Engineering task and calculation objective
The KON1 module calculates condensation in horizontal tubes using an incremental method: the tube is divided into sections, and for each increment the local heat transfer coefficient on the condensate side, the overall heat transfer coefficient of the tube and the local heat flow are determined. This makes it possible to follow the condensation process along the tube instead of calculating with a single mean value for the whole apparatus.
For in-tube condensation, the incremental calculation is practically indispensable, because the flow pattern changes strongly along the tube length: at the inlet there is almost pure vapor at high velocity with shear-controlled film drainage; towards the outlet the condensate fraction grows, the vapor velocity falls, and in horizontal tubes an increasingly stratified flow develops with a condensate pool at the bottom of the tube. The local heat transfer coefficient can change by a factor of several along the way.
The module is used for the design and rating of shell-and-tube condensers, air-cooled condensers and process coolers with tube-side condensation. From the tube inside diameter, tube outside diameter, number of tubes, angle of inclination towards the horizontal and the total mass flow on the condensate side, the section-by-section profile of heat flow and condensate formation is generated, as required by state-of-the-art heat exchanger calculation methods (such as the VDI Heat Atlas).
Calculation workflow
- Define geometry and mass flow: The inputs are the inside and outside diameter of the tubes, the number of tubes, the angle of inclination towards the horizontal and the total mass flow on the condensate side; from these follows the loading of the individual tube.
- Divide the tube into increments: The tube length is broken down into sections that are addressed via the number of the local increment. In each section, the calculation uses the vapor quality valid there and the corresponding fluid properties.
- Determine flow pattern and local heat transfer: For each increment, the condensate-side heat transfer coefficient is determined from the governing mechanism: shear-influenced film condensation at high vapor velocity, gravity-controlled film condensation with condensate stratification at low velocity; the acceleration due to gravity and the angle of inclination enter the condensate drainage.
- Calculate overall heat transfer and local heat flow: From the condensate-side coefficient, the tube wall and the coolant-side heat transfer, the overall heat transfer coefficient of the tube is formed and, together with the local temperature difference, the local heat flow of the increment is calculated.
- March the balance forward: The heat flow removed in the increment determines the mass condensed there; vapor quality and mass flows are updated and the next increment is calculated, until the desired degree of condensation or the end of the tube is reached. The sum of the local heat flows yields the required surface area or duty.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Number local increment | n | - |
| Mean temperature | (n) ϑm | °C |
| Mean pressure | (n) pm | Pa |
| TEn | ϑEn | °C |
| TAn | ϑAn | °C |
| Gradient of condensation curve | (n) Δm/Δϑ | kg/(s·K) |
| ⇒ Heat transfer coefficient condensate side | αK | W/(m²·K) |
| Heat transfer coefficient condensate | αF | W/(m²·K) |
| Heat transfer coefficient vapour | αD | W/(m²·K) |
| Correction function | (n) F (0 - 1) | - |
| Specific mass flow | Gt | kg/(m²·s) |
| Reynolds number liquid | (n) ReF | - |
| Inside diameter of the tubes | di | m |
| Outside diameter of the tubes | da | m |
| Reynolds number vapour | (n) ReD | - |
| Acceleration due to gravity | g | m/s² |
| Vapour mass flow portion | (n) y | - |
| Specific heat capacity liquid | (n) cpF | J/(kg·K) |
| Density liquid | (n) ρF | kg/m³ |
| Dynamic viscosity liquid | (n) ηF | mPa·s |
| Thermal conductivity liquid | (n) λF | W/(m·K) |
| Heat of evaporation | (n) HV | J/kg |
| Specific heat capacity vapour | (n) cpD | J/(kg·K) |
| Density vapour | (n) ρD | kg/m³ |
Frequently asked questions
Why is a mean heat transfer coefficient for the whole condenser often not sufficient?
Because the local coefficient changes strongly with the vapor quality: at the inlet the high vapor velocity produces a thin, sheared film and high values, at the outlet a thick film and condensate pool considerably dampen the heat transfer. A mean value can misjudge the required area significantly, especially when complete condensation or subcooling at the tube end is required. The incremental calculation captures this profile.
What role does the angle of inclination towards the horizontal play?
It determines how the condensate drains. A slight downward slope in the flow direction supports condensate drainage and prevents a pool from backing up at the tube end; an adverse slope can hold condensate back, narrow the effective cross-section and, in the worst case, lead to slug flow and unstable operation. In the calculation, the angle changes the gravity component along the tube and thus film thickness and stratification.
What must be considered when comparing condensation inside versus outside the tube?
For condensation inside a horizontal tube, the condensate must be carried away through the tube itself and the vapor shares the cross-section with the condensate; flow pattern and pressure drop limit the loading per tube. For condensation on the outside of a horizontal tube bundle, the condensate drips off and the classical Nusselt theory with bundle correction is applicable. The methods are not interchangeable; KON1 applies to condensation on the tube inside.
How do inert gases affect the result?
Non-condensable gases accumulate at the phase interface and build up a diffusion resistance that noticeably reduces the heat transfer even at inert gas fractions of only a few percent. Pure film condensation correlations then overestimate the performance. In such cases, the mass transfer resistance must be taken into account additionally and adequate inert gas venting of the apparatus must be provided.