Jet Noise Analysis of a Mixed Turbofan Engine

Jet Noise Analysis of a Mixed Turbofan Engine Jens TRÜMNER 1 ; Christian MUNDT 2 1,2 Institute for Thermodynamics, UniBw München, Germany ABSTRACT Due to constantly increasing flight traffic the aircraft industry is faced with major challenges. Essentially these are reduction of fuel consumption and noise emission. The latter plays an outstanding role in the vicinity of airports where residents are subjected to increased noise disturbance. Strict regulations protect these citizens and force airlines to decrease the noise emission of their fleet to stay cost efficient. Noise is generated by diverse mechanisms at several parts of the aircraft. During take-off jet noise is the most important source since the engines operate at maximum thrust condition. The development of turbofan engines drastically reduced jet velocities and thus sound emission. A further improvement could be achieved by adding forced mixers and expanding both, bypass and core flow through a common nozzle. These mixers increase the energy transport from hot to cold flow and thereby further decrease the maximum jet velocity. In this work such a mixer is aeroacoustically studied using a hybrid approach to determine the noise level at distant observer points. Keywords: Jet noise, DES, Ffowcs-Williams & Hawkings Analogy 1. INTRODUCTION With the development of civil jet engines in the early 50 th the importance of aerodynamically generated noise became obvious. The work of Lighthill(1,2) laid the foundation for a new field of research known as aeroacoustics. Lighthill derived an exact formulation resembling wave equations from classical acoustical problems with a source term depending on the flow field. From these findings he could show that the sound intensity scales with the 8 th power of the jet velocity. Lighthill's analogy was later extended to shear flows by Lilley(3), solid objects in the source region by Curle(4) and objects in motion by Ffowcs-Williams and Hawkings (FW-H)(5). Initially acoustic analogies helped to better understand the fundamental mechanisms of sound generation while engineering problems were investigated experimentally. With increasing computational resources it became possible to numerically integrate the wave equation with its sources and thereby determine the sound pressure level (SPL) at arbitrary observer points. Experiments by Seiner et al.(6) show that noise generation is not only determined by the jet velocity, but also by temperature gradients. Lighthill's 8 th -power law fails on hot jets because he neglected the dipole term for density fluctuations. Tam et al.(7) proved analytically that temperature gradients also increase the instability of Kelvin-Helmholtz waves and thus the growth of turbulent shear layers. The latter finding does not directly affect the source terms in acoustic analogies but leads to an under prediction of Reynolds stresses in most turbulence models and therefore indirectly of Lighthill's stress tensor. To determine the noise level of aircraft engine jets at certain observer locations different approaches are used. Empirical and semi-empirical models such as ISVR/Purdue by Tester et al.(8) are very well validated with scale and full-scale exhaust systems. Theoretically one could directly compute the transient jet and the wave propagation to the observer in a single simulation. However, this would lead to a huge computational domain and by far exceed arguable calculating capacity. Even a transient simulation of a domain which only covers the free jet is not practicable today. Therefore different alternatives have been developed. Tam et al.(9) proposed an adjoint approach to determine the spectral density of the sound pressure field 1 jens.truemner@unibw.de 2 christian.mundt@unibw.de 760

