COMPUTATIONAL INVESTIGATION OF SIMULATION ON THE DYNAMIC DERIVATIVES OF FLIGHT VEHICLE

Transcription

1 OPUTATIONAL INESTIGATION OF SIULATION ON THE DYNAI DERIATIES OF FLIGHT EHILE i Baigang*, Zhan Hao*, Wang Ban* *School of Aeronautics, Northwestern Poltechnical Universit, Xi an, hina Kewords: dnamic ; omputational Fluid Dnamic; numerical validation; anard Rotor/Wing Aircraft Scaled model Abstract Dnamic s are ke parameters to flight vehicle design, which directl affect aircraft fling qualities and control rate, and it has become a hot topic to obtain dnamic s through various s. Here sstematic research is developed with omputational Fluid Dnamic (FD) to calculate each dnamic, and longitudinal dnamic is chose to represent this. Firstl, the combined dnamic s can be calculated b using two unstead s, which are small amplitude pitching oscillation and differential s. Then the lag of wash s can also be obtained b using the unstead of small amplitude plunging oscillation, and the damping s are simpl the difference between the combined and lag of wash s. Finall, the Finner missile is taken as an example to testif the s. The results obtained from the s demonstrate to be consistent with the experimental data and those from references. Further verification of this sstematic is applied in the anard Rotor/Wing Aircraft designed b our team; each longitudinal and lateral directional dnamic is simulated, and the results fit the flight tests data well. The sstematic simulating s are testified to be reliable and useful in engineering. 1 Introduction With the increasing demand for aircraft design, the research of the dnamic stabilit characteristics has attracted much more attention. Dnamic stabilit s [1, ], as ke parameters indicating flight dnamic stabilit, are generall a measurement of how man changes will occur to the forces or moments acting on the vehicle with a fluctuation of parameters in the flight condition, such as angle of attack, airspeed, altitude, etc. These s are the indispensable original aerodnamic parameters for the aircraft navigation sstem, control sstem and dnamic qualit analsis as well. urrentl, there are several was to acquire dnamic s, including theoretical estimations, wind tunnel tests, flight tests or omputational Fluid Dnamics (FD) s [3]. ombined with the basic parameters of aircraft, the theoretical estimation can efficientl calculate the dnamic s based on empirical or semi-empirical formulas, charts, etc. However, the application of this is limited for lack of accurac and invalid in transonic flow. Wind tunnel tests and flight tests can measure all the dnamic s accuratel, and can also capture the details of flow, but it is difficult to perform sstematic research with such huge cost and long design period. With the development of FD, especiall in unstead aerodnamics theor and computation, it is possible to acquire dnamic s with FD s, which have become a promising wa for aircraft design [4, 5, 6]. The s to obtain dnamic s mainl rel on identifing the unstead aerodnamic forces and moments calculated b FD code. Researchers have done much work and developed man s in terms of FD in recent ears, of which the unstead Euler [7], the dual-time 1

2 I BAIGANG, ZHAN HAO, WANG BAN DADAI [8] and the nonlinear reduced frequenc [9] are the most three famous ones. The modern aircraft design needs detailed dnamic s so that the aerodnamic configuration and control rate can be designed more effectivel, which has not been satisfied as most research can onl achieve the combined s. This paper focuses on sstematicall simulating the dnamic s using FD. Firstl, s to calculate combined and single dnamic s are built and testified b using Finner missile, and further verification of the calculating s of dnamic s are done in the anard Rotor/Wing Scale Aircraft model. ompared with results from the sstem parameter identification using the flight tests data, we can complete more analsis of the s ethods to calculate dnamic s Based on resonant perturbation theor, we propose a sstematic to calculate dnamic s through FD code. Now take longitudinal as an example to introduce this in detail..1 ombined dnamic s Two unstead s can be applied to calculate the combined s, namel the small amplitude oscillation and differential..1.1 Small amplitude oscillation This forces the model to oscillate around the centre of gravit. With Talor expansion, the unstead moment can be expressed as 0 (1) ˆ (, ) Where, are the zero and first order pitching moment dnamic s to the angle of attack(aoa),, are the zero and first order pitching moment dnamic s to pitching angular velocit, ˆ denotes the higher order s. When rigid flight vehicles oscillate with circular frequenc in sinusoidal form, the motion equations can be described as 0 sin( t) 0 cos( t) 0 sin( t) () 0 sin( t) 0 cos( t) ombined with formula (1) and omit the higher order values, the unstead pitching moment is simplified as 0 0 ( ) sint ( ) 0 cost (3) When, the initial effect can be ignored, and the unstead moment will be periodical changing, formula (1) can be further interpreted as t n sin (4) tn Using reduced frequenc k l /* to nondimensionalize this, we finall get the formula to calculate the combined s of pitching moment with small amplitude oscillation as 0 t n t n 0 m mq (5) kqsl k Differential The differential solves the combined s b enforcing the aircraft moving upwards at same velocit to the same AOA at different angular velocities. Expand the 1, moment equation and omit high-order terms, then the pitching moments are (6) (7) 0 According to the theor of small disturbance in flight mechanics and subtract the two equations, we get ( ) / ( ) (8) 1 1 The non-dimensional pitching angular velocit is l / * (9)

