Steering mechanism and efforts on the NERVA space launcher.

Bogoi, Alina Tudor ; Tache, Florin ; Rugescu, Dragos Radu Dan 等

1. INTRODUCTION

Numerical simulations of the airflow around the NERVA control ailerons were performed and produced the values of the control lift force that appears at various tilt angles on the surface of the ailerons during the ascent flight into the atmosphere (Tache et al., 2009). It is emphasized during the development of the Romanian NERVA space launcher (Rugescu, 2008) that an additional control means is required when the vehicle exits Earth atmosphere. The same main pneumatic drivers that currently act the aerodynamic rudders of the rocket actuate the gas dynamic control used in this part of the flight. The design of the double flight control system, aerodynamic and gas dynamical, involves estimating the actual loads that have to be controlled by the pneumatic drivers. An aerodynamic couple has been determined, which appears around the steering axis of the aileron. Results of the computations by the research team of University "Politehnica" of Bucharest, by means of CFD simulations, are presented.

2. COMPUTATIONAL BACKGROUND

The size and geometrical aspect of the individual control aileron are shown in Figure 1. This "winglet" is built on a rhomboidal profile, which includes at the basis (next to the fuselage) a rectangular core. All the facets of the aileron are planar and entirely symmetrical in respect to the profile chord. The aerodynamic torque is given by the asymmetrical shape of a profile and by the lift force moment in respect to the axis of resolution (pole). Consequently, a symmetrical profile gives no aerodynamic torque and in this case, at supersonic speed and on zero angle of attack, the coefficient of the aerodynamic moment [C.sub.m0] is nil (Carafoli, 1969; Seebass & Woodhull 1998).

[FIGURE 1 OMITTED]

According to the linear theory of Ackeret, at small a angles of attack, the lift and moment coefficients are given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [M.sub.[infinity]] is the flight velocity, [S.sub.1], [S.sub.2] are the upper and lower winglet surfaces and c is the chord (Carafoli 1969).

Ascent parameters of the space rocket have been computed and the aerodynamic simulations were set for a convenient flight altitude and local velocity. The coefficients for lift and moment become

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

The pole is set at the leading edge of the airfoil and the positive sign of moments means decreasing the angle of attack. It results that the focus of the symmetrical, supersonic wing is at its middle point, the lift location. The values given by the simplified theory are compared below with the viscous flow computations. The 3D aileron is a little bit swept backward and the middle points of the profiles at various sections are not aligned along a unique normal axis in respect to the fuselage. In other words, the line of focuses along the profiles is not normal to the fuselage. The image of the aileron is given in Figure 2. The tilting axis is visible in detail in Figures 1-2 and the computational problem is for the driving torque required to reliably tilt the aileron during the low atmospheric flight.

[FIGURE 2 OMITTED]

The numerical simulation refers to an altitude of 11km, with a travelling speed of Mach 2, while the surrounding pressure and temperature are 22632Pa and 216.65 K, respectively.

3. RESULTS OF CFD SIMULATIONS

The following values for the aerodynamic coefficients of lift and moment in respect to the axis of tilt drawn in Figure 1 were found, as reproduced in diagrams 3 and 4.

The values of the reduced coefficients are given versus the angle of incidence. Values up to the maximal allowable tilt of 28 degrees were computed. They agree well with the theoretical formulae (2). The four separate sections are fairly converging.

For CFD simulations, four different equally spaced sections have been used, along with a 3D model of the complete aileron, thus being able to study the 2D air flow at different locations on the wing's span and also providing an overall image of the three-dimensional flow pattern.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

While keeping the flow parameters to the values presented above, the angle of incidence has been varied from 0 to 20 degrees by 5-degree increment step with the additional value of the maximal pitch of 28 degrees for a complete covering. A total of 24 two-dimensional cases and 6 three-dimensional cases were simulated with the commercially available software Fluent (FLUENT INC., 2009). The k-omega turbulence model was adopted as more appropriate for the simulation.

The use of a k-omega formulation in the inner parts of the boundary layer makes the model directly usable all the way down to the wall through the viscous sub-layer. The model switches to a k-epsilon behavior in the free-stream and thereby avoids the common k-epsilon problem that the model is too sensitive to the inlet free-stream turbulence properties. Authors who use the k-omega model often praise it for its good behavior in adverse pressure gradients and separating flow. Nevertheless, the k-omega model produces a bit too large turbulence levels in regions with large normal strain, like stagnation regions and areas with strong acceleration. This disadvantage is less pronounced however than that involved when a normal k-epsilon model is used (CFD-Wiki, 2009).

4. CONCLUSION

A very small coefficient of aerodynamic torque is encountered through CFD simulations, in agreement with the theoretical values of the moment in respect to the middle axis of the symmetrical profile. In fact, with drag by viscous effects and due to the sweptback geometry for the aileron, a small, positive aerodynamic moment appears. The location of the focus for the entire, 3D aileron is not yet specified, although all the geometrical and mechanical results suffice to determine its position in space. Its locus is important for positioning of the steering axis, which must be set as close as possible to the focus of the 3D profile to minimize the steering couple for the driving mechanism. The driving mechanism will impart some of the power for driving the gas dynamical thrusters, which fortunately require a very low driving moment.

The differences between the coefficients of the individual profiles at the computational sections referred to in Figure 1 are due to the differences in the computational conditions. While for the 2D profiles the flow is ideally planar, for the 3D model the side flow and marginal losses are allowed, fact that diminishes lift. Same applies for the moment coefficient.

5. REFERENCES

Carafoli, E. (1969), Wing Theory in Supersonic Flow, Pergamon Press, Oxford

CFD-Wiki, the free CFD reference (2009), SST k-omega model, http://www.cfd-online.com/Wiki/SST_k-omega_model, accessed 2009-05-20

FLUENT INC. (2009), Fluent Help, accessed 2009-05-17

Haroldsen, D. J. & Sturek, W. B. (2000), Navier-Stokes Computations of Finned Missiles at Supersonic Speeds, 22nd Army Science Conference, Renaissance Harborplace Hotel, Baltimore, MD, 11-13 December 2000

Rugescu, R. D. (2008), NERVA Vehicles, Romania's Access to Space, Sci. Bull. U. P. B., S. D Mechanics, 70 (3) p. 31-44

Tache, F., Rugescu, R. D., Bogoi A. (2009), Airflow study on the NERVA space launcher aileron, Annals of DAAAM for 2009 & Proceedings of the 20th International DAAAM Symposium, Vol. 20, No. 1, Ed. B. Katalinic, Published by DAAAM Int., Vienna, Austria, EU, ISBN 978-3-901509-70-4, ISSN 1726-9679, 25-28th Nov., pp. 0527-0528

Seebass, R & Woodhull, J. R. (1998), Supersonic Aerodynamics: Lift and Drag, paper presented at the RTO AVT Course on "Fluid Dynamics Research on Supersonic Aircraft", held in Rhode-Saint-Gendse, Belgium, 25-29 May 1998, and published in RTO EN-4