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5、Thrust Correction RATIONALE For accurate, indoor ground-level testing of jet engines, the influence of the test cell on the thrust produced by the engine must be established. The “true“ gross thrust may be derived from the measured scale force, if the aerodynamic conditions inside the test cell are
6、known. The “test cell effect“ may also be quantified using correlation factors determined from comparison of test data taken from indoor facilities, and reference outdoor, or “free-air“ test stands. In this report, the influence of the test cell on engine performance is described. The forces measure
7、d in a particular indoor test cell are derived. The results show that if all the aerodynamic forces have been accounted for, the corrected thrust in an indoor cell is the “true“ gross thrust. TABLE OF CONTENTS 1. SCOPE 3 2. REFERENCES 3 2.1 Applicable Documents 3 2.1.1 SAE Publications . 3 2.1.2 Oth
8、er Publications . 3 2.2 List of Symbols 4 2.2.1 General . 4 2.2.2 Subscripts . 5 3. INTRODUCTION. 6 4. CELL DESIGN CONSIDERATIONS . 7 4.1 Air Intake . 7 4.2 Test Section 8 4.3 Exhaust Outlet . 8 4.4 Future Trends 10 5. ANALYTICAL THRUST CALCULATIONS 10 5.1 Literature Survey . 10 5.2 Rationalization
9、of Gross Thrust. 11 5.2.1 Scale Force . 13 5.2.2 Intrinsic Inlet Momentum . 13 5.2.3 Bypass Pressure Drag 13 5.2.4 Thrust Frame Drag 14 5.2.5 Skin Friction Drag 14 5.2.6 Boattail Drag . 15 5.2.7 Wall Friction Drag 15 5.3 Secondary Flow and Wall Interference Effects . 15 SAE AIR5436 Page 2 of 33 6. T
10、HRUST CORRECTIONS 17 6.1 Correction Factor Calculations . 17 6.2 Test Cell Corrections 17 7. CONCLUSIONS 18 7.1 Influence of Test Cell Design 18 7.2 Thrust Measurement . 18 7.3 Use of Cell Correlation Factors . 18 7.4 Summary . 18 8. BIBLIOGRAPHY . 18 9. NOTES 20 APPENDIX A DERIVATION OF THE MOMENTU
11、M EQUATION . 30 APPENDIX B DERIVATION OF THE TEST CELL ENERGY BALANCE . 32 FIGURE 1 TYPICAL TEST CELL LAYOUT . 20 FIGURE 2 ENGINE AND TEST CELL CONTROL VOLUME 21 FIGURE 3 INSTRINSIC INLET MOMENTUM 22 FIGURE 4 BOATTAIL DRAG . 23 FIGURE 5 BYPASS PRESSURE DRAG . 24 FIGURE 6 THRUST FRAME DRAG 25 FIGURE
12、7 WALL FRICTION DRAG . 26 FIGURE 8 SKIN FRICTION DRAG 27 FIGURE 9 TOTAL THRUST CORRECTION 28 FIGURE 10 THRUST CORRECTION COMPARISON 29 SAE AIR5436 Page 3 of 33 1. SCOPE This document describes a method to correct engine thrust, measured in an indoor test cell, for the aerodynamic effects caused by t
13、he secondary airflow induced in the test cell by the engine operating in an enclosed environment in close proximity to an exhaust duct. While it is not recommended to be used to replace test cell correlation, it does provide a means to verify an existing thrust correlation factor. 2. REFERENCES 2.1
14、Applicable Documents The following publications form a part of 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 t
15、he text of this document and references cited herein, the text 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 Dri
16、ve, Warrendale, PA 15096-0001, Tel: 877-606-7323 (inside USA and Canada) or 724-776-4970 (outside USA), www.sae.org. ARP741B Turbofan and Turbojet Gas Turbine Engine Test Cell Correlation ARP755B Aircraft Propulsion System Performance Station Designation and Nomenclature 2.1.2 Other Publications ASH
17、WOOD, P. 1984. Operation and Performance Measurement on Engines in Sea-Level Test Facilities. AGARD-LS-132. National Atlantic Treaty Organization, Neuilly sur Seine, France. COVERT, E.E. 1985. Thrust and Drag: Its Prediction and Verification. AIAA Series Vol. 98. American Institute of Aeronautics an
18、d Astronautics, New York, NY. DUNCOMBE, E., and SMITH, E. 1951. Note on the Effect of Various Intake Ducts on the Indicated Thrust of Turbo-Jet Engines. Division of Mechanical Engineering, National Research Council Canada, Ottawa, Ont. Laboratory Note ET-1-51. FREULER, R.J, and DICKMAN, R.A. 1982. C
19、urrent Techniques for Jet Engine Test Cell Modeling. AIAA/SAE/ASME 18th Joint Propulsion Conference, June 21-23, Cleveland, OH. AIAA-82-1272. General Electric. 1979. F404-GE-400 Engine Qualification Test Phase - Performance Verification. General Electric Co., Cincinnati, OH. R79AEG096. HASTINGS, R.R
20、., 1983. A Simulation of a Jet Engine Test Cell. Division of Mechanical Engineering, National Research Council Canada, Ottawa, Ont. LTR-ENG-110. HAYES, J.D. 1975. An Investigation of the Flow in Turbojet Test Cell Augmentors. Masters Thesis, Naval Postgraduate School. Monterey, CA. HOERNER, S.F. 196
