Acoustic metamaterial noise control method and apparatus for ducted systems

Abstract

An acoustic metamaterial noise control system of embodiments of the disclosed technology combines acoustic metamaterial principles with absorptive materials, with a result of a significant reduction in sound radiation within, or emanating from, an HVAC duct. Sound waves that impinge on the noise control system placed at the end (terminal opening of an air duct to ambient space within a room/building), or at a predetermined place on the duct, cause the sound waves to reflect back to the start of the noise control system and also to be absorbed by sound waves within the absorptive core. This is accomplished by way of the use of micro-perforated panels (MPPs) placed in periodic manner with absorptive layers and air gaps to achieve anisotropic conditions to reflect and absorb sound waves for optimum sound reduction.

Claims

1. A metamaterial muffler forming an acoustic metameterial noise control system comprising: a stack of micro-perforated panels which are made up of at least three perforated sheets of acoustically hard material between an ambient medium forming anisotropic air flow from or to an air duct through each of said at least three perforated sheets.

2. The metamaterial muffler of claim 1, wherein said ambient medium is air and can be any fluid supporting sound wave propagation.

3. The metamaterial of claim 1, wherein each perforated sheet of said at least three perforated sheets is less than, or equal to, 2 mm thick.

4. The metameterial muffler of claim 3, wherein a diameter of each perforation of each said perforated sheet is between 0.1 and 0.4 mm.

5. The metameterial muffler of claim 4, wherein each perforated sheet of said at least three perforated sheets is spaced apart from at least one other perforated sheet between 0.5 to 55 mm.

6. The metamaterial muffler of claim 4, wherein said spaced-apart distance of said at least three perforated sheets and said diameter of each said perforation are determined based on transformation acoustic, using a Jacobian transformation defined by the formula $J=\frac{\partial \left(x,y,z\right)}{\partial \left(u,v,w\right)}=\left[{\hspace{1em}\frac{\partial \left(u,v,w\right)}{\partial \left(x,y,z\right)}\hspace{1em}}^{-1}\right].$

7. The metamaterial muffler of claim 4, wherein said muffler is placed at a beginning of an air duct adjacent to a noise source.

8. The metamaterial muffler of claim 4, wherein said muffler is placed at an end of an air duct adjacent to a terminal opening in said air duct.

9. The metamaterial muffler of claim 4, wherein said muffler conforms to a shape of a duct.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a diagram of acoustic metamaterial with anisotropic inertia, used in embodiments of the disclosed technology.

(2) FIG. 2A shows a diagram of an acoustic metamaterial noise control system, with rectangular muffler placed at the end of a duct to reduce noise, in embodiments of the disclosed technology.

(3) FIG. 2B shows a cross-section of the rectangular area of the muffler of FIG. 2A.

(4) FIG. 3A shows the diagram of FIG. 2B with a circular muffler placed at the end of a duct to reduce noise, in embodiments of the disclosed technology.

(5) FIG. 3B shows a cross-section of the circular area of the muffler of FIG. 3A.

(6) FIG. 4 shows an acoustic metameterial block formed by a periodic stack of micro-perforated panels, used in embodiments of the disclosed technology.

(7) FIG. 5 shows an acoustic metamaterial liner formed by micro perforated sheets.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE DISCLOSED TECHNOLOGY

(8) An acoustic metamaterial noise control system of embodiments of the disclosed technology combines absorptive materials with acoustic metamaterial principles, with a result of a significant reduction in sound radiation within, or emanating from, an HVAC duct. Sound waves that hit the noise control system placed at the end of the duct cause the sound waves to reflect back to the start of the noise control system and to be absorbed by sound waves within the absorptive core. This is accomplished by way of the use of micro-perforated panels (MPPs) for sound absorption. For purposes of this disclosure, an MPP is defined as a device used to absorb sound and reduce sound intensity comprised of, or consisting of, a thin flat plate less than, or equal to, 2 mm thick, with a hole diameter between 0.1 and 0.4 mm.

(9) Perforations in the acoustic metamaterial provide acoustic metamaterial anisotropic (directionally dependent) characteristics of the core of the material. Using acoustic metamaterial principles, the noise control system can operate at lower frequencies and also over a broader frequency range than known in the prior art. Acoustic metamaterials are engineered material systems containing embedded periodic resonant or non-resonant elements which modify the acoustic properties of the material either by added dynamics or by wave scattering. Typical prior art ranges of frequencies are 100 Hz, with a lowest range of 10,000 Hz, similar to the frequency range for the present technology with a lowest range of 100 Hz. However, present technology, based on conventional isotropic acoustics theory, has severe limitations in the lower frequency region (<500 Hz) which can only be solved by increasing thickness and or other parameters of the absorptive material, making it costly, heavy, and thus prohibitive.

