Advances in Acoustics and Vibration

Volume 2016 (2016), Article ID 4785389, 17 pages

http://dx.doi.org/10.1155/2016/4785389

## CAA of an Air-Cooling System for Electronic Devices

^{1}Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 4, 91058 Erlangen, Germany^{2}SIMetris GmbH, Am Weichselgarten 7, 91058 Erlangen, Germany^{3}Vienna University of Technology, Getreidemarkt 9, 1060 Wien, Austria

Received 4 July 2016; Revised 31 August 2016; Accepted 7 September 2016

Academic Editor: Marc Thomas

Copyright © 2016 Sven Münsterjohann et al. 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

This paper presents the workflow and the results of fluid dynamics and aeroacoustic simulations for an air-cooling system as used in electronic devices. The setup represents a generic electronic device with several electronic assemblies with forced convection cooling by two axial fans. The aeroacoustic performance is computed using a hybrid method. In a first step, two unsteady CFD simulations using the Unsteady Reynolds-Averaged Navier-Stokes simulation with Shear Stress Transport (URANS-SST) turbulence model and the Scale Adaptive Simulation with Shear Stress Transport (SAS-SST) models were performed. Based on the unsteady flow results, the acoustic source terms were calculated using Lighthill’s acoustic analogy. Propagation of the flow-induced sound was computed using the Finite Element Method. Finally, the results of the acoustic simulation are compared with measurements and show good agreement.

#### 1. Introduction

In today’s world, the dimensions of electronic components are continuously decreasing. While many electronic devices are consuming less energy than a few years ago, the density of the chips assembled on a printed circuit board is increasing. This higher density leads to less heat dissipation by natural convection, which demands forced convection in order to prevent overheating. Convection can be forced by water or air cooling, with the latter using radial or axial fans to generate an air flow through the devices. As many of these air-cooled devices, measurement equipment or video game consoles, are operated by humans, their noise emission is an important attribute. On the one hand, the noise emission has to be low to please the users; on the other hand, these devices have to meet strict industrial regulations with a maximum allowable noise emission in the working environment. To meet these requirements, the prediction of the noise emission is an essential tool to avoid claims and restrictions. In addition to the experimental investigation of prototypes, the numerical estimation of the noise emission is a useful tool even before a first prototype is built. Acoustic measurements mostly provide an overall sound pressure level of the device without the possibility of closer detection of the acoustic sources. An exception is the microphone array measurement, but the spatial resolution depends strongly on the frequency under investigation. Furthermore, nearly all electronic devices have housing that makes the localization of acoustic sources on the inside virtually impossible. Numerical simulations are not subject to these restrictions and thus provide a strong tool for acoustic optimizations.

In this paper, the numerical calculation of the noise emission of a generic electronic 19-inch slide-in device with two 120 mm axial fans is presented. The computation facilitated an aeroacoustic hybrid approach that uses the Finite Volume (FV) solver ANSYS CFX for the flow simulation and the in-house Finite Element (FE) solver CFS++ [1] for the acoustic simulation. The whole process starting from generation of the CAD model, CFD mesh generation, CFD setup, and solving to acoustic mesh generation and simulation of acoustic wave propagation is described. Two different turbulence models, URANS-SST and SAS-SST, will be compared with a focus on flow field quantities, that is, pressure and velocity, and sound pressure. While the URANS-SST model is only capable of resolving large scaled, triggered phenomena like vortex shedding behind a cylinder or rotor-stator interactions, the SAS-SST model can resolve the turbulence, given that temporal and spatial discretization are fine enough. This will especially improve the acoustic results in frequency ranges where broadband noise caused by turbulence is generated that cannot be resolved by the URANS model. Hence, the SAS-SST model is a good choice for capturing system-triggered as well as turbulence generated noise.

