TELEMAC - Chezy c is really Chezy C

Well, I finally figured it out, TELEMAC uses the dimensional version of the Chezy friction factor.

C = c (g)^1/2

Now my calibration for normal flow is going much smoother.

1-D Modelling - Sanity Check

Been having problems trying to calibrate the TELEMAC models, both the flat and dune geometry to achieve normal flow depth. The models appear to become unstable as they approach the normal depth.  I checked that it was not a problem with the new princi.f file that I developed last week (basically ran the hotstart for a long time - still crashed).

I decided to do a quick 1-D model for comparison and as a sanity check. I know that for my model - Bed Slope = 1/600, D=1mm, Q=0.0455 cms and w=0.76m, I should get a normal depth of around 9.5cm using the Chezy equation. I set up a model in HEC-RAS to verify that I should be getting 9.5cm as my normal depth. In short - yes - after a couple of runs (adjusting mannings n against my Chezy c - which has to be done iteratively) the final normal depth was 10cm. (Note I do not think that HEC-RAS reports the depth any finer than the nearest cm). The plot is shown below. There are several profiles - the normal profile is the lowest set of lines (Profile 4).

The tabular results for the normal flow are shown below.

Schematic of Flow Over a Dune

This is from Best (2005), a great schematic of fluid flow over a dune.

Best, J. (2005). The fluid dynamics of river dunes: A review and some future research directions. Journal of Geophysical Research, 110(F4), 1-21. doi: 10.1029/2004JF000218.

1.  A region of flow separation is formed in the lee of the dune, with reattachment occurring approximately 4–6 dune heights down- stream of the crest. 
2. A shear layer is generated bounding the separation zone, which divides this recirculating flow from the free stream fluid above; large-scale turbulence is generated in the form of Kelvin-Helmholtz instabilities along this shear layer, and as the free shear expands, it creates a wake zone that grows and dissipates downstream. A third region is one of expanding flow in the dune leeside. 
3. Downstream of the region of reattachment, a new internal boundary layer grows as flow reestablishes itself and develops a more logarithmic velocity profile. 
4. Maximum horizontal velocity occurs over the dune crest and bed shear stresses here may be sufficient to generate upper stage plane bed conditions: the exact nature of flow here will determine the rate and periodicity of sediment supply to the dune leeside and hence the nature of sediment sorting in the deposits of the leeside.

Programming the Initial Conditions in Telemac

The current project that I am working in involves looking at the vertical velocity profiles along a dune. By default Telemac3D creates equally spaced vertical layers from your model. This is not really desirable as  one generally wants a greater density of vertical layers near the bottom where the velocity profile changes rapidly and fewer near the free surface to save computational time. Telemac3D does allow you to specify the vertical profiles however you must do so programmatically - by creating a princi.f file and writing your own CONDMIN subroutine to initialize the initial conditions. After playing around with this I found a good example of the princi.f file with the examples and was able to modify it as required.

TELEMAC 3D uses a sigma transformation for the z or vertical access which means that at each point on the mesh z* = z/Zmax. This means that we specify our height from the bottom using values between 0 and 1.

!-----------------------------------------------------------------------
!
!     INITIALISATION OF ZSTAR, VERTICAL COORDINATE
!     IN SIGMA TRANSFORMATION
!
!     CASE WITHOUT REFERENCE PLANE
!     ----------------------------
!
!         ONE MUST HAVE :
!
!            * ZSTAR%R(1)     = 0.D0 ( BOTTOM PLANE )
!            * ZSTAR%R(NPLAN) = 1.D0 ( FREE SURFACE PLANE )
!
!         AND FOR ALL I BETWEEN 1 AND NPLAN-1
!
!            * ZSTAR%R(I) < ZSTAR%R(I+1)
!
!     CASE WITH REFERENCE PLANE
!     -------------------------
!
!         ONE MUST HAVE :
!
!            * ZSTAR%R(1)      = -1.D0 ( BOTTOM PLANE )
!            * ZSTAR%R(NPLINT) =  0.D0 ( REFERENCE PLANE )
!            * ZSTAR%R(NPLAN)  =  1.D0 ( FREE SURFACE PLANE )
!
!         AND FOR ALL I BETWEEN 1 AND NPLAN-1
!
!            * ZSTAR%R(I) < ZSTAR%R(I+1)
!
!     STANDARD IS: EVENLY SPACED PLANES
!
!     IF NO REFERENCE PLANE : NPLINT = 1
!
!     TRANSF IS KEY-WORD "MESH TRANSFORMATION"


