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A Perspective on Measurement Uncertainty Analysis for Commercial Aircraft Test Engines High-accuracy data is critical to vetting engine performance indices such as compressor efficiency and thrust specific fuel consumption. Environmental and engine operating conditions can significantly vary during a flight cycle consisting of takeoff, climb, cruise, descent, and landing – influencing the elemental systematic uncertainties of measurements. (Ref.  provides general definitions of error sources.) Full knowledge of the measurands and measuring systems is a prerequisite to estimating and mitigating the uncertainties of the measurements. The objectives are: 1) to identify and discuss subtle sources of errors for flight-test measurements and 2) demonstrate importance of implementing applicable engineering principles for realistic assessment of such sources of uncertainties. INTRODUCTION SELECT SOURCES OF ERRORS & EXAMPLES Thermal effects can influence zero-shift and operating output of a sensor such as pressure transducer. Acurate determination of sensor operating temperature is imperative for devices exhibiting a high sensitivity to temperature perturbation. Inadequate accounting of thermal interactions between the measurement system and its surroundings can compromise the data validity. Thermal Effects Physical Change Any unaccounted physical mutations that may occur within an instrument during a flight cycle can impact the calibration uncertainties. For instance, the calibration curve of a volumetric turbine flowmeter (Figure 1) may shift due to a variation in the blade tip clearance resulting from a radial displacement of the casing caused by changes in the fuel and ambient pressure / temperature. This is analogous to studies examining the efficiency losses associated with the blade tip clearances in gas turbines [2, 3]. (References on turbine flow meters: [4, 5, 6].) Example: casing of a turbine flowmeter is made of stainless steel – modulus of elasticity (E) ≈195 GPa and Poisson ratio (ν) ≈ 0.3; inside radius (r i ) = 20 mm; outside radius (r o ) = 30 mm; outside pressure (P o ) = 100 kPa, and fuel pressure (P i ) = 5000 kPa. Using the equation below, the inner radial displacement (∆r i ) is estimated to be 0.0012 ± 0.0001 mm. Although the estimated radial displacement may not have any discernible impact on the flow rate uncertainty, the underlying analysis exemplifies the importance of examining the theoretical hypotheses for realistic uncertainty assessment. The inner radial displacement is determined from : 2014 NCSL International Workshop and Symposium © 2014 United Technologies Corporation riri roro Blade Tip Clearance Fuel Figure 1. Schematic of a turbine flowmeter (not to scale). Certain elemental errors, such as hysteresis, are typically prescribed as a percentage of the sensor full span. Hence, congruity between the sensor capacity and the range of interest is important for error control. Optimizing the sensor range, however, may not be feasible in cases where the instrument (e.g., strain-gauge rotary torque sensor) is adhered to the test specimen (e.g., fan shaft). Example: For a torque sensor capacity of 80 kN.m with a systematic uncertainty of ± 0.10% F.S. (dominated by linearity / hysteresis), the torque uncertainty becomes: ± 0.08 kN.m at a 95% C.L. Figure 2 depicts an asymptotically decreasing trend of the relative uncertainty (in percentage of reading) with the increasing part load. For the arbitrary range of interest, 50% – 60% F.S., shown in Figure 2, the relative uncertainty is equal or greater than ± 0.17% of the reading, compared to ± 0.10% of the reading in the ideal scenario (red line). (Dependency of linearity / hysteresis errors on calibration range is also discussed in Ref. .) A pressure transducer, on the other hand, can be isolated (via valves) from the test object, allowing use of multiple devices with various sub- spans – leading to more accurate measurements during a flight cycle. Instrument Span Mismatch Figure 2. Results of an example for rotary torque measurements. (Note: Torque measurement errors due to variations in temperature- dependent material properties of test specimen are not included.)