at a certain observer point. This model directly processes mean flow and turbulence quantities from steady RANS simulations which drastically reduces the computational cost for the flow field simulation. They extended the model to hot jets and achieved very good agreements with experimental data. Ewert(10) formulated a model to synthesize an unsteady pressure field from steady RANS data. In a second step the linearized Euler equations are solved to obtain the unsteady pressure distribution on a surface surrounding the source region. This surface can then be processed by a FW-H solver to calculate the SPL at an observer s location. A considerable more complex approach is to determine the unsteady pressure field from transient flow simulations. In high Reynolds number flows occurring in jet engines this can be done by unsteady RANS or detached eddy simulations (DES). Traub et al.(11) could reproduce the tendencies of the ISVR/Purdue model by using a classical DES in combination with a FW-H surface. In this work the stress blended eddy simulation (SBES) by Menter(12) was used to calculate the unsteady flow field of a mixed nozzle. Afterwards the noise level at different observer points was determined using acoustic analogies. 2. NUMERCAL MODEL 2.1 Flow Simulation 2.1.1 Flow Solver The commercial CFD code ANSYS Fluent was utilized in this study. To account for compressibility effects a pressure-based algorithm solves the Favre averaged Navier Stokes equations in a coupled manner. An implicit second order time discretization with a time step of 2*10-6 s was applied. Likewise spatial discretization of the flow equations was second order. Heat capacity was set to 7J/kgK and the Sutherland law defines the viscosity as a function of the temperature. 2.1.2 Turbulence Model As mentioned in the introduction the SBES model was used for turbulence modelling. This formulation explicitly switches between a RANS and a LES model, whereas classical DES approaches increase the turbulent dissipation of existing RANS models depending on the local cell size. The effective eddy viscosity is calculated using a shielding function f s : μ t SBES = f s μ t RANS + (1 f s ) μ t LES. (1) In this work the k-ω-sst model(13) was applied in wall near and the WALE model(14) in bulk regions. Thereby the free jet is completely covered by the LES model. 2.1.3 Mesh A block-structured mesh was created in ANSYS ICEM-CFD. An attempt was made to create wall near cells with y + =1 to properly resolve the boundary layer. Due to high Reynolds numbers this led to very high aspect ratios, so that in the final mesh y + <=3. The LES region was created to fulfill the following requirement: max 0.1 ( k3 2 ε ) RANS. (2) Since this leads to a very high grid resolution the computational domain had to be drastically diminish to limit computational costs. This was achieved in two ways. First periodic boundary conditions were applied. For the considered geometry this reduces the amount of cells by a factor of 14-1. Second the free jet was only simulated two nozzle diameters downstream of the nozzle exit. The shortcomings of these simplifications will be discussed later on. 2.1.4 Boundary Conditions In this work a cruise operation point at Ma=0.8 was studied. Non-reflecting pressure inlet conditions with turbulence profiles from preliminary 2D simulations were employed. Non-reflecting versions were also used for far field and outlet boundaries. All walls were adiabatic. 761

2.2 Acoustic Analysis 2.2.1 Ffowcs-Williams & Hawkings Method Formula (3) represents the differential form of the Ffowcs-Williams & Hawkings equation with a control surface at rest. As mentioned in the introduction it consists of a part describing the wave propagation (LHS) and source terms depending on the transient flow field (RHS). The function f(x, y,z) is less than zero in the source region, zero on the control surface and greater than zero in the exterior flow. H(f) and δ(f) are Heaviside and Dirac functions. p is the sound pressure, a 0 is the speed of sound in the far field, T ij and P ij are Lighthill s and compressive stress tensor, n i is the unit normal vector pointing toward the exterior region, ρ is density and u i and u n are velocity and control surface normal velocity. 1 2 p 2 a 0 t 2 2 p = 2 {T x i x ij H(f)} {[P j x ij n j + ρu i u n ]δ(f)} + i t {[ρu n]δ(f)} (3) This inhomogeneous wave equation can be integrated by means of the retarded Green s function. Thereby the first term results in a volume integral over the Lighthill stress tensor and represents quadrupole sources. This part corresponds to the source in Lighthill's original formulation. The second and third term contain surface integrals and represent dipole and monopole sources on a control surface. If the control surface surrounds all volume sources, the first term drops due to the Heaviside function and equation (3) needs only to be integrated over the control surface. The latter is depicted in Figure 1. Figure 1: Nozzle with FW-H surface 2.2.2 Far Field Noise Analysis As for the flow calculation a jet parallel free flow at Ma=0.8 was assumed. The pressure distribution on the FW-H surface was recorded at every 10 th time-step for 0.03s. According to the Nyquist theorem this gives a maximum frequency of 25kHz to be found. The Fast Fourier Transform was then performed using Hamming windowing with a bandwidth of 125Hz. 12 fixed observer locations were evaluated in the x-z plane as shown in Figure 2. In this study only the FW-H-surface from Figure 1 instead of a 360 surface was used which leads to a reduction of the SPL. Figure 2: Observer locations 762

