Dynamics, Finite Volume Method, Internal Flow, Lock-up Clutch, Torque Converter 1. Introduction The torque converter is a kind of turbomachine that is widely used as a start-up device for automobiles equipped with a conventional stepped automatic transmission. It has also been applied to continuously variable transmissions (CVTs) quite recently, which are considered to be nextgeneration gearboxes (1), (2). Its functions include damping of engine torque fluctuation, damping of noise and vibration in the drive line, and automatic amplification of torque according to the difference in rotational speed between the input and output shafts without requiring any external control. A typical automotive torque converter consists of three major hydrodynamic elements a pump, a turbine and a stator, as shown in Fig. 1. The characteristic curves of a typical torque converter with a 236-mm nominal diameter are shown in Fig. 2, where the torque capacity coefficient, torque ratio and efficiency are indicated as τ, t and η, respectively, as functions of the speed ratio, e. When the speed ratio (i.e., the ratio of the turbine speed to the pump speed) exceeds the clutch point shown in the characteristic curves in Fig. 2, the stator begins to Received 2nd March, 2005 (No. 05-4016) Department of Mechanical Science and Engineering, Chiba Institute of Technology, 2 17 1 Tsudanuma, Narashino-shi, Chiba 275 0016, Japan. E-mail: ejiri.eiji@it-chiba.ac.jp Fig. 1 Torque converter with lock-up clutch rotate freely, being disengaged from its internal one-way clutch. In this state, the torque converter operates as a fluid coupling. A lock-up clutch is often incorporated in the torque converter as shown in Fig. 1 in order to improve vehicle fuel economy in this speed ratio range. This improvement is obtained because the lock-up clutch can reduce fluid flow losses by engaging the input and output shafts of the torque converter or by allowing the shafts to rotate at relative speeds with only a small amount of slip.

132 Fig. 2 Characteristic curves of typical automotive torque converter When the lock-up clutch engages, the working fluid between the converter cover and the lock-up piston is sucked away towards the shaft by the pressure reduction that occurs there. On the other hand, when the lock-up clutch is released, the working fluid between the converter cover and the lock-up piston is fed from the shaft by the pressure increase that occurs there. The location of the lock-up piston should not be too far from the converter coverwhenthelock-upclutchbeginstoengageinthe higher speed ratio range in order to improve fuel economy on one hand. It should not be too near the converter cover when the torque converter operates in the lower speed ratio range in order to secure the endurance and reliability of the clutch facing on the other hand. Therefore, it is very important to understand and predict the behavior of the lock-up piston activated by the hydraulic pressure. Some experimental work has been done to elucidate the internal flow characteristics of the torque converter. Unsteady flow between the pump and turbine impellers was measured by hot-film anemometry by Browarzik (3) in a detailed study of the effect of the pump-turbine interaction on flow fields. Gruver, Flack and Brun (4) (7) used a laser Doppler velocimeter to investigate the internal flow in the pump and turbine impellers. They analyzed the complex three-dimensional flow fields in the blade passage on the basis of measured steady and unsteady velocities. Pressure measurements made by Marathe et al. (8) with high-response pressure transducers showed strong unsteady hydrodynamic interference between the elements. Ejiri et al. (9) evaluated the performance of each element by measuring flow between any two elements with five-hole Pitot probes. The pump was shown to be Series B, Vol. 49, No. 1, 2006 the major source of loss in the speed ratio range where vehicles are most frequently operated in everyday driving. Flows through the pump impeller (10), (11) as well as through the three elements (9), (12) were computed by using CFD codes. Some of the computational results showed good qualitative agreement with the measured flow patterns. Ejiri et al. (13) and Kubo et al. (14) applied a general CFD code to a practical in-house CAE system to obtain an improved torque converter design. Some of the design parameters, such as the torus flatness ratio and the blade bias angle, were optimized by using the system and an improvement in efficiency wasdemonstrated experimentally. Some studies have been reported so far regarding turbulent flow analysis of a rotating disk in a vessel (15), (16). However, very little is known about the behavior of an axially movable disk that is influenced by the hydraulic force in laminar flow. In this study, the flow through the single-plate lock-up clutch in an automotive torque converter was numerically investigated using a CFD code as the first step toward obtaining a better understanding of this type of problem. The flow was computed under various clearances between the lock-up piston and the converter cover. The thrust on the lock-up piston was then calculated, based on the obtained pressure distribution. Finally, the axially stationary position of the piston was determined so that the thrust acting on it became zero. The computed results were validated using the experimental data obtained with an actual machine. 