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Introduction

Acoustics is “the branch of physics concerned with the properties of sound” [1]. Thus, acoustics is an important field to be taken into consideration for working conditions since the human ear is sensitive to a range of frequencies. [2]

Moreover, money and sound may not be two areas so far apart. Actually, a commercial interest lies in sound control in industry due to the fact that caused vibrations can damage heavy and expensive machines or the systems with it. [3] Gas pipelines are not an exception to the rule. Indeed, vibrations can be the source of damage such as blast [4] or corrosion. [5]

This is why studies are led on both acoustic and thermal insulation for pipelines in order to prevent the surrounding environment to be altered. Usually, these protections are made of a single layer of certain materials which present accurate properties in terms of damping. [6]

At the present time, with applications for gas pipelines being more complex, new insulations are researched using non-organic materials and/or new layers’ density. [7][8]

This project will study acoustic, mechanical and thermal properties of a new designed material using the latest standards and determine how promising it can be.  

This literature review introduces porous and other new-generation materials and compares their performances. It is also shown how standards evolve following the new technologies; new experiment sets and new computational models.

1. Porous materials

Porous materials can be natural or engineered and organic or non-organic. They are made of pores and their nature differs from the size of them. Moreover, their layout is a factor of determining their properties (mechanical or acoustic) as shown by the University of Oslo. [9] Indeed, density and capillarity action influence their resistance to the airflow as well as their sound damping capability. [10] According to their pores size, they are microporous (<2 nm), mesoporous (>2 nm and <50nm) or macroporous (>50nm). [11]

The Acoustical Porous Material Recipes (APMR) claims that porous materials are subdivided into three families depending on their properties; one may find the fibrous materials, the foams and the granular materials. [12] Furthermore, their use is varied; for example, in the industry as vibrations absorbers or in the form of thermal insulation in the private houses. Thus, they are involved in sustainable development since they are the direct link between energy conservation and the environment. [10]

Figure 1: photography of the pores of a porous material (obtained with a scanning electron microscope) [13]

In order to characterize the various porous materials and then to classify them, different parameters are used; the acoustic and visco-elastic ones. [12]

Among the acoustic parameters there are: the porosity, the air flow resistivity and the dynamic tortuosity. The APMR suggests that these three parameters are important since they are directly verifiable, as a matter of fact it is possible to measure them on a sample. Calculation theories and experimental methods are taken up by Brouard and al. [14]

Although there is no real standard for experiments to evaluate these parameters, the same process can be found in several papers. [12][14][15] Some nuances are however made to the experiments in order to stick with the research objective.

Nonetheless, one parameter is still undefined in its evaluation; the impedance surface. The IUPAC suggests an evaluation by the Brunauer-Emmett-Teller (BET) method [11] while Brouard and al. focus on the Two-Microphones-Three-Calibrations method. [14] Binxing has expressed a different view in the conclusion of his paper stating that the new method he has introduced (in-situ measurements) is \"closer to the actual applications\". [16]

In the view of calculating more complex but more relevant parameters in the sizing of acoustic insulations using porous metals, computational models have been created. These models present simplifications or complexifications depending on the precision of the desired result.

Thus, for a sharp characterization, the Johnson-Champoux-Allard-Pride-Lafarge (JCAPL) model can be used because it allows to estimate eight different parameters specific to the tested sample. It includes the porosity in particular but also the visco-inertial effects. [12]

The list of models published by APMR is complemented by the work of Z. BO and al. [17] Indeed, their work reveals that it is possible to couple these previous models with acoustic models, specific to the behaviour of molecules of gas or fluid in gas pipelines. These models can be empirical (EM), phenomenological (PM) or microstructure (MM). Using Biot-Allart acoustic model (BAAM), they showed the convergence between experimental results and theoretical calculations for two parameters. [17]

Once the parameters have been defined, the acoustic, mechanical and thermal performances of the porous materials can be deduced.

- Mechanical: porous materials have naturally excellent mechanical properties in terms of strength in particular. They are distinguished from metals by a viscoelastic behaviour which gives them a complex Young\'s modulus and Poisson\'s coefficient. [12] This behaviour being revealed by the study of L.Stanev and al. for open-cell metallic porous materials. [18]

- Thermal: porous materials must be great in terms of energy dissipation. Indeed, thermal protection of gas pipelines used to be provided by other materials or additional layers of insulation. [14] At this point in time, in a strategy of gaining weight, one single layer has to be both an acoustic and thermal protection. In 2006, it was shown that adaptation of acoustic models was not possible for the study of the thermal properties of materials. [19] Ten years later, a model of study established from a flow of fluid nanoparticles at the state-of-the-art is realized and shows a certain veracity of the results. [20]

- Acoustics: finally, the acoustic properties of porous materials are varied because they depend on a large number of parameters. However, they are classified according to ISO 15665 which gives the porous samples a letter (between A and C) depending on the acoustic protection they can offer to a pipe. [21]

2. New-generation materials

New generation materials or derived from porous materials are also still being studied in a strategy of gaining weight or even reducing manufacturing costs.

