EXPERIMENTAL INVESTIGATIONS ON MIXED FLOW IMPELLER AND VANE DIFFUSER UNDER VARIOUS OPERATING CONDITIONS

Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition, November 9-15, 2012, Houston, Texas, USA IMECE2012 IMECE2012-85695 EXPERIMENTAL INVESTIGATIONS ON MIXED FLOW IMPELLER AND VANE DIFFUSER UNDER VARIOUS OPERATING CONDITIONS D. Ramesh Rajakumar National Trisonic Aerodynamic Facility CSIR-National Aerospace Laboratories Bangalore-India-560017. ramesh0102@yahoo.com S. Ramamurthy Specialist Consultant, NCAD, CSIR-National Aerospace Laboratories Bangalore- India-560017 ramamurthy_srm@yahoo.com M. Govardhan Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India-600036 gova@iitm.ac.in ABSTRACT Experimental Investigations are carried out to study the effect of tip clearance flow in a mixed flow compressor stage. Two configurations, namely; constant and variable clearance gaps between impeller and stationary shroud are considered. For the purpose of the present investigations, a mixed flow compressor stage is designed and fabricated. The flow investigations were carried out in a closed circuit compressor rig. Detailed steady and unsteady measurements were carried out for three clearance gaps, namely; 0.5 mm, 0.75 mm, 0.9 mm. From the experimental investigations it is shown that constant tip clearance configurations show better performance in terms of pressure ratio and efficiency compared to variable clearance configurations. For a given configuration the pressure ratio and efficiency of the stage decrease with increase in the tip gap without indicating any optimum value. Tip clearance flow has considerable effect on the flow through the diffuser and the unsteady flow gets amplified and carried away into the vane diffuser. Key Words: Mixed flow compressor, Tip clearance, Efficiency, Pressure ratio, Loss distribution, Tip leakage flow, Unsteady pressures. NOMENCLATURE C absolute velocity (m/s) D diameter of the shroud (m) N revelation per minute P pressure (Pa) T temperature (K) W relative velocity (m/s) U impeller tip velocity (m/s) Mass flow parameter = m (T 01 / T 01ref ) / (P 01 / P 01ref ) λ= (tip clearance/impeller inlet blade height) Subscripts 0 total 1 impeller inlet 2 impeller outlet i inlet diameter of shroud s static pressure o design value ref reference INTRODUCTION Mixed flow compressor stage is favored for applications in small gas turbine engines as it provides smaller frontal area and higher thrust to weight ratio. The efficiency and reliability of the compressor depends to a great extent on flow behavior in its flow passage and flow near shroud (tip) gap. It is well known that the interaction between mixed flow impeller and diffuser substantially influences the flow field and performance of both the components and thus the entire compressor stage. It is therefore, necessary to study and understand the complex flow field inside the flow channel of the mixed flow compressor. Due to high rotational speed and mechanical strength considerations, most of the high speed mixed flow compressors are unshrouded. The tip leakage flow has considerable effect on the performance and efficiency. The magnitude of this effect is relatively higher in mixed flow compressors than in axial compressors because a mixed flow compressor has a long narrow flow passage and the tip clearance gap occupies a large portion of the flow passage. Work presented by Austin King et al. [1], in 1942, was probably one of the earliest works regarding mixed flow compressors. They experimentally investigated a parallel cutoff mixed impeller with 0.89mm (0.35 ) frontal clearance to study the performance of compressor. A very low value of maximum adiabatic efficiency, 0.76, was reported. Ward Wilcox 1 Copyright 2012 by ASME

[2] tested an impeller pre-whirl vanes designed using Goldstein s method. The impeller had maximum tip diameter of about 176mm and had peak pressure ratio of 3.7 with impeller adiabatic efficiency of 0.78, which is very low value. The same impeller when tested with a supersonic diffuser by Ward Wilcox and Rabbins [3] flow choked before the design mass flow rate could be achieved. Dallenbach [4] presented a method for aerodynamic design for centrifugal and mixed flow compressors to achieve prescribed impeller blade loading distributions for impellers with radial blade elements. He also presented experimental velocity distribution results for 12 impellers including 4 mixed flow impellers designed with this method. Only one impeller gave satisfactory blade loading. All the impeller designs had radial blade elements. Wallace [5] showed that the reduction in cone angle, the velocity distribution over the blade surface improves. But small cone angles also results in comparatively low-pressure ratio due to less