Engineering task and calculation objective
The DRLL module calculates heat transfer and pressure drop for single-phase flow through corrugated (spirally indented) tubes. These are tubes with a helical profile rolled into one or both sides (single-sided or cross-corrugated) that deliberately disturbs the near-wall flow: the enhanced turbulence significantly improves the tube-side heat transfer coefficient compared with a plain tube — at the price of a higher friction factor.
The calculation relies on the experimentally validated methods published in the heat engineering bulletins of hde Metallwerk GmbH (Menden, 1992 and 1994), i.e. on manufacturer-specific correlations for the Nusselt number and the friction factor as functions of the Reynolds and Prandtl numbers, treated separately for laminar and turbulent flow and including the critical Reynolds number of the transition.
If you want to calculate heat transfer in corrugated tubes — for example when designing compact shell-and-tube heat exchangers, in retrofit projects aimed at boosting the duty of existing equipment, or when comparing corrugated versus plain tubes — DRLL delivers the tube-side heat transfer coefficient, the resulting friction factor and the pressure drop over the tube length.
Standard and calculation basis: Wärmeübergang in einphasig durchströmten Drallrohren, Wärmetechnische Information der hde Metallwerk GmbH, Menden, 1994 Druckabfall bei Strömungen in einseitig- und kreuzgedrallten Rohren, Wärmetechnische Information der hde Metallwerk GmbH, Menden, 1992
Calculation workflow
- Specify the fluid properties: Density, specific heat capacity, thermal conductivity, and dynamic or kinematic viscosity are entered at the governing reference temperature; from these, the Prandtl number is obtained.
- Define throughput and geometry: From the total mass flow, the number of tubes and the number of tube-side passes, the mass flow per tube follows. With the tube cross-section and the density, the volume flow per tube and the flow velocity are obtained; the tube length later determines the pressure drop.
- Determine the flow regime: From velocity, tube diameter and viscosity, the Reynolds number is formed and compared with the critical Reynolds number of the corrugated tube. In profiled tubes, the laminar-turbulent transition typically occurs at a different point than in a plain tube.
- Calculate the heat transfer: The tube-specific correlations of the form Nu = f(Re, Pr), with the factors and exponents determined by the manufacturer, yield the Nusselt number and from it the tube-side heat transfer coefficient — separately for laminar and turbulent flow.
- Determine friction factor and pressure drop: In the same way, the friction factor is calculated for laminar and turbulent flow and combined into the resulting friction factor. With tube length, diameter, density and velocity, the pressure drop of the corrugated tube follows.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Mass flow per tube | Mp | kg/s |
| Volume flow per tube | Vp | m³/s |
| Tube length | l | m |
| Velocity | w | m/s |
| Density | ρ | kg/m³ |
| Spezific heat capacity | cp | J/(kg·K) |
| Dynamic viscosity | η | mPa·s |
| Kinematic viscosity | ν | m²/s |
| Thermal conductivity | λ | W/(m·K) |
| Prandtl number | Pr | - |
| Reynolds number | Re | - |
| Nusselt number | Nu | - |
| Heat transfer coefficient inside | α | W/(m²·K) |
| Pressure drop | Δp | Pa |
| Resulting friction factor | ζ | - |
| for laminar flow | ζl | - |
| for turbulent flow | ζt | - |
| Type | Rohrbezeichnung | * |
| Spin depth | h | m |
| Hydraulic diameter | dh | m |
| Spin angle | φ | ° |
| Factor Exponent Re Exponent Pr | f1 e1 e2 | - |
| Factor Exponent Re Exponent Pr | f1 e1 e2 | - |
| Factor Exponent Re Exponent Pr | f1 e1 e2 | - |
Frequently asked questions
How much does a corrugated tube gain over a plain tube?
Depending on the corrugation geometry and Reynolds number range, the helical profile increases the tube-side heat transfer coefficient considerably — but the friction factor also rises disproportionately. Whether the enhancement pays off is decided by weighing the gained heat duty against the additional pumping power; this is exactly why the module reports both quantities consistently from the same set of correlations.
Do the correlations apply to arbitrary corrugated tubes?
No. The methods stem from measurement series by hde Metallwerk GmbH on defined single-sided and cross-corrugated tube geometries. For corrugated tubes from other manufacturers with a different profile depth, pitch or corrugation pattern, the factors and exponents of the correlations are not readily transferable; in case of doubt, use the manufacturer's data for the specific geometry.
Why is the critical Reynolds number a separate input for a corrugated tube?
The corrugation shifts the laminar-turbulent transition away from the plain-tube value of about Re = 2,300. Since heat transfer and friction factor change abruptly in the transition region, the transition point must be set specifically for the corrugated tube — otherwise the wrong correlation is selected in the transition region and heat transfer or pressure drop is significantly misjudged.
Does the module also cover two-phase flow or condensation?
No, the methods apply to single-phase flow through the tubes (liquid or gas without phase change). Evaporation or condensation in the corrugated tube requires different correlations and is not covered by DRLL.