Assessment of Cooling Tower Discharge Recirculation and

§Bechtel Nuclear, Security & Environmental Inc. includes the former Bechtel Systems & Infrastructure Inc. and Bechtel Power Corporation starting

January 01, 2015

ASSESSMENT OF COOLING TOWER DISCHARGE RECIRCULATION AND

DISPERSION USING CFD TECHNIQUES

S. Pal Bechtel Nuclear, Security & Environmental Inc. §

Reston, VA

L. J. Peltier Bechtel Nuclear, Security & Environmental Inc. §

Reston, VA

A. Rizhakov Bechtel Nuclear, Security &

Environmental Inc. § Reston, VA

M. P. Kinzel Pennsylvania State University

State College, PA

M. H. Elbert Bechtel Nuclear, Security &

Environmental Inc. § Reston, VA

Kelly J Knight

Bechtel Nuclear, Security & Environmental Inc. § Reston, VA

S. Rao Bechtel Nuclear, Security & Environmental Inc. §

Reston, VA

1. ABSTRACT

The performance of cooling towers, whether operating by themselves, or in close vicinity of other cooling towers can be adversely affected by the re-ingestion of the cooling tower discharge into the tower intakes. The recirculation of the discharge from a wet cooling tower raises the wet bulb temperature of the air entering a wet cooling tower. Current design strategies, often account for this discharge re-ingestion issue, through a conservative adjustment to the far field ambient wet bulb temperature to calculate the actual intake wet bulb temperature. Critical applications, such as those related to nuclear safety applications where there is concern about cooling tower performance, may require more accurate and comprehensive assessment of the recirculation and dispersion of cooling tower discharge. Gaussian plume models alone are of limited use when dealing with discharges in the vicinity of large structures. This paper discusses the use of a computational fluid dynamics approach to evaluate worst case discharge recirculation effects in cooling towers. The bounding design values of tower intake wet bulb temperature increase due to recirculation (ingestion of tower’s own discharge), and interference (ingestion of another interfering tower’s discharge), are calculated considering the various conditions of cooling tower operation, ambient temperature, humidity and wind conditions. The RANS CFD model used in the study is evaluated against published experimental data for flow over bluff bodies at high Reynolds numbers, and experimental data on buoyant jets in cross flow.

2. INTRODUCTION

This paper presents a summary of the Ultimate Heat Sink (UHS) cooling tower interference and recirculation assessment performed for a proposed Nuclear Power Plant (NPP). The proposed UHS has four mechanical, induced draft, wet cooling towers as shown in figure 1. Each tower has two identical fans in two cells which share a common basin. The proposed design is expected to handle a Design Basis Accident (DBA) with two cooling towers in operation, that will be always available considering one down for single failure, and one down for maintenance. The following sections discuss the decoupled analysis approach, the computational fluid dynamics (CFD) code validation, and the CFD model results.

3. METHODOLOGY

3.1. UHS Design and Sizing With Assumed Intake Wet Bulb Increase

Typically only estimates of interference and recirculation effects are available for a proposed NPP design. Initial UHS design and sizing is performed with assumed recirculation and interference corrections. Computer programs like PDAP and UHSSIM can calculate UHS performance characteristics and response to a specific accident scenario (Ref. 1, 2). It should be confirmed that cooling tower basin water temperature remains below the recommended level in any accident scenario. A subsequent confirmatory study, similar to the one presented in this paper, is necessary to confirm the bounding recirculation and interference values assumed in design calculations.

Proceedings of the ASME 2015 Power Conference POWER2015

June 28-July 2, 2015, San Diego, California

POWER2015-49033

1 Copyright © 2015 by ASME

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Inputs for Calculating Bounding Intake Wet Bulb Increase

To calculate the bounding recirculation and interference the following inputs are used to calculate the highest intake wet bulb increase:

i. Heat load – bounding value based on peak accident heat release

ii. Discharge relative humidity and dry bulb temperature – bounding value calculated based on pure-water vapor pressure and lowest possible dry bulb temperature increase over the ambient value for the specified heat load. This is ensured by forcing 100% relative humidity at the fan discharge for the conditions analyzed. This approach minimizes the plume buoyancy for a given heat load.

iii. Wind speed(s) – selected speeds based on site specific meteorological data and results from a passive scalar dispersion study

iv. Wind direction(s) – selected wind directions for specific operating scenarios based on results from the passive scalar dispersion study

4. CFD MODEL DETAILS

4.1. CFD Model Domain

The computational model extends from the ground to 600m height and extends over all significant structures in the vicinity of the cooling towers shown in figure 1. The CFD model is 1700m x 1700m in plan view and the terrain is assumed flat except the modeled structures. The modeled structures are confined within a 650m diameter circle and include the cooling towers, and other buildings that are expected to affect the local air flow and dispersion of cooling tower discharge.

