Engineering task and calculation objective
With this module, helical coil and tube coil heat exchangers can be thermally designed and rated according to the methods of the VDI Heat Atlas (VDI-Wärmeatlas). Gaseous and liquid media on both sides are covered, as well as the condensation of pure substances; an evaporation calculation is not part of the module. The type of construction and the flow arrangement define the geometry and configuration (e.g., co-current or counter-current flow) of the apparatus.
Engineers need to calculate helical coil heat exchangers wherever compact units of robust construction are required: as heating or cooling coils in vessels and agitated tanks, as helical coils in an annular gap, as coaxial heat exchangers in refrigeration systems, or as heaters for thermal oil, brine, and water circuits. The curved tube path generates a secondary flow (Dean vortices) that significantly improves heat transfer compared with a straight tube, but also increases the pressure drop – the VDI methodology captures both effects.
An extensive media library is included, ranging from water, steam, and air through brine, thermal oils, refrigerants, and flue gas to acids and caustic solutions, so that the fluid properties enter the calculation consistently as functions of temperature and pressure.
Standard and calculation basis: VDI Wärmeatlas
Calculation workflow
- Select the type of construction and flow arrangement: First, the type of construction (e.g., helical coil in a vessel or in an annular gap, coaxial design), the coil geometry with tube diameter, coil diameter, and tube pitch, and the flow arrangement of the two media are defined.
- Define process data and media: For both sides, mass flow rates, inlet and outlet temperatures, and pressures are specified; the fluid properties (density, heat capacity, viscosity, thermal conductivity, Prandtl number) are determined from the media library at the governing reference temperatures. The heat duty to be transferred follows from the energy balance.
- Calculate the inside heat transfer: For the flow in the coiled tube, the Nusselt number is determined with the VDI correlations for helical coils. The ratio of tube diameter to coil diameter shifts the critical Reynolds number and increases the heat transfer coefficient compared with a straight tube; for condensing pure substances, film condensation is applied instead.
- Calculate the outside heat transfer: On the outside, depending on the type of construction, the heat transfer for flow around the coil, in the annular gap, or in the vessel (forced or natural convection) is calculated. Together with conduction through the tube wall and, if applicable, fouling resistances, this yields the overall heat transfer coefficient.
- Determine the area and pressure drop: From the heat duty, the overall heat transfer coefficient, and the log mean temperature difference, the required heat transfer area follows – or, for a given geometry, the achievable duty. In parallel, the pressure drop on both sides is calculated with the increased friction factors of curved-tube flow and compared with the allowable values.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Mass flow | mi ma | kg/s |
| Mass flow | mi ma | kg/s |
| Volume flow | Vi Va | m³/s |
| Volume flow | Vi Va | m³/s |
| Density Density | ρi ρa | kg/m³ |
| Density Density | ρi ρa | kg/m³ |
| Specific heat capacity Specific heat capacity | cpi cpa | J/(kg·K) |
| Specific heat capacity Specific heat capacity | cpi cpa | J/(kg·K) |
| Inlet temperature | ϑe,i ϑe,a | °C |
| Outlet temperature | ϑa,i ϑa,a | °C |
| Inlet temperature | ϑe,i ϑe,a | °C |
| Outlet temperature | ϑa,i ϑa,a | °C |
| Heat duty | Qi Qa | W |
| Heat duty | Qi Qa | W |
| Heat loss | Qv,a | W |
| Heat transfer coefficient (inside) | αi | W/(m²·K) |
| Heat transfer coefficient (outside) | αa | W/(m²·K) |
| Thermal conductivity of tube material | λ | W/(m·K) |
| Total fouling resistance | f | m²·K/W |
| Heat exchanger area | A Af | m² |
| Logarithmic mean temperature diff. LMTD | Δϑlog | K (diff) |
| Overall heat transfer coefficient | k | W/(m²·K) |
| Outside diameter Wall thickness | da si | m |
| Inside diameter | di | m |
Calculation options
Countercurrent flow / Cocurrent flow?
Countercurrent flow · Cocurrent flow
Connection arrangement Nominal width
tangential · radial · axial
Frequently asked questions
Why is the heat transfer in a helical coil better than in a straight tube?
The centrifugal force in the curved tube path generates a secondary flow (Dean vortices) that mixes the velocity and temperature profiles transverse to the main flow. As a result, the Nusselt number rises compared with a straight tube – the more so, the larger the ratio of tube diameter to coil diameter. At the same time, the curvature stabilizes the laminar flow: transition to turbulence only occurs at an increased critical Reynolds number.
Can I also design an evaporator with this module?
No. The module calculates single-phase heating and cooling as well as the condensation of pure substances; evaporation is explicitly not calculated. For evaporation tasks (flow boiling inside the tube or pool boiling on the coil), the corresponding boiling modules or the relevant sections of the VDI Heat Atlas must be used, since entirely different mechanisms (nucleate boiling, flow boiling, critical heat flux) govern there.
Which temperature difference should be used in the design?
The governing quantity is the log mean temperature difference of the chosen flow arrangement; for pure counter-current or co-current configurations, it can be formed directly. During condensation of a pure substance, the temperature on the condensate side remains nearly constant in the saturation region, which simplifies the calculation accordingly. Any desuperheating or subcooling zones should be balanced as separate sections.
What role do fouling resistances play for tube coils?
As with any heat exchanger, fouling deposits reduce the overall heat transfer coefficient – for compact coils with high U-values, the relative influence is particularly large. For media such as cooling water, brine, or thermal oil, realistic fouling resistances should therefore be applied and the area designed with an appropriate margin; excessive allowances, however, lead to oversizing and to changed outlet temperatures in operation.