14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference) 5-7 May 28, Vancouver, British Columbia Canada AIAA 28-286 Over-expansion Effects on Mach. Supersonic Jet Acoustics Taku Nonomura University of Tokyo, Sagamihara, Kanagawa, 229-851, Japan Kozo Fujii Institute of Space and Astronautical Science, JAXA, Sagamihara, Kanagawa, 229-851, Japan For the prediction of acoustic waves from rocket plume, over-expansion effects on Mach. supersonic jet acoustics are investigated with monotonically integrated large eddy simulation. In this study, ideally-expanded Mach number and designed Mach number are used to express the jet conditions. Three designed Mach number.,.5 and 4. are chosen, while ideally-expanded Mach number is constant.. Reynolds number is 1 and coldjet condition is adopted to reduce computational costs. With regard to computation, the seventh order weighted compact non-linear scheme and the tenth order compact scheme are used for solving the jet-flow and near fields acoustics propagation, respectively. Computational results of Mach wave emissions of these three conditions are almost same. This result corresponds to that of relatively low Mach number supersonic which is reported by Tam(AIAA paper 25-298). Present results show that it can be applied to high Mach number supersonic jet. For the the prediction of acoustic waves from rocket plume, this results imply that rocket parameters could be reduced. D nozzle diamitar f frequency M local Mach number p pressure p effective pressure fluctuation St Strouhal number SP L sound pressure level r cylinderical coordinate T temperatrure u x-direction velocity α f coefficiet of filter µ coefficiet of viscosity ρ density Subscript J ideally-expanded condition D nozzle design (exit) condition c chamber condition ref reference value ambient condition Nomenclature Postdoctoral Fellow, Department of Aeronautics and Astronautics, AIAA Member. Professor, Department of Space Transportaion Devision, AIAA Fellow. 1 of 11 Copyright 28 by T. Nonomura and K. Fujii. Published by American the American Institute Institute of ofaeronautics and and Astronautics, Astronautics Inc., with permission.
I. Introduction It is known that a rocket plume emits very strong acoustic waves, mainly Mach waves, which may be harmful to pay-loads of the rocket such as artificial satellites because they are very light and fragile. Thus it is necessary to predict acoustic waves accurately and reduce its level. In order to predict a noise from rocket plume, NASA-SP872 1 model or the modified NASA-SP872 model,? which are semi-empirical methods based on experimental and the actual launch data, have been used worldwide. However, it is known that there is much difference between actual noise and predicted one in Japanese rocket launching, because the detailed mechanisms about noise-emission, noise-directivity and noise-source have not been well-understood. This seems to be due to the difficulty of handling the past experimental data. Therefore practical numerical simulations of rocket launching has been carried out in JAXA s engineering digital innovation center(jedi)/jaxa. 2, In their study, many important data of flow-fields and acousticfields of launching are obtained and discussed. However their simulations are forced to be obtained by the conventional schemes and a limited number of grid points because they need to investigate the effects of various parameters and compute the complex configuration to support JAXA s project such as designing the real launching site. Parallel to the practical analysis in JEDI center, basic characteristics of acoustic from a rocket plume should be investigated, and then a new prediction method based on more accurate engineering models should be constructed. In this study, large-eddy-simulation(les)-like methodology, which is recently developed and shows good results, 4 is applied to clarify the basic acoustic wave emission and propagation, from a simple supersonic free jet. Computation were carried out with the high order difference scheme and fine grid resolution. So far, the computational code are validated and basic