Engineering task and calculation objective
The ACOI module calculates heat transfer for flow around helical tube coils. Helical coils – tube bundles wound in a helix – are widely used in apparatus engineering: as heating or cooling coils in vessels and agitated tanks, in coiled-tube heat exchangers, or as cooling registers in storage tanks. While the flow inside the coil has its own correlations, this module considers the outside, i.e. the flow of the shell-side medium around the coil bundle.
The central result is the external heat transfer coefficient, which together with the internal heat transfer and the tube wall determines the overall heat transfer coefficient of the coil. The calculation takes the configuration into account – for example whether the coil is in open crossflow or whether baffles or a shroud tube guide the flow along the tubes, which improves heat transfer considerably.
The basis is the established heat transfer correlations of engineering thermodynamics, as documented in the VDI Heat Atlas for helical coils in crossflow and longitudinal flow. Anyone who wants to calculate the heat transfer coefficient at a helical tube coil obtains a reliable basis for the thermal design of the apparatus.
Calculation workflow
- Define configuration and geometry: First, the configuration is chosen – open flow around the coil in the vessel or guided flow with baffles or a shroud tube. In addition, the tube outside diameter, coil diameter, pitch, and number of turns are entered, from which the heat transfer surface and the characteristic length follow.
- Determine the flow condition of the external medium: From the volume flow and the flow cross-section, the governing approach velocity at the coil is calculated and the Reynolds number is formed from it. It decides whether laminar or turbulent relationships apply.
- Evaluate the fluid properties: Density, viscosity, thermal conductivity, and heat capacity of the external medium are evaluated at the mean reference temperature; the Prandtl number describes the ratio of momentum to heat transport.
- Calculate the Nusselt number and heat transfer coefficient: With the correlation matching the configuration, the Nusselt number of the coil in crossflow is determined and the external heat transfer coefficient is derived from it. Corrections capture the influence of curvature and tube pitch within the coil bundle.
- Transfer the result into the apparatus design: The external heat transfer coefficient, together with the internal heat transfer, the tube wall, and the fouling resistances, enters the overall heat transfer coefficient with which the transferable duty of the coil is balanced.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Number of coils | N | - |
| Outside diameter of coiled tube | da dh = π/2·da | m |
| Mean crosswise pitch | s1 a = s1/da | m |
| Distance of windings | w b = w/da | m |
| Flow cross-section | F | m² |
| Outside diameter of coiled tube | da dh = π/2·da | m |
| Mean crosswise pitch | s1 a = s1/da | - |
| Distance of windings | w b = w/da | - |
| Mean pressure | p | Pa |
| Inlet temperature | ϑe | °C |
| Outlet temperature | ϑa | °C |
| Mean temperature (ϑe+ϑa)/2 | ϑm | °C |
| Density | ρ | kg/m³ |
| Specific heat capacity | cp | J/(kg·K) |
| Thermal conductivity | λ | W/(m·K) |
| Dynamic viscosity | η | mPa·s |
| Kinematic viscosity | ν | m²/s |
| Prandtl number | Pr | - |
| Mean wall temperature | ϑW | °C |
| Prandtl number at wall temperature | PrW | - |
| Fluid liquid / gaseous ? | <1> | - |
| Mass flow | m | kg/s |
| Velocity in the narrowest cross-section | w | m/s |
| Void fraction | ψ | - |
Calculation options
Fluid liquid / gaseous ?
1 · 2
Type
Longitudinal flow · Guide cylinder
Frequently asked questions
Why does heat transfer at a helical coil differ from that at a straight tube bundle?
The curvature of the coil and the helical arrangement change the flow field compared with an in-line or staggered straight bundle: secondary flows develop, and the effective approach direction lies between crossflow and longitudinal flow. Correlations for straight tube bundles therefore give only approximate values; for coils, dedicated, experimentally validated relationships must be used.
What influence do a shroud tube or baffles have on the result?
Without flow guidance, the shell-side medium takes the path of least resistance and partly bypasses the coil bundle; the effective velocity at the tubes is then small. A shroud tube or baffles force the flow through the annular gap of the coil, increase the velocity at the tube, and thereby raise the heat transfer coefficient considerably – at the cost of a higher pressure drop.
Does the calculation also apply to natural convection, for example a cooling coil in a stagnant tank?
The correlations for forced flow presuppose a defined approach velocity. With a stagnant external medium, natural convection dominates, which is described by the Grashof or Rayleigh number and yields significantly lower heat transfer coefficients. For such cases, the corresponding natural convection relationships must be used; mixed convection lies in between and must be assessed separately.
What are typical sources of error in the design of helical coils?
Common errors are an overly optimistic approach velocity (bypass flow is underestimated), fluid properties evaluated at the wrong reference temperature, neglected fouling resistances, and correlations applied outside their validated Reynolds and geometry range. The thermally effective surface is also occasionally overestimated for tightly wound coils, where adjacent turns shade each other.