High fidelity simulation of jet mixing in a confluent flow nozzle

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1 20th AIAA Computational Fluid Dynamics Conference June 2011, Honolulu, Hawaii AIAA th AIAA Applied Aerodynamics Conference High fidelity simulation of jet mixing in a confluent flow nozzle Dr. Julien Szydlowski * and Arthur Droit * Aerodynamics Powerplant Integration SNECMA Moissy Cramayel, France. High fidelity simulation method is used to investigate the mixing phenomenon in a realistic aircraft-afterbody. An axisymetric jet at an exit Mach Number of 0.86 and a Reynolds number of 1.6x10 6 is computed by Detached Eddy Simulation to predict the development of vortex structures in the long duct mixing flow. To assess the validity of the simulation, the mean aerodynamic fields are compared to LDV measurements. It is found that the numerical simulations agree with the experimental measurements. The DES method is shown to simulate the evolution of the mixing layers in the jet well; therefore this method allows understanding the flow physics in a long duct mixed flow which is an essential step to optimizing the nozzle design to meet both aerodynamic and aero-acoustic requirements. I. Introduction NECMA has developed new, efficient and environmentally friendly propulsion systems for long corporate and Sfor regional aircraft. Latest SNECMA turbofan engines in those categories are equipped with forced mixers and feature a mixed flow exhaust system. The mixed flow nozzle is designed to lead secondary flow into the primary stream. In contrast, for a separate jets configuration, both flows are expanded separately. The internal mixing between core and entrained fan flows inside the exhaust nozzle reduces exhaust jet plume velocity. Exhaust jet velocity is the dominant parameter for the jet noise production, therefore reducing the exhaust velocity results in lower jet noise. Paynter and Birch 1 studied the effect of mixing enhancement on the jet noise reduction. In addition to acoustic concerns, they showed that increasing the mixing allows to augment thrust. Based on those conclusions, numerous works have been carried out to increase mixing with various nozzle geometries such as mixer with lobes, with crenels. In parallel, an impressive research effort was developed worldwide to understand mechanism by which mixing is enhanced. Elliot et al. 2 highlighted two types of instability which contributes to the mixing in a lobed mixer. The first one is the spanwise vortices due to Kelvin-Helmholtz instability in the free shear layer. The second one is the streamwise vortices generated by the geometry of lobed or crenellated mixers. On the computation side, the configuration of mixer ejector is still a challenging case as the flow is strongly dependent on the formation of unsteady vortical structures and turbulent structures which play an important role in the mixing phenomenon 3. The available methodologies to compute unsteady turbulent flows produce different levels of time-space resolution according to the required flow details and to the available computational power. The direct numerical simulation (DNS) which solves the Navier-Stokes equations is restricted to low-reynolds number turbulent flows due to the necessity of resolving all the spatial scales of the motion. On the other hand, the Reynolds averaged Navier-Stokes (URANS) equations simulation is widely used to compute turbulent flows in propulsive jets. The RANS equations simulation are widely used to compute jets, although this method may reproduce some flow physics, the results are far from being totally reliable for understanding the jet mixing. Some authors 4 are pessimistic about the RANS capability to achieve engineering accuracy in the massive three-dimensional separations. Between the DNS and the RANS approaches, the large eddy simulation (LES) provides an effective tool for tackling complex turbulent flows by computing only the largest scale motions and modelling the subgrid scales. For instance, LES is well adapted to handling massive separated flows; nevertheless, the cost of this method becomes quickly prohibitive if one wants to model the dynamic of the turbulence in the boundary layer at practical (high) Reynolds number. In order to combine a good computational efficiency and a reliable prediction of large separation zone, a hybrid technique between URANS and LES has been developed by Spalart & al 5. The so-called detached eddy simulation (DES) combines the fined-tuned RANS model in the attached boundary layer with capabilities of LES in the separated flow region. Encouraging results have been given for a wide range of flow configurations exhibiting propulsive jets 6. The aim of this work is to assess and qualify the DES method to simulate 1 Copyright 2011 by the, Inc. All rights reserved.

