International Journal of Sediment Rearch, Vol. 25, No. 4, 2010, pp. 431–440 - 431 -
International Journal of Sediment Rearch 25 (2010) 431-440
Three dimensional hydrodynamic modeling over bed forms in open channels
K. EL KHEIASHY 1, J. MCCORQUODALE 2, I. GEORGIOU 3, and E. MESELHE 4
Abstract
Three dimensional numerical modeling of idealized sand dunes was ud to asss the capability of
various modeling formulations to capture the flow structure and resistance introduced by bed forms
which are similar to tho in the Lower Mississippi River. The lected models were: ECOMSED
(HydroQual), MIKE 3 [Danish Hydraulic Institute (DHI)] and H3D (Hayco). The study revealed that比肩同行
the hydrostatic versions of models did not capture the flow paration at the crest of the dunes;
however, they did respond to the prence of bed forms and gave a total resistance similar to the non-
hydrostatic models.
Key Words: Bed forms, Alluvial rivers, Three dimensional models, Mississippi river
1 Introduction
泥鳅挂面
The geometry of alluvial rivers is influenced largely by the discharge and diment load. There have been veral attempts from scientists and river engineers to understand this complex relationship between river morphology and hydrodynamics and diment transport. Bed form regime maps have been created in an attempt to capture this inter-relationship (Simons and Richardson, 1966). Bed forms have been classified as lower-flow or upper-flow regimes which roughly correspond to subcritical or supercritical flows respectively (Kennedy, 1963). The bed forms in the Lower Mississippi are in the lower-flow regime which is compod of ripples, dunes, washed out dunes and/or transition dunes.
Laboratory experiments have shown that lower regime bed forms exhibit flow paration at the crest where a negative pressure gradient is exhibited (Kennedy, 1963). Balachandar et al. (2007) performed Lar Doppler Velocimeter (LDV) measurements on the surface of two-dimensional dunes to study the effect of water depth on the flow field. His LDV results confirmed the flow paration phenomenon with a peak in the turbulence and shear stress at a distance equal to 20 %
of the local depth measured from the bed. The form drag associated with flow paration is a major component of the total resistance (Haque, 1988). The form drag increas as the bed forms progress from flat bed to dunes but subquently decreas as the dunes are washed out at higher discharges. Other factors that affect the resistance include the energy expended to transport the bed material load, and the effect of bed load concentration on the boundary shear (Einstein and Chien, 1954).
The purpo of this study is to test the applicability of 3-D hydrostatic models to simulate large alluvial rivers. To accomplish this, three commonly ud 3-D models were applied to idealized sand dunes 1 Principal Engineer, Project Manager, Kellogg Brown and Root Inc. (KBR), 4100 Clinton Drive 03-1130, Houston, TX 77020, USA, E-mail:karim. 2 Prof., Civil and Environmental Engineering Department, University of New Orleans, New Orleans, LA 70148, USA, E-mail:jmccorqu@uno.edu 3 Assis. Prof., Earth and Environmental Sciences Department, University of New Orleans, New Orleans, LA 70148, USA, E-mail:igeorgiou@uno.edu 4 Prof., Civil Engineering Department, University of Louisiana at Lafayette, Lafayette, LA 70504,USA,
E-mail:melhe@louisiana.edu
Note: The original manuscript of this paper was received in Aug. 2009. The revid version was received in July
2010. Discussion open until Dec. 2011.
created from the bathymetry of a lected reach of the Lower Mississippi River. The U.S. Army Corps of Engineers had completed multi-beam bathymetric surveys and Acoustic Doppler Current Profiler (ADCP) studies of this reach from June 2003 to August 2003. The lected models were: ECOMSED (Estuarine and Coastal Ocean Model, HydroQual, Inc., 2002), MIKE 3 (Danish Hydraulic Institute, DHI, 2005) and H3D (Hayco Limited, Stronach et al., 1993). MIKE 3 and H3D are proprietary models which have hydrostatic and non-hydrostatic options. ECOMSED, which was derived from the Princeton Ocean Model (POM), is a public domain model with only a hydrostatic formulation.
2 Study approach
To answer the questions of the applicability of commonly ud 3-D surface water computational fluid dynamics (CFD) models to the simulation of flow in a large alluvial river, the following capabilities were investigated:
1. Ability to simulate the velocity field over bed forms which was assd by comparing the modeled velocities to the experimental data of Nelson et al. (1993).
2. Ability to simulate flow characteristics at the field scale:
a. Does the model capture the bed-water surface pha relationships for dunes?
b. Does the model adequately simulate the resistance due to bed forms?
