SAE ARP 4990B-2015 Turbine Flowmeter Fuel Flow Calculations.pdf

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1、_ SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising there

2、from, is the sole responsibility of the user.” SAE reviews each technical report at least every five years at which time it may be revised, reaffirmed, stabilized, or cancelled. SAE invites your written comments and suggestions. Copyright 2015 SAE International All rights reserved. No part of this p

3、ublication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada) Tel: +1 724-776-497

4、0 (outside USA) Fax: 724-776-0790 Email: CustomerServicesae.org SAE WEB ADDRESS: http:/www.sae.org SAE values your input. To provide feedback on this Technical Report, please visit http:/www.sae.org/technical/standards/ARP4990B AEROSPACE RECOMMENDED PRACTICE ARP4990 REV. B Issued 1997-09 Reaffirmed

5、2007-11 Revised 2015-09 Superseding ARP4990A Turbine Flowmeter Fuel Flow Calculations RATIONALE One of the cited references has been revised - a common calibration curve for Jet-A and Jet-A1 fuels has been replaced by two calibration curves, one for each. The revision will address this change, and r

6、emove any ambiguity that may arise by referring to the old document. TABLE OF CONTENTS 1. SCOPE 3 1.1 Purpose . 3 2. REFERENCES 3 2.1 Applicable Documents 3 2.2 Nomenclature 5 2.3 Greek Symbols 6 3. BACKGROUND 7 4. INTRODUCTION . 7 4.1 True Fuel Mass Flow Rate 7 4.2 LHV Corrected Fuel Mass Flow Rate

7、 . 8 4.3 Turbine Flowmeter Calibration and Corrections . 8 4.4 Fuel Flow Calculation Summary . 10 4.5 Document Summary . 10 5. FUEL PROPERTY MEASUREMENTS AND CORRECTIONS 10 5.1 Density 10 5.1.1 Density: Measurement . 11 5.1.2 Density: Temperature Correction . 11 5.1.3 Density: Pressure Correction .

8、12 5.2 Kinematic Viscosity . 13 5.2.1 Kinematic Viscosity: Measurement 13 5.2.2 Kinematic Viscosity: Temperature Correction 13 5.2.3 Kinematic Viscosity: Pressure Correction 15 5.3 Heat of Combustion/Lower Heating Value 15 5.4 Buoyancy Adjustment . 16 SAE INTERNATIONAL ARP4990B Page 2 of 34 6. TURBI

9、NE FLOWMETER CALIBRATION AND CORRECTIONS . 16 6.1 Turbine Flowmeter: Calibrators . 16 6.2 Turbine Flowmeter: Calibration Curve . 16 6.3 Turbine Flowmeter: Temperature and Pressure Corrections 17 6.4 Turbine Flowmeter: General Recommendations . 18 7. RECOMMENDATIONS . 19 8. NOTES 19 APPENDIX A ASTM A

10、ND API STANDARDS SUMMARY 20 APPENDIX B SAMPLE FUEL FLOW CALCULATION 21 APPENDIX C UNITS CONVERSION FACTORS 34 Figure 1 K-factor calibration curve 9 Figure 2 Break-away point for a Strouhal-Roshko calibration curve . 9 Figure 3 Strouhal-Roshko relationship 17 SAE INTERNATIONAL ARP4990B Page 3 of 34 1

11、. SCOPE This SAE Aerospace Recommended Practice (ARP) provides to the aerospace industry a procedure for the consistent and accurate calculation of fuel flow using turbine flowmeters during development, production, and post overhaul/repair gas turbine engine testing. 1.1 Purpose One of the methods o

12、f measuring fuel-flow-rate in a test-environment is by means of a turbine flow-meter. This recommended practice outlines a process for the calculation of flow-rate when a turbine flow-meter is used for the measurement. 2. REFERENCES 2.1 Applicable Documents The following publications form a part of