As shown in figure 2, the air enters the cooling tower through two rectangular openings on both sides of the tower. The CFD model does not include the details of the flow inside the cooling tower. The flow (entering the cooling tower) leaves the CFD model at the intake openings of the cooling tower. The flow (discharged from the cooling tower) enters the CFD model from the fan discharge openings at the top of the cooling tower. The exact flow conditions at fan discharge are calculated separately outside the CFD model.

4.2. Governing Equations

The governing equations solved for the plume dispersion CFD model are conservation equations for mass, momentum, energy and species. The flow is modeled as multi-component mix of air and water vapor. The flow is a low speed compressible flow. To handle the adiabatic lapse rate, and the associated density and pressure profiles using an incompressible flow formulation, a virtual potential temperature approach is used (Ref. 6). The mathematical formulation is summarized in equations 1 through 8.

The potential temperature ( ) is the temperature of a parcel of moist air adiabatically compressed to the reference

pressure at grade. The virtual potential temperature ( v ) is the

temperature of dry air at reference pressure having the same energy content as the parcel of moist air compressed adiabatically to the reference pressure at grade. The energy

equation is formulated in terms of v . If the water vapor mass

fraction is constant with elevation, the virtual potential temperature does not change with elevation in a neutrally stable atmosphere. The different temperature profiles are shown in figure 3.

q

Cp

R

P

PT

23.010

(1)

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Fig. 3. Physical temperature, potential temperature, and virtual potential temperature profiles in a neutrally stable atmosphere with constant water vapor mass fraction.

Buoyancy effects are accounted for using a Boussinesq approximation with a constant thermal expansion coefficient, .

rvv

0

0 (3)

where,

rv

1 (4)

The governing equation for the mean velocity is the incompressible Reynolds-Averaged Navier-Stokes equation.

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The governing equation for energy conservation is the Reynolds-Averaged advection/diffusion equation written in terms of virtual potential temperature.

0

100

200

300

400

500

600

304 306 308 310 312 314 316

Elevation above grade (m

)

Temperatures in Kelvin

Physical Temperature (K) Potential Temperature (K)

Virtual Potential Temperature (K)


j

vTT

jvj

j

v

xxU

xt

1Pr (7)

where, is the thermal diffusivity, and PrT is the turbulent Prandtl number which is a turbulence model parameter. The governing equation for moisture conservation is the Reynolds-Averaged scalar advection/diffusion equation:

jTT

jj

j x

qSc

xqU

xt

q 1 (8)

is the water vapor diffusivity in air, and ScT is the turbulent

Schmidt number which is a turbulence model parameter. A turbulence model is used to calculate the turbulent

momentum diffusivity T . The turbulence model equations

should incorporate appropriate modifications for buoyancy.

4.3. CFD Model Verification and Validation

The verification and validation of the buoyant plume CFD model used to calculate the actual wet bulb temperature increase at the tower intakes is described in Annexure A. Annexure B describes the verification and validation of the CFD model used in passive scalar study to identify the operating scenarios and wind directions of concern. The buoyant plume model post-processing provides the expected increase in the intake wet-bulb temperature considering effects of plume buoyancy. In contrast, the passive scalar model identifies the expected high recirculation and interference cases by comparing passive scalar ingestion levels.

4.4. Buoyant Plume CFD Model Mesh and Boundary Conditions

The mesh of the computational domain is comprised of polyhedral cells in the interior. Prism layers are provided on the walls and the ground to resolve the boundary layer. The boundary conditions on the model are summarized below:

i. Ground – no-slip impermeable with zero gradients for virtual potential temperature and water vapor mass fraction.

ii. Top of the domain – symmetry conditions i.e., zero gradient normal to the boundary for all variables

iii. Far field wind conditions – (a) prescribed velocity, density (constant), turbulent kinetic energy, turbulence dissipation, water vapor mass fraction (constant), and virtual potential temperature (constant) profiles as function of height on inlet boundaries where far field flow enters the domain. The incoming velocity and turbulence profiles are calculated for the specific turbulence model being used by simulating an equilibrium boundary layer over a flat plate. This is done by imposing a specified pressure gradient between periodic inlet and outlet boundaries. The pressure gradient is adjusted to match the desired nominal velocity at the reference elevation. The calculated velocity profile for 5 m/s nominal wind speed is compared to the log law profile in figure 4.