#### 2. Aeroacoustics in Cooling Systems

Most work performed on the acoustics of cooling systems in electronic devices, that is, computers or notebooks, is done experimentally. Baugh [2] investigated the changes in hydrodynamic and acoustic behavior due to the inlet restrictions in notebooks. By scaling the hydrodynamic performance of fans to isoacoustic fan curves under the condition of inlet restrictions, Baugh found a way to compare the in-system performance and acoustic behavior of different fans if the pressure drop in the system is known. Nantais et al. [3] performed acoustic measurements on the cooling solutions for different graphics processing units and found that the noise to be emitted was dependent not only on the fan size and the cooling requirements, but also on the circumferential speed of the fan and the design of the cooling system. Huang’s group carried out research on computer cooling fan noise. Huang [4] used analytic and empirical models to study the influence of rotor-stator interaction by decomposing this source into axial thrust, circumferential speed, and radial force using point force formulation. He investigated the influence of the number of blades and motor struts and the distribution of the source on the noise emission. Later, Huang and Wang [5] combined experimental investigations and an analysis of the rotor-stator interaction with the point source formulation. They found three main sources within the investigated four-strutted seven-bladed fan: the interaction between the blades and the struts, the additional size of one strut holding the electric wiring for the motor, and the incomplete bell mouth at the intake of the fan.

So far, most work has been performed by applying experimental and/or analytic approaches. Defoe and Novak [6] gave a brief review of methods for computational aeroacoustic (CAA) in electronic devices. They discussed different CAA methods: direct CAA, acoustic analogies, boundary element methods, and broadband methods. Comparing the results obtained by other authors with these different methods, the conclusion was drawn that the use of acoustic analogy is the best trade-off between computational effort and a detailed description of the acoustic sound field.

Using numerical methods our intention is to provide further insight into the sound generation in air-cooling systems of electronic devices. With a combination of CFD and CAA and modal analysis of the housing, a wide range of effects in the final acoustic spectra can be explained.

#### 3. Theory

Various approaches have been proposed for both flow simulation and acoustic simulation, and the theories behind these approaches are explained in Sections 3.1 and 3.2.

##### 3.1. Flow Simulation

The turbulence models applied in the flow simulation are the Shear Stress Transport (SST) turbulence model and the Scale Adaptive Simulation (SAS) developed by Menter [7]. As the acoustic source terms are directly derived from the flow field, sufficient resolution of the flow phenomena producing the acoustic sound emission is essential. The unsteady flow field can be simulated using different turbulence modeling approaches. The Unsteady Reynolds-Averaged Navier-Stokes equations in combination with the -, the -, or the SST model are the common way with the least demands regarding spatial and temporal resolution. More information is gained by using the SAS model, which adapts the turbulence modeling with respect to the spatial and temporal resolution. Further details of the flow field are simulated by a detached eddy simulation (DES) or a large eddy simulation (LES). In contrast to the SAS model, which falls back to a URANS solution when the discretization (temporal or spatial) is too coarse, the DES or LES model has special requirements regarding discretization. The best, but also the most expensive, solution is retrieved by a direct numerical simulation (DNS) of the flow. In this case, the discretization must be able to resolve the majority of the turbulent scales in time and space.

The CFD simulations in this paper were performed using the URANS-SST model and the SAS-SST model.

###### 3.1.1. Shear Stress Transport (SST) Turbulence Model

In the SST - model Menter [7] combined the advantages of the - model [8] and - model [9]. Although the - model has its benefits in free stream regions, the - model leads to a more physical resolution of the flow in near-wall regions. With that knowledge, Menter derived the SST - model: two functions, and , dynamically blend between the original - model and a transformed - model. The blending is dependent on the wall distance and the thickness of the boundary layer at that location. The two-equation set of the - model is multiplied by blending function . Accordingly, the transformed - model, which has a transport equation for depending on , is multiplied by . The corresponding transport equations of the models are added, resulting in the equation set of the SST - model [7].

