Transient Heat Transfer and Energy Balance Model for Hydrodynamic Torque Converters while Operating at Extreme Speed Ratio

Transcription

1 Journal of Mechanical Engineering and Autoation 2016, 6(5): DOI: /j.jea Transient Heat Transfer and Energy Balance Model for Hydrodynaic Torque Converters while Operating at Extree Speed Ratio Darrell Robinette *, Jason Blough Dep t Mechanical Engineering-Engineering Mechanics, Michigan Technological University, Houghton, MI, USA Abstract This investigation details the developent of a siple transient odel to predict the bulk toroidal flow fluid teperature of the autootive torque converter based upon an energy balance and the derivation of an overall convective heat transfer correlation for the entire turboachine. Data collected on a torque converter specific dynaoeter setup is used to derive a Nusselt correlation for overall convective heat transfer fro the using easured paraeters. Diensional analysis applied to three torque converters of nearly exact geoetric siilitude was used to show the applicability of the correlation to prediction of the overall external convective heat transfer echanis. Discussion is focused on operation at low speed ratios for varying lengths of tie. This particular condition represents the worst-case scenario for torque converter operating efficiency and heat rejection. It was found that the external heat rejection fro the torque converter surface is a function of the rotational Reynolds nuber and proportional to the characteristic diensionless perforance nuber unit input speed. The odel is shown to trend with teperature easureents ade at the external of the torque converter over a variety of zero speed ratio transient aneuvers. Overall, the first order, linear differential equation odel and Nusselt correlation for overall heat transfer are a first step in developing an adequate tool for use in future torque converter designs predicated on scalability of the turboachines perforance quantified through diensionless nubers. Keywords Torque converter, Transient heat transfer, Nusselt correlation, Diensional analysis 1. Introduction The torque converter is a particular class of turboachine used in a wide variety of power transfer applications to couple the prie over to the gear syste of an autoatic transission. Torque converters can be found in on or off highway powertrain applications and is ost coonly utilized in autoatic transissions to enhance the ial acceleration perforance of the vehicle. It is also a eans of iproving syste durability since the torque converter has superior cooling characteristics and does not experience wear like that of a friction launch clutch. The odern three-eleent torque converter consists of a closed loop containing a ixed flow pu a ixed flow turbine and an axial flow stator. The device is required to operate over a range of speed ratios fro zero to values greater than one. Speed ratio is defined as the rotation of turbine speed divided by pup speed. At zero speed ratio, axiu torque ultiplication is achieved, while axiu efficiency occurs at speed ratios between 0.85 and 0.95 * Corresponding author: dlrobine@tu.edu (Darrell Robinette) Published online at Copyright 2016 Scientific & Acadeic Publishing. All Rights Reserved depending on the details of the design. As a result, the flow field is three-diensional within the, producing secondary flow structures and the potential for two-phase ixture, e.g. cavitation, depending on the severity of the specific operating condition. A detailed description of the torque converter and previous experiental or nuerical studies can be found in [1-3] for exaple. Selection of a torque converter design is perfored nuerically to atch the torque and speed characteristics of the prie over to a particular powertrain application to balance acceleration and efficiency for the range of operation conditions expected. The geoetry of the and individual eleents is developed through iterative CFD and other nuerical ethods, and then validated through physical hardware testing on a dynaoeter to achieve specific perforance targets, see [4-8]. To eet physical packaging constraints or to iniize the occurrence of perforance inhibiting toroidal flow structures such as stalled or reversed flow and large volue cavitation, further refineent of the diensions, pup and turbine blade angles and stator blade geoetry ay be undertaken. Additionally, the working conditions of the hydraulic fluid iposed upon the torque converter pressure vessel can be calibrated to suppress cavitation or create sufficient through flow cooling to aintain adequate toroidal flow operating

