## Final Report Summary - ADOCHA (Acoustic Design Of High-lift Architectures)

Executive Summary:

Regulation of the sound production of aircraft is becoming stricter, in part due to an increase in the noise generated due to the rising numbers and size of aircraft. As a result identification and reduction of the major sources of sound, particularly in the take-off and landing phases when the aircraft is close to population centres, is paramount. Thus, aircraft noise of modern passenger planes during take-off and landing constitute an increasingly sensitive topic due to their impact on residential areas in the neighbourhood.

Fast and reliable tools for the prediction of the self-noise generated by high-lift configurations are therefore highly desirable in order to integrate noise studies of future regional aircraft into the early design stages. To this end the ADOCHA software suite has been delivered by the Aircraft Research Association (ARA), located in Bedford, UK and the Institute of Sound and Vibration Research (ISVR), University of Southampton, UK, to Italian Aerospace Research Center (CIRA). The software relies on a Boundary Element Method (BEM) and a semi-empirical statistical acoustic model by Agarwal to calculate the self-noise characteristics of high-lift configurations in a fast and robust manner and allows multi-processor runs via MPI. It accepts two- or three-dimensional multi-component geometries in the form of BEM surface meshes and an accompanying steady k-w RANS flow solution. The BEM is employed to propagate the noise into the farfield in the presence of a constant mean flow and the aerodynamic body in question. This frequency domain based method computes the acoustic root means square pressure, its spectral density and sound pressure levels (SPL) at arbitrary observer locations.

Project Context and Objectives:

Regulation of the sound production of aircraft is becoming stricter, in part due to an increase in the noise generated due to the rising numbers and size of aircraft. As a result, identification and reduction of the major sources of sound, particularly in the take-off and landing phases when the aircraft is close to population centres, is paramount.

High lift devices, particularly during the landing phase, are a major source of airframe noise. For example, it has been found that the slat overall A-weighted sound pressure level can scale by M to the power of 4.5 where M is the free-stream Mach number . As a result many studies have been and are being undertaken on this subject. These studies have applied a variety of tools, from high fidelity to semi-empirical, to evaluate this problem.

High fidelity approaches use Large Eddy Simulation (LES) to adequately resolve the flow field and feed those results into an Acoustic Perturbation Equation (APE) solver, high –order computational aero-acoustic (CAA) solver or other propagation method to calculate the sound field.

Approaches using LES or Direct Numerical Simulation (DNS) to calculate the flow field have the advantage of sufficiently resolving the scale to capture both the tonal and broadband noise in a single calculation. The disadvantage is that at realistic model scale and Reynolds numbers the calculation domain and computational costs become excessive.

From these high fidelity approaches it has been observed that the acoustic nature of the problem is largely broadband with high frequency tones present. This presents an obstacle for typically Reynolds Averaged Navier Stokes (RANS) approaches as such solvers tend to miss the broadband contribution entirely.

It is required then, if RANS is to be used to solve such configurations, that an additional model be applied to re-introduce the broadband elements. Such models include semi-empirical models, usually derived from a vast data base of experimental data and Stochastic Noise Generation and Radiation (SNGR) models, which can be thought of as an analytical extension to the empirical models. Propagation of the sources generated with such methods can be handled much as for the LES/DNS calculations using approaches such as Acoustic Perturbation Equations and acoustic analogies.

The benefit of the lower fidelity models lies in the increased speed, which makes them more useful in an industrial context. The drawback is a reduction in the accuracy of the results. Consequently these lower fidelity models are more suitable for early design purposes, where an exact solution is not required.

The objective of this project is to identify suitable methods for a fast prediction of broadband airfoil self noise and to develop a tool using these methods which will compute the acoustic levels from a RANS solution.

Project Results:

ADOCHA Suite - Note figures are in the attached ADOCHA_FR_Figures.pdf.

1 CAPABILITIES OF ADOCHA: SPECIFIC CODE FEATURES

Implemented code features of the ADOCHA software are discussed here in terms of its BEM-core, the acoustic method and in terms of general user friendliness. Software quality related topics are summarised also. For illustration purposes a general flow chart of an aero-acoustic analysis by means of ADOCHA is given in Figure 1.