benefit of centrifugal effect. Moreover, the axial length of the compressor increases. Hence, a balance should be made between the performance and size requirements while selecting the cone angle. Many research have been carried out on flow mechanism, flow structure and performance loss due to the tip leakage flow on radial and axial flow compressors. Pampreen [6] concluded that clearance effects have pronounced influence on the performance of centrifugal and axial compressors compared to Reynolds number effects. Ishida and Senoo [7] used two entirely different types of centrifugal blowers one with a radial blade impeller and the other with a backward blade impeller, measured the pressure distribution along the shroud at five flow coefficient and seven tip clearances. Senoo and Ishida [8] observed the deterioration of compressor performance due to tip clearance of centrifugal impeller. They modified their theory on the tip clearance loss of centrifugal impeller to include the variation of slip co-efficient of the impeller due to the tip clearance, by deriving a rational relationship between two empirical parameters in the theory. They have compared experimental data in the literature with prediction, to select corresponding flow rates of a compressor with different values of tip clearance loss. It has been elucidated experimentally and numerically that leakage flow alters the secondary flow pattern and distribution of the low momentum fluid so that the tip clearance loss accounts for nearly 20-40,% of the total losses by Lakshminarayana, and Myong, [9-10]. Hark-Jin Eum et al. [11] have reported that the performance drop and the efficiency drop were proportional to the ratio of the tip clearance to the blade exit height and tip leakage caused the flow blockage near the shroud. According to Seeno[12], there is mutual relationship between the leakage flow loss, induced drag loss and clearance loss due to the axial pressure gradient. Farge, et al. [13] concluded that the static pressure distribution was found to be almost unaltered by the tip leakages but significant changes in the secondary velocities alters the size and position of the passage wake in centrifugal impellers. Storer and Cumpsty, [14] observed in their model that for a given geometry of axial compressors, the loss is almost exactly proportional to the ratio of tip clearance to blade span. Also they concluded that loss caused by tip clearance for the axial inlet stage was between 20 to 30 percent greater than for the 50 percent reactions stage. The intensive study has been carried out about tip clearances for centrifugal and axial compressors. In the case of mixed flow compressors, the gas density, the blade height, and the meridional component of velocity vary from the inlet to the exit of impeller. Therefore, the equations derived and the theories proposed by all the authors are not fully pertinent parameters for blade of mixed-flow impellers but it can be applied to a short distance along the shroud of the mixed-flow impeller. In the case of mixed flow compressors very few works has been done on design of impeller and diffuser. However, there is no specific paper in the literature that compares the effect of constant and variable tip clearances experimentally over the wide range of mixed flow impeller. OBJECTIVE The objective of this work is to determine the effect of constant and variable tip clearances on the performance of a mixed flow compressor stage. The objectives are achieved by conducting experiments on a mixed flow compressor stage at various speeds and for each speed at various constant and variable tip clearances configurations. EXPERIMENTAL PROCEDURE Experimental Apparatus The experiments were carried out in the Closed Circuit mixed flow Compressor Test Rig (CLOCTER), which is shown in Fig.1(a). The test compressor was driven by an electromechanically coupled twin DC motors. The rated power and speed of the D.C prime mover system are 375 kw and 3000 rpm respectively. Digital thyristor control with feedback mechanism ensures maintenance of the speed to an accuracy of 0.1%. The compressor and DC motor are connected together with a step up gear box (1:20). An electronic torque meter coupled in between the gear box and the compressor is used to measure compressor speed and input power to the compressor. A 10 inch motorized gate valve provided in the closed circuit was used to vary the mass flow rate through the compressor. For finer control of mass flow rate close to the stall region, a 50 mm bypass line connecting in between the main throttle valve was provided with a 50 mm gate valve, through which the mass flow rate was varied at very close intervals to reach stall point on the operating characteristics. An Orifice plate with D and D/2 tapings was used for mass flow measurement. 2 Copyright 2012 by ASME

