Engineering task and calculation objective
The KONR module determines the cooling-water-side tube geometry of a condenser: from the cooling water mass flow, the density of the cooling water and the selected cooling water velocity in the tube, the required number of cooling tubes follows via the continuity equation; together with the tube outside diameter, the effective cooling tube length and the number of tube passes, this yields the condenser cooling surface.
This preliminary sizing stands at the beginning of every condenser calculation in power plant and process plant engineering: before heat transfer and condensation duty can be calculated in detail, the number of tubes, the bundle size and the surface area must be fixed. The cooling water velocity is the central design variable; for copper alloys and steel tubes it is typically chosen around 1.5 to 2.5 m/s as a compromise between good heat transfer and low fouling on the one hand, and pressure drop, pumping power and erosion on the other.
The module links the quantities consistently: if, for example, the number of tubes is rounded for design reasons or the number of passes is changed, the actual velocity and the resulting cooling surface can be recalculated immediately.
Calculation workflow
- Define the cooling water data: The inputs are the cooling water mass flow, the density of the cooling water and the desired cooling water velocity in the tubes; the velocity depends on tube material, water quality and permissible pressure drop.
- Choose tube dimensions and passes: The tube inside diameter and tube outside diameter as well as the number of tube passes and the effective cooling tube length are set as design specifications; more passes increase the velocity and the pressure drop for the same number of tubes.
- Calculate the number of tubes from continuity: From mass flow, density, velocity and the inner cross-section of one tube follows the number of tubes flowing in parallel per pass; multiplied by the number of passes, this gives the number of cooling tubes in the condenser. The number of tubes is then rounded to a bundle layout suitable for fabrication.
- Determine cooling surface and actual velocity: The condenser cooling surface follows from the tube outside diameter, the effective cooling tube length and the total number of tubes. With the rounded tube count, the actual cooling water velocity is back-calculated and checked to remain within the permissible range.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Number of tube passes | Zw | – |
| Effective length of cooling tube | L | m |
| Inside diameter of tube | di | m |
| Outside diameter of tube | da | m |
| Mass flow of cooling water | mW | kg/s |
| Density of cooling water | rhoW | kg/m³ |
| Velocity of cooling water | uW | m/s |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Number of cooling tubes in condenser | Zr | – |
| Cooling area in condenser | A | m² |
Worked example
For a turbine condenser, 300 kg/s of cooling water (ρ = 998 kg/m³) are to be passed through tubes 25 × 1.25 mm (di = 22.5 mm, da = 25 mm) at a target velocity of 2.0 m/s. The condenser is built as a two-pass design, the effective cooling tube length is 6.0 m. Find the number of tubes per pass, the total number of tubes, the actual cooling water velocity and the condenser cooling surface.
Given values
| Cooling water mass flow ṁ | 300 kg/s |
| Density of the cooling water ρ | 998 kg/m³ |
| Target cooling water velocity w | 2.0 m/s |
| Tube inside diameter di | 22.5 mm |
| Tube outside diameter da | 25 mm |
| Number of tube passes | 2 |
| Effective cooling tube length L | 6.0 m |
Solution
Number of tubes per pass from the continuity equation
Inner cross-section of one tube: Ai = π/4 · di² = π/4 · 0.0225² = 3.976·10⁻⁴ m²
Mass flow per tube: ṁtube = ρ · w · Ai = 998 · 2.0 · 3.976·10⁻⁴ = 0.794 kg/s
Number of tubes per pass: n = ṁ / ṁtube = 300 / 0.794 = 378 → selected 380 tubes per pass
Total number of tubes and actual velocity
Total number of tubes with 2 passes: ntot = 2 · 380 = 760 tubes
Actual velocity: w = ṁ / (ρ · n · Ai) = 300 / (998 · 380 · 3.976·10⁻⁴) ≈ 1.99 m/s — within the permissible range.
Condenser cooling surface
Referred to the tube outside diameter:
A = π · da · L · ntot = π · 0.025 · 6.0 · 760 ≈ 358 m²
Result
| Number of tubes per pass | 380 |
| Total number of cooling tubes | 760 |
| Actual cooling water velocity | ≈ 1.99 m/s |
| Condenser cooling surface | ≈ 358 m² |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why is the cooling water velocity the most important design variable?
It determines both: the water-side heat transfer and thus the required surface area, as well as the pressure drop and thus the pumping power. Velocities that are too low, below about 1.5 m/s, additionally promote deposits and sedimentation in the tubes, while velocities that are too high lead to erosion-corrosion depending on the material, especially with copper alloys. The usual design range is therefore about 1.5 to 2.5 m/s.
What is the effect of the number of tube passes?
With several passes, the cooling water flows through the bundle multiple times; per pass, only part of the tubes are connected in parallel. For a given total number of tubes, this increases the velocity in the tube, while at the same time the pressure drop approximately doubles with each additional pass and the cooling water temperature rise is distributed differently across the bundle. Large condensers with ample cooling water are often single-pass, smaller units two-pass or multi-pass.
Why is the cooling surface referred to the tube outside diameter?
Condensation takes place on the tube outside, which is why the transfer surface of a condenser is by convention formed with the outside diameter, and the overall heat transfer coefficient is also referred to this surface. When comparing manufacturer data, always check which surface the values refer to.
Does this geometry sizing replace the thermal calculation of the condenser?
No. The module delivers the hydraulically consistent geometry: number of tubes, velocity and surface area. Whether this surface is sufficient for the required condensation duty at the given cooling water temperature must be shown by the thermal rating with overall heat transfer coefficient and mean temperature difference, for example with the condensation modules; if necessary, the geometry is adjusted iteratively.