Engineering task and calculation objective
The AnnexB module determines the calculation temperature of the furnace tube of a shell boiler according to the informative Annex B of the standard for the calculation of pressure parts (EN 12953-3). The furnace is the most thermally loaded component of a fire-tube shell boiler: it absorbs the radiant heat of the flame directly, and its wall temperature governs the allowable design stress and thus the required wall thickness.
The calculation starts from the firing heat input, the calculation diameter, and the surface area of the furnace. Using the radiation approach with the theoretic flame temperature, the emission coefficient, and the Stefan-Boltzmann constant, the maximum surface heat flux at the furnace surface is determined. From this follow the maximum furnace temperature and the temperature at mid-wall, taking into account the thermal conductivity of the furnace material and, if present, of a fire-side facing.
Anyone who has to calculate the furnace tube temperature – for example when designing a steam boiler, converting the burner, or assessing an increased firing rate – obtains with this module the code-compliant calculation temperature as the input for the strength verification of the furnace.
Calculation workflow
- Record geometry and firing data: The calculation diameter and surface area of the furnace as well as the firing heat input are entered. From the fuel and firing type follow the theoretic flame temperature and the emission coefficient according to Table B.1.
- Determine the radiant heat flow: With the Stefan-Boltzmann constant, the theoretic flame temperature, and the emission coefficient, the radiative exchange between flame and furnace wall is balanced; service parameters and the furnace efficiency capture the cooling of the flame along the furnace down to the temperature at the end of the combustion chamber.
- Determine the maximum surface heat flux: The balance yields the maximum local heat flux at the furnace surface – the governing quantity for the temperature difference across the wall. The associated condition is checked to stay within the range of validity of the approach.
- Calculate the wall temperatures: With the thermal conductivity of the furnace material according to Table B.2 – and, if present, that of a fire-side facing – the maximum furnace temperature and the temperature at the middle of the wall thickness are determined.
- Adopt the calculation temperature for the strength verification: The determined mid-wall temperature serves as the calculation temperature of the furnace; with it, the strength values of the material are evaluated for the wall thickness and stability verifications of the furnace.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Furnaces type | – | – |
| Type of Heating | – | – |
| Applied pressure | pc | – |
| Calculation temperature acc. to chap.6.(e) | tc | – |
| Saturation temperature | thw | – |
| Heat input [MW] | H | – |
| Length of furnace | L | – |
| Furnace facing | es | – |
| Calculated wall thickness of furnace with allowances | efa | – |
| Heat transition coefficient for furnace: water (normally h = 0,018 W/mm2K) | h | – |
| Outside diameter of furnace | D | – |
| Corrugated flame tube outer diameter | Dmax | – |
| Corrugated flame tube inner diameter | Dmin | – |
| Maximum furnace temperature acc to.B1 | ϑhmf | – |
| Furnace temperature at the middle of the wall thickness acc to B2 | ϑmg | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Calculation diameter of furnace (see Figure B.1) | Dg | – |
| Furnace surface | A | – |
| Theoretic flame temperature (see Table B.1) | tfth | – |
| Stefan – Boltzmann - constant | σ | – |
| Emission-coefficient (see Table B.1) | ε | – |
| Service parameter | m | – |
| Service parameter | a | – |
| Service parameter | u | – |
| Flame temperature at the end of the combustion chamber (see Figure B.2) | tfe | – |
| Efficiency of furnace | η | – |
| Contrast factor | k | – |
| Maximum surface heat flux | Φ1 | – |
| Condition of efa | – | – |
| Thermal conductivity of the furnace facing material | λs | – |
| Thermal conductivity of the furnace material (see Table B.2) | λ | – |
| Firing heat input | Φb | – |
Calculation options
Furnaces type
Plain tube · Corrugated tube
Type of Heating
Oil · Gas
Frequently asked questions
Why is it not sufficient to use the saturated steam temperature as the calculation temperature of the furnace?
The furnace absorbs high radiant heat fluxes; through the water-side heat transfer and conduction across the wall, a wall temperature well above the saturated steam temperature develops. The standard therefore requires the calculation temperature to be formed from the saturated steam temperature plus margins for heat transfer and wall thickness – Annex B provides the detailed calculation route via the radiation approach.
What role does the emission coefficient play and where does its value come from?
The emission coefficient describes the radiative behavior of the flame and depends on the fuel: luminous oil and pulverized coal flames radiate more strongly than weakly luminous gas flames. The values are taken, together with the theoretic flame temperature, from Table B.1 of the standard. Setting the coefficient too low underestimates the heat flux and thus the wall temperature – a safety-relevant error.
What is the effect of a fire-side facing or fouling of the furnace?
Every additional layer with low thermal conductivity increases the temperature drop between combustion chamber and water and raises the metal temperature. The calculation accounts for this via the thermal conductivity of the fire-side facing material. In practice this is also why water-side scale deposits must be strictly limited: they act as an insulating layer and can overheat the furnace.
When does the recalculation according to Annex B become particularly important?
Whenever the specific combustion chamber loading is high or changes: for compact boilers with a high firing heat input, when replacing the burner with a different flame geometry, or when uprating existing boilers. Checking that the maximum surface heat flux stays within the allowable limits is also part of the verification in these cases.