2 29 th AIAA Applied Aerodynamics Conference the jet mixing in a confluent flow nozzle at high Reynolds number. The paper is organized in four parts as follows. First, the test case is described to present the geometrical and physical complexity of this industrial propulsive jet. Second, the numerical method comprising the ZDES approach is detailed and meshing choices are explained. As it will be shown later, flow structures predicted by this method make significant improvements over RANS computations. Then, the computed flow fields are compared with LDV measurements and RANS results. Finally, the mixing phenomenon is assessed thanks to detailed information of DES in the jet. We show that the DES approach offers a real improvement of prediction of jet mixing; the capability to predict mixed flow nozzle performances has made a significant step. II. Test case The confluent flow nozzle studied is depicted in Figure 1. This axisymetric exhaust model has been designed by means of CFD calculations with a 5.4 area ratio in cruise operations. They were mounted in the CEPRA19 anechoic test chamber and tested both under flight and static conditions. The aerodynamic flow-field was investigated from the nozzle exit up to 16 downstream diameters at full-power, in static and for one simulated flight condition. The presented simulations have the ambition to reproduce a test case in which the far-field condition is M0=0.24, the Mach number in the core of the jet is Mj=0.86. The Reynolds number of the jet flow based on inner diameter of the common nozzle is ReD = Figure 1. Modeled nozzle geometry LDV measurements were carried out at the CEPRA19 low speed anechoic wind tunnel operated by ONERA and implanted at the Saclay Power Plant Test Center (CEPr). The facility is an open-jet wind tunnel and the test chamber with its ¼ spherical shape covered with foam rubber wedges is anechoic above 200Hz. A general view of the test chamber is shown in Figure 2. The air-supply is provided by a compressor which can deliver a mass-flow rate of 6kg/s. The air outlet temperature is sufficient to achieve secondary flow temperature up to 400K and the temperature of the primary flow can range from 850K to 1150K by heating the air in a combustion chamber operating on propane. A centrifugal fan unit provides a simulated aircraft forward speed up to Mach number The LDV system was configurated to measure the axial and transverse velocity components. Aerodynamic investigations were performed up to 16 diameters from the nozzle exit, in the upper vertical plane through the jet axis. Mean flow velocities, turbulence rms velocities, shear stresses and statistical information were obtained at a given location on the basis of 2000 repeated and validated acquisitions. A complete set of data for one configuration is composed about 750 points. Figure 2. CEPRA19 test chamber 2

3 III. Numerical Method A. General Description Simulations were performed with the elsa 7 code developed by ONERA. The elsa solver is the multi-application object oriented aerodynamic code. It is based on a cell-centered finite volume technique for structured multiblock meshes and includes a wide range of numerical techniques as well as physical models in order to simulate the flowfield around realistic aerospace configurations from the low subsonic to the hypersonic regime. The domain of application includes fixed wing, rotary wing, turbomachinery, space launcher and missile configurations Unsteady and three dimensional Navier-Stokes simulations are highly CPU demanding so that explicit schemes are not efficient enough for this purpose and implicit schemes are required. Time discretization is based on a backward second-order-accurate formulation which guarantees a level of accuracy compatible with that of unsteady computations requirements. Time integration is based on second-order accurate Gear s formulation. A LU factorization is used to simplify its inversion and Gear sub-iterations allow to efficiently converging towards the time-accurate solution. More details concerning the Gear formulation can be found in [8]. Time integration for DES computations is performed with 5 Newton sub-iteration. The physical time step is equal to 10-6 s which corresponds on the next described grid to a maximum CFL number of about 5 in the jet flow. For RANS simulations, the classical 2nd-order centered Jameson s scheme is employed with explicit artificial