Abstract. 1 Introduction

Transcription

1 A numerical method for the simulation and prediction of the sound pressure levels of enclosed spaces. Application to a real workshop R.Sancibrian", F.Viadero", C. De Miguel* and P.Garcia-Femandez*. "Department of Structural Design, E. T. S. de Ingenieros Industrials y de Telecomunicacion. University of Cantabria, Avda. de los Castros, sin, Santander, Cantabria. * Fundimotor S.A., Los Corrales de Buelna, Cantabria. Abstract In this article, a method is presented for the prediction of noise maps in the interior of enclosed spaces. The method is based on the well-known simulation technique denominated Ray-Tracing and is capable of simulating acoustic effects such as diffraction, specular reflection and diffuse reflection. With the aim of verifying the validity of the method, a practical application has been carried out on a real industrial plant. First the machines in the plant have been taken into account as noise sources and then, the sound pressure levels have been obtained throughout the plant. The acoustic levels obtained by simulation are compared with the experimental sound pressure levels in the real plant and some conclusions are made about the degree of precision of the proposed theoretical method. 1 Introduction The study of the acoustic conditions in industrial plants usually causes many problems due to two fundamental reasons: the large number of reflections of sound waves produced in this type of space due to its complex geometry, and the influence of the material properties on the acoustic behaviour. There are many algorithms which attempt to take into account all these factors, in such a way that it is possible to obtain as precise an estimation as possible of the acoustic levels in the particular industrial space. Most of the numerical methods used in acoustic simulations are based on treating the sound waves as rays of energy, obeying the same laws as the light rays used in optics. There are various methods based on this which have been used in

2 112 Computational Acoustics and Its Environmental Applications acoustic simulation for several decades [6]. One of these methods is the Ray- Tracing Method (RTM). The Ray-Tracing Method has demonstrated to be an efficient algorithm in order to calculate the sound pressure levels into enclosed rooms. However, the Ray- Tracing has certain advantages and disadvantages in order to simulate the acoustics parameters. For example, has important disadvantages when obtaining results from parameters that depend on time, such as reverberation time or the response to a sound impulse. It also has the disadvantages that it is impossible to predict beforehand how many rays the source must be discretized into in order to obtain a precise value in the receptor [3]. However, it is an efficient method when complex geometries are considered which cause a large number of reflections. It is also a suitable method when phenomena such as diffusion, diffraction and refraction are taken into account. Since the aim of this work is to simulate the acoustic behaviour of industrial plants, it is necessary that the algorithm used is capable of working correctly in spaces with complex geometry, where a large number of reflections appeal*. In industrial plants there are often irregular surfaces and acoustic screens which favour the appearance of phenomena such as diffuse reflection and diffraction. For all these reasons, the Ray-Tracing method seems to be the most suitable method for acoustic simulations in industrial plants [7] and so, it has be chosen in order to achieve the objectives proposed in this work. 2 The Ray-Tracing Model With the aim of estimating the acoustic levels within a space, a theoretical simulation is carried out based on the aforementioned Ray-Tracing method. Depending on the properties of the material and the type of surface of the obstacle, the ray generated by the source can be reflected through a particular law of reflection which can be specular, through diffuse reflection or through diffraction of the ray itself. This last case only appeal's if the incidence occurs over a convex vertex of a particular surface. In any case, all reflection includes absorption of energy, or in other words, once the ray is reflected, the energy contained in it is less than the energy transported before the reflection. When the ray is reflected the process continues in exactly the same way until the collision with the next obstacles, the process being repeated until the energy level of the ray falls below a particular threshold. 2.1 Source Model The sound sources have been modelled as point sources with the possibility of taking into account directivity. Therefore, for the correct definition of a sound source in the model, it is absolutely necessary to know two parameters, sound power and directivity. In this case, the sound power has been obtained by sound intensity measurements. In order to obtain a uniform share of rays around the source