Mach number effects were investigated. The results show many information of ideally-expanded jets. 5 Now we should set the parameters of free supersonic jets to understand the paramter effects, such as Mach number effects. However there are many ways to choose parameters to determine jet condition. It is important to choose suitable parameters because the model could be simplified. In these parameters, Mach number is important as discussed below. Recently Tam reported that spectra of acoustics of two different M D jet, while M J is constant, are almost same without shock associated noises which are only emitted in upstream side in the case of underor over-expanded jets, 6 where M D and M J are design Mach number and ideally-expanded Mach number defined in the next section, respectively. Our target of the jet acoustics is mainly Mach waves which are low frequency and strong in downstream side because they are critical for the pay-load of rockets. Therefore, from a viewpoint of the prediction of acoustics of rocket plume, M J seems to be effective, but M D does not. However, Tam s results are verified in only relatively low Mach number (2.) jet. It has not been discussed whether this idea could be applied to high Mach number rocket plumes. Besides, Varnier 7 proposed to use M J instead of M D to determine potential core length and Strouhal number in the NASA-P872 prediction method of high Mach number (M J.) jet acoustics. That modified method shows better results than original one. Therefore it seems better to use M J instead of M D. However it is not obvious whether this modification is truly suitable or not because the modified model still has many empirical parameters. In this study, Tam s idea is verified through the computation of ideally- and over-expanded relatively high Mach number jet because the rocket plumes condition on ground is usually over-expanded. Three different jet whose M D are.,,5 and 4., while M J is constant., are computed and then flow-fields and acoustic-fields are discussed. II. Jet Parameters and Flow condition Following four parameters are chosen to represent jet-condition; Ideally-expanded Mach number M J, designed Mach number M D, Temperature ratio T R and Reynolds number Re. M J denotes Mach number when chamber gas is ideally-expanded. M D denotes Mach number at nozzle condition which is determined by the ratio of area of throat and nozzle exit. These parameters are calculated with quasi-one-dimensional 2 of 11
isentropic flow equations as follows. M J = u J a J = ( p c p ) γ 1 γ 1 (1) M D = u D a D (2) T R = T j T t () where, Re = ρ JD J u J µ (4) ( ) 1 +.5 (γ 1) M 2 γ+1 4γ 1 D J = J MD 1 +.5 (γ 1) MD 2 D (5) M J In this study, over-expanded effects are investigated with the computation of the ideally-expanded jet and over-expanded jet. Therefore M D is equal to or grater than M J. As noted before, three jets whose designed Mach numbers are.,.5 and 4., while M J is constant., are computed. Re and T R are set to 1, and 1, respectively. Though these conditions are much different from the rocket plume condition, they are chosen to improve computational efficiency. In these conditions, basic characteristics of flow and acoustic fields of the supersonic jet can be understood, except for the quantitative discussion, such as the quantity of the potential core length. 8 These cases are named as MJ(M J 1)MD(M D 1) like MJMD which is the ideally-expanded jet. More information of these jets are summarized in Table. 1. In addition, St and SP L, which are used in section IV, are defined as follows. St = fd j u j (6) where p ref is defined as follows. SP L = 2 log 1 p ref = 2. 1 5 [P a] 11[P a] p p ref, (7) p (8) Table 1. Jet conditions rho J /rho u J /a p J /p D/D J rho D /rho u D /a p D /p MJMD 2.8 1.79 1. 1. 2.8 1.79 1. MJMD5 2.8 1.79 1. 1.266 1.48 2.92.482 MJMD4 2.8 1.79 1. 1.591.677 2.9.242 III. Numerical Methods Three-dimensional compressible Navier-Stokes equations non-dimensionalized by sound speed of ambient and ideally-expanded condition nozzle diamiter D J are computed. Different computational schemes are used for two regions, jet flow region and acoustic region in computational domain shown in Fig. 1. of 11