Fig.1(a): Details of closed loop compressor test rig The D and D/2 tapings of the orifice plate are connected to a differential pressure transducer to measure the pressure drop across the orifice. This transducer is interfaced with the computer for online mass flow measurement. A shell and tube type heat exchanger as used to cool the compressor exhaust gas and ensure steady inlet temperature conditions to the compressor. An independent forced lubrication system was provided for the gear box and compressor module. The facility can be operated either in closed loop or open loop mode, depends on the medium to be handled and the operating condition required at the compressor inlet. In order to get three constant clearance gaps between the rotating impeller and stationary shroud, three different shrouds were manufactured and they were used to maintain 0.5 mm (λ=0.011), 0.75 mm (λ=0.016) and 0.9 mm (λ=0.019) clearances. For variable clearance configurations, the shroud with 0.5 mm clearance was axially moved by providing a suitable metal shims between shroud flange and diffuser flange. The thicknesses of the two shims used are 0.25 mm and 0.4 mm respectively. This arrangement makes the clearance between the impeller and the shroud from 0.5mm at inlet to 0.82mm at impeller exit in one set of configuration and 0.5mm at inlet to 1.02mm at impeller exit at the other set of configuration. Figure 1(b), shows a crosssectional view of the mixed compressor. Tip clearance distribution from leading edge to the trailing edge of mixed flow impeller is shown in Figs.2 (a)-2(b). All the experiments were carried out up to 65% of the design speed due to mechanical limitations on the bearings used. Specifications of the mixed flow compressor is shown in Table 1. Mixed flow impeller stage was designed for 2.72 kg/s and static to total pressure ratio of 3.8 with design speed of 39836 rpm. Fig. 1(b): Cross-sectional view of the mixed compressor stage The impeller had 11 main blade and 11 splitter blades with cone angel of 60 o. The stage had a matched vane diffuser with 14 blades. Machined impeller and vane diffuser are shown in Figs-3(a)-3(b). Fig.2 (a): Constant tip clearance gap from leading edge to the trailing edge Fig.2 (b): Variable tip clearance gap from leading edge to the trailing edge 3 Copyright 2012 by ASME

Table 1: Specifications of mixed flow impeller Impeller inlet parameter Value Impeller inlet tip diameter d 1it (m) 0.156 Impeller inlet hub diameter d (m) 0.0625 Impeller rotational speed N (RPM) 39836 Hub to tip diameter ratio 1ih 1it Relative blade angle at tip β (deg) 61.8 1ih d d 0.40 1it Relative blade angle at hub β (deg) 36.7 1ih Impeller exit parameter Impeller exit tip diameter d 2it (m) 0.253 Impeller exit hub diameter d (m) 0.239 2ih Impeller exit blade height b 2i (m) 0.0141 Relative blade angle at tip β 2itI (deg) 58.5 Relative blade angle at hub β (deg) 46.8 Absolute flow angle α (deg) 70 2it 2ihI Impeller main blades 11 Impeller splitter blades 11 Diffuse vanes 14 Fig.3(b): Photograph of machined conical diffuser A Detailed instrumentation was provided to measure the time averaged pressure and temperatures at different locations of the compressor stage. A combination probe was used to measure flow properties at impeller outlet. A dedicated on line National Instruments data acquisition system with LAB-VIEW software was used to collect on line data during experiments. In addition to steady state pressure measurements, the unsteady flow through the impeller and diffuser channel were measured using high response miniature pressure transducers and 4- channel simultaneous data acquisition system using DASY LAB software. Eddy current probe signal from the shaft was used for triggering the transducer signal. Fig.3 (a): Photograph of machined mixed flow impeller Fig.4: Locations of unsteady and static pressure ports 4 Copyright 2012 by ASME

This type of signal helps in getting ensemble average signal of the transducer. Figure-4 shows locations of the static pressure, total temperature and unsteady pressure taps. RESULTS AND DISCUSSION Constant tip clearance Figures 5(a) and 5(b) represent the impeller and the stage characteristics in terms of mass flow parameter versus pressure ratio for four different operating speeds. At each speed, curves are drawn for three constant tip clearance values. The impeller total pressure was estimated from measured static pressure and mass flow rate using Wisner slip correlation calculated based on number of blades and blade exit angle and conservation of mass. The vane diffuser outlet static pressure was measured at three circumferential locations and the values were averaged. Impeller