3 Computational Acoustics and Its Environmental Applications 113 a deterministic method, which divides an imaginary sphere around the source into equally spaced points using a particular algebraic formula, has been chosen [8]. 2.2 Reflection Model When the sound energy rays from the sources incide on the surfaces of the model, two main questions arise. The first refers to the amount of energy which will be absorbed by the incident surface. The calculation of this energy does not cause any problem if there are experimental data about the absorption coefficient of the surface, that is, if experimental measurements can be made about the reverberation time within the space, obtaining in this way a global absorption coefficient. This coefficient is shown to be quite precise in most cases. A second problem, with a more difficult solution, requires the specification of whether the reflection is specular or diffused [4]. As a general rule, the specular type reflection is produced when the surfaces that reflect the acoustic energy rays are smooth and hard. In this case, the energy is reflected in such a way that the angle formed by the reflected ray with the incident surface is equal to the angle of the incident ray. The easiest way of implementing this type of reflection is by the creation of an imaginary source equidistant from the surface. The rays emitted by this imaginary source make up the reflections of the real rays once they have left the surface of the wall of the space. Nevertheless, the diffuse reflection is produced when the sound waves incide on flexible surfaces with a certain degree of roughness. In this case, the incident ray is not reflected in a single direction, but includes all the directions throughout the surface. This case of reflection can be understood as if there were a new sound source at the point where the ray incides on the surface. This new sound source, situated on the reflecting surface (see figure 1), is not omnidirectional, but emits energy in different amounts depending on the angle formed with the reflecting surface. Normally, it can be assumed that the predominant angle of emission of energy in this type of reflection is perpendicular to the incident surface, and the angle of least emitted energy is parallel to the surface [1]. It is important to highlight that a single surface can produce both specular and diffuse reflection. The condition for producing one or another depends on the wavelength inciding on the surface. If the frequency of the incident wave corresponds to a wavelength greater than the biggest of the predominant dimensions of the surface roughnesses, the reflection will be specular. On the other hand, if the wavelength of the incident ray is smaller than the biggest predominant length in the surface, the reflection will be diffuse. Figure 2 shows a surface where the principal roughness has a dimension L and the wavelength of the incident ray is X. Thus, the type of reflection depends on the wavelength, in such a way that if X is greater than L, specular reflection is produced, and in the contrary case the reflection is diffuse. Normally, the formulation used to modelizate the energy reflecte by diffusion and reflection is the following [4], (1)

4 114 Computational Acoustics and Its Environmental Applications where HT is the total incident energy over the surface, a is the absorption coefficient and y is the diffusion coefficient. specula Figure 1: distribution of the different energies in reflection effect. Figure 2: geometry of diffuse reflection. Another important fact which should be highlighted in the diffuse reflection is the enormous computational cost required if it is necessary to simulate a new sound source each time a ray incides on a surface. In order to solve this problem, a method has been proposed to decrease the number of rays used in the diffuse reflection and reduce the computational cost of each simulation. This method consists of considering that a single ray is reflected diffusely, and that, the direction of this reflected ray varies in each case according to a probabilistic law in which perpendicular reflections predominate with fewer reflections parallel to the plane of the surfaces. Although, in principle, it might appeal* that this method undervalues the sound pressure level near the wall, the trials carried out showed good results. The reason these results approximate well to reality is fundamentally due to the fact that although a single ray can undervalue the results, the sum of the reflection effects of all the rays eliminates this lack of precision. 2.3 Diffraction Model One of the solutions habitually used for noise reduction is the use of acoustic barriers. The acoustic barriers introduce the effect denominated diffraction which at the moment is not frequently studied due, fundamentally, to the large number of

