Mitsubishi Heavy Industries Technical Review Vol. 49 No. 1 (March 2012) 98 *1 Reasearch Manager, Nagasaki Research & Development Center *2 Nagasaki Research & Development Center *3 Reactor Safety Engineering Department, Nuclear Plant Engineering Division, Nuclear Energy Systems *4 Professor, (Wind Engineering Section, Division of Renewable Energy Dynamics,) Reaserch Institute for Applied Mechanics, Kyushu University *5 Associate Professor, (Wind Engineering Section, Division of Renewable Energy Dynamics,) Reaserch Institute for Applied Mechanics, Kyushu University Development of Numerical Simulation Technique for Unsteady Turbulent Dispersion over Complicated Terrain - As an Alternative to Wind Tunnel Experiments - Kazuki Okabayashi *1 Yoshinori Nagayama *2 Tomohiro Hara *2 Eiichi Hori *3 Yuji Ohya *4 Takanori Uchida *5 The Standards Committee of the Atomic Energy Society of Japan has recently launched efforts to form the basis of standards aiming to substitute numerical simulations for conventional wind tunnel experiments to evaluate radiation exposure around nuclear facilities in safety assessments. As such, Mitsubishi Heavy Industries (MHI) applied an unsteady numerical simulation technique to dispersion fields over complicated terrain using a Large-Eddy Simulation (LES) model and compared the simulation results with the corresponding wind tunnel experiment. This simulation model assures highly-accurate predictions within practical computation times, showing that this analytical method is an unsteady turbulent flow and dispersion simulation model that can become an alternative to wind tunnel experiments. | 1. Introduction Large-scale unsteady turbulent flow simulations have required very long computational times, but recent advancements in computer performance and fast computation technology have made it more possible to complete the simulations within practical times. Meantime, the Atomic Energy Society of Japan has launched a standardization of numerical simulations as an alternative approach to conventional wind tunnel experiments 1 to evaluate exposure around nuclear facilities. 2 Currently, the most widely and commonly used turbulent model is the Reynolds Averaged Navier-Stokes Simulation (RANS) due to its lower computational time. RANS focusing on rather flat terrain and simple buildings has started to be validated with the aim of substituting RANS for wind tunnel experiments, 3 but there are few validation studies for complicated terrain. Moreover, if RANS is applied to complicated flows and dispersion fields, it requires simulation accuracy validation and there are accuracy limitations in RANS. 4,5 In this study, we tried to apply a Large-Eddy Simulation (LES) turbulent model to an unsteady dispersion field over complicated terrain. LES directly solve turbulent structures larger than the computational grid by modeling the structures smaller than the grid, requiring longer computational times than RANS. There are many studies on LES, but most are focused on simple structures in the fundamental research of atmospheric dispersion, 6 and there is a lack of practical large-scale simulation cases targeting complicated terrain. As such, we conducted an unsteady dispersion simulation using LES targeting complicated terrain, and we validated the model by comparing the simulation results with the corresponding experimental data, which have been carried out by us and other research facilities. | 2. Outline of atmospheric dispersion model 2.1 Airflow simulation model The governing equations of airflow are the continuity equation and Navier-Stokes equation of the incompressible flow, as shown in Equations (1) and (2). In this study, we used the RIAM-COMPACT 7 code, i.e. airflow model developed by the Research Institute for Applied Mechanics, Kyushu University.
*1 Reasearch Manager, Nagasaki Research & Development Center *2 Nagasaki Research & Development Center
*3 Reactor Safety Engineering Department, Nuclear Plant Engineering Division, Nuclear Energy Systems
*4 Professor, (Wind Engineering Section, Division of Renewable Energy Dynamics,) Reaserch Institute for Applied Mechanics, Kyushu University
*5 Associate Professor, (Wind Engineering Section, Division of Renewable Energy Dynamics,) Reaserch Institute for Applied Mechanics, Kyushu University
Development of Numerical Simulation Technique for Unsteady Turbulent Dispersion over Complicated Terrain
- As an Alternative to Wind Tunnel Experiments -
Kazuki Okabayashi*1 Yoshinori Nagayama*2
Tomohiro Hara*2 Eiichi Hori*3
Yuji Ohya*4 Takanori Uchida*5
The Standards Committee of the Atomic Energy Society of Japan has recently launched
efforts to form the basis of standards aiming to substitute numerical simulations for conventionalwind tunnel experiments to evaluate radiation exposure around nuclear facilities in safetyassessments. As such, Mitsubishi Heavy Industries (MHI) applied an unsteady numericalsimulation technique to dispersion fields over complicated terrain using a Large-Eddy Simulation (LES) model and compared the simulation results with the corresponding wind tunnel experiment.This simulation model assures highly-accurate predictions within practical computation times,showing that this analytical method is an unsteady turbulent flow and dispersion simulation model that can become an alternative to wind tunnel experiments.
