diff --git a/docs/source_docs/user_guide/inputs/boundary_conditions.rst b/docs/source_docs/user_guide/inputs/boundary_conditions.rst index bd0a719a4c7b3eac5fc133b05124c3a5dadcc4f0..0a899de2fd1d5b86652236278f69b82bb30588e7 100644 --- a/docs/source_docs/user_guide/inputs/boundary_conditions.rst +++ b/docs/source_docs/user_guide/inputs/boundary_conditions.rst @@ -285,7 +285,13 @@ temperature sees an abrupt spike from 300 up to 500 at t = 3s and then back down again after 4s. Note that the timestep is not adjusted to sync with transient BCs. -.. image:: ./images/transient-bc.png +.. figure:: ./images/transient-bc.png + :height: 4in + :align: center + :alt: Plot of boundary conditions versus time. Fluid velocity increases linearly from 0 to 15 cm/s over the first 3 seconds and then remains constant. Temperature stays at 300 K from 0 to 3 seconds, rises abruptly to 500 K between 3 and 4 seconds, and then returns to 300 K after 4 seconds. + + Linear velocity ramp to 15 cm/s (0–3 s), constant thereafter; temperature step from 300 K to 500 K (3–4 s) then return to 300 K + Thermal boundary conditions --------------------------- @@ -328,12 +334,13 @@ inputs defined using the prefix ``bc.[region_name].eb``. | | A valid is required for ``constant`` EB temperature model. | | | +----------------------+-----------------------------------------------------------------------+-------------+-----------+ -The conjugate heat transfer model approximates heat transfer through the embedded boundary using one-dimensional, -steady-state conduction. The external environment is treated as a thermal reservoir with a constant temperature -in both space and time. This approach is illustrated in :numref:`fig_conjugate_heat_transfer_bc`, where heat flows -through a series of thermal resistances: from the fluid to the inner wall surface, through the wall, and finally -to the environment. The direction of heat transfer---into or out of the system---is governed by the temperature -gradient between the fluid and the surroundings. +The conjugate heat transfer model approximates heat transfer through the embedded boundary using a one-dimensional thermal +resistance representation. By default, the wall temperature is computed from an algebraic heat balance; optionally, a +lumped-capacity transient wall model can be enabled. + +The external environment is treated as a thermal reservoir with constant temperature :math:`T_{\infty}`. Heat is +transferred from the fluid to the inner wall surface, through the wall, and then from the outer wall surface to +the environment, as illustrated in :numref:`fig_conjugate_heat_transfer_bc`. .. _fig_conjugate_heat_transfer_bc: @@ -344,22 +351,38 @@ gradient between the fluid and the surroundings. Schematic of the conjugate heat transfer boundary condition. -An effective resistance is calculated based on the convective heat transfer coefficient between the fluid -and wall, :math:`h_{int}`, conduction through the wall with thickness :math:`L_w` and thermal conductivity -:math:`\kappa_w`, and convective heat transfer from the exterior wall to the environment :math:`h_{ext}`. +The effective outward thermal conductance per unit area is .. math:: - R_{eff} = \left( \frac{1}{h_{int}} + \frac{L_w}{\kappa_w} + \frac{1}{h_{ext}} \right)^{-1} + G_{out} = \left( \frac{L_w}{\kappa_w} + \frac{1}{h_{ext}} \right)^{-1} + +where :math:`L_w` is the wall thickness, :math:`\kappa_w` is the wall thermal conductivity, +and :math:`h_{ext}` is the external convective heat transfer coefficient. This expression +represents the combined resistance of conduction through the wall and convection from the +outer wall surface to the environment. -The interior wall temperature is determined by balancing the heat flux contributions from internal -convection, wall conduction, and external convection, resulting in a closed-form expression based -on the effective thermal resistance of the system. +For the zero-capacity wall model, the inner wall temperature is determined from an algebraic +heat balance between internal convection, radiation, and heat transfer to the environment: .. math:: - T_{w,int} = T_f - \frac{1}{h_{int}}\left[ \frac{T_f - T_{\infty}}{R_{eff}} \right] + T_{w,int} = \frac{ h_{int} T_f - q_{rad} + G_{out} T_{\infty}}{h_{int} + G_{out}} + +where :math:`h_{int}` is the internal convective heat transfer coefficient. Positive :math:`q_{rad}` +denotes radiative heat loss from the wall. By default, the CHT-1D wall has no thermal storage, +so the wall temperature responds instantaneously to changes in the local heat balance. +If a wall heat capacity :math:`C_A` [J/(m\ :sup:`2`\ K)] is specified, the wall is modeled as a lumped thermal +mass with a single spatially uniform temperature. In that case, the wall temperature evolves according to + +.. math:: + + C_A \frac{dT_{w,int}}{dt} = h_{int} \left( T_f - T_{w,int} \right) - q_{rad} - G_{out} \left( T_{w,int} - T_{\infty} \right) + +In this lumped-capacity approximation, the inner and outer wall temperatures are not resolved separately; instead, +the wall is represented by a single transient temperature. When :math:`C_A = 0` or is not specified, the algebraic +wall temperature model is used. The model settings are defined using the prefix ``bc.[region_name].eb.temperature.CHT-1D``: @@ -389,6 +412,8 @@ The model settings are defined using the prefix ``bc.[region_name].eb.temperatur +----------------------------+------------------------------------------------------------------------+-------------+-----------+ | wall.thickness | Wall thickness. | Real | None | +----------------------------+------------------------------------------------------------------------+-------------+-----------+ +| wall.heat_capacity | Lumped wall heat capacity per area [J/(m\ :sup:`2`\ K)] | Real | 0. | ++----------------------------+------------------------------------------------------------------------+-------------+-----------+ | phase_averaged_temperature | Use a phase averaged temperature for simulations containing particles. | Bool | false | | | The phase averaged temperature is computed as the volume fraction | | | | | weighted sum of the fluid and averaged particle temperatures. | | | diff --git a/docs/source_docs/user_guide/inputs/output/plotting.rst b/docs/source_docs/user_guide/inputs/output/plotting.rst index 4770b834435edc6d31d25c41d193778d99b50850..4c9aa3d5eae4e9680f22d38280400fb30ed9558b 100644 --- a/docs/source_docs/user_guide/inputs/output/plotting.rst +++ b/docs/source_docs/user_guide/inputs/output/plotting.rst @@ -73,6 +73,8 @@ The following inputs must be preceded by the prefix ``mfix`` and control which v +---------------------+-----------------------------------------------------------------------+-------------+-----------+ | plt_X_g | Plot fluid species mass fractions. | Int | 0 | +---------------------+-----------------------------------------------------------------------+-------------+-----------+ +| plt_T_eb | Plot EB wall temperature. Only applicable for CHT-1D BCs. | Int | 0 | ++---------------------+-----------------------------------------------------------------------+-------------+-----------+ The following inputs must be preceded by the prefix ``mfix.solids`` and allow to write additional plotfiles which contain only solids variables in specific regions at fixed timesteps or approximated simulation times.