Thermodynamics¶

Thermodynamics statistics track system-level energy and heat transfer quantities throughout the simulation. These outputs provide a global view of how energy is generated, transferred, and dissipated within the system, including contributions from reaction, heat transfer, mechanical work, and viscous effects. All quantities are reported as total rates (e.g., Watts) integrated over the domain or relevant surfaces. The name of this file is Thermodynamics.txt. The data is written as a time series, with each row corresponding to a simulation time and appended at the Statistics Output Write Interval.

Statistics Table¶

The table below shows the statistics that can appear in the Thermodynamics output file. Within this table, each statistic corresponds to a column in the output table that evolves with the time column. If no data from this list is available, the code will not produce the file.

Statistics	Units	Details
Time	s	simulation time
Heat of Reaction Heat Rate	W	total heat of reaction rate
Heat Transfer Rate	W	total heat transfer rate
Moving Body Power	W	rotational power based on torque from fluid on moving body
Resolved Viscous Dissipation	W	resolved component of energy dissipation rate from viscous effects
Thermal Contact Heat Flux	W	total heat flux for thermal contact
Viscous Dissipation	W	total energy dissipation rate from viscous effects including resolved and unresolved components

Usage and Interpretation¶

These statistics are used to quantify system-level energy balances and identify how energy is generated, transferred, and dissipated across different physical mechanisms.

At a high level, the system energy balance can be written as

\[Q_{\text{reaction}} + Q_{\text{transfer}} + \sum_n P_{\text{moving body}} = E_{\text{dissipation}} + Q_{\text{contact}} + \frac{dE_{\text{system}}}{dt},\]

where each term corresponds to quantities reported in this output.

The Heat of Reaction Heat Rate represents energy generation or consumption due to chemical reactions,

\[Q_{\text{reaction}} = \int_V q_{\text{reaction}} \, dV.\]

The Heat Transfer Rate captures total heat exchange across boundaries or between phases,

\[Q_{\text{transfer}} = \int_A q'' \, dA.\]

Similarly, the Thermal Contact Heat Flux represents heat transfer across contacting surfaces,

\[Q_{\text{contact}} = \int_{A_{\text{contact}}} q'' \, dA.\]

The Moving Body Power represents mechanical energy input from rotating or translating bodies. Note that the sum is indexed over each individual moving body, which are reported individually in the output file.

The Viscous Dissipation quantifies the rate at which mechanical energy is converted into thermal energy due to viscous effects,

\[E_{\text{dissipation}} = \int_V \varepsilon \, dV,\]

where \(\varepsilon (= 2 \, \nu \, S_{ij} S_{ij})\) is the local viscous dissipation rate. The Resolved Viscous Dissipation includes only the directly resolved contribution, while the total Viscous Dissipation includes both resolved and modeled (unresolved) components.

In steady-state systems, the accumulation term vanishes [Equation], and these terms can be directly compared to assess energy balance closure. In transient systems, differences between input, transfer, and dissipation terms reflect changes in stored thermal or mechanical energy.