2 Journal of Mechanical Engineering and Autoation 2016, 6(5): teperatures. In autootive powertrain applications, the ega trend is towards increasingly power dense prie overs with greater torque availability at lower operating speeds due to turbocharging. Siultaneously, the diensions of the torque converter are being significantly reduced to accoodate increased gear and clutch content of the autoatic transission to achieve 8, 9, 10 or ore forward fixed gear ratios. Additionally, ore space is being allocated for the lockup clutch daper to bypass the hydrodynaic circuit to further reduce fuel consuption once the vehicle has launched, see Figure 1. The cobination of these two design trends results in greater deands on the turboachine, particularly for extended operation at extree speed ratios and elevated levels of torque transfer. The purpose of this investigation is to develop a first principal based odel validated with experiental data that can predict the internal toroidal flow teperature of the torque converter. The ethod presented is based upon that reported by [9] for powertrain cooling and protection strategy based upon a predicted teperature internal to the torque converter. Predictions of these teperatures can be critical in deterining required cooling capacity, establishing operating liitations for coponent durability, preventing cavitation and preservation of quality fro excessive theral cycling. Figure 1. Cross-sections of typical three eleent, autootive torque converters showing typical design trend over past 20 years, fro left to right, oldest to newest 2. Torque Converter Fundaentals The principals of torque converter operation and details of flow theory are contained in a nuber of sources found in the literature, [1, 4-8 and 10-14], for exaple. A brief discussion is provided here for reference and continuity of the aterial contained in this paper Perforance Characteristics Torque converter perforance is typically defined by diensionless or sei-diensionless quantities to atch the turboachine to specific applications are suarized in Equations 1 through 3. The quantities of torque ratio, TR, output (turbine) to input (engine or pup) torques and K-factor, K, input speed to square root of input torque are plotted versus speed ratio, SR, output to input speeds and fors the ainstay of atching torque converter prie over, see Figure 2. TR t (1) K p N p (2) N p t SR (3) K-factor is transfored into the diensionless quantity unit input speed,, with the addition of diaeter, D, to the 5/2 power and square root of the density, ρ, of the operating fluid, N p N p D 5 (4) Unit input speed is the inverse, square root of the ore coon diensionless nuber referred to as the torque coefficient. The designation for a given torque converter are norally specified by the diaeter of the pup and the K-factor value realized at zero speed ratio, known as stall One-Diensional Flow Theory A significant aount detailed research, both analytical and experiental, has been perfored on torque converters, [4-8 and 10-14]. The fundaental laws of fluid echanics and therodynaics can be applied to create a one-diensional flow odel capable of useful predictions. The principles of conservation of angular oentu and energy for a control volue, CV, encopassing the fluid and bladed surfaces of the turboachine eleents are used to the define the odel as given by Equations 5 and 6, though a thorough description is outside of scope for this paper and is readily available in the literature, see [10-14]. t CV p r vdv r vvda (5) de dt Q W (6) The key output of the one-diensional odel are fluid operating paraeters that are not easily easured experientally, naely the voluetric or ass flow rate of the toroidal flow. Having this inforation is iportant in the prediction of heat transfer fro the toroidal flow to the external surface of the torque converter. This topic will be discussed in detail later in the paper. One-diensional odels for the torque converters tested for this investigation and exaple data showing correlation with dynaoeter data is provided in Figure 2. Excellent correlation of the odel is noted at low speed ratios, which are the focus of the discussion. Figure 3 contains toroidal ass flow rate for the stall, zero speed ratio, condition at a range of pup torques

