Coherent Structures and Mass Exchange Processes in Channel Flow with Spanwise Obstructions (Corresponding to Groyne Fields in Rivers)

 

1.General sketch of flow in a channel with lateral obstructions (groynes).  Simulation mesh contains around 3 million gridcells.  1-groin_FINAL.tiff

 

 

2.  Instantaneous streamlines in a plane situated 45-degrees from lateral channel wall showing the evolution and structure of the horseshoe vortex system in time.  Window corresponds to an area close to the bottom and the tip of the upstream groyne.  Time gap between frames is 0.25D/U.

long-angle-45-strmlines.avi  (17.6 MB)

 

3. Mean turbulence statistics in a plane 45o from lateral channel wall a) mean velocity streamlines; b) ; c) ;  d) ;  e) ;  f) 3-statistics-color-web.tif

 

 

4. Velocity time series and velocity & pressure power spectra within the HV system a) u-velocity time series at p1; b) u-power spectrum at p1; c) Pressure power spectrum at p1 (inset shows pressure power spectrum as a log-log plot); d) Pressure power spectrum at p2.  The position of p1 and p2 are shown in the figures displaying mean turbulence statistics. 4-figures-HV.tif

 

5. Instantaneous streamlines in planes situated 25o, 30o, 35o, and 45o from lateral channel wall showing the evolution and structure of the horseshoe vortex system in space and time.  Time gap in each frame is 0.04D/U, considerable smaller than in animation 1 to allow detailed observation of the evolution of coherent structures.

short-angles-combined.avi  (4.0 MB)

 

6.  Non-dimensional bed shear stress relative to the mean value corresponding to fully turbulent flow in a channel without spanwise obstructions a) Mean distribution; b) Instantaneous distribution; c) Mean distribution.  Entrainment region as predicted by Shield’s theory; d) Instantaneous distribution. Entrainment region as predicted by Shield’s theory.  6-norm-shear-stress-color-web.tif

7. Non-dimensional bed shear stress distribution; a) mean; b) Instantaneous; c) Time series at p1; d) Time series at p2; and e) Time series at p3. The time series demonstrate turbulent fluctuations are as much as 100 percent higher than mean condition

 8.  Instantaneous contours of out-of-plane vorticity magnitude in the free surface plane (top) showing the evolution of coherent structures in the upstream recirculation zone, the detached shear layer, in the embayment, and downstream of the groynes.  Bottom picture shows contours of the normalized bed shear stress magnitude.  The spatio-temporal evolution of the regions characterized by high bed stress are highlighted.  They correspond to regions where scour will develop in the case of a loose bed.  The largest values are observed beneath the horseshoe vortex system but high values are also present beneath the detached shear layers.

long-vort-BSS-combined.avi   (29.0 MB)

 

9.  Instantaneous contours of out-of-plane vorticity magnitude in the free surface plane (top) and contours of the normalized bed shear stress magnitude (bottom).  Time gap between frames is 0.04D/U, considerable smaller than in animation 3 to allow detailed observation of the evolution of coherent structures in the two planes.

short-vort-BSS-combined.avi   (3.9 MB)

 

10.  Flow dynamics in the detached shear layer at the free surface a) Instantaneous contours of out-of-plane vorticity magnitude; b) Pressure time series at p3; c) Pressure power spectrum at p3.

10-figures-DET-color.tif

11. Vortex Merging in detached shear layer.  Consecutive vortices a and b merge over a time interval of 0.32 D/U corresponding  to a St = 3.1.

12. Instantaneous contours of passive scalar concentration in the channel at three planes situated at the free surface at 0.5D and 0.1D from the channel bottom, respectively (D is the channel depth).  Mixing starts at t=0D/U when the concentration in the embayment is set to C/C0=1.0 and continues through 75.75D/U until less than 1% of the original scalar mass is left in the embayment area.  Time gap between frames is 0.25D/U.  To allow visualization of the flow structures the maximum concentration contour level in the movie corresponds to C/C0=0.1. 

long-scalar-combined.avi   (18.8 MB)

 

13.  An equation which describes the 1D mass exchange of a conservative pollutant flowing in a channel with embayments (Uijttewaal et al., 2001) is: 
 

                                                                                                   (1)
 

                                                                                          (2)   
 

                                                                                                                                (3)

 

where  is the pollutant mass fraction in the embayment ((t=0)=- initial pollutant mass),  is initial pollutant mass fraction in main channel (=0),  is the non-dimensional exchange coefficient related to the characteristic decay time T of the 1D exchange process, is mean water depth (=D),  is water depth at the interface (=D),  is embayment width (0.625D),  is main channel velocity (=U).  The variation of total scalar mass in the embayment is shown in the attached figure.  The two straight lines corresponding to two values of the dimensionless mass exchange coefficients k (initial and final phase of decay) are also shown.   11-exchange-coef-total.tif

 

14. Cumulative mass transport into main channel respective of depth in embayment.  The top volume transports 149 percent of its original pollutant into the main channel, only 48 percent of the original pollutant in the bottom is transported into the main channel at the bottom volume.  This shows the importance of vertical motions in the primary transport process for this geometric configuration consisting of pollutant advection from the bottom to the top and into the channel from there.

