Engineering guide
The KON2 module calculates condensation in vertical tubes using an incremental method: the tube is subdivided from top to bottom into sections, and for each increment the film thickness, the local heat transfer coefficient and the condensate formation are determined. The basis is film condensation as described by the Nusselt film theory and as treated in the VDI Heat Atlas with extensions for wavy and turbulent films.
In a vertical tube, the condensate film drains down the tube wall under gravity and grows continuously thicker towards the bottom, because the condensate from all sections above is added to it. The local heat transfer therefore decreases along the tube as long as the film remains laminar; with increasing film loading, waves and eventually turbulence set in, which improve the heat transfer again. In addition, a high vapor velocity can shear and accelerate the film. An incremental calculation captures these transitions where a mean-value formula only gives a rough estimate.
The module is used for the design and rating of vertical shell-and-tube condensers, falling-film condensers and overhead condensers of columns. The inputs are the inside and outside diameter of the tubes, the number of tubes and the total mass flow on the condensate side; the module delivers the profile of the heat transfer along the tube length and thus the required condensation surface.
Scope
- Condensation in vertical tubes Incremental calculation
Typical workflow
Define geometry and loading
From the inside diameter, outside diameter and number of tubes together with the total mass flow on the condensate side, the loading of the individual tube is determined, i.e. the condensate mass flow per unit of tube circumference (film loading).
Divide the tube into increments
The tube length is broken down into sections that are addressed via the number of the local increment. In the topmost section, the film starts with zero thickness and grows with every increment by the condensate formed there.
Assess the film state for each increment
From the local film loading, the film Reynolds number is formed and from it the flow state of the condensate film is determined: smooth laminar, wavy laminar or turbulent. The acceleration due to gravity enters the film thickness via the drainage mechanics of the film.
Calculate local heat transfer and heat flow
For the respective film state, the local heat transfer coefficient is calculated from the film condensation correlations and combined with the wall resistance and the coolant-side heat transfer into the overall heat transfer coefficient; from this follows the local heat flow of the increment.
March the condensate balance forward
The local heat flow determines the mass condensed in the increment; film loading and remaining vapor flow are updated and the next increment is calculated. At the end of the tube, the total duty, the condensate quantity and the profile of the heat transfer coefficient over the length are available.
Frequently asked questions
Why does the heat transfer of a laminar film decrease towards the bottom?
The condensate film is the governing thermal resistance between vapor and wall. Towards the bottom, the condensate from all sections above accumulates, the film becomes thicker and the conduction path longer; according to the Nusselt theory, the local coefficient falls with running length. Only when waves and turbulence set in do they mix the film, and the heat transfer rises again despite the growing film thickness.
Up to which film Reynolds number is the laminar calculation valid?
As a rough guide, the film remains laminar up to Reynolds numbers of the order of 400, with waviness already occurring from about 30 onwards, which improves the heat transfer compared with the smooth Nusselt solution by typically 15 to 25 percent. Above the transition, turbulence correlations must be used. The incremental calculation checks the film state in every section and switches the correlation accordingly.
What changes when the vapor flows downwards in the tube at high velocity?
The shear stress of the vapor pulls the film additionally downwards, makes it thinner and improves the heat transfer compared with the pure gravity solution; the Nusselt theory then yields conservative values. With upward-flowing vapor, the shear stress can, on the contrary, hinder the condensate drainage; above the flooding limit, condensate is entrained and operation becomes unstable. Verifying a sufficient margin to the flooding limit is therefore part of the design of reflux condensers.
How strongly do inert gases disturb the condensation?
Even a few percent of non-condensable gases can reduce the heat transfer drastically, because the inert gas accumulates at the phase interface and the vapor must diffuse through this layer. Film condensation correlations for pure vapor are then no longer adequate; the coupled heat and mass transfer must be considered and inert gas venting must be provided in the design.
Worked example
In a vertical shell-and-tube condenser, saturated steam at 1.013 bar (Ts = 100 °C) condenses on the inner wall of 20 tubes 25 × 2 mm (di = 21 mm) with a heated length H = 2.0 m. The mean wall temperature is 90 °C. Find the mean heat transfer coefficient of the condensate film according to the Nusselt film theory, the condenser duty and the condensate mass flow.
Given
| Saturation temperature Ts | 100 °C (1.013 bar) |
|---|---|
| Wall temperature Tw | 90 °C (ΔT = 10 K) |
| Tube inside diameter di | 21 mm |
| Tube length H | 2.0 m |
| Number of tubes n | 20 |
| Condensate density ρ (at approx. 95 °C) | 962 kg/m³ |
| Thermal conductivity λ | 0.68 W/(m·K) |
| Dynamic viscosity η | 2.97·10⁻⁴ Pa·s |
| Enthalpy of vaporization Δh_v | 2,257 kJ/kg |
Solution
Mean heat transfer coefficient according to Nusselt
For the laminar condensate film on a vertical tube (vapor density neglected compared with the liquid density):
αm = 0.943 · [ρ² · g · Δhv · λ³ / (η · ΔT · H)]1/4
αm = 0.943 · [962² · 9.81 · 2,257,000 · 0.68³ / (2.97·10⁻⁴ · 10 · 2.0)]1/4
αm = 0.943 · [1.085·10¹⁵]1/4 ≈ 5,410 W/(m²·K)
Duty and condensate quantity
Effective area: A = π · di · H · n = π · 0.021 · 2.0 · 20 = 2.64 m²
Q̇ = αm · A · ΔT = 5,410 · 2.64 · 10 ≈ 142.8 kW
Condensate mass flow: ṁ = Q̇ / Δhv = 142,800 / 2,257,000 ≈ 0.063 kg/s ≈ 228 kg/h
Check of the film state
Film loading at the tube end per tube: Γ = ṁ / (n · π · di) = 0.063 / (20 · π · 0.021) ≈ 0.048 kg/(m·s)
Film Reynolds number: Re = Γ / η = 0.048 / 2.97·10⁻⁴ ≈ 161 < 400 → the film remains laminar (wavy laminar), the Nusselt solution is applicable and, because of the film waviness, on the safe side.
Result
| Mean heat transfer coefficient αm | ≈ 5,410 W/(m²·K) |
|---|---|
| Condenser duty Q̇ | ≈ 142.8 kW |
| Condensate mass flow ṁ | ≈ 228 kg/h |
| Film Reynolds number at the tube end | ≈ 161 (laminar) |
Technical content source: LV-Solved-Problems-Content 628d313247e7