3. Results 3.1 Flow Field Since the RANS model only operates in a thin wall attached region, a very quick transition to turbulent structures is predicted by the SBES model. In Figure 3 this becomes obvious at the high temperature surface (red) starting on the lower side of the mixer. Small Kelvin-Helmholtz instabilities occur close to the mixer s trailing edge and turn into larger turbulent structures soon. This makes the exhaust jet fully turbulent at a very early stage and therefore has an important influence on the fine scale turbulence noise sources. Figure 3: Temperature on iso-vorticity surface (ω =6000s -1 ) One further observation in Figure 3 is a diminishment of turbulent structures in the middle region. This follows from the assumption of periodicity which forces resolved turbulence to be zero on the axis of rotation and is therefore non-physical. On the one hand this area represents only a small fraction of the total mass flow, on the other hand it contains the highest temperatures and thus velocities, as it rarely comes in touch with the cold bypass flow. These effects were studied in detail in (15). Another problem becomes obvious in Figure 4 looking at an instantaneous pressure field on the outlet boundary. A short-wave pattern with relatively high amplitudes is visible. These structures developed after a longer simulation time and reached even higher amplitudes inside the nozzle. Since no physical explanation could be found, they are assumed to be resonances artificially introduced by the periodic boundaries. With a wave length of approximately λ 2cm and a speed of sound of a 0 300m/s they appear at a frequency of f 15kHz in the noise spectra. Figure 4: Pressure pattern on outlet boundary 763

Sound Pressure Level [db] Sound Pressure Level [db] Sound Pressure Level [db] INTER-NOISE 2016 3.2 Acoustic During the evaluation of the far field noise spectra two problems identifiable in Figure 5 became obvious. The first one corresponds to the pressure patterns observed in the flow field analysis. In the noise spectrum they create an increased SPL between 8kHz and 25kHz with a maximum at about 15kHz. Although these frequencies are usually neglected since they are strongly damped by the atmosphere, it is a difficult task to determine where their sphere ends and if other resonances exist which influence the low-frequency part of the spectrum. The second problem concerns the Fast Fourier Transformation where the setup, in particular the window size, had a distinct influence on the noise spectrum. In Figure 5 two different window sizes are compared. The shift becomes apparent between 1kHz and 2kHz where a smaller window size (Hz) predicts the local minimum and the following local maximum at about 200Hz higher in comparison to a larger window size. The same effect was observed with the Hann window function. 0 00 Figure 5: Comparison of FFT window size As stated in the previous paragraph the main focus in jet noise analysis is usually on lower frequencies. In this work the spectra up to 2kHz are discussed. In Figure 6 and Figure 7 each graph corresponds to one angle of φ with three distances respectively. In Figure 6 on the left side the spectra for φ=30 show relative low SPLs. A local minimum is located at 1kHz followed by two weak maxima at 1.1kHz and 1.8kHz. As the FW-H-surface is inclined itself, the effective angle is very acute in this case, which explains the low noise level. For φ=60 in the low-frequency region all values move up by about 9dB. Since the shifting reduces towards higher frequencies, steeper gradients arise. Especially for the 15m-curve the afore mentioned local maxima become more distinct and enclose a local minimum at 1.5kHz. 30deg_15m 30deg_50m 30deg_m 0 Figure 6: Noise spectra at 30 and 60 60deg_50m_125Hz 60deg_50m_Hz 60deg_15m 60deg_50m 60deg_m 0 764