13、this document to the extent specified herein. The latest issue of SAE publications shall apply. The applicable issue of other publications shall be the issue in effect on the date of the purchase order. In the event of conflict between the text of this document and references cited herein, the text

14、of this document takes precedence. Nothing in this document, however, supersedes applicable laws and regulations unless a specific exemption has been obtained. 2.1.1 SAE Publications Available from SAE International, 400 Commonwealth Drive, Warrendale, PA 15096-0001, Tel: 877-606-7323 (inside USA an

15、d Canada) or +1 724-776-4970 (outside USA), www.sae.org. ARP741 Turbofan and Turbojet Gas Turbine Engine Test Cell Correlation 2.1.2 API Publications Available from API, 1220 L Street, NW, Washington, DC 20005-4070, Tel: 202-682-8000, www.api.org. Manual of Petroleum Measurement Standards, Ch. 4: Pr

16、oving Systems Manual of Petroleum Measurement Standards, Ch. 11.2.1: Compressibility Factors for Hydrocarbons: 0-90 API Gravity Range Manual of Petroleum Measurement Standards, Ch. 12.2.5.1: Correction for the Effect of Temperature on Steel, Cts Manual of Petroleum Measurement Standards, Ch. 12.2.5.

17、2: Correction for the Effect of Pressure on Steel, Cps Technical Data Book - Petroleum Refining, API Procedure 11A5.7, Liquid Viscosity of High-Molecular-Weight Pure and Mixed Hydrocarbons at High Pressure 2.1.3 ASTM Publications Available from ASTM International, 100 Barr Harbor Drive, P.O. Box C70

18、0, West Conshohocken, PA 19428-2959, Tel: 610-832-9585, www.astm.org. ASTM D240 Standard Test Method for Heat of Combustion of Liquid Hydrocarbon Fuels by Bomb Calorimeter ASTM D287 Standard Test Method for API Gravity of Crude Petroleum and Petroleum Products (Hydrometer Method) ASTM D341 Standard

19、Viscosity-Temperature Charts for Liquid Petroleum Products SAE INTERNATIONAL ARP4990B Page 4 of 34 ASTM D445 Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (and the Calculation of Dynamic Viscosity) ASTM D1018 Standard Test Method for Hydrogen in Petroleum Fractions A

20、STM D1217 Standard Test Method for Density and Relative Density (Specific Gravity) of Liquids by Bingham Pycnometer ASTM D1250 Standard Guide for Petroleum Measurement Tables, Volume X: Background, Development, and Implementation Procedures ASTM D1298 Standard Practice for Density, Relative Density

21、(Specific Gravity), or API Gravity of Crude Petroleum and Liquid Petroleum Products by Hydrometer Method ASTM D2382 Standard Test Method for Heat of Combustion of Hydrocarbon Fuels by Bomb Calorimeter (High Precision Method) ASTM D3701 Standard Test Method for Hydrogen Content of Aviation Turbine Fu

22、els by Low Resolution Nuclear Magnetic Resonance Spectrometry ASTM D4052 Standard Test Method for Density and Relative Density of Liquids by Digital Density Meter ASTM D4809 Standard Test Method for Heat of Combustion of Liquid Hydrocarbon Fuels by Bomb Calorimeter (Intermediate Precision Method) 2.

23、1.4 Coordinating Research Council, Inc., Aviation Fuel Properties, CRC Report No. 530. 2.1.5 Craft, D. William, High Accuracy Fuel Flowmeter - Final Report - Phase IIC and Phase III, The Mass Flowrate Calibration of High Accuracy Fuel Flowmeters, NASA CR 187108, February, 1992. 2.1.6 Grabe, W., Fuel

24、 Flow Measurement in Gas Turbine Testing, National Research Council of Canada, TR-ENG-001, NRC No. 29808, 1988/08. 2.1.7 Hochreiter, H. M., Dimensionless Correlation of Coefficients of Turbine-Type Flowmeters, ASME Paper No. 57-A-63, Transactions of the ASME, October 1958. 2.1.8 IEEE Std. 268 - 1982

