Equivalent Homogeneous Temperature Model

The Equivalent Homogeneous Temperature (EHT) model can be used to predict non-uniform thermal comfort of people in an environment such as a room in a building or the cabin of a car.

The equivalent temperature is incorporated into the ISO 14505 standard for the evaluation of thermal environments in vehicles or other confined spaces with asymmetric climatic conditions that are close to thermal neutrality [403]. The equivalent temperature $T_{e q}$ corresponds to the wall temperature of a uniform enclosure that has calibrated conditions. These calibrated conditions assume that the mean radiant temperature is equal to the air temperature, the air has zero velocity, and the heat exchange between a person and the environment due to convection and radiation is the same as under actual, non-uniform conditions. The dry heat exchange and the equivalent temperature become the same in both the calibrated and the real environments. The equivalent temperature allows a quantification of the heat exchange: high $T_{e q}$ values signify lower heat losses and low $T_{e q}$ values indicate higher heat losses.

In Simcenter STAR-CCM+, the air temperature, the mean radiant temperature, the air velocity, and the radiant and convective heat losses are calculated. $T_{e q}$ is then determined based on the equations for convective and radiative heat transfer:

\dot{Q} = h_{e q} (T_{s} - T_{e q})

where:

$\dot{Q}$ is the heat flux on the manikin surface in the non-uniform actual conditions.
$h_{e q}$ is the heat transfer coefficient in calibration conditions.
$T_{s}$ is the skin temperature.

$h_{e q}$ is evaluated as a linear function of $T_{e q}$ . Using a linear approximation, $h_{e q}$ can be written as:

Figure 1. EQUATION_DISPLAY

h_{e q} = x_{1} | T_{e q} - T_{s} | + x_{0} = \frac{\dot{Q}}{| T_{s} - T_{e q} |}

(1803)

where the constants $x_{0}$ and $x_{1}$ are evaluated by running calibration simulations in standard uniform, steady conditions at different $| T_{e q} - T_{s} |$ values and performing a linear regression. The default values for the model are taken from the calibration simulations run by Rommelfanger, et. al.[418].

Simplifying the equation above yields, for $\dot{Q} > 0$ :

Figure 2. EQUATION_DISPLAY

T_{e q} = T_{s} + \frac{x_{0}}{2 x_{1}} - \frac{\sqrt{x_{0}^{2} + 4 x_{1} \dot{Q}}}{2 x_{1}}

(1804)

Similarly, for $\dot{Q} < 0$ :

Figure 3. EQUATION_DISPLAY

T_{e q} = T_{s} - \frac{x_{0}}{2 x_{1}} + \frac{\sqrt{x_{0}^{2} - 4 x_{1} \dot{Q}}}{2 x_{1}}

(1805)

To calculate user-specified EHT segment constants

x_{0}

and

x_{1}

, calibration conditions are required:

The conditions specified by the standard DIN EN ISO 14505-2 are: Flow velocity 0.05m/s; Temperature gradient < 0.4K.
Under this standard condition, multiple simulations are run at a constant skin temperature and varying equivalent temperature values.
A range of heat transfer coefficient values are obtained from these calibration simulations. Heat transfer coefficient values can be plotted against absolute value of difference between skin and equivalent temperature, $| T_{e q} - T_{s} |$ .
A linear regression is then performed in a range of -25 ℃ to 25 ℃ for $T_{e q}$ as $h_{e q} = x_{1} | T_{e q} - T_{s} | + x_{0}$ to evaluate $x_{0}$ and $x_{1}$ .