3 130 Darrell Robinette et al.: Transient Heat Transfer and Energy Balance Model for Hydrodynaic Torque Converters while Operating at Extree Speed Ratio and ass flow rate across the speed ratio range at a pup torque of 150 N. At stall, ass flow rate is a linear function with pup torque, corresponding to an increasing pressure head, which will be later shown to adversely affect cooling through at elevated pup speeds. Toroidal ass flow rate follows an inverse power law with respect to speed ratio. Figure 2. Correlation of one-diensional flow theory odel with easured dynaoeter data Figure 3. Toroidal ass flow rate as a function of pup torque at stall and speed ratio for a fixed pup torque 2.3. Energy Balance An energy balance for the torque converter operating with or without the lockup clutch applied is shown in Figure 4. Shaft work input fro the prie over at the cover and pup (green) is converted to useful shaft work through the fluid and extracted in the turbine and lockup clutch daper (blue) assebly and then transitted to the autoatic transission via the turbine shaft. The reainder of the energy not converted to useful shaft work is rejected as heat through two principal pathways. Cooling through flow, Q, is supplied to the torque converter fro the autoatic c transissions high pressure supply which enters through the turbine shaft and ixes with the flow and exhausts back to the sup via passages between stator and pup shafts. Energy is also dissipated as heat fro the to the external via forced convection fro to, Q, and to air, Q, as well as conduction through the. The overall heat transfer echanis fro the external surface can be difficult to easure or quantify using traditional ethods and will be a focus of discussion in the paper. Based upon the energy balance in Figure 4, a linear, first order, differential equation can be written for the teperature of the toroidal fluid teperature, T, as seen in Equation 7. It should be noted that for this odel, it is assued that teperature is equivalent to the exhaust or outlet teperature fro the torque converter. C C dt dt UA T T W c, overall T air T The individual heat transfer echaniss of (7) Q and Q in additional to conduction through the can be cobined into an overall heat transfer ter,, given by, Q overall, UA overall T air T Q overall, (8) The solution of the differential equation of Equation 7 for teperature becoes, T t t T e 1 e (9) where and are equal to the following, and UA overall Tair Tc, (10) C C W overall (11) UA C Assuing an ial condition for the teperature,, to be equal to the cooling through flow inlet T teperature, T c,, which is assued to be tie invariant. A siplification can be ade to Equation (9) if the aount of heat energy rejected through the external surface is assued a known quantity,, C C dt dt Q overall, Q T T W c, overall, (12) which results in the following solution for teperature with the sae ial condition,

4 Journal of Mechanical Engineering and Autoation 2016, 6(5): Figure 4. Energy balance across a three torque converter with lockup clutch and cooling through flow circuit Figure 5. Torque converter specific dynaoeter test cell and test fixture instruentation

5 132 Darrell Robinette et al.: Transient Heat Transfer and Energy Balance Model for Hydrodynaic Torque Converters while Operating at Extree Speed Ratio T T e t Q t (13) overall, W, 1 Tc e C C Equation 13 will be the foundation for the reainder of the discussion in this paper for estiating the toroidal flow teperature of the torque converter during transient operation. Detail will be provided in the results section as to the echanis enabling the siplification through the developent of a proportional relationship between overall external surface heat rejection and input power based upon the specific design details of the torque converter. 3. Experiental Setup A torque converter specific dynaoeter test cell, Figure 5, was used to test three torque converters of nearly exact geoetric scaling, see Figure 6, at stall. The testing was originally perfored to deterine the appropriateness of applying the diensional analysis to developing a prediction tool for incipient cavitation in torque converters using a nearfield acoustical technique, see [8]. The dynaoeter data collected during this testing can be further utilized to develop a odel to predict teperatures during transient, high input power aneuvers when operating at low overall efficiency. The dynaoeter was setup for the stall condition, zero output speed, only and all three torque converters were painted flat black to create the sae radiation surface eissivity and to enable a ore suitable infrared surface teperature easureent. The details of this easureent setup can be