With regard to the jet-flow region in Fig. 1, seventh order WCNS is used for advection term. WCNS is a shock caputuring high order scheme which was developed as a combination scheme of WENO 9 and compact schemes 1 by Deng and Zhang. 11 Seventh and ninth order WCNS was developed by Nonomura et al. 12 In the seventh order WCNS, a seventh order upwind WENO-like cell-node to cell-center interpolation and an eighth order explicit cell-center to cell node difference scheme are used. Special treatment for metrics proposed by Nonomura et al is adopted to keep geometric conservation law. 1 In the flux evaluation procedure in the WCNS, simple high-resolution upwind scheme 14 is adopted, which is the robust, high resolution and computationally cheap advection upwind splitting method 15 type flux splitting scheme. With regard to viscose term, the sixth order central difference scheme is used. In the acoustic-wave propagating region shown in Fig. 1, tenth order penta-diagonal compact scheme 1 and tridiagonal tenth order filtering 16 are used to compute the first and second derivatives. The filtering parameter α f is set to.45. In this study MILES 17 approach is adopted with using the upwinding scheme. Therefore any explicit LES sub grid scale models are not used. Recently this MILES approach using WCNS is validated 18, 19 in basic turbulence flows. Third order total variation diminishing Runge-Kutta scheme is used for the time integration. Computational grids are shown in Figs. 2 and. The computational grids are made as axis-symmetric at r >.D J. However, near axis region, in order to get rid of restriction in t due to Courant Fredrich Lewy condition which comes from very small minimum grid spacing of azimuthal direction of axis symmetric type grid, a square type grid is used at r <.25D J (see Fig. ). These two type grid are gradually changed and whole computational grid is divided to seven zones to be suitable to our in-house computational codes. Axial, azimuthal and radial grid points are set to 185, 6 and 224, respectively. Total grid points are almost 12 million. Minimum grid spacing is.d J,.2D J and.1d J for axial, azimuthal and radial direction. For axial direction equal grid spacing is set. For radial direction, maximum grid spacing is.5d J and.1d J in jet-flow region and acoustic-wave propagating region. Although these grid points are not enough for accurate LES, present grid points are enough to resolve low frequency noise emissions as in the past study of high sub-sonic jet noise study in which very high resolution schemes and one million grid points were used. For the outer boundary condition, grid-stretched buffer region 2 is set to non-physical emission or reflection of acoustic waves. For the jet flow boundary, jet-profile is set to top-hat type while 1/7 law for boundary layer is adopted near jet boundary region. The thickness of boundary layer is set to.25d J. This very thin boundary layer easily excites shear layer instability without any numerical disturbances. With regard to the near field computational region, pressure history are stored and computed as the sound pressure level directly. Concerning the spectrum of the sound pressure level, fast Fourier transformation (DFT) is used. Because DFT include much numerical noises, the data are averaged with 12 azimuthal points. In addition, the low cut-off and high cut-off frequencies were investigated in reference. 8 BUFFR-REGION ACOUSTIC-REGION FLOW-REGION D 1D ~1D Figure 1. Computational domain. 4 of 11
