Modelling the convective Modelling the convective zone of a utility boilerzone of a utility boiler

Norberto Fueyo Norberto Fueyo Antonio GómezAntonio Gómez

Fluid Mechanics GroupFluid Mechanics GroupUniversity of ZaragozaUniversity of Zaragoza

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

MotivationMotivation

Furnace modellingFurnace modellingAim:

• Modelling• Simulation • Validation

of• Multiphase flow (including

turbulence),• Heat transfer (including

radiation)• Pollutant (NOx) formation

in• Furnace of power-production

utilities

Strategy (‘divide and Strategy (‘divide and conquer’)conquer’)

==FurnaceFurnace

Convectivezone

Convectivezone

++(Model

coupling through boundary

conditions)

(Model coupling through boundary

conditions)

Convective-zone Convective-zone modellingmodelling

Aim:• Modelling• Simulation • Validation

of• Fluid flow (including

turbulence) and• Thermal fields (gas and

tube sides)• Heat transfer

in• Convective zone of

boiler

InIn OutOut

Model inputModel inputModel inputModel input

Geometrical data (tubes, banks, etc)Geometrical data (tubes, banks, etc) Fluid (shell-side and tube-side) and solid Fluid (shell-side and tube-side) and solid

(tube) properties(tube) properties Operating conditions (inlet mass-flow rates, Operating conditions (inlet mass-flow rates,

inlet temperatures, etc)inlet temperatures, etc)

Model outputModel outputModel outputModel output

Detailed fields of:-Detailed fields of:- VelocityVelocity PressurePressure TurbulenceTurbulence Shell fluid, tube fluid and wall temperatureShell fluid, tube fluid and wall temperature Shell-to-wall and tube-to-wall heat-transfer Shell-to-wall and tube-to-wall heat-transfer

coefficientscoefficients Heat-transfer rate (W/m3)Heat-transfer rate (W/m3)

Overall heat-transfer rate, per tube-bank (W)Overall heat-transfer rate, per tube-bank (W)

A 2D exampleA 2D example

Complex 2D caseComplex 2D caseComplex 2D caseComplex 2D case

Vapour in/out

Hotter gas in

Colder gas out

Manifold

2D: pressure contours2D: pressure contours2D: pressure contours2D: pressure contours

2D: shell-side temperature2D: shell-side temperature2D: shell-side temperature2D: shell-side temperature

2D: Tube-side temperature2D: Tube-side temperature2D: Tube-side temperature2D: Tube-side temperature

2D: Wall (tube) 2D: Wall (tube) temperaturetemperature2D: Wall (tube) 2D: Wall (tube) temperaturetemperature

2D: Shell-side heat-transf 2D: Shell-side heat-transf coefcoef2D: Shell-side heat-transf 2D: Shell-side heat-transf coefcoef

2D: Tube-side heat-transf 2D: Tube-side heat-transf coefcoef2D: Tube-side heat-transf 2D: Tube-side heat-transf coefcoef

Geometrical modellingGeometrical modelling

The problemThe problemThe problemThe problem Geometrically complex problemGeometrically complex problem

TubesTubes Tube-banksTube-banks InterconnectionsInterconnections

Tubes representented as distributed, sub-Tubes representented as distributed, sub-grid featuresgrid features

Specify geometry in ASCII fileSpecify geometry in ASCII file Subordinate mesh to geometrySubordinate mesh to geometry

Strategy (schematic)Strategy (schematic)Strategy (schematic)Strategy (schematic)Convective-zone

database(ASCII)

Convective-zonedatabase(ASCII)

Geometricaldata, mesh,

etc

Geometricaldata, mesh,

etc

Simulation parameters

(Q1)

Simulation parameters

(Q1)

Parser program(in-house made)Parser program(in-house made)

Simulation (Earth) Simulation (Earth)

Numerical resultsNumerical resultsGraphical results:

(PHOTON, TECPLOT)Graphical results:

(PHOTON, TECPLOT)

Element typesElement typesElement typesElement types

General dataGeneral data 2D tubebanks (tube wall)2D tubebanks (tube wall) 3D tube banks3D tube banks Bank arrays (2D, usually)Bank arrays (2D, usually) Manifolds (virtual)Manifolds (virtual)

InternalInternal InletsInlets OutletsOutlets

Data required for each Data required for each elementelementData required for each Data required for each elementelement

Feature nameFeature name Position and dimensionsPosition and dimensions Tube orientationTube orientation Internal and external tube diameterInternal and external tube diameter Tube pitchTube pitch Tube materialTube material Fluid velocityFluid velocity Fluid Cp, Prandtl number, density, Fluid Cp, Prandtl number, density,

viscosityviscosity Tube-bank conectivityTube-bank conectivity Some others ...Some others ...

