numerical investigation of pressure recovery in an induced ... · natural draught mechanical...

Numerical investigation of pressure recovery in aninduced draught air-cooled condenser for CSP

application

Gerhard Bekker

Solar Thermal Energy Research GroupStellenbosch University

9th Renewable Energy Postgraduate SymposiumSeptember 2018

G. M. Bekker (STERG) Pressure recovery in an ACC REPS 2018 1 / 23

Table of contents1 Background2 Problem statement3 Objective4 Draught equation5 Pressure recovery

Kinetic energy factorArea ratioDiffuser loss coefficient

6 Validation case: ERCOFTAC conical diffuserMeshing and boundary conditionsTurbulence models2D axisymmetric versus 3D simulations

7 Full-scale M-fan simulationsCase 1: Outlet guide vanesCase 2: Conical diffuser

8 ConclusionsG. M. Bekker (STERG) Pressure recovery in an ACC REPS 2018 2 / 23

Background

Figure: Khi Solar One

BackgroundLimited water resources

Figure: Kathu Solar Park

BackgroundDry-cooling

Dry-cooling systems are typicallyemployed:

Natural draughtMechanical draught

Forced draughtInduced draught

Figure: Mechanical draughtFigure: Natural draught

Natural draught

Mechanical draughtForced draughtInduced draught

Figure: Mechanical draught

Figure: Natural draught

Problem statement

Outlet kinetic energy lost to atmosphereThis is a system lossDecreases the total-to-static efficiency of the fan

Figure: Induced draught air-cooled condensers (ACCs)

Objective

Minimise the outlet kinetic energy loss of the M-fan

The M-fan was designed by Wilkinson et al. (2017) for CSPapplication

Table: M-fan specifications

Diameter 24 ft (7.3152 m)Number of blades 8Hub-tip-ratio 0.29Rotational speed 151 rpmFlow rate 333 m3/sFan static pressure 116.7 Pa

Objective

Minimise the outlet kinetic energy loss of the M-fanThe M-fan was designed by Wilkinson et al. (2017) for CSPapplication

Table: M-fan specifications

Diameter 24 ft (7.3152 m)Number of blades 8Hub-tip-ratio 0.29Rotational speed 151 rpmFlow rate 333 m3/sFan static pressure 116.7 Pa

Draught equation

Draught equation:Energy supplied = energydissipated

Dimensionless pressureloss/gain coefficient:

K =∆pρv2/2

Heat exchanger

Diffuser

Support

Induced draught ACC:

∆pFs + αeFρv2FC/2 = ∆psys + Kdifρv2

FC/2 + αe7ρv27/2

Draught equation

K =∆pρv2/2

Heat exchanger

Diffuser

Support

FC/2 + αe7ρv27/2

Draught equation

K =∆pρv2/2

Heat exchanger

Diffuser

Support

FC/2 + αe7ρv27/2

Pressure recovery

Draught equation:

FC/2 + αe7ρv27/2

∆pFs + Krecρv2FC/2 = ∆psys

Pressure recovery term:

Krec = αeF − αe7(AFC/A7)2 − Kdif

Pressure recovery

Draught equation:

FC/2 + αe7ρv27/2

Pressure recovery

Draught equation:

FC/2 + αe7ρv27/2

Pressure recovery

Draught equation:

Krec = αeF−αe7(AFC/A7)2−Kdif

Volume flow rate [m3/s]

a] ∆psys

∆pFs

∆pFt

∆pF/dif s

V̇min V̇max

Kinetic energy factorPressure recovery

Kinetic energy factor: ratio of actual to mean kinetic energy through asection

αeF =1

v3FCAFC

x + c2θ + c2

= αeFx + αeFθ+ αeFr

240 260 280 300 320 340 360 380

αeF = 1 + 58.367 × 109V̇−4.404

M-fan: 8 bladesγroot = 34◦dF = 7.3152 mρ = 1.2 kg/m3

N = 151 rpm

αeF =1

v3FCAFC

x + c2θ + c2

= αeFx + αeFθ+ αeFr

240 260 280 300 320 340 360 380

αeF = 1 + 58.367 × 109V̇−4.404

N = 151 rpm

αeF =1

v3FCAFC

x + c2θ + c2

= αeFx + αeFθ+��:

0αeFr

240 260 280 300 320 340 360 380

N = 151 rpm

240 260 280 300 320 340 360 380

N = 151 rpm

Area ratioPressure recovery

Want A7 as large as possibleAvoid flow separation

150 200 250 300 350 400

N = 151 rpmαe7 ≈ αeFKdif ≈ 0

A7/AFC :

1.2 1.6 2.5

Figure: Efficiency characteristic

Area ratioPressure recovery

Want A7 as large as possibleAvoid flow separation

150 200 250 300 350 400

N = 151 rpmαe7 ≈ αeFKdif ≈ 0

A7/AFC :

1.2 1.6 2.5

Diffuser loss coefficientPressure recovery

Kdif represents the total pressureloss across the diffuserOwing to viscous effectsAim to keep as small as possible

