next generation canada france hawaii telescope (ngcfht

Next Generation Canada France Hawaii

Telescope (ngCFHT) Enclosure CFD

Study

Chowdhury Mohammad Jubayer, Ashkan Rasouli and Horia Hangan

Wind Engineering, Energy and Environment Research Institute (WindEEE),

Western University, London, ON, N6A 5B9, Canada

Prepared for: National Research Council-Herzberg Institute of Astrophysics

Date: October 23, 2013

Table of Contents

Items Page Number

Introduction 1

Details of the numerical setup 1

Results and discussion 3

Concluding remarks 5

References 5

Tables 6

Figures 7

List of Tables

Table 1: Details of the cases 6

Table 2: Thermal boundary conditions 6

Table 3: Properties of air 6

List of Figures

Figure 1: Computational domain 7

Figure 2: (a) CFD model of the enclosure without the truss elements (b) Truss elements

on the actual model

7

Figure 3: (a) Overall mesh of the computational domain (b) mesh at the North-South

plane section close to the enclosure (c) mesh on the telescope components and vents

8

Figure 4: Optical path 8

Figure 5: Mean volume fraction of outside air in optical path 9

Figure 6: Mean volume fraction of outside air along the optical axis 9

Figure 7: Contours of volume fraction at the XY plane 10

Figure 8: Mean temperature inside the optical path 11

Figure 9: RMS temperature inside the optical path 11

Figure 10: Mean temperature along the optical axis 12

Figure 11: RMS temperature along the optical axis 12

Figure 12: Contours of mean temperature at the XY plane 13

Figure 13: Temperature at point 1 14



Figure 16: Wind Speed at point 1 15



Figure 19: Turbulent kinetic energy at point 1 17



1

INTRODUCTION

Computational fluid dynamics (CFD) approach is undertaken to study flow around and inside of

the Next Generation Canada France Hawaii Telescope (ngCFHT) enclosure. The ngCFHT is a

concept to replace the current Canada France Hawaii Telescope on summit of Mauna Kea on the

Big Island of Hawaii. Previous studies have been performed to understand the flow behaviour

inside and around the telescope enclosure by using CFD (De Young, 1996; Vogiatzis et al.,

2004; Fitzsimmons et al., 2004). In this study, unsteady Reynolds Averaged Navier-Stokes

(URANS) simulations are performed using Shear Stress Transport k-ω (SST k-ω) turbulence

model. In total of 7 cases, which include different combination of venting systems, telescope

orientations and inflow conditions, are simulated. In all cases approaching wind is in the East-

West direction with the camera having 30o zenith angle. The objectives of this study are to

compare the performance of all these cases by finding the air exchange time and flow profiles in

the optical path and confirming that minimum turbulence is generated (i.e., turbulent kinetic

energy is low close to mirror 2) and temperature does not vary significantly inside the enclosure.

DETAILS OF THE NUMERICAL SETUP

Initially, the geometry of the telescope enclosure along with the topography is created using

SolidWorks (SolidWorks Corp.). Then the mesh for the model is generated using Pointwise

v17.0 (Pointwise, Inc.) and the simulations are performed using ANSYS Fluent 13.0 (ANSYS,

Inc.). Details of the computational domain, mesh, boundary conditions and numerical schemes

are provided here in this section.

Computational Domain and Mesh

The overall dimension of the computational domain is 800m in X direction (+X is east), 500m in

Y direction (+Y is North) and 300m above the origin (Fig. 1). Here, origin is at the center of the

circular base of the cylindrical section of the enclosure. The height (H) of the enclosure from the

origin is 41m. In terms of H, the upstream distance is 11.4H, downstream distance is 7.3H and

distance between the top of the enclosure and the top of the domain is 6.3H. Before creating the

mesh for the domain, some simplification is made to the model provided. Truss structures, that

hold the camera, is not modeled (Fig. 2). This is done to reduce the number of cells inside the

domain and thus the computational time. The generated mesh consists of hexahedral, prismatic

and tetrahedral cells. Hexahedral cells are used at the vents; prismatic cells are used on the

bottom of the domain with 15 layers and on the primary mirror surface with 10 layers; and

tetrahedral cells elsewhere. The total number of cells is approximately 1.7 million. Figure 3

shows three snapshots of mesh at various positions.