3 OPUTATIONAL INESTIGATION OF SIULATION ON THE DYNAI DERIATIES OF FLIGHT EHILE Then the differential to simulate pitching dnamic s is simplified as m 1 m m mq (10) 1 m m0 m zm cos k (19). Single dnamic s The first order dnamic pitching moment of AOA m is also named as the lag of wash. If this can be acquired b FD, then the combined s minuses will get the other dnamic m mq, which is the aim of this sstematic FD. We use small plunging oscillation to identif, the unstead pitching moment is (11) m 0 While the motion equation of flight vehicle is z( t) z sin( t) (1) m v z( t) z cos( t) (13) z z m v z t z t (14) ( ) msin( ) When the AOA is, the additional AOA due to the motion of flight vehicle is zm cos( t)cos (15) zm sin( t)cos (16) Now the pitching moment changes to zm cos( t)cos 0 (17) zm sin( t)cos When t n /, we get 0 (18) zm cos Similar to the small amplitude oscillation, we can finall nondimensionalize this formula to 3 Dnamic s calculation of Finner missile The Finner missile is one of the most famous dnamic simulation models. The geometr is showed in Fig.1. We will first use this model to calculate the longitudinal dnamic s to verif the FD. The ach number is 1.58 and the initial AOA is 0, Fig. is the surface grid generated b ANSYS IE FD. Fig.1. Geometr of Finner missile Fig.. Surface grid of Finner missile 3.1 ombined dnamic s Small amplitude oscillation Enforce the model to oscillate around the centre of gravit with motion law 0 m sin( t) 1 sin(17t) The reduced frequenc k is , the hsteresis loops of moment coefficient and the pressure contour of wall when transient angle of attack is degree are showed in Fig. 3. 3

4 I BAIGANG, ZHAN HAO, WANG BAN m transient pitch moment at AOA, Table shows the details of the process, and the differential is effective to simulate combined s. Table. Longitudinal combined dnamic Angular velocit oment coefficient 5 alculation Experiment Error /s 10 / s % alpha(deg) a. Hsteresis loops of pitching moment coefficient 3. Single dnamic s The combined is the summation of two single s marked as and, m mq and the single dnamic can be identified b small plunging oscillation. The motion equation is z( t) 0.sin(17 t) with reduced frequenc The unstead pitching moment coefficient and the pressure contour of wall when the transient vertical displacement equals 0.13m are showed in Fig. 4. m b. Pressure coefficient contour of wall Fig.3. Results of small amplitude oscillation Based on this we can finall obtain the combined dnamic in Table 1, the result indicates good consistenc with experiment data. Table 1. Longitudinal combined dnamic m t(s) a. Unstead pitching moment coefficient m t n mz0 alculation Experiment Error % 3.1. Differential The Finner missile model is forced to move to 5 in two different constant angular velocities 5 / s,10 / s. Then the combined dnamic can be obtained b the 4

5 OPUTATIONAL INESTIGATION OF SIULATION ON THE DYNAI DERIATIES OF FLIGHT EHILE b. Pressure coefficient contour of wall Fig.4. Results of small plunging oscillation The lag of wash computed is , and the pitching damping equals with the difference between mq m the combined and the lag of wash, which matches ref. [10] well. 4 Dnamic s calculation of anard Rotor/Wing Aircraft Scaled model Further verification of the calculating of dnamic s is performed on the anard Rotor/Wing Aircraft Scaled model designed b our team, which is shown in Fig. 5. The flight vehicle consists of prepositive canard, postpositive horizontal tail and central rotor/wing. anard Rotor/Wing Aircraft shares the fling character of both rotorcraft and fixed wing aircraft. During take-off and landing, it flies like a helicopter, and when fling in highspeed cruising, it works like a fixed-wing aircraft which has three lifting-surfaces. During the transformation from helicopter mode to fixed-wing mode, rotor/wing slows down graduall and then it will be locked. ompared to general flight vehicle, the RW aircraft is a STOL (short take-off and landing) and economical flight vehicle. Fig.5. anard Rotor/Wing Aircraft Scaled model As a vital approach in aerodnamic research and new-tech validation, flight tests with scaled model will pla a more significant role in the future, not onl for the reason it can get a lot of data with less costs, but also that the combination of flight tests with this reusable scaled model and FD calculation is also beneficial for minimizing risks and reducing design period. Based on the FD s developed before, the dnamic s of scaled model in fixed-wing mode are simulated both in longitudinal and lateral directional. The surface gird of simplified scaled model is shown in Fig. 6. Parameters are determined according to the flight tests at an ensemble of isolated points given in Table 3. The centre of gravit is chosen as the moment center and rotation points when simulating dnamic s. Fig.6. Surface grid of simplified scaled model 5

