c
TU Delft, The Netherlands, 2006
FLUID STRUCTURE INTERACTION AT THE ARIANE-5
NOZZLE SECTION BY ADVANCED TURBULENCE
MODELS
Heinrich L¨udeke ∗, Javier B. Calvo†, Alexander Filimon†† ∗DLR Braunschweig
Lilienthalplatz 7, D-38108 Braunschweig e-mail: heinrich.luedeke@dlr.de
Tel: +49 (531) 295 3315
† e-mail: javier.bartolomecalvo@dlr.de †† e-mail: alexander.filimon@dlr.de
Key words: Buffeting Coupling, Fluid Structure Interaction, Detached Eddy Simulation,
Ariane-5
Abstract. Substantial requirements for future rocket technologies are the cost-efficient
access to orbit as well as the increase in the system reliability. Concerning these require-ments a deeper insight into the unsteady phenomena during the start phase of modern launchers is essential. Especially unsteady side-loads, induced by the interaction of flow separation inside the nozzle, the launcher wake and the nozzle structure will play an impor-tant role for the design of future main stage propulsion systems. This so called buffeting coupling phenomenon is one of the main challenges during ascent. For the Ariane-5 con-figuration unsteady Detached Eddy Simulations were carried out under transonic wind tunnel conditions and validated with experimental data. For this configuration also a first coupled simulation of the flow field and the original nozzle structure of an Ariane-5 wind tunnel model is carried out to investigate resonances and loads on the nozzle.
1 INTRODUCTION
Figure 1: Mach number contours of the Ariane-5 launcher atM∞= 0.8. Steady RANS simulation
Schwane2. However until now it was not possible to simulate the unsteady turbulent flow
field of the whole launcher configuration and the interaction with the nozzle structure simultaneously. The purpose of this study is to investigate these conditions with recent turbulence models like detached-eddy simulation (DES). DES is a hybrid technique pro-posed by Spalart et.al3,4 for the simulation of these turbulent unsteady flows. The idea is to combine the best features of Reynolds-averaged Navier-Stokes (RANS) and the large eddy simulation (LES) for the computation of realistic configurations at high Reynolds-numbers. In the following simulations of the Ariane-5 nozzle section under transonic wind tunnel conditions are carried out. The typical Mach number field for this configuration, including nozzle flow and plume is shown in Fig. 1. For the CFD part of the study the hybrid structured-unstructured DLR-τ -code was used which is extensively validated for sub- trans- and hypersonic cases5. In former investigations steady and unsteady Ariane-5
simulations under turbulent conditions are carried out at transonic wind tunnel conditions including jet flow and launcher wake6,7. Especially DES simulations are compared with respect to their capabilities in resolving the highly unsteady flow field between central EPC-nozzle and boosters. While in the former studies simplified generic configurations of the launcher were investigated a completely new unstructured grid including Helium shell, connectors between booster and main body as well as various other details was generated. To give an impression of these details the NLR model, which was used for wind tunnel testings is shown in Fig. 2. The unsteady DES results are compared with experimental data of the FFA T1500 wind tunnel facility of the FOI Sweden. In the next step a first coupled simulation of the flow field and the original EPC nozzle structure is carried out to investigate resonances and loads. For this preliminary coupling a simplified structural description of the Vulcain 2 nozzle was delivered by EADS-ST and mapped on the CFD grid. The FEM computations of the structure were carried out by the commercial tool ANSYS8 and the coupling by MPCCI9 routines.
