Hydraulic Analysis of a Reversible Fluid

Charles N. McKinnon1 Danamichele Brennen1 Christopher E. Brennen Boeing North American, McGettigan Partners, California Institute of Technology, Downey, CA Philadelphia, PA Pasadena, CA

ABSTRACT Tp,Tt Shaft for the pump, turbine Ts in seal between pump + turbine rotors This paper presents a hydraulic analysis of a fluid cou- Tpw,Ttw Windage torques for the pump, turbine pling which is designed to operate either in a forward or ui Meridional component of fluid velocity at reverse mode when a set of turning vanes are respectively stations i =1, 2, 3(= Q/Ai) withdrawn or inserted into the flow between the driving vi Tangential fluid velocity at i =1, 2, 3 and driven rotors. The flow path is subdivided into a set αp,αt,αv Angles of attack of flow on pump, turbine, of streamtubes and an iterative method is used to adjust turning vanes (relative to axial plane) the cross-sectional areas of these streamtubes in order to βp,βt,βv Discharge vane angles for pump, turbine, satisfy radial equilibrium. Though the analyis requires turning vanes (relative to axial plane) ∗ the estimation of a number of loss coefficients, it predicts βv Effective discharge angle for turning vanes coupling performance data which are in good agreement δp,δt,δv Inlet vane angles at pump, turbine, with that measured in NAVSSES tests of a large reversible turning vanes (relative to axial plane) coupling intended for use in a ship drive train. η Overall coupling efficiency, η = NtTt/NpTp ρ Fluid density NOMENCLATURE

Ai Cross-sectional area of flow at i =1, 2, 3 5 2 1. INTRODUCTION Cp Pump torque coefficient, Cp = Tp/ρR Np 5 2 Ct Turbinetorquecoefficient,Ct = Tt/ρR Np Fluid and torque converters are now commonly Cpw,Ctw Pump and turbine windage loss coefficients used in a wide variety of applications requiring smooth Csw Seal windage torque coefficient torque , most notably in automobiles. They Cpa,Cpb Pump hydraulic loss coefficients usually consist of an input shaft that drives a pump im- Cta,Ctb Turbine hydraulic loss coefficients peller which is closely coupled to a turbine impeller that Cv Loss coefficient for the turning vanes transmits the torque of an output shaft coaxial with the in- Hp,Hpi Actual, ideal total pressure rise across pump put shaft. The fluid is usually hydraulic oil and the device Ht,Hti Actual, ideal total pressure drop across turbine is normally equipped with a cooling system to dissipate Hpl,Htl,HvTotal pressure losses in pump, turbine, turning 2 2 the heat generated. In a typical fluid coupling used, for ex- vanes (non-dimensionalized by ρR Np ) ample, in a ship propulsion system, the pump and turbine k Turning vane discharge blockage ratio are mounted back to back with little separation between Np,Nt Angular velocities of the pump, turbine (rad/s) the leading and trailing egdes of the two impellers. It is Pi Fluid pressure at locations i =1, 2, 3 common to use simple radial blades and a higher solidity Q Volume flow rate of fluid (the present pump rotor has 30 vanes) than would be uti- R Outer shell radius (0.5m) lized in most conventional pumps or turbines (Stepanoff ri Radial position in the flow (m) [1], Brennen [2]). A as used in automo- rb Outer core radius/R tive transmission systems has an added set of stator vanes rc Inner core radius/R mounted between the turbine discharge and the pump in- rd Inner shell radius/R let. r¯j,i Mean radius of jth streamtube/R In the present paper we present a hydraulic analysis of − S Slip = 1 Nt/Np another variant in this class of fluid transmission devices, 1Formerly with WesTech Gear Corporation, now part of Philadel- namely a reversible fluid coupling. This device was devel- phia Gear. oped and built by Franco Tosi in Italy in conjunction with

