Page 25 - Oil and Gas Simulations

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LUBRICATION
to ‘tweak’ the numerical parameters of
the multigrid method in order to get
convergence.”
FIGURE 2. Typical calculated oil film thickness (red curves) and pressure (blue curves) for èEXAMINING POINT
an elastohydrodynamically lubricated line contact. The simulations were performed for an CONTACTS IN FUTURE WORK
oil temperature of 373 K and a contact entrainment speed of 10 m/s, which is typical for
gear contacts. The results are from Shell’s proprietary solver. The Shell team is also interested in
lubricated ‘point contacts,’ such as rolling
The Shell team has found that this use COMSOL for more difficult analyses,” element bearings, as there are many
approach has converged reasonably well says Taylor. “One of the fundamental billions of these in machines across the
for pressures less than 1 GPa. For higher advantages of COMSOL is that we can world. Some of them are lubricated with
pressures from higher loads, it becomes develop models without any lines of code grease, a viscoelastic material, rather than
necessary to dampen oscillations in the whatsoever. This makes maintenance and a liquid lubricant. “Whereas the Reynolds’
calculated pressure distribution. Taylor modification of models much simpler. lubrication equation cannot be used for
explains: “Small diffusive terms can be It is also much easier when we need to viscoelastic fluids without significant
added to the Reynolds’ equation, or even consider real lubricated contacts. These modification, multiphysics simulation
better, SUPG (Streamline Upwind Petrov are rough, at the micron scale, and so a could solve the same lubricated contact
Galerkin) methods can be used to add typical 3 mm contact would need to be with the full Navier-Stokes equations,
residual based stabilizing terms to the described by approximately 1,000 nodes, using the correct viscoelastic properties
original equation. This approach then if we model it accurately. This would of the grease,” Taylor observes. “As most
enables successful simulation of contacts take up too much computer time and lubricated contacts are subject to time
for pressures up to 4 GPa.” memory for the direct method used in varying loads, the ability to predict the
Over the years the Shell team has the proprietary solver. While we could use time dependence of oil film thickness
conducted many simulations using a multigrid methods, it is often necessary and friction is essential. We have in
proprietary direct solver, which also uses fact already used COMSOL to look at
adaptive meshing. The software, written such effects for gear teeth, which are
in a mixture of FORTRAN and C, consists effectively line contacts.”
of approximately 20,000 lines of code The accurate modeling of grease-
(although this includes the solver code lubricated rolling element-bearing
as well). “This solver works very well contacts is now an active area of current
for smooth surfaces; a small number of research for many companies, including
discretization nodes; ‘simple’ rheology, Shell, and Taylor expects to be making
with no viscoelasticity; and it assumes even more use of COMSOL Multiphysics. v
Reynolds’ equation holds.” The results
shown in Figure 2 are from this solver.
However, the proprietary solver code is
not so straightforward to modify and it
sometimes poses a steep learning curve for
newcomers. Members of the Shell team are
increasingly turning to
COMSOL Multiphysics® software for
complex lubrication problems (see Figure 3).
èMODELING AT THE MICRON FIGURE 3. Calculation of pressure distribution in lubricated line contact, using COMSOL®
SCALE software. The conditions are the same as those used in Figure 2.
Over the past three years the team has
been using both systems to confirm
that they obtain the same results from
COMSOL Multiphysics as they do from
their own solver. “It is still easy to use
the solver for some problems, but we
COMSOL NEWS 25
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