This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
About River2D Morphology The River2D Morphology model (referred hereafter as R2DM) was originally developed in 2006 by Robert G. Millar and Jose “Pepe” Vasquez at the University of British Columbia as an add-on module to River2D (written by F. Hicks, A. Ghanem, J. Sandelin, P. Steffler, and J. Blackburn at the University of Alberta). In 2009, Stephen Kwan developed the graphical user interface, the mixed sized sediment transport module and the secondary flow correction algorithm under the guidance of Robert Millar. Stephen added the Struiksma non erodible area algorithm, advanced output features and fish egg survival algorithm in 2010. Limitations R2DM solves the bedload sediment continuity equation; suspended transport of fine material is ignored. The model is intended for modeling general bed changes, local scour, which is caused by three-dimensional flow, cannot be modeled. The upwinding scheme implemented is very simple and has not been fully tested; stability and accuracy of the solutions cannot be guaranteed. As shown in this manual, R2DM has been tested with a limited number of laboratory flume cases. Conditions of Use R2DM, in the form of a Windows XP/Vista/Windows 7 executable program, is available in the public domain. The program is supplied as seen, with no warrant of completeness or applicability to any particular problem. The program, example data files, and documentation may be freely copied and distributed as long as this notice is included and use of the model is properly acknowledged. R2DM development and the documentation is an on-going process and so whenever significant functionality is added, an updated program will be released. Any feedback (constructive or otherwise), bug reports, and discussion will be greatly appreciated. Inquiries should be directed to [email protected] or [email protected].
Contents List of Symbols .............................................................................................................................................. 4
4.0 Special Features .................................................................................................................................... 22
4.1 Fish Egg Survival Algorithm ............................................................................................................... 22
4.1.1 Procedure to estimate fish egg survival during a flow event ....................................... 22 4.2 Non Erodible Areas ........................................................................................................................... 23
5.1 Vector Data ....................................................................................................................................... 25
A local element area (m2) a constant used for empirical sediment transport equation b constant used for empirical sediment transport equation c bed load-surface mixing coefficient C Chezy friction coefficient (m1/2/s) dz change in bed elevation D50 size of 50th percentile grain size Dsm median surface grain size Di grain size in fraction i fbi bed load fraction fs = k1 /k2 , calibration factor for transversal slope Fi proportion of fraction i in the surface size distribution Fb proportion of fraction i in bed load size distribution Fs proportion of sand in surface size distribution g gravitational acceleration h water depth k1 constant (used to calculate fs for transversal slope) k2 constant (used to calculate fs for transversal slope) ks effective roughness height in River2D L length of flume Ls surface layer thickness Pi proportion of fraction i in transport size distribution qs sediment transport rate per unit width qbi sediment transport rate of size fraction i per unit width qbT total bed load transfer rate qsIN upstream sediment supply rate (m2/s) qx sediment flux in x direction qy sediment flux in y direction Q sediment flux (m3/s) going into an element. s specific gravity of sediment
T = */c -1, Transport stage parameter (used for Van Rijn Equation) t time (s) u* shear velocity u velocity component in x direction UW up-winding coefficient v velocity component in y direction Wi
* dimensionless transport rate of size fraction i Wr
* reference value of dimensionless transport rate (=0.002) zb bed elevation
Surface – Substrate mixing coefficient (0-1) These can be set by selecting W/C settings button on the sediment options dialog box. Since the grain size distribution on the surface of a riverbed is rarely uniform, R2DM allows the user to specify a different initial distribution according to the bed roughness, ks. Figure 3 shows how the grain size distributions can be initialized for the ks ranges: ks < 0.1; 0.1 < ks < 0.3; 0.3 < ks < 0.7; 0.7 < ks < 1.0.
Figure 3. The Sediment Options Dialogue Box
2.1.3.1 The Gravel Transport Function
The gravel transport function assumes that the active surface layer remains at a constant thickness, Ls, set by the user (Depth of Surface Layer in the “Set Grain Size Distribution” dialogue box, Figure 3). At each time step the grain size distribution for the surface layer distribution is recalculated according to the volume of sediment entering or leaving the element. If there is aggradation, the net volume of
sediment into an element is positive and the new fraction of grain size i in the surface layer of the element can be calculated according to the formula:
Eisiiii AFdzLdtQQQV )1(*)()( 312312 (14)
where Vi = volume of fraction i in the surface, Fi = surface layer fraction i, and Ls = surface layer thickness, Q12i = volume of sediment in fraction i entering or leaving through side 12 of the element per unit time. If there is degradation, sediment leaves the element and the surface layer mixes with the substrate to maintain a constant Ls (see Figure 4). The new volume of fraction i is therefore:
siEisiiii FdzAFdzLdtQQQV *)1(*)()( 312312 (15)
Where Fsi is the fraction of grain size i in the substrate.
