FLUID136 Element Description

FLUID136 models viscous fluid flow behavior in small gaps between fixed surfaces and structures moving perpendicular to the fixed surfaces. The element behavior is based on the Reynolds squeeze film theory and the theory of rarefied gases. As such, it is limited to structures with lateral dimensions much greater than the gap size. In addition, the pressure change must be small relative to the ambient pressure, and any viscous heating is neglected. FLUID136 is particularly applicable to modeling squeeze-film effects in microstructures. However, it can also model thin-film fluid behavior in macrostructures.

As a fluid-only element (PRES dof), the element can be used to determine the stiffening and damping effects that a fluid exerts on a moving structure by applying a known normal velocity. The velocity normal to the element surface is specified as a body force. If the velocity of the moving surface is not known, FLUID136 can determine the fluid response from the eigenmodes of the structure using the Modal Projection Method.

FLUID136 is applicable to static, harmonic, and transient analyses. A static analysis is used to determine the damping effects for low operating frequencies where fluid stiffening effects are negligible. A harmonic analysis is used to determine the fluid stiffening and damping effects for high operating frequencies where fluid stiffening effects are not negligible. A transient analysis is used to determine the fluid stiffening and damping effects for non-harmonic loadings. The Modal Projection Method can also be used to extract frequency-dependent damping ratios for use with the MDAMP and DMPRAT commands; and Alpha and Beta damping parameters for use with the ALPHAD and BETAD commands.

As a fluid-structure element (PRES, UX, UY, UZ), the element can be combined with solid structural elements in a coupled-field solution where pressure effects are computed from the structure's motion. In this mode, the element is applicable to a static or transient analysis. Compressibility options are available when considering large displacements and/or large pressure changes. Contact options are also available when the structural degrees of freedom are active in order to model opening and closing contact conditions.

FLUID136 can be used to model three different flow regimes: continuum theory, high Knudsen number, and high Knudsen number with accommodation factors.

See FLUID136 in the Mechanical APDL Theory Reference for more details about this element.

FLUID136 Input Data

The element is defined by four corner nodes with an option to include mid-side nodes (KEYOPT(2) = 1). The element should be oriented such that the element normal is pointing toward the fluid domain. If solid elements are used for the structural domain, the fluid element normal vector is automatically computed. If necessary, the fluid element normal vector can be flipped using ENSYM.

Figure 136.1: FLUID136 Geometry

KEYOPT (1) specifies the flow regime. The Knudsen number can be calculated from the mean free fluid path at a reference pressure, the operating or absolute pressure, and the gap.

For a PRES degree of freedom (KEYOPT(3) = 0) and a linearized Reynolds equation (KEYOPT(4) = 0 or 2),

For PRES, UX, UY, UZ degrees of freedom (KEYOPT(3) = 1 or 2) and a nonlinear Reynolds equation (KEYOPT(4) = 1),

where:

For continuum theory to be valid (KEYOPT(1) = 0), the Knudsen number should be less than 0.01. If the Knudsen number is greater than 0.01 (KEYOPT(1) = 1 or 2), the dynamic viscosity is adjusted to account for the slip flow boundary. See Flow Regime Considerations in the Fluids Analysis Guide for a complete discussion of flow regimes and calculation of the Knudsen number.

The type of reflection of the gas molecules at the wall interface is specified using accommodation factors. Squeeze film models assume diffuse reflection of the gas molecules at the wall interface (accommodation factor = 1). This assumption is valid for most metals, but is less accurate for micromachined surfaces, particularly those fabricated from silicon. Materials, such as silicon, cause specular reflection. Typical accommodation factors for silicon are between 0.80 and 0.90.

KEYOPT (3) sets the element degrees of freedom. Setting KEYOPT (3) to 1 or 2 activates the displacement degrees of freedom. When displacement DOFs are active both fluidic and mechanical contact pressures can be generated. FLUID136 can only be used for static and transient analyses when the displacement DOFs are activated.

If KEYOPT(5) = 2, the element is ignored from a fluid pressure standpoint when the fluid gap goes below a specified minimum fluid gap (fluid_mingap). If KEYOPT(6) = 1 or 2, mechanical contact pressure is applied to a structure if the fluid height goes below a specified minimum mechanical gap (mech_mingap).

For the fluid-only option (PRES dof), the fluid velocity normal to the surface may be specified using nodal or element loading with the FLUE body load label on the BF or BFE commands. If FLUID136 is used in conjunction with the Modal Projection Method, the fluid velocities are obtained from the modal displacements and applied using the DMPEXT command.

FLUID136 Input Summary

Nodes

I, J, K, L (KEYOPT(2) = 0)

I, J, K, L, M, N, O, P (KEYOPT(2) = 1)

Degrees of Freedom

See KEYOPT(3)

Real Constants

See Table 136.1: FLUID136 Real Constants.

Material Properties

MP command: VISC (dynamic viscosity)

Surface Loads

None

Body Loads

FLUE (velocity) (For KEYOPT(3) = 0 only)

Special Features

None

KEYOPT(1)

Continuous flow options

0 -- 

Continuum theory

1 -- 

High Knudsen numbers (greater than 0.01)

2 -- 

High Knudsen numbers and accommodation factors

KEYOPT(2)

Element geometry

0 -- 

Four node element

1 -- 

Eight node element (not available if KEYOPT(3) = 1 or 2)

KEYOPT(3)

Degrees of Freedom

0 -- 

PRES (Valid for static, harmonic, and transient analyses.)

1 -- 

PRES, UX, UY, UZ - explicit treatment of cross-coupling terms. Produces a symmetric matrix. Valid for static and transient analyses only. Convergence issues may be experienced if the fluid gap approaches zero.

