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Turbulence forced external mixing...depth (cm) Time (min) Interface depth vs Time Graph (1) Graph...
1
cm ωy 1/s cm Fig (3b) 60 sec average with interface ωy 1/s Fig (3a) 60 sec average with no interface An average of 60 sec Velocity/Vorticity plot with an interface An average of 60 sec Velocity/Vorticity plot with no interface Process and Environmental Research Division Summer Placement 2011 By Mohamed Elmaghrbi Supervisor: Dr Matthew Scase Turbulence forced external mixing Introduction: Turbulent/laminar boundaries occur in a vast range of environmental and industrial fluid flows. For example smoke from chimneys and volcanic eruption columns propagating through the atmosphere, fuel ignited in an engine, and dense water flows from the edge of Antarctica which drive the ocean conveyor belt. The interest in the characteristics of the interfacial mixing between the ambient and turbulent layers, has led to numerous detailed laboratory studies aimed at improving the mixing models employed in these situations. A large number of studies have investigated this phenomena using turbulence generated by an oscillating grid, producing zero-mean turbulent flow. The first attempt to do so was by J. S. TURNER in 1968. The experiment consists of two layers of fluid with different density, one of which is stirred by oscillating the grid creating a turbulent motion, and the other layer is quiescent. Theory: The entrainment rate (the interface velocity) is expressed as a power law of the form: = − (1) Where is the ratio of the entrainment velocity to the turbulent velocity scale, and are constants and are to be determined from the experiments. is Richardson number and it is a function of the relative density between the fluids, the turbulent length scale ( ) and root mean square velocity scale () at the interface and is given by the equation : = ∆ 2 (2) The length scale only depends on the distance from the grids origin, where as the velocity scale is dependent on the grid characteristics as well as the distance from the grid. ‘∆′ is the density difference between the two fluids and ‘’ is a reference density (density of fresh water) and is gravitational acceleration. = 0.1 (3) = 0.25 1.5 0.5 −1 (4) Where is the distance of the interface from the grids origin (m), is the frequency (Hz), is the stroke length (m), is the mesh size (distance between the grids bar centres) (m), and z is the distance from a virtual origin. Detailed experiments by Hopfinger & Toly showed that this virtual origin lies at the grid mid-plane in its equilibrium position (i.e. at the interface = ) cm cm cm cm cm cm cm Figures (3a) to (3f) are a time sequence with 0.2 sec time step interval. The velocity and vorticity plots here are instantaneous and not averaged unlike in figures (2a) and (2b), and the interface is at depth 6cm from an arbitrary origin. From this time series it can be seen what exactly happens as a jet or an eddy impacts on the interface. In fig(3a) an eddy rotating anti clockwise is impacting on the interface between 4 and 6 cm horizontally. It can be seen that it is directed away from the interface, and at the same time generates another eddy that rotates clockwise between 7 and 9 cm starting from fig(3b). The second eddy propagates through the interface and causes the two layers to mix. Particle Image Velocimetry (PIV) was used to study the behaviour of the fluid near the interface in order to create an understanding of the mixing procedure. The colour background represents the vorticity (red signifies anti-clockwise motion, and blue is clockwise motion).The arrows show the velocity of the fluid, (an arrow size is proportional to the magnitude of the velocity). Fig (3a) is a 60 sec time average with 200 frames a second. It can be seen the there are no major vortices present away from the grid in the absence of an interface, in fig (3b) where