Figure 2. Computational grids. Figure. Zoomed computational grids. IV. Results and Discussion First, instantaneous flow-fields of these three jets are shown in Fig. 4. There are no strong shock in the case of MJMD, while shock-cells or Mach disc are observed in the case of MJMD5 and MJMD4. In addition, Mach wave emission of these three jets seems almost same in downstream region, while acoustic wave of over-expanded jets, MJMD5 and MJMD4 seems slightly stronger than ideally-expanded jet MJMD in upstream region. Averaged velocity fields of these three jets are shown in Fig. 5. From Fig. 5, shock-cells or Mach disc, as noted before, are clearly observed. In addition, Fig. 6 shows averaged velocity distribution on axis which is oscillatory in over-expanded cases, while the distribution of ideally-expanded jet does not have any oscillations. It is known that the potential core length has important role on acoustic noise sources position. However it is difficult to determine the potential core length from the data of over-expanded jets because of oscillation of jet velocity on axis. However in Fig. 6 jet velocity of all cases start to decrease around = 12, which shows that potential core length do not change much, at least qualitatively, when only M D changes. Then, overall sound pressure level (OASPL) distribution of these three jets are shown in Fig. 7. Comparing distributions of MJMD5 and MJMD in downstream side, the distribution of MJMD5 resembles very much to what is the one of MJMD slightly moved to the downstream side. The results show that Tam s idea is applicable to high Mach number jet M J =.. This little difference is because of difference of the position where the shear layer oscillation starts. On the other hand, comparing distributions of MJMD and MJMD4 in downstream side, there are little difference of contour lines of over all sound pressure level in Fig. 7, while the level is almost same. For the objective of this research these difference are little enough. Besides, in upstream region, Fig. 7 shows that sound pressure level of over-expanded jets are stronger than that of ideally-expanded jet because of shock associated noise. Finally, sound pressure spectrum at several points are discussed. Positions of measurement point A, B, C 5 of 11
and D are shown in Fig. 8 and table 2. Figure 9 shows narrow band spectra at point A, B, C and D. There are almost no difference among these three cases at the point C and D in downstream region while sound pressure level of over-expanded jet cases, especially MJMD5, are stronger than that of ideally-expanded jets around St=.2 at the point A and B in downstream region. This difference seems to be caused by the existence of the shock acoustics in the case of MJMD5 and MJMD4. However the Strouhal number of the shock acoustics is relatively low compared with Tam s Mach 2. jet results. The reason why the frequency of shock associated noise is lower than that of relatively low Mach number jet experiment is now investigated. However, the objective of this research is to obtain the information of basic acoustic emission. Whichever the reason is a physical or computational one, our results shows that shock is not so effective to the Mach wave emission, while it adds shock associated acoustic wave in the upstream region. Table 2. Location of measurement point A, B, C and D A 1 B 1 1 C 2 1 D 1 Therefore the results show that Tam s idea is also applicable to high Mach number. supersonic jet which is the same as a rocket plume. This knowledge is very important to build a new prediction model because we can reduce one the jet-parameter M D to predict Mach wave emission. V. Conclusion For the prediction of acoustic waves from rocket plume, over-expansion effects on Mach. supersonic jet acoustics are investigated. Three designed Mach number.,.5 and 4. are chosen while ideally-expanded Mach number is constant.. As a results, computational results of Mach wave emissions of these three conditions are almost same. This fact of relatively low Mach number supersonic jet was reported by Tam. Present results shows that it can be applied to high Mach number supersonic jet. For the prediction of acoustic waves from rocket plume, this result implies that rocket parameters could be reduced. With regard to upstream-ward acoustics propagating, there are different among three cases due to the shock associated broadband acoustic waves. Acknowledgments This work is partially financed by the Japan Society for the Promotion of Science (Project 16-1764). The first author would like to appreciate their support. References 1 Eldred, K. M., Acoustic Loads Generated by Propulsion System, SP 872, NASA, 1971. 