The turbulence quantity profiles from the periodic flat plate boundary layer model are similarly used as a boundary conditions at the far field inflow locations. (b) Prescribed pressure (hydrostatic) is applied at outflow boundaries where the external flow is expected to leave the domain.

iv. Cooling tower fan discharges for towers in operation – these are inlet boundaries in the CFD model where a uniform plug velocity profile with specified turbulence intensity and length scale is applied. Calculated values of water vapor mass fraction and virtual potential temperature are applied at the fan discharges. For the 5 m/s nominal wind speed the ratio of the fan discharge speed to the free stream wind speed at 60m elevation is approximately 1.246 in the buoyant plume CFD model. It decreases as the nominal wind speed is increased. The fan discharges at the non-operating towers are modeled as impermeable walls.

v. Cooling tower intake openings for towers in operation – these are reverse inlets with outgoing uniform plug velocity profiles corresponding to calculated mass inflows into the tower intakes. The intakes on the non-operating towers are modeled as impermeable walls.

Fig. 4. Far field velocity profile calculated using CFD model of an equilibrium boundary layer compared to a standard logarithmic profile with appropriate roughness parameter.

4.5. Calculation of CFD Model Boundary Conditions at Cooling Tower Fan Discharges

The calculation of the tower discharge conditions is done using the peak accident heat load, specified far field ambient dry and wet bulb temperatures, and assuming steady state in the basin. The cooling tower intake temperature and water vapor mass fraction are taken from the buoyant plume CFD model. These inputs are summarized in table 2. The discharge condition calculation illustrated in figure 5 enforces the mass, momentum, energy, and species balance subject to the specified relative humidity constraint at the cooling tower discharge.

0

20

40

60

80

100

120

140

160

180

200

0 1 2 3 4 5 6 7

Elevation (m)

Velocity (m/s)

Velocity[i] Velocity‐loglaw (m/s)

Conditions chosen to match field data at 60m


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6: Loosely-coue wet bulb incr

Wind DirectionPassive Scalar

This is an optioe CFD model i

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harge ingestion en different wprocessing the

cooling tower tion are compen wind direct

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Table

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5. INCM

5.1. ASc

Tintakeusingbuoya4.

Tabledue

Operscen

BBBE

wet ease e as ence

ation e

retation of thxure B.

7: Wind angle ma

e 3: Wind direc

nd ction or #

Wind blowing

from

1 N 2 NNE 3 NE 4 ENE 5 E 6 ESE 7 SE 8 SSE

NTERFERENCALCULATIOMODEL FOR

Assessments forcalar Study

The actual incres was calcula

the loosely-cant plume eval

e 4: Calculatede to recirculatio

scen

rating nario

Windirec

(winfrom

B SEB SEB SEE W

he passive sc

measurement farrow is wind d

ctions considerwind directio

Median wind angle

[degrees]

0.0 22.5 45.0 67.5 90.0

112.5 135.0 157.5

NCE AND RECON USING BU

SELECTED C

r Selected Case

rease in wet bated with the coupled approluation of selec

tower intake won and interfernarios and win

nd ction nd m)

Nomwind s

(m/

E 5E 7.E 10

W 5

calar study is

for given wind direction).

red in the operaon study.

Wind direction sector #

Wblow

fro

9 S10 SS11 SW12 WS13 W14 WN15 N16 NN

CIRCULATIOUOYANT PLUCASES

es Identified in

ulb temperaturbuoyant plum

oach. The rescted cases are

wet bulb temperence for selectnd directions.

minal speed

/s)

Intaincre

affect

5 5 0

5

s described in

direction (blue

ating scenario-

Wind wing om

Medianwind angle

[degrees

S 180.0SW 202.5W 225.0SW 247.5W 270.0NW 292.5

NW 315.0NW 337.5

ON UME CFD

Passive

re at the toweme CFD modesults from thshown in tabl

erature increaseted operating

ake wet bulb ease for more ted tower (ºF)

0.91 1.74 2.23 1.49

n

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e


Fig. 8: Relative levels of plume ingestion for operating scenarios A through F for sixteen wind direction sectors 1 through 16 at 5 m/s nominal wind speed (5.50 m/s actual wind speed at 60 m elevation with a log-linear profile).

5.2. Buoyant Plume Model Evaluation for Operating Scenario B and Wind Direction Perturbations East and South of South Easterly wind

The analysis of meteorological data showed higher likelihood of elevated wind speeds around the South Easterly direction, coincident with high ambient wet bulb temperatures and low evaporation potential conditions. The somewhat wide range of wind directions around the South-Easterly wind direction, that showed potential for elevated discharge ingestion levels in the passive scalar study, necessitated a finer wind direction perturbation study. The wind direction perturbations for 10 m/s nominal wind speed were analyzed to further search for any increases in wet bulb increase with small changes in wind direction. The results shown in figure 9 were obtained for operating scenario B and the wind direction perturbations East and South of South Easterly wind. Table 5 shows the highest tower wet bulb increase from these analyses.

Fig. 9: Calculated tower intake wet bulb temperature increases for operating scenario B at 10 m/s nominal wind speed.

