Log Polynomial in T Reference

You can specify the thermal conductivity of gas species as a function of temperature by using the Log Polynomial in T method. The Log Polynomial in T method is available only when an ECFM combustion model is selected in Simcenter STAR-CCM+ In-cylinder and when either the Mass-Weighted Mixture or Mathur-Saxena Averaging method is used to specify mixture thermal conductivity.

Logarithmic temperature polynomials are specified in piece-wise fashion, where each interval $i$ spans the range $T_{i}$ to $T_{i + 1}$ , has $m_{i}$ number of terms, and is of the form:

\ln (λ) = \sum_{k = 0}^{m_{i}} a_{i, k} \cdot \ln (T^{b_{i, k}}); T_{i} \leq T \leq T_{i + 1}

where $λ$ is the thermal conductivity of a gas species.

The polynomial has $n$ intervals with interval bounds:

T_{0}, T_{1}, T_{2}, \dots, T_{n}

The number of terms in each interval are:

m_{0}, m_{1}, m_{2}, \dots, m_{n}

The exponents are:

\begin{matrix} b_{0, 0}, b_{0, 1}, b_{0, 2}, \dots, b_{0, m_{0}} \\ b_{1, 0}, b_{1, 1}, b_{1, 2}, \dots, b_{1, m_{1}} \\ :       :       :              : \\ :       :       :              : \\ b_{n, 0}, b_{n, 1}, b_{n, 2}, \dots, b_{n, m_{n}} \end{matrix}

The polynomial coefficients are:

\begin{matrix} a_{0, 0}, a_{0, 1}, a_{0, 2}, \dots, a_{0, m_{0}} \\ a_{1, 0}, a_{1, 1}, a_{1, 2}, \dots, a_{1, m_{1}} \\ :       :       :              : \\ :       :       :              : \\ a_{n, 0}, a_{n, 1}, a_{n, 2}, \dots, a_{n, m_{n}} \end{matrix}

Log Polynomial in T Properties

LogPolynomial

Allows you to define the logarithmic polynomial that specifies thermal conductivity. Click the custom editor (

) to open the Log Polynomial in T - LogPolynomial dialog with more properties.

Number of Intervals: Specifies the number of temperature intervals.
Interval Ranges: Sets the values that bound the intervals.; For example, if you want to specify the thermal conductivity of a logarithmic polynomial using two temperature intervals, like the following:
$\begin{matrix} λ = \exp (1 + 2 \ln (T)); 100 \leq T < 500 \\ λ = \exp (3 + 4 \ln (T) + 5 {\ln (T)}^{2}); 500 \leq T < 1000 \end{matrix}$
Then you set Interval Ranges to [100, 500, 1000].; Specify a temperature range of the polynomial sufficiently large such that the polynomial is not evaluated outside the range during the analysis. If the polynomial is ever evaluated outside this range, the property is assigned a value of the polynomial at the respective range limit.
Number of Coefficients: Specifies the number of coefficients that appear in each interval in succession.; For the example in this section, you would set Number of Coefficients to [2, 3].
Coefficients: Sets the coefficients for each interval in succession.; For the example in this section, you would set Coefficients to [1, 2, 3, 4, 5].
Exponents: Sets the exponents in successive intervals.; For the example in this section, you would set Exponents to [0, 1, 0, 1, 2].
Use Real Exponents: When activated, you can enter any values for the exponents. When deactivated, the exponents are determined using the number of coefficients in each range (default).
Input Units: Selects the units of temperature.; The polynomial coefficients and polynomial ranges (and therefore the x- and y-axes on the polynomial plot) do not rescale when you change the units. These unit selectors serve as an indicator of the units that Simcenter STAR-CCM+ uses when calculating thermal conductivity with the polynomial.
Output Units: Selects the units of thermal conductivity.