2

Boundary Conditions

The details of the 7 cases studied here are listed in Table 1. For all cases, the wind flow is in the

East-West direction. East side of the domain (+X) is treated as velocity inlet type boundary.

North and South sides (+Y, -Y) and top of the domain (+Z) are treated as symmetry type

boundary. West side of the domain (-X) is modeled as outflow type boundary. The horizontal flat

part of the bottom of the domain is modeled as symmetry and the hill part of the bottom is

modeled as wall. For the cases with vents (Case 1, 4-6), vents are modeled as interior volumes

and the well surface is modeled as wall. For the cases with the well operating (Case 2, 3), the

outside surfaces of the vents are treated as walls and the well surface is modeled as velocity inlet

boundary type with negative flow direction which eventually works as velocity outlet boundary

type. For Case 7, both outside surfaces of the vents and well surface are modeled as walls. All

other surfaces and structures of the enclosure are treated as walls. At the domain inlet, the

magnitude of the wind velocity is chosen such that it matches the velocity at the meteorological

station at the telescope site by using the speed up factor for the hill from ASCE 7-10. Also, the

turbulence intensity of 5% and integral length scale of 40 m is applied at the domain inlet. For

Cases 2 and 3, velocities of 4.25 m/s and 8.50 m/s are employed at the well which resulted in the

flow-rate of 90,000 cfm and 180,000 cfm respectively. Thermal boundary conditions and the air

properties used in this study are given in Table 2 and 3 respectively.

Numerical Schemes

In this study 3D unsteady RANS simulations are performed using the SST k-ω turbulence model.

PISO (Pressure Implicit with Splitting of Operators) algorithm is used for Pressure-Velocity

coupling. First order upwind schemes are used for the spatial discretization. For the transient

formulation, first order implicit scheme is used. Convergence criteria for energy equation and

VOF model residuals are 10-6

and 10-5

, respectively. For the rest of the equations, 10-4

is

employed. For energy equation, the convergence criteria is 10-6

. For Cases 1 and 2, simulations

are run for a total of 480s of flow time. After the first 270s of flow time, VOF (Volume of Fluid)

model is activated to monitor flushing of the air inside the telescope enclosure. However, for

Cases 3-6, simulations are run for around 370s of flow time and the VOF model is activated at

around 160s. For Cases 3-6, the VOF model is activated earlier than Cases 1-2 to reduce

simulation run time. However, it is made sure that the solution is stable before activating the two

phase modelling. For Case 7, simulation is run for 770s and this longer period of flow time is

chosen. This is because in Case 7 there are no vents and also the well is not operating. To

monitor the flushing, the air is assigned to two different names with the same property just

monitor flushing in phase contour plots. The separate phases are patched inside (phase-2) and

outside (phase-1) of the enclosure. After the VOF model is activated, time step size is manually

varied to keep the Courant number around 1.

3

RESULTS AND DISCUSSION

In this study, volume fraction of outside air, mean and RMS temperatures inside the optical path

and also at the optical axis are monitored over time for all 7 cases. Here, the optical path is an

interior cylindrical volume on top of the primary mirror surface with a radius equal to the mirror

radius and a height of 20 m (Fig. 4) and the optical axis is the axis of the optical path. Also, the

wind velocity, temperature and turbulent kinetic energy are measured at three locations by using

point probes located on the optical axis. Point 1 is in the middle of the primary mirror surface

and the octagonal support structure, Point 2 is in the middle of the camera and the octagonal

support structure and Point 3 is in the middle of the camera and the enclosure opening. Results

from all these measurements are reported and discussed in this section.