Table 5: Calculated bounding tower intake wet bulb temperature increase due to recirculation and interference.

Operating Scenario

Wind speed (m/s) at 60 m elevation

Wind direction

Calculated recirculation and interference (F)

B 10.0 5° East of South Easterly

Tower 3: 2.28 3.35% Tower 4: 1.53 8.84%

The wet bulb increases shown in tables 4 and 5, and figure 9 reflect numbers at the end of the iterative loosely-coupled calculation process. The convergence of the loosely coupled approach usually takes several iterations depending on the initial starting point. The convergence of the iterative calculation procedure for the case reported in table 5 is shown in figure 10. The process converged in three iterations for the case shown in figure 10. A good initial starting solution was available for this case with same operating conditions but a 5° different wind direction.

Fig. 10: Convergence of the loosely-coupled calculation process for UHS intake wet bulb temperature increase for the case in table 5.

5.3. Numerical Uncertainty in Wet Bulb Temperature Rise

The reported values in tables 4 and 5, and figure 9 are fine grid results. The GCI uncertainty is also reported along with the fine grid result. The GCI uncertainty was calculated from results on three different grids obtained with the same exact boundary conditions. The GCI uncertainty calculation was done for operating scenario B, South Easterly wind at 10 m/s nominal wind speed. The three meshes used in GCI study were refined based on global scaling factor. The finest grid resolution parameters were applied to all buoyant plume CFD model meshes, with changes to accommodate the difference in wind direction and location of operating towers. The GCI for the wet bulb temperature increase from the representative case was applied as a percentage value to other results.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Fraction of discharge in

tower intake for more

affected tower

Wind Direction Sector #

A B C D E F

0.00

0.50

1.00

1.50

2.00

2.50

25° S ofSE

20° S ofSE

15° S ofSE

10° S ofSE

5° S of SE SE 5° E of SE 10° E ofSE

Intake W

et Bulb Tem

perature

Increase (degrees Fah

renheit)

Wind Direction (blowing from)

Tower 3 intake wet bulb increase (°F) Tower 4 intake wet bulb increase (°F)

0.00

0.50

1.00

1.50

2.00

2.50

0 1 2 3Intake W

et Bulb Tem

perature

Increase (degrees Fahrenheit)

Iteration Number for Tower Intake and Discharge Update

Tower 3 Tower 4


6. CFD MODEL RESULTS

The calculation of bounding case interference and recirculation considered wind directions and operating scenario combinations that were selected using a passive-scalar dispersion study to identify potential high interference and recirculation cases. The results of the external plume dispersion show that the interference and recirculation is very dependent on external wind direction, wind speed and the configuration of operating towers. The relative levels of interference and recirculation show strong urban terrain effects which define the flow field. The following operating scenarios and wind direction sectors were identified as high recirculation and interference cases based on dispersion study with 5 m/s nominal wind speed (at 60m elevation).

Operating Scenario B, Wind direction 007 (SE wind)

Operating Scenario E, Wind direction 013 (W wind) The identified cases were evaluated further using the

buoyant plume CFD model. The loosely-coupled calculation process converged quickly in three updates for most cases with a good initial starting point. The operating scenario B, wind direction sector 7 (South Easterly wind) was further examined by varying the wind angle in smaller steps of ±5º to establish bounding recirculation and interference wet bulb increase at tower intake as 2.28 3.35% for 5° East of South Easterly wind at 10 m/s nominal wind speed. The GCI method is used to calculate numerical uncertainty in reported wet bulb temperature increases at the tower intake. The input uncertainty is not considered for simulation results as inputs were chosen as bounding (maximum heat load, minimum plume buoyancy, high ambient wet bulb temperature, and steady basin temperature), or varied (wind speeds, operating scenarios, wind directions) to get the bounding result.

The results for actual intake wet bulb temperature increases calculated correlate with the passive scalar study predictions. The passive scalar study captured the broad peak for operating scenario B around the South Easterly wind direction. The operating scenario E, wind direction sector 13 was also identified as an elevated recirculation and interference case. Buoyancy contributes to additional plume dilution for cases with larger separation of upstream and downstream operating towers.

7. CONCLUSIONS

An incompressible formulation using commercial CFD code has been verified and validated against published experimental data. This has addressed the requirements of NQA-1 Quality Assurance as well as the ASME V&V 20-2009 guidelines. The validation cases individually addressed sub-sets of the actual problem physics but did not have all relevant non-dimensional numbers simultaneously at the actual application scale. A more complete assessment of the scale and the interaction effects in the significant non-dimensional numbers is facilitated by availability of appropriate model test data, or

full scale data from a similar configuration. If direct measurements of validation metric at or near scale are not available, an assessment of the model error in calculated results will require sophisticated roll-up techniques.