2. Nomenclature C M : torque coefficient (= 2T/(1/2 ρω 2 r 5 )) e : speed ratio (= N 2 /N 1 ) K : capacity factor (= N 1 ) T1 N : rotational speed p : static pressure p : reduced pressure (= p+1/2 ρω 2 (rt 2 r 2 )) Q : flow through lock-up clutch Re : Reynolds number r :radius r t : pump exit outer radius s : clearance between the lock-up clutch facing and converter cover T : torque t : torque ratio (T 2 /T 1 ) η :efficiency ν : kinematic viscosity ρ : density τ : torque capacity coefficient (= T 1 /N1 2) ω : angular velocity ω : angular velocity of rotating system of reference Subscripts 1 : pump 2 : turbine JSME International Journal

133 3. Numerical Analysis 3. 1 Computation method Viscous flow computations were performed with a general-purpose thermofluids analysis code employing the finite volume method of spatial discretization. Axi-symmetric three-dimensional incompressible Navier- Stokes equations were solved with the code. The Navier- Stokes equations and the continuity equation in cylindrical coordinates can be written as follows if the flow is assumed to be axi-symmetric, v r v r r v2 θ r +v v r z z p r +ν ( 2 v r r 2 + 1 r = 1 ρ v θ v r r + v rv θ v θ +v z r z ( 2 v θ = ν r + 1 2 r v θ r v θ r + 2 v θ 2 z 2 v z v r r +v v z z z = 1 p ρ z +ν v r r v ) r r + 2 v r 2 z 2 ) ( 2 v r r + 1 v z 2 r r + 2 v z z 2 v r r + v r r + v z z = 0 (4) where r, θ, andz denote the radial, azimuthal and axial coordinates, respectively. In discretizing the convection terms of Eqs. (1) to (3), the QUICK scheme (17),a third-order (second-order in accuracy) upwind differencing scheme, was used to obtain a stable solution while suppressing numerical diffusion. The diffusive and source terms were discretized by second-order accurate forward or backward differencing schemes. The SIMPLE algorithm (18) was employed to solve the algebraic finitevolume equations resulting from the discretization operation. Two flow directions are possible in the channel between the converter cover and lock-up piston. One is from the outer radius of the lock-up clutch to the shaft, and the other is from the shaft to the outer radius of the lock-up clutch. In the author s experience, the latter case more often gives rise to serious difficulties in the development stage of the torque converter. Therefore, computations were limited to this flow direction in this study. The flow was assumed to be steady and laminar. A torque converter with a 250-mm nominal diameter and a low profile torus cross section as shown in Fig. 3 was used as the computation object. An example of the computational grid is given in Fig. 4. The incorporated parts, such as the damper springs, the damper case and the rivets, were modeled by simple geometries. Altogether 20 480 grid cells were used, and the clearance, s, between the lockup clutch facing and the converter cover was 2.0 mm in this figure. Three types of grid systems, having grid num- ) (1) (2) (3) Fig. 3 Cross-sectional view of analyzed torque converter Fig. 4 Computational grid (s = 2.0 mm) bers of 10 240, 20 480 and 81 920, respectively, were used to evaluate the grid number dependence of the computed flow in the lock-up clutch. The computed thrust results in all three grid systems fell in the range of ±1%, which suggests that a sufficiently grid-independent solution was obtained with 20 480 grid cells for all practical purposes. Mesh point clustering was performed near the boundary. The distance of the nearest grid point from the wall was 0.007 mm typically when s, the clearance between the lock-up facing and the converter cover, was 0.15 mm as shown in Fig. 9 (a), where y + was about 0.6 in terms of v r and the distance from the converter cover. A uniform velocity, calculated from the volume flow