Volume fraction of outside air

Mean volume fractions of outside air in the optical path and at the optical axis are monitored for

all cases and are presented in Figure 5. Cases 1, 4 and 5 showed better flushing of inside old air

from the optical path than the other cases. Although all vents are fully open in Case 6 as in Cases

1, 4 and 5, flushing takes longer in Case 6. This is because of the low wind speed (2 m/s at the

meteorological station) in the surrounding environment than in Cases 1, 4 and 5. Two well

operating cases (Case 2 and 3) will take really higher flushing time than the vent cases. However,

understandably the worst case is Case 7 where none of the vents and well are operating even

though the outside wind speed is maximum in this case (10 m/s at the meteorological station).

The mean volume fractions of outside air along the optical axis (Fig. 6) show similar trend as in

Figure 5. Contours of volume fraction of outside air in the X-Y plane for all cases at the

respective final time steps are shown in Figure 7. From Figure 7 it can be seen that, for Case 1, a

small portion of inside air is trapped at the upper left hand corner whereas for Cases 4 and 6,

inside air is trapped over the mirror.

Temperature

Another important aspect of this study is to monitor temperatures inside the enclosure with time.

Spatial mean and RMS temperatures in the optical path are plotted in Figure 8 and 9

respectively. For Cases 1 and 2, solution is initialized with 271.3K, however for the rest of the

cases 275K is used as the initial temperature. This difference in initial temperatures reflects in

both Figure 8 and 9. Mean temperature inside the optical path varied within 0.25K for Cases 3-7

(Fig. 8). Similar observation can be made for Case 1 after the mean temperature inside the

enclosure reaches the outside reference temperature (275K). Within the simulation period, the

mean temperature inside the optical path was not able to reach outside reference temperature

from the initial temperature for Case 2. From Figure 9, it can be seen that the temperature RMS

is within 0.1K for Cases 3-7. Higher fluctuation in the RMS temperature for Case 1 and 2 could

have been avoided if the initial temperature is set to the outside reference temperature (275).

Similar trend is observed for spatial mean and RMS temperature along the optical axis (Fig. 10,

4

11). Temperature contours for all cases at the respective final time steps at the XY plane are

shown in Figure 12. Overall temperature variation inside the enclosure is about 1K which is a

favourable condition in terms of temperatures inside the telescope enclosure. Temperature is also

measured at three different point probes, locations of which are mentioned at the beginning of

this section. Temperature at Point 1, 2 and 3 with flow time are shown in Figure 13, 14 and 15

respectively. Temperatures at point probes (Figs. 13-15) show a similar trend as mean

temperatures in the optical path (Fig. 8) and the optical axis (Fig. 10). Except for Case 1 and 2,

for which the large temperature variations could have been avoided using initial temperature of

275K, temperature deviance at all three points for the rest of the cases (Case 3-7) are within

0.25K.

Wind speed

Wind speeds at the same three point probes (Point 1, 2 and 3) are measured for all cases and

plotted in Figure 16-18. The sudden spikes in all three figures occur at the beginning of the

simulation when the solution is unstable and also at the flow times when VOF model is

activated. The cases with all vents fully open and higher wind speed surrounding the telescope

enclosure (Case 1, 4, 5) show slightly higher wind speed at point 1 than the rest of the cases (Fig.

16). However, for all cases the wind speed at Point 1 is about 1 m/s or less. From Figure 17,

higher wind speed at Point 2 can be clearly seen for Case 5 than all other cases. Case 5 is the

west facing case and in this case, a jet is formed between the octagonal structure and the primary

mirror resulting in higher wind speed at Point 2. For all other cases, wind speed is around or

below 1 m/s for Point 2. For Point 3, only Case 3 shows higher velocity than the rest of the cases

(Fig. 18). This is due to the higher well flow rate in Case 3 where only inlet within the telescope

enclosure is the camera opening and only outlet is the well. Therefore, the flow rate through the

opening has to match the flow rate through the well to satisfy continuity and thus resulting in

higher wind speed at Point 3. For Case 7, the wind speed is slightly higher at Point 3 than at

Point 1 and 2. This is obvious as the flow in this case is coming inside the enclosure only through

the camera opening with none of the vents and well functioning.