Boundary Element Method (BEM): The BEM analyses 2D or 3D multi-component bodies in a largely generic way that allows serial or multiprocessor runs based on ScaLAPACK through a distributed memory parallelisation. As with all BEM methods it allows for an accurate sound propagation and scattering by means of Green’s functions. Attractive features of BEM-approaches include an analytical treatment of the farfield boundary condition and a direct, meshless projection of the solution on the surface to any point in space, which means that meshing of complex geometries is only required on the body surface and not in the volume. This greatly simplifies the task for the user, as only a surface mesh of the target application, a complex high-lift geometry, has to be provided. Additionally, arbitrary free stream directions can be described in ADOCHA, which enables angle-of-attack studies, for example, without the need to change the mesh. A special analytical treatment of the derivative of Green’s functions removes the need for their numerical calculation, increasing the accuracy and robustness of the code. Finally, the well-known issue of the ’spurious frequencies’, inherent to the BEM-approach is avoided through an implementation of the CHIEF-methodology (via interior points).

Acoustic model: The employed acoustic model for the noise generation based on the provided RANS flow solution is a recent broadband noise model by Agarwal. This fast statistical model operates directly in the frequency domain where all calculations are performed, and exhibits three semi-empirical model parameters that have to be calibrated to an available base case. Four filter functions (arbitrary spatial windows of interest, minimum and maximum cut-off values of the analysed turbulent quantities, a filter acting on relative source strength and a prescribed minimal distance from the body wall) allow the user to concentrate on the most relevant sound sources within the RANS solution, thus speeding up the overall turn-around time. Possible outputs are Green’s functions, spectral density, sound pressure level (SPL) and overall sound pressure levels.

User friendliness: ADOCHA is flexible with respect to acoustic input meshes and accepts data in either Tecplot, AVS(UCD) or GRD format. Once read in, an automatic orientation check is performed which re-orientates input meshes if the surface normal is not pointing outwards as expected by ADOCHA. Likewise, the output formats that can be visualised by Tecplot or gnuplot are flexible: frequency information can be written as a single or multi-file and with or without directivity information. In particular, a fast restart capability makes parameter tuning efficient and easy. Prior to the calculations, an automatic analysis of acoustic resolution per component and frequency is performed that informs the user whether the mesh resolution was sufficient. Finally, selected validation cases are provided with the software as tutorial test cases.

2 SOFTWARE QUALITY AND PARALLELISATION

To ensure platform independence the ADOCHA source code has been developed under two different compilers (gfortran-4.3.2 and Intel fortran v11.1) to a strict Fortran 95 standard without utilising compiler specific extensions. The software has been successfully installed and run on different LINUX platforms at ARA, ISVR and CIRA. The distributed, high-performance memory parallelisation of the ADOCHA code relies on the opensource library ScaLAPACK1, the scalable version of the well-known linear algebra package LAPACK.

All tests were conducted with a version of ADOCHA that was linked to scaLAPACK- 1.8.0 which in turn requires BLACS and the MPI-implementation MPICH2-1.2.1.

The ADOCHA software is based on an extendable structure organised in modules. When compiled, ADOCHA will automatically build and run extensive unit tests checking the correct functioning of the compiled module subroutines against functional tests, analytical solutions or otherwise trusted results.

3 TESTING AND VALIDATION OF ADOCHA

3.1 Code verification against CIRA’s finite element method OptyδB

A verification of the BEM-module of ADOCHA against results of CIRA’s finite element method (FEM) OptyδB has been performed for two-dimensional and three-dimesional test cases. They predict the scattering of a spherical incident wave emitted from a single source from a cylinder and sphere, respectively, as sketched in Figure 2. For all tests, an acoustic unit source of frequency f in the form of a Diracdelta concentrated at xq was employed and the real and imaginary part of the volume Green’s function G, which corresponds to the complex acoustic disturbance pressure of the resultant acoustic field, evaluated at the given observer positions. As the acoustic model was not utilised, this constitutes a verification of the BEM-module of ADOCHA for stagnant air (M=0,c=340m/s, r =1.225Kg/m3 ). Stagnant air cases represent the only class of test cases where perfect agreement is achievable, as the FEM-method accounts for local changes in the flow velocity while the BEM has to assume a constant mean flow everywhere. To test the Mach number terms, the flow over a thin, flat plate is an appropriate test case, as the velocity difference to the free stream can be expected to be negligible with regard to trailing edge noise.

