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