Laboratory studies on colliding gravity currents. Qiang ZHONG. Environmental Fluid Dynamics Group University of Notre Dame October

Transcription

1 Laboratory studies on colliding gravity currents Qiang ZHONG Environmental Fluid Dynamics Group University of Notre Dame October 8 25

2 Outlines Introduction 2 Experiments 3 Currently Result 4 Conclusion 2

3 . Introduction 3

4 4 Introduction Granite Mountain 22 2 Temperature and velocity data before collision occurred (4:5 UTC 22:5 MDT)

5 Introduction Time series of UU LiDAR data located at the slope. Here shows the initial collision between the downslope (red) and valley flow (blue). The collision events great impact the TKE production and temperature flux. 5

6 6 Introduction m contours map of Granite Mountain -km grid used for mesoscale models

7 Introduction Important: () the length and time scale of collision events (2) buoyancy and momentum flux T bw bt wt dt b t bt b t w t w t w t bw f U U h h,,,,,,,,

8 2. Experiments 8

9 28cm 2. Facilities 2.. Channel Lock Exchange Rectangular Channel 3cm 5cm 3cm 5cm 2 H 2,,,,,,,,,,,,,,, f U U h h f h f h curr uh f curr C gh curr hcurr Re C g hcurr hcurr 9 curr

10 2. Facilities 2..2 Particle Image Velocimetry (PIV) and Planar Laser-Induced Fluorescence (PLIF) L=3cm 5cm L=3cm Front View H Rhodamine 6G Measurement window Laser Rhodamine 6G 57.5cm Vertical View 5cm High-pass filter lens PIV camera Low-pass filter lens PLIF camera

11 2.2 Experimental Parameters Case H m kg/m 3 kg/m 3 u f m/s Re u f h curr /v Basic parameters H whole water depth density of light fluid h curr =H/2 depth of gravity currents density of dense fluid u g' g f.57 g ' h curr reduced gravity front velocity

12 2 3. Current Result Scale Average Process Turbulence Fluctuation

13 3. Time, length and velocity scale The density of heads is smaller than that of current bodies. During collision, mixing both happens between two heads and between current and ambient. Strong vertical motion is triggered by collision. The dense fluid itself is stratified after collision.

14 3. Time, length and velocity scale Point 3 u/u f 2.5 Horizontal velocity at Point GOOD Case 4 Case 5.5 Case 6 Point Point t / ( h curr / u f ) w/u f Vertical velocity at Point 2 Case 4 GOOD t / ( h curr / u f ) Case 5 Case 6 w/u f Vertical velocity at Point 3 Case 4 GOOD t / ( h curr / u f ) Case 5 Case 6

15 3. Time, length and velocity scale t* hcurr / u t* L / u f f.2 Vertical velocity at Point 2 Case 4.2 Veritcal velocity at Point 2 Case 4 w/u f GOOD Case 5 Case 6 w/u f Not GOOD Case 5 Case t / ( h curr / u f ) t / ( L / u f ) Velocity Scale Length Scale u f h curr Time Scale * / t h u curr f

16 3.2 Average Process 3.2. Vertical motion of dense fluid front dense fluid height in the collision area Define the dense fluid height in the collision area in the black box as: h t 2h curr h h curr curr /2 2h /2 curr x, z, t dzdx

17 3.2 Average Process 3.2. Vertical motion of dense fluid front t h u t*2 L / u f * curr / f Dens fluid height in collision area Re Dens fluid height in collision area Re Coincide Re h/h cur.2.8 Coincide hcurr h/h cur t / ( h curr / u f ) t / ( L / u f ) There are two time scale for h(t). t * can scale the collision section but can not scale the entire durations, and t *2 is just the opposite. This indicates that the currents approaching, deceleration and colliding phase are dominated by the local parameters h curr and u f, but the entire duration has relationship with the total amount of dense fluid (L is the length of the dense water tank).

18 3.2 Average Process 3.2. Vertical motion of dense fluid front w f / u f I II Vertical front velocity III / w t dh t dt t / (h curr / u f ) f IV Re The vertical front velocity process shows 4 period obviously. w f achieves maximum at the end of period I. The negative buoyancy force slows the upward motion in period II. At the end of period II water surface comes into play and the acceleration changes. The dense fluid reaches the highest position at the end of period III and then starts to return to the bed, thus w f changes to negative. The maximum vertical front velocity can be considered as the initial velocity w f of period II.

19 w f (blue points) is the maximum vertical front velocity, and w max (red points) is the maximum vertical velocity inside the dense fluid from PIV data. It can be seen that w f /u f is about and w max is about.2. This is similar as the velocity structure in gravity currents, where the velocity inside is about.5 times front velocity. Although the vertical front velocity equals to the horizontal front velocity of typical gravity current, the front size after collision is smaller than 2h curr. Thus, in general there are some kinetic energy lost during collision. 3.2 Average Process 3.2. Vertical motion of dense fluid front Initial vertical front velocity.4.2 <2h curr w/u f Re wf f wmax h curr u f u f u f h curr

20 3.2 Average Process Pressure Distribution Case 6, h curr =25mm, Re=698, t/(h curr /u f )=-.4 Cp p 2 p u ref 2 f where p ref is the average pressure in the filed. There are two high pressure area during collision. The water surface inhibition causes the upper one. In the atmosphere, the water surface does not exist. Thus, the lower high pressure area is more interesting, and it is cased by the horizontal velocity decreasing. The area range changes during collision, we can find the maximum situation as the characteristic range. This figure is the maximum situation of case 6, and the width and height of high pressure area are both about h curr.

21 3.2 Average Process Pressure Distribution Case 5, h curr =5mm, Re=346, t/(h curr /u f )=-.38 The width and height of high pressure area for different cases are both about h curr. The time of occurrence is just after the heads hit each other. Direction of flow is deflected by this high pressure core between two gravity currents and convection is triggered.

22 3.3 Turbulence fluctuation 3.3. turbulent kinetic energy 2 hcurr hcurr /2 2 2 K i, t u x, z, t, i w x, z, t, idxdz 4h 2 hcurr /2 curr K t N K i, t N i (u 2 +v 2 )/u 2 K/u 2 f f Mean TKE Evolution in 2h cur *2h cur box Re t/t *

23 3.3 Turbulence fluctuation Buoyancy flux x, z, t, i x, z, t, i bw x, z, t bx, z, t, iwx, z, t, i b x, z, t, i g bw t bw/g u f N i t/t * N 2 2h curr hcurr,, 4h 2 curr h curr bw x z t dx dz Re

24 3.3 Turbulence fluctuation Buoyancy flux b g g g b w bw b w bw b w bw b w bw Before collision 24

25 3.3 Turbulence fluctuation Buoyancy flux b g g g b w bw b w bw b w bw After collision 25

26 4. Conclusion 26

27 4. Conclution () Mixing both happens between two heads and between current and ambient. Strong vertical motion is triggered by collision. The dense fluid itself is also stratified after collision. (2) The width and height of high pressure area for different cases during collision are both about h curr. The time of maximum area occurrence is just after the heads heat each other. Direction of flow is deflected by this high pressure core between two gravity currents and convection is triggered. (3) Velocity, length and time scale for collision phase are u f, h curr and h curr /u f respectively. The bores propagating phase and entire duration have relationship with the total amount of dense fluid. (4) The value of initial vertical front velocity (just after the heads hit each other) is u f. (5) TKE increase very quickly when gravity currents approaching to each other and achieves maximum just after the heads hitting each other. (6) Buoyancy flux is totally different before and after collision.

28 28 Thank you very much for your attention!