1 Figure 2: Sketch showing the subdivision of the flow into streamtubes.

dence angles on the impeller blades tend to be very large thus generating substantial flow separation at the leading Figure 1: Cross-section of reversible fluid coupling show- edges as well as much unsteadiness and high turbulence ing key locations in the fluid cavity. levels. To accomodate these violent flows and to force the flow to follow the vanes at impeller discharge, the solid- ity of the impellers is usually much larger than would be SSS Gears Ltd. in the U.K. and in described in detail in optimal in other turbomachines. Fortunato and Clements [3], Clements and Fortunato [4] Though several efforts have been made to compute these and Clements [5]. Tests on the device conducted by the flows from first principles (By et al. [11], Schulz et al. US Navy (NSWC Philadelphia) and are documented in [12]), such complex, unsteady and turbulent flows with Nufrio et al. [6] (see also, Zekas and Schultz [7]). This intense secondary flows are very difficult to calculate be- paper presents a method of analysis of the performance of cause of the lack of understanding of unsteady turbulent such devices and uses one of the Franco Tosi designs tested flows. In the present paper we begin with a simple one- by NSWC as an example. As shown diagrammatically in dimensional analysis of the flow in a reversible fluid cou- figure 1, the reversible fluid coupling has an added feature, pling. This one-dimensional analysis may be used as a first namely a set of guide vanes. With the vanes retracted the order estimate of the coupling performance. Alternatively device operates as a conventional fluid coupling and the it can be applied to a series of streamtubes into which the direction of rotation of the output shaft is the same as the coupling flow is divided. Such a multiple streamtube (or input shaft. When the vanes are inserted, the direction two-dimensional flow) analysis allows accommodation of of rotation of the output shaft is reversed. In traditional the large variations in flow velocity and inclination which terms, the reversible fluid coupling can, in theory, oper- occur between the core and the shell of the machine. ate over a range of slip values from S =0toS =2.In In the multiple streamtube analysis the flow is sub- the present paper, we utilize overall coupling performance divided into streamtubes as shown in figure 2; all the data obtained by NSWC and several investigations of flow data presented here used ten streamtubes of roughly sim- details carried out by WesTech Gear Corporation. ilar cross-sectional area. The flow in each streamtube is A number of recent papers have demonstrated how com- characterized by meridional and tangential components of plex and unsteady the flow is in torque converters (see, for fluid velocity, ui and vi, at each of the transition stations, example, By and Lakshminarayana [8], Brun et al. [9], i =1, 2, 3, between the turbine and the pump (i =1), Gruver et al. [10]. Due, in part, to the need to operate between the pump and the turning vanes (i =2)andbe- the machines over a wide ranges of slip values, the inci- tween the turning vanes and the turbine (i =3).Atypi-

2 2. BASIC EQUATIONS

The process of power transmission through the coupling (operating under steady state conditions) will now be de- lineated. In the process, several loss mechanisms will be identified and quantified so that a realistic model for the actual interactions between the mechanical and fluid- mechanical aspects of coupling results.