134 measured experimentally, was given as the inlet boundary condition of the flow field, and a uniform pressure was given as the exit boundary condition. The no-slip condition was imposed on the wall boundary. The converter cover was rotating at the same speed as that of the pump impeller, N 1. All the other solid walls, such as the lock-up piston, the modeled damper spring and the turbine shell, were rotating at the same speed as that of the turbine impeller, N 2. Thesolutionwasassumedtohaveconverged when all the normalized residuals in the mass and momentum conservation equations were less than 10 3. The density and the kinematic viscosity of the working fluid were ρ = 830 kg/m 3 and ν = 10 10 6 m 2 /s, respectively. The flow was computed under various clearances, s, between the lock-up piston facing and the converter cover at a fixed speed ratio, e. In so doing, the computational grid was modified to match the increased or decreased computational domain according to the change in the flow field. The thrust on the lock-up piston was then calculated, based on the pressure distribution obtained over both sides of the piston. Finally, the axially stationary position of the piston was determined so that the thrust acting on it became zero. 3. 2 Preliminary computation As the first step, the flow around a 200-mm-diameter rotating disk in a 240-mm-diameter stationary hermetic cylindrical vessel, as shown in Fig. 5, was computed to determine the appropriate computational conditions for obtaining sufficient accuracy for practical use within a reasonable CPU time. Computation accuracy was checked under two rotational speed conditions (N = 200 rpm and 2 000 rpm) using 6 000 grid cells in total. The ratio of the clearance between the disk surface and the vessel wall, s, to the disk radius, r, was 0.02. The torque coefficient of the disk, C M, calculated from the peripheral flow velocity distribution near the disk wall is shown in Fig. 6 (19),in which the values are plotted against the Reynolds number, Re, based on the disk radius, r, and the peripheral velocity of the disk, rω. C M and Re are defined by the following formulae. C M = 2T/(1/2 ρω 2 r 5 ) (5) Re = r 2 ω/ν (6) The relation is very simple when the flow is laminar, Re < 10 5, and when the clearance is very small. The torque coefficient analytically becomes C M = 2π(r/s)Re 1 (7) This equation is plotted as curve (1) in Fig. 6 for a value of s/r = 0.02. It shows very good agreement with the experimental values reported by Zumbusch. Schultz-Grunow (20) investigated this flow both for laminar and turbulent cases. The torque coefficient becomes C M = 2.67Re 1/2 (8) This equation is plotted as curve (2) in Fig. 6. It agrees with the measured values up to about Re = 2 10 5 and connects fairly well with Eq. (7). For Reynolds numbers Re > 3 10 5 the flow around a disk rotating in a vessel becomes turbulent as usual. This case was also solved by Schultz-Grunow, who used an approximation method. The tangential velocity was assumed to obey the 1/7th power law and it was shown that the core revolves with about half the angular velocity. The moment coefficient was shown to be equal to C M = 0.062Re 1/5 (9) This equation has been plotted in Fig. 6 as curve (3). Compared with the experimental data, it results in values that are too small by about 17%. The present computational results denoted as the open squares in the figure coincide well with both the analytical and experimental results. The figure also shows Fig. 5 Rotating disk in stationary hermetic vessel Fig. 6 Torque coefficient of rotating disk in hermetic vessel (19) Series B, Vol. 49, No. 1, 2006 JSME International Journal

135 that the flow around a rotating disk in a stationary hermetic cylindrical vessel is laminar with a Reynolds number under 10 5. The Reynolds number based on the differential peripheral velocity between the converter cover and the lock-up clutch is 6.54 10 4 if the clutch diameter d, N 1 and N 2 are assumed to be 250 mm, 2 000 rpm and 1 600 rpm (i.e. speed ratio, e = 0.8), respectively. This means that the flow through the lock-up clutch in the highspeed ratio range of the torque converter, where the difference between the pump and turbine rotational speeds is small, has to be computed as laminar flow. The preliminary computation was carried out under the assumption of laminar flow, and this assumption was shown to be right as a result. 4. Experimental Procedure and Results Fig. 7 Outline of experimental apparatus An outline of the experimental apparatus is shown in Fig. 7. The input shaft (i.e., the pump driving the converter cover) and the output shaft (driven by the turbine) of the torque converter were connected to DC dynamometers, with tachometers and torquemeters installed in between. These dynamometers were controlled so that the input torque was a constant 98 Nm at a given speed ratio. An ordinary automatic transmission fluid was provided from an external pressure source as the working fluid and controlled so that the pressure difference between the inlet and exit of the torque converter (P IN P OUT )waskept to 98 kpa. The exit temperature of the torque converter was controlled to 80 ± 1 deg. C. The working fluid was