15.  Mass flux through multiple cross sections a) Cumulative mass through cross sections; b) Mass flux through embayment plane and spanwise plane located at x = 3.75; c) Mass flux through planes located at x = 5.0, x = 7.50, and x= 10.0; d) Mass flux through planes located at x = 12.5, x = 15.0, and x = 17.0; e) Plane locations.    15-cumul-mass-mass-flux-through-mult-cross-sections.tif

 

16. Coherent Structures.  Mean and Instantaneous velocity streamlines illustrating flow patterns at three depths in channel.  The Instantaneous frames capture complex interactions upstream the obstruction and in the detached shear layer.

 

17. Upstream Recirculation Area.  Mean velocity streamlines illustrating three-dimensional structure of upstream recirculation zone.  The Instantaneous solution shows more complex interaction with between primary corner vortex and three secondary vortices upstream.

18. Coherent Structures in Embayment.  Mean structure 1 shows the calculated streamlines released in the embayment specifically in the upstream embayment half.  Mean structure 2 shows the extent of the statistically averaged vortex system near the embayment formed by the detached shear layer.  Mean Structure 3 shows the extent of the statistically averaged vortex system in the downstream half of the embayment.  Instantaneous Structure 2 shows a contrast with Mean Structure 2.  The single dominant time-averaged vortex structure serves to move fluid particles toward the surface (Mean Structure 2) while in Instantaneous Structure 2 fluid particles are transported both away from and to the surface.

19.Coherent Structures in Downstream Area.  Vortices in the mean downstream recirculation area and the corner vortex illustrate the extent of the statistically averaged vortex system in the downstream recirculation zone. 


Comparison of LES with RANS k-w

20. Contours of the mean non-dimensional bed shear stress relative to the mean bed shear stress (,) corresponding to fully turbulent flow in a channel of identical section without obstructions.  Frame a shows the distribution calculated using RANS with a k-w turbulence model.  Frame b displays the mean distribution calculated with LES and to illustrate the complexity of the flow, frame 6c is an instantaneous solution using LES.  Frames 6d-6e show the non-dimensional bed shear stress time series calculated with LES through 75 D/U time units. 

21. Spatial extent of HV system as calculated with RANS closed with k-w SST turbulence model and compared to the mean LES results.  Vertical Planes a-h located on figure below and progress from 25o through 65o.  The HV System is spatially more persistent in RANS calculations further from obstruction.

22.  Instantaneous contours of passive scalar concentration in the channel at three planes situated at the free surface at 0.5D and 0.001D from the channel bottom, respectively (D is the channel depth) calculated with RANS closed with k-w SST turbulence model.  Mixing starts at t=0 D/U when the concentration in the embayment is set to C/C0=1.0 and continues through 54.0D/U until less than 1% of the original scalar mass is left in the embayment area.  Time gap between frames is 1.0 D/U.  To allow visualization of the flow structures the maximum concentration contour level in the movie corresponds to C/C0=0.1.

23. Variation of total scalar mass in the embayment comparing RANS closed with k-w SST and LES.  The straight lines correspond to dimensionless mass exchange coefficients.  The RANS model calculates mass exchange occurring three times quicker than LES.

24. Mass Transport Through Channel.  It is immediately clear that scalar is transported from the embayment much more quickly in the LES results than in the RANS simulation.  This is confirmed by examining the frames comparing the mass fluxes passing through the embayment plane and through three planes downstream, the embayment plane, x/D = 3.75, and x/D = 15.0. 

25.  Mean Flow patterns at D = 0.4. For the LES results the solution has been averaged over 75 D/U, a time period significantly long enough to include every important time scale.  Overall major flow features identified with streamlines are similar in both solutions including the upstream recirculation area, downstream recirculation area, and the recirculation patterns delineating the detached shear layer. 


26.  Flow Patterns in Embayment. 

 27. Upstream Recirculation Area.   The major differences include the LES result showing clear interaction between upstream secondary vortices and the primary corner vortex while in the RANS solution the secondary vortices and the primary vortices remain separate.