2 NUMERICAL SIMULATION TOOLS 2.1 CFD-solver τ
Figure 2: NLR wind tunnel model for buffeting forces measurements (figure from Maseland10)
solver for the Euler and Navier-Stokes equations in the integral form. Different numerical schemes like cell-centered for sub- and transonic flow and AUSMDV for super- and hy-personic flow conditions are implemented. Second-order accuracy for upwind schemes is obtained by the MUSCL extrapolation, in order to allow the capturing of strong shocks and contact discontinuities. A three-stage explicit Runge-Kutta scheme as well as a point implicit LUSGS scheme are options to advance the solutions in time for steady flow fields. For convergence acceleration local time stepping, implicit residual smoothing and full multigrid are implemented. Fast and accurate transient flow simulations are computed by a Jameson type dual time step-ping scheme, as an implicit algorithm which is not restricted in the choice of the smallest time step in the flow field. To overcome this limit the time derivative in the Navier-Stokes equations is discretized by a second order back-wards difference, resulting in a non-linear equation system which converges toback-wards the subsequent time step by using an inner pseudo-time. Within this inner loop all mentioned acceleration techniques are applicable. Several one- and two equation turbulence mod-els are available for steady simulations. In the presented RANS-cases the one-equation Spalart-Allmaras (SA) model is used which is briefly described in the following. The model defines the eddy viscosity field as
μt= ρνt = ρ˜νfν1 (1)
with ρ as the density, νtas the turbulent kinematic viscosity and fν1as a near wall-function that guarantees linear behavior of the turbulent transport quantity in the vicinity of walls:
with ν as the molecular viscosity. The distribution of the transport quantity˜ν is deter-mined by the solution of
D(ρ˜ν) Dt = c b1Sρ˜˜ ν P − cw1fwρ ν˜ d 2 D +ρ σ ∇ [(ν + ˜ν)∇˜ν] + cb2(∇˜ν)2 DF (3)
with d as the wall distance. This transport equation contains phenomenological models of production P , destruction D and diffusion DF . The destruction term D is needed to model the blocking effects near walls. In the production term P a modified vorticity ˜S appears that maintains the linear behavior of the model near walls:
˜
S = S + ν˜
k2d2fν2, fν2 = 1−
χ
1 + χfν1 (4)
The function fν2 is constructed in a way that the vorticity S maintains its log-layer behavior all the way to the wall. The destruction term
D = cw1fwρ
ν˜
d
2
(5) is constructed by using the wall function fw:
fw = g 1 + c6w3 g6+ c6 w3 1/6 g = r + cw2r6− r (6) r = ν˜ ˜ Sk2d2
The different model constants cν1, cb1, cb2, cw1, cw3 are determined by experimental data and analytical solutions and are well known for turbulent flow fields4.
During the last years more recent turbulence models like DES are implemented3. DES is a
hybrid RANS-LES approach that bases on a modification of the wall distance term in the SA model. While RANS is used in the unsteady boundary layer flow with a standard grid resolution where it performs reasonable results, LES is used in separated regions where relevant turbulent scales can be modeled. The switching between RANS and LES bases on a characteristic length scale, chosen to be proportional with Δ which is the largest cell dimension:
Δ = max(Δx, Δy, Δz) (7)
For the standard DES formulation the wall distance d in the SA model is replaced by ˜d which is defined as:
˜
d = min(d, CDESΔ) (8)
2.2 Fluid Structure coupling
The equation which governs the structural dynamics in a Finite Element model11 is [M ]{¨q(t)} + [C]{ ˙q(t)} + [K]{q(t)} = {R(t)} (9) with R(t) as the aerodynamic forces, q(t) as the nodal displacement vector, ˙q(t) as the nodal velocity vector and ¨q(t) as the nodal acceleration vector. Three matrices are taken into account, which are named with [M ] for the mass matrix, [C] for the damping matrix and [K] for the stiffness matrix In our analysis, the applied external load is only given by the pressure inside and outside of the nozzle. Temperature and conduction across the wall of the nozzle is not a goal of the present study and consequently not taken into account in the coupling procedure.
Figure 3: Coupling procedure of fluid and structural solver (figure from Mack12)
For the coupling of the aerodynamic and structural dynamic simulations in the time domain, a loose scheme has been implemented in which a Dirichlet-Neumann iteration is performed until the convergence is achieved. The quality of the coupling is considered by equilibrium verification of loads, energies and work at each physical time step. The scheme is conservative with regards to the forces, moments and the work performed on both the aerodynamic and structure dynamic side. The main characteristics of the aero-elastic fluid structure interaction in the time domain are as follows:
• loose coupling of computational fluid dynamics (CFD) and computational structure dynamics (CSD) through file input/output,
• use of an implicit or explicit Newmark algorithm for the time integration of the CSD equations of motion,
• data exchange based on adjusted conventional serial staggered (CSS) algorithm which is second order in time. The coupling structure of the algorithm is shown in Fig. 4
t2
t0 t1 t3
TAU
ANSYS
Figure 4: Second order coupling scheme between the structural ANSYS solver and the TAU CFD solver in time.