25、, IEEE Standard Metric Practice, Institute of Electrical and Electronics Engineers. 2.1.9 Mattingly, G. E., The Characterization of a Piston Displacement-Type Flowmeter Calibration Facility and the Calibration and Use of Pulsed Output Type Flowmeters, Journal of Research of the National Institute of

26、 Standards and Technology, Volume 97, Number 5, September-October 1992, pp. 509-531. 2.1.10 Olivier, Paul D., Determination of Turbine Flowmeter Usable Turndown, Proceedings of National Conference of Standards Laboratories Workshop and Symposium, July 1995. 2.1.11 Ruffner, Donald F, and Olivier, Pau

27、l D., Improved Turbine Meter Accuracy by Utilization of Dimensionless Data, Proceedings of National Conference of Standards Laboratories Workshop and Symposium, August 1994. 2.1.12 Schoonover, Randall M. and Jones, Frank E., Air Buoyancy Correction in High-Accuracy Weighing on Analytical Balances, J

28、ournal of Analytical Chemistry, Volume 53, Number 6, May 1981, pp. 900-902. 2.1.13 Shafer, M. R. and Ruegg, F. W., Liquid-Flowmeter Calibration Techniques, ASME Paper No. 57-A-70, Transactions of the ASME. SAE INTERNATIONAL ARP4990B Page 5 of 34 2.2 Nomenclature API American Petroleum Institute ASTM

29、 American Society for Testing and Materials Bo buoyancy adjustment to convert from “in-vacuo“ to “in-air“ (dimensionless) Cpfd pressure correction on fuel density (dimensionless) Cpfv pressure correction on fuel viscosity (dimensionless) Cpk pressure correction factor due to flowmeter expansion to o

30、btain Kop (dimensionless) Cpr pressure correction factor due to flowmeter expansion to obtain Roop (dimensionless) Ctk temperature correction factor due to flowmeter expansion to obtain Kop (dimensionless) Ctr temperature correction factor due to flowmeter expansion to obtain Roop (dimensionless) D

31、bore diameter of flowmeter (in or m), measured at Tcal E modulus of elasticity of the flowmeter meter material (psi or bar) f flowmeter frequency (Hz or cycles/s) F compressibility factor of the fuel (1/psia or 1/bar-a) HYC stem correction for glass hydrometer thermal expansion (dimensionless) K, K-

32、factor flowmeter coefficient (cycles/US-gal or cycles/L) Kop K-factor at operating conditions (cycles/US-gal or cycles/L) LHV measured lower heating value (Btu/lb or kJ/kg) LHVcf lower heating value correction factor (dimensionless) LHVref reference lower heating value (Btu/lb or kJ/kg) patm atmosph

33、eric pressure at operating conditions (psia or bar-a) patm, cal atmospheric pressure during flowmeter calibration (psia or bar-a) pcal absolute pressure of fuel at the flowmeter during calibration (psia or bar-a) peq equilibrium pressure of the fuel (psia or bar-a) pgage gage pressure of fuel at the

34、 flowmeter during operation (psig or bar-g) pop absolute pressure of fuel at the flowmeter during operation (psia or bar-a) Q fuel volume flow rate (US-gal/s or L/s) RD relative density formerly referred to as specific gravity (dimensionless) SAE INTERNATIONAL ARP4990B Page 6 of 34 RF radio frequenc

35、y Ro Roshko number (dimensionless) Roop Roshko number at operating conditions (dimensionless) St Strouhal number (dimensionless) Stop Strouhal number at operating conditions (dimensionless) t wall thickness of the flowmeter (in or m) Tcal calibration temperature of the flowmeter (F or C) Tref refere