seen in Figure 5, along with nearfield icrophones to detect cavitation enclosed in a nitrile cover to prevent containation. The torque converters tested were 245, 258 and 300 diaeters as easured at the pup outside diaeter and had a stall unit input speed rating of 140, corresponding to K-factors of 163, 146 and 101, respectively. Figure 7 contains perforance data, K-factor and torque ratio as a function of speed ratio, fro dynaoeter testing for the three torque converters tested in this investigation. The near perfect geoetric scaling of all three torque converters results in the value of the diensionless unit input speed to be equivalent across the range of speed ratios tested as noted in Figure 8. Figure 6. Geoetrically scaled torque converters tested with U = 140, fro left to right, 300, 258 and 245 pup diaeters Figure 7. K-factor and torque ratio vs. speed ratio for the three torque converters tested for this investigation Figure 8. Unit input speed and torque ratio vs. speed ratio for the three torque converters tested for this investigation 4. Results 4.1. Stall Speed Sweeps A coon set of stall speed sweep tests were perfored for this investigation, raping pup speed of the torque converter fro 100 r/in to axiu speed ranging between 2500 to 2900 r/in depending on the design being tested. Pup speed was swept at four rap rates of 40, 100, 200 and 500 r/in/s. These rap rates were selected to span those realized during vehicle operation. The worst case condition is 40 r/in/s for internal heat build-up in the fluid to a rap rate of 500 r/in/s ore typical of operation in a vehicle powertrain. Once the peak pup speed was achieved, pup speed was raped down to a 100 r/in at a rap rate of -300 r/in/s. Once pup speed reached 100 r/in, an extended cool down period was allowed for fluid teperature to stabilize to that of the supply. The stall speed sweep test procedure and easureents of cooling through flow rate and teperatures at the inlet, outlet and surface of the torque converter is suarized in Figure 9 for a sweep rate of 40 r/in/s. Figure 10 contains

6 Journal of Mechanical Engineering and Autoation 2016, 6(5): the stall speed sweep teperature data for all sweep rates for the 258 torque converter showing only the rap up in speed portion of the test. significantly. The ost severe operating scenario occurs with the slow sweep rates cobined extended operation at elevated power input. The effect of torque converter size on output and surface teperatures are found in Figure 11. As the physical size of the torque converter increases, the rate of change of teperatures decreases, though the tie required to return to a steady state teperature equal to the inlet teperature reains roughly constant for all three diaeters. Figure torque converter, cooling ass flow rate and operating teperatures during a 40 r/in/s stall speed sweep and subsequent cool down period Figure 11. Effect of torque converter size on surface and outlet teperatures at a 40 r/in/s stall speed sweep rate and cooling cycle Figure torque converter surface and outlet teperatures during various stall speed sweep tests As expected, the rate of teperature rise and absolute value achieved is proportional to the sweep rate, however, cooling flow rate through the torque converter drops equivalently and independently of the sweep rate. The drop in cooling flow rate is a direct result of the pressure head developed in the as pup speed increases and rises above the charging pressure, ipeding flow. Cooling through flow increases once the charging pressure is higher than the pressure developed in the toroidal flow. Thus, a tie lag between the rise in outlet teperature of the fluid exiting the torque converter and the peak pup speed during the test can be noted in Figure 9. As sweep rate increases the rise in teperatures decreases sharply as the aount of energy input into the torque converter is reduced 4.2. Cooling Flow Heat Transfer The cooling through flow to the torque converter acts as a ixing flow heat exchanger. Cooler autoatic transission enters the through flow passages in the turbine shaft and ixes with warer fluid, causing displaceent of warer fluid to exit through passages in the stator shaft. This process is roughly depicted in Figure 4 and can be approxiated as a heat exchanger with the aount of heat transferred deterined fro the following, (14) Q c C Tc, T It was assued that the outlet or exhaust teperature fro the torque converter was equal to the internal teperature. Any heat transfer occurring in the passages within