First, composite materials. S.Vakhitova and al. studied the acoustic and thermal properties of a sample after injection at different levels of an additional chemical component. [22] Nevertheless, composite materials do not excel at all acoustic properties, so metamaterials took over them. These materials, non-natural since they have been created from an engineering process, can offer better results. Indeed, recreating the structure of one of these samples so as to select their interaction with the waves can significantly increase their acoustic performances in terms of damping. [7]

In the same way, fibrous metal materials have been studied on the basis of Dupere’s model which confirms the BAAM already used for porous sintered fibrous materials (part. 1). [23] F.Sun concludes that the acoustic absorption of these materials increases with the temperature, which is also pointed out by the work of B.Kang on open-cells aluminium foams. [8]

Moreover, it has been demonstrated that the size of their pores induces their acoustic performance. This parameter is also highlighted by the work of A.Navacerrada focusing on aluminium foams whose manufacturing process was different. [13] In this way, the National Aeronautics and Space Administration (NASA) argues that the size of the pores plays directly on the energy transfer that can take place between pores in order to dissipate (Fig 2). [24] In the case of open cells, conducive to good thermal and noise insulation, sound absorption was evaluated at 10-20%. [8] Even an industrial application has already been found for them, namely heater.

Figure 2 illustrates how the pores size influences on energy transfer into the material [23]

3. Experimental sets

Experimental measurements in acoustics are made today by means of advanced technologies like, for example, microphones whose calibration and behaviour at low and high frequencies do not vary over time, which is a guarantee of accuracy. [25]

In addition to the parameters mentioned earlier such as porosity, airflow resistance and tortuosity, transmission loss and sound absorption coefficient, complex impedance and heat transfer are also measurable. [17][26] One of the first modern standardised experimental methods was written by Chung and Blaser in 1980. [27] This method was then followed by the ISO 15665:2003 norm which governs the standard experiments to perform to characterize samples in terms of acoustic performance. [21]

Numerous works have relied even recently on these sets of standardised experiments, notably the works of Z.Bo in 2007 and F.Sun in 2009 using the two-microphones transfer-function method. [17][23] Even more recently, B.Zhang reports that these standards are still relevant since they allow researchers to approach the most recent calculation codes. [15] The author also indicates that with the technological evolution of the microphones, it is even possible to adapt the initial experimental set.

In order to get used to the plurality of calculations to be carried out to validate a new acoustic material, new experimental sets have been studied. One may underline the two-microphones-three-calibrations method for calculations of acoustic performances and mechanical properties [14] or the 3-microphone tube impedance method for acoustic and non-acoustic calculations whose results stick with numerical projections. [28]

Figure 3: Experimental setup for the 3-microphone method [28]

Finally, the work carried out by M. Swift in 2012 proposes a new method for calculating the transmission loss parameter. Indeed, the measurement of it required by the standard ISO 15665 necessitates a lot of equipment and tools [21], which is confirmed by O.Doutres. [28] Nevertheless, this new method does not take into account certain complex behaviours such as the poro-elastic behaviour of the material. [21]

4. Numerical modelling

At the present time, numerical simulation has become a must in research and industry. Indeed, it makes it possible to validate models or to design them. Nevertheless, it can very quickly find itself very expensive.

In the case of studying porous materials, one must first consider the size of the model. Indeed, several parameters will be required when developing a complex and precise model and less for simpler simulations. APMR regroups the different possible models created to date. There are the models of sound propagation in porous materials (diphasic, motionless skeleton or uniform pressures models) as well as the different acoustic models evoked earlier (Delany-Bazley-Miki model for fibrous materials or Johnson-Champoux-Allard-Lafarge depending on the sample’s pore size and structure for example). [12] The choice of the model will therefore strongly influence the number of parameters involved. D. Oliva has carried out a research work on all these models to make a synthesis on the accuracy of these. He concludes that the Allard-Champoux model, which takes into account the viscous forces, tends to be the most accurate. [29]

About the numerical resolution itself. Several calculation methods are identified today, such as the open source VORO++ code for modelling foams [30] or the MAINE3 code for the resolution of the Biot model which uses the matrix transfer approach giving as a result the insertion loss coefficient. [14], [31]

Figure 4: Numerical creation of the model using VORO++ code [30]

Another widespread method of resolution is the Finite Element (FEM) one. Nevertheless, the limits of this method are quickly reached since it is extremely expensive in time and in memory storage. [32] Authors admits they had to mesh their model using only small 3D meshes [32] and compute it only in low frequencies [14] since in high frequencies, current computers are not powerful enough to complete calculations. However, the other methods invoked earlier also have limitations; the VORO++ code does not know how to treat extrema such as spatial boundaries or particular frequencies for example. [30]

Conclusion

The project focuses on the study of an entirely new material whose acoustic and thermal properties are expected to be sufficient enough to use one layer. Experimental studies should first be carried out in order to deduce all its mechanical properties. The results will then be implemented in COMSOL for a numerical simulation of its acoustic performances. The data can be validated once a final experimental protocol is created.

This literature review helps to take stock of the progress made in research today on the study of the acoustic performances of new generation materials, whether for experimental or numerical analyses. Many studies still rely today on 20-year old standards but many innovations are also proposed as can be seen with the nanofluid flow in porous media to determine its properties. [20] High-tech researches comes alongside those in acoustics.

The industry, in several fields, whether it is for boats or for space vehicles, finances this type of research because the gain is very promising. Indeed, the protection of pipelines is an economic stake as well as a guarantee of reliability by avoiding any damage. This is a field where innovation has to keep progressing.

Further research

Several axes of future research are to be imagined. In order to fulfil all the criteria of the industry (light, low manufacturing costs, excellent acoustic, thermal and mechanical properties ...), a new family of materials may be born such as the hybrid material NASA proposed. [24] Metamaterials are also a good example of this new generation. Similarly, computational codes may become obsolete, too slow to cope with the rise of complexity (Boundary and finite element methods) and experiments will no longer allow access to the data desired by researchers. Thus, it is necessary to continue working in these areas, to adapt existing technology to the challenges and researches of tomorrow.

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