1. Modelling the convective zone of a utility boiler Norberto Fueyo Antonio Gómez Fluid Mechanics Group University of Zaragoza

2. Contents Motivation 2D example Geometrical modelling
Mathematical modelling
2D validation
Application to a 350 MW(e) boiler
Conclusions
Further work

3. Motivation

4. Furnace modelling Aim: Modelling Simulation Validation of
Multiphase flow (including turbulence),
Heat transfer (including radiation)
Pollutant (NOx) formation in
Furnace of power-production utilities

5. Strategy (‘divide and conquer’)+ =
(Model
coupling
through
boundary
conditions)
Convective
zone
Furnace

6. Convective-zone modelling
Aim:
Modelling
Simulation
Validation of
Fluid flow (including turbulence) and
Thermal fields (gas and tube sides)
Heat transfer in
Convective zone of boiler In
Out

7. Model input Geometrical data (tubes, banks, etc)
Fluid (shell-side and tube-side) and solid (tube) properties
Operating conditions (inlet mass-flow rates, inlet temperatures, etc)

8. Model output Detailed fields of:- Velocity Pressure Turbulence
Shell fluid, tube fluid and wall temperature
Shell-to-wall and tube-to-wall heat-transfer coefficients
Heat-transfer rate (W/m3)
Overall heat-transfer rate, per tube-bank (W)

9. A 2D example

10. Complex 2D case
Hotter gas in
Colder gas out
Manifold
Vapour in/out

11. 2D: pressure contours

12. 2D: shell-side temperature

13. 2D: Tube-side temperature

14. 2D: Wall (tube) temperature

15. 2D: Shell-side heat-transf coef

16. 2D: Tube-side heat-transf coef

17. Geometrical modelling

18. The problem Geometrically complex problem Tubes Tube-banks
Interconnections
Tubes representented as distributed, sub-grid features
Specify geometry in ASCII file
Subordinate mesh to geometry

19. Strategy (schematic) Convective-zone database Parser program (ASCII)
(in-house made)
Geometrical
data, mesh,
etc
Simulation
parameters
(Q1)
Simulation (Earth)
Numerical results
Graphical results:
(PHOTON, TECPLOT)

20. Element types General data 2D tubebanks (tube wall) 3D tube banks
Bank arrays (2D, usually)
Manifolds (virtual)
Internal
Inlets
Outlets

21. Data required for each element
Feature name
Position and dimensions
Tube orientation
Internal and external tube diameter
Tube pitch
Tube material
Fluid velocity
Fluid Cp, Prandtl number, density, viscosity
Tube-bank conectivity
Some others ...

22. Typical database entry
[tubebank]
type = 3D
long_name = Lower_Economizer_1
short_name = Ecoinf1
[[descrip]]
posi = (14.323,1,22.61)
dime = (6.34,8.24,2.3)
alig = +2
diam = 50.8
pich = (146.26,0,83.3)
poro
dint = 46
velo
dens
enul
pran
mate = SA.210.A1
[[connect]]
From_bank = ent1
In_face = South
Out_face
Link

23. Mathematical modelling

24. Main physical models - shell side
Full Navier-Stokes equations, plus enthalpy equation, plus turbulence statistics (typically, k-epsilon model)
Full account of volume porosity due to tube-bank presence
Shell-side pressure-loss via friction factors in momentum equations
Shell-side modification of turbulent flowfield due to presence of tubes
Empirical heat-transfer correlations, based on tube-bank geometry (diameters, pitch, etc)
Simple (but flexible) account of shell-side fouling

25. Main physical models - tube side
One-directional enthalpy equation (along the tube direction)
Mass-flow rates in the tubes obtained from mass balance
Empirical heat-transfer correlations, based on tube geometry (diameter)

26. Results

27. Applications
2-D, multiple tube-bank configuration (functional validation)
2-D, single tube-bank configuration (numerical validation)
3-D convective zone (validation in real-case application)

28. 2D validation Validation with single-bank configuration: Air V T1 STSL D NL Tw NT T2

29. Single-bank: Test cases

30. Single-bank: thermal results
Theory: Log Mean Temp Difference method (1-4) and Number of Transfer Units method (5)

31. Single-bank: pressure loss
Theor 1: Grimison correlation
Theor 2: Gunter and Shaw correlation

32. 350 Mw boiler NB: still not fully converged, but nevertheless ...
Physically plausible
Results follow

33. Boiler layout 1SH Primary Superheater 2SH Secondary superheater
Turbine V L
Turbine
Final reheater
Dividing walls
2SH
Reheater
1SH
Vapour UE
1SH Primary Superheater
2SH Secondary superheater
UE Upper economizer
LE Lower economizer
Gases LE
Flue gas
Vapour
Gases

34. Typical geometry As interpreted by the graphics program from database
Some bounding walls not plotted for the sake of clarity

35. Computational mesh
75x64x142
Approx 680,000 cells

36. Shell-side temperature

37. Flow field (velocity vectors)

38. Pressure field

39. Shell temperature

40. Tube-side temperature

41. Tube-wall temperature

42. Heat-transfer rate
NB per cell

43. Tube-side heat-transfer coeff

44. Comparison with measurements
Results not fully converged
Effect of fouling to be studied
Geometry not 100% accurate

45. Computational details
Finite-volume formulation of equations
Number of cells: approx 670,000 (75x64x142)
Number of dependent variables: 8 (pressure correction, 3 shell-side velocity components, k, epsilon, tube-side and shell-side enthalpy)
Running time:
Around 12 minutes CPU time per sweep (PENTIUM 300)
Around 1500 iterations to convergence