Turbulent kinetic energy

Similarly as wind speeds, turbulent kinetic energies at all three points for all seven cases are

plotted in Figure 19-21. For Point 1, only Case 5 shows slightly higher turbulence than other

cases. This is may be due to the orientation of the telescope in this case as the flow coming in

through the vents on east side of the enclosure get obstructed and separated by the primary

mirror resulting in higher turbulence at Point 1. For Point 2, Case 1 and 4 show higher

turbulence (Fig. 20). These two cases are almost similar except the vent sizes. Therefore, it can

be said that the telescope orientation, vents’ opening condition and the enclosure surrounding

wind speed are responsible for higher turbulence at Point 2 for Case 1 and 4. For Point 3, all

cases show lower turbulence (Fig. 21). Overall, for all three points in all seven cases, turbulence

is below 1 m2/s

2, which can be considered as favourable condition for large telescopes.

5

CONCLUDING REMARKS

Unsteady Reynolds Averaged Navier Stokes simulations have been performed to study flow

around and inside the Next Generation Canada France Hawaii telescope enclosure. Telescope

orientation, venting system and approaching wind speed are varied in total of seven cases.

Overall, cases with all vents fully open (Case 1, 4-6) require a lot less air flushing time than other

cases (Case 2, 3, 7). However, approaching wind speed influence the air flushing time as the

flushing time in Case 6 (with 2 m/s reference wind speed at the meteorological station) is more

than in Case 4 (with 5 m/s reference wind speed). In terms of air flushing time, Case 7 is the

worst which is obvious as neither vents nor well is operating in this case. Other than Case 2,

temperature range inside the optical path, along the optical axis and at the point probes are within

0.25K for all cases. Except for wind speed at point 2 for Case 5 and the numerical instabilities,

wind speeds at the three point probes for all cases are below 2 m/s. Turbulent kinetic energy at

the point probes for all configurations are below 1 m2/s

2.

REFERENCES

ASCE/SEI 7-10, 2010. Minimum design loads for buildings and other structures, American

Society of Civil Engineers.

De Young, D. S., 1996. Numerical simulations of airflow in telescope enclosures. The

Astronomical Journal 112, 2896-2933

Fitzsimmons, J., Dunn, J., Herriot, G., Jolissaint, L., Roberts, S., Mamou, M., and Cooper, K.,

2004. Predicting the aerodynamic performance of Canadian very large optical telescope.

Proceedings of SPIE 5497, 31.

Vogiatzis, K., Sgurson, A., and Angeli, G. Z., 2004. Estimating the effect of wind loading on

extremely large telescope performance using computational fluid dynamics. Proceedings of SPIE

5497, 30.

WindEEE/UWO ngCFHT CFD Study Assessment Report 10-16-2013

Konstantinos Vogiatzis 7140 E. Clayridge Dr.

Tucson, AZ 85750

General comment: The grids used in this study were appropriately fine and their quality good. The solver methodology and turbulence model were sound, even though the time-step required by the passive scalar equation solver used to represent the fresh-to-old volume fraction was excessively small, due to stability issues. The study consisted of 7 simulations. In all cases the wind was from the East and the telescope zenith angle was 30o. The major criteria for successful ventilation (passive or active) are the volume fraction of fresh air after a certain time and the standard deviation of the temperature fluctuations inside the optical volume. The enclosure design should maximize the former and minimize the latter. Even though they both have individual merit, it is the temperature gradients that are responsible for image quality degradation. The following table summarizes the simulations and the approximate values of the criteria after 3.5min. As secondary information, the table also contains the ratio of wind speed at the top end level to external wind speed. It is important for wind jitter purposes to confine this ratio to <0.2.

