Engineering task and calculation objective
This module calculates helical-coil waste heat boilers: heat exchangers in which one or more concentric coil baskets of helically wound tubes are swept by flue gas on the outside, while hot water or thermal oil is heated inside the tubes. The calculation is based on the VDI Heat Atlas (VDI-Wärmeatlas) as well as the standard works by F. Brandt (Wärmeübertragung in Dampferzeugern und Wärmetauschern) and H. Hausen (Wärmeübertragung im Gegenstrom, Gleichstrom und Kreuzstrom). The flue gas composition can be entered freely or selected from standard compositions for gas, fuel oil and solid fuel firing.
Calculating waste heat boilers is required wherever waste heat from combustion processes is recovered: downstream of combined heat and power units and gas turbines, at industrial furnaces, thermal oil plants and process firing systems. The helical-coil construction combines a compact design with good absorption of thermal expansion and a defined gas routing through the annular gaps between shell, coil baskets and displacement body. On the gas side, convection and — owing to the CO2 and H2O content of the flue gas — gas radiation act together, which distinguishes the calculation from a purely convective design.
Standard and calculation basis: VDI Wärmeatlas, F. Brandt, Wärmeübertragung in Dampferzeugern und Wärmetauschern, Vulkan Verlag 1995 H. Hausen, Wärmeübertragung im Gegenstrom, Gleichstrom und Kreuzstrom, Springer 1976
Calculation workflow
- Define the geometry of the helical-coil boiler: The inputs are the number of coil baskets, the tube dimensions and the mean lengthwise pitch ratio, the free gap widths between the baskets, at the shell and at the displacement body, as well as the shell inside diameter and the diameter of the displacement body. From these follow the gas-side flow cross-sections and the actual heat transfer area.
- Define the flue gas and the heated medium: The flue gas composition is entered or chosen as a standard composition for gas, fuel oil or solid fuel combustion; from it, the temperature-dependent gas properties are determined. On the inside, hot water or thermal oil is specified with its mass flow and temperature program.
- Calculate heat transfer inside and outside: Inside, the heat transfer coefficient of the tube flow in the helix is calculated (with the enhancement due to the centrifugal effect of the curvature); outside, the heat transfer of the helical tube bundle in crossflow. On the gas side, the radiation contribution of the flue gas is added to the convection; it depends on the CO2 and H2O partial pressures, the equivalent layer thickness and the emissivity of the wall.
- Determine the overall heat transfer and required area: From the transfer coefficients, the thermal conductivity of the tubes and the outside fouling resistance, the overall heat transfer coefficient is formed; with the logarithmic mean temperature difference follows the required heat transfer area A_req.
- Evaluate performance margin and film temperature: The performance factor LZ = A_act/A_req shows whether the selected boiler is sufficient. For thermal oil, the maximum film temperature is additionally determined from the temperature increase at the wall and checked against the permissible film temperature of the oil, to rule out cracking and coking.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Coil 1 | 1.Wendel | m |
| Coil 2 | 2.Wendel | m |
| Coil 3 | 3.Wendel | m |
| Coil 4 | 4.Wendel | m |
| Coil 5 | 5.Wendel | m |
| Coil 1 | 1.Wendel | - |
| Coil 2 | 2.Wendel | - |
| Coil 3 | 3.Wendel | - |
| Coil 4 | 4.Wendel | - |
| Coil 5 | 5.Wendel | - |
| Coil 1 | 1.Wendel | - |
| Coil 2 | 2.Wendel | - |
| Coil 3 | 3.Wendel | - |
| Coil 4 | 4.Wendel | - |
| Coil 5 | 5.Wendel | - |
| innen | innen | - |
| Thermal conductivity Thermal conductivity | innen | W/(m·K) |
| Specific heat capacity Specific heat capacity | innen | J/(kg·K) |
| Mean temperature Mean temperature | T_i | °C |
| Inlet pressure (abs.) Inlet pressure (abs.) | innen | Pa |
| Mass flow Mass flow | innen | kg/s |
| Volume flow Mean volume flow | Temp. | m³/h |
| Density Mean density | innen | kg/m³ |
| Inlet temperature Inlet temperature | T_Ei | °C |
Frequently asked questions
Why must gas radiation be taken into account for flue gas?
The polyatomic flue gas constituents CO2 and H2O emit and absorb thermal radiation in their bands, whereas diatomic gases such as N2 and O2 practically do not. At gas temperatures above about 400 to 500 °C, the radiation contribution in the gas passes can reach the same order of magnitude as convection. It depends on the partial pressures, the equivalent layer thickness of the gas space and the emissivity of the wall — which is why entering the flue gas composition is essential for accuracy.
What is the significance of the maximum film temperature in thermal oil heaters?
Organic heat transfer oils begin to crack above their permissible film temperature; the decomposition products coke the tube wall, degrade the heat transfer and can lead to tube failure. What matters is not the mean oil temperature but the temperature of the near-wall boundary layer at the hottest spot. The module therefore calculates the temperature increase at the wall and reports the maximum film temperature — it must stay below the oil manufacturer's limit, if necessary by means of a higher flow velocity or a larger area.
What is the purpose of the displacement body in the center of the boiler?
Without a displacement body, a large part of the flue gas would flow through the aerodynamically favorable free core and bypass the tube coils. The displacement body forces the gas into the annular gaps between the coil baskets and establishes there the velocities needed for heat transfer. The free gap widths at the shell, between the baskets and at the displacement body determine the distribution of the gas flow — gaps that are too large act as a bypass and degrade the performance noticeably.
What must be considered regarding fouling on the flue gas side?
Depending on the fuel, soot, ash and — if the acid dew point is undershot — corrosive deposits accumulate. The outside fouling resistance enters the overall heat transfer coefficient directly and should be chosen according to the fuel — natural gas being considerably more favorable than heavy fuel oil or solid fuel firing. In addition, the flue gas outlet temperature must be set so that the water or sulfuric acid dew point is not unintentionally undershot at the coldest walls.