viscosity. For a better accuracy the numerical diffusion of the scheme is set to the minimum necessary for maintaining stability. Indeed, the artificial viscosity adds to the molecular and turbulent viscosity, and may result in the damping of large eddies which occur in the mean flow if the space discretization is too diffusive. This point of numerical diffusion even requires larger attention for DES or LES because, although excessive dissipation does not result in a meaningless solution, the simulation does not take full advantage of the grid fineness. The energy cascade is stopped by the resulting viscosity at larger scales than possible. In order to avoid this problem, a particular attention has been paid to the minimization of the intrinsic dissipation of the scheme. Very low levels of 2 nd and 4 th order dissipation have been used ; furthermore a damping of the artificial dissipation of the Jameson scheme is also used in the boundary layers. The well-tried elsa solver has been successfully used to compute DES of dynamic stall 10, of engine jet under a wing 11, and of mixing enhancement in a supersonic round jet 12. B. Turbulence Modeling Zonal Detached Eddy Simulation Approach The DES model was originally based on the Spalart-Allmaras (SA) model described above. In this SA model, the destruction term is a function of d, the distance to the closest wall. When balanced with production, this term adjusts the eddy viscosity as a function of the local deformation rate S %, giving: ~ 2 ν Sd (1) Following these arguments, Spalart et al suggested to replace d with a new length d % given by: d% = min( d, C DES ) (2) where = max( x, y, z) is the computational mesh size. This modification produces a single hybrid model that acts as the original SA one in the boundary layer near the wall and as a subgrid scale (LES) model outside of it. The mesh size implicitly controls the switch between RANS modeling and LES. The smooth transition region between RANS and LES is not clearly localized and so-called grey-zone by Spalart. Far from the wall, the DES model is formally similar to the Smagorinsky subgrid-scale model. As a matter of fact, for an isotropic and homogeneous turbulence, the left hand side as well as the diffusion term cancel out in equation (14), giving: 2 Cb 1 2 ν % t = CDES S % C (3) w with 0.65 DES C =. This expression for the eddy viscosity is close to the Smagorinsky subgrid scale model: ν Smagorinsky = C { s c S% (4) 3

4 where C s =0.18 is the Smagorinsky constant and c the characteristic length of the cell. In fact, DES can be considered as an LES with a classical wall function. Concerning the treatment of the so-called grey-zone, initially DES was a non-zonal approach. Furthermore, one should notice that DES tends towards LES and even DNS when the grid size is decreased since the destruction term tends to infinity and µ t 0. Consequently, as suggested by Deck 13, we chose to force the grey-zone to stay out of the boundary layer of the attached flow. This modification has two consequences. At first, the boundary layer is fully solved with the RANS approach, and this is important because the boundary layer quantities modify the development of the wake. This modification does not prevent the formation of coherent structures in the LES region because the shear layer quickly develops instabilities responsible for the unsteadiness of the flow. The model becomes zonal but there still is no issue of smoothness between the RANS and the LES region. This approach is called Zonal DES or ZDES, RANS and DES domains are selected individually. The ZDES approach is well adapted to treat free shear flows 13 and has been adopted for the present work. C. Computational Grid The design of a DES grid is of first importance because a bad mesh can lead to unphysical results. The scale of the meshed geometry is the experimental one. Preliminary RANS calculations, not presented in this paper have been taken into account to design the DES mesh in terms of estimation of boundary layers thickness, potential jet core and splaying of the jet. The computational domain used is extended over 20D in the radial direction and over 14D upstream and 30D downstream of the nozzle throat. The upstream extension of the mesh allows to correctly compute the boundary layer on the nacelle with the RANS approach. Boundary layers inside the nozzle and along the external fairing are descretized with 