NeuralFlow uses wall closures to connect the cell-centred RANS state to
wall shear and heat flux without requiring the first cell centre to
remain at one prescribed . The
currently documented branch uses continuous viscous/logarithmic blends
for momentum and temperature. The same wall quantities are
differentiated in the implicit boundary assembly when they depend on
active solution variables.
10.1 Tangential relative
velocity
Let be the fluid
velocity at the wall-adjacent cell and the wall velocity. With wall
normal , define the
relative tangential velocity The wall distance is the normal/near-wall distance
supplied by the wall-distance infrastructure.
10.2 Velocity scale and wall
distance
For the GE-RANS wall treatment, a blended velocity scale is (10.1) and (10.2) This construction retains a molecular
contribution near the wall and a turbulence-related contribution when
is active.
10.3 Continuous velocity blend
The viscous and logarithmic limits are
with and in the documented current
branch. The continuous blend is (10.3) It approaches the viscous law for
small and the logarithmic law
for sufficiently large without
a discrete switch.
10.4 Thermal wall law
Define the molecular Prandtl number with turbulent
Prandtl number . A Kader-type
continuous thermal blend (Kader 1981) uses (10.4)(10.5) and (10.6) The corresponding unblown gas-side
heat-transfer coefficient is (10.7) The same expression spans the conductive
sublayer, buffer layer, and logarithmic region.
10.5 Wall shear and heat flux
A wall shear vector has the generic form
where is supplied by the
active wall-function relation. Its face-integrated momentum contribution
is .
For a stationary thermal wall with no blowing, the convective part of
the gas-side heat flux is represented as (10.8) with optional viscous-heating
correction where enabled. Adiabatic, prescribed-temperature,
prescribed-flux, external-convection/radiation, and conjugate
configurations require different closure equations for and ; they must all reduce to a
dimensionally consistent energy flux in .
10.6 Turbulence wall
quantities
For –-class closures, the nondimensional
specific dissipation is The near-wall treatment blends
viscous and logarithmic asymptotes rather than switching abruptly at one
grid threshold. Turbulence production, turbulent viscosity, and the
wall-normal distance must be recomputed consistently whenever the
solution, turbulence model, or multigrid level changes.
10.7 Implicit boundary
assembly
A boundary heat flux contributes to
the total-energy residual. If it depends on active cell variables, NeuralFlow
uses AD in the active boundary path so the local thermal/momentum
response can enter the coupled Jacobian. This is particularly important
for wall laws in which , , , turbulence, and wall temperature are
mutually dependent.
10.8 10.8 Current limitations and user checks
The velocity and Kader-type thermal relations above are used by the wall treatment and the boundary-attached charring model. For non-adiabatic conjugate-heat-transfer and moving-wall cases, qualify the total energy balance carefully: compare heat transferred from the fluid with heat received by the solid, monitor wall heat flux and verify that moving-wall mechanical work is negligible or otherwise accounted for in the intended case.
For customer simulations, this means that adiabatic walls and the standard wall-function relations can be interpreted directly from the equations in this chapter, while advanced non-adiabatic CHT or moving-wall energy studies should include an explicit conservation check and, where important, comparison against a validation case.