The results of the external dispersion show that the interference and recirculation is very dependent on external wind direction, speed and configuration of operating towers and cells. This is expected in dense urban terrain with large buildings. The complex flow patterns associated with particular NPP layout require accurate assessment of recirculation and interference with 3-D CFD techniques or test measurements at appropriate scale.

The bounding value for tower recirculation and interference is calculated as 2.28º F 3.35%. This is based on worst operating scenario-wind direction combination, maximum realistic sustained wind speed (expected to be less than 10 m/s), peak accident heat release, and minimum limiting plume buoyancy. The result supports a decoupled UHS sizing and design assessment which uses an intake wet bulb correction to calculate UHS system response to an accident.

8. NOMENCLATURE

ReD = buoyant jet Reynolds number FrD = buoyant jet Froude number = buoyant jet to wind velocity ratio = ambient stratification parameter ReH = Reynolds number for flow over bluff body β = thermal expansion coefficient = potential temperature v = virtual potential temperature v

r = reference virtual potential temperature T = absolute temperature P0 = reference pressure P = pressure = density 0 = reference density R/Cp = gas constant to specific heat ratio for dry air q = water vapor mass fraction Ui = ith velocity component xi = ith spatial coordinate t = time = molecular momentum diffusivity T = turbulent momentum diffusivity = molecular thermal diffusivity = molecular mass diffusivity of water vapor in air uτ = friction velocity for flow over no-slip surface PrT = turbulent Prandtl number ScT = turbulent Schmidt number E = model bias or comparison error S = simulation result D = experimental measurement unum = uncertainty due to numerics uinput = uncertainty due to inputs uD = uncertainty in experimental data uval = validation uncertainty


s = signed simulation error model = signed model error input = signed input error num = signed numerical error Fs = Factor of safety for GCI calculation GCI = Grid Convergence Index ij = Kronecker delta

= forced plume momentum length scale = forced plume buoyancy length scale

9. ACKNOWLEDGMENTS

The authors would like to acknowledge the contributions of Solomon Abdi, Natasha Jones, Kathryn Richards, and Jeff Tracewski from Bechtel Corporation.

10. REFERENCES

1. Sullivan, S. M. and Dunn, W. E., Method for Analysis of Ultimate Heat Sink Cooling Tower Performance, Performed for U.S. Nuclear Regulatory Commission, April 1986, Accession Number ML12146A145.

2. Zheng, D., Jarvis, J. M., and Vieira, A. T., Assessing the Design Margins for an Ultimate Heat Sink Sizing, Paper No. ICONE 21-16396, Proceedings of the 21st International Conference on Nuclear Engineering, Chengdu, China, July 29- August 2, 2013.

3. Jirka, G. H., Integral Model for Turbulent Buoyant Jets in Unbounded Stratified Flows, Part 1: Single Round Jet, Environ. Fluid Mech., v 4, 2004.

4. Chu, V. H. and Goldberg, M. B., Buoyant Forced-Plumes in Cross Flow, ASCE J. Hydraulics Division, 100, 1203-1214, 1974.

5. Lim, H. C., Castro, I. P., and Hoxey, R. P., Bluff Bodies in Deep Turbulent Boundary Layers: Reynolds-number Issues, J. Fluid. Mech., 571(1), 2007.

6. Sorbjan, Z., The Large-Eddy Simulations of the Atmospheric Boundary Layer. Chapter 5B of Air Quality Modeling - Theories, Methodologies, Computational Techniques, and Available Databases and Software, Vol. II – Advanced Topics. (P. Zannetti, Editor), 2004. Published by The EnviroComp Institute (www.envirocomp.org) and the Air & Waste Management Association (www.awma.org).

7. Lindenburg, M. R., Mechanical Engineering Reference Manual, 12th ed., Professional Publications Inc., Belmont, California, 2006.

8. Buck, A. L., New Equations for Computing Vapor Pressure and Enhancement Factor, Journal of Applied Meteorology, v 20, December 1981.

9. Huang, P. H., Thermodynamic Properties of Moist Air Containing 1000 to 5000 PPMV of Water Vapor, Proceedings of the RL/NIST Workshop held at the National Institute of Standards and Technology, Gaithersburg, MD, April 5-7, 1993.

10. Lemmon, E. W., Jacobsen, R. T., Penoncello, S. G., and Friend, D. G., Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon and Oxygen from 60 to 2000 K at Pressures to 2000 MPa, Journal of Physical and Chemical Reference Data, v 29, n 3, 2000.

11. Wagner, W. and Pruss, A., International Equations for the Saturation Properties of Ordinary Water Substance. Revised According to the International Temperature Scale of 1990; Addendum to Journal of Physical and Chemical Reference Data, 16, 893 (1987), v 22, n 3, 1993.