supplied from the external pressure source through a horizontal hole in the output shaft, passed through a thin radial flow channel between the lock-up piston and the converter cover, and was then introduced into the main flow field formed by the three major hydrodynamic elements of the torque converter. At the same time, the same amount of the working fluid was sucked away from the main flow field through the annular channel near the one-way clutch and returned to the external pressure source. The whole flow field was pressurized (P IN = about 400 kpag) so that it was filled only with liquid, precluding the occurrence of cavitation except in rare cases. Therefore, it is reasonable to think that the volume flow of the supplied working fluid was equal to the volume flow through the lock-up clutch. In addition, the influence of the flow supplied through the lock-up clutch on torque converter performance can be ignored. The reason is that the volume flow of the supplied working fluid is normally estimated to be less than 1% of that of the circulating flow in the three major hydrodynamic elements of the torque converter. The clearance, s, between the lock-up clutch facing and the converter cover was measured in the speed ratio range from 0.3 to 0.9 approximately while the speed of the pump as well as that of the converter cover were kept at a constant 2 000 rpm. The speed of the turbine as Fig. 8 Measured flow through lock-up clutch well as that of the other parts assembled with it, including the lock-up clutch, were varied from 600 to 1 800 rpm. The distance between the lock-up piston and the converter cover (both metal surfaces) was measured by two noncontact gap sensors installed at 90 deg. circumferential intervals on the converter cover. The clearance, s, was then estimated by subtracting the thickness of the clutch facing paper from the measured gap. The output of the precalibrated sensors was amplified electronically and transmitted outside by means of a slip ring. The flow rate through the lock-up clutch was measured by a gear-type flowmeter installed just downstream of the external pressure source and the results are shown in Fig. 8. Uncertainty of the measurement obtained with the gap sensors and the flowmeter was estimated as 2% and 5%, respectively. 5. Results and Discussion 5. 1 Velocity vectors Figure 9 shows the computed velocity vectors of the major flow fields in the case of s = 0.15 mm at a speed ratio of 0.7, where the lock-up clutch is regarded as stable or balanced, as almost no thrust acts on it. At this speed ratio, the rotational speed of the pump and the converter cover is 2 000 rpm and the rotational speed of the

136 (a) Inside clutch facing (b) Outside clutch facing (c) Just downstream of lock-up piston (d) Near exit Fig. 9 Velocity vectors of major flow fields (e = 0.7, s = 0.15 mm) turbine and the other parts assembled with it, including the lock-up clutch, is 1 400 rpm. In each figure, the location of the close-up velocity field is shown by an open square in the small figure on the right. Figure 9 (a) shows the radial flow field inside the clutch facing, Fig. 9 (b) that outside the clutch facing and Fig. 9 (c) and (d) the axial flow fields downstream of the clutch facing. Figure 9 (a) shows that the flow spreads outward at high speed because the channel between the clutch facing and the converter cover narrows. The radial velocity profile in the narrow channel indicates a typical laminar flow, which has a steep peak in the middle. However, the flow reverses inward near the lock-up piston just upstream and downstream of the narrow channel owing to the adverse pressure gradient produced by the average flow (see Fig. 9 (a) and (b)). This is because the fluid has a relatively low peripheral velocity component and only small centrifugal force is exerted there. Figure 9 (b) also shows that only a small flow is seen on the left side of the lock-up piston, which means the fluid there almost stands still relative to the turbine impeller. In other words, the fluid on the left side of the lock-up piston rotates almost as a solid body at the same speed as the turbine impeller. The channel outer radius decreases toward the exit in the axial flow channel near the exit, so that the flow near Series B, Vol. 49, No. 1, 2006 the outer radius reverses, driven outwards due to stronger centrifugal force than that of the average flow (Fig. 9 (d)). This also causes a large amount of reverse flow seen near the outer wall of the channel far upstream of the exit (Fig. 9 (c)). As a result, the reverse flow forms a recirculating flow region near the outer radius at the exit. In terms of hydrodynamic design, the difference between the inner and outer radius of the channel should be smaller near the exit than in the present case in order