Code Manual for CONTAIN 2.0 - Federation of American Scientists

Flow Time Co nstants. The flow calculations are done with either a Runge-Kutta timestep, in the
explicit flow option, or a convective timestep, in the implicit flow option. In the latter case, the flow
timestep is set to the minimum of convection timestep or the system timestep. With the
recommended implicit flow option, there is relatively little advantage to using a system timestep that
is much larger than the flow timestep, and the system timestep should be set to a comparable value.
Since the system timestep determines the frequency at which global conditions are provided to other
modules, use of a system timestep much larger than the flow timestep may mean that the conditions
are not updated frequently enough. In general, one should check on the sensitivity to the system
timestep by reducing it by a factor of two or more in the time domain of interest.
The convection time will depend on the relative pressure differences between cells. In the blowdown
of cell at high pressure, the cell contents will convect out with a time constant equal to the pressure
relaxation time. A simple rule of thumb for such transient conditions is that if the system timestep
is short enough to resolve a 20% change in the pressures, it should be adequate with respect to the
cell convection time of the blowdown cell.
If the initial pressure difference is not large, the cell contents will not convect out significantly during
the pressure relaxation to the steady state. In this case, most of the convection, if any, will occur
under low, steady-state pressure differences. The timestep to use in this case is less obvious than the
one to use for transients. For cases in which the gas convection time controls the flow timestep, the
steady-state convection time, t,, for cell i with total volume Vi should be obtained from
where the k sum is carried out over all flows into cell i and the j sum is carried out for all flows out
of cell i, Wij is the mass flow rate, and pij is the flow density in the flow path. The steady-state
convection time is typically much longer than the pressure relaxation time in such cases.
Fluid-Structure Time Constant. Another important potential source of inaccuracy or instability due
to explicit coupling occurs at the cell level, where a bulk fluid may transfer an excessive amount of
heat into a structure, because the effect on the surface temperature is not properly taken into account.
A criterion for the maximum cell timestep can be obtained if the fluid-to-structure heat transfer
coefficient his known. By requiring the temperature rise in the first node during a single timestep
Atl to be less than the fluid-structure temperature difference, one obtains for an insulated first node,
Atl