Engineering task and calculation objective
Module AC performs the thermal design of tube-bank heat exchangers — heat exchangers with rectangular tube bundles, as widely used in plant engineering as air coolers, air heaters, economizers, duct-mounted coil banks and heating coils. The calculation is based on the recognized correlations of the VDI Heat Atlas and the Verfahrenstechnische Berechnungsmethoden (VCH Weinheim).
Different media can be selected inside and outside the tubes from an extensive property database — from air, flue gas, water and steam through thermal oils and refrigerants to acids, caustics and brines. The heat transfer can be calculated single-phase; in addition, evaporation (tube-side) and the condensation of pure substances are covered. The module thus also handles applications such as steam coil banks, evaporator coils and flue gas condensation, including dew point assessment and wall temperatures.
The results of the calculation are the heat transfer coefficients on both sides, the overall heat transfer coefficient, the corrected logarithmic mean temperature difference, pressure drops, and the surface margin of the selected exchanger area relative to the required heat duty. This makes it possible to calculate, size and rate a tube-bank heat exchanger.
Standard and calculation basis: Verfahrenstechnische Berechnungsmethoden, Teil 1, VCH Weinheim & VDI Wärmeatlas
Calculation workflow
- Define the tube-bank geometry: The bundle dimensions (horizontal and vertical), the bundle length, tube diameter, tube pitch and arrangement (in-line/staggered) as well as any finning and the number of tube-side passes are entered. From these follow the heat transfer area and the flow cross-sections.
- Select media and operating data: For the tube inside and outside, the media are chosen from the property database, and mass flows as well as inlet and outlet temperatures and pressures are specified. The fluid properties (density, viscosity, thermal conductivity, Prandtl number) are evaluated as functions of temperature; the required heat duty is set as the target value.
- Calculate the heat transfer on both sides: The heat transfer coefficients are determined with the Nusselt correlations of the VDI Heat Atlas: tube-side for laminar to turbulent pipe flow, with flow boiling in the case of evaporation; outside for the tube row or bundle in crossflow, with film condensation for pure-substance vapor. The associated Reynolds numbers and wall temperatures (minimum, mean, maximum) are reported.
- Form the overall heat transfer and temperature difference: From both heat transfer coefficients, the tube wall and the fouling resistances follows the overall heat transfer coefficient. The logarithmic mean temperature difference is corrected with the correction factor for the actual flow arrangement (cross/counterflow, passes).
- Duty balance and pressure drop: The transferable duty k·A·ΔTlog,corr is compared with the required heat duty; the performance ratio and the surface margin of the exchanger area appear as results. In parallel, the pressure drops on both sides and the influence of fouling are calculated so that the fan or pump can be sized.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Fouling factor Fouling factor | innen | m²·K/W |
| Fouling factor Fouling factor | aussen | m²·K/W |
| Volume flow (inlet) | aussen | m³/s |
| Vapour volume flow (outlet) | Austritt | m³/s |
| Liquid volume flow (outlet) | Austritt | m³/s |
| Density (inlet) | aussen | kg/m³ |
| Density (outlet) | aussen | kg/m³ |
| Vapour density | innen | kg/m³ |
| Vapour volume flow | Eintritt | m³/s |
| Velocity (Inlet nozzle) | innen | m/s |
| Velocity (Outlet nozzle) | innen | m/s |
| Total number of tubes | Ntotal | - |
| Outside tube diameter | DRA | m |
| Crosswise pitch | s1 | m |
| Longitudinal pitch | s2 | m |
| Pitch for partly staggered bundle | s3 | m |
| Thermal conductivity of tube material | λG | W/(m·K) |
| Thermal conductivity of fin material | λR | W/(m·K) |
| Outside fin diameter | D | m |
| Fin thickness | s1 | m |
| Thickness at the root of fin | s2 | m |
| Flow cross-section | F | m² |
| Outlet | (aussen) | kg/kg |
| Type of pitch | Teilungsart | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Pressure drop Pressure drop | - - | - |
| Overall heat transfer coefficient | k | W/(m²·K) |
| Logarithmic temperature difference | dT_log' | K (diff) |
| Oversize Transfer area | A_a | m² |
| at Reynolds | innen | - |
| Heat transfer coefficient Heat transfer coefficient | α α | W/(m²·K) |
| at Reynolds at Reynolds | aussen | - |
| Performance factor | VZ | - |
| Fan performance | Lüfterleistung | W |
| Required thermal performance | Q_soll | kW |
| Heat transfer coefficient Heat transfer coefficient | α α | W/(m²·K) |
| Logarithmic temperature difference corrected | dT_log | K (diff) |
| Correction factor | dT_log | - |
| Heat transfer Heat transfer | - - | - |
| Mean wall temperature Mean wall temperature | T_Wi | °C |
| Mean wall temperature Mean wall temperature | T_Wa | °C |
| Fan arrangement | Lüfteranordnung | - |
| Fouling at Δp | - - | - |
| Oversize Transfer area | Leistungsreserve | % |
| Min. wall temperature Min. wall temperature | innen | °C |
| Max. wall temperature Max. wall temperature | innen | °C |
| Min. wall temperature Min. wall temperature | aussen | °C |
| Max. wall temperature Max. wall temperature | aussen | °C |
| Wall temperature | - | - |
Calculation options
Type of pitch
aligned · staggered · partly staggered
Tube design
Straight tube · U-Tube
Flow direction
Cross counterflow · Cross cocurrent flow
Frequently asked questions
When is a single-phase calculation sufficient, and when must I model evaporation or condensation?
Single-phase calculation applies as long as the medium remains without phase change throughout the unit — even with a large temperature change. As soon as a pure-substance vapor is cooled below its saturation temperature, condensation must be modeled; as soon as a liquid in the tubes reaches its boiling temperature, evaporation. The module calculates evaporation only on the tube side and condensation only for pure substances; mixture condensation with a gliding dew point or inert gas fractions can only be approximated and should be assessed conservatively.
What does the surface margin of the exchanger area tell me?
It indicates by what percentage the installed area is larger than the area computationally required for the target duty. A margin covers uncertainties of the correlations, scatter of the fluid properties and progressive fouling. Depending on the application, 10 to 25 % is common; a very large margin, however, can lead to control and stability problems in evaporators and is not a quality feature in itself.
Why are the minimum and maximum wall temperatures reported?
The wall temperature governs several design risks: with flue gases, the minimum wall temperature must not fall below the acid or water dew point (corrosion risk); with thermal oils and products prone to decomposition, the maximum wall temperature must not exceed the allowable film temperature. In addition, wall temperatures enter the property corrections of the Nusselt correlations and the nucleate boiling assessment.
How is fouling taken into account in the calculation?
Fouling is included as an additional conductive resistance on one or both sides of the overall heat transfer and reduces the overall heat transfer coefficient. Deposits also narrow the flow cross-section and increase the pressure drop — the module therefore also reports the fouling influence on Δp. The applied values should come from operating experience or standard tables (e.g. TEMA) and should not be maximized across the board, since excessive fouling resistances lead to unnecessarily large equipment.