Engineering task and calculation objective
The HEAT module calculates the condensation heat of vapor-gas mixtures incrementally along the cooling path. Instead of estimating the released heat globally from a mean enthalpy of vaporization, the condensation process is broken down into temperature or enthalpy steps: for each increment, the condensing mass fraction, the released latent and sensible heat and the properties of the remaining gas phase and the forming condensate phase are determined.
This Q-T curve (heat release curve) is needed whenever vapor condenses in the presence of inert gas, or when a multi-component mixture is partially liquefied over a temperature range from the dew point down to the outlet state – typical cases are exhaust gas condensers, vapor condensers with an air fraction, and process condensers in chemical engineering. Since the composition, density, heat capacity, viscosity, thermal conductivity and Prandtl number of both phases change continuously along the path, the incremental treatment is a prerequisite for a zone-by-zone condenser design.
The module works as a property and balance supplier in the background of the heat exchanger design: for each increment it hands over the state and property data (Properties) with which the downstream heat transfer and surface area calculation is carried out section by section.
Calculation workflow
- Define the mixture and end states: The composition of the vapor-gas mixture, the pressure and the inlet and outlet temperatures are specified; from these it follows whether and from which temperature condensation sets in.
- Determine the dew point: From the partial pressures of the condensable components, the dew point of the mixture at operating pressure is determined – above it only sensible heat is removed, below it partial condensation begins.
- Divide the cooling path into increments: The range from the inlet state down to the outlet temperature is divided into temperature steps. For each increment, the condensing vapor fraction is balanced via the phase equilibrium.
- Calculate heat and properties per increment: For each increment, the latent condensation heat, the sensible heat of the gas and condensate streams, and the properties of both phases (density, heat capacity, viscosity, thermal conductivity, Prandtl number) are evaluated at the respective state.
- Hand over the Q-T curve: The summed heats give the heat release curve over temperature. Together with the associated properties, it is handed over to the condenser design, which uses it to calculate the overall heat transfer and surface area zone by zone.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| File name of condensation curve | ('.tab') | - |
| Inlet temperature Outlet temperature | ϑE ϑA | °C |
| Inlet temperature Outlet temperature | ϑE ϑA | °C |
| Inlet pressure Outlet pressure | pE pA | Pa |
| Inlet pressure Outlet pressure | pE pA | Pa |
| Number of components (maximum: 10 components) | i | - |
| Number of increments (maximum: 10 increments) | N | - |
| ⇒ Temperature interval width | Δϑ | K (diff) |
| Number local increment | n | - |
| ⇒ Mean temperature (n) | ϑm | °C |
| ⇒ Mean pressure (n) | pm | Pa |
| ⇒ Inlet temperature (n) | ϑEn | °C |
| ⇒ Outlet temperature (n) | ϑAn | °C |
| ⇒ Condensate vapour mass flow (n) | Δm | kg/s |
| ⇒ Gradient of condensation curve (n) | Δm/Δϑ | kg/(s·K) |
| x1E | x1E | - |
| x2E | x2E | - |
| x3E | x3E | - |
| x4E | x4E | - |
| x5E | x5E | - |
| x6E | x6E | - |
| x7E | x7E | - |
| x8E | x8E | - |
| x9E | x9E | - |
Calculation options
Properties
Calculation of fluid properties · Handeingabe der mittl. Stoffdaten
Frequently asked questions
Why is a mean enthalpy of vaporization not sufficient for condenser design?
For mixtures and for vapor with an inert gas fraction, the heat release over temperature is strongly nonlinear: near the dew point much condenses per kelvin, at the cold end less and less because the partial pressure of the remaining vapor drops. Linear averaging overestimates the driving temperature difference in the critical zones and leads to undersized surfaces – the incremental Q-T curve reveals such bottlenecks (pinch points).
What influence does inert gas have on condensation?
Inert gas lowers the partial pressure of the vapor and thus the local condensation temperature; in addition, the vapor must diffuse through the inert gas layer that accumulates at the cooling surface. Both degrade the effective heat transfer considerably – even a few percent of inert gas can enlarge the condenser significantly. The incremental calculation captures the growing inert gas concentration along the path.
What distinguishes the dew point from the boiling point of a mixture?
The dew point is the temperature at which, on cooling, the first droplet forms; the boiling point (bubble point) is the one at which, on heating, the first bubble appears. For pure substances both coincide; for mixtures the two-phase region lies in between, in which condensation proceeds gradually over a temperature range – exactly this range is computed incrementally.
How fine must the increments be chosen?
Fine enough that the Q-T curve behaves approximately linearly within one increment. In regions of strong curvature – just below the dew point and near pinch points – tighter steps are needed than in the flat tail. Too coarse a division smooths the curve and can hide a temperature pinch in the condenser.