Sound Pressure Level [db] Sound Pressure Level [db] INTER-NOISE 2016 Looking at a observer angle the Sound Pressure Level is again shifted up by about 8dB at low frequencies. The gradients also become steeper than those of the 60 cases and form a very concise minimum at 1kHz. The absolute values at this point are even lower than those in Figure 6, whereas the following local maximum at 1.2kHz is higher and therefore appears much more distinct. Moving upstream of the nozzle exit to the locations all maxima only slightly increase. The lowest local maxima become more apparent and the minimum at 1kHz moves up for the 50m and m positions. deg_15m deg_50m deg_m deg_15m deg_50m deg_m 0 0 Figure 7: Noise spectra at and 4. Conclusion The purpose of this work was the buildup of a numerical model for the investigation of the far field noise level caused by the exhaust jet of a mixed turbofan engine. The main focus was on a qualitative determination of important influencing variables and not on the precise definition of noise levels for a specific engine at a relevant condition. A hybrid model was used to determine the transient pressure field of the exhaust jet and to evaluate the noise level at distant observer points. The application of the SBES model allowed for high resolved turbulent structures on the one hand but on the other hand determined a very limited computational domain in size due to high requirements on the grid resolution. These limitations have several shortcomings. First only two nozzle diameters downstream the nozzle exit were regarded, whereas Neifeld et al.(16) found approximately 30 nozzle diameters to be sufficient for far field noise predictions. Secondly the assumption of periodicity has three negative effects, namely the creation of unphysical pressure patterns, decreasing eddy size towards the axis of rotation and a FW-H-surface covering only 360 /14=25.7 of the jet. The last problem can be solved by rebuilding a 360 surface from the periodic part, which in turn could introduce unwanted interference effects. The far field analysis showed the expected tendencies concerning spectral distributions and noise levels. It became apparent that acute angles to the control surface lead to lower SPLs at distant points. This can also be an advantage as only a certain angle of the afore mentioned 360 surface contributes to the noise at an observer s point. In a next step the domain will be stepwise enlarged circumferentially to better understand the mechanisms behind the unwanted pressure patterns and to find a sufficient sector for the FW-H analysis. An examination of further operational conditions such as take-off and side-line is also planned. Concerning the FFT additional investigations are necessary to better understand the effect of window functions, window size and requirements on the time period to be recorded. 765

ACKNOWLEDGEMENTS This work was conducted within the scope of a Munich Aerospace scholarship. Furthermore the authors like to thank the MTU Aero Engines AG and Dr. Ramm for the technical support. REFERENCES 1. Lighthill MJ. On Sound Generated Aerodynamically I. General Theory. 2. Lighthill MJ. On Sound Generated Aerodynamically II. Turbulence as a Source of Sound. 3. Lilley GM. The generation and radiation of supersonic jet noise. IV. Theory of turbulence generated jet noise, noise radiation from upstream sources and combustion noise. US Air Force Aero Propuls Lab. 1972;TR-72-53. 4. Curle N. The influence of solid boundaries upon aerodynamic sound. Proc R Soc Lond. 1955;231:505 14. 5. Ffowcs Williams JE, Hawkings DL. Sound Generation by Turbulence and Surfaces in Arbitrary Motion. Phil Trans R Soc Lond A. 1969;264:321 42. 6. Seiner JM, Ponton MK, Jansen BJ, Lagen NT. The Effects of Temperature on Supersonic Jet Noise Emission. In: 14th DGLR/AIAA Aero-acoustics Conference. 1992. 7. Tam CKW, Ganesan A. Modified k-epsilon Turbulence Model for Calculating Hot Jet Mean Flows and Noise. AIAA J. 2004;42(1):26 34. 8. Tester B, Fisher M, Dalton W. A Contribution to the Understanding and Prediction of Jet Noise Generation in Forced Mixers. In: 10th AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics; 2004. 9. Tam CKW, Auriault L. Jet Mixing Noise from Fine-Scale Turbulence. AIAA J. 1999;37(2):145 53. 10. Ewert R. RPM-the fast Random Particle-Mesh method to realize unsteady turbulent sound sources and velocity fields for CAA applications. In: 13th AIAA/CEAS Aeroacoustics Conference. 2007. 11. Traub P, Broszat D, Röber T, Wellner J. Exhaust (broadband) noise simulation of a realistic turbofan forced mixer by using a CFD/CAA-approach. 34th AIAA Aeroacoustics Conf. 12. Menter FR. Best Practice: Scale-Resolving Simulations in Ansys CFD. 2015. 13. Menter FR. Improved two-equation k-omega turbulence models for aerodynamic flows. NASA Tech Memo. 1992; 14. Nicoud F, Ducros F. Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor. Flow Turbul Combust. 1999;62:183 200. 15. Truemner J, Mundt C. Advanced Modelling of Turbulent Heat Flux in Mixed Turbofan Engines. In: accepted on AIAA Aviation. 2016. 16. Neifeld A, Ewert R. Jet mixing noise from single stream jets using stochastic source modeling. In: 17th AIAA/CEAS Aeroacoustics conference. 2011. 766