Thus, the new surface layer fraction at time step, t+t is:
)1(
AL
V
V
VF
s
i
Total
inew
s (16)
This formulation of this function models the actual physical phenomena and satisfies mass continuity.
2.1.3.2 Transport Rate Factor
Since the Wilcock and Crowe mixed sediment transport function is empirical, it may be necessary to adjust it using a weighting factor. The recommended range would be between 0.01 – 100 to remain within the range of experimental results.
Figure 4. Conceptual model of a gravel bedded river during aggradation. The bed load mixes with the surface layer to form a new grain size distribution. The surface layer thickness is assumed to be a constant thickness Ls.
Figure 5. Conceptual model of a gravel bedded river during degradation. The surface layer mixes with the sub-surface layer to form a new grain size distribution. The surface layer thickness is assumed to be a constant thickness Ls
2.1.3.3 Roughness Height
In River2D, once the roughness height, ks, is defined in the computational domain, it remains unchanged throughout the simulation since the bed morphology remains constant. For simulations where the bed and/or surface grain distribution change over time, this method of defining ks is therefore not suitable. When the mixed Wilcock and Crowe sediment transport equation is selected in R2DM, the roughness height is recalculated after the surface distribution is updated according to the following Manning- Strickler formulation:
9090 * DCks (17)
where D90 is the size of the surface material such that 90% is finer and C90 is an order-one dimensionless number. C90 is specified in the “Set Grain Size Distribution” dialogue box in Figure 3.
2.2 The Sediment Options Dialog Box The following boxes are self explanatory and do not require detailed description:
Porosity is the porosity of the sediment (0-1),
D50 is the median grain diameter in metres (required if the Wilcock and Crowe formula is not selected),
Figure 11. Points located along the same streamline used to calculate the local value of rc at the node (x2, y2).
This approach to calculate the local radius of curvature has proven to be numerically stable, can be
applied to irregular and complex river geometries, and does not require a priori assumptions of
streamline geometries.
2.2.6.1 Applying secondary flow correction
1. Calculate the cumulative discharge. Flow>Cumulative Discharge
2. Check the “Apply Secondary Flow Correction” check box
3. Specify a number (~5-10) for Nc
4. Bed Shear Deviation Angle (shown under “Curvature”) and 1/radius can be displayed under
Display>Contour/Colour only during or after a morphodynamic simulation.
5. If 1/radius looks odd then stop the simulation and change the Nc value.
Figure 12 shows the bed shear deviation angle in a typical river.
Figure 12. Bed shear deviation angle in a typical meandering river . When the channel bends towards the right the bed deviation angle is positive. When the channel bends to the left the bed deviation angle is negative
3.0 Running a R2DM simulation The normal steps involved in modeling transient sediment flow with R2DM are as follows:
1. Calibrate the hydrodynamic model for a given flow scenario by adjusting the roughness values (bed values for open water, bed) until model results agree with observed data.
2. Run a model using the steady solver until it reaches steady state. 3. Save the CGD file. 4. Load the CGD file for the initial conditions for the morphological simulation. 5. Specify parameter for the morphological flow simulation in the “Sediment Options” Dialog box
or load a SED file. 6. Select the “Run Morphology” option (it replaces the Run Transient option) under the
“Hydrodynamics” menu item. 7. Select the type and frequency of transient output for the simulation (if any is desired).
All the information pertaining to a morphodynamic simulation are under the “Sediment” menu item.
1. The bottom of the BFC grid follows the bed topography and the top is a flat surface (Figure 21).
2. The top and bottom of the BFC grid follow the bed topography (Figure 22).
The specifications of the grid are input from the .BFC file (Input>read BFC file..) which has the format:
zmax -50 numz 10 xoffset 405000 yoffset 7783000 zmax If this number is positive then zmax is the top elevation of the grid (format 1). If this number is negative then the absolute number represents the height between the top and lower surfaces of the grid (format 2). E.g in the above example the top cell is 50 m higher than the bottom cell. numz is the number of cells in the z direction The PHOENICS program reads in the numbers in scientific format (6E12.6) so if the coordinate system of
your CDG file is in UTM it will be necessary to decrease the numbers by specifying xoffset and yoffset.
