Engineering task and calculation objective
The K5 module calculates thermal radiation in combustion chambers according to the VDI Heat Atlas (VDI-Wärmeatlas), 12th edition 2019 — the standard German reference for heat transfer engineering. In the furnace of a steam generator or process furnace, by far the largest part of the heat is transferred by radiation from the hot flame and the combustion gases to the enclosing walls (membrane walls, cooling surfaces, refractory lining). The calculation delivers the radiative heat flow to the furnace walls and thus the basis for the furnace exit gas temperature and the sizing of heating surfaces.
This calculation is needed for the design and rating of boiler furnaces, process furnaces and combustion chambers: the furnace exit temperature governs slagging tendency, NOx formation and the split of heat absorption between radiant and convective heating surfaces. Since the radiating flame consists of combustion gases (H2O, CO2) and particles such as soot and coal ash, the module builds on the methods for gas and gas-solid radiation.
Because an exact solution of the radiation problem in a combustion chamber with locally varying temperatures is not possible in closed form, the VDI Heat Atlas works with proven furnace models (e.g. the well-stirred furnace), between which the module allows a choice. In addition to radiation, the convective contribution to the wall is also taken into account.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Select the calculation model: First, the furnace model is chosen, for example the well-stirred furnace model, in which the furnace is described by one representative gas temperature. The choice of model determines how the local temperature distribution is converted into an effective radiation temperature.
- Set up the firing data and balance: From fuel, air ratio and firing rate, the flue-gas mass flow, flue-gas composition and the adiabatic combustion temperature follow as the starting point of the furnace energy balance.
- Determine the radiative properties of the flame: The emissivity of the furnace medium is determined from the gas radiation of water vapor and carbon dioxide and — depending on the fuel — the contribution of soot, char and ash particles; the governing quantities are partial pressures, particle loading and the mean beam length of the furnace.
- Characterize the wall side: For the furnace walls, an effective wall temperature and emissivity are assumed; fouling and slagging can be accounted for via an effectiveness or fouling factor of the heating surface, which reduces the effective heat absorption.
- Iterate the heat flow and furnace exit temperature: Radiative exchange between furnace medium and wall, the convective contribution and the energy balance of the flue gas are solved as a coupled system: the heat release lowers the gas temperature, which in turn governs the radiation. The results are the heat flow transferred to the walls and the furnace exit gas temperature.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Combustion chamber volume | V | m³ |
| Wall surface | A | m² |
| Layer thickness seq | K3 (9) | m |
| Temperature in the furnace | Tg,n-1 | K |
| Wall temperature | Tw | K |
| b_0(1) | b0i | – |
| b_0(2) | b0i | – |
| b_0(3) | b0i | – |
| b_1(1) | b1i 1/K | 1/K |
| b_1(2) | b1i 1/K | 1/K |
| b_1(3) | b1i 1/K | 1/K |
| Eq. (2) | ai(Tg,n-1) - | – |
| Eq. (2) | ai(Tg,n-1) - | – |
| Eq. (2) | ai(Tg,n-1) - | – |
| Eq. (5) | ai(Tw) - | – |
| Eq. (5) | ai(Tw) - | – |
| Eq. (5) | ai(Tw) - | – |
| Partial pressure H20 | pH2O | bar |
| Partial pressure CO2 | pCO2 | bar |
| Gas pressure pH2O + pCO2 | pg | bar |
| k_g(1) | kgi 1/m∙bar | 1/(m·bar) |
| k_g(2) | kgi 1/m∙bar | 1/(m·bar) |
| k_g(3) | kgi 1/m∙bar | 1/(m·bar) |
| Emissivity | εg | – |
Calculation options
Model
Formulation by a weighted sum of exponential functions · The radiation of all particles is considered to be grey.
Frequently asked questions
Why is the furnace modeled as 'well-stirred' although the flame is locally much hotter?
The real temperature and concentration distribution in a furnace can only be resolved with CFD radiation models. For design purposes, a zero-dimensional model is usually sufficient, describing the furnace by an effective radiation temperature between the adiabatic combustion temperature and the exit temperature. The models of the VDI Heat Atlas are calibrated against measurements on built furnaces and deliver reliable mean values for heating-surface design.
What role does the fuel play in the flame emissivity?
Natural-gas flames radiate predominantly via the gas bands of H2O and CO2 and have comparatively low emissivities; oil flames and above all pulverized-coal flames additionally contain soot, char and ash particles, which radiate continuously and raise the emissivity considerably. The particle phase must therefore be calculated fuel-dependently — the same firing rate does not mean the same radiative heat absorption.
How do wall fouling and slagging affect the result?
Deposits increase the thermal resistance of the wall and raise its surface temperature; the net heat absorption drops and the furnace exit temperature rises. In the calculation, this is captured via fouling or effectiveness factors of the heating surface. Over-optimistic assumptions lead to excessive exit temperatures in operation and can thermally overload downstream heating surfaces.
Why is the furnace exit gas temperature the decisive result?
First, it determines the split of heat absorption between the evaporator radiant surfaces and the downstream convective surfaces; second, it decides whether the ash has already cooled below its softening point at the furnace outlet. If the exit temperature is too high, slagging of the first convective bundles and elevated metal temperatures threaten.