Advances in Acoustics and Vibration

Volume 2017, Article ID 1960898, 18 pages

https://doi.org/10.1155/2017/1960898

## Vibroacoustic Analysis of a Refrigerator Freezer Cabinet Coupled with an Air Duct

Mechanical Engineering Faculty, Istanbul Technical University, Gumussuyu, 34439 Istanbul, Turkey

Correspondence should be addressed to Haluk Erol; rt.ude.uti@ahlore

Received 29 April 2016; Revised 19 October 2016; Accepted 10 November 2016; Published 9 February 2017

Academic Editor: Sven Johansson

Copyright © 2017 Onur Çelikkan and Haluk Erol. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this study, the vibration and acoustic interactions between the structure and the cavity inside the freezer cabinet were investigated. Thus, a set of numerical and experimental analyses were performed. In the numerical analysis, the acoustic characteristics of the freezer cavity were solved, and the mixed finite element method was then implemented to analyse the coupled behaviour of the cavity with the air duct using the Acoustic Fluid-Structure Interaction (AFSI) technique. In the experimental analyses, an acoustic modal analysis of the freezer cavity and a structural modal analysis of the air duct were performed for the validation process. A good agreement was obtained among the results. Thus, the accuracy of the numerical model was confirmed. The validated models were used for optimizing the design. To solve the noise generation mechanism inside the freezer cabinet, the noise primarily generated by the freezer fan unit was measured under normal working conditions of the refrigerator, and the resonance frequencies were obtained. This information was compared with the normal modes of the air duct, and the overlapping frequencies were identified. To reduce the interaction between the source and the structure, a few design modifications were applied to the air duct. Thus, the structural-borne noise radiating from the air duct into the freezer cavity was reduced.

#### 1. Introduction

One modern innovation is the no-frost (or frost free) type of refrigerator, which uses an autodefrost technique that regularly defrosts the evaporator in a refrigerator or freezer. This type of refrigerator is equipped with an additional ventilation fan mounted in the air duct to circulate the cooled air and aid in the defrosting process. In this type of configuration, the fan and the compressor become a source of noise, which is the primary contributor to the overall noise level of the refrigerator, thus increasing the vibration and resulting in sound level a few decibels compared to static cooling refrigerators. Furthermore, the increasing demand for larger fresh-food storage capacities results in refrigerators with larger volumes, which need faster ventilation fans to generate larger flow rates. This high-speed rotation generates more sound energy, and this situation increases the priority of the fan among the other noise sources in the refrigerator. This case demonstrates that applying new technologies in refrigerators involves additional noise and vibration sources, which need to be investigated.

Baran et al. observed that the primary source of vibration typical for a no-frost refrigerator is the imbalance of the blades of the ventilation fan, which stimulates the plenum and effectively causes the entire structure to vibrate [1]. Seo et al. achieved a reduction in the refrigerator’s sound pressure level by isolating the transmission of ventilation noise between the freezer compartment and the machinery room [2]. Takushima et al. searched for the sound sources using the sound intensity method, which indicated that the noise radiated through the openings of the front board [3]. Igarashi and Kitagawa performed CFD (Computational Fluid Dynamics) analyses by evaluating the flow fields of a propeller fan used in the freezing compartment of household refrigerators [4]. Kim et al. identified the source of excessive noise in a small fan-motor system for household refrigerators. They investigated an undesirable effect of cogging torque from the BLDC motor, which prevented the smooth rotation of the rotor and resulted in noise [5]. Gue et al. conducted experimental and numerical investigations on the aerodynamic noise of an axial fan to develop a low noise fan, which was used to cool a compressor and a condenser in the mechanical room of a household refrigerator [6]. Öztürk and Erol showed that the contribution of structure-borne noise from the vibrating panels to the overall noise levels is significant for end users because of its relationship to noise and comfort, especially at low frequencies [7].

The goal of this study is to analyse the acoustic characteristics of the freezer compartment coupled with the air duct. Hence, the study is divided into two sections. In the first section, fluid analyses have been performed with the fan blade in the air duct, and the pressure distribution is solved in the interior surfaces of the fan louver and the evaporator cover. In the second section, coupled acoustic modal analyses have been performed between the air duct and the freezer compartment using the acoustic-structure interaction techniques. The results obtained from the numerical solutions have been validated by the experimental results. In the validation process, an experimental modal analysis was performed for the air duct, and an experimental acoustic modal analysis was performed for the freezer compartment using an external sound source. Consequently, the vibration characteristics of the air duct have been resolved, and the contribution to the noise generation in the freezer compartment has been observed.