21、5. Fluid-Dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance. S.F. Hoerner, Midland, NJ. KARAMANLIS, A.I., HOELMER, W., BELLOMY, D.C., FREULER, R.J., and LEE, J.D. 1985. A Universal Turboshaft Engine Test Cell - Design Considerations and Model Test Results. AIAA 23rd
22、Aerospace Sciences Meeting, January 14-17, Reno, NV. AIAA-85-0382. SAE AIR5436 Page 4 of 33 KARAMANLIS, A.I., SOKHEY, J.S., DUNN, T.C., and BELLOMY, D.C. 1986. Theoretical and Experimental Investigation of Test Cell Aerodynamics for Turbofan Applications. AIAA/ASME/SAE/ASEE 22nd Joint Propulsion Con
23、ference, June 16-18, Huntsville, AL. AIAA-86-1732. KROMER, S.L., and DIETRICH, D.A. 1985. Flowfield Analysis of Low Bypass Ratio Test Cells. Journal of Aircraft, 22 (2): 99-100. LEE, J.D., and FREULER, R.J. 1985. Engine Simulator Techniques for Scaled Test Cell Studies. AIAA/SAE/ASME/ASEE 21st Joint
24、 Propulsion conference, July 8-11, Monterey, CA. AIAA-85-1282. OATES, G.C. 1984. The Aerothermodynamics of Aircraft Gas Turbine Engine and Rocket Propulsion. American Institute of Aeronautics and Astronautics, New York, NY. Pratt however, there is enough information available to describe the compone
25、nts of thrust in an enclosed ground level test cell. A summary of this information from these articles follows. 5.1 Literature Survey From the existing literature, four representative samples of information regarding the definitions of thrust components and correction factors for external drag force
26、s have been reviewed. Ashwood (1984) gives the definitions of gross thrust and its components. The standard gross thrust is the sum of the intrinsic thrust and the intrinsic momentum drag. The standard gross thrust is the stream force at the exit plane of the nozzle and is mathematically defined as
27、Fg= WeVe+ Ae(Pe- P) (Eq. 1) where: We= nozzle exit airflow Ve= nozzle exit velocity Ae= nozzle exit area Pe= nozzle exit static pressure P= ambient free stream static pressure The intrinsic momentum drag is calculated by Fimd= W0V0+ A0(P0- P) (Eq. 2) SAE AIR5436 Page 11 of 33 where: W0= inlet airflo
28、w V0= inlet velocity A0= inlet area P0= inlet static pressure P= ambient static pressure Duncombe and Smith (1951) take the definition of gross thrust and expand it to compare the effects of various intake ducts on the measured thrust of a jet engine. From their analysis it is apparent that the conf
29、iguration of the intake, i.e., whether it attached to the engine thrust measuring device or not, makes a significant difference in the magnitude of the measured thrust. General Electric (1979) describes the component forces of a “cell factor.“ These flow-induced forces are broken down into three com
30、ponents: a. an external friction force acting on the bellmouth, engine, and thrust frame; b. an exhaust nozzle boattail drag; and c. a momentum drag force. The friction force is described as a function of cell bypass ratio, while the two drag forces are related to a pressure differential between the
31、 engine inlet and exhaust planes. To estimate the airflow through the test cell, a total energy balance formula is used. This formula relies on an accurate measurement of the average exhaust stack temperature, which is often difficult to obtain. To overcome this, the test cell flow must be measured
32、by a flow survey and calibrated against the test cell static pressure depression. A slightly different approach to thrust accounting is outlined by Ashwood (1984). This paper describes the experimental investigation of thrust measurement errors at the Royal Aeronautical Establishment (Pyestock). The
33、se errors were attributed to the secondary flow generating forces that act on the thrust frame. The main effects were divided into d. a force on the inlet bellmouth caused by the air entering it; e. a force on the nozzle caused by the reduced external static pressure resulting from the increased vel
34、ocity of the secondary air entering the exhaust collector; and f. a drag force on the frame supporting the engine, resulting from the secondary flow over it. The general conclusion from the literature survey is that there appears to be some commonalty on the subject of making corrections to the meas
35、ured thrust to offset external aerodynamic drag. There is, however, no complete derivation of the forces generated by an engine in an indoor cell with clearly defined planes of accounting. Since the work of Duncombe and Smith (1951) has been confirmed by more recent results by General Electric (1979