(10) The acoustic metamaterial noise control system can be positioned or placed at the beginning or end of the ducting to reduce the noise radiating out of the end of the HVAC ducting. Absorptive lining (defined as a sheet of material with a thickness between 0.1 and 5 mm) periodically placed inside the metamaterial noise control system around the interior spaces further enhances noise reduction over broadband frequency range.

(11) The following principles are used in conjunction with embodiments of the disclosed technology. Transformation acoustics is a mathematical tool which completely specifies the material parameters needed to control the wave propagation through the material. It allows control over a two-dimensional acoustic space with anisotropic characteristics. A transformation from the real (r) space described by the (x, y, z) coordinates to the desired, virtual (v) space specified by the (u, v, w) coordinates is shown below.

(12) ${\stackrel{\prime }{\rho }}^r=\frac{\det \left(J\right){\left(J^{-1}\right)}^T}{J}{\stackrel{\prime }{\rho }}^v$
{acute over (κ)}.sup.r=det(J){acute over (κ)}.sup.v

(13) $J={\left(\begin{array}{ccc}\frac{\partial u}{\partial x}& \frac{\partial u}{\partial y}& \frac{\partial u}{\partial z}\\ \frac{\partial v}{\partial x}& \frac{\partial v}{\partial y}& \frac{\partial v}{\partial z}\\ \frac{\partial w}{\partial x}& \frac{\partial w}{\partial y}& \frac{\partial w}{\partial z}\end{array}\right)}^{-1}$

(14) $\mathrm{as},J=\frac{\partial \left(x,y,z\right)}{\partial \left(u,v,w\right)}={\left[\frac{\partial \left(u,v,w\right)}{\partial \left(x,y,z\right)}\right]}^{-1}$

(15) Here, ρ is fluid mass density and κ is fluid bulk modulus, r and v superscripts denote the real and virtual spaces, and J is Jacobian transformation.

(16) FIG. 1 shows a diagram of acoustic metamaterial with anisotropic inertia, used in embodiments of the disclosed technology. Using the transformation acoustics (TA) approach, the densities and bulk modulus in two dimensions on a structure can be engineered to be anisotropic. In FIG. 1, 120 indicates a two-dimensional metamaterial block having anisotropic characteristics with two different densities, ρ.sub.1, ρ.sub.2 along two directions 112 (x-axis) and 114 (y-axis). In conventional, isotropic acoustics, these densities are assumed to be the same in two directions. 102 and 104 show layered media, with 102 being one fluid medium (e.g., air) whereas the layer 104 is made of a different material, such as aluminum, or plastic usually having a greatly different acoustic impedance than 102.

(17) FIG. 2A shows a diagram of an acoustic metamaterial noise control system, with a rectangular muffler placed at the end of a duct to reduce noise, in embodiments of the disclosed technology. FIG. 2B shows a cross-section of the rectangular area of the muffler of FIG. 2A. A noise source 202, such as a fan, motor, impeller, or other moving or rotating part of an HVAC system propagates sound waves 204 through a duct 206 into a metamaterial structure 208. The metamaterial design comprises a stack of perforated sheets 210 made of an acoustically hard material, defined as a surface having almost infinite acoustic impedance (greater than 1*10^7 kg/(m2s)) compared to the characteristic impedance of the ambient medium, separated by a sound-supporting fluid (e.g., air), The elementary constituent parts of the stack of plates is a 2D rigid hole array, shielding sound near the onset of diffraction. Such a structure thus can be made practical by fabricating it out of micro-perforated panels (MPP) which allow anisotropic variables to be achieved.

(18) FIG. 3A shows the diagram of FIG. 2B with a circular muffler placed at the end of a duct to reduce noise, in embodiments of the disclosed technology. FIG. 3B shows a cross-section of the circular area of the muffler of FIG. 3A. Here, elements of FIGS. 2A and 2B have been incremented by 100. Thus, the noise-producing region 302 causes sound waves 304 to flow through an HVAC duct 306 into the muffler 308. The muffler 308 has a curricular cross-section, in this embodiment, with a series of perforated sheets 310.

(19) FIG. 4 shows an acoustic metamaterial block formed by a periodic stack of micro-perforated panels, used in embodiments of the disclosed technology. It has been shown that these metamaterial blocks with perforated stacks exhibit broad-angle negative refraction, unlike fishnet electromagnetic metamaterials, which operate within narrow angular ranges. The proposed metamaterials also do not rely on diffraction to achieve negative refraction, in contrast to phonon crystals. Each perforated layer in this figure indicates a layer made of a hard material or surface, having much higher acoustic impedance (defined as “greater than 1000 times”) than the adjoining layer, which is usually the ambient medium, such as air. In this layer, 302 indicates a hole of a certain diameter and spacing from the next hole, whereas 304 denotes the hard material or unperforated part. of the layer.