2.3 Interpolation between structural and aerodynamic part
In order to apply the calculated aerodynamic forces, they have to be transformed to the structural grid points. Since obviously the aerodynamic and structural grids do not coincide, a methodology for the transfer of loads and displacements between the grids has to be employed. In this study the commercial software MpCCi was used which is meanwhile a kind of standard for the simulation of coupled problems (see Fig. 3). Conservative as well as non Conservative interpolation algorithms are implemented. The advantage of the conservative formulation lies in the higher numerical accuracy as well as in the physical justification for the transfer of forces and displacements between different surface discretizations. This approach was used for the present study.
3 COMPUTATIONAL GRIDS 3.1 CFD-grid
In former investigations6 a structured grid for the Ariane-5 launcher was provided by
ESA13,14. For the present study an unstructured tetrahedral grid was generated by the grid generator Centaur. The whole launcher geometry, taken from the CAD file provided by FOI15, was discretized by surface triangles with a strongly increased grid density in
the nozzle region and around the helium tank where unsteady turbulence had to be investigated (see Fig. 5). Due to the well known problem of highly time consuming DES simulations all regions without special interest for the buffeting coupling are discretized as coarse as possible to receive a grid with about 5· 106 nodes totally. Nevertheless this grid contains the whole non symmetric launcher with lots of details. The booster nozzles, which were not included in the CAD description, were designed by following the shape and dimensions of the structured grid to resolve the principle experimental setup, where a double sting with outlets was mounted inside these nozzles13. Also the helium tank
aside of the EPC nozzle was modified to provide better grid resolution in the boundary layer by simplifying geometrical constraints. Fuel tubes at the body, included in the wind tunnel model, were omitted with the exception of the fittings at the end that can have significant influence on the nozzle. A detailed view of the nozzle section is given in Fig. 6 to get an overview of the grid resolution between boosters and EPC Nozzle.
Figure 6: Cut-out of the nozzle plane with boosters and EPC nozzle
3.2 Ansys-grid
while on the right hand side the simplified version, mapped on the geometry of the wind tunnel model nozzle is displayed. For this mapping the ring is removed and the nozzle is shortened to fit the model configuration. The material properties of the simplified nozzle were modified in a way, that the eigenfrequencies of the first three structural modes are comparable with the original configuration. Due to the enlarged thickness of the model nozzle the resulting amplitudes at a given force are significantly smaller. Nevertheless our interest was mainly focused on the investigation of the modal behavior of the structure.
Figure 7: ANSYS grid of the Vulcain 2 Nozzle and respective grid of the wind tunnel model nozzle.
4 NUMERICAL RESULTS
4.1 Flow and boundary conditions
4.2 Experimental data used for validation
For the validation of the numerical predictions experimental results are taken from from the detailed database of the FOI test campaign at the T1500, funded by ESA15. The study provides data for a large amount of steady and unsteady pressure sensors, located at different circumferential rings. Data is taken from selected sensors and cuts, given in Fig. 8. Particularly one external nozzle cut with steady pressure sensors, one with unsteady pressure sensors for Root Mean Square values of Cp (CpRMS)and a line of pressure sensors inside the nozzle at φ = 5◦. Finally in Fig. 8 the orientation of the azimuth angle φ is given.
Figure 8: Definition of angular coordinate system, external ring with pressure sensors and nozzle-internal cut.
4.3 Steady RANS-results
DES, as a method for the description of unsteady turbulent flow, needs a steady tur-bulent solution as a restart which is generated with the same RANS model DES bases on. Such a RANS solution for the full configuration at Mach 0.8 is shown in Fig. 1. The interaction between the different plumes as well as the structures between the boosters and the central nozzle in the symmetry plane can be seen clearly, even for this steady simulation
4.4 Unsteady DES Results
Figure 9: Snapshot of the Ariane-5 Cp distribution and instantaneous stream traces. Three different views.
