What Methods Are Available for Exchanging Heat Transfer Coefficients?

For turbulent flows, the central concept for modeling convective heat transfer at the wall is given by the standard wall function, which can be written as:

Figure 1. EQUATION_DISPLAY

{\dot{q}}_{w}^{"} = \frac{ρ_{f} (y_{c}) C_{p, f} (y_{c}) u^{*} (y^{+} (y_{c}))}{T^{+} (y^{+} (y_{c}))} (T_{w} - T_{r})

(550)

where $y_{c}$ is the distance to the near wall cell center, $y^{+}$ is the non-dimensional wall distance, $u^{*}$ is the reference velocity, and $T^{+}$ is the non-dimensional temperature -- both of which are determined by the chosen wall treatment. $ρ_{f}$ and $C_{p, f}$ are the density and specific heat of the fluid. Note that $ρ_{f}$ , $C_{p, f}$ , $u^{*}$ , and $T^{+}$ are functions of the distance from the wall.

Comparing Eqn. (550) with Eqn. (548), the heat transfer coefficient can be written as:

Figure 2. EQUATION_DISPLAY

h (y_{c}) = \frac{ρ_{f} (y_{c}) C_{p, f} (y_{c}) u^{*} (y^{+} (y_{c}))}{T^{+} (y^{+} (y_{c}))}

(551)

This expression is the foundation for various definitions of heat transfer coefficient in Simcenter STAR-CCM+. These coefficients, and their corresponding fluid reference temperatures, are listed in the table below.


Field Function	Reference Temperature for Data Exchange
Local Heat Transfer Coefficient	Local Heat Transfer Reference Temperature
Specified Y+ Heat Transfer Coefficient	Specified Y+ Heat Transfer Reference Temperature
Heat Transfer Coefficient	User-defined reference temperature
Virtual Local Heat Transfer Coefficient	N/A

Local Heat Transfer Coefficient

This is the heat transfer coefficient evaluated at the centroid of the cell next to the boundary, that is $h (y = y_{c})$ . It is given by:

Figure 3. EQUATION_DISPLAY

h_{l o c a l} = \frac{ρ_{f} (y_{c}) C_{p, f} (y_{c}) u^{*}}{T^{+} (y^{+} (y_{c}))}

(552)

The corresponding fluid reference temperature is given by:

Figure 4. EQUATION_DISPLAY

T_{l o c a l} = T_{w} + \frac{{\dot{q}}_{w}^{"}}{h}

(553)

Specified Y+ Heat Transfer Coefficient

This is the heat transfer coefficient evaluated at a user specified value of $y^{+}$ , such that $y^{+} (y) = Y_{u s e r}^{+}$ . It follows that:

Figure 5. EQUATION_DISPLAY

h_{y^{+}} = \frac{ρ_{f} (y_{c}) C_{p, f} (y_{c}) u^{*}}{T^{+} (Y_{u s e r}^{+})}

(554)

The corresponding fluid reference temperature, the Specified Y+ Heat Transfer Reference Temperature is given by:

Figure 6. EQUATION_DISPLAY

T_{f, y^{+}} = T_{w} + \frac{{\dot{q}}_{w}^{"}}{h_{y^{+}}}

(555)

As this definition does not guarantee that $T_{f, y^{+}}$ lies within the temperature range of the local region, the following conditions are enforced to give realistic values:

Figure 7. EQUATION_DISPLAY

T_{f, y^{+}} = {\begin{matrix} T_{w} + \frac{{\dot{q}}_{w}^{"}}{h_{y^{+}}} & T_{\min} \leq T_{w} + \frac{{\dot{q}}_{w}^{"}}{h_{y^{+}}} \leq T_{\max} \\ T_{\min} & T_{w} + \frac{{\dot{q}}_{w}^{"}}{h_{y^{+}}} < T_{\min} \\ T_{\max} & T_{w} + \frac{{\dot{q}}_{w}^{"}}{h_{y^{+}}} > T_{\max} \end{matrix}

(556)

In the latter two cases, $h_{y^{+}}$ will be re-evaluated such that

Figure 8. EQUATION_DISPLAY

h_{y^{+}} = \frac{{\dot{q}}_{w}^{"}}{(T_{f, y^{+}} - T_{w})}

(557)

For these field functions, the

y^{+}

value is set on the Specified Y+ Heat Transfer Coefficient field function node within Automation > Field Functions.

Virtual Local Heat Transfer Coefficient

This is an approximation to the true Local Heat Transfer Coefficient that does not require an energy model to be activated. It is defined as the heat transfer coefficient evaluated at $y = y_{c}$ , where $y_{c}$ is the distance of the near wall cell center from the wall.

Figure 9. EQUATION_DISPLAY

h_{v i r t u a l} = \frac{ρ_{f} (y_{c}) C_{p, f} (y_{c}) u^{*}}{T^{+} (y^{+} (y_{c}))}

(558)

Since thermal material properties are not available, the specific heat,

C_{p, f}

is specified as a reference value, as well as the molecular and turbulent Prandtl numbers. These are set on the Virtual Local Heat Transfer Coefficient field function node, as shown below. The fluid density,

ρ_{f}

is obtained locally from the simulation.

Heat Transfer Coefficient

This is yet another choice for defining heat transfer coefficients. It is evaluated based on a specified bulk temperature $T_{b u l k}$ .

Figure 10. EQUATION_DISPLAY

h_{b u l k} = \frac{{\dot{q}}_{w}^{"}}{(T_{b u l k} - T_{w})}

(559)

This definition does not guarantee that the evaluated heat transfer coefficient is positive. When exchanging data with other CAE codes, if the evaluated $h_{b u l k}$ is not positive, then the local heat transfer coefficient, $h_{l o c a l}$ , and its corresponding reference temperature, $T_{l o c a l}$ , are exchanged instead.

The bulk temperature is set as a property of the Heat Transfer Coefficient field function node.