3D SPH Simulation of Dynamic Water Surface and Its Interaction with Underlying Flow Structure for Turbulent Open Channel Flows Over Rough Beds
Summary (4 min read)
- In this study a fully 3D numerical model based on the Smoothed Particle Hydrodynamics (SPH) approach has been developed to simulate turbulent open channel flows over a fixed rough bed.
- The comparison has demonstrated that the proposed 3D SPH model can simulate well the complex free surface flows over a fixed rough bed.
- Savelsberg and Van de Water  reported that although there are several appealing relations between subsurface flow field and water surface gradient, the water surface of fully developed turbulent flow exhibits a dynamic behaviour of its own.
- This feature is implemented to recognize the free surface parti l s. Lee et al.  and Farhadi et al.  suggested that a threshold criterion rangig from 1.2 to 1.5 can be used to determine which particles belong to the water surface.
3.1 SPHysics code
- //www.sphysics.org) is a free open-source SPH code that was released in 2007 and developed jointly by researchers at the Johns Hopkins University (U.S.A.), the University of Vigo , the University of Manchester (U.K.) and the University of Roma La Sapienza, also known as SPHysics code (http.
- It is programmed in the FORTRAN language, and has been developed specifically for free surface hydrodynamics [Gómez-Gesteira et al., 2012].
- In SPHysics, four different time integration schemes are implemented, i.e. the PredictorCorrector, Verlet algorithm, Symplectic algorithm and Beeman algorithm.
- One is called the Shepard filter and the other is the Moving Least Squares (MLS) filter.
- The dynamic wall particle treatment is advantageous mainly because of its computational simplicity, since the wall particles are computed inside the same loop as the fluid particles, and thus the computational time is reduced.
3.2 Model setup and computational parameters
- To be dimensionally consistent with the experiment, the numerical flume width was taken as 0.46 m wide for the four flow conditions listed in Table 1.
- The real water viscosity ( 60 10 m2/s) was used and the MLS filter was applied every 30 time steps to smooth out the density and pressure fluctuations.
- The computational time step was automatically adjusted to follow the Courant stability requirement [Gómez-Gesteira et al., 2012].
- To reduce the time of simulation and to reach the stable flow quicker, an analytical solution based on the power law )/1(max )/( mHyUU was initially imposed within the fluid block for each flow condition.
- Similar to the previous 2D model [Gabreil et al., 2018], the bed reference level 0y was taken 4.0 mm below the top of the spheres , from which the mean flow depth wh is measured.
3.3 Treatment of turbulence and roughness elements in 3D model
- Czernuszenko and Rylov  proposed a simple analytical model based on the generalisation of Prandtl’s mixing length approach that could be used to obtain the mean velocity and shear stress distributions in 3D nonhomogeneous turbulent flows.
- This simple model was also implemented in the current 3D SPH model by modifying the original SPS model.
- (c) In 3D turbulent open channel flow, the flow is not only influenced by the existence of the roughness element on the channel bed, but it is also influenced by the vertical side walls.
- The vertical drag forces were only computed on the sidewalls where high vertical velocities occur due to the interaction between the flow and sidewall corners.
4.1 Aims of the experiments
- The aim of these experiments was to measure the temporal change in water surf c elevations at different locations in the streamwise and lateral directions.
- These measurements are then used to support the application of the SPH approach for use in open channel shallow, turbulent free surface flows.
- This will allow examination of the underlying flow patterns and the water surface spatial pattern.
4.2 Hydraulic flume setup
- Measurements were carried out in a 0.459 m wide and 12.6 m long rectangular open channel flume including a recirculating water system.
- At the upstream end the hydraulic flume is supported on a fixed pivot joint, and on a pivot joint attached to an adjustable jack at the downstream end.
- The sidewalls of the flume were composed of glass to enable flow observation.
- These flow conditions were selected to investigate the influence of rough bed elements on the water surface patterns of the turbulent flows.