to reduce the pressure loss caused by the reverse flow. In addition, the absolute tangential flow velocity close to the wall (not shown) is almost identical to the peripheral component of the wall velocity everywhere, and it varies almost linearly with the distance from the wall across the flow channel width between any two walls. These characteristics are typical of laminar flow. The capacity factor, K, orwhatisreferredtoasthe K-factor, is sometimes used in place of the torque capacity coefficient, τ, as a parameter of torque converter performance and is defined as follows (21), (22). K = N 1 (10) T1 The capacity factor, K, indicates a value proportional to the pump speed required to absorb the input torque and is inversely proportional to the root of the torque capac- JSME International Journal

137 (a) s = 0.1mm (b) s = 1.0mm Fig. 10 Pressure distribution (e = 0.7) ity coefficient, τ. This factor was calculated for the fluid between the lock-up clutch piston and the converter cover for three speed ratios, 0.7, 0.874 and 0.9. Here, K was obtained from the computed drag torque exerted on the converter cover inner surface, which was rotating at a speed of 2 000 rpm. The results show that K = 2 980, 5 440 and 6 490 rpm/(n m) 1/2, respectively. The corresponding K values for the torque converter are 154, 189 and 212 rpm/(n m) 1/2, respectively. It is noteworthy that the order of the drag torque exerted on the converter cover is far less than 1/100 of the input torque of the torque converter. 5. 2 Pressure distribution Figure 10 (a) and (b) show the pressure distribution for clearance, s, of 0.1 mm (thrust acts from right to left) and 1.0 mm (thrust acts from left to right) at a speed ratio of 0.7. At this speed ratio, the rotational speed of the pump and the converter cover is 2 000 rpm and the rotational speed of the turbine and the other parts assembled with it, including the lock-up clutch, is 1 400 rpm. Note that the lock-up piston is not in a stable position in either case. The contour numbers in the figures indicate the relative pressure in MPa, which has been normalized by the exit pressure. The pressure distributions between the turbine shell and the lock-up piston are almost the same in both cases because the fluid on the left side of the lock-up piston rotates as a solid body at almost the same speed as that of the turbine impeller. However, the pressure distributions between the lock-up piston and the converter cover differ considerably between the two cases. Figure 11 (a) and (b) show the pressure distribution on the lock-up piston surface as a function of the radius. In the case of s = 0.1 mm shown in Fig. 11 (a), the pressure acting on the right-hand-side surface decreases between r = 111 mm and 125 mm as the radius increases, whereas the pressure acting on the left-hand-side surface steadily increases there. As a whole, the pressure acting on the right-hand-side surface is greater than that acting on the left-hand-side surface. In the case of s = 1.0 mm shown in Fig. 11 (b), on the contrary, the pressure acting on the left-hand-side surface is greater than that acting on the right-hand-side surface as a whole. As a result, more negative pressure on the lefthand-side surface of the lock-up piston draws the piston to the left in the case of s = 0.1 mm (Fig. 11 (a)), and more negative pressure on the right-hand-side surface draws the piston to the right in the case of s = 1.0 mm (Fig. 11 (b)). Figure 12 (a) and (b) show the reduced pressure distribution for both clearances, corresponding to Fig. 11 (a) and (b). The reduced pressure, p,isdefinedas p = p+1/2 ρω 2 (rt 2 r 2 ), (11) where ω is assumed to have a value of (ω 1 +ω 2 )/2 inthe narrow channel between the lock-up piston and the converter cover and in the flow field having a radius larger than 125 mm between the turbine shell and the lock-up piston. ω is also assumed to have a value of ω 2 in the flow field having a radius smaller than 125 mm between the turbine shell and the lock-up piston. The reduced pressure indicates static pressure minus centrifugal pressure, which is caused by the rotating system. Therefore, the reduced pressure difference between two points along the flow shows the pressure loss owing to fluid flow itself. Figure 12 (a) shows that most of the loss occurs in the nar-

