SCMMixingChenTodreas

Class that models the turbulent mixing coefficient for wire-wrapped triangular assemblies using the Chen Todreas correlations.

Overview

This closure class is used to model the turbulent mixing coefficient using the Chen-Todreas correlations for triangular assemblies with wire-wrapped pins. Two mixing-model parameterizations are available: the original Cheng-Todreas (1986) model and the Pacio-Chen-Todreas model.

The implementation is based on:

  • Hydrodynamic models and correlations for bare and wire-wrapped hexagonal rod bundles—bundle friction factors, subchannel friction factors and mixing parameters, Cheng and Todreas Cheng and Todreas (1986).

  • The Pacio-Chen-Todreas formulation Pacio et al. (2022), which introduces an updated mixing treatment to improve the prediction of flow redistribution between interior, edge, and corner subchannels.

The desired parameterization is selected using the mixing_model parameter:

  • 1986 uses the original Cheng-Todreas mixing correlation. In addition it calculates the sweep coefficient for the periphery gaps.

  • Pacio retains the original Cheng-Todreas treatment where applicable and applies the Pacio mixing formulation to center-edge and edge-corner interfaces.

Cheng-Todreas (1986) mixing

For the 1986 model, the base turbulent mixing parameter is applied to gaps connected to a center subchannel. The mixing parameter is used in the global turbulent crossflow relation

The laminar and turbulent mixing coefficients are calculated using the original Cheng-Todreas formulation and the center-subchannel projected wire area and bare flow area .

The flow-regime transition limits are

and

In the intermittent regime, the interpolation factor is evaluated with the bulk Reynolds number,

which simplifies Cheng and Todreas (1986). Their Eqs. (10a) to (10c) and (11) use one interpolation factor per type of subchannel, from the local Reynolds number between the bounds and , with the laminar and turbulent flow splits and . The mixing coefficient is interpolated according to

The resulting turbulent mixing parameter is

Pacio-Chen-Todreas mixing

When mixing_model = Pacio is selected, the Pacio formulation is applied specifically to interfaces involving the edge subchannel:

  • center-edge interfaces use the Pacio mixing formulation;

  • edge-corner interfaces use the Pacio mixing formulation;

  • center-center interfaces retain the original Cheng-Todreas (1986) mixing formulation.

  • sweep-flow implementation remains unchanged.

Thus, selecting Pacio does not globally replace the original Cheng-Todreas mixing model. Instead, it replaces or supplements the mixing treatment at the interfaces for which the Pacio formulation is applied.

The Pacio mixing coefficient depends on the flow-split parameters

where and are the axial velocities of the two types of subchannels on either side of the gap and is the bundle bulk velocity. As in the PCTD model, where the flow split is defined per type of subchannel, the velocity of each type (interior, edge, or corner) is lumped over all subchannels of that type in each axial cell: the sum of their mass flow rates divided by the sum of their density times flow area. The velocities of the three types are divided by their area-weighted mean, so that the flow splits satisfy the mass balance of Eq. (11) of Pacio et al. (2022) at every axial level, also in a heated assembly, where the bulk velocity rises above its inlet value as the density decreases. The Pacio mixing coefficients are therefore computed once per axial cell for the center-edge and edge-corner gaps, before the turbulent crossflow is computed. The Cheng-Todreas (1986) mixing and sweep-flow coefficients depend only on the geometry and the bulk Reynolds number and are computed once per solve.

For the turbulent regime, the flow-split dependence is evaluated from Eq. (31) of Pacio et al. (2022):

with the turbulent wire mixing coefficient and the turbulent exponent of Table 5 of Pacio et al. (2022).

The denominator is rather than the of Eq. (32) of Pacio et al. (2022), which is the effective crossflow and already includes the mean velocity of the two subchannels. SCM applies that mean velocity to the mixing parameter through the average mass flux of the gap.

When , the limiting value of the fractional term is used to avoid division by zero:

For the Pacio parameterization, the transition limits are

For the laminar regime, Eq. (33) of Pacio et al. (2022) gives

with the laminar wire mixing coefficient of Table 5, and in the intermittent regime the mixing coefficient is interpolated with the same transition formula as the Pacio-Chen-Todreas friction factor, Eq. (35) of Pacio et al. (2022),

with and of Table 5 of Pacio et al. (2022),

where the intermittency factor is evaluated with the bulk Reynolds number, as in Eq. (34) of Pacio et al. (2022),

In the transition regime, Eq. (36) of Pacio et al. (2022) evaluates the flow-split term with the turbulent flow splits and . SCM evaluates it with the current flow split of each subchannel type. Because the flow-split term varies as about , this changes the mixing parameter by less than 1% for flow splits between 0.8 and 1.2.