the shafting or test fixture were ignored. The heat rejection fro cooling can directly be calculated since the ass flow rate of cooling, inlet and exhaust teperatures are easured during the test. Heat rejected during a 40 r/in/s stall speed sweep and following cooling cycle is plotted in Figure 12 along with ass flow rate of cooling for the three diaeter torque converters tested. As indicated in Figure 12, heat rejection is inial during the rap up in pup speed as an increasing teperature differential between inlet and outlet is offset by a decreasing flow rate of cooling. All significant reoval of heat fro the through flow cooling circuit occurs after the stall event, ranging between 36 and 45 kw. During the stall event, the doinant

7 134 Darrell Robinette et al.: Transient Heat Transfer and Energy Balance Model for Hydrodynaic Torque Converters while Operating at Extree Speed Ratio ode of heat reoval is forced convection at the outer. closer approxiation to the rotating torque converter in the test fixture. The Nusselt correlations utilized are fro testing conducted by [17] and are as follows, 0.49 Nu Re (18) 0.8 Nu Re (19) For the external surface geoetry, rotation speeds between 100 and 3000 r/in and the fluid properties of air result in heat transfer coefficients in the range of 0.01 to 0.25 kw/ 2 -K. These values are an order of agnitude less than those coputed for internal heat transfer and will be a liiting factor on overall heat rejection fro the external surface. The net result will be prediction of fluid teperatures being unrealistically high for the stall speed sweep tests as will be presented next. Figure 12. Heat rejection fro cooling through flow for 245, 258 and 300 torque converters during 40 r/in/s stall speed sweep and cool down cycle 4.3. Overall External Heat Transfer Coefficient Conventional Approach This section will detail calculations of heat transfer coefficients and rates related to deterining the aount of heat rejected through the external surface of the torque converter. The rotational Reynolds nuber, Equation 15, was used in this investigation to characterize the turboachines operating flow regie for both internal and external flows. For internal flow, the critical Reynolds nuber for transition to turbulent flow is 2500 while for external flow the transition point was taken to be Internal Convection 2 R Re (15) The heat transfer coefficient for forced convection fro the flow was deterined using the Nusselt correlations in Equations 16 and 17 for lainar and turbulent flow, respectively, approxiating the individual blade passages within the torque converter eleents as rectangular passages. Nu 4.36 (16) f/ 8 Re 1000 Pr Nu f / 8 Pr External Convection 05. 2/ 3 (17) External heat transfer coefficients were sought out fro ultiple sources, naely flow over a flat plate, [15], and rotating disks or cylinders in air, [16,-18]. Both approaches yielded siilar heat transfer coefficients for the given geoetry and boundary conditions. However, those derived specifically for rotating disks in air were selected due to the Figure 13. Torus fluid teperature prediction using available Nusselt relationships and Equation 9 for 258, 140 unit input speed torque converter during 40 r/in/s stall speed sweep and cooling cycle Overall Heat Transfer Coefficient The internal and external heat transfer coefficients found using available Nusselt relationships were cobined with the conduction coefficient through the torque converter to define an overall heat transfer coefficient as described in any heat transfer textbooks, [19] for exaple. The liiting factor for the overall heat transfer coefficient becoes the external forced convection with a heat transfer coefficient an order of agnitude less than that of internal convection for the to the. The result is inial heat rejection through the external to the air, which during a slow stall speed sweep in which power input is relatively high throughout the ajority of the stall aneuver will produce extree teperatures. An exaple prediction of flow teperature using Equation 9 and an overall heat transfer coefficient fro Equations 16 to 19 for a 258 torque converter is shown in Figure 13. Also included in Figure 13 are easured surface and outlet teperatures during the 40 r/in/s stall speed sweep. As expected with the inial overall heat transfer coefficient for external surface