the interface is at depth 20 cm from the grid mid-plane (the origin), it is clear that two rotational motions are present just above the interface, to the right (clockwise) and (anti-clockwise) to the left. This happens because the interface acts like a boundary not allowing the fluid to pass through, and directs the fluid horizontally and then vertically away from the denser bottom layer. As this happens it generates vorticity at the interface opposite to the motion above it, which essentially causes the two fluids to mix. Interface depth Results and discussion: 0 0.5 1 1.5 2 2.5 0 5 10 15 20 25 30 35 40 45 Interface depth (cm) Time (min) Interface depth vs Time Graph (1) Graph (1) shows the interface height vs time. The initial depth was 14 cm from the grid mid- plane. The range of Richardson numbers for this experiment was : 190.5 < Ri <396. It can be seen that the interface velocity (the gradient of the fitted line) decays with time, and reaches a linear relationship where the velocity is constant with time. Further investigation was carried out to investigate the dependency of the velocity with the interface initial position and distance from the grid. Stroke length: 4cm Stroke frequency: 0.671 Hz Fig (4a) Fig (4f) Fig (4e) Fig (4d) Fig (4c) Fig (4b) Interface depth Motor to drive the grid 5cm 1cm 2cm Fig (2b) 0 1 Interface Free water surface Tank Grid movement Fig (2a) Grid Fig (2a) shows the set up of the experiment. A tank of cross section (35×35cm) was used. Fig (2b) shows the dimensions of the grid used. W. MOHTAR (2011) z Fig (1) Fig (1) shows the mixing procedure at the interface between the two layers of fluid. And the density profile in relationship with the depth. It also illustrates the quantities of both the turbulence length scale and velocity scale. H. J. S. FERNANDO & J. C. R. HUNT (1997) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 20 40 60 80 100 120 140 160 Interface depth (cm) Time (min) Interface depth vs Time Stroke length: 4cm Stroke frequency: 1.147 Hz ` Graph (2) Graph (2) shows the interface depth vs time for 3 different experiments. The parameter varied here in the initial distance of the interface from the grid mid-plane. The results obtained show that the interface velocity at a certain time depends on the initial position of the interface as well as the other parameters mentioned before. These results are not mentioned in any previous studies and further investigation in this area is encouraged. ωy 1/s ωy 1/s ωy 1/s ωy 1/s ωy 1/s ωy 1/s
Transcript of Turbulence forced external mixing...depth (cm) Time (min) Interface depth vs Time Graph (1) Graph...
cm
ωy 1/s
cm
Fig (3b) 60 sec average with interface
ωy 1/s
cm
Fig (3a) 60 sec average with no interface
An average of 60 sec Velocity/Vorticity plot with an interface An average of 60 sec Velocity/Vorticity plot with no interface
Process and Environmental Research Division
Summer Placement 2011
By Mohamed Elmaghrbi Supervisor: Dr Matthew Scase
Turbulence forced external mixing
Introduction: Turbulent/laminar boundaries occur in a vast range of environmental and industrial fluid flows. For example smoke from chimneys and volcanic eruption columns propagating through the atmosphere, fuel ignited in an engine, and dense water flows from the edge of Antarctica which drive the ocean conveyor belt. The interest in the characteristics of the interfacial mixing between the ambient and turbulent layers, has led to numerous detailed laboratory studies aimed at improving the mixing models employed in these situations. A large number of studies have investigated this phenomena using turbulence generated by an oscillating grid, producing zero-mean turbulent flow. The first attempt to do so was by J. S. TURNER in 1968. The experiment consists of two layers of fluid with different density, one of which is stirred by oscillating the grid creating a turbulent motion, and the other layer is quiescent.