(20) FIG. 5 shows an acoustic metamaterial muffler configuration formed by micro-perforated sheets. A face sheet 406 has a plurality of perforations, as do the plurality of perforated sheets 402 extending parallel and perpendicular to each other in a lattice formation between the face sheet 406 and a back sheet 408.

(21) Since the material parameters for the metamaterial panel are given by the first partial derivatives of the transformation functions, in order to obtain a homogeneous perforated MPP panel, the transformation functions are linear. One such choice suitable for the rectangular object considered here is:
u=x,
v=y
w=w.sub.zz
It is to be noted that the expression of v may not be linear inside the whole transformation domain; however, it is linear inside each one of the x<0 and x>0 domains. This translates into same material parameters in each half of the metamaterial panel, but different directions of the principal axis, defined as the directions along which the material parameter tensors are diagonal. The constant w.sub.z represents a degree of freedom that allows for a tradeoff in performance for fabrication simplicity.

(22) The material parameters inside the metamaterial MPP panel, i.e., mass density pseudotensor and bulk modulus, are given by . . . >>>(Equation . . . below)
J.sup.−1


ρ=det(J)
where ρ.sub.0=1.29 kg/m.sup.3 and B.sub.0=0.15 MPa are the parameters of air, and J is the transformation Jacobian:

(23) $J=\frac{\partial \left(x,y,z\right)}{\partial \left(u,v,w\right)}=\left[{\hspace{1em}\frac{\partial \left(u,v,w\right)}{\partial \left(x,y,z\right)}\hspace{1em}}^{-1}\right].$

(24) According to the coordinate transformation theory, the mapping functions given by the above translate to the following material parameters:
ρ.sub.11.sup.pr=K .sub.1ρ.sub.0,
ρ.sub.22.sup.pr=K .sub.2ρ.sub.0,
B.sup.pr=K.sub.3B.sub.0,
a=α°.  (3)

(25) Here K.sub.1, K.sub.2, K.sub.3 are constants. To obtain anisotropic metamaterial, perforated plastic plates are used. The size and shape of the perforation determines the momentum in the rigid plate produced by a wave propagating perpendicular on the plate, and, therefore, can he used to control the corresponding mass density component seen by this wave. This property is used to obtain the higher density component. If, on the other hand, the wave propagates parallel to the plate, it will have a very small influence on it, and, consequently, the wave will see a density close to that of the background fluid. The compressibility of the cell, quantified by the second effective parameter, the bulk modulus, is controlled by the fractional volume occupied by the plastic plate.

(26) Expressed in another way, using perforated sheets with acoustically absorbent layers and air gaps in anisotripic metamaterial systems is manipulated by the size and shape of the perforations of the perforated sheets. The spacing between sheets is 0.5 to 55 mm, with a sheet thickness between 0.1 and 0.5 mm. The percentage open areas for perforated sheets are between 0.1 and 2% open. An absorptive layer whose thickness is between. 0.5 and 55 m can also be used. This determines the momentum of air particles in the sheets, produced by a wave-propagating perpendicular on the sheets as designed and optimized. The thickness and number of acoustically absorbent layers are also optimized, using metamaterial principles as follows: The perforated anisotropic metamaterial layers and absorptive layers of a particular thickness are arranged in a periodic manner, as shown in FIG. 1, to achieve anisotropic properties of the fluid in the area directly next to the face sheet (see FIGS. 4 and 5). In this manner, the sound in air can be fully and effectively manipulated, using realizable transformation acoustics devices. All the geometric parameters of perforated layers and absorptive layers are determined, using numerical simulation based on equations above. This approach can be used to design a duct noise control system to control and manipulate sound waves for the purpose of enhancing noise attenuation, although the required material parameters are highly anisotropic.

(27) Another innovative feature of the duct noise control system is that it can he designed using periodic arrangement of noise blocking and/or reflecting (i.e., perforated layers) and noise absorbing MPP layers separated by air gaps. The parameters of each of the constitutive elements of the system are: hole diameter, sheet thickness, hole spacing, POA (percent open area), absorbing layer sheet thickness, absorptive layer parameters including porosity, tortuosity, flow resistivity, density, viscous and thermal characteristic lengths, etc. The spacing between each MPP layer and the absorptive layer thickness is determined by rnetarnaterial theory described herein. Acoustical characteristics of noise blocking and/or reflecting or noise absorbing MPP layer etermined by suitably designed hole patterns using metamaterial theory.

(28) While the disclosed technology has been taught with specific reference to the above embodiments, a person having ordinary skill in the art will recognize that changes can be made in form and detail without departing from the spirit and the scope of the disclosed technology. The described embodiments are to be considered in all respects only as illustrative and not restrictive. All changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope. Combinations of any of the methods and apparatuses described hereinabove are also contemplated and within the scope of the invention.