8 Journal of Mechanical Engineering and Autoation 2016, 6(5): heat rejection, teperature is predicted to peak at an unreasonably value of 900 C. It was concluded that the available Nusselt relationships cannot be applied to this particular situation with good confidence and that an alternative Nusselt relationship ust be derived Overall External Heat Transfer Coefficient Derived Nusselt Correlation A Nusselt correlation unique to this particular heat transfer aspect for torque converter applications is derived to predict the external heat transfer echanis ore appropriately. Siilar approaches to predict heat transfer have been defined by [20, 21] as applied to autootive turbochargers and torque converter lockup clutches, respectively. The heat energy rejected through the torque converter external surface can be reduced to the relationship of Equation 20 assuing the heat energy rejected is proportional to the input power by the scaling factor,. Q (20) surf W p Such an assuption is appropriate given the energy balance of Equation 12, knowing that the balance of input power ust be absorbed in the fluid to be reoved by the cooling through flow or rejected fro the external surface. As shown earlier, inial aount of energy is reoved by cooling flow during the high power input stall speed swee thus a significant aount of the input power is transferred to the fluid to be rejected fro the external surface. Utilizing traditional Nusselt correlations and cobining internal and external convection with conduction through the into an overall heat transfer coefficient, an insufficient aount of heat rejection was deterined to be coputed by this ethod. The result was an unrealistic fluid teperatures approaching 900 C for the slowest sweep rates. Owing to siilitude and previous Nusselt correlation work for rotating disks and asseblies by [16, 17 and 18], it is known that a siilar Nusselt relationship should result for this particular turboachine. The scaling factor,, should be a function of the torque converter design, size and perforance attributes, such as unit input speed and operating fluid properties. For this investigation, it was found that scaling the input power by Equation 21 resulted in a universal Nusselt correlation, see Equation 22, for the three diaeter torque converters tested K 2 D K (21) Curve fitting a power function to the data reveals the Nusselt correlation of the for Nu 2e 15 Re (22) as shown in Figure 14. The rotational Reynolds nuber for the testing perfored extend to a value of 300,000, corresponding to the transition region reported by [17] and thus can be assued to reside ainly in the lainar region for external forced convection fro a rotating assebly in quiescent air. Interestingly, the values of the power law curve for Nusselt verse Reynolds nuber are siilar in for and value to those found by [17] for the transition region for rotating disk heat transfer. The Nusselt correlation in Equation 22 is applied in the prediction of torque converter fluid teperature expressed by the first order, linear differential equation expressed by Equation 13. Equation 22 is valid for the stall operating condition only and for torque converters with diensions scaled fro the designs tested in this investigation that yield a stall unit input speed of 140. Figure 14. Derived Nusselt correlation for overall heat transfer coefficient fro torque converters of constant unit input speed and geoetric scaling Fro a torque converter design standpoint, the scaling factor found in Equation 21 shows that torque converters of increasingly higher unit input speed and K-factor will result in higher heat rejection through the external. However, further dynaoeter testing of such designs is required to substantiate the observation and establish design guidelines Model Correlation and Torus Fluid Prediction The derived Nusselt correlation of Equation 22 was used as an input for the solution of the differential equation describing the energy balance of the torque converter, Equations 12 and 13, at stall to predict the fluid teperature. The odels prediction capability is shown for two exaples, the results of which are contained in Figures 15 and 16. In the first exaple, the 258 torque converter is perforing a 40 r/in/s stall speed sweep and cool down cycle. The predicted teperature leads the surface teperature easureent in very close association, while outlet teperature lags predicted teperature as cooling flow drops during high stall speeds then surges once pup speed drops. It can be noted that teperature drops rapidly once cooling ass flow rate increases, and sufficient cooling flow ixes with the hot fluid, being fully replaced within a period of approxiately 15 seconds.

