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Analytical Evaluation of Nonsimple One-Dimensional Steady Compressible Flow in Ducts and Nozzles
In preparation for publication
Erich A. Wilson, Dan Adler, Pinhas Bar-Yoseph
Faculty of Mechanical Engineering
Technion - Israel Institute of Technology, Haifa, Israel 32000
Solution of the one-dimensional steady compressible flows is common in closed analytical form for the simple flows: Area change, mass injection, heat transfer and friction. With the combination of any of these simple flows, the differential equations become difficult to solve analytically due to the combination of the variables in the influence coefficients and the variational values. The seperation of variables for any combination of flows has not yet been achieved. Such nonsimple flows, until now, have been solvable only through numerical techniques. In this work, a method for seperating the variables in the nonsimple flow of combined friction and area change is presented. This has allowed for the development of a polytropic equation system, presented here, useful in determining performance coefficient equations in ducts and nozzles as a function of roughness, specific heats ratio, Mach and geometric properties. This polytropic equation system includes an additional degree of freedom trough the inclusion of the geometric divergence angle for the specific application to converging-diverging nozzles and ducts. A new term for the flow-geometrics-roughness interaction is introduced and analyzed. This polytropic equation system reduces to the Isentropic and Fanno flow equations with zero friction or divergence angle, respectively, and forms the basis of analytical performance evaluations of all nozzle types.
Submitted for publication to the AIAA Journal of Propulsion and Power
Aug 1999
Erich A. Wilson, Dan Adler, Pinhas Bar-Yoseph
Faculty of Mechanical Engineering
Technion - Israel Institute of Technology, Haifa, Israel 32000
Geometrically variable converging-diverging thrust-vectoring nozzles, such as the two-dimensional pitch-only type on the F-22 and the axisymmetric yaw-pitch type tested in the F-15 ACTIV program, directly affect the jet flow geometry and rotation angle at the nozzle exit, thus altering the nozzle aerodynamic performance as a function of geometry, pressure ratio and flight velocity. When the nozzle is rotated at the throat, the effective nozzle expansion length and divergent volume are reduced from the actual geometric nozzle expansion length and divergent volume as a function of the nozzle area control ratio defining new nozzle performance characteristics at each vectoring position. The consideration of nozzle divergence and dynamic nozzle geometry dictating the effective-geometric nozzle relation during thrust-vectoring is investigated here. In this study an explicit algorithm is presented as a function of nozzle geometry only, at constant nozzle pressure ratio, zero velocity and altitude. Comparison of the theoretical prediction of the algorithm with experimental data of four axisymmetric thrust-vectoring nozzle configurations verifies that in the quasi-ideal expansion length nozzle, the algorithm predicts the effective vectoring angle and flow coefficient within experimental accuracy for the NPR peak performance level. This algorithm is applicable in dynamic thrust-vectoring nozzle design performance predictions or analysis of fixed- or variable -area convergent or convergent-divergent nozzles as well as in the definition of initial jet flow conditions in numerical VSTOL/'TV jet performance studies.
Fourth International Symposium on Experimental and
Computational Aerothermodynamics of Internal Flows, Aug 31 to Sept 2, 1999, Dresden, Germany
Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel
Erich Wilson, Dan Adler, Pinhas Bar-Yoseph
Yaw-pitch-roll engine thrust-vectoring (TV) is a growing military and civil aircraft technology that provides alternative flight control to conventional aerodynamic flight control (CAFC). It is performed through deflecting engine jet(s) away from the engine axis in the pitch, yaw and roll directions. TV is obtained through implementing different engine nozzle design families in various modes of jet deflections under flight conditions such as TV-assisted post-stall maneuvers, conventional, short and vertical take-off and landing, cruise, and emergency situations. The engine thus becomes the primary controller of aircraft flight. Hence, the understanding of TV dynamic nozzle performances and their influences on aircraft performance throughout the flight envelope by way of attainable moments and forces is a key design criterion to TV/aircraft developmental technology.
AIAA Journal of Propulsion and Power, Vol. 16, No. 1, January-February 1999.
Joint Mechanical/Aero Laboratories Bldg.
Technion - Israel Institute of Technology, Haifa, Israel, 32000
Erich A. Wilson, Dan Adler, Benjamin Z. Gal-Or, Valery Sherbaum and Michael Lichtsinder
Engine thrust-vectoring (TV) is a potential technology for military and future civil aircraft in which the Technion - Israel Institute of Technology has made significant contributions. This paper provides realistic predictions of steady-state engine performance during steady-state pitch vectoring. The results obtained comprise a required fundamental step for advancing aircraft/TV implementation. This work is a part of the Lockhedd Martin yaw-pitch TV F-16/F-100 research study conducted here at the Jet Laboratory. To this end, a unique TV-engine computer algorithm has been developed that expands the conventional steady-state modeling capabilities of on-and off-design as well as the conventional transients (via throttle changes) to create steady-state and dynamic TV-engine simulations at various altitudes and Mach numbers. This paper reviews the steady-state performances and the optimization observations initially obtained. The subcritical flow realm of the nozzle performance provides trends aiding in the prediction of thrust benefits beyond the conventional nozzle design of the F-100 model are available as the efective nozzle throat area is allowe to contract through vectoring.