5 Computational Acoustics and Its Environmental Applications 115 parameters that intervene in its modelling. It is important to highlight that the use of this type of solution in enclosed spaces with low absorption by the walls is not usually adequate. The reduction of noise levels by acoustic barriers is only recommendable when they are used in open spaces, or when the reflections within the enclosure are low and the sound waves have a predominant transmission direction through space [2]. Nevertheless, although the work presented here aims at an application in enclosed spaces, a diffraction model has been implemented with the aim of including the largest number of possible cases. The diffraction model used consists of reducing the sound pressure level in the receptor through an empirical value, when there is a barrier between the receptor and the source [5]. In order to obtain the value of reduction of sound pressure levels in the receptor due to the insertion of the barrier, it is necessary to calculate the so-called Fresnel number which depends on the geometrical characteristics of the barrier and on the position relative to the source and the receptor. Once these parameters are determined, the Fresnel number is obtained using the expression; 2(a+b-d) (2) where a, b, d represent the distances indicated in figure 3, and X is the wavelength. Once the Fresnel number is calculated, the reduction of sound pressure level is calculated using the expression AL,, = Login ' (3) When the barrier can be considered as a single length the Fresnel number is calculated for only one of its vertices. However, if the length of the barrier is finite in several of its vertices, the Fresnel number must be calculated for each one of them as indicated (see figure 3). Receptor Figure 3. Geometrical Parameters intervening in the modelling of the diffraction effect in the space.

6 1 16 Computational Acoustics and Its Environmental Applications 2.4 Fittings Normally, in the interior of industrial plants there are numerous elements that cannot be considered as noise sources, given that they do not emit acoustic energy, but which do distort the acoustic waves travelling through the enclosed space. These elements, of various sizes, are called Fittings and they represent elements such as stored stock or machinery not in use [7]. The Fittings usually have a complex geometry with irregular surfaces and, in general, very distinct characteristics. Therefore, it is impossible to attempt to model each of the elements of these characteristics by trying to define their particular geometry in each case so that it resembles the real geometry. To solve this problem, the fittings are modelled as volumes whose surfaces reflect the sound waves diffusely. This type of modelling is especially valid in reference to the modelling of industrial plants where the products in stock, the major producers of this type of effect, can be represented as regular volumes. 2.5 Receptor Model The ultimate aim of a method such as the Ray-Tracing method is to obtain a noise map and so to quantify the sound pressure level to which the workers are submitted in their work place. It is therefore necessary to model and distribute the receptors correctly, so they are capable of detecting the energy rays emitted by the different sources and then converting this energy in sound pressure levels. An acoustic energy receptor must fulfil the condition of being omnidirectional. That is, the energy is captured in the same way, independently of the direction of the ray which incides on the receptor. In turn, the transformation of energy into sound pressure in the receptor must be done simply and rapidly, without costly calculation procedures. One of the receptor models widely used in the RTM is the cubic receptor, but it has both the drawback of the influence of the incidence angle of the ray on the receptor and the geometrical difficulty of transforming the energy crossing the cube in sound pressure. The spherical receptor model eliminates both these drawbacks. Owing to its geometrical characteristics the energy captured by this type of receptor is independent of the angle of incidence of the ray, and the calculation of this energy is very simple. According tofigure4 the energy captured by the receptor is e = -^lt( Watt -sec) (4) where P (Watts) is the energy contained in the ray when it crosses the receptor, L (metres) is the ray length is the interior of the receptor and c (m/sec) is the velocity of sound.

7 Computational Acoustics and Its Environmental Applications 117 Spherical Recptor Figure 4: Model receptor. The size of the receptor used requires special attention, since if this is of small dimensions the precision will be high, but the drawback arises in the large number of rays necessary in the discretization of sound power of the source and, consequently, the computational cost of the model increases considerably. On the contrary, if the size of the receptor is large, the computational cost is low, but the reliability of the results obtained is reduced. For this reason, it is necessary to find a compromise between the size of the receptors chosen and the calculation time used to solve the problem The studies carried out by various researchers [8] show that for a model of a medium-sized industrial building, like that of the study, a spherical receptor model of radius r = 0.5 metres is precise enough and has a relatively low computational cost. 3 The Real Plant With the aim of validating the Ray-Tracing model approached in this work, a real industrial building has been modelled using the criteria described in the previous section. The industrial building used was a workshop for elimination of flash on cast engine blocks belonging to Fundimotor S.A, in Los Corrales de Buelna (Cantabria, Spain). The building is a nonsymmetrical metallic structure with roof pitch. The covering is made up of corrugated metal panels supported by purlins. All the walls are composed of concrete blocks up to a height of 2 metres, above which there are corrugated metallic panels and, in some cases, translucent polyester panels. The floor is a single level of concrete. The engine blocks arrive from the foundry and they undergo a number of operations to eliminate the flash. There are 15 sources within the enclosure which correspond to the machines in use. The total number of workers in the plant depends on the production, up to a maximum of 15 when the workshop is at maximum output. In order to simulate the noise map into the building all factors mentioned before have been considerated as it is showing in figure 5.