2.1 Pump

The power input to the pump shaft is clearly NpTp.Some Figure 3: Velocity triangle at the turbine/pump transition of this is consumed by windage losses in the fluid annulus station, i = 1. Flow is from the right to left, the direction between the pump shell and the stationery housing. This of rotation is upward and the angles are shown as they are is denoted by a pump windage torque, Tpw , which will be when they are positive. 2 proportional to Np . Included in this loss will be the shaft seal loss as it has the same functional dependence on pump Table 1: Basic geometric data for the reversible coupling. speed. It is convenient to denote this combined windage and seal torque, Tpw, by a dimensionless coefficient, Cpw, ◦ 5 2 Pump discharge vane angle, βp,atshell 0 where Tpw = CpwρR Np . Appropriate vales of Cpw can ◦ Pump discharge vane angle, βp,atcore 0 be obtained, for example, from Balje [13] who indicates ◦ Turbine discharge vane angle, βt,atshell 31.5 values of the order of 0.005. ◦ Turbine discharge vane angle, βt,atcore 44 Furthermore the labyrinth seal in the core between the ◦ Turning vane discharge angle, βv −55 pump and turbine rotors causes direct transmission of ◦ Pump inlet vane angle, δp,atshell −17 torque from the pump shaft to the turbine shaft. This ◦ 2 Pump inlet vane angle, δp,atcore −10 torque which is proportional to (Np − Nt) will be de- ◦ Turbine inlet vane angle, δt,atshell 0 noted by Ts and is represented by a seal windage torque ◦ Turbine inlet vane angle, δt,atcore 0 coefficient, Csw, defined as ◦ Turning vane inlet angle, δv 55 3 2 2 2 Ts = CswρR (rb − rc )(Np − Nt) (1) Outer core radius/Outer shell radius, rb 0.861 Inner core radius/Outer shell radius, rc 0.592 A comparison with the experimental data (section 4) sug- Inner shell radius/Outer shell radius, rd 0.29 gests a value of Csw of about 0.014. In referring, to this labyrinth seal, we should also observe that the leakage through this seal has been neglected in the present anal- ysis. cal velocity triangle, in this case for the transition station It follows that the power available for transmission to i = 1, is included in figure 3; the velocity triangles for the the main flow through the pump is Np(Tp −Tpw −Ts)and other transition stations are similar. this manifests itself as an increase in the total pressure of Later we will present measured performance data for the flow as it passes through the pump. For simplicity, the the reversible coupling whose basic geometry is listed in present discussion will employ a two-dimensional represen- Table 1. tation of the fluid flow in which the flow is characterized In the multiple streamtube analysis, the mean radius of at any point in the circuit by a single meridional velocity, the jth streamtube (the numbering of the streamtubes is ui, and a single tangential velocity, vi, at the appropriate shown in figure 2) at each of the locations i =1, 2, 3isde- rms radius. In practice, these quantities will vary over the fined byr ¯j,i. Since the distribution of velocity will change cross section of the flow and this variation is considered from one station to the other, only one of these three sets later. At this stage it is not necessary to introduce this of streamtube radii can be selected apriori.Wechose complexity. The power balance between the mechanical to select the seriesr ¯j,1 at the turbine/pump transition. input, the losses and the ideal fluid power applied to the It follows thatr ¯j,2 andr ¯j,3, the streamtube radii at the pump, then yields pump discharge and at the turning vane discharge must Np(Tp − Tw − Ts)=QHpi (2) then be calculated as a part of the solution. Discussion of how this is accomplished is postponed until the solution where, from the application of angular momentum con- methodology is described in section . siderations in the steady flow between pump inlet (i =1)

3 and pump outlet (i = 2), the pump head rise, Hpi,isgiven 2.2 Turbine by Hpi = ρNp(r2v2 − r1v1)(3)We now jump to the turbine output shaft and work back from there. The power delivered to the turbine shaft is More specifically, Hpi will be referred to as the ideal pump NtTt. As in the pump there are windage losses, NtTtw, total pressure rise in the absence of fluid viscosity when where the windage torque, Ttw, is described by a dimen- 2 the pump would be 100% efficient. However, in a real, sionless coefficient, Ctw = Ttw/ρNt . Then the power de- viscous flow, the actual total pressure rise produced, Hp, livered to the turbine rotor, Nt(Tt + Ttw − Ts), by the is less than Hpi; the deficit is denoted by Hpl where main flow through the turbine is related to the ideal total pressure drop through the turbine, Hti,by Hp = Hpi − Hpl (4) Nt(Tt + Ttw − Ts)=QHti (7) This total pressure loss, Hpl, is difficult to evaluate accu- rately and is a function, among other things, of the angle where, again, from angular momentum considerations of attack on the leading edges of the vanes. Note that the angle of attack, αp, on the pump blades is given by Hti = Nt(r2v3 − r1v1)(8)   −1 v1 − r1Np With an inviscid fluid, Hti would be the actual total pres- αp = tan − δp (5) u1 sure drop across the turbine. But in a real turbine the actual total pressure drop is greater by an amount, Htl, In the present context the total pressure loss, Hpl,isas- which represents the total pressure loss in the turbine, and cribed to two coefficients, Cpa,andCpb. The first co- hence efficient, Cpa, describes a loss which is a fraction of the Ht = Hti + Htl (9) dynamic pressure based on the component of relative ve- In a manner analogous to that in the pump, the total locity parallel to the blades at the pump inlet. The second pressure loss in the turbine, Htl, is ascribed to two coeffi- coefficient, Cpb, describes a loss which is a fraction of the cients Cta and Ctb. The first coefficient, Cta, describes a dynamic pressure based on the component of the pump loss which is a fraction of the dynamic pressure based on inlet relative velocity perpendicular to the blades. Thus the component of relative velocity parallel to the blades at    ρ 2 2 2 the turbine inlet. This coefficient essentially determines Hpl = u +(v1 − r1Np) Cpa +(Cpb − Cpa)sin αp 2 1 the minimum loss at the design point where the angle of (6) attack, αt, is zero. The second coefficient, Ctb, describes a The coefficients Cpa and Cpb can be estimated using loss which is a fraction of the dynamic pressure based on previous experience in pumps. Though there are many the component of the turbine inlet velocity perpendicular possible representations of the pump total pressure loss, to the blades. Thus the above form has several advantages. First, at a given    ρ 2 2 2 flow rate, the loss is appropriately a minimum when αp Htl = u +(v3 − r3Nt) Cta +(Ctb − Cta)sin αt 2 3 is zero, a condition which would correspond to the design (10) point in a conventional pump. And this minimum loss where the the angle of attack, αt, on the turbine blades is is a function only of Cpa. On the other hand at shut-off given by   (zero flow rate) the loss is a function only of Cpb.These − −1 v3 r2Nt − relations permit fairly ready evaluation of Cpa and Cpb in αt = tan δt (11) u3 conventional pumps given the head rise and efficiency as a function of flow rate. Typical values of Cpa and Cpb are of As in the case of the pump, appropriate values of Cta the order of unity; but the value of Cpa must be less than and Ctb are of the order of unity and should be such as the value of Cpb, the difference representing the effect of to yield a stand-alone turbine efficiency, Hti/Ht of the the inlet vane angle on the losses in the pump. order of 0.85. However, Ctb must be greater than Cta to The hydraulic efficiency of the pump, ηp,is1−Hpl/Hpi. reflect the appropriate effect of the inlet vane angles on In a conventional centrifugal pump for which v1 =0,the the hydraulic losses. maximum design point efficiency, ηp, is expected to be about 0.85. With the kind of uneven inlet flow to be 2.3 Turning Vanes expected in the present flow a lower value of the order of 0.80 is more realistic. This value provides one relation for The geometry of a turning vane used in the coupling dis- Cpa and Cpb. cussed here is shown in figure 4.