Case Log Description VEXT

(m/s) TRMS in OV

(K) Fresh air in OV

(fraction) VTOPEND /VEXT

1. Open vents

two-layer Pointing S

5m/s 0.04 ~1.00 0.15

2. Floor well 90,000cfm (~10 vol/h) Pointing S

5m/s 0.30 0.13 0.30

3. Floor well 180,000cfm (~20 vol/h) Pointing S

5m/s 0.065 0.15 0.40

4. Open vents Single layer Pointing S

5m/s 0.02 >0.95 0.12

5. Open vents Single layer Pointing W

5m/s 0.035 ~1.0 <0.10

6. Open vents 2m/s ~0.02 >0.80 0.15

Single layer Pointing S

7. Closed vents Single layer Pointing S

10m/s 0.06 <0.04 0.10

where: VEXT: reference (upwind) wind speed TRMS: standard deviation of temperature fluctuations (around the mean) OV: Optical Volume, cylinder of D=10m and L=20m starting from M1 surface The first group of three simulations was intended to show which ventilation configuration minimizes dome seeing, passive or active. Case 1, passive ventilation with "generous" projected area and two layers, shows excellent dome flushing, low temperature fluctuations and adequate top end wind protection. For Case 2 and 3, the asymmetric location of the floor well results in a flow pattern with fresh air not necessarily passing through the optical volume. Moreover, there is bound to be higher velocities around the top end, since the aperture is the effective fresh air entrance. Depending on relative-to-wind telescope orientation, that may or may not cause higher velocity fluctuations as well. In any case, higher wind speeds add to pointing errors. Cases 2 and 3 are not directly comparable for temperature, since Case 2 had an initial temperature field that was not realistic. The bulk temperature inside the dome was still adjusting, hence the high temperature fluctuations. (The same holds for Case 1, but even so passive ventilation was effective enough to adjust the bulk temperature fast.) This, however, should not have affected the flow pattern and the fresh air volume fraction. Perhaps a more uniform distribution of openings around the floor could have produced a better flow pattern for flushing, but the added complexity, risk associated with top end protection and operation costs weigh against the active ventilation option. To minimize construction costs and maximize simplicity, a revised single layer venting configuration was tested. Case 4 suggests that it works just as well or better than the two layer configuration. Having accepted this new design, three more cases were simulated to assess the venting performance under a different orientation, Case 5 facing downwind and under low external wind speed, Case 6. Case 5 suggests that passive ventilation performs well under various relative-to-wind angles. Note that the Calotte dome design results in asymmetric venting when perpendicular to wind (Case 4) but in a flow-through pattern when pointing downwind (Case 5), with air coming in through the vents and out through the aperture. It is expected (and shown by the results) to have higher temperature gradients when pointing downwind. Case 6 shows that passive ventilation will maintain flushing even at low wind speeds, increasing the wind speed range of acceptable performance. Finally, Case 7 was supposed to test performance when the vents are closed, but no active ventilation exists. Naturally the external wind speed is high when vents are closed. This is also a safer test for top end protection assessment. As expected the optical volume air is not exchanged fast enough but the temperature fluctuations indicate that the image quality will not suffer dramatically, and the top end is well protected. Therefore overall

performance is not worse than active ventilation as in cases 2 and 3. Note that, from Keck experience, dome temperature fluctuations are minimum in the range 3-5m/s. At high wind speeds dome seeing is worse anyway, since the external wind direction over the aperture hinders the desired, smooth flow through it. As a final conclusion, under the assumptions and typical conditions simulated, the current dome design (as described in Case 4 to 7) and venting configuration will provide adequate flushing and protection to ngCFHT.