For example, if your area is within the region (405001, 7783000) and (405900,7783900) then xoffset=
405000 and yoffset=7783000; and coordinate (405050,7783100) will become (50,100).
After the file is created you will need to edit the numbers using a text editor since C++ creates scientific
number in the format, 5.486534e+005 whereas PHOENICS requires them in the format, 5.486534e+05.
Use a text editor (e.g notepad) to replace e+00 with e+0.
Figure 21. Body fitted coordinate grid with flat upper surface (format 1).
Figure 26. Two corner must be selected to extract a Grid CSV or SHP file. file and the points extracted using the new “Extract points to CSV/SHP File” command.
5.3.2.4 Tecplot Output
Output>Dump TECPLOT file
This feature dumps the variables in Table 2 into an ASCII .dat Tecplot file. Details of the simulation are
6.1 Tutorial 1: Aggradation in a Straight Flume The flume used by Soni et al. (1980) uses a straight flume of length=30m, width = 0.2m with an initial
bed slope of 0.036 and covered by uniform sand with a median diameter of 0.32mm.
1. Launch R2DM. 2. Choose File->Open SONI-STEADY.CGD. 3. Choose Options->Sediment Options. Set the parameters to those shown in Figure 30. 4. Choose Hydrodynamics->Run Morphology. Set present time = 0, Final time = 2400, time step = 0.1. 5. Choose Point Output (.csv file format). To save an excel file of the transient solution at various time
steps: a. select a CSV file containing the coordinates (in this case choose SONI-cords.CSV. b. select box “Bed Elevation” so that you can see the bed changes. c. select an appropriate name and destination folder for the file. d. output the variable data every 100 time steps.
6. When the simulation is complete, open the CSV file and plot the bed height at t=15 minutes and t=40 minutes.
7. Repeat simulation with a different sediment input rate.
Figure 30. Parameters for the Tutorial 1: Aggradation in a Straight Flume.
The flume used by Suryanarayana (1969) uses a straight flume of length=18.29m, width = 0.61m with an
initial bed slope of 0.007 and covered by uniform sand with a median diameter of 0.45mm. Bed
degradation occurs when the upstream sediment supply is shut off.
1. Launch R2DM. 2. Choose File->Open SURY-STEADY.CGD. 3. Choose Options->Sediment Options. Set the parameters to those shown in Figure 32. 4. Make sure that you select “Apply Upstream Sediment Supply” and set Upstream sediment supply =
0 to ensure that there no sediment enters at the inflow. 5. Choose Hydrodynamics->Run Morphology. Set present time = 0, Final time = 36000, time step = 0.1. 6. Choose Point Output (.csv file format). To save an excel file of the transient solution at various time
steps: 7. Select a CSV file containing the coordinates (in this case choose SURY-cords.CSV. 8. Select box “Bed Elevation” so that you can see the bed changes. 9. Select an appropriate name and destination folder for the file. 10. Output the variable data every 100 time steps. 11. When the simulation is complete, open the CSV file and plot the bed height at t=36000s (10 hours). 12. The bed profile is shown in Figure 33.
Figure 32 Parameters used for Suryanarayana (1969) degradation experiment.
Figure 33 Computed bed profile after 10 hours in the flume used by Suryanarayana (1969). Degradation at the inflow is caused by sediment supply shut off.
These aggradation and degradation test cases were reported by Vasquez et al. (2007).
6.3 Tutorial 3: Effects of Up-winding This tutorial illustrates the effects of increasing the up-winding coefficient on a bed form shaped with a
Gaussian distribution.
1. Launch R2DM. 2. Choose File->Open GAUSSIAN-STEADY.CGD. 3. Choose Options->Sediment Options. Set the parameters to those shown in Figure 34. 4. Choose Hydrodynamics->Run Morphology. Set present time = 0, Final time = 1000, time step = 1. 5. Choose Point Output (.csv file format). To save an excel file of the transient solution at various time
steps: 6. Select a CSV file containing the coordinates (in this case choose GAUSSIAN-cords.CSV. 7. Select box “Bed Elevation” so that you can see the bed changes. 8. Select an appropriate name and destination folder for the file. 9. Output the variable data every 200 time steps. 10. When the simulation is complete, open the CSV file and plot the bed height at various time steps. 11. Repeat the simulation with different lower up-winding coefficients. 12. Bed profiles with different up-winding coefficients are shown in Figure 35.