4 conditions, u3 and v3 are independent of circumferential position and the flux of angular momentum entering the turbine is proportional to u3v3. If the swirl angle were de- fined by the turning vane discharge angle then this reduces 2 to u3 tan βv . On the other hand a partial admission flow ∗ ∗ consisting of jets with velocity components u3, v3 alter- nating with stagnant wakes of zero velocity would have a ∗ ∗ flux of angular momentum equal to ku3v3 where k is the fraction of the cross-sectional area occupied by the jets (0

∗ Hp = Ht + Hv with the turning vanes inserted (12) tan βv =tanβv/k (15)

Hv = 0 with the turning vanes retracted (13) Hence by inputting a somewhat larger than actual turn- ing vane discharge angle we can account for these partial It is this balance which essentially determines the flow admission effects. rate, Q, and the meridional velocities, ui. The total pres- The problem therefore reduces to estimating an appro- sure drop across the vanes, Hv, is described a loss coeffi- priate value for k from the experimental measurements. cient defined by For this purpose, we develop the relation between k and 2 2 the loss coefficient for the turning vanes, Cv. If the total Cv =2Hv/ρ(v3 + u3) (14) head of the jets is assumed to be equal to the upstream total head (at location i = 2), then it is readily shown Though both Hv and Cv will vary with the angle of attack that the mean total head of the discharge (including the of the flow on the turning vanes, αv, we have not exercised wakes) implies the following relation between k and Cv: that option here since there is no independent information   1 on the turning vane performance. Estimates from experi- 2 2 1 − Cvtan βv ence suggest that Cv should lie somewhere between about k = (16) 0.3and1.0. 1+Cv The value of Cv =0.36 which is deployed later along with ◦ ∗ ◦ 2.4 Turbine Partial Admission Effect the appropriate βv = −55 yield βv = −72.8 and a block- age ratio (or partial emission factor) of k =0.44 which Due to the large blockage effects of the turning vanes, seems reasonable given the geometry of the turning vane the flow discharging from the vanes consists of an array cascade. of jets interspersed with relatively stagnant vane wakes. This means that during reverse operation the turbine ex- 3. SOLUTION OF THE FLOW periences inlet conditions similar to those in a partial ad- mission turbine. In the hydraulic analysis we can approx- 3.1 Solution for an individual streamtube imately account for these partial admission effects by tak- ing note of the following property of partial admission. Consider first the solution of the flow in an individual Consider and compare the flux of angular momentum in streamtube where it is assumed that the velocity at any the flow into the turbine, first, for full admission and, sec- location in the circular path (figure 2) can be character- ond, for partial admission. Under uniform, full admission ized by a single meridional and a single tangential velocity.