of 28.5. Special care was taken on the resolution of the lower part of the EPC nozzle where the most important flow phenomena for buffeting coupling appear in the exper-iments (see Fig. 6). Time series of the pressure were extracted from various positions of the configuration corresponding to the unsteady q-lite sensors locations. Furthermore averages and RMS values of pressure and velocities are computed in the whole flow field. DES results for three different views of the launcher are shown in Fig. 9 which is a snapshot taken 32ms after the start of the DES. The flow structures that appear on the EPC nozzle, generated by the vortical flowfield near the edge of the cylindrical part of the EPC are clearly visible. The difference of the pressure distribution on the central nozzle
Figure 11: RMS values of unsteady Cp distribution of the configuration. Three different views.
for the 90◦ and 270◦-view is significant and obviously influenced by the position of the LBS (see Fig. 8) which is the only non symmetric feature of the configuration in the x-y plane. in the middle of Fig. 9 (180◦) this influence can be seen clearly. The difference in the position of the pressure maximum near the end of the EPC-nozzle for 90◦ and 270◦ is a direct result of the displacement of the wake vortex coming from the edge of the EPC, which is shown in Fig. 10 for 180◦ by averaged stream lines.
Another important detail of the investigated configuration is the asymmetry of the launcher generated by the helium-shell which is obviously of significant size. Different experimential studies have shown influences of this sphere on the unsteady behavior of the flow on both sides of the EPC nozzle. A shading effect on the pressure fluctuations in that region where the shell is located was stated in former studies16and numerical simulations
without this sphere have shown stronger unsteadiness. Nevertheless the mechanisms of the the shading effects are still not fully understood. The present investigations clearly show differences between the unsteady flow of the left- and right side of the cut-plane between boosters and central nozzle (Fig. 9, 90◦-view). Even the trace of the pressure contour fo the He-shell is visible on the surface aside of the shell. If we take again a look on the flow topology of a typical DES-snapshot (Fig. 9) the shading mechanism becomes clear. While in the part without sphere the unsteady flow from the gap between booster and central stage can directly hit the nozzle where a much more detailed vortex system develops, this mechanism is blocked by the shell on the opposite side.
x [m] P/ Pc 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0 0.008 0.016 0.024 DES Experimential data Y Z X
Figure 12: Averaged pressure ratio at inner nozzle wall.
In the experiments an unsteady behavior of the vortex flow was investigated at the lower part of the PTM (on top of the EPC nozzle). This maximum in σCp is clearly visible at the 180◦-view of Fig. 11 just were in Fig. 10 the two small recirculation regions in the upper part of the EPC nozzle appear.
4.5 Validation of DES results
To compare the DES predictions with the experimental data base from the FFA T1500 wind tunnel different measurement cuts were chosen and extracted from the numerical results. For the inner part of the nozzle a cut at 5◦ azimuth was taken, the pressure ratio is shown in Fig. 12. The DES result is slightly below the wind tunnel measurements, but the position of the separation is well predicted.
For the much more complex flow field in the external nozzle region a steady and an unsteady ring of pressure sensors is compared with the DES output (Fig. 13). The results for the averaged Cp distribution are in good agreement with the measurements although the numerical results along the ring are slightly lower. It have to be pointed out, that all maxima and minima are located at the correct positions. Even the standard deviation
φ <Cp > 0 90 180 270 360 DES Experimential data φ σ Cp 0 90 180 270 360
Figure 14: Deformation of EPC nozzle at four different times, exxagerated view.
of the pressure is predicted in the correct range, although it is about 30% larger than the measured data. This is a typical behavior of DES computations which was already investigated in former simulations6. Also here maxima and minima are found at the right position.
4.6 Fluid structure coupling
t [s] Δ z/ Dnoz z le 0.01 0.02 0.03 0.04 0 5E-05 0.0001 Y Z X
Figure 15: Displacement of a single point on the model nozzle over time.
In Fig. 15 the displacement of a single point, normalized by the nozzle diameter is presented. As visible the resonance frequency of the structure is about 180Hz. The displacement is visibly small as expected from the material properties chosen for the model nozzle.
5 CONCLUSIONS
6 ACKNOWLEDGMENTS
This was only possible possible with contributions of many different people. Concerning the wind tunnel data we have to acknowledge Richard Schwane from the ESA and Joergen Olssen from the FOI for providing the T1500 data and the CAD models for grid generation. the ANSYS data of the Vulcain-2 nozzle was kindly provided by EADS-ST.
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