6

TABLES

Case No. of Vents Well Flow

Rate (cfm)

Camera

Orientation

Wind Speed at the

meteorological station (m/s)

1 26 0 South Facing 5

2 0 90,000 South Facing 5

3 0 180,000 South Facing 5


5 23 0 West Facing 5



Table 1: Details of the cases

Location Temperature (K)

Inlet 275

Exterior of the dome 269

Exterior of the cylindrical base 274

Ground/bottom of the domain 269

Inside dome surface and bottom of the dome 274

Mirror and whole M1 cell 276

Camera 276

All other structures 274

Table 2: Thermal boundary conditions

Property Value

Reference Pressure 61000 Pa

Reference Temperature 275 K

Density 0.8 kg/m3

Kinematic viscosity 2x10-5

m2/s

Table 3: Properties of air

7

FIGURES

Figure 1: Computational domain

(a) (b)

Figure 2: (a) CFD model of the enclosure without the truss elements (b) Truss elements on the

actual model

8

(a)

(b) (c)

Figure 3: (a) Overall mesh of the computational domain (b) mesh at the North-South plane

section close to the enclosure (c) mesh on the telescope components and vents

Figure 4: Optical path

Vents Camera

Well Primary mirror

9

Figure 5: Mean volume fraction of outside air in optical path

Figure 6: Mean volume fraction of outside air along the optical axis

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 300 400 500 600

Volu

me

fract

ion

Flow time (s) (after two phase modelling is activated)

Case 1Case 2Case 3Case 4Case 5Case 6Case 7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 300 400 500 600

Volu

me

fract

ion

Flow time (s) (after two phase modelling is activated)

Case 1Case 2Case 3Case 4Case 5Case 6Case 7

10

Case 1 Case 2

Case 3 Case 4

Case 5 Case 6

Case 7

Figure 7: Contours of volume fraction at the XY plane (Volume fraction of outside air; Red: 1

and Blue: 0)

11

Figure 8: Mean temperature inside the optical path

Figure 9: RMS temperature inside the optical path

271.0

271.5

272.0

272.5

273.0

273.5

274.0

274.5

275.0

275.5

0 100 200 300 400 500 600 700 800

Mea

n t

emp

eratu

re (

K)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 100 200 300 400 500 600 700 800

RM

S t

emp

eratu

re (

K)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

12

Figure 10: Mean temperature along the optical axis

Figure 11: RMS temperature along the optical axis

271.0

271.5

272.0

272.5

273.0

273.5

274.0

274.5

275.0

275.5

0 100 200 300 400 500 600 700 800

Mea

n t

emp

eratu

re (

K)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 100 200 300 400 500 600 700 800

RM

S t

emp

eratu

re (

K)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

13

Case 1 Case 2

Case 3 Case 4

Case 5 Case 6

Case 7

Figure 12: Contours of mean temperature at the XY plane (temperature range 274K to 276K)

14

Figure 13: Temperature at Point 1


271.0

271.5

272.0

272.5

273.0

273.5

274.0

274.5

275.0

275.5

0 100 200 300 400 500 600 700 800

Tem

per

atu

re (

K)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

271.0

271.5

272.0

272.5

273.0

273.5

274.0

274.5

275.0

275.5

0 100 200 300 400 500 600 700 800

Tem

per

atu

re (

K)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

15


Figure 16: Wind speed at point 1

271.0

271.5

272.0

272.5

273.0

273.5

274.0

274.5

275.0

275.5

0 100 200 300 400 500 600 700 800

Tem

per

atu

re (

K)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0 100 200 300 400 500 600 700 800

Vel

oci

ty (m

/s)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

16



0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0 100 200 300 400 500 600 700 800

Vel

oci

ty (

m/s

)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0 100 200 300 400 500 600 700 800

Vel

oci

ty (

m/s

)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

17

Figure 19: Turbulent kinetic energy at point 1


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 100 200 300 400 500 600 700 800

Tu

rbu

len

t k

inet

ic e

ner

gy (

m2/s

2)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 100 200 300 400 500 600 700 800

Tu

rbu

len

t k

inet

ic e

ner

gy (

m2/s

2)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

18


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 100 200 300 400 500 600 700 800

Tu

rbu

len

t k

inet

ic e

ner

gy (

m2/s

2)

Flow time (s)

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

next generation canada france hawaii telescope (ngcfht

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