5 Assume for the moment that the radial positions of the Table 2: Power transmission and losses. streamtube are known; then the inlet and discharge angles encountered by that particular streamtube at those radial Pump shaft power = NpTp positions at each of the transition stations can be deter- Power lost in pump windage = NpTpw mined. Then for a given slip, S =1− Nt/Np, the first Power to turbine through seal = NpTs step is to solve the flow equation (12) or more specifically: Power to main pump flow = QHpi = Np(Tp − Tpw − Ts) Hpi − Hpl = Hti + Htl + Hv (17) Powerinmainflowoutofpump =Q(Hpi − Hpl) to obtain the flow rate and velocities. The procedure used Power lost in turning vanes = QHv Power in flow entering turbine = Q(Hpi − Hpl − Hv) starts with a trial value of u1.Valuesofu2, u3 follow from = Q(Hti + Htl) continuity knowing the areas Ai: Power to turbine rotor by flow = QHti − ui = u1A1/Ai ,i=2, 3 (18) = Nt(Tt + Ttw Ts) Power to turbine through seal = NtTs Furthermore, it is assumed that the relative velocity of Power lost in turbine windage = NtTtw the flow discharging from the pump, the turning vanes or Turbine shaft power = NtTt the turbine is parallel with the blades of the respective device (or the effective angle in the case of the turning vanes). Given the high solidity of the pump and turbine, The principle by which the streamtube geometry is ad- this is an accurate assumption. This allows evaluation of justed is that the flows in each of the three locations should the tangential velocities: be in radial equilibrium. This implies that, at each of the

v1 = r1Nt + u1 tan βt (19) locations i =1, 2, 3, the flow must satisfy   2 ∂P ρvi v2 = r2Np + u2 tan βp (20) = (21) ∂r i ri where r1 and r2 are rms channel radii at each location and where P is the static pressure. Application of this condi- v3 = v2 for the turning vanes retracted and v3 = u3 tan βv tion at the turbine/pump transition station (i =1)estab- for the turning vanes inserted. These relations can then lishes the static pressure difference between each stream- be substituted into the definitions (3), (8), (6), (10) and tube. Then using the information from the flow solution (14) to allow evaluation of all the terms in equation (17). on the static pressure differences between transition sta- That equation is not necessarily satisfied by the initial tions we can establish the pressure distribution between trial value for u1. Hence an iteration loop is executed to the streamtubes at transition stations i =2andi =3. find that value of u1 which does satisfy equation (17). The Then using equation (21) we examine whether the flows velocities and flow rate are thus determined for a given in these locations are in radial equilibrium. Given the ini- value of the slip. tial trial values ofr ¯j,2 andr ¯j,3, this will not, in general, be true. The method adjusts the values ofr ¯j,2 andr ¯j,3 and 3.2 Multiple Streamtube Solution then repeats the entire process until radial equilibrium is indeed achieved at transition stations i =2andi =3. As described in the last section, the multiple streamtube This requires as many as 30 iterations. analysis begins with a set of guessed values for the stream- tube locations at the transition stations, i =2andi =3. 3.3 Power Transmission Summary It also begins with an assumed value for the flowrate in each streamtube (more specifically an assumed value of This completes the description of the power transmission u1 = 1.) Then the method of the last section is used through the coupling which is summarized in Table 2. The to solve for the flow and allows evaluation of the total overall efficiency of the coupling, η,isgivenby pressure changes and losses in each streamtube. Then, NtTt QHti − NtTtw + NpTs the degree to which equation (17) is satisfied is assessed. η = = (22) This leads to an improved value of u1 and the process is NpTp QHpi + NpTpw + NpTs repeated to convergence (only three or four cycles are nec- or substituting from equations (4) and (9): essary). By doing this for each streamtube we obtain the total pressure and the static pressure differences between Nt(r2v3 − r1v1) − (NtTtw + NtTs)/Q η = (23) all three locations for each streamtube. Np(r2v2 − r1v1)+(NpTpw + NpTs)/Q

6 Figure 6: Velocity of turning vane discharge jets for the same conditions as listed in figure 5.

reverse mode. Apart from the overall efficiency, η, two other cou- pling characteristics will be presented, namely the pump torque coefficient, Cp, and the turbine torque coefficient, Ct. Note the choice of Np in the denominator for Ct.