36、nce temperature (60 F or 15 C) Top operating temperature of the fuel at the flowmeter (F or C) Top,abs absolute operating temperature of the fuel at the flowmeter (R or K) Ts temperature of the fuel sample (F or C) Ts,abs absolute temperature of the fuel sample (R or K) UVC universal viscosity curve

37、 VCF volume correction factor (dimensionless) Wf,t true fuel mass flow rate (lbm/h or kg/h) Wf,LHV LHV corrected fuel mass flow rate (lb/h or kg/h), i.e., true fuel mass flow rate referenced to a standard heat of combustion 2.3 Greek Symbols F,Trefcoefficient of thermal expansion of the fuel at refe

38、rence temperature (Tref) (1/F or 1/C) l coefficient of linear thermal expansion of the flowmeter (1/F or 1/C) (observed inlet total absolute pressure)/(absolute pressure of ISO sea level standard day reference atmosphere) (dimensionless) s dynamic viscosity of the fuel sample (centipoise) op kinemat

39、ic viscosity of the fuel sample corrected for operating temperature (Top) and pressure (pop) (cSt) s kinematic viscosity of the fuel sample (cSt) Top kinematic viscosity of the fuel sample corrected for operating temperature (Top) (cSt) (observed inlet total absolute temperature)/(absolute temperatu

40、re of ISO sea level standard day reference atmosphere) (dimensionless) a air density (kg/m3) op density of the fuel corrected for operating temperature (Top) and pressure (pop) (kg/m3) SAE INTERNATIONAL ARP4990B Page 7 of 34 s fuel sample density (kg/m3) s,hyc fuel sample density corrected for glass

41、 hydrometer thermal expansion (kg/m3) Top density of the fuel corrected for operating temperature (Top) (kg/m3) Top,gcc density of the fuel corrected for operating temperature (Top) (g/cm3) ref density of the fuel at reference temperature (Tref) (kg/m3) ref,gcc density of the fuel at reference tempe

42、rature (Tref) (g/cm3) w balance weight density (kg/m3) water,ref density of water at reference temperature in vacuo (Tref) (kg/m3) 3. BACKGROUND A variety of fuel flow determination methods have evolved throughout the aerospace industry. Most fuel property and flow measurement methods as well as tem

43、perature/pressure corrections have been based on established techniques published in the literature. Often, however, notable differences in measured fuel properties and calculated fuel flow have become apparent upon comparison of results between parties. A portion of these differences could be justi

44、fiably attributed to experimental uncertainty and the reproducibility of the measurement technique in different laboratories. Other disparities, due to differences in the measurement and/or correction techniques, have resulted in considerable time and effort being devoted to the justification and/or

45、 validation of each facilitys methodology. A procedure adopted by the entire industry would provide a common basis for the consistent and accurate calculation of fuel flow and help alleviate points of confusion or inconsistency. As such, the procedure defined herein is based on ASTM and API standard

46、 test methods as well as temperature and pressure correction methodologies and can be used to establish the physical quantities required in the determination of fuel flow such as relative density, viscosity, lower heating value and for calibrating turbine flowmeters. The data and processes outlined

47、in this document represent a recommended practice for the calculation of fuel flow from measurements using a turbine flow meter. Minor deviations to the calculation process and/or data used in the correction of fuel property state conditions may differ for a particular fuel or class of fuels or even

48、 a specific fuel meters operating condition. Allowances should be made under those conditions to support individual laboratory-data and experience. 4. INTRODUCTION 4.1 True Fuel Mass Flow Rate The basic building blocks for determining fuel flow with volumetric flowmeters are shown in Equation 1. A m

49、ass per unit volume quantity (density) is multiplied by a volume per unit time quantity (volume flow rate) to obtain true mass per unit time (true mass flow rate). timemasstimevolumevolumemass= (Eq. 1) or similarly, density * volume flow rate = true mass flow rate (Eq. 2) Fuel sample density is measured and/or reported at a reference temperature and pressure. If the fuel is subjected to conditions a