|1. Introduction
Large-scale unsteady turbulent flow simulations have required very long computationaltimes, but recent advancements in computer performance and fast computation technology have made it more possible to complete the simulations within practical times. Meantime, the AtomicEnergy Society of Japan has launched a standardization of numerical simulations as an alternativeapproach to conventional wind tunnel experiments1 to evaluate exposure around nuclear facilities.2
Currently, the most widely and commonly used turbulent model is the Reynolds AveragedNavier-Stokes Simulation (RANS) due to its lower computational time. RANS focusing on rather flat terrain and simple buildings has started to be validated with the aim of substituting RANS forwind tunnel experiments,3 but there are few validation studies for complicated terrain. Moreover, ifRANS is applied to complicated flows and dispersion fields, it requires simulation accuracy validation and there are accuracy limitations in RANS.4,5 In this study, we tried to apply a Large-Eddy Simulation (LES) turbulent model to an unsteady dispersion field over complicatedterrain. LES directly solve turbulent structures larger than the computational grid by modeling thestructures smaller than the grid, requiring longer computational times than RANS. There are manystudies on LES, but most are focused on simple structures in the fundamental research ofatmospheric dispersion,6 and there is a lack of practical large-scale simulation cases targeting complicated terrain. As such, we conducted an unsteady dispersion simulation using LES targetingcomplicated terrain, and we validated the model by comparing the simulation results with the corresponding experimental data, which have been carried out by us and other research facilities.
|2. Outline of atmospheric dispersion model 2.1 Airflow simulation model
The governing equations of airflow are the continuity equation and Navier-Stokes equation of the incompressible flow, as shown in Equations (1) and (2). In this study, we used the RIAM-COMPACT7 code, i.e. airflow model developed by the Research Institute for AppliedMechanics, Kyushu University.
A : filtering operation for each quantity A (averaged by the computational grid width in this case)
xi: i-direction coordinate (x1 = x, x2 = y and x3 = z denote the downwind, crosswind and vertical directions, respectively)
ui: velocity component in the i-direction ui': variation of velocity component in the i-direction p: pressure Re: Reynolds number vSGS: eddy viscosity of sub-grid scale (equal or smaller than the computational grid
width) Cs: Smagorinsky constant(= 0.1) fs: damping function z+: wall coordinate hx, hy, hz: filtering width of each direction (the computational grid width in this case)
Here, the standard Smagorinsky model is used to represent the stress of the sub-grid scale
eddies. The sum rules can be applied to the duplicated suffixes in the above equations, i.e., the ajbj
means
3
1jjjba . Slip conditions are applied to the side and upper boundary surfaces, a convective
outflow condition to the outflow boundary surface and a non-slip condition to the ground surface. 2.2 Dispersion model
The following equation is used as the atmospheric dispersion model.
qz
CK
zy
CK
yx
CK
xz
Cw
y
Cv
x
Cu
t
C
(3)
turb
SGSKScScRe
1
where,
C: concentration K: dispersion coefficient Sc: Schmidt number Scturb: turbulent Schmidt number q: source strength of emission
The turbulent Schmidt number Scturb is set as low as possible for the subsequent comparison
with experimental data because Scturb does not have a large effect on the simulation results. TheSchmidt number Sc is set to 0.71.
In this model, 3rd-order upwind difference and 2nd-order central difference schemes are used for the advection and diffusion terms respectively, the same as in RIAM-COMPACT. Euler's explicit method is used as the time difference scheme. The concentration is set to 0 at the inflow
boundary, and the Neumann boundary condition is used for the other boundaries including theground surface.
|3. Validation method In joint EU research (SMEDIS project),8 some research groups conducted numerical
simulations using CFD models (STAR-CD, FLUENT, CFX, etc.) to reproduce wind tunnel experimental data. Based on these efforts, model accuracy validation guidelines were established(COST 732).9 We used COST 732 to verify the performance of our model described in Chapter 2.The appropriateness of the COST 732 criteria for model performance is defined based on the bestperformance cases in gas concentration evaluations where the gas is emitted from a downwindground-level source behind a rectangular building. In this validation process, the following 3standard metrics are used in compliance with the basic validation protocol shown in COST 732. (1) FAC2 (Fraction of Xp within a factor of two of Xo)
FAC2 is defined as the following equation and means a fraction which has the ratio of thepredicted value Xp to the observed (experimental) value Xo within 0.5 - 2.0.