Theory: The entrainment rate (the interface velocity) is expressed as a power law of the form:
𝐸 = 𝑘𝑅𝑖−𝑛 (1) Where 𝐸 is the ratio of the entrainment velocity to the turbulent velocity scale, 𝑘 and 𝑛 are constants and are to be determined from the experiments. 𝑅𝑖 is Richardson number and it is a function of the relative density between the fluids, the turbulent length scale ( 𝑙 ) and root mean square velocity scale (𝑢) at the interface and is given by the equation : 𝑅𝑖 = 𝑔∆𝜌𝜌
𝜌𝑢2 (2)
The length scale 𝑙 only depends on the distance from the grids origin, where as the velocity scale 𝑢 is dependent on the grid characteristics as well as the distance from the grid. ‘∆𝜌′ is the density difference between the two fluids and ‘𝜌’ is a reference density (density of fresh water) and 𝑔 is gravitational acceleration. 𝑙 = 0.1𝐷 (3)
𝑢 = 0.25𝑓𝑠1.5𝑚0.5𝑧−1 (4) Where 𝐷 is the distance of the interface from the grids origin (m), 𝑓 is the frequency (Hz), 𝑠 is the stroke length (m), 𝑚 is the mesh size (distance between the grids bar centres) (m), and z is the distance from a virtual origin. Detailed experiments by Hopfinger & Toly showed that this virtual origin lies at the grid mid-plane in its equilibrium position (i.e. at the interface 𝑧 = 𝐷)
cm
cm cm cm cm cm cm
Figures (3a) to (3f) are a time sequence with 0.2 sec time step interval. The velocity and vorticity plots here are instantaneous and not averaged unlike in figures (2a) and (2b), and the interface is at depth 6cm from an arbitrary origin. From this time series it can be seen what exactly happens as a jet or an eddy impacts on the interface. In fig(3a) an eddy rotating anti clockwise is impacting on the interface between 4 and 6 cm horizontally. It can be seen that it is directed away from the interface, and at the same time generates another eddy that rotates clockwise between 7 and 9 cm starting from fig(3b). The second eddy propagates through the interface and causes the two layers to mix.
Particle Image Velocimetry (PIV) was used to study the behaviour of the fluid near the interface in order to create an understanding of the mixing procedure. The colour background represents the vorticity (red signifies anti-clockwise motion, and blue is clockwise motion).The arrows show the velocity of the fluid, (an arrow size is proportional to the magnitude of the velocity). Fig (3a) is a 60 sec time average with 200 frames a second. It can be seen the there are no major vortices present away from the grid in the absence of an interface, in fig (3b) where the interface is at depth 20 cm from the grid mid-plane (the origin), it is clear that two rotational motions are present just above the interface, to the right (clockwise) and (anti-clockwise) to the left. This happens because the interface acts like a boundary not allowing the fluid to pass through, and directs the fluid horizontally and then vertically away from the denser bottom layer. As this happens it generates vorticity at the interface opposite to the motion above it, which essentially causes the two fluids to mix.
Interface depth
Results and discussion:
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0.5
1
1.5
2
2.5
0 5 10 15 20 25 30 35 40 45
Inte
rfac
e de
pth
(cm
)
Time (min)
Interface depth vs Time
Graph (1)
Graph (1) shows the interface height vs time. The initial depth was 14 cm from the grid mid-plane. The range of Richardson numbers for this experiment was : 190.5 < Ri <396. It can be seen that the interface velocity (the gradient of the fitted line) decays with time, and reaches a linear relationship where the velocity is constant with time. Further investigation was carried out to investigate the dependency of the velocity with the interface initial position and distance from the grid.
Stroke length: 4cm Stroke frequency: 0.671 Hz
Fig (4a) Fig (4f) Fig (4e) Fig (4d) Fig (4c) Fig (4b)
Interface depth
Motor to drive the grid 5cm
1cm
2cm
Fig (2b) 𝑠
𝐷
𝜌0
𝜌1
Interface
Free water surface
Tank
Grid movement
𝑚
Fig (2a)
Grid
Fig (2a) shows the set up of the experiment. A tank of cross section (35×35cm) was used. Fig (2b) shows the dimensions of the grid used. W. MOHTAR (2011)
z
Fig (1)
Fig (1) shows the mixing procedure at the interface between the two layers of fluid. And the density profile in relationship with the depth. It also illustrates the quantities of both the turbulence length scale and velocity scale. H. J. S. FERNANDO & J. C. R. HUNT (1997)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 20 40 60 80 100 120 140 160
Inte
rfac
e de
pth
(cm
)
Time (min)
Interface depth vs Time
Stroke length: 4cm Stroke frequency: 1.147 Hz `
Graph (2)
Graph (2) shows the interface depth vs time for 3 different experiments. The parameter varied here in the initial distance of the interface from the grid mid-plane. The results obtained show that the interface velocity at a certain time depends on the initial position of the interface as well as the other parameters mentioned before. These results are not mentioned in any previous studies and further investigation in this area is encouraged.
ωy 1/s ωy 1/s ωy 1/s ωy 1/s ωy 1/s ωy 1/s