9 136 Darrell Robinette et al.: Transient Heat Transfer and Energy Balance Model for Hydrodynaic Torque Converters while Operating at Extree Speed Ratio prediction of toroidal flow teperatures during transient stall aneuvers. The predicted values show that extended operation at extree speed ratios can be detriental to the fluid, breaking down viscosity odifiers and coproising long ter durability of internal transission coponents as teperatures can reach beyond the typical recoended operating teperature of 120 C for ost autoatic transission fluids. Additionally, the predicted fluid teperatures during the extended stall operation at high input powers can proote cavitation. Figure 15. Torus fluid teperature prediction using derived Nusselt relationship and Equation 13 for 258 torque converter during a 40 r/in/s stall speed sweep and cool down period overlaid with surface and outlet teperatures The sae general observations are ade for the case of the 245 torque converter perforing a stall speed sweep at 200 r/in/s followed by a subsequent cooling cycle. Predicted teperature leads easured surface teperature with good association followed with a lagging outlet teperature during the cooling phase, continuing until convergence after adequate ixing of cooling and flows at approxiately 80 seconds in Figure Future Developents The transient odel presented in this investigation was derived focusing on the stall operating condition, which is an extree condition, but ost severe for theral loading of the fluid. Future testing should focus on the developent and validation of the odel for transient or steady state speed ration operation between 0 and 1. This is will require potential further developent of the derived Nusselt relationship which ay take the following functional relationshi Nu fnc Re, U, SR (23) including the additional ters of speed ratio, SR, and unit input speed,, in the case of different torque converter designs. Expansion of the Nusselt relationship and scaling factor on external heat rejection as a function of input power would increase the predictive capability of the odel and ethodology presented to future torque converter designs across the entirety of their operating range. 5. Conclusions Figure 16. Torus fluid teperature prediction using derived Nusselt relationship and Equation 13 for 245 torque converter during a 200 r/in/s stall speed sweep and cool down period overlaid with surface and outlet teperatures Overall, the linear first order, differential equation describing the fluid teperature based on the energy balance of the torque converter cobined with the derived Nusselt relationship for overall heat transfer fro the external surface provides sufficient capability for adequate A first order, linear differential equation odel based upon an energy balance of the torque converter was developed to predict internal fluid teperatures at the extree stall operating condition, zero speed ratio. A Nusselt correlation was derived specific to the overall turboachine for external heat transfer as it was found that conventional relationships were inadequate in accurate prediction. The heat rejected fro the torque converter external surface was found to be proportionally scaled by the two ties the square root of the torque converters diaeter to the power of 5 and operating fluid density and a sei-diensionless attribute, K-factor, raised to the power of 1.5. This relationship was shown to collapse the Nusselt relationship to a single function of the rotation Reynolds nuber for three torque converters of geoetric siilitude. Prediction of teperatures trended with easured teperature data acquired at the surface and outlet flow during dynaoeter testing. The next steps in this research would be to develop fully the Nusselt relationship to include speed ratios other than stall to enhance its prediction capability for all operating conditions the torque converter experiences during typical powertrain aneuvers in vehicle applications.

