UvA-DARE (Digital Academic Repository) Free-surface flow simulations for discharge-based operation of hydraulic structure gates

We combine non-hydrostatic ﬂ ow simulations of the free surface with a discharge model based on elementary gate ﬂ ow equations for decision support in the operation of hydraulic structure gates. A water level-based gate control used in most of today ’ s general practice does not take into account the fact that gate operation scenarios producing similar total discharged volumes and similar water levels may have different local ﬂ ow characteristics. Accurate and timely prediction of local ﬂ ow conditions around hydraulic gates is important for several aspects of structure management: ecology, scour, ﬂ ow-induced gate vibrations and waterway navigation. The modelling approach is described and tested for a multi-gate sluice structure regulating discharge from a river to the sea. The number of opened gates is varied and the discharge is stabilized with automated control by varying gate openings. The free-surface model was validated for discharge showing a correlation coef ﬁ cient of 0.994 compared to experimental data. Additionally, we show the analysis of computational ﬂ uid dynamics (CFD) results for evaluating bed stability and gate vibrations.

∇u i gradient operator, defined as ∇u i ¼ @u i =@x @u i =@z ∇ Áũ divergence operator, defined as ∇ Áũ ¼ @u 1 =@x þ @u 3 =@z q r number of combinations of r objects out of q objects (0 r q), defined as q! r! q À r ð Þ! ⌊r⌋ floor function, defined as ∀r ∈ R, ⌊r⌋ ¼ max(n ∈ Z:n r) ⌈r⌉ ceiling function, defined as ∀r ∈ R, Barrier operation is commonly based on water level predictions from system-scale far-field flow models. The procedures are aimed at fulfilling the main function of the structure: for a weir in a river this is to maintain the upstream water level; for a discharge sluice this is to transfer river water out to the sea while keeping a safe inland level. Proper design studies pay attention to all functions of a structure and assess the impact of all relevant flow features.
In addition, sometimes the design criteria that were originally applied cannot be retrieved, yielding uncertainty about safety levels and allowable limits of gate settings in the present.
There are several aspects in contemporary barrier management for which an informed view on discharge and flow around gates is essential. First, the prediction of bed material stability and scour, including local erosion (

APPROACH
For obtaining a timely prediction of the flow around gates, we propose a multi-step physics-based modelling strategy which uses data input from a system-scale model. The work-flow of the suggested gate operation system is shown in Figure 1.
The first step consists of the extraction of predicted water levels on both sides of the structure from a far-field A multi-gated discharge sluice with underflow gates will be used to describe the modelling method. The central question addressed is how to find the set of gate configurations capable of delivering the required discharge that also meet the relevant constraints on flow properties.

METHOD Discharge computations
Configurations of multi-gated structure Let us consider the gate configurations of a discharge structure consisting of n similar openings, each accommodating a movable gate, see Figure 2. In its idle state, all n gates close off the openings between the piers and the total discharge is zero. During a discharge event, m gates will be opened partially or completely, allowing a certain discharge through the structure. A 'gate configuration' is defined as the allocation of a number of gates (m n) that are opened with a gate opening a(t) while the other gates remain closed. All gates selected for opening will be operated similarly, i.e.
with the same a(t).
Before deciding which gates to open, first the possible combinations of opening gates are identified and counted.
In general, flow instabilities are not favourable for maintaining an efficient and controllable discharge. As in other parts of physics, symmetry is a global measure for stability of freesurface flows. If asymmetry is allowed, m gates can be chosen freely from the total of n available slots. Then the number of possible combinations is obviously n m , using the common notation for combinatorial choice of m objects out of n. For the condition of symmetry to hold, gates may only be opened in such a way that the pattern is symmetric about the vertical plane of symmetry in flow direction (see Figure 2). This implies that the number of options reduces For a structure with seven gates (n ¼ 7), for instance, the total number of possible ways to open 1, 2, …, 7 gates is P 7 This shows that the symmetry constraint greatly reduces the number of ways to open a given number of gates. Furthermore, an even number of gates has roughly half the number of possibilities, because opening any odd number of gates then results in asymmetric inflow. This could also hold for an odd-numbered gate structure which misses one (or any odd m < n) of the gates due to maintenance or operational failure.

