Engineering task and calculation objective
This module calculates the pressure drop for cross-flow over tube bundles with finned circular or oval tubes according to Section L1.4 of the VDI-Wärmeatlas (VDI Heat Atlas, 12th edition, 2019). Finned tubes are used whenever a fluid with poor heat transfer flows on the outside – typically air or other gases in air coolers, condensers, dry coolers and flue gas heat exchangers. The fins enlarge the exchange surface but at the same time increase the flow resistance of the bundle.
Anyone who wants to calculate the air-side pressure drop in a finned tube bundle must consider the fin geometry in addition to tube diameter and pitch: fin height, fin thickness and fin pitch change the free flow cross-section and the wetted surface and therefore enter the drag correlations. The module provides the correlations documented in the VDI Heat Atlas for in-line and staggered arrangements.
The result is the basis for fan sizing: the pressure drop of the bundle, together with the other resistances of the air path, determines the operating point and thus the drive power of the fan.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Enter tube and fin geometry: Via the tube selection (V44), the core tube diameter or oval tube dimensions as well as fin height, fin thickness and fin pitch are defined. From these follow the contraction ratio of the flow cross-section and the area ratio of finned to plain surface.
- Define the bundle arrangement: Transverse and longitudinal pitch as well as in-line or staggered arrangement determine the narrowest free cross-section between the finned tubes and the number of main flow resistances in the flow direction.
- Form the reference velocity and Reynolds number: From the volume flow rate and the narrowest free cross-section the governing velocity is calculated; with the gas properties at the mean temperature, the Reynolds number follows, referred to the core tube diameter.
- Determine the drag coefficient from the correlation: The correlation valid for finned tube bundles yields the drag coefficient as a function of Reynolds number, pitch ratios and fin geometry; in-line and staggered arrangements are treated separately.
- Calculate the pressure drop of the bundle: The total pressure drop follows from the drag coefficient, the number of tube rows and the dynamic pressure of the reference velocity; it enters directly into the sizing of the fan or induced draft system.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Temperature (inlet) | Eintrittstemperatur | °C |
| Temperature (outlet) | Austrittstemperatur | °C |
| Mean temperature | Temperatur | °C |
| Mean density | ρ | kg/m³ |
| Dynamic viscosity | η | mPa·s |
| Total mass flow | m | kg/s |
| Total volume flow | V | m³/s |
| Arrangement in-line=1/ staggered=2 | versetzt=2 | - |
| Outside diameter of bare tube | d | m |
| Fin thickness | s | m |
| Fin pitch | t | m |
| Fin height | h | m |
| Tubes in a row | Nq | – |
| Number of tube rows | NR | - |
| Crosswise pitch | s1 | m |
| Longitudinal pitch | s2 | m |
| Tube length | L | m |
| Crosswise pitch ratio | a | - |
| Longitudinal pitch ratio | b | - |
| Auxilliary value | c=f(a) c | - |
| Free cross-section | A0 | m² |
| Narrowest cross-section | Ae | m² |
| Mean velocity in A0 | w0 | m/s |
| Mean velocity in Ae | we | m/s |
Calculation options
Tube
Finned circular tube bundle · Finned oval tube bundles
Frequently asked questions
Why can't the pressure drop of a finned tube bundle be calculated with plain tube correlations?
The fins narrow the free cross-section, generate additional friction surface and change the vortex formation in the wake of the tubes. The drag coefficient therefore additionally depends on fin height, fin thickness and fin pitch. Plain tube correlations usually underestimate the pressure drop of finned tube bundles considerably.
What advantage do oval tubes offer over circular tubes?
Oval tubes are more streamlined: the wake behind the tube is smaller and the form drag decreases, so that for the same heat duty a lower air-side pressure drop is achieved. This is offset by higher manufacturing costs and lower pressure resistance of the non-circular cross-section.
Which velocity is the drag coefficient referred to?
To the velocity in the narrowest free cross-section of the finned bundle, where the fins also narrow the cross-section. If the superficial approach velocity is inserted by mistake, the calculated pressure drop is far too small – one of the most common sources of error with finned tube bundles.
Does the module also account for fouling of the spaces between the fins?
The correlations apply to clean bundles. Deposits between the fins narrow the cross-section further and can significantly increase the pressure drop in operation; a plant-specific margin or fouling reserve must be provided for this in the fan sizing.