20 points placing the first point at y+=0.6 in wall units at the nozzle lip and y+=0.9 on the nacelle. As the mesh is structured, the refinement of the boundary layers propagates in the jet and results in an excessive resolution in the radial direction. The generating line of the mesh just after the nozzle exit has been deviated with respect to the splaying of the jet. In the downstream direction, the mesh has been built as square as possible during a length of 16 diameters in order to resolve the scales of the mixing layers and of the fully developed jet most accurately. After 16 diameters, the mesh is stretched to the non reflective boundary condition at the outlet in order to dissipate spurious reflecting pressure waves. In the azimuthal direction, 128 points have been used in order to obtain nearly cubic cells in the jet. The jet core is discretized by means of a O-H block topology to properly capture the resolved scale in the jet. Finally, the grid used for the present jet contains n r n n z = = points. (a) Figure 3. General 2D view of the mesh around the afterbody(b), zoom on the blocking near the exhaust area. (b) 4

5 Figure 4. Transverse cross section downstream the exhaust section IV. Results and Discussion A. Computational Description The studied case was computed in two steps. First, a RANS computation was carried out with the Spalart- Allmaras turbulence model. This model is widely used in complex compressible flows, it was also chosen for this work because the DES approach is based on this model. RANS simulation was fully converged and results have been compared to experimental data and DES simulations. The RANS simulation is used to initialize the ZDES calculations. DES computations were performed without artificial excitation. In order to be as close as possible to the experimental configuration, the boundary layer profile measured at ONERA CEPRA19 has been imposed on the nacelle surface in the inflow of the computational domain. This point is of paramount importance to compute the stability of the mixing layer between the far-field flow and the exhaust jet. The turbulent eddies present in the flow and shown in Figure 5 show that the shear layer was able to develop a growing instability leading to a fully developed turbulent jet. This result is very satisfying and comes from the well adapted resolution of the mesh in the jet and from a good simulation of the boundary layers which leads to an unstable mixing layer. Furthermore, the DES zones located inside the nozzle (blocks 1, 2 and 3shown on Figure 3) and on the nacelle (blocks 5 and 6 shown on Figure 3) allow to develop unstationarities before the beginning of the mixing layer development. The development of the boundary layer is preserved by fixing the switch between RANS and LES outside of the boundary layer. The estimation of the boundary layer thickness was obtained by a preliminary RANS computation. Figure 5. Snapshot of isosurface of Q- criterion colored by spanwise vorticity Figure 6. Snapshot of isosurface of temperature B. Instantaneous and time-averaged flow fields The main characteristics of the instantaneous flow field are presented in Figure 5, 6. These figures depict snapshots of isosurface of Q-criterion colored by the spanwise vorticity and isosurface of temperature between primary and secondary flows. The mixing layer between core and fan flows develops fastly. The transition to turbulent jet can be observed inside the common nozzle. The azimuthal vortical structures grow rapidly after the confluent section and are rapidly replaced by three dimensional structures before the exhaust section. No measurement are available in the common nozzle, the prediction of the mixing phenomenon is done by analyzing velocity profiles at the exhaust (see section C) and by evaluating the mixing efficiency of the exhaust system (see section D). The flow developments from transitional shear layers to turbulent jet appear to be close to the exhaust area. The jet seems to develop fastly showing that the flow is well resolved in the region and that the mixing layer is correctly destabilized after the 5

6 junction of the boundary layers. One can notice in Figure 5 the roll-up of azimuthal vortical structures and the transition into three-dimensionnal structures. The development of the mixing layer close to the exhaust area can be observed on Schlieren visualizations shown on Figure 7. Figure 7. Schlieren visualizations of the mixing layers solved by RANS-SA (left) and DES (right) simulations Figure 8. Instantaneous streamwise velocity distribution in the confluent mixing flow for RANS-SA (top) and DES (bottom) simulations 6