The following models were lected becau of their common application in 3D modeling of coastal, riverine and estuarine environments:
Hydrostatic: ECOMSED; MIKE 3 and H3D
Hydrostatic and non-Hydrostatic: MIKE 3 and H3D
ECOMSED (HydroQual, Inc., 2002), is a public domain finite volume hydrostatic and diment transport model which computes water circulation, temperature, salinity, mixing and transport, deposition and resuspension of cohesive and non-cohesive diments. The Mellor-Yamada turbulence closure model (Mellor and Yamada, 1982) is ud for vertical mixing and the Smagorinsky formulation (Smagorinsky 1963) for the horizontal mixing. It is bad on the Princeton Ocean Model by Blumberg and Mellor (1987). ECOMSED utilizes a horizontal, orthogonal curvilinear coordinates system and sigma coordinates in the vertical.
MIKE 3 (DHI, 2005) is a proprietary three dimensional, baroclinic hydrostatic and non-hydrostatic modeling system that simulates unsteady 3D flows. MIKE 3 solves the time dependent non-linear equations of continuity and conrvation of momentum in three dimensions using finite difference techniques on Cartesian coordinates, and employs a uniform z-level discretization in the vertical. Several turbulence models are available to characterize the eddy viscosity (Smagorinsky model, k model, k-εmodel, mixed Smagorinsky / k-ε model and a constant eddy viscosity model). The non-hydrostatic version of MIKE 3 utilizes the artificial compressibility approach.
H3D (Stronach et al., 1993), is a proprietary finite difference hydrostatic and non-hydrostatic numerical model that solves the three-dimensional Reynolds averaged Navier-Stokes equation on ei
ther a Cartesian or an orthogonal curvilinear grid with a variable z-level discretization in the vertical. The Volume of Fluid (VOF) method is ud to fit the free surface and the bathymetry. H3D is bad on models described in Backhaus (1985) and Stronach et al. (1993). H3D us a shear-dependent turbulence formulation in the horizontal, (Smagorinsky, 1963) and a shear- and stratification-dependent formulation in the vertical for momentum transfer referred to as the Mellor-Yamada Level 2 scheme (Mellor and Yamada, 1982). The non-hydrostatic version utilizes the pressure correction method.
3 Governing equations and approximations
The governing three dimensional primitive variable equations describing the free surface flows are the RANS equations and are derived from the Navier-Stokes equations after Reynolds averaging (Pedlosky, 1979). In general, the pressure is given by,
p = ρ g (h-z) + N HP (1) where N HP(x, y, z, t) is the non-hydrostatic pressure; z is the vertical coordinate and h is the water surface elevation. The hydrostatic approximation becomes increasingly inaccurate as the curvature of the flow paths increas. Several numerical models have been developed that solve for the non-hydrostatic pressure either by
correcting the pressure term by solving a Poisson equation for the pressure (Casulli, - 432 - International Journal of Sediment Rearch, Vol. 25, No. 4, 2010, pp. 431–440
International Journal of Sediment Rearch, Vol. 25, No. 4, 2010, pp. 431–440 - 433 - 1998) or by utilizing the artificial compressibility approach where the time derivative of the density in the mass conrvation equation is replaced with the pressure term in the equation of state (Chorin, 1967).
4 Study methodology
For the lected model, the following evaluation procedures were conducted:
Laboratory validation: Flow pattern at dunes which was assd by comparing the modeled velocities to the experimental data of Nelson et al. (1993). A numerical model grid was tup for the laboratory scale bed forms in the physical model prented in Nelson et al. (1993) (Fig. 1). The non-hydrostatic H3D, non-hydrostatic MIKE 3 and hydrostatic ECOMSED were tested; however, MIKE 3 was unstable for the laboratory scale dunes. The details of the dunes, grids, time steps, turbulence closure models, and bed roughness for each application are shown in Table 1. The pha relationsh
ip between surface and bed waves was assd by modeling idealized dunes and comparing the results to energy bad computations, in addition to qualitative information in the literature.
Fig. 1 Definition of dune geometry and flow Table 1 Parameters for modeling laboratory dunes (Fig. 1)
ECOMSED hydrostatic H3D non-hydrostatic Max depth (D) m 0.20 0.20
Dune height (H d ) m 0.04 0.04
Dune wave length (λd ) m
0.825 0.825 Lee length (x p ) m 0.20 0.20
Lee slope 0.20 0.20
Mean velocity m/s 0.50 0.50
Horizontal grid 0.01 m × 0.01 m 0.01 m × 0.01 m变成萌妹子
Vertical grid 20 sigma layers: non-uniformly distributed from: 0.0025m at bed to 0.0175m at surface.
