Engineering task and calculation objective
This module calculates film condensation of pure vapors flowing inside horizontal tubes according to Section J1 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019), the standard German reference work for heat transfer. Unlike condensation from stagnant vapor, here the two-phase flow governs the process: along the tube the flow quality decreases, the flow pattern changes from shear-dominated annular or mist flow to gravity-dominated stratified and wavy flow, and with it the local heat transfer coefficient changes.
This calculation is the core of the design of tube-side condensers as commonly used in air-cooled condensers, refrigerant condensers, and process condensers. The module works through the condensation length section by section: from the total mass flow, local vapor quality, and vapor velocity it obtains local Nusselt numbers and heat transfer coefficients, which are combined with the coolant-side heat transfer, the tube wall, and the fouling resistances into the local and mean overall heat transfer coefficients.
As results, the calculation delivers the required heat transfer area or tube length of the condenser as well as the tube-side pressure drop — the central quantities for equipment design per the VDI Heat Atlas.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the geometry and process data: Inputs are the tube inside and outside diameters, wall thickness, thermal conductivity of the tube material, number of tubes, as well as the total mass flow of vapor and condensate, the condensation temperature, and the vapor qualities at the inlet and outlet of the calculation length.
- Divide the condensation length into sections: Since the vapor quality changes along the tube, the length is subdivided into steps of flow quality; for each section the local vapor and condensate mass flows and the vapor velocity are determined.
- Determine the local flow pattern and Nusselt number: For each section it is checked whether condensation is shear-dominated (annular flow at high vapor velocity) or gravity-dominated (stratified flow with a condensate pool); the corresponding correlations of the VDI Heat Atlas yield the local Nusselt number and from it the local heat transfer coefficient.
- Couple the overall heat transfer with the coolant side: The condensation-side coefficient is combined with the heat transfer of the cooling medium (from mass flow, heat capacity, inlet and outlet temperatures), the wall conduction, and the fouling resistances inside and outside into the local overall heat transfer coefficient.
- Integrate area, tube length, and pressure drop: The required area and tube length follow from the heat duty and the mean overall heat transfer coefficient; in parallel, the two-phase pressure drop is summed over the condensation length and checked against the allowable pressure drop.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Local mass flow of condensate | MF | kg/s |
| Tube inside diameter | di | m |
| Dyn. viscosity | ηF | mPa·s |
| Dyn. viscosity | ηW | mPa·s |
| Density | ρF | kg/m³ |
| Thermal conductivity | λF | W/(m·K) |
| Specific heat capacity | cpF | J/(kg·K) |
| Kinematic viscosity | νF | m²/s |
| Prandtl number | PrF | - |
| Density | ρD | kg/m³ |
| Vapour mass fraction | x | -- |
| for else | fwell | - |
| Vapour mass fraction | x | -- |
| Total mass flow (vapour + condensate) Mtotal | Kondensat) | kg/s |
| Heat transfer area | A | m² |
| Specific heat capacity | cp | J/(kg·K) |
| Mass flow | m | kg/s |
| Velocity of vapour | uD | m/s |
| Dyn. viscosity | ηD | mPa·s |
| Local Nu number | Nu•F,x | - |
| Heat transfer coefficient | α•F,x | W/(m²·K) |
| Outlet temperature | ϑa | °C |
| Inlet temperature | ϑe | °C |
| Local mass flow of vapour | MD | kg/s |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Local trickle density | Γx,e | kg/(m·s) |
| Volumetric vapour fraction | ε | - |
| Volumetric vapour fraction | ε | - |
| Characteristic length | L | m |
| Local Reynolds number of film | ReF,x | - |
| for else | fwell | - |
| Correction factor | fη | - |
| Local laminar Nu number | NuF,x,l | - |
| Local turbulent Nu number | NuF,x,t | - |
| Local Nu number (without shear) | NuF,x | - |
| Local heat transfer coefficient | αF,x | W/(m²·K) |
| Hydraulic diameter | dh | m |
| Relative gas Reynolds number | ReD-F | - |
| Friction factor hydraulic smooth | ξ°g | - |
| Friction factor | ξ°r | - |
| Flow parameter | F | - |
| Film thickness | δ+F | m |
| Dimensionless shear stress | τD* | - |
| Shear stress | τD | N/m² |
| Local laminar Nu number | Nu+F,x,l | - |
| Local turbulent Nu number | Nu+F,x,t | - |
| Local Nu number | Nu•F,x | - |
| Correction factor, laminar | KPh,l | - |
| Correction factor, turbulent | KPh,t | - |
Frequently asked questions
Why must in-tube condensation be calculated section by section?
Because the flow quality changes from nearly 1 at the inlet to almost 0 at the outlet, and with it the vapor velocity, flow pattern, and heat transfer coefficient vary strongly. A single mean value over the whole length can misestimate the area considerably; the stepwise integration over the vapor quality is state of the art per the VDI Heat Atlas.
What role does the flow pattern play in a horizontal tube?
At high vapor velocity, shear distributes the condensate as a thin annular film around the circumference — the heat transfer is high. At low velocity, the condensate collects at the bottom as a pool that thermally blocks part of the circumference; Nusselt condensation on the wetted upper circumference then governs. The transition between the two regimes is determined via flow pattern maps or criteria based on vapor velocity and liquid fraction.
Why is the pressure drop particularly critical in condensers?
The tube-side pressure drop lowers the local saturation pressure and hence the condensation temperature along the tube — the driving temperature difference to the cooling medium shrinks. In vacuum condensers, an excessive pressure drop can drastically reduce the capacity or raise the process pressure inadmissibly. That is why the module balances the pressure drop in parallel with the heat transfer.
How strongly does fouling influence the design?
Fouling resistances inside and outside add directly to the reciprocal of the overall heat transfer coefficient. Given the high condensation-side coefficients, the overall heat transfer quickly becomes fouling- or coolant-side limited: a deposit of 0.0002 m²K/W can already reduce the overall coefficient by double-digit percentages. Realistic, service-proven fouling values therefore matter more than a third decimal place in the condensation model.