2 -- 

PRES, UX, UY, UZ - implicit treatment of cross-coupling terms. Produces an unsymmetric matrix. Valid for static and transient analyses only.

KEYOPT(4)

Compressibility. If PRES is the only degree of freedom (KEYOPT(3) = 0), the compressible linearized Reynold equation is used (KEYOPT(4) = 0). The following are valid when degrees of freedom are PRES, UX, UY, and UZ (KEYOPT(3) = 1 or 2).

0 -- 

Compressible linearized Reynolds equation. (large displacement and small pressure changes)

1 -- 

Compressible nonlinear Reynolds equation. (large displacement and large pressure changes)

2 -- 

Incompressible linearized Reynolds equation. (large displacement and small pressure changes)

For more information on the linearized Reynolds equation, refer to Flow Between Flat Surfaces in the Mechanical APDL Theory Reference.

KEYOPT(5)

If the element gap goes below fluid_mingap:

0 -- 

Trap it as an error.

1 -- 

Reset it to fluid_mingap.

2 -- 

Ignore this element from a fluid pressure standpoint. This element is considered dead from a fluids standpoint. However, for postprocessing, a fluid pressure can be specified. See real constants PENP and SPRES.

For KEYOPT(5) = 1 or 2, mechanical contact may be included by KEYOPT(6) or TARGE170 and CONTA174 elements.

If the element gap is above fluid_mingap, fluid pressure is applied on the structure.

KEYOPT(6)

If the element gap goes below mech_mingap:

0 -- 

Do not apply mechanical contact pressure on the structure. This element is considered mechanically dead.

1 -- 

Apply mechanical contact pressure on the structure using the penalty method. Specify a stiffness parameter (real constant STIFFP). Damping is input by real constant DAMPP and it defaults to zero.

2 -- 

Apply mechanical contact pressure on the structure using the augmented Lagrangian method. Specify an initial stiffness (real constant STIFFP) and a penetration tolerance (real constant MPTF). Damping is input by real constant DAMPP and it defaults to zero.

The fluid environment is defined by the following set of real constants.

Table 136.1: FLUID136 Real Constants

No.	Name	Description	Default value
1	GAP	Element gap separation
2	blank	—
3	blank	—
4	PAMB	Ambient (that is, surrounding) pressure
5	ACF1	Accommodation factor for top moving surface.
6	ACF2	Accommodation factor for bottom fixed surface.
7	PREF	Reference pressure for the mean free fluid path
8	MFP	Mean free fluid path at reference pressure PREF
9	GAPX	Gap vector global Cartesian component X	0
10	GAPY	Gap vector global Cartesian component Y	0
11	GAPZ	Gap vector global Cartesian component Z	1
12	MMGF	mech_mingapf (minimum mechanical gap as a fraction of GAP)	1.E−3
13	FMGF	fluid_mingapf (minimum fluid gap as a fraction of GAP)	1.E−3
14	PENP	Penalty parameter for fluid dead element (KEYOPT(5) = 2)
15	SPRES	Specified pressure for fluid dead element (KEYOPT(5) = 2)
16	STIFFP	Stiffness parameter for mechanical contact (KEYOPT(6) = 1 or 2)
17	DAMPP	Damping parameter for mechanical contact (KEYOPT(6) = 1 or 2)
18	MPTF	mech_pen_tolf (KEYOPT(6) = 2) (mechanical penetration tolerance as a fraction of mech_mingap)
19	MINPABSF	minpabsf (minimum absolute pressure as a fraction of Pamb)	1.E−2

For continuum theory (KEYOPT(1) = 1), GAP and PAMB must be specified.

For high Knudsen numbers (KEYOPT(1) = 1), GAP, PAMB, PREF, and MFP must be specified. PREF and MFP are used to adjust the dynamic viscosity. ACF1 and ACF2 are assumed to be 1.

For high Knudsen numbers with accommodation factors (KEYOPT(1) = 2), GAP, PAMB, PREF, MFP, ACF1, and ACF2 must be specified. Different accommodation factors may be specified for each surface.

For small deflections, GAP is assumed to be constant. For the fluid-only option (PRES dof) and large deflections, GAP can be updated using SETFGAP.

Real constants GAPX, GAPY, and GAPZ are the unit vector components of the normal gap vector g in the global Cartesian system (see figure below).

Figure 136.2: Moving Structure with Thin Film of FLUID136 Elements

Real constants FMGF and MMGF determine the minimum fluid gap (fluid_mingap) and minimum mechanical gap (mech_mingap) as shown below:

Figure 136.3: Minimum Fluid and Minimum Mechanical Gaps

Real constant MPTF determines the mechanical penetration tolerance as shown below:

Figure 136.4: Mechanical Penetration

Figure 136.5: Fluid Penetration

Real constant MINPABSFA determines the minimum absolute pressure as shown below. The minimum absolute pressure is used in the definition of Knudson number.

Stiffness is input by real constant STIFFP and it is typically large. Damping is input by real constant DAMPP and it is typically zero.

FLUID136 Output Data

The solution output associated with the element is in two forms:

A general description of solution output is given in Table 136.2: FLUID136 Element Output Definitions. See the Basic Analysis Guide for ways to view results.

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file jobname.out. The R column indicates the availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a letter or number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Contact pressure is computed as an element centroidal quantity:

CONTPRES= STIFFP*mech_penetration + DAMPP*mech_velocity

Table 136.3: FLUID136 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 136.3: FLUID136 Item and Sequence Numbers:

FLUID136 Assumptions and Restrictions

FLUID136 Product Restrictions

There are no product-specific restrictions for this element.