24 levels distributed uniformly over the depth. Time step Δt conds
0.0001 0.0001 Horizontal turbulence model Smagorinsky formulation Smagorinsky formulation Vertical turbulence model Mellor-Yamada, level 2.5 scheme Mellor-Yamada level 2 scheme Bottom roughness (Z o ) mm 3 3
Field scale application: Bed resistance was assd by modeling a grain roughened flat and a bed with idealized bed forms that is reprentative of the Lower Mississippi River. All models were tested with the parameters and dunes shown in Table 2. The model water free surface and kinetic energy heads were converted mean energy slopes to estimate Manning’s n values which were compared wi
th typical Lower Mississippi River n (0.024 to 0.035). The out of pha water level was compared with the energy bad reference difference. For this test ca, the bathymetry of the bed forms was created using information obtained from the spectral analysis of bathymetric data prented in Kheiashy et al. (2007). Bed form wave length (λd = 30 m) and height (H d = 3 m) were ud to create a one dimensional (laterally averaged) profile of bed forms. The bathymetry file contains a ries of five identical bed forms (5 × 30m = 150 m) with a width of 10 m.
The MIKE 3 model ud the velocity profile directly as a boundary condition; ECOMSED ud defined the discharge per sigma layer and cell; H3D us a uniform discharge as its boundary condition which
- 434 - International Journal of Sediment Rearch, Vol. 25, No. 4, 2010, pp. 431–440
may account for a different initial shear stress. For consistency, it was tested and confirmed that all boundary conditions gave the same total discharge near the upstream boundary. The logarithmic velocity profile bad on an enmble average of ADCP measurements from the Mississippi River (collected by the U.S. Army Corps of Engineers around the same time period that the multi-beam data were collected, June 2003 to September 2003) was applied at the upstream boundary.
For consistency, a constant water level was impod at the downstream side for all the models. Full slip assumption at the side walls was ud in all of the models.
Table 2 Parameters for modeling field-scale dunes
玩扑克牌
ECOMSED hydrostatic MIKE 3 non-hydrostatic H3D non-hydrostatic Max depth (D) m
Downstream Boundary
10 10 10 Dune height (H d ) m 3 3 3 Dune wave length (λd ) m
30 30 30 Lee length (x p ) m
9 9 9 Lee slope
0.3 0.3 0.3 Mean velocity m/s
0.75 0.75 0.75 Upstream boundary
Log distributed flow Log distributed velocity Uniform velocity Horizontal grid
0.5 m × 0.5 m 0.5 m × 0.5 m 0.5 m × 0.5 m Vertical grid
piano的复数形式
20 sigma layers distributed non-uniformly 40 levels with constant spacing of 0.25 m 40 levels with constant spacing of 0.25 m Time step
0.005 c 0.005 c 0.01 c Horizontal turbulence
model
Smagorinsky formulation Smagorinsky formulation Smagorinsky formulation Vertical turbulence
model
Mellor-Yamada level 2.5 scheme k-ε turbulence model Mellor-Yamada level 2 scheme Model roughness m Bottom roughness
height: 0.003 Bottom roughness height: 0.003 Bottom roughness height: 0.003
5 Model results
Model evaluation by comparison the flow over a laboratory scale dune: The predicted velocity profiles by ECOMSED and H3D are shown in Figs. 2 and 3. Figure 2 indicates that the logarithmic pr
ofile prented by the Nelson et al. (1993) for the adver slope of the dune is captured by both models. The extent of the paration (where the paration length is defined as the distance downstream of the crest of the dune where flow reversal occurs) is better simulated by the non-hydrostatic H3D compared to the hydrostatic ECOMSED; however, H3D significantly over-predicted the paration length obrved by Nelson et al. (1993) while ECOMSED under-estimated the paration length. MIKE3 was computationally unstable at the length scale of the physical model; therefore no results are prented from this test. Table 2 compares the magnitude of the out-of-pha surface wave height (δ12) relative to the mean Hydraulic Grade Line (HGL) predicted by the numerical models with the nominal difference in kinetic energy between the crest and the trough:
Δh reference ≈ ⎥⎥⎦⎤⎢⎢⎣
⎡⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛21222112d d g q (2) where d 1 = (D + H d /2) and d 2 = (D - H d /2) are the depths at points 1 and 2 respectively; D is the mean depth and q is the flow per unit width (Fig. 1). H3D predicted a weaker out of pha relationship than ECOMSED. A possible reason for this is the stair-stepping effect resulting from H3D application of the volume of fluid method at the lower most computational cell and the over-estimation of the leeside wake. ECOMSED on the other hand, may have over-predicted the out-of-pha relationship
due to the curvature of the sigma coordinates near the dunes. The results for the laboratory scale dunes tests are summarized Table 3.
裘皮服装
International Journal of Sediment Rearch, Vol. 25, No. 4, 2010, pp. 431–440 - 435 -
Fig. 2 Laboratory-scale simulated laterally averaged velocity profiles
高尔夫球多大
桐生祥秀
Fig. 3 Laboratory-scale simulated stream-wi velocity vectors