4. COMPARISON WITH EXPERIMENTS

4.1 Experimental Data

The efficiency, torque coefficients and fluid velocities mea- sured during tests of the coupling conducted by NAVSSES (using an oil of density 849 kg/m3) at a input (or pump) speed of 1000rpm will be compared to the results of the present analytical model. Note that although three graphs for η, Cp and Ct are presented, these only represent two independent sets of data since η = Ct(1 − S)/Cp.

4.2 Performance

Figure 5: Efficiency and torque coefficients for the re- A typical set of results for the performance of the cou- versible coupling using Cpa = Cta =0.7, Cpb = Ctb =1.0, pling are presented in figures 5 and 6. The coefficients Cv =0.36, Csw =0.02, Cw =0.005 and an effective turn- Cpa, Cpb, Cta, Ctb,andCva (and, to a lesser extent, Cw ing vane discharge angle of −72.8◦. and Csw) were chosen to match the experimental data by proceeding as follows. First note that Cw and Csw have little effect except close to S = 0. In fact, the peak in η This expression demonstrates an important feature of the near S = 0 is almost entirely determined by Cw and values reversible coupling. In the forward mode with the vanes of Cw =0.02 were found to fit the data near S =0quite removed, v2 = v3, and the quantities in parentheses in the well. This value is also consistent with previous experience numerator and denominator are identical. Therefore, if on windage coefficients (Balje [13]). Similarly past expe- the windage torques, Ttw and Tpw,aresmallasisnormally rience would suggest a value of 0.005 for the seal windage thecaseandifQ is not close to zero (as can only happen coefficient, Csw. close to S = 0) then the coupling efficiency is close to Turning to the pump, turbine and turning vane loss Nt/Np =1− S. Thus, in the forward mode, only the coefficients, it is clear that the turning vanes have no effect windage losses cause the efficiency to deviate from 1 − S. on forward performance (S<1). Hence the pump and On the other hand no such simple relation exists in the turbine loss coefficients were chosen to match this data. In

7 Figure 7: Meridional velocity distributions at the transition stations for four different slip values. this regard the efficiency is of little value since the forward sitions. As the slip increases in forward operation this non- efficiency is always close to (1−S). Values of Cpa = Cta = uniformity decreases; near S = 1 it has disappeared at the 0.7andCpb = Ctb =1.0 seemed to match the forward pump-to-turbine transition but remains at the turbine-to- torque coefficients well. These could be supported by the pump transition. When the turning vanes are inserted, argument that all the dynamic head normal to the vanes the velocity profiles show a highly non-uniform character at inlet will likely be lost (thus Cpb = Ctb =1.0) and a in the pump-to-turning-vane transition but this is almost high fraction of that parallel with the vanes is also likely completely evened out by the turning vanes. The turbine- to be lost (thus Cpa = Cta =0.7). Note that the results to-pump non-uniformity near S = 1 is not too dissimilar presented are not very sensitive to the precise values used to that in forward operation near S = 1. However, it is for these loss coefficients. It should also be noted that interesting to note that this non-uniformity is reversed as these loss coefficients yield sensible peak efficiencies for S = 2 is approached. These changing non-uniformities are the pump or turbine when these are evaluated for stand- important becaause they imply corresponding changes in alone performance (respectively 79% and 86%). the distribution of the angles of attack on the pump, turn- Finally, then, we turn to the reverse performance (S> ing vanes, and turbine. Consequently, the optimal vane 1) with only one loss coefficient left to determine, namely inclination distributions (which would have as their ob- the loss due to the turning vanes, Cva. In the example jective uniform angles of attack) are different for forward shown a value of Cva of 0.36 yields values of the efficiency and reverse operation. which are consistent with the experimental results. Note that if the coefficients described above were used 5. CONCLUSIONS with the actual turning vane discharge angle, there would be substantial discrepancies between the observed and cal- This paper presents a hydraulic analysis of a reversible culated results; this helps to confirm the analysis of section fluid coupling operating over a range of slip values in and the use of the effective turning vane discharge angle, both forward (0