12
1
Nnn
NFAC
n
ii
0
0.25.01
else
X
Xfor
N o
p
(2) FB (Fractional Mean Bias)
FB is defined as the following equation where A is the average of the quantity A. It is equivalent to the average of differences (errors) between the observed value Xo and the predicted value Xp, which is value to evaluate the overall bias.
)/()(2 popo XXXXFB
(3) NMSE (Normalized Mean Square Error) NMSE is defined as the following equation, meaning the range of the mean square error.
)/())(( 2popo XXXXNMSE
|4. Validation of numerical model To validate the atmospheric dispersion model described in Chapter 2, we compared the
simulation results with the corresponding wind tunnel experimental data from a safety assessment of nuclear facilities that we previously conducted, etc., using the COST 732-based performance crteria9 described in Chapter 3. 4.1 Comparison with experiment for flat terrain
First, the reproducibility of this numerical model was validated by comparing airflow and concentration fields at several smoke source heights at a flat-plate condition between the simulation and the experiment. In this calculation, we reproduced a similar spire (an isosceles triangle with aheight of 520 mm) as the experiment was used as a surface roughness to control the boundary layerand the turbulence boundary layers developing in the downwind direction over the flat plate weresimulated. The gas dispersions from different heights within the boundary layers were also calculated. The computational grid widths are 13 - 26 mm in the flow direction, 6.5 mm fixed in the crosswind direction and 1.5 - 130 mm in the vertical direction. The vertical mesh size becomesnarrower as it approaches the ground surface, totaling about 19M meshes. The combination of both 16-CPU parallel computers and an airflow database to be described hereafter makes it possible tocomplete the simulation within 50 hours.
Figure 1 shows a comparison of vertical profiles of the average wind velocity in the downwind direction and the 3-turbulent intensity component at the location of the source ofemission between the simulation and the experiment. The simulated values were averaged by a 6.5sec duration time and in advance, it was confirmed that the values were unaffected by the difference of averaging time. Figure 1 also shows the good agreement between the simulation andexperiment. The simulation results are denoted at actual scale by the same scale of 1/2000 as thewind tunnel experiment.
Figure 1 Airflow profile on flat-plate condition These are comparisons of average wind velocity and vertical distribution of 3-turbulent intensity components between the experiment and calculation. (The values are at an actual scale changed by a model scale of 1:2000 in a wind tunnel experiment.)
Figure 2 shows a comparison of the maximum ground-level concentration distributions (ground-level concentration distribution along the plume axis) in the downwind direction atdifferent source heights between the experimental and simulation data. The concentration C isdenoted by the normalized concentration UC/Q (m2), where U is the uniform wind velocity and Qis the source strength. Figure 2 indicates the ground-level concentration distributions along the plume axis at each source height is in a good agreement between the experiment and simulation.
Figure 3 is a comparison of the dispersion width in the vertical direction (equivalent to the standard deviation of the concentration distribution) from a ground point source between theexperiment and simulation. The dispersion widths were determined from the wind tunnel data bythe least-square method assuming that the concentration is normally-distributed. The dispersion widths are plotted in Figure 3 with the Pasquill-Gifford chart,1 in which a dispersion width is defined for each atmospheric stability class. From Figure 3, it is found that the dispersion width isin a good agreement between calculation and experiment and are plotted nearby the targeted neutralatmospheric stability zone (between Class-C and D).
Figure 2 Downwind distributions of ground-level concentration at different source heights
This is a comparison of ground-level concentration along the plume axis at different source heights (0, 20, 40, 60, 80, 100 and 200 m) at a flat-plate condition. (The values are at an actual scale changed by a model scale of 1:2000 in a wind tunnel experiment.)
Figure 3 Profile of vertical plume width This is a comparison of vertical plume width between the simulation and the experiment. (The values are at an actual scale changed by a model scale of 1:2000 in a wind tunnel experiment.)
In the calculation regarding complicated terrain to be described in Section 4.2, the simulation
time can be dramatically reduced by omitting approaching flow region A from the wholecalculation domain. The details are as follows. First, air flow in region A is calculated to make a database at a downwind boundary of region A. Next, the airflow database of region A is used as theinflow boundary condition into domain B, as shown in Figure 4.
Figure 4 Reduction of calculation domain The airflow data of the downwind section in entrance section A is used as the inflow condition of calculation domain B with complicated terrain.