- The experimental Reynolds Numbers (R ) ranged from approximately 11000 to 43000, so all the flows were fully turbulent.
4.3 Water surface measurement
- The temporal changes in the water surface were measured using conductance wave probes.
- The wave probes consisted of two thin wires, which were laterally separated by a istance of 13.0 mm.
- At the bottom of the flume, the upper layer of spheres were drilled with 1.0 mm diameter holes, and each probe was carefully attached into these holes.
- All the probes were connected to wave monitor modules provided by Churchill Controls.
- This procedure was repeated for a number of six flow depths ranged from 30 mm to 130 mm, so that a linear trend between the water depth and voltage was achieved for each wave probe.
4.4 Water surface data collection
- Before water surface measurements were taken, the uniform steady flow condition was first achieved and was allowed to stabilise for at least one hour.
- For all flow conditions the water temperature change was within 5.0% of the mean measured value.
- It can be seen that the behaviour of the PDF closely follows a Gaussian distribution.
- The measured data here will be used to support the development of the 3D SPH numerical model which is demonstrated in the following section.
- Fig.4. Probability Density Function (PDF) of the measured water surface fluctuations for all flow conditions in Table 1.
5.1 Water surface pattern
- Similar to the 2D SPH model, the water surface elevations were extracted from the SPH particle data using the principle of the divergence of particle position [Gabreil et al., 2018].
- Therefore this was used to compute the instantaneous water surface elevations in the streamwise and lateral directions as follows.
- The particle divergence r was then computed at each of these locations.
- Here it should be noted that the proposed 3D SPH model still predicts the s andard deviation of water surface fluctuations smaller than that in the experiments.
- In the current SPH model, the drag force was used to model the rough bed rather than modelling the real roughness geometry.
5.2 Spatial distribution of the computed mean water level
- The time averaged water surface elevations at each grid point were computed and plotted in Fig.6.
- Contour plots of the computed mean free surface elevations for the four flow condition (dashed lines: flume centreline) Condition (3) Condition (4) Condition (2) wh (mm) wh (mm) wh (mm) Table 2 presents a comparison of the computed mean water surface elevations along the flume centreline with the experimental data.
- Additionally the mean water surface elevations measured by the two lateral wave probe arrays were compared with the computed data as presented in Figure 7.
5.3 Propagation of water surface pattern
- This section looks at the dynamic behaviour of the water surface along the flume centrelin .
- The black-dashed lines in Figure 8 represent the depth averaged streamwise velocity U listed in Table 1.
- It should be noted that using a much more refined particle size, longer simulation time and longer flume length would allow for more accurate water surface patterns to be simulated.
- For conditions 3 and 4, the behaviour of the computed cross correlation function does not fluctuate as observed in the experiments.
5.5 Correlation function of the underlying vertical flow velocity
- In the previous section, it has been shown that the proposed 3D SPH model can initially simulate the free surface behaviour which was found to be closely related to the underlying main flow velocity.
- This section applies the spatial correlation function to the computed vertical velocity along the flume centreline and throughout the flow depth.
- All of these numerical findings provide evidence that SPH model has the capability in simulating such flows if a suitable SPH particle size is selected.
- By comparing with the previous 2D simulations [Gabreil et al., 2018], it was found that the 2D model was not able to show the change in the water surface standard deviation for the different flow conditions.
- Also the particle size used in both models is about four times larger than the measured standard deviation of water surface, which may suggest that the magnitude of water surface fluctuation was underestimated.
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Q1. What contributions have the authors mentioned in the paper "This is a repository copy of 3d sph simulation of dynamic water surface and its interaction with underlying flow structure for turbulent open channel flows over rough beds" ?
In this study a fully 3D numerical model based on the Smoothed Particle Hydrodynamics ( SPH ) approach has been developed to simulate turbulent open channel flows over a fixed rough bed. The model focuses on the study of dynamic free surface behaviour as well as its interaction with underlying flow structures near the rough bed.