8 118 Computational Acoustics and Its Environmental Applications # O 25 3O 35 * Omniderectional Source Directional Source : Fittings Figure 5: Industrial plant and localisation of different sound sources. 4 Experimental Measurements of the Noise Levels With the aim of evaluating the results obtained with the Ray-Tracing theoretical model, experimental measurements of noise were carried out inside the plant, both at the level of the operator in his workplace and in different points of the plant, in order to elaborate a general noise map. In order to measure the sound pressure level to which the operators are exposed precision sound level meter and dosimeters have been used. The results of the measurements carried out can be seen in the noise map of the plant shown in figure 6. Figure 6: Noise map obtained by experimental measurements.

9 5 Results Computational Acoustics and Its Environmental Applications 119 The model used in the computer simulation and the results obtained using the Ray- Tracing algorithm described before are shown in figure 7. The floor of the building is represented as a rectangle containing both the noise emitting machines and the elements denominated fittings. The total number of sound sources used was 15. The fittings simulated represent the engine blocks stored in the plant. The quantities shown in the figure indicate the sound pressure levels in the different zones of the plant. db G D Figure 7: Noise map obtained by computer simulation. 6 Conclusions Comparing the simulation results with the noise map obtained experimentally, the following conclusions can be drawn. Firstly, the form of the noise map is very similar in both cases, although the numerical values of the sound pressure levels have been overestimated in the numerical simulation case by a quantity oscillating between 1 and 2 db. This fact can be explained in two ways: firstly, the difficulties in estimating the power and directivity of the sound sources in the plant, and secondly, the lack of information about the absorption coefficients of the materials in the plant, most importantly the panels forming the walls and ceiling. Secondly, in spite of all these difficulties, it can be said that the sound pressure level estimated in the work places approximates to the actual levels, with a precision of approximately ±2 db. This is a high level of precision for a situation such as that studied here. In sum, it can be said that the RTM is a suitable method for the prediction of the sound pressure levels in industrial plants. Furthermore, the method can be easily used to improve the acoustics characteristics of enclosed room and, in this way, to achieve a important acoustic pollution abatement. The precision of the method

10 120 Computational Acoustics and Its Environmental Applications could be improved if the measurements of the machine power are carried out with precise techniques like the sound intensity technique. The method of determining the coefficients of surface absorption also requires greater precision and necessitates a series of experimental studies. 7. References 1. Ahnert, W. and Feistel, R. Using Different Methods to Calculate Scattering Effects, 15th International Congress on Acoustics, Trondheim, Norway, 1995, Benedetto, G. and Spagnolo, R. A Study of Barriers in Enclosures by a Ray Tracing Computer Model, Applied Acoustics, 1984, Berntson, A. Comparasions Between Ray-Tracing and the Reality, 15th International Congress on Acoustics, 1995, Dalenback, B., Kleiner, M. and Svensson, P. A Macroscopic View of Diffuse Reflection, J. Audio Engineering Society, Vol. 42, No. 10, 1994, Dance, S.M., Roberts, J.P. and Shield, B.M. Computer Prediction of Insertion Loss due to a Single Barrier in a Non-Diffuse Empty Space, Proceedings of the Institute of Acoustics, Vol. 15, Part 3, 1993, Geest, E. and McCulloch, C.F. Numerical Modelling in Geometrical Acoustics using the Beam Method, with Application in Architecture, Industry and the Environment, Euronoise '92, Vol.14, Part 4, 1992, Hodgson, M. Measurements of the Influence of Fittings and Roof Pitch on the Sound Field in Panel-Roof Factories, Applied Acoustics, 1983, 16, Kulowski, A. Algorithmic Representation of the Ray Tracing Technique, Applied Acoustics, 1985, 18,