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Mitigation of turbidity currents in reservoirs
with passive retention systems: validation of
CFD modeling
4. Initial and Boundary Conditions
The numerical solution of the governing equations was achieved by employing the Finite Volume Method (Figure 2). At the inflow section, a uniform streamwise velocity distribution
and a low level of turbulence intensity I = 0.01 (I=urms/U with urms being the root-mean square of turbulent velocity fluctuations and U the mean velocity) were imposed. At the outlet,
in order to maintain a constant domain water level regardless of the upstream mass flow rate, a mixed boundary condition was attempted, i.e., associated to an orifice at
atmospheric pressure a significant portion of the outlet was prescribed as a no-slip smooth wall. The free surface was modeled as a free slip rigid lid and in the bottom and lateral
walls of the channel, including the obstacle, the no-slip condition with a scalable wall function formulation was introduced. Furthermore, the simulation was initialized with
hydrostatic conditions.
Figure 2 - Mesh detail of the CFD model in the obstacle´s vicinity
Edgar A. C. Ferreira1, Elsa C. T. L. Alves1 and Rui M. L. Ferreira2
1
Hydraulics and Environment Department – LNEC, Portugal (email: [email protected]; [email protected] )
2
CEHIDRO – IST – TULisbon, Portugal (email: [email protected])
1. Introduction
Density or gravity currents are predominantly slender flows that are impelled through density differences, established either by salinity, temperature or
particles in suspension within a fluid [1]. The latter, currents where fine sediments in suspension are accountable for the extra density are titled turbidity
currents. Some of the reported outcomes of these stratified flows in large deep reservoirs comprise, among other consequences, inlet and bottom outlet
structures blockage and storage capacity lessening [2], and, at broader scales, water quality and biodiversity degradation [3]. In virtue of multiple water
bodies stressors (e.g. climate change, increasing population, among others), the loss of storage in reservoirs caused by turbidity currents is currently a
topic of forceful scientific research ([4], [5], among others). In this context, the use of Computational Fluid Dynamics (CFD) tools as an appliance of
water bodies monitoring programs is undoubtedly of foremost importance.
The main objective of this study is to validate a CFD code (ANSYS-CFX) applied to the simulation of the interaction between turbidity currents and
passive retention systems, designed to induce sediment deposition. To accomplish the proposed objective, laboratory tests were initially conducted
using a straightforward obstacle configuration exposed to the passageway of a turbidity current. Afterwards, the experimental data was used to build a
benchmark case to validate the 3D CFD software ANSYS-CFX.
5. Results
The spatio-temporal turbidity current evolution is shown in Figure 3. In regards to the adequacy of the ASM approach, experimental and numerical results were likened (Figures 4 and
5).
2. Experimental Facilities and Instrumentation
Figure 3 - ASM model results at time t = 17 s (left), 53 s (center) and 200 s (right)
The experiments were performed at LNEC in a 16.45m long, 0.30m wide and 0.75m maximum height flume with its bottom devised to simulate
hyperpycnal turbidity currents in reservoirs. During the experiments, longitudinal velocities were measured in five control sections with an Ultrasound
Velocity Profiling (UVP) system and suspended sediment concentration profiles were collected at two control sections using syphon probes (Figure 1).
The experimental conditions for the present study case are summarized in Table 1.
hobst
[mm]
d50
[m]
Cs0
[%]
U0
[mm/s]
Hwat
[cm]
200
0.00002
0.59
Figure 4 - Non-dimensional time-averaged streamwise velocities, where Z denotes vertical coordinates, X is the distance to domain´s downstream section and
Z0.5 is an outer length scale defined as the height at which the time-averaged velocity 𝐔 is equal to half the maximum time-averaged velocity 𝐔 max
64.81
53.77
Table 1 - Experimental conditions (hobst refers to the obstacle height, d50 to the
medium value of particles diameter, Cs0 to the initial sediments concentration,
U0 to inlet velocity and Hwat to the initial ambient fluid height). The downstream
side of the barrier is located 8.25 meters from the domain final section.