3.1.1 2D verification: scattering of a point source from a cylinder

The setup detailed in Figure 2 was run for a low and a medium frequency f1 = 31.83 Hz and f2 = 500 Hz with the parameters rbody = 1m, rq = 20m, robs = 4m and 360 observers, resulting in the nondimensionalised parameter k1 r = 0.588 and k2 r = 9.234 based on the wave number k. Figures 3 and 4 show excellent agreement in the total as well as in the scattered field. The latter was obtained from the former by subtracting the incident acoustic field in order to highlight any potential differences just in the reflected part. Within ADOCHA, the cylinder was approximated by 60 linear panels, which results in a panel length of 2π rbody/60 = 0.105m. The corresponding acoustic wavelengths are λf1 = c/f = 11.0m and λf2 = 0.68m respectively, which results in a resolution of about 100 points per wavelength for f1 and 7 points for f2, respectively. Due to the minimal differences between the two codes around the observer angles φ = 0 and φ = 180 degrees both solutions have been recompared to the analytical solution. ADOCHA is able to reproduce the analytical solution exactly.

3.1.2 3D verification: scattering of a point source from a sphere

The setup detailed in figure 2 was run for a frequency f1 = 31 Hz with the parameters rbody = 1m, rq = 20m, robs = 4m and 360 observers. As in the 2D-case, Figure 6 shows excellent agreement in the total as well as in the scattered field. Within ADOCHA the sphere was approximated by 1800 plane panels, which results in an average panel area of 4π rbody/1800 = 0.007m2 which (assuming square panels) gives us a typical length scale of about square root(4π rbody/1800) = 0.084m. Thus, the corresponding acoustic wavelength of λf1 = cf = 11.0m was well resolved with about 130 points per wavelength.

3.2 Validation of multi processor results

Six different geometrical configurations have been considered for a detailed validation with 2001 observers each:

1. A reflecting unit sphere with radius a = 1.0 at the origin. The only point source is located at rq = 2.0 (xq = 2.0 yq = zq = 0) and the observers at robs = 1.5 (xobs = 1.5 sin(υobs)cos(φobs), yobs = 1.5 sin(υobs) sin(φobs), zobs = 0). υobs = 90 degrees and φobs = 0 . . .360 degrees.

2. As in 1. but the observers are now located at robs = 4.0.

3. A reflecting unit sphere with radius a = 1.0 at the origin. The only point source is located at rq =20.0 (xq =20.0 yq =zq =0) and the observers at robs =10.0 (xobs =10.0 sin(υobs)cos(φobs), yobs = 10.0 sin(υobs) sin(φobs), zobs = 0). υobs = 90 degrees and φobs = 0 . . .360 degrees.

4. As in 3. but the observers are now located at robs = 40.0.

5. A reflecting unit circle with radius a = 1.0 at the origin. The only point source is located at rq = 2.0 (xq = 2.0 yq = 0). and the observers at robs = 1000.0 (xobs = 1000.0 cos(φobs), yobs = 1000.0 sin(φobs)). φobs = 0 . . .360 degrees.

6. A reflecting unit circle with radius a = 1.0 at the origin. The only point source is located at rq = 20.0 (xq = 20.0 yq = 0) and the observers at robs = 1000.0 (xobs = 1000.0 cos(φobs), yobs = 1000.0 sin(φobs)). φobs = 0 . . .360 degrees.

A successful grid refinement study and comparison with the analytical solution in 2D and 3D has been carried out and is documented in the user guide that accompanies the release version ADOCHA v1.0 released on 30/11/2010.

Here, due to space restrictions, only the validation of the parallel version is given. To this end, computations in parallel on 2, 3 and 4 processsors have been carried out and a comparison to the serial computation is given for the following configurations for 3D and 2D, respectively:

- Configuration 1

- Configuration 6

Figures 7(a) - 7(d) show no dependency of the results on the number of processsors, all solutions lie on top of each other.

3.3 Validation for high frequency cases

So far all testcases have been performed for low to medium frequencies up to 500Hz. The setup detailed in Figure 2 was run for two high frequencies f1 = 10,000 Hz and f2 = 20,000 Hz with the parameters rbody =1m, rq =2m, robs =4m and 1800 observers, resulting in the non-dimensional parameter k1 r= 0.588 and k2 r = 9.234 based on the wave number k. Figures 8 and 9 show good agreement for the total flow field with the analytical solution. A grid refinement study showed that 120 panels on the body surface were still insufficient, so that 600 panels were utilised for Figure 8. For 20,000Hz this proved to be still insufficient, so that 1200 had been used to obtain Figure 9. This equates to a panel length of l1 = 2π rbody/600 = 0.0105m and l2 = 2π rbody/600 = 0.0052m respectively. The corresponding acoustic wavelengths are λf1 = c/f =0.034m and λf2 =0.017m which results in a resolution of about 3.2 points per wavelength in both cases, sufficient to capture the less modulated part around 180 degrees accurately. Higher resolutions of the body have not been tried, but the calculation required only seconds on a single CPU.