7 C.Comparisons with LDV data In this section, a quantitative comparison including turbulent quantities is done with LDV measurements.a comparison of the axial mean velocity distribution along the jet centerline is plotted in Figure 9. As can be observed a much faster decay is found with the RANS-SA simulation. As seen before, the ZDES needs more time to well converge the statistics but the prediction of the potential core is already satisfactory. This good correlation between ZDES and experimental results can be interpreted by a better prediction of the mixing process. This good estimation of mixing process can come from the good prediction of the boundary layers thanks to experimental profile imposed on the input of the computational domain (14). The axial velocity is accurate even if the profile at the exit is slightly different between experiments and simulation. Figure 9. Centerline profile of time-averaged axial velocity. Solid line denotes ZDES, dashed-line RANS-SA and squares measurements In Figure 10, streamwise averaged velocity is considered and shown at different axial positions. One diameter after the exhaust section (a), ZDES simulation is in remarkable agreement with measurements. It is interesting to remark that the velocity gradients in the mixing layers between core and fan and between mixed flow and stream flow are very well predicted with the ZDES approach, showing the quality of the grid. The good prediction of the shear layer between mixed flow and stream flow is all the better as the experimental boundary layer developing on the nacelle is taken into account in the simulation. With the same grid, the RANS prediction of the gradient is less satisfactory. As seen in Figure 9, velocity is slightly underestimated with ZDES in the wake of the plug (at the axis) in the vicinity of the exhaust. Interaction between the recirculating region located immediately downstream of the plug and the mixed flow present in the common nozzle is not well predicted. Far from the exhaust (Figure 10 (b) and (c)), the prediction of shear layer with ZDES remains satisfactory. The development of mixing layers between core and fan flows and between fan and free stream flows far from the exhaust, which can be seen on Schlieren visualization in figure 7, is correctly predicted. Indeed, velocity gradients in these mixing layers match the experimental data well as shown in figure 10 (b) and (c). One can notice that the axial evolution of these mixing layers is correctly modeled up to 10 diameters. 7

8 (a) x/d = 1 (b) x/d = 2 (c) x/d = 4 (d) x/d = 10 Figure 10. Radial profiles of predicted and measured velocity. See also legend to Figure 9 The Reynolds stresses u v are presented in Figure 11 at the same locations into the jet. The profiles have been adimensioned by their maximal value and staggered according to their axial location. Positions of the peaks in shear stresses are well localized near the exhaust. At the two first sections, shear stresses are overestimated near the axis in the wake of the plug. Elsewhere, experimental values and ZDES results are in good agreement. In particular, regions of development of mixing layers on which a particular attention has been paid during meshing step are well simulated. 8

9 Figure 11. Radial profiles of predicted and measured uv correlations. The profiles have been staggered according to their axial location. See also legend to Figure 9 D.Mixing efficiency A key point of mixed flow exhaust system is the mixing efficiency which allows the thrust augmentation and the exhaust velocity reduction which results in lower jet noise. A comparison of mixing efficiencies predicted by RANS-SA simulation, Z-DES simulation and measurements is presented in Figure 12. Mixing efficiency obtained with ZDES simulation is presented in terms of minimum, mean, maximal and rms value. The range of variations of mixing efficiency obtained by DES is in good agreement with the experimental estimation. This shows that DES well simulate complex phenomena in the common nozzle like mixing and thermal effects. Figure 12. Comparison of mixing efficiency between experiment, RANS-SA and ZDES calculations This result, correlated