Contents

1. Modelling the convective zone of a utility boilerNorberto Fueyo Antonio GómezFluid Mechanics GroupUniversity 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 Out In

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 (ASCII) Parserprogram (in-house made) Geometrical data, mesh, etc Simulation parameters (Q1) Simulation (Earth) Graphical results: (PHOTON, TECPLOT) Numerical results

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 ST SL 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 Turbine V L Turbine Final reheater Dividing walls 2SH Reheater 1SH Vapour UE Gases 1SH Primary Superheater 2SH Secondary superheater UE Upper economizer LE Lower economizer 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