4.2 Comparison with wind tunnel experiment for complicated terrain Next, the applicability of this simulation model to complicated terrain was validated by
comparing the experimental and simulation data targeting complicated terrain shown in Figure 5. In this simulation, source locations are at A and B and 5 wind directions I to V shown in Figure 5are chosen. Table 1 is a list of all 7 simulation cases in this study,10 which have different source locations, wind directions and source heights. Figure 6 shows the ground-level concentrations along the plume axis in the 2 representative cases; with a breeze over flat terrain from the sea(Wind direction I) and a complicated flow from upwind terrain (Wind direction V). As shown in Figure 6, both cases indicate the good agreement between the experiment and simulation.
Table 1 List of calculation cases
CaseNo.
Wind direction
Source location
Source height
(m)①
I A 144
② A 58③ B 63④ II A 58⑤ III A 144⑥ IV B 63⑦ V B 63
This table indicates the wind direction, source location and height in each case.
Figure 5 Complicated terrain in the calculation This map illustrates wind directions (I - V), 2 smoke source locations (A and B) and the contour lines of the targeted area’s geometry.
Figure 6 Comparison of downwind ground-level concentration profile These are comparisons of the ground-level concentrations along the plume axis vs. the downwind distance between the experiment and calculation. (The values are at an actual scale changed by a model scale of 1:2500 in a wind tunnel experiment.)
Table 2 is a list of the 3 standard metrics (FAC2, FB and NMSE) for model performance ofall 7 cases evaluated in compliance with the COST 732 protocol described in Chapter 3. Table 2 shows that all cases meet the criteria of each metric, indicating the adequate prediction accuracy ofthis simulation model.
Table 2 Performance evaluation of this calculation model
This is a comparison between the experiment and calculation data for the 3-standard metrics (FAC2, FB and NMSE) based on the ground-level concentrations along the plume axis and the total surface concentrations. The criterion of FAC2 is from COST 732 and those of FB and NMS are from Chang et al. cited in COST 732.11
4.3 Comparison with simple building experiment Finally, we validated this simulation model by using wind tunnel experiment data published
by the University of Hamburg, which is experimental data12 around a simple building (L =100 mm, W = 150 mm, H = 125 mm). The published data lack the information for LES simulation on theupwind roughness conditions to make turbulent boundary layer develop at the front-side of the building, and therefore it is difficult to set front-side airflow conditions strictly in an unsteady numerical simulation. However, it is considered that the turbulence generated by the building is adominant factor to the phenomenon behind the back-side of a building, and the effects of the roughness condition are small. Hence in this validation, a diffusion structure around a simple building was calculated under turbulent boundary layer developed by 2-D blocks as dummies of the roughness in the experiment.
Figure 7 illustrates the good agreement of downwind distribution of ground-levelconcentrations along the plume axis behind the building between this simulation and theexperiment. The FAC2 of the ground-level concentration along the plume axis is 1.0 (the criterion:more than 0.89), showing acceptable prediction accuracy. The FAC2 of the total ground-level concentration and spatial concentration (total concentration) is 0.57, which is slightly higher thanthe criterion 0.54. The reason seems to be that the simulation could not fully reproduce theturbulent boundary layer developed in the wind tunnel experiment due to the lack of the information on the roughness conditions of the database, as described above.
Data for comparison FAC2 (Criterion) Ground-level
concentration along the plume axis
1.00 (0.89)
Concentration at all measurement points
0.57 (0.54)
Figure 7 Profile of ground-level concentrations along plume axis This is a comparison of dimensionless concentration (K = UCHb
2/Q) at a certain dimensionless downwind distance (X/Hb), where U is the wind velocity, C the ground-level concentration along the plume axis, Hb the building height and Q the source strength.
|5. Conclusions We conducted an unsteady flow dispersion simulation targeting complicated terrain using a
kind of turbulent model, Large Eddy Simulation (LES), and validated the prediction accuracy based on the COST 732 protocol, which are model evaluation guidelines developed in the EU. First, weconfirmed that this simulation model well reproduced wind tunnel experiment results at flat terrainconditions. Next, we confirmed that this simulation model reproduced wind tunnel experiment results at complicated terrain conditions to a satisfactory level. The 3 standard metrics (FAC2, FBand NMSE) of this simulation sufficiently meet the criteria suggested in COST 732. The metricsdetermined in another simulation using another research facility’s experimental data also met thereferences. From these results, we have confirmed that this newly developed numerical model hassufficient prediction accuracy and we would expect to substitute this model for wind tunnel experiments. This model would become an alternative approach that ensures significant reductionin examination durations compared with conventional wind tunnel experiments.
Acknowledgements We would like to express our appreciation to the Japan Atomic Power Company for
providing us with the wind tunnel experimental data.
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