3.4 Advanced BEM verification against CIRA’s finite element method OptyδB : Trailing edge noise scattering from a NACA0012-airfoil

3.4.1 Trailing edge scattering at Mach 0

The validation so far was only concerned with simple geometric shapes like circles and spheres, which by definition do not exhibit any sharp changes in curvature or corners. As the ability to predict trailing edge scattering is one of the most important requirements for ADOCHA, a NACA0012 airfoil was utilised for test purposes, with a single sound source within only 1.41cm of the sharp trailing edge. The base run was conducted for stagnant air (M= 0, c = 342.8m/s ρ = 1.244Kg /m3, p = 104420Pa). Its surface mesh consisted of 128 panels with a minimum panel size of 0.002m an average panel size of 0.004852m and a maximum panel size of 0.006487m resulting in a ratio of minimum to maximum size of 3.24. For the target frequency of 3000Hz, this corresponds to a resolution of 57 panels per wave length for the smallest panel, a resolution of 24 panels per wavelength on average and a resolution of 18 panels per wavelength for the largest panel. Further grid refinement utilising 500 panels in total resulting in a resolution of 100, 92 and 83 panels per wavelength, respectively, led to only marginal changes in the corresponding Green’s function. Furthermore, an increase of the interior points from 10% to 30%, with additionally enforcing a different distribution of the randomly placed points, nearly perfectly agreed with the original solution for the standard profile. It follows that the original ADOCHA result was already grid resolved. The run took less then a second on a single core of a 1.25Ghz-AMD Phenom(tm) 9850 Quad-Core machine.

Figure 10 demonstrates excellent agreement between the real and imaginary part of the acoustic solution of CIRA’s FEM OptyδB and ADOCHA for the transport of sound emitted from a unit source diagonally (0.3148m;0.01m) above the trailing edge (0.3048m;0.0m) of a NACA0012 airfoil at 3000Hz, for an observer circle of radius 1.22m centred at the trailing edge. This shows that the BEM is able to transport sound scattered from a sharp trailing edge accurately.

3.4.2 Trailing edge scattering at Mach 0.21

Up to now, all test cases have been performed in stagnant air. The target applications of ADOCHA, high-lift configurations, are relevant for approach speeds of aircraft during landing, which typically exhibit a Mach number around 0.2. In order to validate the Mach number terms, the configuration of the previous section 3.4.1 was used to compare results from the BEM and the FEM at M = 0.208. Moderate differences are to be expected as the FEM-method additionally takes local velocity gradients within the flow field into account, whereas ADOCHA assumes free-stream velocities everywhere. Indeed, Figure 11 shows some deviation most notably around observer angles of 0 and 180 degrees. An extremely refined grid of 2000 panels gave results that were nearly identical to the standard resolution of 128 panels, so that the BEM was grid-resolved. No grid refinement study was conducted for the FEM. However, the overall good agreement between two completely different numerical approaches suggests that the Mach terms were implemented correctly. The run took less then a second on a single core of a 1.25GHz-AMD Phenom(tm) 9850 Quad-Core server.

3.5 Validation of the acoustic model: comparison of NACA0012 airfoil self-noise against measurements of Brooks, Pope & Marcolini

The previous validation and verification cases tested the correct implementation of the BEM as a means of sound transportation and scattering. The last part of the ADOCHA code to be validated is the acoustic model and its support modules that filter the RANS-input data according to the user input and turn them into sound sources to be propagated by the BEM. To this end, a comparison with the experimental data of Brooks, Pope & Marcolini has been compared to 2D runs of ADOCHA based on two RANS results from CIRA originally utilised by Casalino & Barbarino, which are used here with permission. The validation case comprises the self-noise of a NACA0012 airfoil at zero angle of attack at the Mach numbers of M1 = 0.208 or V1 = 71.3ms and M2 = 0.162 or V2 = 55.5ms was conducted for the so-called “natural transition” series of the experiment, where the boundary layer was not tripped. As is to be expected for this configuration, the noise field was found to be dominated by trailing edge noise in the experiment, so that the data window shown in Figure 12(a) was utilised as the spatial filter. With a length of one chord starting at midchord, it is designed to capture the turbulent boundary layer over the second half of the airfoil, the trailing edge region and the wake. Its width was set to maximum profile thickness plus 8mm, the boundary layer thickness observed at 95% chord of the profile, to guarantie the inclusion of the entire boundary layer.

