Construction and Processing of Model

The approach to developing a suitable FEA model is similar to that used for the CFD model in chapter 3, therefore only the specific differences when processing the acoustic simulation are described here. One important difference is the orientation of the 2-d plane; in the fluid CFD simulation the model described thex-yplane and neglected thez-axis, across width, direction as it was assumed that thex-yflow field was significantly more important. With the acoustic field, it can be seen in figure 4.1(a) that during operation, other than the strongery-axis primary axial force, the lateral forces acting in thez direction are of most interest as these form the striated patterns, therefore suggesting acoustic simulation of they-zplane.

Pre-processor

The finite element analysis investigation uses plane acoustic fluid elements, requiring the input of acoustic property values including density, sonic velocity and absorption coefficient at boundaries. The acoustic fluid elements are used for both the fluid and solid phase layers of the separator; although solid elements are available giving similar modal results, they are not as convenient for submission and extraction of acoustic parameters within solid phase regions. Also, use of fluid elements does not support the analysis of structural modes, therefore analysis results only include acoustic enclosure modes.

Using the 2-d plane elements and appropriate boundary conditions, it is possible to approximate the 1-d as well as the 2-d case. Figure 4.2(a) illustrates schematically the use of a single pressure release surface and a horizontally constrained one element wide model to simulate the acoustic field in the fluid and reflector (Pyrex) layers. In this case the field varies only in theydirection and is effectively a 1-d simulation. Figure 4.2(b) simulates the 2-d aspect of the fluid and reflector layers where the reflector layer is seen to encase the fluid region. Pressure release boundaries exist on the top and side of the reflector and to simplify the simulation only half the structure is modelled, facilitated by the use of a symmetry plane on the left side.

Figure 4.2: Schematics of (a) 1-dimensional and (b) 2-dimensional models indicating the fluid and reflector elements and boundary conditions. Boundary conditions applied include zero displace- ment boundaries (

.

Although the FEA software is capable of simulating all the layers included in the separator design, only the reflector and fluid layers are included in the current study. Once a degree of confidence is established with this level of modelling, subsequent work may include simulation of the silicon matching layer, glue and transducer, but is beyond the remit of this thesis.

Solution Phase

Both modal and harmonic analyses can be completed on the model, giving the response to modal frequencies or a chosen frequency, respectively. For harmonic analyses, the applied pressure at the vibrating surface may be input as a complex number, indicating a phase difference between the acoustic pressure and velocity fields, and allows for losses in the media. The modal analyses are used to identify the resonant behaviour of the layers and are used throughout this study.

Post-processor

In the output listings of the ANSYS package the modal analysis gives a real component of the acoustic pressure field. However, the harmonic analysis gives real and imaginary components of

Figure 4.3: Example of mode shape pressure maxima and minima in a rectangular cavity for m= 2andn= 3.

pressure and particle velocity and so can be used to determine the acoustic radiation force. Also, vectory and z quantities are given as separate components corresponding directly to axial and lateral radiation force components.

4.2.3 2-Dimensional Fields in Rectangular Enclosures

To investigate the accuracy of the model a 2-dimensional resonant pattern is simulated. A simple rectangular waveguide is used as the basic resonant characteristics can be determined analytically. Kinsler et al. [133] give an expression for the resonant frequencies of a rectangular waveguide,

f = c 2 s _l Lx 2 + _m Ly 2 + _n Lz 2 , (4.1)

where the various dimensions of the waveguide are given byLx, Ly andLz with relative mode

orders of l, m andn. If the x dimension is assumed large compared to the other dimensions,

equation (4.1) is reduced to a 2-d description of they-z plane. As an example, a mode pattern

resulting from m = 2 and n = 3 is shown in figure 4.3 which indicates regions of acoustic

pressure maxima and minima. For the reflector layer, based on a thickness of 1525µm, device

external width of 6.8mm andc= 5430m/s for Pyrex, this mode shape would occur at a frequency

of 3.76MHz.

The same geometry is simulated in the FEA model and comprises simply of a 2-d rectangular structure with pressure release boundaries on all sides. A modal analysis then identifies various resonant frequencies and the associated mode shape. The mode shape described in figure 4.3 has

Figure 4.4: Modelled example of resonance in a rectangular cavity.

been modelled and is shown in figure 4.4. The analytically calculated and modelled frequencies are in agreement, providing confidence in the FEA approach used.

It can be seen in figure 4.4 that 2-dimensional resonant fields are characterised by acoustic pres- sure variations occurring in both directions. In the fluid filled cavity it is expected that similar 2-d enclosure modes give rise to pressure gradients and, therefore, acoustic forces in the lateral zdirection as well as the y direction, as initially intended for particle manipulation. Further, it can be imagined that all 3 dimensions would be subject to similar modes. Whilst the mode shape and resonant frequency in a simple rectangular cavity can be determined analytically, the geom- etry and therefore the mode shapes in layered ultrasonic devices is more complex and cannot be solved analytically, supporting the use of computational approaches such as FEA. The following subsections now progress with an FEA model and attempt to simulate the layered structure of the

device both in 1-d and 2-d.