System model and gate control
The basis is formed by a classic box model, see for example Stelling & Booij (). The focus is on submerged flow through a multi-gated outlet barrier that blocks seawater from entering the lake at high tide and discharges river water to sea at low tide, see Figure 3. This basic model serves in the present study as a surrogate system-scale model. The water levels it generates will be used as boundary conditions for the near-field modelling.
Assuming barrier gates are closed (except when discharging under natural head from lake to sea) and assuming zero evaporation and precipitation, the system is described by: where Q river is discharge from a river, Q barrier is the total discharge through the gates of the barrier, h lake is the water level in the lake, A lake is the area of the lake assumed independent of h lake .
Submerged flow past an underflow gate is by definition affected by the downstream water level. The associated discharge depends on both water levels (sea and lake), the gate opening a and a discharge coefficient for submerged flow C D .
The discharge Q through a barrier gate at time t is written as: where w is the flow width (see Figure 2) and the subscript 'barrier' is dropped from now on. Sea level h sea is approximated by a sine function. The total discharged volume that passes the barrier in the period during which h lake > h sea is found after summing over all m gates and integrating with respect to time.  Two gate opening scenarios will be considered. In both scenarios equal gate openings a(t) are applied to all m gates selected for opening. The first scenario uses a constant gate opening a const for the whole discharge period (from t start to t end ). The opening required to lower the lake level to a desired lake level h target is found by estimating the average required discharge Q tot,req to achieve this and by making estimates of the average discharge coefficient and water levels during the discharge period: where bars are time-averages and primes indicate predictions of future values. In the second scenario, the discharge is regulated by a proportional integral derivative (PID) controller (Brown ). The goal of this scenario is to have a more constant gate discharge by varying the gate openings in time, whilst still achieving the same h target as in the first scenario. The discrete PID formula for discharge at t i is: where K i are the gain parameters and the error value is defined as e(t i ) ¼ Q set À Q(t iÀ1 ). In the simulations, K P ¼ 0.10, K I ¼ 0.45 and K D ¼ 0.55 are used. The setpoint Q set is constant and equal to Q tot,req , except for linear setpoint ramping applied at the start of discharge to prevent undue fluctuations of gate position. At each time step, the required gate opening is derived from this discharge divided by . Figure 4 shows the flow chart of the system model. It includes computations of the two gate operation scenarios. Figure 4 shows that the total discharge computed by the system model Q tot is being used to calculate the new lake level. Additionally, it shows that at the start of each discharge event, i.e. when the gates are opened, the prediction of the discharge coefficient C D 0 is updated using data from the discharge model. For both situations, with and without PID control, this coefficient is found by a relaxation function with the mean discharge coefficient C D * of the previous discharge event computed by the discharge model. For the nth discharge event, the update formula reads: In all computations, a relaxation factor β ¼ 0.75 is applied.
Discharge coefficients actually depend on numerous factors. Also, flows through neighbouring gates influence each other. To distinguish between different gate configurations with the same total flow-through area m Á w Á a const , these two things need to be taken into account. This is done in the discharge model described in the next subsection, see also the bold block in Figure 4.

CFD SIMULATIONS
Step 4 in Figure 1 consists of two parts: free-surface CFD simulations (discussed in this section) and flow analysis (discussed in the next section).

ANALYSIS
The second part of step 4 in Figure 1 is the analysis of the modelling results obtained in previous steps. In this section, three aspects of analysis are discussed: flow parameters, vibrations and bed stability.

Flow parameters
Three parameters that are required for assessing various types of flow impact are extracted from the CFD model: the contraction coefficient C c , the velocity in the vena contracta U vc and the Froude number (Fr). The flow field is interpolated to a regular grid, so that the edge of the separated layer is found, see Figure 10. The contraction coefficient is thus found directly.
The cross-sectional averaged velocity in the vena contracta is defined by a spatial average in the separated shear zone: where f gate is the response frequency of the structure in Hz; L is a characteristic length scale of the gate, usually the thickness of the gate bottom, and U vc as defined in the pre- where 〈::〉 denotes spatial averaging over the whole water depth, k is the turbulent kinetic energy (TKE), d is the local water depth, U is the mean flow velocity magnitude and α is an empirical parameter for bringing into account the turbulence (that depends on flow type and local geometry, e.g. slopes in bottom profile).

MODEL VALIDATION RESULTS
A series of validation runs was performed for the free-sur-

TEST CASE RESULTS
The described methods are illustrated by a test case example. The results of three modelling steps are discussed: the sluice model containing the system model (for water levels) plus the discharge model (Figures 4 and 6), the free-surface model ( Figure 8) and analysis of vibrations and bed stability. Four tidal cycles and four discharge events were modelled for a discharge sluice with seven gates regulating a lake with constant river inflow. The goal of the computations is to determine the optimal number of gates to open and the best gate operation scenario.

