25th INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES MODELLING OF DYNAMIC STABILITY DERIVATIVES USING CFD Sean Tuling CSIR Keywords: Navier-Stokes, CFD, Dynamic Derivatives Abstract List of Symbols c Damping force, Nm:(deg=s)¡1 An exploratory investigation into the use of a CA Store axial force coefficient commercial Navier-Stokes time accurate code, Cm Moment coefficient about the store Fluent, for simulating and predicting the com- y body axis bined pitch damping derivatives, Cmq +Cmα˙ , was Cmq Moment coefficient about the store conducted. body pitch axis due to pitch veloc- The stable store, a low l/d finned missile like ∂Cm ¡1 ity, ∂ ql , rad configuration, was used for the investigation. The 2V C Moment coefficient about the store derivatives were extracted from the response of mα˙ the store, which was simulated by providing a ini- body pitch axis due to time rate ∂Cm change of angle of attack, ∂ α˙ l , tial disturbance and allowing the store to oscillate 2V freely at the system natural frequency. The same rad¡1 setup, as used for the numerical simulations, was CN Store normal force coefficient used for the experimental simulations. F Force Static steady state runs were initially per- I Mass moment of inertia, kg:m2 formed, and compared favourably to experimen- Ksupport Support or flexure stiffness/spirng tal results providing confidence in the mesh and constant, Nm:deg¡1 solver parameters. l Reference length, m The results of the numerical simulations did M Mach number not compare favourably with the experimental re- q Angular time rate of change about sults. The numerical investigations (both inviscid the store y body axis, rad:s¡1 and viscous) overpredicted the derivatives com- ωl rf Reduced frequency, 2V pared to the experimental results by a factor of S Reference Area, m2 three. The time taken for the simulations was V Free-stream velocity, m:s¡1 considered reasonable. α Angle of attack, degrees The two main factors that need to be inves- ρ Freestream air density, kg:m¡3 tigated, which may be causing the poor correla- θ Angle about the store body pitch tion, are the time step size and the experimental axis apparatus sting effects. Nomenclature CFD Computational Fluid Dynamics LSWT Low Speed Wind Tunnel MSWT Medium Speed Wind Tunnel 1 SEAN TULING 1 Introduction ing methodology to predict the pitch damping derivatives for a ballistic shell in the supersonic In the process of designing and engineering a flight regime. This method reduces the unsteady, flight vehicle to meet stated specifications and moving geometry problem to a static steady state objectives, the prediction of aerodynamics loads case, though the frame of reference needs to be is required for structural stressing, and the predic- transformed. tion of performance and stability and handling. Murman [5] has used the reduced frequency Of the many sub-disciplines in aeronautical engi- technique to predict the dynamic stability deriva- neering, flight load load prediction is one of the tives for the standard dynamics model for the most difficult, yet one of the primary inputs to sub- and transonic Mach numbers, the basic achieving efficient and safe flight. finner missile in the supersonic regime, and mod- Non-experimental prediction methodologies ified finner missile configuration for transonic have matured over the last 100 years of power and supersonic flight regimes. The reduced fre- manned flight, to the extent where time in- quency method represents the response of a vehi- dependent or steady state predictions compare cle with a small predictable number of frequency favourably with experimental predictions. The components. time dependent or dynamics stability derivative Green et al [1] attempted to use a time depen- predictions are, however, inadequate. Probably dent panel method code to predict the dynamic the best available prediction techniques available stability derivatives for the F16XL configuration. are semi-empirical. Characterisation of dynam- The code, however, failed to capture the basic and ics stability derivatives are, however, still ob- essential features of the experimentally measured tained experimentally, even though the experi- dynamic data for the F16XL configuration. mental techniques provide limited information. One of the unique features of the exploratory Recently, attempts using lower order computa- investigation was to perform the simulations us- tional techniques have yielded limited success ing commercially available codes such as CFD- [1], pointing towards the complex flow mecha- RC Fastran and Fluent. The simulations are thus nisms involved in time dependent responses for time dependent (in contrast to the above men- flight vehicles. It would thus be appropriate to tioned methods). attempt to use higher order techniques to develop The code chosen was Fluent. Fluent has a prediction capabilities. time accurate moving body capability, requires The modelling and simulation of dynamic an unstructured tetrahedral mesh, while the mo- stability