Numerical Simulation of the Free Pitch Oscillation for a...

Numerical Simulation of the Free Pitch Oscillation for a Reentry Vehicle in Transonic Wind Tunnel Flow

Bodo Reimann German Aerospace Center (DLR) Braunschweig 8th European Symposium on Aerothermodynamics for space vehicles Lisbon, 2-6 March 2015

• Introduction • Numerical tool (DLR TAU Code) • Simulated cases and flow conditions • Grid and grid convergence study • Steady-state results • Simulation procedure for coupled simulations • Unsteady coupled results • Computation of dynamic pitch damping derivatives • Conclusion

www.DLR.de Bodo Reimann • 8th European Symposium on Aerothermodynamics for Space Vehicles - Lisbon, 2-6 March 2015

Contents

• Numerical simulation of the free oscillation of a reentry vehicle in transsonic flow.

• Computation of dynamic derivatives from pitch oscillation. • Influence of wind tunnel mounting.


Introduction


• Finite volume method • Steady and unsteady Euler/Navier-Stokes equations • Structured, unstructured and hybrid meshes • Different upwind and central schemes • Runge-Kutta or implicit approximately factored LU-SGS time stepping

scheme • Multi-grid, Residual smoothing, Parallel computing via domain splitting • Different one- and two-equation turbulence models, RSM, DES, LES

(here: Menter SST model) • Overlapping grid technique (Chimera technique) with semi-automatic hole

cutting • Python interface • Flight mechanics and structure mechanics coupling

DLR TAU Code

• Rigid-body dynamics solver (RBD, 6-DoF) • Newton‘s second law and Euler equation (of rigid body dynamics) • „Strong coupling“


DLR TAU Code Flight mechanics coupling

time step n n+1 n+2

RBD

CFD

Flow condition


TMK run 18 TMK run 19 TMK run 23 TMK run 10 M 0.80 0.95 1.10 2.01 Re 2.816 106 3.693 106 4.599 106 4.385 106

u [m/s] 251.87 291.28 333.64 506.43 ρ [kg/m3] 1.413 1.537 1.633 0.750 T [K] 246.2 233.9 227.5 158.5 Twall adiabatic adiabatic adiabatic adiabatic flow Menter SST Menter SST Menter SST Menter SST

mass = 0.743212 kg Moment of inertia = 9.78 10-4 kg m2

Values for half-configuration

Computational domain


Ø3.75m LIXV=0.125m 5.37 million points 17.71 million points


Computational domain


Wind tunnel configuration Chimera mesh

sting

vehicle

sting hole vehicle hole


Wind tunnel configuration Chimera mesh


Grid convergence study Steady-state simulations, run 19 (M = 0.95)


TMK run 19 (M = 0.95, α = 60°)

leeward

windward

wind tunnel

wind tunnel

free flight

free flight


TMK run 10 (M = 2.01, α = 43°)

leeward

windward

wind tunnel

wind tunnel

free flight

free flight

Simulation procedure unsteady coupled Simulations


• Steady state flow (RANS) simulations at different angles of attack to find the trim angle (Cm = 0)

• A steady state flow solution close to the trim angle is used as the inital restart solution for the unsteady simulation

• Unsteady flow (URANS) simulations with full coupling of rigid body motion (1-DoF - only pitch)

• For cases with sting only the vehicle is free to oscillate the sting is fix (overlapping grids, chimera technique)

• Pitch damping derivatives (Cmq + Cmα) are computes from the pitch angle vs. time curve

• Frequencies (f, ω, RFP) and Cmα results from steady or unsteady data

.

Computation of damping derivatives

ODE �̈�𝜗 + 𝐶𝐶𝐼𝐼�̇�𝜗 + 𝐷𝐷

𝐼𝐼𝜗𝜗 = 0

Solution 𝜗𝜗 𝑡𝑡 = 𝑒𝑒−𝛿𝛿𝛿𝛿𝜗𝜗0 cos(𝜔𝜔𝑡𝑡 + 𝑝𝑝) ϑ(t) fit → δ 𝐶𝐶𝑚𝑚𝑚𝑚 + 𝐶𝐶𝑚𝑚�̇�𝛼 = 4𝑢𝑢∞𝐼𝐼𝛿𝛿/ 𝜌𝜌∞

2𝑢𝑢∞2𝑆𝑆𝑟𝑟𝑟𝑟𝑟𝑟𝐿𝐿𝑟𝑟𝑟𝑟𝑟𝑟2

Cm(α) fit 𝐶𝐶𝑚𝑚 𝛼𝛼 = 𝐷𝐷2𝛼𝛼2 + 𝐷𝐷1𝛼𝛼 + 𝐷𝐷𝑜𝑜

Cm(αtrim) = 0 𝛼𝛼𝛿𝛿𝑟𝑟𝑡𝑡𝑚𝑚 = ± 𝐷𝐷12

4𝐷𝐷22− 𝐷𝐷0

𝐷𝐷2+ 𝐷𝐷1

2𝐷𝐷2

1st derivative 𝑑𝑑𝐶𝐶𝑚𝑚𝑑𝑑𝛼𝛼

= 2𝐷𝐷2𝛼𝛼 + 𝐷𝐷1

𝜔𝜔 = 2𝐷𝐷2𝛼𝛼𝑡𝑡𝑡𝑡𝑡𝑡𝑚𝑚+𝐷𝐷1𝐼𝐼

𝜌𝜌∞2𝑢𝑢∞2𝑆𝑆𝑟𝑟𝑟𝑟𝑟𝑟𝐿𝐿𝑟𝑟𝑟𝑟𝑟𝑟(180

𝜋𝜋)



Cmq+Cmα = 1.7650 . Cmq+Cmα = 0.8100 .

logaritmic decrement 𝐶𝐶𝑚𝑚𝑚𝑚 + 𝐶𝐶𝑚𝑚α̇ 𝑡𝑡= log

𝜗𝜗𝑟𝑟,𝑡𝑡𝜗𝜗𝑟𝑟,𝑡𝑡+1

8𝑢𝑢∞𝐼𝐼

𝜌𝜌∞𝑢𝑢∞2𝑆𝑆𝑟𝑟𝑟𝑟𝑟𝑟𝐿𝐿𝑟𝑟𝑟𝑟𝑟𝑟2 𝑡𝑡𝑟𝑟,𝑡𝑡+1 − 𝑡𝑡𝑟𝑟,𝑡𝑡

Computation of damping derivatives


Dynamic derivatives

Conclusion

• Nonlinear effects for deflection (pitch) angles larger 1° • Strong effect of the sting on the pitch derivative (in subsonic flow) and trim

angle • Presence of the sting as well as larger oscillation amplitudes

decrease the pitch damping derivative • CFD results carried out independent from experiments Future Work (ESA TRP DYNAST) • Modification of wind tunnel sting • LES computations planned


Numerical Simulation of the Free Pitch Oscillation for a...

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