Typical database entryTypical database entryTypical database entryTypical database entry

[tubebank]type = 3Dlong_name = Lower_Economizer_1short_name = Ecoinf1

[[descrip]]posi = (14.323,1,22.61)dime = (6.34,8.24,2.3)alig = +2diam = 50.8pich = (146.26,0,83.3)porodint = 46velodensenulpranmate = SA.210.A1

[tubebank]type = 3Dlong_name = Lower_Economizer_1short_name = Ecoinf1

[[descrip]]posi = (14.323,1,22.61)dime = (6.34,8.24,2.3)alig = +2diam = 50.8pich = (146.26,0,83.3)porodint = 46velodensenulpranmate = SA.210.A1

[[connect]]From_bank = ent1In_face = SouthOut_faceLink

[[connect]]From_bank = ent1In_face = SouthOut_faceLink

Mathematical modellingMathematical modelling

Main physical models - shell sideMain physical models - shell sideMain physical models - shell sideMain physical models - shell side

Full Navier-Stokes equations, plus enthalpy Full Navier-Stokes equations, plus enthalpy equation, plus turbulence statistics (typically, k-equation, plus turbulence statistics (typically, k-epsilon model)epsilon model)

Full account of volume porosity due to tube-Full account of volume porosity due to tube-bank presencebank presence

Shell-side pressure-loss via friction factors in Shell-side pressure-loss via friction factors in momentum equationsmomentum equations

Shell-side modification of turbulent flowfield Shell-side modification of turbulent flowfield due to presence of tubesdue to presence of tubes

Empirical heat-transfer correlations, based on Empirical heat-transfer correlations, based on tube-bank geometry (diameters, pitch, etc)tube-bank geometry (diameters, pitch, etc)

Simple (but flexible) account of shell-side Simple (but flexible) account of shell-side foulingfouling

Main physical models - tube sideMain physical models - tube sideMain physical models - tube sideMain physical models - tube side

One-directional enthalpy equation (along One-directional enthalpy equation (along the tube direction)the tube direction)

Mass-flow rates in the tubes obtained from Mass-flow rates in the tubes obtained from mass balancemass balance

Empirical heat-transfer correlations, based Empirical heat-transfer correlations, based on tube geometry (diameter)on tube geometry (diameter)

ResultsResults

ApplicationsApplicationsApplicationsApplications

2-D, multiple tube-bank configuration2-D, multiple tube-bank configuration(functional validation)(functional validation)

2-D, single tube-bank configuration2-D, single tube-bank configuration(numerical validation)(numerical validation)

3-D convective zone3-D convective zone(validation in real-case application)(validation in real-case application)

2D validation2D validation2D validation2D validation Validation with single-bank configuration:Validation with single-bank configuration:

SL

Air V T1

D

ST

NL

NT

Tw

T2

Single-bank: Test casesSingle-bank: Test casesSingle-bank: Test casesSingle-bank: Test cases

Single-bank: thermal resultsSingle-bank: thermal resultsSingle-bank: thermal resultsSingle-bank: thermal results

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

Single-bank: pressure lossSingle-bank: pressure lossSingle-bank: pressure lossSingle-bank: pressure loss

Theor 1: Theor 1: Grimison correlationGrimison correlation Theor 2: Theor 2: Gunter and Shaw correlationGunter and Shaw correlation

350 Mw boiler350 Mw boiler350 Mw boiler350 Mw boiler

NB: still not fully converged, but NB: still not fully converged, but nevertheless ...nevertheless ...

Physically plausiblePhysically plausible

Results followResults follow

Boiler layoutBoiler layoutBoiler layoutBoiler layoutLV

Flue gas

Gases

GasesVapour

Turbine

Vapour

Turbine

LE

UE

Reh

eate

r

2SH

1SH

Div

idin

g w

alls

Fin

al re

heate

r

1SH Primary Superheater

2SH Secondary superheater

UE Upper economizer

LE Lower economizer

Typical geometryTypical geometryTypical geometryTypical geometry As interpreted by the As interpreted by the

graphics program graphics program from database from database

Some bounding walls Some bounding walls not plotted for the not plotted for the sake of claritysake of clarity

Computational meshComputational mesh

75x64x14275x64x142 Approx 680,000 cellsApprox 680,000 cells

Shell-side temperatureShell-side temperature

Flow field (velocity Flow field (velocity vectors)vectors)

Pressure fieldPressure field

Shell temperatureShell temperature

Tube-side temperatureTube-side temperature

Tube-wall temperatureTube-wall temperature

Heat-transfer rateHeat-transfer rate

NB per cellNB per cell

Tube-side heat-transfer coeffTube-side heat-transfer coeff

Comparison with Comparison with measurementsmeasurements

Results not fully convergedResults not fully converged Effect of fouling to be studiedEffect of fouling to be studied Geometry not 100% accurateGeometry not 100% accurate

Computational detailsComputational detailsComputational detailsComputational details

Finite-volume formulation of equationsFinite-volume formulation of equations Number of cells: approx 670,000 Number of cells: approx 670,000

(75x64x142)(75x64x142) Number of dependent variables: 8 Number of dependent variables: 8

(pressure correction, 3 shell-side velocity (pressure correction, 3 shell-side velocity components, k, epsilon, tube-side and components, k, epsilon, tube-side and shell-side enthalpy)shell-side enthalpy)

Running time: Running time: Around 12 minutes CPU time per sweep Around 12 minutes CPU time per sweep

(PENTIUM 300)(PENTIUM 300) Around 1500 iterations to convergenceAround 1500 iterations to convergence