with more local results on velocity fields or Reynolds stresses previously seen, is very satisfactory as it puts forward the sensitivity of the ZDES approach to simulate the developing flows in mixed air flow nozzles. The contribution compared to the RANS approach is undeniable, enabling to solve the flow in a mixer equipped nozzle as precisely as a confluent flow nozzle. V. Conclusion The numerical simulation of the unsteady flow in a mixed flow exhaust system is a problem of outstanding importance but is very difficult and challenging case for DES. The refined simulation of different scales located in flow areas such as boundary layers, internal and external mixing layers and the fully developed jet allow a good prediction ofvelocityand turbulence fields in the jet and estimating mixing in the nozzle with a good precision. The RANS approach does not allow capturing very fine effects of geometry on the mixing phenomenon. The results gathered using DES seem to indicate that this technique will enable a refined qualification of mixing characteristics for mixer equipped nozzles. The presented work is seen as an essential step to advance the DES method to a long duct mixed flow nozzle that will aim at assessing the mixing effects on performances of a lobed mixed nozzle. In this paper, it is clearly demonstrated that a realistic industrial exhaust system can be simulated with a high fidelity method like DES. SNECMA owns experimental data on lobed mixed flow nozzle, the next step is to simulate experimental cases with DES method and understand the mixing process to even further improve the performances of mixed flow exhaust 9

10 systems. Furthermore, the interest of DES for such complex configuration is that it allows a detail prediction of turbulent field needed for the numerical evaluation of complex exhaust jet noise. VI. Acknowledgments The authors wish to express their thanks to Olivier Piccin from ONERA CEPRa19 for the boundary layer data. Thanks are expressed to Vincent Brunet and Julien Dandois from ONERA and to Guillaume Bodard from the acoustics department of SNECMA for fruitfuldiscussions. VII. References 1 Paynter G. C and Birch S. C, An experimental and Numerical Study of the 3-D Mixing Flows of a Turbofan Engine Exhaust System, 15 th Aerospace Sciences Meeting, AIAA , Los Angeles, CA., Elliot J. K, Manning Y. J, Qiu Y. J, Greitzer E. M, Tan C. S, and Tillman T. G, Computational and Experimental Studies of Flow in Multi-Lobed Forced Mixers, 28 th AIAA/SAE/ASME Joint Propulsion Conference, Nashville, TN., Hu H, Kobayashi T, Saga T and Taniguchi N, PIV and LIF Measurements on the Lobed Jet Mixing Flows, Experiments in Fluids, Vol. 29, No. 7, 2000, pp. 141, Strelets M, Detached Eddy Simulation of Massively Separated Flows, AIAA Paper , 39 th AIAA Aerospace Sciences Meeting and Exhibit (Reno, NV, USA), Spalart P R, Jou W H, Strelets and Allmaras S R, Comments on the feasibility of LES for wings on a hybrid RANS/LES approach, Proc. 1 st AFSOR Int. Conf. On DNS/LES (Ruston), pp137-47, Chauvet N, Deck S, Jacquin L, Numerical Study of Mixing Enhancement in a supersonic Round Jet, AIAA Journal, Vol. 45, No. 7, 2007, pp. 1675, Cambier L. and Gazaix M., elsa: an efficient object-oriented solution to CFD complexity, 40 th AIAA Aerospace Science Meeting and Exhibit (Reno, NV, USA), Péchier M., Guillen P. and Caysac R., Magnus Effect over Finned Projectiles, Journal of Spacecraft and Rockets, Vol 38, No. 4, 2001, pp Mary I. and Sagaut P., Large eddy simulation of flow around an airfoil near stall, AIAA Journal, Vol. 36, No., 2002, pp Szydlowski J., Costes M., Simulation of Flow Around a NACA0015Airfoil for Static and Dynamic Stall Configurations using RANS and DES, 4th Decennial Specialist s Conference on Aeromechanics, American Helicopter Society (San Francisco, CA, USA), V. Brunet V. and Deck S., Zonal Detached Eddy Simulation of a Civil Aircraft Engine jet Installation,3 rd Symposium on Hybrid RANS/LES Methods (Gdansk, Poland), Chauvet, N., Deck, S., and Jacquin, L., Numerical Study of the Mixing Enhancement in a Supersonic Round Jet, AIAA Journal, Vol. 45, No. 7, 2007, pp Deck S., Zonal Detached Eddy Simulation of the Flow Around a High-Lift Configuration, AIAA Journal, Vol. 43, No. 11, 2005, pp Vuillot F., Lupoglazoff N., Huet M., Effect of Chevrons on Double Stream Jet Noise from Hybrid CAA Computations, 49 th AIAA Aerospace Sciences Meeting, Orlando, 4-7 jan