138 (a) s = 0.1mm (b) s = 1.0mm Fig. 11 Pressure distribution on lock-up piston surface (e = 0.7) (a) s = 0.1mm (b) s = 1.0mm Fig. 12 Reduced pressure distribution (e = 0.7) row clearance between the lock-up clutch facing and the converter cover. The pressure loss amounts to as much as 40 kpa there. However, Fig. 12 (b) shows that reduced pressure gradually decreases along the flow channel from the inlet to the exit, which means small loss is constantly generated along the channel. This is clearly demonstrated in Fig. 13, where the reduced pressure distribution on the right-hand-side surface of the lock-up piston is shown as a function of the radius for the cases of s = 0.1mm and s = 1.0 mm. As a matter of course, the narrower the clearance is, the greater the loss becomes. The pressure distribution could be predicted by a simple one-dimensional analysis. However, such an analysis would not capture either the above-mentioned reverse flow near the lock-up clutch facing or that near the exit of the channel, with the result that the pressure loss, especially Fig. 13 Reduced pressure distribution on right side of lock-up piston (e = 0.7) Series B, Vol. 49, No. 1, 2006 JSME International Journal

139 Fig. 14 Thrust acting on lock-up piston Fig. 15 Clearance between lock-up facing and converter cover in the outer radius area, could not be estimated accurately. As a result, the thrust could not be predicted with reasonable accuracy because the pressure in the outer radius area contributes more to the thrust than that in the inner radius area due to the nature of the surface integral. 5. 3 Thrust acting on lock-up piston Figure 14 shows the computed thrust when the clearance, s, was varied over three speed ratios (e = 0.7, 0.874 and 0.9), each indicated by the closed circles, squares and triangles, respectively. Thrust is indicated here in N/deg, which means the thrust acting on the lock-up piston per unit angle of the piston. The clearance measured with the non-contact gap sensors for e = 0.7 and 0.874 is also shown in the figure by the open circle and square, where the thrust acting on the lock-up piston is regarded as zero. The measured stable position of the piston is 0.20 mm at e = 0.7, whereas the computed one is about 0.14 mm. The measured stable position of the piston is 1.00 mm at e = 0.874, whereas the computed one falls in the range from 0.3 to 1.5 mm, where the thrust is almost zero. This means the computation method provides a reasonable solution because the piston can be stationary at any position within the range if the effect of an external disturbance is taken into account. Furthermore, for e = 0.9 a computation was carried out in the case of s = 2.0 mm only, and the result showed that the piston was pushed to the turbine side, which coincided with the experimental result (a stopper was installed at the position of s = 2.0mm in the experimental apparatus). 5. 4 Clearance between lock-up facing and converter cover Figure 15 shows the change in the clearance between the lock-up clutch facing and the converter cover as a function of the speed ratio. The clearance measured with the non-contact gap sensors for e = 0.7, 0.874 and 0.9 is also shown in the figure by the open circles. The experiment revealed that the clearance sharply increased near e = 0.874, and the computation predicted this phenomenon with good accuracy. This phenomenon can be explained as follows. Because the fluid on the left side of the lock-up piston rotates almost as a solid body at the same speed as the turbine impeller, ω 2, the pressure is proportional to ω 2 2 on the one hand. On the other hand, the fluid between the lock-up piston and the converter cover rotates on average at a speed approximately between that of the pump and the turbine impellers, (ω 1 +ω 2 )/2,whichisalwayslarger than ω 2, so that the pressure is, roughly speaking, proportional to {(ω 1 + ω 2 )/2} 2, which is always larger than ω 2 2, too. These two flow regions produce the pressure difference between the two sides of the lock-up piston. The two flow regions connect at the left end of the lock-up piston s outer radius where their pressure is the same. If no through-flow between the lock-up piston and the converter cover occurred, the pressure would be lower on the righthand side of the lock-up piston than on the left-hand side, which would push the lock-up piston to the right. In reality, through-flow does occur, which generates friction loss and separation loss especially around the lock-up clutch facing in the thin radial flow channel. These losses increase the pressure upstream of the lock-up clutch facing, that is, the pressure in the radial inner flow field. As a result, the lock-up piston should stand still at an axial position where the thrust acting on it becomes zero. Moreover, in the higher speed ratio range, where ω 2 is close to ω 1, the clearance, s, should become larger in order to reduce the pressure losses noted above. In the lower speed ratio range, where ω 2 is much smaller than ω 1, the clearance, s, should be smaller in order to produce the larger pressure losses. Because the relation between the pressure losses and the clearance has a strong non-linear characteristic, a sharp increase in clearance occurs in the higher speed ratio range.

