NOISE-CON 98
Ypsilanti, Michigan
1998 April 5-8
A FORMULATION AND PRELIMINARY VALIDATION
OF AN
ALGORITHM PRESCRIBING THE PROPELLERS OF AN
AIRCRAFT AS
EXCITATION IN AN BOUNDARY ELEMENT ANALYSIS
Nickolas Viahopoulos Karen H. Lyle Casey L. Burley
Department of NA&ME US Army NASA Langley
The University of Michigan Vehicle Technology Center Research Center
Ann Arbor, MII Hampton, VA Hampton, VA
INTRODUCTION
In general aviation aircraft the interior noise levels must be acceptable to the general public as passengers. Simulation tools can be utilized in computing and minimizing the interior noise levels
in an aircraft subjected to the external acoustic load originating from the propellers. The finite
elerrnt method (FEM) [1] can be utilized for computing the structural vibration due to the external acoustic load, and the boundary element method (BEM) [2-4] for computingthe interior
noise levels. In order to evaluate accurately the interior noise level, and in order to determine the
structural changes which will reduce the interior noise, it is important to have an accurate description in terms of magnitude and phase for the external acoustic load exerted on the fuselage.
A formulation for modeling the operating propellers of an aircraft as a noise source in a boundary
element acoustic analysis was developed, implemented into software, and verified through comparison to test data. It is based on an elaborate simulation for the velocity field induced in the acoustic medium due to the operation of the propellers and a linear solution for the pressure field. It constitutes the
initial phase of integrating sophisticated rotorcraft models[5-lO] to a
conventional boundary element analysis. This approach can compute the acoustic loading on the fuselage of an aircraft thus, provide the excitation for an interior noise analysis and reduction. Itcan account for the presence of the fuselage within the acoustic field, and for multiple operating
propellers. The initial validation was performed by comparing nurrrica1 results to test data for
the external acoustic pressure on the surface of a tilt-rotor aircraft for one flight condition. TECHNICAL BACKGROUND
Previous work on helicopter or aircraft propeller noise prediction has concentrated in computing the free field noise from a single propeller based on the Ffowcs Williams and Hawkings integral
equation which provides a solution to the noise radiated from a body in arbitrary motion.[5, 6] This approach is based on computing the free field acoustic pressure as an integral of the thickness and loading terms over the surface of the blade in a reference frame moving with the blade surface. Work has been done in evaluating the noise in the free feld based on information
Ltboratorium voor
Scheepshydromecha.
.rchif Meketweg 2, 2628CD Delft - Fw 1813 639about the geometry of the blade and information about the blade loading.(6} Special procedures were developed for handling correctly the retarded time, and the relationships between rotating and stationary systems. Recently, a system approach (TRAC) has been developed[7J by integrating a rotorcraft operating condition simulation to either a CFD or a lifting line theory based codes for computing the blade loads with high resolution. In order to exploit these recent developments and develop a simulation based design methodology for computing the acoustic loads exerted on the fuselage, the propellers must be modeled as noise sources in a conventional acoustic BEM analysis. The aircraft has to be part of the acoustic BEM model, and the analysis will compute the acoustic pressure on the fuselage. The work presented in this paper establishes the ground work for such an effort. In order to identify the feasibility for a load generating
approach based on the BEM the following steps were completed:
An acoustic BEM model was constructed. It was comprised by the aircraft and its propellers. An acoustic velocity boundary condition was computed for every element of the propellers. It
included detailed information for the velocities induced in the acoustic medium by the propellers.
An acoustic BEM analysis was perfonxd. The acoustic pressure on all the surfaces (including the fuselage was computed). The solution was based on the wave equation which is derived from Euler's and continuity equations under a linear approximation.[l 1] This approach simplified the analysis requirements during this feasibility stage.
Results were compared successfully to one set of test data[12] for the external acoustic
pressure under flight conditions.
NUMERICAL IMPLEMENTATION
In order to perform the process of generating the velocity boundary conditions for an acoustic BEM analysis, three separate computer programs were created. Their functionality is presented.
Generation of BEM model for the propellers. An individual time history is generated for each element of the propeller's model, therefore, it is necessary to contain within the numerical algorithm information about the numbering scheme and the location of the nodes and elements comprising the propellers. In order to accomplish it, a code was developed for generating automatically the BEM model for each propeller. The necessary input information is: (i) center location for the propeller; (ii) inner and outer radius; (iii) a characteristic thickness for the propeller; (iv) the starting node and element ID and the required number of elements in the radial and angular directions.
The BEM model for each propeller is comprised by two disks
representing the top and bottom surfaces of the blades. The characteristi thickness defines howmuch apart the two disks must be located. The code must be executed as many times as number of propellers present in the aircraft. The outcome is the BEM model of the propeller in a format
suitable to a general purpose acoustic analysis code.[l4}
Generation of the time history velocity files. This code computes accurately the velocity field induced by the blades in the acoustic medium. The required input is: (i) description of the airfoil sections of the propeller blade; (ii) the operating conditions. The normal velocity time history is computed for the top and bottom surface of one radial column of elements in the propeller model.
