Engineering task and calculation objective
The SPIR module calculates heat transfer and pressure drop for flow through tubes – either for the plain (empty) tube or for tubes with a twisted-tape insert. Twisted tapes generate a swirl flow, increase the effective flow velocity and improve radial mixing; the tube-side heat transfer coefficient can thus be raised considerably, at the price of a higher pressure drop. Anyone who wants to calculate in-tube heat transfer and quantify the benefit of a turbulence promoter gets both cases here in a direct comparison.
Inputs are the tube geometry (tube length, inside diameter, cross-sectional area and circumference), the tape geometry (twisted-tape thickness and width, pitch H and twist ratio y) and the operating data: total mass flow, number of tubes with parallel flow, inlet and outlet temperature and the fluid properties (density, dynamic viscosity, thermal conductivity, specific heat capacity, Prandtl number at the wall). The module delivers flow velocity and Reynolds number for the empty tube and the tube with tape, the heat transfer coefficient α, the wall temperature and the pressure drop Δp for both variants.
Typical applications in process equipment engineering are the retrofit of existing shell-and-tube heat exchangers, viscous media with laminar tube flow, and cases in which the tube side turns out to be the limiting resistance and replacing the tubes is not an option.
Calculation workflow
- Enter geometry and operating data: Tube length, inside diameter and – for the case with insert – twisted-tape thickness, width, pitch H and twist ratio y are entered. From the total mass flow and the number of tubes with parallel flow, the module determines the mass flow per tube.
- Determine fluid properties at mean temperature: The mean temperature ϑ<sub>m</sub> is formed from inlet and outlet temperature; density, dynamic viscosity, thermal conductivity and specific heat capacity are evaluated there. To correct for the wall influence, the Prandtl number at wall temperature is additionally taken into account.
- Calculate the flow parameters: For the empty tube and the tube with tape, the actual flow velocities and the corresponding Reynolds numbers are calculated; the twisted tape reduces the free cross-section and lengthens the flow path, which increases both parameters.
- Determine the heat transfer coefficient: Depending on the flow regime (laminar, transition region, turbulent), the applicable correlation is used to determine the Nusselt number and from it the heat transfer coefficient α(s) – once for the empty tube, once for the tube with twisted tape. In addition, the heat flux and the wall temperature ϑ<sub>w</sub>(s) are reported.
- Compare the pressure drop: Finally, the module calculates the pressure drop Δp(s) for both variants. Comparing the gain in α with the increase in Δp shows whether the twisted-tape insert pays off for the specific application.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Tube length Inside diameter | ² | m |
| Tube length Inside diameter | D | m |
| A | = ∙ ∙ | m² |
| Cross section area F Circumference | U | m² |
| Cross section area F Circumference | U | m |
| Tw.-tape height H Tw.-tape gradient y | - | m |
| Tw.-tape height H Tw.-tape gradient y | - | – |
| Inlet temperature ϑe Outlet temperatureϑa | Te | °C |
| Inlet temperature ϑe Outlet temperatureϑa | Ta | °C |
| Mean temperatureϑm | Tm | °C |
| Wall temp: ϑw(s)= | ϑw = | °C |
| Therm.conductiv.λ Specific heat capacity cp | cp | J/(kg·K) |
| Dynam.viscosity η Density | ρ | mPa·s |
| Dynam.viscosity η Density | ρ | kg/m³ |
| Prandtl wall | Prandtl Pr PrW | – |
| Prandtl wall | Prandtl Pr PrW | – |
| Reynolds empty tube | Re | – |
| Nu_s' | = | – |
| Nu_s | Nusselt: Nu(s) = Nu = | – |
| Therm.conductiv.λ Specific heat capacity cp | lam | W/(m·K) |
| Flow velocity empty tube | w | m/s |
| Total mass flow | Mg | kg/s |
| Number of tubes with parallel flow | Z - | – |
| Mass flow per tube | M | kg/s |
Worked example
For the reference case of the empty tube, the tube-side heat transfer coefficient is to be calculated as a worked example: water at a mean temperature of 40 °C is pumped through a tube of 20 mm inside diameter and 3 m length; the flow velocity is 1.5 m/s. Required are the Reynolds number, the Nusselt number and the heat transfer coefficient α according to the Gnielinski correlation (VDI Heat Atlas).
Given values
| Inside diameter di | 20 mm |
| Tube length L | 3 m |
| Flow velocity w | 1.5 m/s |
| Medium | Water, ϑm = 40 °C |
| Kinematic viscosity ν | 0.658 · 10⁻⁶ m²/s |
| Thermal conductivity λ | 0.631 W/(m·K) |
| Prandtl number Pr | 4.33 |
Solution
Reynolds number
Re = w · di / ν = 1.5 · 0.020 / (0.658 · 10⁻⁶) ≈ 45,590
The flow is fully turbulent (Re > 10⁴), so the Gnielinski correlation is applicable.
Friction factor according to Konakov
ξ = (1.8 · log Re − 1.5)⁻² = (1.8 · log 45,590 − 1.5)⁻² ≈ 0.0211
Nusselt number according to Gnielinski
Nu = (ξ/8) · (Re − 1000) · Pr / [1 + 12.7 · √(ξ/8) · (Pr2/3 − 1)] · [1 + (di/L)2/3]
Nu = (0.0211/8) · 44,590 · 4.33 / [1 + 12.7 · √(0.0211/8) · (4.332/3 − 1)] · [1 + (0.020/3)2/3] ≈ 244.7 · 1.035 ≈ 253
Heat transfer coefficient
α = Nu · λ / di = 253 · 0.631 / 0.020 ≈ 7,990 W/(m²·K)
With a twisted-tape insert, this value would increase significantly further – at a correspondingly higher pressure drop.
Result
| Reynolds number Re | ≈ 45,590 |
| Nusselt number Nu | ≈ 253 |
| Heat transfer coefficient α | ≈ 7,990 W/(m²·K) |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
When is a twisted tape in the tube actually worthwhile?
The benefit is greatest for laminar or weakly turbulent flow of viscous media, where the tube-side heat transfer dominates the overall resistance. There, the tape can increase the heat transfer coefficient several-fold. With flow that is already highly turbulent, the relative gain is small but the added pressure drop is substantial – in that case the insert is usually not worthwhile.
What do pitch H and twist ratio y mean for a twisted tape?
The pitch H is the axial length for a 180° rotation of the tape; the dimensionless twist ratio y = H/d<sub>i</sub> is the central geometry parameter of the common twisted-tape correlations. Small y values (strong swirl) mean a large heat transfer gain but also a steeply rising pressure drop; typical designs lie roughly in the range y = 2 to 6.
Why is the Prandtl number at the wall requested?
For liquids whose viscosity depends strongly on temperature – oils, for example – the viscosity at the wall differs markedly from that in the core. The correlations correct for this via the ratio of the Prandtl numbers (or viscosities) at mean and wall temperature. When heating viscous media, the thinner boundary layer at the wall improves heat transfer; when cooling, it impairs it.
Does the calculation with tape also apply to evaporation or condensation in the tube?
No. The implemented correlations apply to single-phase tube flow. With boiling or condensing media, the mechanisms change fundamentally; dedicated two-phase calculation methods are required there. Heavily fouling media are also critical, because twisted tapes obstruct mechanical cleaning of the tubes.