150 200 250 300 350 400

N = 151 rpmαe7 ≈ αeFA7/AFC = 1

Kdif :

0.2 0.5 1

Diffuser loss coefficientPressure recovery

Kdif represents the total pressureloss across the diffuserOwing to viscous effectsAim to keep as small as possible 150 200 250 300 350 400

N = 151 rpmαe7 ≈ αeFA7/AFC = 1

Kdif :

0.2 0.5 1

Validation case: ERCOFTAC conical diffuser

Experiments performed by Clausen et al. (1993)Swirling flow in a conical diffuser

Total divergence angle: 20◦

Area ratio: 2.84

Swirl sufficient to avoid boundary layer separationSwirl insufficient to cause recirculating core flow

Figure: Experimental setup (Clausen et al., (1993))

Validation case: ERCOFTAC conical diffuser

Experiments performed by Clausen et al. (1993)Swirling flow in a conical diffuser

Total divergence angle: 20◦

Area ratio: 2.84Swirl sufficient to avoid boundary layer separationSwirl insufficient to cause recirculating core flow

Figure: Experimental setup (Clausen et al., (1993))

Meshing and boundary conditionsValidation case: ERCOFTAC conical diffuser

Meshes:Two-dimensional axisymmetric and three-dimensional meshesOutlet extension added: 10 inlet diameters longHigh-Re turbulence models: 30 < y+ < 100Low-Re turbulence models: y+ < 5

Boundary conditions:Inlet: measurements of Clausen et al. (1993)Used turbulence viscosity of µt/µ = 27.3 to calculate other inletturbulence quantitiesWalls: no-slip conditionExtension: slip conditionOutlet: total pressure with static pressure set to zero

Turbulence modelsValidation case: ERCOFTAC conical diffuser

Tested six turbulence models:High-Re models with wall functions:

Standard k–ε (SKE)Realisable k–ε (RKE)SST k–ω (SST)v ′2–f (V2F)

Low-Re models with integrated boundary layers:SST k–ω (SSTLR)v ′2–f (V2FLR)

0 50 100 150 200y [mm]

SKERKESST

V2FSSTLRV2FLR

Figure: Streamwise velocity

0 10 20 30 40 50 60 70y [mm]

2 0(×

SKERKESST

V2FSSTLRV2FLR

Figure: Turbulent kinetic energy

2D axisymmetric versus 3D simulationsValidation case: ERCOFTAC conical diffuser

Test axisymmetric assumptionUsed standard k–ε model

0 50 100 150 200y [mm]

2D axisymmetric 3D

Figure: Streamwise velocity

0 10 20 30 40 50 60 70y [mm]

2 0(×

2D axisymmetric 3D

Figure: Turbulent kinetic energy

Full-scale M-fan simulations

Realisable k–ε model with wall functionsTwo-dimensional axisymmetric mesh

Seven configurations to test:1 Outlet guide vanes2 Conical diffuser3 Conical diffuser with guide vanes at its inlet4 Conical diffuser with guide vanes at its outlet5 Annular diffuser6 Annular diffuser with guide vanes at its inlet7 Annular diffuser with guide vanes at its outlet

Realisable k–ε model with wall functionsTwo-dimensional axisymmetric meshSeven configurations to test:

1 Outlet guide vanes2 Conical diffuser3 Conical diffuser with guide vanes at its inlet4 Conical diffuser with guide vanes at its outlet5 Annular diffuser6 Annular diffuser with guide vanes at its inlet7 Annular diffuser with guide vanes at its outlet

Case 1: Outlet guide vanesFull-scale M-fan simulations

A guide vane with nine blades was designedNumerically modelled with the actuator disc model

Pressure recovered: 15.9 Pa (Krec = 0.37)13.6 % of fan pressure rise at design flow rate

Case 1: Outlet guide vanesFull-scale M-fan simulations

A guide vane with nine blades was designedNumerically modelled with the actuator disc model

Pressure recovered: 15.9 Pa (Krec = 0.37)13.6 % of fan pressure rise at design flow rate

Case 2: Conical diffuserFull-scale M-fan simulations

Diffuser length set equal to fan diameterTested different divergence angles to find best diffuserperformance

Best angle: 2θ = 20◦

Pressure recovered: 20.0 Pa(Krec = 0.46)17.1 % of fan pressure rise atdesign flow rate

0 10 20 30 40Diffuser angle, 2θ [deg]

re,∆

Case 2: Conical diffuserFull-scale M-fan simulations

Diffuser length set equal to fan diameterTested different divergence angles to find best diffuserperformance

Best angle: 2θ = 20◦

Pressure recovered: 20.0 Pa(Krec = 0.46)17.1 % of fan pressure rise atdesign flow rate

0 10 20 30 40Diffuser angle, 2θ [deg]

re,∆

Conclusions

Validation study:Two-dimensional axisymmetric simulationsRealisable k–ε with wall functions

M-fan simulations:Swirl removal: 13.6 % pressure increaseConical diffuser with 20◦ divergence angle: 17.1 % pressureincrease

Conclusions

numerical investigation of pressure recovery in an induced ... · natural draught mechanical...

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