140 6. Concluding Remarks Flow in the single-plate lock-up clutch of an automotive torque converter was analyzed by using a CFD code. The flow was found to be laminar in the higher speed ratio range. The computation results showed that the fluid flowed outwards in the narrow channel between the lock-up clutch facing and the converter cover, whereas the flow reversed inwards near the lock-up piston surface upstream and downstream of the narrow channel in most cases. Along the outer surface of the axial flow channel near the exit, the flow also reversed far upstream of the channel. The pressure distribution between the turbine shell and the lock-up piston was almost the same regardless of the speed ratio, whereas the pressure distribution between the lock-up piston and the converter cover differed considerably according to the speed ratio. The largest pressure loss in the flow channel occurred at the narrow channel between the lock-up clutch facing and the converter cover. With the computational method presented here, it is possible to predict the location of the lock-up piston with good accuracy in relation to the speed ratio. It is especially notable that the sharp increase in clearance in the coupling range can be clearly captured with this method. One may ask what the difference is between a simple one-dimensional estimation and the CFD results presented here. A one-dimensional analysis would be possible if the flow channel geometry is very simple. However, application of the analysis to actual machines with a complicated geometry like in the present case will result in a large error in the estimation of the pressure distribution over the surface of the lock-up clutch piston. The reason is that such an analysis cannot predict with reasonable accuracy the friction and separation losses generated around the lockup clutch facing due to the through-flow. The torque converter used in this study was a specific prototype model. For more generality and applicability, interaction between the three elements of the torque converter should be taken into account as a topic of further study because the exit flow condition of the lock-up clutch varies considerably depending on the torque converter s hydrodynamic performance. Acknowledgement The author is grateful to Dr. Yasutoshi Senoo, Professor Emeritus of Kyushu University, for his instructive advice throughout the course of this study. References ( 1 ) Abo, K., Kobayashi, M. and Kurosawa, M., Development of a Metal Belt-Drive CVT Incorporating a Torque Converter for Use with 2-Liter Class Engines, SAE Paper, 980823, (1998). ( 2 ) Kumura, H., Nakano, M., Hibi, T., Sugihara, J. and Kobayashi, K., Performance of a Dual-Cavity Half- Toroidal CVT for Passenger Cars, Proceedings of SAEJ International Conference on Continuously Variable Power Transmission, (1996), pp.135 140. ( 3 ) Browarzik, V., Experimental Investigation of Rotor/Rotor Interaction in a Hydrodynamic Torque Converter Using Hot-Film Anemometry, ASME Paper, 94- GT-246, (1994). ( 4 ) Gruver, J.K., Flack, R.D. and Brun, K., Laser Velocimeter Measurements in the Pump of a Torque Converter, Part I Average Measurements, Trans. ASME, Journal of Turbomachinery, Vol.118 (1996), pp.562 569. ( 5 ) Brun, K., Flack, R.D. and Gruver, J.K., Laser Velocimeter Measurements in the Pump of a Torque Converter, Part II Unsteady Measurements, Trans. ASME, Journal of Turbomachinery, Vol.118 (1996), pp.570 577. ( 6 ) Brun, K. and Flack, R.D., Laser Velocimeter Measurements in the Turbine of an Automotive Torque Converter, Part I Average Measurements, Trans. ASME, Journal of Turbomachinery, Vol.119 (1997), pp.655 662. ( 7 ) Brun, K. and Flack, R.D., Laser Velocimeter Measurements in the Turbine of an Automotive Torque Converter, Part II Unsteady Measurements, Trans. 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