8 coefficients, the values of the coefficients do appear to be [4] Clements, H.A. and Fortunato, E., 1982, “An ad- valid over a wide range of operating points, slip values vance in reversing transmissions for ship propulsion,” and speeds. Moreover, though these coefficients are nec- ASME Paper No. 82-GT-313. essarily specific to the particular coupling studied, they nevertheless provide benchmark guidance for this general [5] Clements, H.A., 1989, “Stopping and reversing high class of machine. power ships,” ASME Paper No. 89-GT-231. When the coupling is operated in the forward mode, [6] Nufrio, R., Schultz, A.N. and McKinnon, C.N., 1987, the flow rates are small and hence the hydraulic losses are “Final report - reverse reduction gear/reversible con- quite minor. Thus the efficiency is close to the ideal. How- verter coupling test and evaluation,” PM-1500B. ever, as the slip increases, the flow rates become larger and the hydraulic losses (which increase like the square of the [7] Zekas, B.M. and Schultz, A.N., 1997, “Unique reverse flowrate) become substantial. Under these conditions the and maneuvering features of the AOE-6 reverse re- device behaves much more like an interconnected pump duction gear,” ASME Paper No. 97-GT-515. and turbine than a conventional fluid coupling and the overall efficiency is similar to that one would expect from [8] By, R.R. and Lakshminarayana, B., 1995, “Measure- a device which links drive trains through a combination ment and analysis of static pressure field in a torque 117 of a pump and a turbine. Even under the best of circum- converter pump,” ASME J. Fluids Eng., , pp. stances the analysis suggests that the efficiency of this 109–115. generic type of coupling could not be expected to exceed [9] Brun, K., Flack, R.D. and Gruver, J.K., 1996, “Laser 60% in the reverse mode. velocimeter measurements in the pump of an auto- The analysis presented here also demonstrates that, motive torque converter. Part II - Unsteady measure- since it is used over a wide range of slip values, a re- ments,” ASME J. Fluids Eng., 118, pp. 570–577. versible fluid coupling must operate over a wide range of angles of attack of the flows entering the pump and tur- [10] Gruver, J.K., Flack, R.D. and Brun, K., 1996, “Laser bine rotors. With fixed geometry rotors, this inevitably velocimeter measurements in the pump of an auto- results in substantial hydraulic losses, particularly in the motive torque converter. Part I - Average measure- reverse mode. Choosing the inlet blade angles in order to ments,” ASME J. Fluids Eng., 118, pp. 562–569. minimize those losses is not simple and it is not clear how [11] By, R.R., Kunz, R. and Lakshminarayana, B., 1995, the fixed geometry should be chosen in order to achieve “Navier-Stokes analysis of the pump flow field of an that end. automotive torque converter,” ASME J. Fluids Eng., 117, pp. 116–122. ACKNOWLEDGEMENTS [12] Schulz, H., Greim, R. and Volgmann, W., 1996, The analyses described were performed for WesTech Gear “Calculation of three-dimensional viscous flow in Corporation, now part of Philadelphia Gear, and the au- hydrodynamic torque converters,” ASME J. Fluids 118 thors are very grateful to both organizations for their con- Eng., , pp. 578–589. currence in the publication of this paper. We are also very [13] Balje, O.E., 1981, “Turbomachines. A guide to de- appreciative of the help and advice of Tom Gugliuzza of sign, selection and theory,” John Wiley and Sons, WesTech Gear. New York.

REFERENCES

[1] Stepanoff, A.J., 1957, “Centrifugal and axial flow pumps,” John Wiley and Sons, Inc.

[2] Brennen, C.E., 1994, “Hydrodynamics of Pumps,” Oxford University Press and Concepts ETI, Inc.

[3] Fortunato, E. and Clements, H.A., 1979, “Marine re- versing gear incorporating single reversing hydraulic coupling and direct-drive for each turbine,” ASME Paper No. 79-GT-61.

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