36、), Covert (1985), and Oates (1984), it is considered that their combined efforts should form the basis of the rationalization of the gross thrust measured in a test cell. 5.2 Rationalization of Gross Thrust Consider the engine and test cell control volume as shown in Figure 2. In this installation,
37、the bellmouth is mechanically coupled to the engine stand. The locations of the planes of accounting are somewhat arbitrary, except for the exhaust exit plane. The requirements for planes 0 and b are uniform static pressure and velocity. Definition of planes 0 and b might prove difficult in test cel
38、ls that have distorted flow fields, which may occur with a vertical inlet. SAE AIR5436 Page 12 of 33 The sum of the forces acting on the control volume, under steady- state conditions, is equal to the change in axial momentum across the control volume. A comprehensive algebraic derivation of the mom
39、entum equation is given in Appendix A. A summary of the pertinent equations is as follows. Fm+ A0P0- AbPb- ApbtPbt- AePe+ Ftf+ Ff- Ffw= WeVe+ WbVb- W0V0(Eq. 3) where: Ftf= drag force on the thrust frame Ff= friction drag on the engine Ffw= friction drag on the walls Given that the bypass ratio is de
40、fined as =WbW0Wbfffffffffffffffffthen Wb=+1fffffffffW0(Eq. 4) and Vb=+1fffffffffA0AbfffffV0(Eq. 5) where: Ab= A0- Abt- Ae(Eq. 6) Substituting Equations 4, 5, and 6 into Equation 3, and solving for Fmgives Fm= WeVe+1fffffffffde2A0Abfffff1HJIKW0V0+ A0PbP0bc+ ApbtPbtPbbc+ AePePbbcFtfFf+ Ffw(Eq. 7) From
41、 Equation 3, the force measured in the test cell is equivalent to the intrinsic thrust, from Equations 1 and 2, plus some additional terms which result from the flow of secondary air over the external carcass of the engine. Since the gross thrust, from Equation 1 is defined as Fg= WeVe+ Ae(Pe - P0)
42、or Fg= WeVe+ Ae(Pe- Pb) + Ae(Pb- P0) (Eq. 8) SAE AIR5436 Page 13 of 33 then, Fg= Fm+ 1+1fffffffffde2A0AbfffffHJIKW0V0+ AbP0Pbbc+ ApbtP0Pbtbc+ Ftf+ FfFfw(Eq. 9) These seven terms are referred to as scale force, intrinsic inlet momentum, bypass pressure drag, boattail drag, thrust frame drag, skin fri
43、ction drag, and wall friction drag. Each of these terms is described separately in the following sections. 5.2.1 Scale Force Having defined the thrust of an engine, the next step in measuring it is to determine what thrust is being measured in the test cell. In most indoor ground level test cells, t
44、he engine is mounted on a thrust frame which is secured to the ground by flexures in a pendulum arrangement. The thrust frame pushes against a load-measuring device such as a strain gauge load cell. The force that is measured by this device is known as the scale force. 5.2.2 Intrinsic Inlet Momentum
45、 The most significant aerodynamic component of the thrust measurement is the intrinsic inlet momentum, which produces a force on the engine as a result of drawing air into the test cell (Oates 1984). For static engine testing, the magnitude of this force may be substantial. Since this force is, in e
46、ffect, a drag term, it must be added to the measured thrust of the engine. The intrinsic inlet momentum is calculated as Fim= 1+1fffffffffde2A0AbfffffHJIKW0V0where: A0= test cell area Ab= bypass area W0= test cell mass flow V0= test section or engine approach velocity From this equation, it is obvio
47、us that the intrinsic inlet momentum is a function of the engine airflow and the bypass secondary flow, and is therefore strongly affected by both the size of the engine and the aero- dynamic qualities of the test cell. Therefore, this thrust component must be accounted for in all indoor testing. 5.
48、2.3 Bypass Pressure Drag The bypass pressure drag is that force generated by a pressure deficit immediately behind the bellmouth and caused by the sudden expansion of the secondary flow as it spills past the engine intake. Sometimes referred to as bellmouth form drag, this force is a strong function
49、 of the cell bypass ratio. For test cells with low secondary flow, the magnitude of the bypass pressure drag may be small enough to be neglected. For higher bypass ratios, this force can become significant and may be approximated by Fb= (P0- Pb) AbSAE AIR5436 Page 14 of 33 where: P0= static pressure at plane 0 Pb= static pressure at plane b Ab= bypass area Since bypass pressure drag is a function of the bypas
