Slide film damping occurs if two surfaces separated by a thin fluid film move tangentially with respect to each other, because energy is dissipated due to viscous flow. Typical applications are damping between the fingers of comb drives and horizontally-moving seismic masses.
FLUID139 is used to model slide film damping. FLUID139 can model Couette and Stokes flow (Figure 5.1: Slide Film Damping at Low and High Frequencies). Couette flow assumes a constant velocity gradient across the fluid gap. Tangentially moving surfaces at low frequencies produce a nearly constant velocity gradient in the fluid, so Couette flow is applicable to low frequencies.
Stokes flow assumes that the velocity gradient is not constant across the fluid gap. Tangentially moving surfaces at high frequencies do not produce a constant velocity gradient, so the Stokes flow is applicable to high frequencies. The transition from Couette to Stokes flow occurs near the cut-off frequency.
where ρ is the fluid density, η the dynamic viscosity and d the gap separation.
Couette flow does not occur at high frequencies, because inertial effects are important and viscous friction is only able to accelerate a thin fluid layer near the moving surface. The penetration depth is given by
FLUID139 models the effect of viscous flow in the thin film with a series of mass-damper elements, as shown in Figure 5.2: Viscous Slide Film Element FLUID139. Couette flow is modeled using a two-node option. Stokes flow is modeled using a 32-node option. In the 32-node option, the end nodes (node 1 and 32) are connected to the structural portion of the model with structural degrees of freedom, and the series of mass-damper elements are contained within "auxiliary" nodes (nodes 2-31).
The gap separation distance (GAP) and the overlap area of the surfaces (AREA) are specified as real constants for FLUID139. If the overlap area changes during the analysis, the area change rate (DADU) must also be specified as a real constant. A changing overlap area is typical in lateral comb drives.
AREA is the initial overlap area, DADU is the change in the overlap area with respect to the surface displacement, and un and ui are the location of the interface nodes (1 and 32). Note: For a constant surface area, DADU is the width of the overlap surface.
FLUID139 may be used for a prestress static analysis in conjunction with a prestress harmonic analysis, as well as a full transient analysis. Prestress analysis is required if the plate area changes due to the structural displacement. A typical command sequence for a prestress harmonic analysis would include the following:
/solu antyp,static pstress,on . . solve fini /solu antyp,harmonic pstress,on . . solve finish
KEYOPT(3) specifies the continuous flow options. For a no-slip assumption at the wall, use the continuum theory (KEYOPT(3) = 0). For slip flow where the Knudsen number is much less or much greater than 1.0, use the first order slip flow condition (KEYOPT(3) = 1). For slip flow with a Knudsen number of approximately 1.0, use the extended slip flow option (KEYOPT(3) = 2).
