Engineering task and calculation objective
The RIR module calculates the thermal performance of a tube-in-tube element: an inner tube sits inside an outer tube, and the medium first flows through one of them and then returns through the annular gap between the two tubes. This design – known as a bayonet tube or field tube – is used when a heat exchanger is accessible from one side only, for example as an immersion heating tube in vessels, in reactors or in flue gas passes.
The calculation captures the geometry via tube length, hydraulic diameter, flow cross-section and diameter ratio in the gap, and determines the internal heat transfer from the mass flow and the physical properties via the Nusselt number. Together with the specified external heat transfer coefficient and the fouling resistances inside and around the double tube, the overall heat transfer coefficients of the two transfer paths are obtained. Because the inner-tube flow and the annular-gap flow are thermally coupled in a bayonet tube, the evaluation leads to a characteristic equation whose roots yield the temperature profile and the temperature at the tube end.
As a result, the module compares the actual duty against the required target duty and reports the outlet temperature, the NTU parameters and the efficiency of the element – the basis for fixing the tube length or the number of tubes of a bayonet-tube apparatus.
Calculation workflow
- Define the geometry of the double tube: Tube length, hydraulic diameter in the gap, flow cross-section in the gap and diameter ratio describe the tube-in-tube element; in addition, it is specified at which tube the medium enters (inner tube or annular gap).
- Enter the operating data: Mass flow, inlet temperature and desired outlet temperature of the medium as well as the mean temperature outside the double tube define the task; the target duty follows from the required temperature change.
- Determine heat transfer and overall heat transfer coefficients: From the flow in the tube and in the annular gap, the internal heat transfer coefficient is calculated via the Nusselt number; together with the external heat transfer coefficient and the fouling resistances inside and around the double tube, the overall heat transfer coefficients of the two transfer surfaces are obtained.
- Solve the coupled temperature profiles: The energy balances of the inner-tube flow and the annular-gap flow form a coupled system of equations; from the NTU of the apparatus and the NTU ratio, the roots of the characteristic equation are determined, and from these the dimensionless temperature and the temperature at the tube end are calculated.
- Evaluate the performance: From the temperature profile follow the efficiency, the actual outlet temperature and the actual duty; comparison with the target duty shows whether the element is sufficient or whether the length or the number of tubes must be adjusted.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| (Innenrohr) | dii | m |
| (Innenrohr) | dai | m |
| dia | dia | m |
| daa | daa | m |
| \u03bbRi | λRi | W/(m·K) |
| \u03bbRa | λRa | W/(m·K) |
| L | L | m |
| mp | mp | kg/s |
| Ta | Ta | °C |
| T1 | T1 | °C |
| T2 | T2 | °C |
| TMR | TMR | °C |
| TMS | TMS | °C |
| \u03c1R | ρR | kg/m³ |
| cpR | cpR | J/(kg·K) |
| \u03b7R | ηR | mPa·s |
| \u03bdR | υR | m²/s |
| \u03bbR | λR | W/(m·K) |
| PrR | PrR | - |
| PrWR | PrWR | - |
| wR | wR | m/s |
| ReR | ReR | - |
| NuR | NuR | - |
| \u03b1R | αR | W/(m²·K) |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| \u03beR | ξR | - |
| NuL2R | NuL2R | - |
| NuL3R | NuL3R | - |
| NuLR | NuLR | - |
| NuTR | NuTR | - |
| \u03b3R | γR | - |
| \u03beS | ξS | - |
| \u03b3S | γS | - |
| RePrdhL | RePrdhL | - |
| NuL1Si | Nu1 laminar NuL1Si | - |
| NuL2Si | NuL2Si | - |
| NuL3S | NuL3S | - |
| NuLSi | NuLSi | - |
| NuTSR | NuTSR | - |
| NuTSi | NuTSi | - |
| NuL1Sa | NuL1Sa | - |
| NuL2Sa | NuL2Sa | - |
| NuLSa | NuLSa | - |
| NuTSa | NuTSa | - |
Calculation options
Eintritt
Innenrohr · Spalt
Frequently asked questions
How does the bayonet tube differ from an ordinary double-pipe heat exchanger?
In a classical double-pipe apparatus, two different media flow separately in the inner tube and in the annular gap. In a bayonet tube, one medium passes through the inner tube and the annular gap in succession; the heat is transferred through the outer wall to a third, surrounding medium. As a result, the outgoing and returning streams also exchange heat with each other – this internal short circuit reduces the effective temperature difference and makes the closed-form solution via the characteristic equation necessary.
Why can a simple log mean temperature difference not be applied here?
The LMTD method assumes two decoupled streams with monotonic temperature profiles. In a bayonet tube, the inner and annular-gap flows influence each other, so the temperature profile is governed by two exponential terms with the roots of the characteristic equation. An LMTD approach overestimates the duty, especially at high heat transfer between the inner tube and the annular gap.
What role does the choice of inlet (inner tube or annular gap) play?
It affects both performance and wall temperatures. If the medium enters through the inner tube and returns through the annular gap, the returning stream is in direct contact with the transfer surface at the outer tube; in the reverse case, the inner tube acts more strongly as a recuperator. Which variant is more favourable depends on the ratio of the overall heat transfer coefficients – the module allows a direct comparison via the medium-inlet input.
How do the fouling resistances affect the result?
Fouling inside the double tube (between inner tube and annular gap) reduces the unwanted internal heat exchange and can even slightly improve the performance; fouling around the double tube, on the other hand, directly degrades the useful heat transfer to the surroundings. Both resistances should therefore be applied separately and realistically.