derivatives using the Navier-Stokes tion is simulated using a user-defined function. computational fluid dynamics (CFD) approach is This paper details the attempt in simulating a current research topic. This is a natural ex- the pitch dynamic stability derivatives Cmq +Cmα˙ tension of the maturation of Navier-Stokes CFD with a Navier-Stokes CFD code, Fluent, using the as a prediction technique, firstly in in modelling time dependent free oscillation technique, of the steady state or time averaged/independent cases stable store configuration at low subsonic condi- and then unsteady or time dependent cases. tions, and comparing these to experimentally ob- To this end, an exploratory investigation of tained results. The question of whether the dy- using CFD to model dynamic stability derivatives namic stability derivatives can reasonably (with- was initiated, with a view to developing a predic- out significant computational effort) be simulated tion capability. The exploratory investigation is using the time dependent free oscillation tech- the topic of this paper. The results of the investi- nique using Fluent was being investigated. Suc- gation are compared to experimental data. cessful prediction can provide a useful prediction A number of previous attempts at predict- tool for the conceptual or initial design phase. ing dynamic stability derivatives have been at- tempted. Weinacht [2],[3],[4] used the lunar con- 2 MODELLING OF DYNAMIC STABILITY DERIVATIVES USING CFD 2 Dynamic Stability Derivatives ond system from which the derivatives of inter- est are extracted. Varying the frequency to char- The aerodynamic loads on a flight vehicle are tra- acterize the derivative as a function of reduced ditionally expressed as a first order Taylor series frequency is, however, more difficult, requiring of derivatives [6]. For example, in coefficient changes in the system stiffness or model inertia. form, the pitching moment, Cm can be expressed For most free oscillation tests, the support system as: has a stiffness (in the form of a flexure) which can be used to control the natural frequency, in combination with the model inertia, to the desired ∂C ∂C ∂C ∂F C = m α + m β + ::: + m q + α˙ + ::: value. m ∂α ∂β ∂q ∂α˙ (1) The forced oscillation technique forces the The derivatives of interest are the time rate model to oscillate at the required frequency, from which derivatives can be extracted from the time dependent derivatives, namely Cmq and Cmα˙ and so forth. response of the system and model. The experi- The two longitudinal dynamic stability mental apparatus is, however, an order of magni- tude more complex than for a free oscillation test, derivatives that are of greatest interest are Cmq and C . Experimental apparatus require com- since the apparatus needs to control the model mα˙ oscillation amplitude and frequency, whereas the plex mechanisms to measure Cmq alone. The most common technique employed is to measure free oscillation technique only requires a trigger mechanism. the combined derivative Cmq +Cmα˙ by simply os- cillating the model about the centre of gravity i.e. 2.2 Governing Equations a single rotational degree of freedom. The deriva- tive Cmα˙ can be obtained from a second test (util- The equation of motion describing the single de- ising different apparatus) by heaving the model gree of freedom is expressed as: up and down. The derivative Cmq is then sim- ply the difference between the combined deriva- Iθ¨ + cθ˙ + kθ = F (2) tive and Cmα˙ . For the purposes of the exploratory investigation only the combined derivative was For the method used is this investigation, F = simulated. 0 i.e. free oscillation, and c ´ Cmq +Cmα˙ . I is the moment of inertia of the store and K is the spring 2.1 Experimental Prediction of Dynamic constant of the system. Stability Derivatives The spring constant of the system is algebraic sum of the support stiffness and pitching moment Since the most accurate simulation method of ob- due to angle of attack variation, Cmα i.e. K ´ taining dynamic stability derivatives has been ex- Ksupport +Cmα . perimental, a large number of techniques have The system response, or solution to the equa- been developed. This has further been exacer- tion of motion 2 can be written as: bated by the limited capabilities of experimental c t techniques, simply due to mechanical and mea- θ = θ0e 2I cos(ωdt + φ) (3) surement constraints. The most common tech- θ φ niques used the free and forced oscillation meth- where 0 and are arbitrary constants, and ω ods [7]. d is the damped natural frequency. The free oscillation technique essentially pro- The combined damping derivative Cmq +Cmα˙ vides an initial disturbance to the model in the is thus obtained by non-dimensionalised the 1 ρV 2Sl2 2 1 ρ 2 plane or about the axis of interest and allows the damping force c by 2V , where 2 V is the model to respond without interference. The re- freestream dynamic pressure and S is the refer- sponse of the model is easily modelled as a sec- ence area.