6 I BAIGANG, ZHAN HAO, WANG BAN Table 3. Parameters for FD calculation c Parameter h(altitude) (velocit of far field) (mean aerodnamic chord) b S (span of rotor/wing) (reference wing area) alue 500m 3m/s 0.13m 1.3m 0.17m 4.1 Dnamic s of longitudinal ombined dnamic s The small amplitude oscillation is used with enforcing the model to oscillate around the centre of gravit as 0 m sin( t) 1 sin( t) The reduced frequenc is k c / 0.05, while the differential requires model ascend to 1 of AOA at two different constant angular velocities 1 / s, / s. Table 4 shows the FD solutions of the combined s b these s. Table 4. ombined dnamic s ethod alculating value Flight test value oscillation differential Single dnamic s With the reduced frequenc 0.05, the motion equation when using small plunging oscillation to obtain is z( t) 0.1sin( t), then the longitudinal single dnamic can be calculated. The results are given in Table 5. Table 5. Longitudinal dnamic s m Dnamic alculating value Flight test value m mq Dnamic s of lateral directional 4..1 ombined dnamic s Similar to longitudinal, the combined dnamic s of lateral directional can be obtained b small amplitude oscillation and differential, the motion law is 1 sin( t) with reduced frequenc k b / 0.05 for oscillation. When using differential, the model is forced to roll or aw to 1 at constant angular velocities 1 /, / s from these two s are showed in Table 6. Table 6. Lateral directional combined dnamic s Dnamic sin l sin n lp np cos lr l cos nr n s s, and the combined dnamic Oscillation Differential Flight test value Single dnamic s In order to calculate the single dnamic s of lateral directional, we need to excite the model to move with sinusoidal oscillation to get the single dnamic s and, then the other dnamic l n s will be separated. The model moves as ( t) 0.1sin( t) with reduced frequenc k b / The result can be seen in Table 7 Table 7. Lateral directional single dnamic s Dnamic lp np lr nr alculating value Flight test value The longitudinal and lateral directional dnamic s calculation values of anard Rotor/Wing Aircraft Scaled model match well with the flight test results, which shows that the is effective

7 OPUTATIONAL INESTIGATION OF SIULATION ON THE DYNAI DERIATIES OF FLIGHT EHILE 5 onclusions Sstematic simulation with FD of dnamic s is one ke aspect of unstead aerodnamics, and fundamental s are developed in this paper for calculating the combined and single dnamic s. The Finner missile and anard Rotor/Wing Aircraft scale model have been applied to verif the. In conclusion, the small amplitude oscillation and differential s to obtain combined dnamic s as well as the small plunging oscillation to identif single dnamic s have been validated to be effective, which can also be used for dnamic identification of longitudinal and lateral directional. The combination of FD s and flight tests with scale model ma provide technical support for flight vehicle design with less costs and time. However, more research is still needed due to the large complicated work for calculations and tests, while it is also in pressing demand to improve the accurac of obtaining dnamic s. References [1] Park.A., Green L.L. Stead-state computation of constant rotational rate dnamic Stabilit s. 18th AIAA Applied aerodnamics onference, Denver, O, AIAA , pp , 000. [] Ka Jacob. Acquiring and modeling unstead aerodnamic characteristics. AIAA Atmospheric Flight echanics onference, Denver, O, AIAA , pp 1-13, 000. [3] Greenwell D.l. Frequenc effects on dnamic stabilit s obtained from small-amplitude oscillator testing. Journal of Aircraft, 1998, 35(5): [4] A.Da Ronch, D.allespin. omputation of dnamic s using FD. 8th AIAA Applied aerodnamics onference, hicago, Illinois, AIAA , pp 1-7, 010. [5] Green L L, Spence A, urph P, omputation s for dnamic stabilit and control s. AIAA Atmospheric Flight echanics onference, Reno, Nevada, AIAA , pp 1-1, 004. [6] Jouannet, Krus P. Lift oefficient predictions for delta wing under pitching motions. 3nd AIAA Fluid Dnamics onference and Exhibit, St. Louis, issouri. AIAA , pp 1-7, 00. [7] Erdal Okta, Hasan U. Aka. FD predictions of dnamic s for missiles. 40th AIAA Aerospace Sciences eeting & Exhibit, Reno, Nevada, AIAA , pp 1-11, 00. [8] Soo Hung Park, Yoonsik Kim, Jang Huk Kwon. Prediction of dnamic damping coefficients using unstead dual-time stepping. 40th AIAA Aerospace Sciences eeting & Exhibit, Reno, Nevada, AIAA , pp 1-9, 00 [9] Scott. urman_eloret orp. A reducedfrequenc approach for calculating dnamic s. 43rd AIAA Aerospace Sciences eeting, Reno, Nevada, AIAA , pp 1-17, 005 [10] Ye, a D L. Aircraft dnamic s calculation using FD techniques. Journal of Beijing Universit of Aeronautics and Astronautics. ol. 39, No., pp , 013. (in hinese) ontact Author Address mibaigang@mail.nwpu.edu.cn opright Statement The authors confirm that the, and/or their compan or organization, hold copright on all of the original material included in this paper. The authors also confirm that the have obtained permission, from the copright holder of an third part material included in this paper, to publish it as part of their paper. The authors confirm that the give permission, or have obtained permission from the copright holder of this paper, for the publication and distribution of this paper as part of the IAS 014 proceedings or as individual off-prints from the proceedings. 7