Engineering task and calculation objective
The TWIS module calculates heat transfer and pressure drop for flow through tubes with and without twisted-tape inserts. It is based on the experimentally validated methods from the Heat Exchanger Design Handbook (Bergles) and the Hong and Bergles correlation for laminar tube flow with tape inserts.
Twisted-tape inserts impose a swirl on the tube flow: the secondary flow increases the velocity at the wall, reduces the effective flow cross-section, and improves transverse mixing. Especially in the laminar regime — with viscous media such as thermal oils — the heat transfer coefficient can be increased severalfold, at the cost of a higher pressure drop. The module calculates both cases in parallel (plain empty tube and tube with inserts), so the benefit of the inserts — more heat transfer versus more pumping power — can be assessed directly.
In practice, this calculation is needed when upgrading existing heat exchangers, for oil coolers and heaters with laminar tube-side flow, and wherever a tube bundle delivers too little duty and a retrofit with tape inserts is being evaluated.
Standard and calculation basis: A.E. Bergles: "Augmentation of heat transfer" HEDH (Heat Exchanger Design Handbook) 1983, Hemisphere f.C. S.W. Hong; A.E. Bergles: "Augmentation of laminar flow heat transfer in tubes by means of twisted-tape inserts" Technical Report, Engineering Research Institute, Iowa State University
Calculation workflow
- Record operating data and fluid properties: The inputs are the inlet and outlet temperatures of the fluid and its properties at the mean temperature: density, specific heat capacity, thermal conductivity, and viscosity. From these the module forms the Prandtl number; in addition, the Prandtl number at wall temperature is taken into account to correct for the temperature-dependent viscosity effect.
- Define the insert geometry: The twisted tape is described by tape thickness, tape width, and twist pitch (the length for a 180° rotation); from these follows the twist ratio y as the ratio of half pitch to tube inside diameter — the key parameter of the swirl flow.
- Determine the flow regime: From the total mass flow or volume flow and the number of tubes in parallel, the mass flow per tube is calculated. The module determines the flow velocity in the empty tube and — because of the cross-section blockage by the tape — the higher velocity with inserts, along with the corresponding Reynolds numbers.
- Calculate the heat transfer: For the tube with tape inserts, the Nusselt number is determined with the Hong and Bergles correlation from Reynolds number, Prandtl number, and twist ratio; in parallel, the empty tube is calculated with the classical relations for laminar tube flow. From the Nusselt numbers follow the heat transfer coefficients and the transferable heat duty.
- Compare the pressure drop: For both variants, the friction factor and the pressure drop are calculated. Comparing the heat transfer enhancement against the pressure drop increase shows whether the inserts pay off for the specific application.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Tube length | L | m |
| Width of the tape | D | m |
| Cross sectional area of the tube | F | m² |
| Circumference of the tube | U | m |
| Pitch for 180° rotation of tape | H | m |
| Twist ratio of the tape | y = H/D | - |
| Inlet temperature | ϑe | °C |
| Outlet temperature | ϑa | °C |
| Mean temperature | ϑm | °C |
| Specific heat capacity of the fluid | cp | J/(kg·K) |
| Dynamic viscosity of the fluid | η | mPa·s |
| Density of the fluid | ρ | kg/m³ |
| Prandtl number | Pr | - |
| Prandtl number at wall temperature | PrW | - |
| Thermal conductivity of the fluid | λ | W/(m·K) |
| Flow velocity without inserts | w | m/s |
| Total mass flow | Mg | kg/s |
| Number of tubes with parallel flow | Z | - |
| Mass flow per tube | M | kg/s |
| Heat flux | Q | W |
| Thickness of the tape | s | m |
| Flow velocity with inserts | ws | m/s |
| Total volume flow | Vg | m³/s |
| Kinematic viscosity of the fluid | ν | m²/s |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Reynolds number | Re | - |
| Nusselt number | Nu(s) | - |
| Heat transfer coefficient | α(s) | W/(m²·K) |
| Nusselt number | Nu | - |
| Heat transfer coefficient | α | W/(m²·K) |
| Pressure drop coefficient | ξ(s) | - |
| Pressure drop coefficient | ξ | - |
| Pressure drop | Δp(s) | Pa |
| Pressure drop | Δp | Pa |
| Reynolds number | Re(s) | - |
Worked example
In the tubes of a water cooler (inside diameter 20 mm), water at about 30 °C flows laminar with Re = 1,000. To increase the duty, a twisted tape with twist ratio y = 5 (pitch for a 180° rotation = 100 mm) is installed. Find the heat transfer coefficient with inserts compared to the empty tube — a worked example of a twisted-tape heat transfer calculation.