Figure 1 - Flow evolution of the turbidity current at inlet (top left) and outlet
(top right) and the sampling system below
3.The Algebraic Slip Model (ASM) – Theoretical Background
The numerical simulation of the turbidity current evolution was carried out using the ASM approach [6]. The ASM is a single-phase multi-component
simplified model which basically comprehends a mixture conservation equation,
𝜕𝜌𝑚
+ 𝛻 ∙ 𝜌𝑚 𝒖𝑚 = 0
𝜕𝑡
a momentum equation,
𝜕𝜌𝑚 𝒖𝑚
𝜕𝑡
+ 𝛻 ∙ 𝜌𝑚 𝒖𝑚 ⊗ 𝒖𝑚 = −𝛻𝑝 + 𝛻 ∙ 𝝉𝑚 + 𝜌𝑚 𝒈
and, additionally, a solids mass conservation equation
where: 𝜌𝑚 = mixture density, 𝑡 = time, 𝒖𝑚
𝜇𝑓𝑡
𝜕𝜌𝑚 𝑌𝑝
+ 𝛻 ∙ 𝜌𝑚 𝑌𝑝 𝒖𝑚 + 𝒖𝑑𝑟𝑖𝑓𝑡,𝑝 − 𝜇 +
𝛻𝑌𝑝 = 0
𝜕𝑡
𝜎𝑝
= mixture velocity vector, 𝑝 = pressure, 𝝉𝑚 = stress tensor, 𝒈 = gravity acceleration vector, 𝑌𝑝 = sediments
mass fraction, 𝒖𝑑𝑟𝑖𝑓𝑡,𝑝 = drift velocity, 𝜇 = dynamic viscosity (8.899 × 10−4 𝑘𝑔 𝑚−1 𝑠 −1 ), 𝜇𝑓𝑡 = eddy viscosity and 𝜎𝑝 = Turbulent Schmidt number.
Closure for the Reynolds stress tensor was computed through the Boussinesq assumption whilst closure for the Reynolds flux vector was calculated via
the flux-gradient hypothesis [7]. In this work, one made use of a buoyancy modified ƙ-ε two-equation model (where ƙ represents the turbulent kinetic
energy and ε denotes the dissipation rate of ƙ) [6]. With the exception of buoyancy turbulence terms, modeling constants were adopted from Launder
and Sharma (1974) proposal [8]. Buoyancy terms incorporated in ƙ and ε equations were estimated, respectively by
𝑃ƙb = −
𝜇𝑓𝑡
𝜌𝑚 𝜎𝑝
𝑔 ∙ 𝛻𝜌𝑚
𝑃εb = 𝐶3 ∙ max(0, 𝑃ƙb )
In what concerns 𝜎𝑝 and the dissipation coefficient 𝐶3 no universality is foreseeable. Quite on the contrary, several authors have concluded from
empirical evidence that, on the one hand, the eddy viscosity and diffusivity and hence the turbulent Schmidt number is related to the level of
stratification and, on the other hand, buoyancy effects in the ε equation can have, for particular cases, an irrelevant role in the turbulence dynamics.
Following the studies of [9] and [10], in this work it has been assumed 𝜎𝑝 = 1.3 and 𝐶3 = 0.
Figure 5 - Variation of suspended sediment concentration with water depth.
Experimental profiles were obtained during a brief sampling period whilst
the numerical ones were acquired at t = 216 s (x = 5.75 m) and at t = 186 s
(x=10.25m)
6. Conclusions
In this work ASM fulfillment for modeling turbidity currents was assessed. Apart its demanding computational requirements and even though the numerical solution represents a
fairly reasonable prediction of the observed flow, results reveal, at the present stage, its inadequacy to describe a number of aspects: i) the velocity maximum is under-predicted; ii)
a sharp difference is observed at the near wall region and iii) a significant discrepancy between experimental and numerical suspended sediment concentration outcomes is verified
downstream the obstacle. Issues i) and ii) may be due to a variety of factors, namely the grid density and the goodness of the choice of the turbulence model and its parameters,
and issue iii) to the overprediction of sediment deposition upstream the obstacle. In the near future, the impact of these uncertainties will be investigated by means of a systematic
sensitivity analysis.
References
[1] Simpson, J. E (1999). Gravity Currents: In the Environment and the Laboratory. Cambridge University Press.
[2] Oehy, C. D., Schleiss, A. J. (2007). Control of turbidity currents in reservoirs by solid and permeable obstacles. Journal of Hydraulic Engineering, 133(6), 637-648.
[3] Chung, S.W., Hipsey, M.R., Imberger, J. (2009). Modeling the propagation of turbid density inflows into a stratified lake: Daecheong Reservoir, Korea. Environmental Modelling and Software,
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[6] Ansys, CFX-Solver Theory Guide (2009).
[7] W. Rodi (1993). "Turbulence models and their application in hydraulics - a state of the art review", International Association for Hydraulic Research, Delft, 3rd edition 1993, Balkema.
[8] B. Launder, B. Sharma (1974). Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc, Letters in Heat Mass Transfer, 1, 131–
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Acknowledgements
This study was funded by the Portuguese Foundation for Science and Technology through the project PTDC/ECM/099485/2008. The first author thanks the assistance of Professor Moitinho from
ICIST, to all members of the project PTDC/ECM/099485/2008 and to the Fluvial Hydraulics group of CEHIDRO.