12. Reid, R. C., Prausnitz, J. M., and Sherwood, T. K., The Properties of Gases and Liquids, 3rd ed., McGraw-Hill Book Company, New York, 1977.

13. Cooling Tower Manual, Chapter 2, Introduction to CTI Thermal Design, Cooling Tower Institute, 1998.

14. Feltzin, A. E. and Benton, D., A More Nearly Exact Representation of Cooling Tower Theory, Paper No. TP91-02, CTI Annual Meeting, New Orleans, Louisiana, February 6 to 8, 1991.

15. Kloppers, J. C. and Kroger, D. G., Cooling Tower Performance: A critical Evaluation of Merkel Assumptions, R&D Journal, 20(1), 2004.

16. STAR-CCM+ User Guide, Version 7.04.006, CD-Adapco, 2012.

17. Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer, ASME V&V 20, 2009 edition.

18. Roache, P. J., Fundamentals of Verification and Validation, Hermosa Publishers, 2009.

19. Martinuzzi, R. and Tropea, C., The Flow Around Surface-Mounted, Prismatic Obstacles Placed in a Fully Developed Channel Flow, ASME Journal of Fluids Engineering, v 115, 1993.

20. Iaccarino, G., Ooi, A., Durbin, P. A., and Behina, M., Reynolds Averaged Simulation of Unsteady Separated Flow, International Journal of Heat and Fluid Flow, 24(2), 2003.

21. Hussein, H. J. A. and Martinuzzi, R. J., Energy Balance for Turbulent Flow Around a Surface Mounted Cube Placed in a Channel, Physics of Fluids, 8(3), 1996.

22. Richards, P. J., Hoxey, R. P., and Short, L. J., Wind Pressures on a 6m Cube, Journal of Wind Engineering and Industrial Aerodynamics, 89(14-15), 2001.

23. Richards, P. J., Hoxey, R. P., Connell, B. D., and Lander, D. P., Wind-tunnel Modeling of the Silsoe Cube, Journal of Wind Engineering and Industrial Aerodynamics, 95(9-11), 2007.

24. Easom, G., Improved Turbulence Models for Computational Wind Engineering, Doctoral Dissertation, University of Nottingham, January 2000.

25. Meroney, R. N., CFD Prediction of Cooling Tower Drift, Colorado State University, 2005.

26. Blevins, R. D., Applied Fluid Dynamics Handbook, Krieger Publishing Company, Malabar, Florida, 2003.

27. Fan, Loh-Nien, Turbulent Buoyant Jets into Stratified or Flowing Ambient Fluids, Report No. KH-R-15, June 1967.


ANNEX A

VALIDATION OF BUOYANT PLUME CFD MODEL

A.1 Buoyant Plume CFD Model Settings

A steady state solver is suitable for performing buoyant plume simulations using the loosely-coupled calculation process. The buoyant plume CFD model is constant density incompressible flow model that uses the segregated solver based on SIMPLE algorithm. The far field wind velocity and turbulence profiles are calculated from an equilibrium boundary layer model as explained in section 4.4. The convection scheme for all transported variables is second order upwind with slope limiters. The diffusion fluxes and pressure gradients are calculated with second order accuracy. The solutions are run in steady state. The mesh used in the solver is a polyhedral mesh with prism layers on all walls to resolve the boundary layer profile. The turbulence model used was the realizable model with enhanced wall treatment (EWT). The EWT is a hybrid approach based on two-layer Wolfstein shear driven formulation and wall function approach based on blended near wall profiles. The turbulence model includes modification to account for thermal buoyancy. This model converges well in steady state for the buoyant plume simulation, and the computational cost is only marginally higher than the standard

model.

A.2 Code Verification and Validation

The commercial code STAR-CCM+ is used in this study (Ref. 16). Bechtel calculation procedures require compliance with NQA-1 and additional requirements before software can be used for nuclear safety related calculations. It is required that STAR-CCM+ capabilities required to solve the current problem be tested by solving problems with experimental data or known results. As part of the validation exercise several test problems were identified and simulated using STAR-CCM+. The numerical solutions were compared to measured experimental data and the validation error was determined (Ref. 17, 18). The verification and validation (V&V) effort follows ideas outlined in the ASME V&V 20-2009 Standard. The method involves three steps, code verification, solution verification, and solution validation to quantify model bias and uncertainty in predicted output. The verification and validation metrics are quantified estimates of the model bias, , and of the validation uncertainty, as explained below.

