Verify turbulent enthalpy mixing

[moosebuild]

Imported from https://github.inl.gov/ncrc/subchannel/issues/28 : @moose-ncrc created issue at Jun 11, 2021 07:06AM MST:

In GitLab by @kyriv1980 on Jun 11, 2021, 08:06

Turbulence causes both momentum and enthalpy mixing. Because the model for turbulent mixing is gradient-driven, it is necessary to make a gradient in either energy or momentum. There is no net transfer of mass due to turbulent mixing in single phase unheated flows, so it is not possible to analyze mass transfer in this case. If we choose to look at turbulent mixing of momentum, we will need to set velocity of one channel higher than the other. The result will be migration of velocity due to pressure-driven directed cross-flow as well as turbulent mixing of the momentum. We can disable the friction model to stop the pressure-driven directed cross-flow. However, because the axial velocity profile will not be constant in the channel, the convective terms of the momentum equation cannot be eliminated, which requires a complicated solution of the equations.

It is easier to focus on the energy equation and deactivate the density calculation. The problem consists of two identical channels connected by a gap. Channel geometry is based on typical PWR rod-lattice geometry. Forming an analytical solution for the enthalpy distribution requires us to form and solve the enthalpy conservation equations. To test the model the temperature of one channel is raised by 10 degrees Celsius. Turbulent enthalpy mixing will transfer heat from the hot channel to the cold. The solution given by the code is compared to the analytical solution.

[moosebuild]

Issue closed at: Jan 16, 2023 06:59PM MST by @moose-ncrc