#### 2. Theory

For the acoustic-structure system, the structure is described by the differential equation of motion for a continuum body assuming small deformations whereas the fluid is described by the acoustic wave equation. Coupling conditions at the boundary between the structural and fluid domains ensure the continuity in displacement and pressure between the domains. The governing equations and boundary conditions, as described in detail by Carlsson [8], can be written as follows:where denote stresses, denote body forces, denotes dynamic density, and show displacements for the structural domain and fluid, separately, denote the Cartesian coordinates, denotes time in seconds, denotes dynamic pressure, denotes added fluid mass per unit volume, Ω’s show domains, is the speed of sound, and denotes a gradient of a variable; that is,and the differential operator can be written asThe finite element formulation of both the continuum body and the acoustic fluid is used for modelling the fan louver and freezer cavity. The structure of interest in most acoustic-structure problems is two-dimensional and therefore often described using the plate or shell theory.

The structure is described by the equation of motion for a continuum body. The finite element formulation is derived with the assumption of a small displacement. The governing system of equations can be written as follows [9]:where where contains the finite element shape functions for the structural domain, is the finite element approximation of the displacement, is the nodal weight functions, is the surface traction vector, andwhere and are the Lame coefficients expressed in the modulus of elasticity, , the shear modulus, , and Poisson’s ratio.

In Acoustic Fluid-Structure Interaction problems, the structural dynamic equation must be considered along with the Navier-Stokes equations of fluid momentum and the flow continuity equation. The governing equations for an acoustic fluid can be derived using the following assumptions for the compressible fluid: the fluid is inviscid; the fluid only undergoes small translations; and the fluid is irrotational. Thereby, the governing equations for an acoustic fluid are the equation of motionthe continuity equationand the constitutive equationThe system of equations for an acoustic domain becomeswherewhere contains the finite element shape functions for the fluid and* n*’s denote normal vectors.

At the boundary between the structural and fluid domains, denoted as , the fluid particles and the structure move together in the normal direction of the boundary. Furthermore, the acoustic-structure problem can be described by an unsymmetrical system of equations as follows:where denotes spatial coupling matrix.

#### 3. Numerical Studies

The numerical simulations were performed using the FEM solver ANSYS Workbench R15.0. In the frame of this study, each component composing the freezer compartment was first investigated individually. Thus, acoustic analyses of the freezer cavity and the modal analysis of the fan louver and evaporator cover were performed so that the mode frequencies and mode shapes could be obtained. Then, to create a realistic model, the flow field inside the air duct was modelled and included in the analyses. Lastly, a coupled modal analysis was performed to solve the problem between the structure and the acoustic cavity. The change in the acoustic modes of the freezer cavity was observed.

The fluid-structure interaction simulations were performed using the multifield solver, which used an implicit sequential coupling to calculate the interactions between the fluid and structural analyses. The FSI techniques are used to compute the effects between the acoustic and structural domains using specialized acoustic elements.

In the details of the analysis process, the state variables were defined, and the mathematical model was built to describe the physical phenomena. The mathematical model may deviate from the actual model due to various assumptions, such as viscosity and compressibility for the fluid flow and stiffness and damping for the structure.

It is widely accepted that the element size in element-based acoustic computations is related to the wavelength. In modelling, the element size has been chosen very small to ensure the sufficient number of elements per wavelength that corresponding to upper limit of frequency. The properties such as density and bulk modulus have a significant role in specifying the wavelength also defined for the fluid media. Before performing an experimental analysis to validate the numerical studies, it is possible to perform a preliminary examination basically. To show the cause of the similarity of the freezer cavity to the rectangular box, the analytical solution is also available. The equivalent box model with the same outer size could be easily used to represent the cavity model [10].

The interior of a freezer compartment resembles a closed rectangular volume, which has a simple analytical solution for its natural frequencies and acoustical modes. The natural frequencies can be calculated as follows:

Furthermore, the mode shapes can be calculated as follows:where m and is the width of the freezer cabin; m and is the height of the freezer cabin measured from the bottom to the top; and m and is the depth of the freezer cabin measured from the fan louver to the freezer door. The speed of sound is calculated at room temperature (at 25°C), and the indexes for the normal modes of vibration , , and . Figure 1 depicts the inner dimensions of the freezer compartment and the isometric 3D model.