###### 3.1.2. Scale Adaptive Simulation (SAS) Approach

Three types of two-equation turbulence models have been developed in the past: the - model by Kolmogorov [9], the - model by Launder and Spalding [8], and the - model by Rotta [10]. Compared with the - and - transport equations, Rotta found a formulation of the transport equations that hold a natural length scale. The advantage of this length scale is the possibility of dynamically reacting to resolved structures within the flow. In turn, the first and third spatial derivatives of the velocity are inherent in the transport equations.

Based on Rotta’s formulation, Menter and Egorov [11, 12] showed that turbulent transport equations include the second instead of the third derivative of the velocity (as used in Rotta’s approach). The turbulent transport quantities form a model that is known as the SAS model (Scale Adaptive Simulation). The first formulation of the model [12] has undergone some modifications, resulting in the current version of the SAS model [13], which is also implemented in ANSYS CFX 14.0+. Assuming that the turbulent structure is resolved within the flow field and not modeled, the turbulent frequency is increased and finally less modeling of the turbulence occurs due to a reduced eddy viscosity. The advantage of the model is obvious: the SAS-SST model dynamically reduces the modeling provided that turbulent structures can be resolved within the flow field (except for a limiter function to keep a minimum value for eddy viscosity [14]).

##### 3.2. Acoustic Simulation

The process used here to compute the flow-induced sound is a hybrid method; that is, the acoustic simulation is performed as a second step after the results of the flow simulation have become available. The propagation of flow-induced sound is governed by Lighthill’s inhomogeneous wave equation [15]:where is the average speed of sound in air and is a fluctuating pressure, which approaches the acoustic pressure outside the flow region (for details, see [1]). The wave equation is loaded on the right-hand side with the second-order spatial derivative of the Lighthill tensor:which depends on data for the turbulent flow precomputed by the flow simulation, such as the velocity , the aerodynamic pressure , the density , and the viscous stress tensor . For isentropic flow at low Mach number, this can be approximated by , where is the average density of air.

The inhomogeneous wave equation is solved using the Finite Element Method (FEM). Before the spatial and temporal discretization can be applied, the variational formulation of (1) must be derived [16]. This is done by multiplying with a test function and integrating the equation over the simulation domain :Green’s integral theorem is then applied in order to reduce the second-order spatial derivatives to first order:where is the boundary of the simulation domain and is the surface normal vector on . If we set the boundary integral to zero, an acoustically hard wall (i.e., ideally reflecting) is assumed at the boundary. In order to achieve free-field radiation where the boundary is purely artificial (denoted by ), we use an absorbing boundary condition expressed bySubsequently, the computational domain is discretized using Lagrangian finite elements of first order. This allows us to set up a linear system of equations that needs to be solved in each time step in order to obtain the transient sound field.

In order to achieve good accuracy of the numerical solution, the following procedure has proven to provide the best results. First, the source term on the right-hand side of (4) is computed using the FE approach on the fine CFD grid. Then the source terms are transferred to another grid, which is better suited for the wave equation, using an energy-conserving interpolation technique. The sound emission from these sources is then computed using FEM on the acoustic grid.

#### 4. Experimental Setup

The air-cooling of a generic electronic device was subjected to the investigations and simulations performed. As the interaction of the flow field with the obstacles, that is, electronic chips, pins, and heat sinks, can be a source of noise due to the production of, for example, vortex shedding or turbulent shear stresses, these geometric details are present in the experimental and numerical setup.

##### 4.1. Generic Electronic Device

The model of the generic electronic device can be divided into four regions: the inflow area in front of the fans, the fans producing the air flow used for cooling, the settling chamber to generate an even flow through each card slot, and the card slots where the electronic components are located. In the real system, which served as a model for the generic device under investigation, the settling chamber is used to even the flow through the different card slots, especially if not all slots are in use.

The overall dimensions of the electronic device (Figure 1) are mm. It holds eleven card slots, each with an electronic component installed inside. The flow is generated by two axial, five-bladed 119 mm fans with an outer rotor diameter of mm. The design of the electronic components is based on real components for personal computers (i.e., network, sound, and graphic cards).