SCMFrictionChenTodreas

Upgraded Chen-Todreas parameterization

For friction_model = Upgraded, the laminar and turbulent transition Reynolds numbers are given by Eqs. (3) and (2) of UCTD,

and

The turbulent wire-drag coefficient is evaluated as in Eq. (14) of UCTD, with the sign of the linear term corrected in Chen et al. (2018),

with the laminar coefficient from Eq. (19) of UCTD,

The turbulent wire-sweep coefficient is given by Eq. (21) of UCTD,

with Eq. (20) of UCTD,

The intermittent-regime interpolation, Eq. (4) of UCTD, uses

Pacio-Chen-Todreas parameterization

For friction_model = Pacio, the transition Reynolds numbers are independent of and are given by Eqs. (13) and (12) of PCTD with the coefficients of its Table 5,

The turbulent wire-drag coefficient is evaluated using Eq. (21) of PCTD as

with the laminar coefficient from Eq. (22) of PCTD,

The turbulent wire-sweep coefficient is given by Eq. (1) of PCTD,

with Eq. (26) of PCTD,

The intermittent-regime interpolation, Eq. (35) of PCTD, uses

Flow-regime interpolation

For both triangular-lattice parameterizations, the interpolation factor in the intermittent regime is evaluated using the bulk Reynolds number as in Eq. (5) of UCTD and Eq. (34) of PCTD,

The laminar and turbulent subchannel friction factors, Eqs. (A1) and (A2) of UCTD and Eqs. (16) and (15) of PCTD, are

and

where is the local subchannel Reynolds number and and include the appropriate bare-pin and, when present, wire-wrap contributions.

The intermittent friction factor is calculated as in Eq. (4) of UCTD and Eq. (35) of PCTD,

The values of , , , and are determined by the selected friction_model. Table 5 of PCTD compares all coefficients of both parameterizations.

Both and are evaluated at the local Reynolds number of the subchannel, from its current mass flux, as Eq. (35) of PCTD is written. The example calculation of PCTD, its Section 6.1.3, instead evaluates with the laminar flow split and with the turbulent flow split of the subchannel type, computed before the transition regime. In the transition regime this gives a different flow split than the PCTD curves of the paper, up to about 0.14 in the corner subchannel of a 37-pin bundle; the laminar and turbulent regimes are not affected. Friction Factor Closures Verification compares the two.

Applicability

For triangular lattices, the closure flags a solution warning when , wire-wrap , number of pins, or the bulk Reynolds number is outside the data range associated with the selected friction correlation. Both sets of ranges are the reported ranges of validity in Table 1 of PCTD.

For the Upgraded parameterization, the implemented applicability ranges are

and

For the Pacio parameterization, the implemented applicability ranges are

and