 WRITE(lu,*) 'TRANSF IS KEY-WORD "MESH TRANSFORMATION"'
!
      IF(TRANSF.EQ.2) THEN
        WRITE(LU,*)
        IF(LNG.EQ.1) THEN
          WRITE(LU,*) 'AVEC TRANSFORMATION DU MAILLAGE = 2'
          WRITE(LU,*) 'DONNER DANS CONDIM LES VALEURS DE ZSTAR'
        ENDIF
        IF(LNG.EQ.2) THEN
          WRITE(LU,*) 'WITH MESH TRANSFORMATION = 2'
          WRITE(LU,*) 'GIVE THE VALUES OF ZSTAR IN CONDIM'
        ENDIF
        WRITE(LU,*)
!       CALL PLANTE(1)
!        STOP
!       EXAMPLE WITH 3 PLANES     
        ZSTAR%R(1)=0.D0
        ZSTAR%R(2)=0.01D0
        ZSTAR%R(3)=0.03D0 
        ZSTAR%R(4)=0.05D0
        ZSTAR%R(5)=0.07D0
        ZSTAR%R(6)=0.09D0
        ZSTAR%R(7)=0.11D0
        ZSTAR%R(8)=0.13D0 
        ZSTAR%R(9)=0.15D0
        ZSTAR%R(10)=0.25D0
        ZSTAR%R(11)=0.368D0
        ZSTAR%R(12)=0.5D0
        ZSTAR%R(13)=0.75D0
        ZSTAR%R(14)=1.D0
      ELSEIF(TRANSF.EQ.3) THEN
        IF(NPLINT.GE.2) THEN
          DO IPLAN = 1,NPLINT-1
            ZSTAR%R(IPLAN) = DBLE(IPLAN-NPLINT)/DBLE(NPLINT-1)
          ENDDO
        ENDIF
        DO IPLAN = NPLINT,NPLAN
          ZSTAR%R(IPLAN) = DBLE(IPLAN-NPLINT)/DBLE(NPLAN-NPLINT)
        ENDDO
      ELSEIF(TRANSF.EQ.4) THEN
        WRITE(LU,*)
        IF(LNG.EQ.1) THEN
          WRITE(LU,*) 'AVEC TRANSFORMATION DU MAILLAGE = 4'
          WRITE(LU,*) 'DONNER DANS CONDIM LES VALEURS DE ZSTAR'
          WRITE(LU,*) 'COTES REELLES SOOUHAITEES DES PLANS'
        ENDIF
        IF(LNG.EQ.2) THEN
          WRITE(LU,*) 'WITH MESH TRANSFORMATION = 4'
          WRITE(LU,*) 'GIVE THE VALUES OF ZSTAR IN CONDIM'
          WRITE(LU,*) 'REAL ELEVATION OF PLANES'
        ENDIF
        WRITE(LU,*)
        CALL PLANTE(1)
        STOP
!        EXAMPLE WITH 4 PLANES        
!        ZSTAR%R(1)=-10.D0
!        ZSTAR%R(2)=-9.D0
!        ZSTAR%R(3)=-8.D0
!        ZSTAR%R(4)=-7.D0
      ELSE
!       SIGMA TRANSFORMATION AND OTHER CASES
        DO IPLAN = 1,NPLAN
          ZSTAR%R(IPLAN) = DBLE(IPLAN-1)/DBLE(NPLAN-1)
        ENDDO
      ENDIF

Extracting a Profile From Blue Kenue

It is fairly easy to extract profiles along a line from Blue Kenue. For example, while setting up my flume models I needed to check the water depth to ensure that the flow was uniform along the length of the domain. First thing I did was digitize a line where I wanted to extract the profile. Once completed, I right-click the line in the Workspace menu and select Resample. Resampling will add verticies along the line, where the values will be extracted from the surface you are profiling. For my case I selected 10cm. This creates a new line subset.

As I was interested in checking the flow depth, I generated an average depth from the water depth profile. This was done by selecting the water depth in the Workspace menu, selecting Tools/ExtractSurface/Temporal Means.

Once you have prepared your surface, select the resampled line and select Tools/Map Object and select the surface you are interested. This will generate a 3D Line Set which can be plotted in Blue Kenue or saved and opened in Excel.

Meeting Notes

Based on the initial modelling of the A3DOWN bed forms in Telemac 2D and 3D, I am going to start again using a much more controlled approach. First I will create a flat bed with a small slope and try to get uniform flow. Next I will create a set of periodic dunes, taking the best dune from the A3DOWN and repeating it approximately 12 times with the same slope as my previous flat bed experiment. Both these will be run in Telemac 2d and 3d.

Issues to Resolve and Actions

• Vertical layers in Telemac 3D - is it possible to change the distribution of the vertical layers so that the mesh is finer near the bed surface.
• Extraction of vertical/longitudinal  profiles- will need to find a nice way to extract from Blue Kenue and plot in either EXCEL or R. 
• Read up on papers for people doing similar work.

Telemac Modelling Notes

This weekend I worked with the 2D Flume models and explored using the different turbulence models (see pg 39 in Telemac manual for explanation). These models all use the hotstart (cas_hotstat.txt) result and run for 2 minutes.

• cas_flume_default.txt – no turbulence model specified
• cas_flume2_turb-1.txt – constant viscosity model specified
• cas_flume2_turb-2.txt – Elder model
• cas_flume2_turb-3-k-e.txt – K-Epsilon Model

Did not focus on the Elder model and the model did not run correctly. Was trying to determine the difference between the default (no turbulence set) and the constant viscosity model. I assume that these should be the same.