DSE (A-1)

222Dinputnumval uuuu (A-2)

∈ , (A-3)

A.3 Specific Test Problems

The test problems listed in table A-1 were simulated in steady state to determine the comparison error in the physical parameter range of interest. For the validation, is calculated using results from three grids. The is calculated based on scatter in data. The input uncertainty is set to

zero as the inputs were known well or, the simulation results of interest (non-dimensional solution variables) were insensitive to small variations in physical input values. The calculations ensured that results were not sensitive to the domain sizes. The inlet profiles for far field ambient wind were calculated based on equilibrium boundary layer for atmospheric external flows. For wall bounded flows, reasonable values for turbulence levels were prescribed at the inlets and the domain included adequate upstream section for the incoming flow to develop.

Table A-1: Summary of validation test problems.

Description Non-dimensional

parameter

Validation metric(s)

1 Turbulent flow over a cube in fully

developed channel flow with channel

height equal to twice the height (Ref. 19-

21)

4 4 Rear flow reattachment

length

2 Atmospheric flow over 6 m cube placed

on open flat terrain (Ref. 22-24)

4.1 6 Rear flow reattachment

length

3 Laboratory scale negatively buoyant

sinking plumes (Ref. 4) – simulated using

full scale, case 4 CFD model for positively

buoyant rising plume, with appropriate

change in conditions to match experimental

parameters

⁄0.7354.1710.8

representing gradual

transition from buoyancy

dominated to strongly forced

plumes

Plume rise

4 Full scale buoyant plume in cross flow –

Chalk Point Tracer Study (1977), 27.4m

diameter stack discharge at 124m

above grade (Ref. 25).

0.56 7.4 6 0.96

0 ( ⁄ 1.26

Plume rise and plume

spread

A.4 Validation Results

For the cases 1 and 2 in table A-1, we have significant model bias that exceeds the validation uncertainty. The causes of the model bias include the steady state assumption and intrinsic turbulence model shortcomings with respect to separated external flow. The flow coming on to the cube separates at the sharp edges on the front face and the flow reattachment and pressure recovery is sensitive to predicted levels of turbulence. It is common to have errors in prediction of flow reattachment lengths in the range of several tens of percentages. Thus, somewhat elongated wake recirculation regions are expected with the buoyant plume CFD model.

A very substantial improvement in rear reattachment lengths for cases 1 and 2 was obtained by employing the


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Validation Conc

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correlations i 3 results. Thse 4 study. Th

y examining thfile at 100m anwn in figures Aexpected contraction at 100m

veraging of thaveraging als

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summarized ien validated fo

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Fig. A

Fig. Avector

Fig. AcharacAmeriGauss

A-1: CFD mod

A-2: Plume disrs at vertical pl

A-3: Plume sprcteristic radius ican Meteorolosian plume mod

del of large scal

scharge concenlane 100m dow

read from CFD(white dashed

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Table A-2: Summary of validation results.

Description Validation metric

Maximum validation

uncertainty,

(% of data)

Model bias,

(% of data)

1 Cube in channel experiment

Rear reattachment

length to cube height ratio

±17.6% +66.2%

2 6m cube in open terrain

Rear reattachment

length to cube height ratio

±18.1% +100%

3 Laboratory scale plumes

(Ref. 4),

⁄0.7354.1710.8

Plume rise ±8.5% ±10.6% ±12.1%

| |

4 Buoyant plume in cross flow (Chalk Point,

1977)

Plume rise ±8.5% | |

Plume spread rate

- Qualitative validation of flow pattern - Good comparison to plume cross-section radius

ANNEX B

INTERPRETATION AND VALIDATION OF PASSIVE SCALAR STUDY

B.1 Defining a Threshold Recirculation and Interference

The tower discharge spreadsheet calculation was used to calculate the volumetric level of tower discharge recirculation at the cooling tower intakes, which would cause the maximum tolerable wet bulb increase (available from decoupled UHS accident analysis). The threshold value is 12% for the chosen ambient conditions and heat load used. This threshold value conservatively neglects the buoyancy of the saturated plume.

The associated simulation error (δs = δnum + δinput + δmodel) for the computational results shown in figure 8 needs to be calculated. Numerical uncertainty in the passive scalar study was determined by computing the time averaged transient results on two grids for same time step size, and for two different time step sizes on the same grid. GCI numerical uncertainty is calculated in table B-1 with assumed order of convergence for space and time. The variable of merit in our simulation is the time averaged flux of passive scalars into the tower intakes. The solution method is a mixed order method with minimum discretization order being first order. The Factor of Safety in GCI calculation, Fs is taken as 1.25 along with assumed order of convergence of 1 in time and space. The combined GCI is calculated by adding the coarse grid and larger time step GCI’s in time and space. δnum is bounded as

29.5% . The equal plume discharges imposed at all the tower fan

discharges in the passive scalar study, can introduce some error in the evaluation due to the extra flow inlets and outlets existing

at non-operating towers. The input error on account of having all towers flowing is bounded by calculating the difference in predicted interference and recirculation in the operating case and wind direction expected to be most affected by flows into and out of non-operating towers. Table B-2 shows the input error in passive scalar ingestion from having all towers operating for operating scenario E, wind direction sector 13.