outlet total pressure and diffuser outlet static pressure were normalized with reference to impeller inlet total pressure. The inlet total pressure was measured using a Pitot probe connected to a pressure transducer. In these figures, the mass flow parameter is calculated based on measured mass flow rate and normalized inlet total pressure and total temperature condition with reference to standard atmospheric pressure and temperature. The impeller speeds are normalized with reference to design speed and shown as percentage. From Fig. 5(a), it is observed that impeller total to total pressure ratio drops with increase in clearance gap. This drop is higher at higher speeds. The variation of total pressure with the mass flow rate exhibits nearly a flat behavior as the impeller is highly backswept. These characteristics were obtained almost close to the stall conditions by observing pressure fluctuations on a CRT scope at impeller outlet using high response transducers. Fig.5 (b): Variation of stage static to total pressure ratio for different speeds and constant clearance gaps Figure 5(b) shows that the effect of tip clearance gap on the compressor stage consisting of impeller and vane diffuser. In this figure the diffuser outlet static pressure is normalized by impeller inlet pressure and this value is plotted against mass flow parameter for different impeller speeds. As the flow passes through the vane diffuser there is a static pressure rise with a drop in total pressure. The drop in total pressure indicates the losses in the diffuser due to wall friction, mixing and sudden expansion at the diffuser exit. Though there is a static pressure recovery in the vane diffuser, the static pressure recovery decreases with increase in clearance gap. The stage characteristics are steeper compared to impeller characteristics as the losses in the diffuser are larger at larger flow rate. This is because the incidence to the diffuser plays an important role in the stage performance. This incidence which is large negative at high flow gradually decreases and becomes positive towards low flow. Fig. 5(a): Variation of impeller pressure ratio for different speeds and constant clearance gaps Fig.5(c): Variation of impeller isentropic efficiency at 65% of design speed for constant clearance gaps 5 Copyright 2012 by ASME

Fig.5 (d): Variation of stage efficiency at 65% of design speed for constant clearance gaps From the estimated total pressure at impeller outlet and measured total temperature, the isentropic efficiency of the impeller was calculated for all speeds and clearance gaps. The variations of impeller efficiency with mass flow parameter for different clearance gaps at 65% of speed are shown in Fig. 5(c). Similarly the estimated stage efficiency for the same speeds is shown in Fig. 5(d). Efficiency decreases with flow rate as well as with tip clearance gap. The diffuser efficiency is smaller than impeller efficiency by the amount of losses in the diffuser. Though the impeller total pressure characteristics showed flat behavior, the impeller efficiency at the larger flow rate is smaller as compared to the value a lower flow rate. This is because the incidence to the impeller is largely negative with a possibility of flow separation on the blades. From the pressure ratio and efficiency, the decrement in pressure ratio and efficiency of the impeller and diffuser for different speeds and clearances are estimated as percentage and are shown in Figs. 6(a) 6(c). Fig. 6(b): Percentage decrement of impeller efficiency for various constant tip clearance gaps relative to λ = 0.011 From Fig. 6(a), it is observed that percentage of drop in pressure ratio increases with increase in speed, indicating rotational speed has an effect on the clearance flow in addition to pressure gradient along the impeller channel. As the rotational speed increases the coriolis force and cross flow through the clearance gap increases. Pressure drop is varying between 1.8% at lower clearance gap to 4% at larger clearance gap at 65% of designed speed. On the other hand at 50% design speed, pressure drop could be as less as 0.3% to 1.5%. Observation from Fig. 6(b) shows that the drop in efficiency increases marginally with increase in clearance gaps for a given speed. The drop in impeller efficiency could vary from an average of 3% at 50% speed to 11% at 65% speed. The drop in stage efficiency from Fig. 6(c) seems to be more pronounced with change in clearance gaps. At a given speed, efficiency could vary from 2.5% to 5.5% with variation in clearance gap at higher speed. Similar observation is seen at other speeds also. Fig. 6(a): Percentage decrement of impeller pressure ratio for various constant tip clearance gaps relative to λ = 0.011 Fig.6 (c): Percentage decrement of stage efficiency for various tip clearance gaps relative to λ=0.01 6 Copyright 2012 by ASME