The original base run comprised a geometry with 500-panels evaluated for 21 frequencies (in 1/3 octave format) for 9180 noise sources and a single experimental observer position 90 degrees perpendicular to the chord line 1.22m over the trailing edge position at x = 0.3048m and took 25 minutes (1.2 minutes per frequency) on 4 cores of a 1.25GHz-AMD Phenom(tm) 9850 Quad-Core server. It seems reasonable to assume a speed-up of a factor of 2-4 on a modern high performance cluster with optimised communication, caches and higher clock rates.

For small 2D cases the runtime is a linear function of the number of sources. The four provided filters had been utilised to cut down the number of potential sources from 229376 (the total number of cells in the RANS solution) to the most relevant noise sources: the spatial window from Fig. 44(a), minimal filtering through cut-off of extreme values of the turbulence kinetic energy k and the specific dissipation rate w, filtering at 0.5% of the maximum source strength and finally omitting sources closer than 1mm to the body surface.

* Number of sound sources before filtering = 229376

Sources left after filter 1 (spatial windows) = 36654

Sources left after filter 2 (TKE & Omega limits) = 34270

Sources left after filter 3 (source strength) = 10534

Sources left after filter 4 (dist. from surface) = 9180

* Number of sound sources used in BEM calc = 9180

ADOCHA automatically displays the acoustic resolution per component and frequency. First preliminary tests suggest that 30 points per wave length can be considered as being very well resolved, 20-30 as well resolved and at least 10-20 points are recommended for the highest frequency for grid converged results. The profile resolution of 500 panels allowed for 17.2 points per wavelength at 16,000Hz for the average panel size.

This baseline run had been conducted with the original model parameter of

cl = 0.256 ct = 0.05 A = 0.6 .

found by Agarwal as a best fit to experimental noise measurements in the slat cove of an MD 11 aircraft. These parameters produced a solution that was of the right order of magnitude, but qualitatively monotonically growing over the whole frequency domain investigated. In order to capture the high frequency roll-off observed in the experiment, as shown in Figure 12(b), the model parameters have been refitted utilising ADOCHA’s restart capability, which allow a very fast re-evaluation of a conducted run with different model parameters, if the Green’s functions have been saved in a restart file. Typical run-times of restart runs for this particular case took about 4 seconds. The best fit was found for the parameters:

cl = 0.617 ct = 1.35 A = 0.5 .

The resulting solution is displayed in Figure 12(b). It follows that Agarwal’s parameters have to be re-calibrated for new configurations as it is typical for empirical model parameters. The excellent agreement found in Figure12(b) over nearly the entire range of human hearing suggests that the acoustic model from Agarwal has been implemented correctly.

Potential Impact:

Aircraft noise of modern passenger planes during take-off and landing constitute an increasingly sensitive topic due to their impact on residential areas in the neighborhood. Steady increases in aircraft operations and the accompanying noise levels potentially restricts airport operations (especially at night), expansions and their overall economics. Recognised as a separate point within the ACARE 2020-goals, noise reduction has therefore become a major focus of European research effort as demonstrated by numerous FP7 and Clean Sky projects. Post-design or even post-production noise reduction steps are typically labour intensive, costly and often come with an aerodynamic performance penalty. Therefore, experts such as Argawal emphasise that it would be highly desirable to routinely assess the noise performance of a particular high-lift configuration in the early design stages, so that noise considerations become an integral part of aircraft design, not just an afterthought.

The current project was driven by these requirements. Higher-order methods from the field of computational aero-acoustics (CAA) as well as highly accurate base flows in the form of large-eddy simulations (LES) or direct numerical simulations (DNS) are ruled out, as an industrial viable solution requires rapid turn-around times of no more than about 12 hours (overnight calculations), preferably shorter. Steady RANS solutions on the other hand still constitute the backbone of aerodynamic analysis in aircraft design, and are typically available relatively early for a new design. ADOCHA was therefore designed to provide a fast and robust method utilising steady RANS. It has been delivered to CIRA to complement their tool kit for the design of future regional aircraft.

One dissemination activity of the achieved results was planned in the form of a joint scientific paper between ARA, CIRA and ISVR. Accordingly, an abstract was submitted for the upcoming AIAA/CEAS Aeroacoustic Conference in June 2011 in Portland, USA. However, this paper was not accepted and as such another suitable journal or conference is being sought for resubmission.

List of Websites:

Contact Details:

Dr. David Lawrie

Aircraft Research Association Ltd.

Manton Lane, Bedford, MK41 7PF

Email:

dlawrie@ara.co.uk