Table B-1: Calculation of GCI numerical uncertainty from two grid and two time step study for operating scenario B, with 5 m/s nominal wind speed and wind direction sector 007.

Number of facets in Tower

3 and 4 intakes

Number of facets in Tower 3

and 4 discharges

Plume ingestion for

most affected

tower

Time step size

Number of iterations per time

step/ sampling

period Temporal GCI calculation

Baseline grid # 0

627 181 0.2986 1.0 s 20/50s

Baseline grid # 0

627 181 0.2899 0.5 s 25/50s

Extrapolated value=0.2812 using refinement ratio, r=2.0

Temporal GCIcoarse = 0.0218

Spatial GCI calculation Baseline grid # 0

627 181 0.2823 0.5 s 25/100 s

Fine grid # 1

1321 254 0.2658 0.5 s 25/100 s

Extrapolated value = 0.2127 using refinement ratio, r=1.31§

Spatial GCIcoarse

=0.0663

Combined GCI and unum calculation Combined GCIcoarse

0.0881

0.0881 29.5%

§ using the geometric mean of the spatial refinement ratios at two significant locations

The model error includes errors caused by modeling assumptions, the most significant one being the turbulence model. The validation exercise establishes the range of model error for the validation problems as ∈ ,

.

B.2 Passive Scalar Study CFD Model Settings

The CFD model for passive scalar study used a coupled implicit formulation based on ROE-FDS scheme. The solver employs preconditioning for low speed flows. The unblended form of ROE-FDS scheme is chosen with the discretization option set to first order. The turbulence and passive scalar transport equations use a second order accurate convection scheme with slope limiters. The molecular Schmidt number for all the passive scalars is set to 0.9. The diffusion flux evaluation is second order accurate. The flow is modeled as unsteady and the temporal discretization is first order implicit. The turbulence model used is non-linear cubic version of turbulence model with low Reynolds number effects and an all

near wall treatment. The Durbin scale limiter is used to limit eddy viscosity in stagnation regions. The turbulence model required time accurate solution, and use of lower order convection scheme for the momentum equation to solve high


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B.5 Operating Scenarios and Wind Directions with Potentially High Recirculation and Interference Levels

The following operating scenario and wind direction sectors were identified for further evaluation using a buoyant plume CFD model:

Operating Scenario B, Wind direction sector 007 Operating Scenario E, Wind direction sector 013

The selection of these cases was based on following considerations: i. For conservatism in picking up the operating scenarios and

wind directions, s for figure 8 results is calculated as

. ∈ 32.1%

Based on this, operating scenarios and wind directions with tower discharge ingestion level less than 0.091 in figure 8 are not considered further.

ii. The likelihood of persistent wind speeds exceeding 2.5 m/s in the different directions (from site specific wind rose) in high ambient wet bulb temperature and low evaporation potential conditions.

iii. Some cases will likely see more benefit from plume buoyancy because of separation of the upstream and downstream towers.

iv. The similarity in flow configurations is used to reduce the number of cases that need to considered

v. Wind speed and direction sensitivity of selected operating scenarios and wind directions was also considered in selecting cases for further evaluation. The sensitivity for operating scenarios B and E (with non-operating towers not flowing) is shown for wind speeds ranging from 1 m/s to 20 m/s in figures B-5 and B-6 respectively. Operating scenario B, wind direction sector 7, and operating scenario E, wind direction sector 13 were compared to adjacent directions (±22.5º) at a higher nominal wind speed of 10m/s. This confirmed that they were higher plume ingestion cases compared to adjacent wind directions as shown in figures B-7 and B-8.

Fig. B-5: Sensitivity of plume ingestion to wind speed for operating scenario B and wind direction sector 007.

Fig. B-6: Sensitivity of plume ingestion to wind speed for operating scenario E and wind direction sector 013.

Fig. B-7: Sensitivity of plume ingestion to wind direction for operating scenario B at 10 m/s nominal wind speed.

Fig. B-8: Sensitivity of plume ingestion to wind direction for operating scenario E at 10 m/s nominal wind speed.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

1.0 2.5 5.0 10.0 20.0



affected tower

Nominal wind speed (m/s)

Operating Scenario B ‐Wind Direction Sector 007

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

1.0 2.5 5.0 10.0 20.0



affected

tower

Nominal wind speed (m/s)

Operating Scenario E ‐Wind Direction Sector 013

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

#006 #007 #008



affected tower


Operating Scenario B ‐ 10 m/s Nominal Wind Speed

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

#012 #013 #014



affected

tower


Operating Scenario E ‐ 10 m/s Nominal Wind Speed


Documents

Assessment of Cooling Tower Discharge Recirculation and