For both center-edge and edge-corner interfaces, the Pacio mixing parameter uses the edge-subchannel projected wire area and bare flow area :

The last factor adapts the lumped crossflow of Pacio et al. (2022) to the gaps of SCM. In the PCTD model, the effective crossflow between all subchannels of two types is times the contact perimeter between them, Eqs. (30), (A.24), and (A.25) of Pacio et al. (2022), while SCM multiplies by the width of each gap. is the contact perimeter per gap, so that the sum over the gaps of SCM gives the crossflow of PCTD:

  • center-edge gaps: over the pin-pin gaps of width , so ;

  • edge-corner gaps: over the 12 pin-duct gaps of width , so ,

where is the number of pin rings around the center pin and is the pin-to-duct gap. The text of Pacio et al. (2022) states that half of the geometric perimeter is used for , while its Eqs. (A.24) and (A.25) apply the factor of one half to ; the equations are used here. Eq. (A.25) subtracts the wire term once from the whole edge-corner perimeter, while Eq. (A.24) subtracts it from every center-edge gap. The corrigendum of the paper, Nucl. Eng. Des. 395 (2022) 111846, corrects the authors' implementation to be consistent with Eq. (A.25) as printed, so that form is used here.

The Pacio mixing treatment is therefore applied according to the following interface behavior:

Interface1986Pacio
center-centerCheng-Todreas (1986)Cheng-Todreas (1986)
center-edgeCheng-Todreas (1986)Pacio-Chen-Todreas
edge-edgenonenone
edge-cornernonePacio-Chen-Todreas
corner-cornernonenone

Peripheral sweep flow

The Cheng-Todreas peripheral sweep-flow model is treated separately from the base turbulent mixing parameter.

For edge and corner gaps, computeSweepFlowMixingParameter() returns the sweep-flow parameter used by the triangular-assembly enthalpy equation. This contribution is not added to the global turbulent crossflow parameter which in the Cheng-Todreas (1986) case is zero for the periphery gaps.

The peripheral sweep-flow correlation always uses the original Cheng-Todreas (1986) formulation, including when mixing_model = Pacio is selected. The Pacio parameterization modifies only the turbulent mixing treatment described above and does not replace the Cheng-Todreas peripheral sweep-flow correlation.

The sweep-flow transition limits therefore remain

for both values of mixing_model.

The sweep-flow parameter uses the edge-subchannel projected wire area and bare flow area .

The sweep-flow parameter is calculated as

where is the Cheng-Todreas sweep-flow coefficient evaluated according to the flow regime.

Applicability

The closure flags a solution warning when , , the number of pins, or the bulk Reynolds number is outside the data range associated with the selected mixing correlation.

commentnote

Information about the use of can be found in Turbulent crossflow. Additionally, the user may opt to provide the turbulent momentum mixing parameter CT. Information about the use of this parameter can be found in Turbulent momentum transfer.

Input Parameters

  • CT1Turbulent momentum, modeling parameter [-].

    Default:1

    C++ Type:Real

    Unit:(no unit assumed)

    Controllable:No

    Description:Turbulent momentum, modeling parameter [-].

  • mixing_model1986Mixing-model parameterization for triangular wire-wrapped Chen-Todreas correlations.

    Default:1986

    C++ Type:MooseEnum

    Options:1986, Pacio

    Controllable:No

    Description:Mixing-model parameterization for triangular wire-wrapped Chen-Todreas correlations.

Optional Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

Advanced Parameters

  • prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

  • use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

References

  1. Shih-Kuei Cheng and Neil E Todreas. Hydrodynamic models and correlations for bare and wire-wrapped hexagonal rod bundles—bundle friction factors, subchannel friction factors and mixing parameters. Nuclear engineering and design, 92(2):227–251, 1986.[Export]
  2. J Pacio, SK Chen, YM Chen, and NE Todreas. Analysis of pressure losses and flow distribution in wire-wrapped hexagonal rod bundles for licensing. part i: the pacio-chen-todreas detailed model (pctd). Nuclear Engineering and Design, 388:111607, 2022.[Export]