Internation Journal of Turbo and Jet Engines, Vol. 16, No. 1, 1999.
Joint Mechanical/Aero Laboratories Bldg.
Technion - Israel Institute of Technology, Haifa, Israel, 32000
Erich A. Wilson, Dan Adler, Benjamin Z. Gal-Or, Valery Sherbaum and Michael Lichtsinder
Engine thrust vectoring (TV) is an emerging new technology for future military and civil aircraft in which the Technion has made significant contributions. Rapidly deflecting engine jets to maneuver the aircraft with or without conventional aerodynamic flight control (CAFC) significantly enhances the flight safety, agility, and combat kill-ratio capabilities of fighter aircraft in the near term and enhances the safety of civil transport jets in the long term. There are yet no realistic predictions of engine dynamic responses to yaw-pitch-roll TV commands in the public domain. Hence, the primary aim of this work is to provide such a first. The results obtained comprise, therefore, a required fundamental step for advanced aircraft/TV implementation. The selection of this work focuses on the Lockheed-Martin TV F-16/F-100 research study conducted at the Technion. A unique TV-engine computer algorithm has been developed that expands the conventional steady-state modeling capabilities of on- and off-design as well as the conventional transients (via throttle changes) to create realistic dynamic TV-engine simulations at various altitudes and Mach numbers. This work has been expanded to include predictions for TV in civil aircraft (via a fixed geometry nozzle) under the same conditions. It is concluded that the military TV configuration, as expected, produces no variations in engine performance while providing TV flight control benefits. It is also demonstrated that under the same dynamic conditions, the civil configuration provides an increase in thrust, enhancing the benefits available from TV in the civil domain.
27th Israel International Conference on Mechanical Engineering,
May 19-20, 1998, Haifa, Israel
Faculty of Mechanical Engineering
Technion - Israel Institute of Technology, Haifa 32000, Israel
E. A. Wilson, D. Adler and P.Z. Bar-Yoseph
Throat-hinged geometrically variable converging-diverging thrust-vectoring nozzles directly affect the jet flow geometry and rotation angle at the nozzle exit as a function of the nozzle geometry, the nozzle pressure ratio and flight velocity. The consideration of nozzle divergence in the effective-geometric nozzle relation is theoretically considered here for the first time. In this study, an explicit calculation procedure is presented as a function of nozzle geometry at constant nozzle pressure ratio, zero velocity and altitude, and compared with experimental results in a civil thrust-vectoring scenario. This procedure may be used in dynamic thrust-vectoring nozzle design performance predictions or analysis for civil and military nozzles as well as in the definition of initial jet flow conditions in future numerical VSTOL/'TV jet performance studies.
M.Sc. Thesis, July 1997, Technion - IIT
Faculty of Mechanical Engineering
Technion - Israel Institute of Technology, Haifa 32000, Israel
E. A. Wilson
Engine thrust-vectoring (TV) is an emerging new technology for aircraft post-stall flight control design in which the Technion has made significant contributions. Rapidly deflecting engine jets to maneuver the aircraft with or without conventional aerodynamic flight control (CAFC) significantly enhances flight safety, agility, and kill-ratio capabilities of fighter aircraft in the near term and civil transport jets in the long term. The emerging new technology has been well demonstrated in the military domain since 1993 by the YF-22, US-German X-31 and Sukhoy-37. The first production TV aircraft, military as well as civil, may be developed in the future to provide low drag and low weigth for increasing aircraft range and reducing operational costs.
Predictions of engine dynamic responses to TV commands is a required fundamental step for implementation of TV in future military and civil aircraft. In this work, a two-spool turbofan jet engine with various afterburning capabilities is modeled algorithmically for that purpose and for the first time. A new computer program has thus been developed to provide a multi-dimensional, dynamic model of a real TV-engine. The dynamic responses studied include internal-related transients during rapid throttle changes and variations in altitude, Mach number, angles of attack and slip.
Engine TV capability is added through an algorithmic model of a converging-diverging nozzle. Major TV-engine-related parameters have been fundamentally defined and studied. TV benefits in engine/arcraft performance are investigated for military and civil aircraft under
(ii) Steady-state of-design point conditions
(iii) Transient conditions without TV
(iv) Transient conditions with TV.
The work demonstrates the benefits of TV for a new generation of military and civil aircraft.