Variation of wall static pressures The static pressure along the shroud from impeller inlet to diffuser outlet and beyond were measured by providing static pressure taps and connecting them to electronic scanners. The static pressure taps in the vane diffuser were provided in the middle of diffuser channels. Variation of wall static pressure for different clearance gaps at a given speed were measured and plotted as non-dimensional pressure against non- dimensional distance for two different flow coefficients. Fig.7(a): Variation of normalised wall static pressure ratio with tip clearance gap at φ = 0.315 Fig.7(b): Variation of normalised wall static pressure ratio with tip clearance gap at φ = 0.480 Fig.8: Measured ensemble averaged unsteady static pressure at different locations along the shroud wall 7 Copyright 2012 by ASME

At higher flow coefficient the normalized static pressure uniformly increases from impeller inlet to diffuser exit. The effect of tip clearance is different from that observed in the case of lower flow coefficient. The steep increase in static pressure in the vane-less gap is not observed. The lowest flow coefficient is chosen close to stall condition whereas the larger flow coefficient is taken at fully open throttle condition (Figs. 7(a) and 7(b)). Static pressure increases continuously from impeller inlet to diffuser outlet with a special behavior in vane-less gap from impeller exit to vane diffuser leading edge (Fig. 7(a)). In this gap, the static pressure increase is very large as the operating point is close to design. The rate of static pressure raise in the impeller is larger as compared to vane diffuser. This behavior is observed for all clearance gaps. The static pressure rise in the vane diffuser is proportionally decreases with increase in clearances and the effect of clearances is obtained clearly as compared to impeller wall static pressure. However, the static pressure continuously increases at uniform rate from impeller inlet to diffuser outlet for all clearances. In the diffuser clearance the variation in wall static pressure is marginal and no steep increase as observed in Fig.7(a). Slight drop in static pressure with increase in clearance gaps is observed throughout the region of measurement. Unsteady pressure measurements Eight equally spaced high response miniature Kulite transducers were mounted on the shroud walls to capture unsteady pressure variation. Two transducers were located in the region between impeller inlet and splitter blade, two in the region between splitter blade leading edge and impeller outlet and remaining four in the vane diffuser channels. The pressure signals from the transducer were triggered by taking the signal from the shaft eddy current probe. The pressure signals of about 50 numbers from the transducers were ensemble averaged and recorded in a computer. The analog pressure signals in terms of millivolts are converted to actual pressure using the static pressure measured at the same location at the same instant of time. The measured pressure signals for one revolution of a given speed for 3 different tip clearances are shown in Fig.8 In this figure the measured pressure signal location are given at nearly constant flow coefficient. It is observed from Fig. 9, the flow in the channel of impeller is uniform and every channels behavior is identical. As this flow enters the diffuser channels the symmetry of the flow is lost and flow becomes more unsteady. Fig.9(a): unsteady pressure measurements along the shroud for λ =0.011 At lower flow coefficient, the unsteady diffuser flow is larger as compared to larger flow coefficient as the flow is nearer to unstable rotating stall. From the measured unsteady pressure signals the average of maximum and minimum values were calculated for different flow coefficients and clearance gaps at each transducers location. The variations of these values along the shroud are shown in Figs. 9(a) and 9(b). Though the average static pressure increases along the shroud, maximum and minimum pressure variations in the diffuser channels behave differently at the two clearance gaps considered. This indicates the tip clearance has large influences on the impeller exit flow and there off. Fig.9(b): unsteady pressure measurements along the shroud for λ =0.019 Comparison of constant and variable tip clearances A comparison of total pressure ratio and efficiency between constant clearance and variable clearance configurations is shown in Figs. 10(a) 10(b). 8 Copyright 2012 by ASME