Figure 34. Parameters for Tutorial 3: Effects of Up-winding.
Figure 34 below shows that increasing the up-winding coefficient also increases the stability of moving
6.4 Tutorial 4: Scour and deposition in a Curved Flume This tutorial illustrates the effects of using secondary flow correction. We use the Laboratory of Fluid
Mechanics (LFM) flume which has a 180-degree bend with a radius R = 4.25 m, width b = 1.7 m, water
depth h = 0.20 m and discharge Q = 170 L/s.
1) Launch R2DM. 2) Choose File->Open LFM-STEADY.CGD. 3) Choose Options->Sediment Options. Set the parameters to those shown in Figure 36. 4) Choose Hydrodynamics->Run Morphology. Set present time = 0, Final time = 10800. 5) Choose Output Options. To save a video file of the transient solution: check “Video output”, select
an appropriate name and choose a screen resolution. 6) To save a CGD file at particular time intervals: Check the “cdp output” box, select a prefix for the
filenames, a place to store the outputs and the time interval.
Figure 36. Morphology Output Options Dialog Box
Notice that shear stress distribution shows maximum shear in the entrance to the bend along the inner
bank, while shear stress is minimum along the opposite outside bank.
6.5 Tutorial 5: Mixed Sediment Transport in a Straight Flume This tutorial uses The St Anthony Falls Laboratory flume (SAFL) is a straight flume 50m long, 0.305m
wide and has a slope of 0.002.
1. Launch R2DM. 2. Choose File->Open SAFL-STEADY.CGD. 3. Choose Options->Sediment Options. Set the parameters to those shown in Figure 42. 4. Leave the Wilcock and Crowe parameters at default values. 5. Choose Hydrodynamics->Run Morphology. Set present time = 0, Final time = 60600, max time
step = 1.0. 6. Choose Point Output (.csv file format). To save an excel file of the transient solution at various
time steps: a. select a CSV file containing the coordinates (in this case choose SAFL-50m cords.csv. b. select box “Bed Elevation” so that you can see the bed changes. c. select an appropriate name and destination folder for the file. d. output the variable data every 3600 time steps (every hour if t=1).
7. When the simulation is complete, open the CSV file and plot the bed height at various time steps.
8. Repeat the simulation with a different surface grain distribution. 9. Computed bed profiles are shown in Figure 43.
Figure 42 Parameters used for Tutorial 5: Mixed Sediment Transport in a Straight Flume.
7.0 Advice and Trouble shooting i. Morphodynamic simulations usually demand long CPU times, for large domains a mesh coarser
than normally used for flow simulations is sometimes required. ii. For sand bed rivers, equilibrium upstream boundary condition and the Engelund-Hansen
equation usually provide reasonable results. iii. The test cases shown of aggradation, degradation and bend scour were best modeled without
using upwinding (UW=0) because of its diffusive nature. iv. If spurious migrating bedforms are observed, this may indicate the need for upwinding. v. In areas with very high local velocity sediment will normally go into suspension and will be
carried away by the flow. Since suspension is ignored by R2DM, sediment eroded will immediately deposit downstream where velocity is lower, potentially leading to numerical instabilities.
vi. If the simulation crashes early on, try using a smaller time step. vii. If the simulation still crashes, you may have to change the roughness, ks, in the bed file,
generate a new mesh, and then run a fresh steady state simulation. viii. Do not stop and start a mixed sediment simulation (the Wilcock and Crowe feature) because this
will alter your results. (At the start of a simulation, the surface grain distribution resets to the initial values)
ix. Do not stop and start a sediment simulation with secondary flow because this will alter your results since at the start of a simulation, the radius of curvature is computed.
A.3 Header Information for a fixed bed simulation # C:\Users\Nelly\Desktop\files\8-1-2010 17cms converged.CDG # Date: 6/23/2010 # Time: 15:26:21 # fixed bed simulation
A.4 Header Information for a morphodynamic simulation # C:\Users\Nelly\Desktop\files\8-1-2010 17cms converged.CDG # Date: 6/23/2010 # Time: 16:21:45 # Porosity:, 0.3000 # Upstream Sediment Supply:, 0.0000 # Upwinding Factor:, 0.9000 # Engelund-Hansen Equation used # D50:, 0.0003
A.5 Header Information for a morphodynamic simulation using Wilcock and