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A fluid structure coupling of the Ariane-5 nozzle section during start phase by detached eddy simulation

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Abstract

Concerning the requirements of future rocket technologies, providing a cost-efficient access to orbit as well as an increase in system reliability, a deeper insight into the unsteady phenomena during ascent of modern launchers is essential. Unsteady interactions and resonances of the turbulent separated launcher wake and the nozzle structure play an important role for the design of future main stage propulsion systems. The so-called buffeting coupling phenomenon is one of the main challenges during ascent. In the present study, a coupled simulation of the afterbody of the Ariane-5 launcher with a realistic structural and aerodynamic representation of different nozzle configurations is carried out. On the computational fluid dynamics side, unsteady detached eddy simulations are coupled with structural computations for different nozzle configurations. The essential features of the interaction process are well captured. The coupling algorithm is validated by a nonlinear supersonic panel flutter simulation with highly transient mechanical interaction.

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Abbreviations

ANSYS:

ANalysis SYStem: FEM Software

AUSMDV:

Advection upstream splitting method

CAD:

Computer aided design

CFD:

Computational fluid dynamics

DES:

Detached eddy simulation

DLR:

Deutsches Zentrum für Luft und Raumfahrt (German Aerospace Center)

EADS:

European Aeronautic Defence and Space Company

FEM:

Finite element method

FFA:

Flygtekniska FörsöksAnstalten (Swedish Institute for Aeronautic Research)

IMENS:

Integrated Multi-disciplinary dEsigN of hot Structures

LCO:

Limit cycle oscillation

LES:

Large eddy simulation

MPCCI:

Multi-purpose code coupling interface

MUSCL:

Monotonic upwind scheme for conservation laws

NLR:

Nationaal Lucht- en Ruimtevaartlaboratorium (Dutch National Aerospace Laboratory)

RANS:

Reynolds Averaged Navier–Stokes simulation

RMS:

Root mean square value

SA:

Spalart–Allmaras turbulence model

TEG:

Turbine exhaust gas manifold

VTK:

Visualization tool kit

cb1, cb2:

Coefficients of source and diffusion term in the turbulence model

cw1, cw2, cw3:

Coefficient of destruction term

cν1:

Coefficient of wall damping function

C DES :

Detached eddy simulation (DES) constant

d :

Wall distance

\(\tilde{d}\) :

Modified wall distance in the DES model

d s :

Nodal displacement of the nozzle structure

E :

Young’s modulus

fν1, fν2, f w :

Near-wall damping coefficients for eddy viscosity

h :

Plate-thickness

l :

Plate-length

M ∞ :

Free-stream Mach number

M, C, K:

Mass, damping, and stiffness matrices in FEM

P, D, DF:

Production, destruction, and diffusion term

\(q, \dot{q}, \ddot{q}\) :

Nodal displacement, velocity, and acceleration vector

R x :

Dimensionless in-plane force

\(\tilde{S}\) :

Modified shear stress

u ∞ :

Free-stream velocity

W :

Plate-deflection amplitude

\({\Updelta}x, {\Updelta}y, {\Updelta}z\) :

Cell dimensions in x, y, z direction

\(\Updelta\) :

DES filter width

ε:

Convergence criterion of the coupling cycle

ε q :

Total change of deformation

κ:

von Kármán constant of logarithmic wall layer

λ p :

Dimensionless dynamic pressure

μ t :

Turbulent dynamic viscosity (= ρν t )

ν:

Poisson-ratio for calculation of supersonic panel flutter

ν t :

Kinematic eddy viscosity (= μ t /ρ)

\(\tilde{\nu}\) :

Transported quantity in Spalart–Allmaras turbulence model

ρ:

Density

ρf :

Fluid-density for calculation of supersonic panel flutter

ρs :

Structural-density for calculation of supersonic panel flutter

σ:

Turbulent Prandtl number

σ * x :

Dimensional shear stress in x-direction

σ x :

Dimensionless shear stress in x-direction

τ:

Dimensionless time

χ:

Ratio of turbulent to Spalart–Allmaras viscosity \((=\tilde{\nu}/\rho)\)

ξ, ζ:

Dimensionless co-ordinates in x and z-direction

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Acknowledgments

The authors acknowledge EADS-ASTRIUM for kindly providing the structural data of the Vulcain-2 nozzle and Alexander Filimon for the grid generation during his time as a diploma student at DLR. The coupling software to interpolate CFD onto FEM grids was designed by the Institute for Aircraft Design and Lightweight Structures of the Technical University of Braunschweig. It has been developed within the Integrated Multi-disciplinary design of hot Structures (IMENS+) DLR project. A major part of the study was carried out under the scope of the Pan European infrastructure research programme on High Performance Computing: HPC-Europa. The authors acknowledge the EPCC at the University of Edinburgh for their kind assistance and the possibilities to use their Blue-Gene super-computing facility during a grant at their institute and furthermore the University of Glasgow for hosting the first author and providing the ANSYS FEM-solver during that time.

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Authors and Affiliations

  1. Institute of Aerodynamics and Flow Technology, Lilienthalplatz 7, 38108, Braunschweig, Germany

    Heinrich Lüdeke & Javier B. Calvo

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  1. Heinrich Lüdeke
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  2. Javier B. Calvo
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Correspondence to Heinrich Lüdeke.

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Lüdeke, H., Calvo, J.B. A fluid structure coupling of the Ariane-5 nozzle section during start phase by detached eddy simulation. CEAS Space J 1, 33–44 (2011). https://doi.org/10.1007/s12567-010-0002-6

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  • DOI: https://doi.org/10.1007/s12567-010-0002-6

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