Fig.10(a): Impeller total to total pressure ratio for variable and constant tip clearance gaps The pressure ratio developed by the impeller with constant clearance gap is higher than the same impeller with variable clearance gap. This is because the tip gap at impeller exit is higher for a variable clearance configuration though the gap at impeller inlet is same (Fig. 10(a)). Figure 11(b), indicates the isentropic efficiency of impeller is also lower for variable tip clearance gaps as compared to constant tip clearance gaps. An estimate of the drop in pressure ratio and isentropic efficiency for two tip clearance configurations at different speeds are shown in Figs. 11(a) and 11(b). Both drop in pressure ratio and drop in efficiency are higher for variable clearance configurations at all speeds. Fig. 11(a): Decrement of impeller pressure ratio for variable and constant tip clearance gaps relative to 0.5mm (λ=0.019) tip clearance gaps CONCLUSIONS The experimental study show that the impeller total to total pressure ratio and efficiency drop with increase in clearance gap. This effect is higher at higher impeller speeds. Diffuser efficiency is smaller than Impeller efficiency by the amount of losses in the diffuser and losses associated with exit complex flow at impeller exit. At lower flow coefficient, the unsteady diffuser flow is large as compared to larger flow coefficient as the operating point is close to rotating stall. Total to total pressure ratio drop is very prominent in variable tip clearance configurations because of the larger tip gap at the trailing edge of the impeller. It is recommended to use a constant tip clearance configuration for practical use. Fig. 10(b): Impeller isentropic efficiency for variable and constant tip clearance gaps Percentage of decrement in pressure ratio and isentropic efficiency were considered with reference to the values obtained for a configuration with constant clearance gap of 0.5 mm (λ =0.011). At lower speed the relative drop in pressure ratio and efficiency for various tip clearance gaps is higher. Fig.11(b): Decrement of impeller efficiency for variable and constant tip clearance gaps relative to λ=0.019 9 Copyright 2012 by ASME

ACKNOWLEDGMENTS The authors would like to thank The Director NAL for the his approval for publishing this paper and V. Nagarajan, HOD, NTAF, Mr. M.N. Varadarajan & his teams also CLOCTER staff for their valuable support during the experiments. REFERENCES [1] Austin King, J., and Edward Glodeck July-1942, Performance characteristics of Mixed flow impeller and vaned diffuser with several modifications, NACA-WR-E197. [2] Ward W. Wilcox,and William H. Rabbins, April-30, 1951, Design and Performance of an Experimental Axial Discharge Mixed Flow Compressors III-Over- All performance of impeller and Supersonic-Diffuser Combination, NACA RM E51A02. [3] Ward W. Wilcox and Rabbins, Aug-12, 1948, Design and Performance of an Experimental Axial Discharge Mixed Flow Compressors II- Performance of impeller, NACA RM E8F07. [4] Dallenbach,F., 1961, The Aerodynamic Design and performance of Centrifugal and Mixed flow compressors, SAE Technical Progress Series, Vol-3, pp.2-30. [5] Wallace, F. J., et al. July-1975, A Computer- aided design procedure for radial and Mixed-flow compressors, Computer Aided Design, Vol 7, No 3, pp.163-170. [6] Pampreen, R.C., July -1973, Small Turbomachinery Compressor and Fan Aerodynamics," Journal of Engineering for Power, 95, pp. 251-256. [7] Shida, M., and Senoo,Y.,1981, On the pressure losses due to the tip clearance of centrifugal blower, Trans. of ASME J1. of Engg. for power, 03, pp.271-278. [8] Senoo, Y., and Ishida,M., 1987, Deterioration of compressor performance due to tip clearance of centrifugal impellers, Trans. of ASME J1. of Turbomachinery, 109, pp.55-61. [9] Lakshminarayana, B., 1970, Methods of Predicting the Tip Clearance Effects in Axial Flow Turbomachines, Journal of Basic Engineering, Vol. 92, pp. 467-482. [10] Myong, H. K., and Yang, S., Y., 2003, Numerical Study on Flow Characteristics at Blade Passage and Tip Clearance in a Linear Cascade of High Performance Turbine Blade, KSME lnternational Journal, Vol. 17, No. 4, pp. 606-616. [11] Hark-jin Eum, Young-Seok Kang and Shin-Hyoung Knag 2004, Tip clearance Effect on through-flow and performance of a Centrifugal compressors, KSME International Journal, Vol. 18, No. 6, pp. 979-989. [12] Senoo,Y., 1991, Mechanics on the tip clearance Loss of Impeller Blades, Trans. of ASME J1. of Turbomachinery, 113, pp. 680-685. [13] Farge,T.Z.,Johnson M.W., and Maksoud T.M.A., 1991, Tip leakage in a Centrifugal Impeller. Trans. of ASME J1. of Turbomachinery, 111, pp.244-249. [14] Storer. J.A., and Cumpsty. N.A., 1994, An approximate Analysis and Prediction Method for Tip CLeracne Loss in Axial Compressors, Trans. of ASME J1. of Turbomachinery, 116, pp.648-656. 10 Copyright 2012 by ASME