Was able to extract the shear velocity and the bed shear using Telemac and Blue Kenue. The shear velocity can be output by telemac using the variable, US.:
VARIABLES FOR GRAPHIC PRINTOUTS ='U,V,H,S,B,US'

From that you can calculate the bed shear in Blue Kenue using the calculator.:
1000 * A^2

Parameters for 1mm grain:

Material Number: 25.296
Ycr: 0.037
v*cr: 0.024 m/s
tcr: 0.598 N/m2

Literature Review Notes - 2004

Short Description of Turbulence Modelling. If I have this right, Boussinesq hypothesis uses the turbulent eddy viscosity (v _t)whereby the molecular viscosity for laminar flows is replaced by the v _t. Prandtl introduced the additional concept of the mixing length and boundary layer. Then we get into the more complex models k-e, Smagorinsky etc.

Relevant paper to current research.

Lane, S. N., Hardy, R. J., Elliott, L., & Ingham, D. B. (2002). High-resolution numerical modelling of three-dimensional flows over complex river bed topography. Hydrological Processes, 16(11), 2261-2272. doi: 10.1002/hyp.5034.

Excellent description on the issues with trying to model dynamic bed forms. They use a porosity model to model the bed forms.

Another significant paper – describing the development of a 1-D hydrodynamic model using the complete momentum equation:

Cao, Z., Pender, G., Wallis, S., & Carling, P. (2004). Computational Dam-Break Hydraulics over Erodible Sediment Bed. Journal of Hydraulic Engineering, 130(7), 689. doi: 10.1061/(ASCE)0733-9429(2004)130:7(689).

In the context of computational study of dam-break hydraulics,several basic observations are warranted. First, it is recognized that the flow, sediment transport, and morphological evolution can be strongly coupled to each other, the rate of bed deformation being considerable compared to that of flow evolution. Therefore a coupled modeling strategy with the use of the complete conser- vation equations and synchronous solution procedure is essential, in contrast to decoupled modeling using an asynchronous solution of simplified conservation equations (Cao et al. 2002). In this connection, the models of Ferreira and Leal (1998) and Yang and Greimann (1999) are problematic because of the simplified con- servation equations used.

Dam-break flows over mobile beds can provoke very active sediment exchange between the water column and the bed, and also produce a sharp spatial gradient of concentration, which must be incorporated in the momentum equation. Otherwise significant errors result (Fig. 11), in contrast to Brufau et al. (2000) for debris flows. Previous models for dam-break problems can be improved by using the complete, instead of simplified, momentum equations (e.g.,CADAM 1998, 1999a,b).

Literature Review Notes 2002-2004

Literature Review Notes

This morning spent time reading through articles from between 1999 to 2002 and two really stuck out:

citation FRACCAROLLO, L., & CAPART, H. (2002). Riemann wave description of erosional dam-break flows. Journal of Fluid Mechanics, 461. doi: 10.1017/S0022112002008455.

??citation??Cao, Z., Pender, G., Wallis, S., & Carling, P. (2004). Computational Dam-Break Hydraulics over Erodible Sediment Bed. Journal of Hydraulic Engineering, 130(7), 689. doi: 10.1061/(ASCE)0733-9429(2004)130:7(689).

Fraccarollo and Capart is interesting as they performed a number of physical model runs using different densities of sediment. These runs show quite clearly the debris type flow occurring at the nose of the wave, followed by “clear water”.

Cao et al in particular had a number of very interesting observations regarding dam break flows over mobile beds relevant to both modelling the flows and the need to account for the impacts of the bed for emergency response purposes:

The mobile bed can be significantly scoured; the dimensions of the scour hole are of similar order of magnitude to those of the flow itself Figs. 2 and 12 a. Therefore the rate of bed deformation is not negligible compared to that of flow change, characterizing the need for coupled modeling of the strongly interacting flow-sediment-morphology system as asserted by Cao et al. (2002). Previous models need to be reformulated if refined results are to be sought (e.g., CADAM 1998, 1999a,b)

Dam-break flows over mobile beds can provoke very active sediment exchange between the water column and the bed, and also produce a sharp spatial gradient of concentration, which must be incorporated in the momentum equation. Otherwise significant errors result Fig. 11, in contrast to Brufau et al. 2000 for debris flows. Previous models for dam-break prob- lems can be improved by using the complete, instead of sim- plified, momentum equations e.g., CADAM 1998, 1999a,b.

'It is also found that the free surface profiles and hydrographs are greatly modified by bed mobility, which has considerable implications for flood prediction.'

Also read through:

??citation??Chauhan, S. S., Bowles, D. S., & Anderson, L. R. (2004). Do current breach parameter estimation techniques provide reasonable estimates for use in breach modeling? 2004 Annual conf assoc of state dam safety officials, Phoenix, AZ, USA. Citeseer. Retrieved May 7, 2011, from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.935&amp;rep=rep1&amp;type=pdf.

Which states the need for improved physical models for breach flow estimation and comments on some of the common production-type models (BREACH, MIKE11) in used for predicting breach hydrographs for embankment type dams.