2 Tsutsumi, S., Shima, E., Takaki, R., and Fujii, K., Generation and Propagation of Pressure Waves from H-IIA Launch Vehicle at Lift-off, AIAA Paper 28-9, 28. Kawai, S., Tsutsumi, S., Takaki, R., and Fujii, K., Computational Aeroacoustics Analysis of Overexpanded Supersonic Jet Impingement on a Flat Plate With/Without Hole, ASME FEDSM 27-2756, 27. 4 Bodony, D. J. and Lele, S. K., Review of the Current Status of Jet Noise Prediction Using Large-Eddy Simulation, AIAA Paper 26-468, 26. 5 Nonomura, T. and Fujii, K., Computational Analysis of Characteristics and Mach Number Effects on Noise Emission from Ideally Expanded Highly Supersonic Free-Jet, ASME FEDSM 27-759, 27. 6 Tam, C. K., Dimensional Analysis of Jet Noise Data, AIAA Paper 25-298, 25. 7 Varnier, J., Experimental Study and Simulation of Rocket Engine Freejet Noise, AIAA Journal, Vol. 9, No. 1, 21, pp. 1851 1859. 8 Nonomura, T., Characteristics of Acoustic Waves Generated by Flow Instability of Supersonic Jets, Ph.D. thesis, University of Tokyo, 28. 6 of 11
9 Jiang, G.-S. and Shu, C.-W., Efficient implementation of weighted ENO schemes, Journal of Computational Physics, Vol. 126, 1996, pp. 22 228. 1 Lele, S. K., Compact Finite Difference Schemes with Spectral-like Resolution. Journal of Computational Physics, Vol. 1, 1992, pp. 16 42. 11 Deng, X. G. and Zhang, H., Developing High-order Weighted Compact Nonlinear Schemes, Journal of Computational Physics, Vol. 165, 2, pp. 22 44. 12 Nonomura, T., Iizuka, N., and Fujii, K., Increasing Order of Accuracy of Weighted Compact Nonlinear Scheme, AIAA Paper 27-468, 27. 1 Nonomura, T., Iizuka, N., and Fujii, K., Uniform Flow Preserving Property of High Order Upwind Scheme on Generalized Coordinate System, Proceedings of International Conference on Computational Fluid Dynamics, 26. 14 Shima, E. and Jounouchi, T., Role of CFD in Aeronautical Engineering (No.14) -AUSM type Upwind Schemes-, Proceedings of the 14th NAL Symposium on Aircraft Computational Aerodynamics, NAL, 1997, pp. 7 12. 15 Liou, M. S. and Steffen, Jr, C., A New Flux Splitting Scheme, Journal of Computational Physics, Vol. 17, 199, pp. 2 9. 16 Gaitonde, D. V. and Visbal, M. R., Further development of a Navier-Stokes solution procedure based on higher-order formulas, AIAA Paper 99-557, 1999. 17 Boris, J. P., Grinstein, F. F., Oran, E., and Kolbe, R. J., New Insights Into Large Eddy Simulation, Fluid Dynamics Research, Vol. 1, 1992, pp. 199 228. 18 Ishiko, K., Ohnishi, N., and Sawada, K., Implicit LES for Two-Dimensional Turbulence Using Shock Capturing Monotone Scheme, AIAA paper 26-7, 26. 19 Ishiko, K., Ohnishi, N., and Sawada, K., Implicit LES of Compressible Turbulent Flow, AIAA Paper 27-92, 27. 2 Colonius, T., Lele, S. K., and Moin, P., Boundary Condition for Direct Computation of Aerodynamics Sound Generation, AIAA Journal, Vol. 1, No. 9, 199, pp. 1574 1582. 7 of 11
1 1 (a) MJMD 1 1 (b) MJMD5 1 1 (c) MJMD4 Figure 4. Instantaneous flow-fields. Velocity fields and pressure fluctuation. For velocity fields, threshold is set to to u J, where color is changed from white to darkblue. For pressure fluctuations, threshold is set to -.1P to.1p, where color is changed from dark red to dark blue via white. 8 of 11
(a) MJMD (b) MJMD5 (c) MJMD4 Figure 5. Avereaged velocity fields. Threshold is set to to U J, where color is changed from red to blue via green. 1.2 1.8 u/uj.6.4.2 MJMD MJMD5 MJMD4 5 1 15 2 x/dj Figure 6. Velocity distribution on axis. 9 of 11
r/d 1 x/d (a) MJMD r/d 1 x/d (b) MJMD5 r/d 1 x/d (c) MJMD4 Figure 7. OASPL distributions. Threshold is set to 1dB to 17dB, every 2dB contour is drawn. 1 A B C D r 15 x Figure 8. Measurement points of sound pressure level. 1 of 11
SPL+log1(a1/DJ f)[db] SPL+log1(a1/DJ f)[db] SPL+log1(a1/DJ f)[db] SPL+log1(a1/DJ f)[db] 17 16 15 MJMD MJMD5 MJMD4 17 16 15 MJMD MJMD5 MJMD4 14 14 1 1 12 12 11 11 1.1.1 1 1 St 1.1.1 1 1 St (a) A (b) B 17 16 15 MJMD MJMD5 MJMD4 17 16 15 MJMD MJMD5 MJMD4 14 14 1 1 12 12 11 11 1.1.1 1 1 St 1.1.1 1 1 St (c) C (d) D Figure 9. Spectrum of sound pressure level at A, B, C and D. Shaded region denotes the out of the cut-off-frequency. 8 11 of 11