Given values
| Tube inside diameter di | 20 mm |
| Reynolds number Re (empty tube) | 1,000 |
| Prandtl number Pr (water, approx. 30 °C) | 5.4 |
| Thermal conductivity λ | 0.60 W/(m·K) |
| Twist ratio y | 5 |
Solution
Nusselt number with tape inserts (Hong-Bergles)
Nu = 5.172 · [1 + 5.484 · 10−3 · Pr0.7 · (Re/y)1.25]0.5
With Pr0.7 = 5.40.7 = 3.256 and (Re/y)1.25 = 2001.25 = 752.1:
bracket term = 1 + 0.005484 · 3.256 · 752.1 = 1 + 13.43 = 14.43
Nu = 5.172 · √14.43 = 19.6
Heat transfer coefficient
α = Nu · λ / di = 19.6 · 0.60 / 0.020 = 589 W/(m²·K)
Comparison with the empty tube
For the fully developed laminar flow in the empty tube at constant wall temperature, Nu = 3.66, hence α = 3.66 · 0.60 / 0.020 = 110 W/(m²·K).
The twisted tape thus increases the heat transfer coefficient by a factor of ≈ 5.4 — set against this is a considerably higher pressure drop, which the module reports in parallel.
Result
| Nusselt number with inserts | ≈ 19.6 |
| Heat transfer coefficient with inserts | ≈ 589 W/(m²·K) |
| Heat transfer coefficient, empty tube | ≈ 110 W/(m²·K) |
| Enhancement factor | ≈ 5.4 |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
For which flow regime is the Hong and Bergles correlation valid?
The correlation was established for fully developed laminar flow with approximately constant wall temperature and validated experimentally with water and aqueous glycol solutions, i.e. for moderate Prandtl numbers and Reynolds numbers below the transition range. In the transitional and turbulent regimes, other methods apply (e.g. Manglik/Bergles); applying the laminar correlation above Re ≈ 2,300 underestimates the heat transfer, but above all it no longer reliably predicts the enhancement effect of the tape.
What does the twist ratio y mean and which values are common?
y is the ratio of the pitch for a 180° rotation of the tape to the tube inside diameter. Small y values (2 to 3) mean strong swirl with a high heat transfer enhancement but also a strongly increased pressure drop; large y values (6 to 10) act more weakly. Typical values of y lie between 2.5 and 6; y approaching infinity corresponds to a straight, untwisted tape.
Why does the pressure drop with tape inserts increase disproportionately?
Three effects superimpose: the tape blocks part of the cross-section and increases the mean velocity, the hydraulic diameter decreases, and the helical flow path is longer than the tube axis. Together, depending on the twist ratio, this yields a multiple of the empty-tube pressure drop. Whether the inserts are worthwhile is therefore always a trade-off between the gained heat duty and the additional pumping power — in the laminar regime it usually favors the inserts, in the turbulent regime often not.
When are twisted-tape inserts the right choice compared to other measures?
Tape inserts are particularly effective when the tube-side heat transfer is laminar and thus the limiting resistance — typical for oils and viscous media. They can be retrofitted into existing tube bundles without modifying the apparatus. With already turbulent flow, with heavily fouling media (risk of clogging, harder cleaning), or when the limiting resistance is on the shell side, they offer little benefit.