Results of system and discharge model
Model parameters The sluice model was run for 1 m 7. When opening only one gate, the target lake level could not be reached even when lifting the gate completely. When using two gates, the target level is reached, but the modular flow limit is exceeded for the greatest part of the discharge period.
This results in unwanted transitions to intermediate and free flow with fluctuating discharges that are hard to control.
For 3 m 7 strictly submerged flow exists and the target is met. Therefore, only these configurations are modelled further. The plotted water levels ( Figure 12) show that the lake level fluctuates in a controlled way and is nearly identical for the scenarios with and without discharge control.
In Figure 13, the gate openings and achieved gate discharges in time are plotted for one tidal period for the situations with three or seven gates opened during the discharge event. Intermediate numbers of operated gates (4 m 6) lie between the shown curves for m ¼ 3 and m ¼ 7, but are not plotted for clarity. It can be seen that constant gate openings give discharges that vary in time following the time-dependent hydraulic head difference. In the PID-controlled scenario, the gate opening is automatically operated in such a way that the discharge stabilizes quickly after the start.  Nago (1978Nago ( , 1983. Left: sorted by gate opening (a/h1) and downstream level (h3/a). Right: direct comparison of the same data. Dashed lines mark 10% deviation.
In this multi-scale modelling approach, averaged values from the discharge model are used to improve discharge predictions at system scale. However, instantaneous discharges and gate openings computed in both models inevitably differ. The largest discrepancies are around 10%. This could be improved by examining different update methods, at the cost of longer computation time.
Three configurations are selected for evaluation by freesurface simulations. These cases are marked in Figure 13 as runs I, II and III. Runs I and III represent extremes: a constant gate opening with only three gates in use (high Q) and a controlled opening with all seven gates in use (low Q).
All three runs are at the time of maximum head difference.
In real-life practice, more cases could be selected for simulation depending on specific interests and available computing power.

Results of CFD simulations
To simulate the two selected runs I and II within the validated range, the levels and opening are scaled down with length scale 1:10, see Table 1.
The near-gate flow velocities, pressures, TKE and dissipation are simulated. Figure 10 shows  past the gate. Run I has a steeper surface behind the gate than run II (shown in Figures 10 and 14) and higher TKE levels, while run III has the lowest TKE levels and the most level surface downstream of the gate.

Results of flow analysis
The output of the CFD free-surface model is used for computing the values of the three flow parameters that were discussed in an earlier section, see Table 2. The results are plotted in Figure 15.  Turning to the assessment of gate vibrations, it is calculated that for an assumed range of structural response frequencies of 2-5 Hz (typical values for large hydraulic gates), the reduced velocity number Vr lies in the range 3.5-8.5 for runs I and II and in the range 2.5-6 for run III.
For illustration purposes, a response curve is devised, see Based on the discussed modelling results and flow analysis, it may be decided to implement the discharge scenario of run II, because it leads to acceptable vibration levels and gives a lower impact on the bed material than run Iwhile still ensuring sufficient discharge volume to reach the target lake level. Specific gate uses are to be simulated and evaluated. For the last two barriers just mentioned, the operational modelling system will be mostly aimed at widening the window of  operation. The introduced methods can also be adapted for weirs in rivers. Coupling the presented models with a midfield or far-field model of regional scale would enable an operational impact assessment for water management issues such as salt water intrusion.

RECOMMENDATIONS
The inclusion of measurement data (from field sensors or laboratory tests) is necessary for the calibration of empirical parameters (such as entrance and exit losses), for the process of model validation and for providing actual model input (water levels). Experiences from the field of hydroinformatics should be added to the present research to make the extension towards data-driven modelling components. The link with data assimilation that is to be accommodated by the higher-level models is obvious.
A longstanding issue in the engineering practice of detailed hydrodynamics is turbulence modelling. The right balance between accuracy and computational costs needs to be found for specific applications. Again, smart use of measurement data for numerical validation and calibration could be the key. It is furthermore expected that intermediate and free flow conditions where hydraulic jumps occur away from the gate, including the Venturi flow type, can be modelled more universally using other numerical methods such as Phase Field or Volume of Fluid. If needed, the model can thus be extended to account for dynamic effects directly related to opening and closing actions of the gates. Active setpoint ramping of the PIDcontrol using feed-forward model predictions is another recommendation related to this.

CONCLUSIONS AND FUTURE WORK
The purpose of the current study was to set up physics-based modelling methods for a flow-centred operation of gates of hydraulic structures. The described case of a multi-gated outlet barrier sluice has shown how discharge estimates and free-surface simulations can aid in deciding on optimal gate configuration and opening scenarios.
The application of a PID-controller to achieve a more constant discharge during changing head differences The physics-based model of this study is logically complemented by data-driven techniques in future studies. It is believed that hydroinformatics provides the required tools for this. Use of sensor data from real-life structures and coupling to system-scale water level prediction models are seen as next steps. Moreover, it should be investigated how operational decisions should be derived when taking into account the various criteria and flow constraints.