The velocity histories for all the remaining elements are produced from the time delay between the
different angular positions (depending on the rotational speed). In this manner the number of computations are limited to the mminmm necessary amount. Within the time history representing one full rotation, there are three areas of non-zero values corresponding to the time intervals that
each one of the three blades passes through each
element. MATLAB[13} is utilized forgenerating the frequency content of the velocities.
Generation of velocity time histories for a BEM acoustic analysis. This code processes the information generated from MATLAB and creates a file with the element velocities in an appropriate format for the BEM analysis. The direction of rotation of the propeller is defined at this point. For multiple same propellers only one set of frequency domain data must be available. The direction of rotation determines the sequence of processing the data. In this manner counter-rotating propellers can be handled easily. This program associates each file containing the frequency components of the velocity, to the elements of the BEM propeller model. It constitutes the last part of the pre-processing process for generating the boundary conditions for the acoustic analysis.
APPLICATION
Tiltrotor aircraft are utilized so far by the military.
Their capability for operating both in helicopter and airplane mode makes the concept viable for civil transportation. Thus, the interior noise and vibration levels must become acceptable to the general public as passengers. In order to utilize simulation based design technology for predicting and reducing the interior noise, it isnecessary to have reliable information about the external acoustic pressure loading on the fuselage. A series of measurement data were collected under flight conditions.[12] The rrasurements were focused on the exterior pressure loading on the fuselage. The BEM based numerical approach which was developed in this work was utilized for an analysis. The condition of forward flight at 103m/s (200 knots), 522RPM, and 40.60 collective angle was selected for
comparing test data to the numerical results produced in this work.
A BEM model was constructed for the aircraft. Each propeller was comprised by 1152 elements and 1152 nodes. The complete model consisted of 3954 elements and 3925 nodes. The developed approach was utili7ed for generating the velocity boundary conditions for an acoustic BEM analysis at the first three harmonics. The harmonic frequencies were computed at 26.17Hz., 52.35Hz, and 78.53Hz. They matched well the expected values (corresponding to 522RPM and a propeller with three blades) of 26.1Hz, 52.2Hz, and 78.3Hz respectively. Three areas were identifiedfor comparingthe numerical results and the test data. They are summarized in Table 1. Overall there is good correlation between them.
Table 1. Summary of Test Data and Numerical Results
Currently the analysis is based on detailed information about the velocity field induced in the medium by the propellers, but a linear solution for the corresponding pressure field. It is expected
that the correlation will improve once this development is expanded to incorporate in the BEM
Test Data 1gHarmonic 2 Harmonic 3 Harmonic
Location A 125.53dB 125.06dB 124.0dB Location B 124.18dB 125.12dB 120.0dB
LocationC
123.7dB 124.0dB 125.0dB Numerical Results Location A 124.79dB 120.8dB 117.8dB Location B 127.9dB 125.6dB 121.8dBLocationC
127.5dB 125.5dB 123.12dB .5: Vlahopoulos, et al. 641642 ANALYSIS
analysis pressure information from the CH.) solution available in rotorcraft prediction codes.[5-lo] From the BEM analysis the loading can be computed on the entire aircraft. As expected the highest noise is generated in the plane of the rotor. This information can be utilized as excitation for either computing the structural vibration of the fuselage and the interior noise, or for fatigue computations of the control surfaces. In addition, the radiated noise can also be computed.
CONCLUSIONS
A new formulation was developed for modeling the propellers of an aircraft as noise sources in a conventional acoustic BEM analysis. The benefits of this approach are: (i) the presence of the aircraft within the generated acoustic field can be easily taken into account; (ii) the acoustic loading (magnitude and phase), can be readily available from the BEM solution, and it can be utilized as excitation for a structural vibration and interior noise analysis,
or for fatigue
computations; (iii) it provides a computation based on a detailed simulation for the velocity field, and a linearized solution for the pressure field, which can constitute an initial, but fast simulation for the propellers as noise sources. An initial validation was completed by comparing successfullynunrical results to test data for the acoustic loading on the surface of the XV15 aircraft for one flight condition.
AKNOWLEDGEMENTS
The authors wc*xld like to express their appreciation to Dr. Farassat (NASA Langley Research Center) for sharing his knowledge in the field of aeroacc*istics dunng this project Dr. Jones (US Army Vehicle Technology Center) and Dr. Parikh (PARAGON Research Associates, hic.) for providing the CAD data for constncting the BEM model for the XVI5 aircrafi
during this work. Mr. Pzichard (Lockheed Martin Engineering and Science Corporation) for his insight in the current rotcroraft
codes developed at NASA Langley. This work was partially supported by the NASA ASEE Summer Faculty Fel1ohip
ProgTam.
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