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

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

Motivation

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

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

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

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)

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)

A 2D example

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

2D: pressure contours

2D: shell-side temperature

2D: Tube-side temperature

2D: Wall (tube) temperature

2D: Shell-side heat-transf coef

2D: Tube-side heat-transf coef

Geometrical modelling

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

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)

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

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 ...

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

Mathematical modelling

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

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)

Results

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)

2D validation Validation with single-bank configuration: Air V T1 ST SL D NL Tw NT T2

Single-bank: Test cases

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

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

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

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

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

Computational mesh 75x64x142 Approx 680,000 cells

Shell-side temperature

Flow field (velocity vectors)

Pressure field

Shell temperature

Tube-side temperature

Tube-wall temperature

Heat-transfer rate NB per cell

Tube-side heat-transfer coeff

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

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