10 Journal of Mechanical Engineering and Autoation 2016, 6(5): Noenclature Variable Description Units A Area 2 C p Specific heat kj/kg CV Control volue - D Diaeter E Energy kj K Torque converter K-factor r/in/n 0.5 N Rotational speed r/in Nu Nusselt nuber - Q Voluetric flow rate 3 /s Q Heat transfer kw Pr Prandlt nuber - R Radius Re Reynold nuber - SR Torque converter speed ratio - Torque N T Teperature C TR Torque converter torque ratio - U Overall heat transfer coefficient W/ 2 -K Torque converter unit input speed - W Power kw da Torque converter eleent differential area 2 dv Torque converter fluid differential volue 3 f Friction factor - Mass kg Mass flow rate kg/s r Position vector t Tie s v Velocity vector rad/s Dynaic viscosity kg/-s Density kg/ 3 Angular velocity rad/s REFERENCES [1] Jandasek, V. J., "Design of Single-Stage, Three Eleent Torque Converter," SAE Design Practices: Pass. Car Auto. Trans., 3rd Ed., , [2] Abe, H., Tsuruoka, M., Muto, A., Kato, M. and Fujiwara, H., Developent of Super Flat Torque Converter with Multi Plate Lock-up Clutch, SAE Technical Report, , 2009, doi: / [3] Usui, T., Okaji, T., Muraatsu, T., and Yaashita, Y., "Developent of a Copact Ultra-Flat Torque Converter Equipped with a High-Perforance Daper," SAE Int. J. Engines 8(3): , 2015, doi: / [4] Bahr, H. M., Flack, R. D., By R. R. and Zhang, J. J., Laser Velocieter Measureents in the Stator of a Torque Converter, SAE J. of Pass. Cars, 99: , [5] By, R. R. and Lakshinarayana, B., Measureent and Analysis of Static Pressure Field in a Torque Converter Turbine," ASME J. of Fluids Eng., 117(3): , [6] Schweitzer J., Gandha, J., Coputational Fluid Dynaics in Torque Converters: Validation and Application, International Journal of Rotating Machinery, vol. 9, pp , [7] Robinette, D., Grier, M., Horgan, J., Kennell, J. et al., "Torque Converter Clutch Optiization: Iproving Fuel Econoy and Reducing Noise and Vibration," SAE Int. J. Engines 4(1):94-105, 2011, doi: / [8] ] Robinette, D. L., Schweitzer, J. M., Maddock, D. G., Anderson, C. L., Blough, J. R. and Johnson, M. A., Predicting the Onset of Cavitation in Autootive Torque Converters Part II: A Generalized Model, Int. J. of Rotating Machinery., Vol. 2008, , [9] Willias, B., Kelly, J., Varda, D. and Shockley, S., Transission and Torque Converter Cooling Control, Patent, 6,959,239, filed February 24, 2004, and issued October 25, [10] Ishihara, T. and Eori, R., "Torque Converter as a Vibration Daper and Its Transient Characteristics," SAE Technical Paper , 1966, doi: / [11] Tsangarides, M. and Tobler, W., "Dynaic Behavior of a Torque Converter with Centrifugal Bypass Clutch," SAE Technical Paper , 1985, doi: / Subscript c overall p surf t Description Torque converter cooling through flow Initial Torque converter Overall heat Pup Torque converter Surface Turbine Torque converter [12] Xia, H., and Oh, P., A Dynaic Model for Autootive Torque Converters, Int. J. of Vehicle Design, 21(4/5): , [13] Hrovat, D., and Tobler, E., Bond Graph Modeling and Coputer Siulation of Autootive Torque Converters, J. of Franklin Institute, 319(1/2):93-114, [14] Fujita, K. and Inukai, S., "Transient Characteristics of Torque Converter-Its Effect on Acceleration Perforance of Auto-Trans. Equipped Vehicles," SAE Technical Paper , 1990, doi: / [15] Incorpera, F., et. al., Fundaentals of Heat and Mass Transfer, 7th Edition, Wiley, New Jersey, ISBN , 2011.

11 138 Darrell Robinette et al.: Transient Heat Transfer and Energy Balance Model for Hydrodynaic Torque Converters while Operating at Extree Speed Ratio [16] Becker, K., Measureents of Convective Heat Transfer fro a Horizontal Cylinder Rotating in a Tank of Water, International Journal of Heat Transfer, Vol. 6, pp , [17] Cardone, G., Astarita, T., and G. M. Carloagno, Heat Transfer Measureents on a Rotating Disk, Int. J. of Rotating Machinery, vol. 3, no. 1, pp. 1-9, doi: /s x [18] Ozerda, B., Measureent of Convective Heat Transfer Coefficient for a Horizontal Cylinder in Quiescent Air, Int. Co. Heat Mass Transfer, Vol. 27, No. 3, pp , [19] Bergan, T., Lavine, A., Incropera, F., Fundaentals of Heat and Mass Transfer, 7th Edition, Wiley Global Education, 2011, ISBN , [20] Corerais, Mickaël, Pascal Chesse, and Jean-François Hetet. "Turbocharger Heat Transfer Modeling Under Steady and Transient Conditions." International Journal of Therodynaics, Vol 12, No. 4, pp , [21] Karaavruc, A., Shi, Z., and Gunther, D., "Deterination of Epirical Heat Transfer Coefficients via CFD to Predict the Interface Teperature of Continuously Slipping Clutches," SAE Technical Paper , 2011, doi: /