Ali Jalalzadeh-Azar, Ph.D., PE Depending on the instrument, the response characteristics of a measuring device can vary with altitude as illustrated in the examples below. Pressure sensor: The time constant of a pressure sensor for the engine intake air is in part influenced by the velocity of the compression / expansion wave propagating through the pressure tubing. Treating air as a perfect gas, the wave velocity is approximated by that of sound (α) as a function of the specific heat ratio (γ), gas constant (R ), and absolute temperature (T ): The delay in the instrument response time due to the connecting line ≈ L / α, where L is the length of the conduit. When the ambient temperature decreases from 25 o C (298 K) at the takeoff to -20 o C (253 K) at a cruise altitude, the delay in the instrument response time will increase by about 8%, whose uncertainty can be estimated based on the uncertainties of the conduit length and the confined air temperature. In addition, any variation within the transducer during a flight cycle can potentially impact the sensor time constant, which is a function of the damping ratio and natural frequency . (The effective time constant of the entire measurement system can be analytically estimated based on historical test data .) Thermocouple : The response time is negatively corrolated with the convection heat transfer coefficient. Altitude-induced change in ambient pressure and temperature alters inlet air density, influencing the Reynolds number and, hence, the heat transfer coefficient. Similarly, the response behavior of gas-path thermocouples varies with the changing operating conditions in a flight cycle. Instrument Response Variation This study aimed to stress 1) the need for addressing the elemental errors that are not necessarily captured in the calibration data for the measurement devices used in flight tests and 2) the importance of applying engineering principles to help quantify such uncertainties. The error sources examined in this paper are : Thermal Effects, Instrument Span Mismatch, Physical Change, and Instrument Response Variation, of which the last two are more likely to be overlooked. Quantifying thermal effects can be challenging in cases where the effective operating temperature of the instrument is subject to complex installation and / or conceptual errors. Unavoidable Instrument Span Mismatch refers to a limitation of certain devices, such as rotary torque sensors, that are inseparable from the test specimen and, hence, do not allow a span specification commensurate with the operating range of interest. In contrast, pressure transducers are not subject to this constraint. Physical change within an instrument (e.g., volumetric turbine flowmeter) can potentially alter the effective calibration curve. This additional source of error can be a concern for both steady-state and transient modes in test flights. Instrument Response Variation is of particular importance for transient modes (e.g, climb, ascent, and descent). Such a variation was elaborated in conjunction with the temperature-dependent compression / expansion wave velocity affecting the response time of pressure transducers. CONCLUSIONS Acknowledgments : The author wishes to thank Douglas S. Breindel, John C. Breslin, James W. Dunn, and Al Krejmas of Pratt & Whitney, a United Technologies Company, for their support. References 1.H.W. Coleman and W.G. Steele, Jr., Experimentation and Uncertainty Analysis for Engineers, 3 rd ed. John Wiley & Sons, Inc, New York, NY, 2009. 2.P.J. Newton, G.D. Lock, S.K. Krishnababu, H.P. Hodson, W.N. Dawes, J. Hannis, and C. Whitney, Heat Transfer and Aerodynamics of Turbine Blade Tips in a Linear Cascade, Transaction of the ASME, Vol. 128, pp. 300-309, 2006. 3.T.C. Booth, P.R. Dodge, and H.K. Hepworth, Rotor Tip Leakage: Part 1: Basic Methodology, ASME J. Eng. Power, 104, pp. 154-161, 1982. 4.R. Kalivoda, Fundamentals of Liquid Turbine Meters, TP02001/Technical Paper 103B, FMC Technologies, 1998. 5.P.W. Stoltenkamp, Dynamics of turbine flow meters, Technische Universiteit Eindhoven. 2007. 6.Warshawsky, H.F. Hobart, and H.L. Minkin, Small Turbine-Type Flowmeters for Liquid Hydrogen, NASA Technical Memorandum, NASA TM X-52984, 1971. 7.A.P. Boresi, R.J. Schmidt, Advanced Mechanics of Materials, 6th ed, John Wiley & Sons, 2003. 8.G. Wegener, W. Nold, J. Andrae, and K. Molitor, K. Measurement Uncertainty of Rotating Torque Transducers When Used in Partial Load Ranges, XVIII IMEKO World Congress, Metrology for a Sustainable Development, September 17 – 22, Rio de Janeiro, Brazil. 2006. 9.E.O. Doebelin, Measurement Systems Application and Design, McGraw-Hill, New York, NY, 2004. 10.A.A. Jalalzadeh-Azar, Analytical Evaluation of Response Characteristics of Temperature and Pressure Measurement Systems for Gas Turbine Engines, Proceedings of NCSL International Workshop and Symposium. Nashville, TN, July 14-18, 2013, 2013. 2014 NCSL International Workshop and Symposium © 2014 United Technologies Corporation
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