A new approach to the simulation of flow transfer between 1D and 2D domains at 2D Manholes

1      Introduction

Inspection of the simulation results can show that the flow into the manhole from the 2d zone does not follow the head-discharge relationship specified by the user. The transfer of the flow into the manhole is limited, based on the available water volume in the 2d element associated with the manhole and the run time step specified by the user in the run dialog. The reason behind this limitation is to set a safety coefficient to avoid mass conservation errors in the flow exchanged between the 1d and 2d domains. There is nothing to ensure that the flow towards the 1d system which is calculated in a 1d-2d connection (either through a head-discharge relation, a standard weir calculation or any other method) is physically valid. For example a head-discharge relationship can be set arbitrarily regardless of the actual flow in the surface. Therefore some kind of flow limitation method needs to be set in order to reconcile the exchange of flow between the 1d and 2d domains to the actual flow conditions in the surface. The flow limiting is recorded via the ‘Total cumulative limited volume’, ‘Cumulative Limited Volume’ and ‘Cumulative Limited Volume Rate’ results parameters and a warning is also present in the simulation log if flow limiting has been applied.  These complement the ‘Flow Limited‘ and ‘Duration of Flow Limiting‘ results parameters added in 5.5.

2      A new approach

The solution is implemented in version 6 in ICM as a new method “Inflow-based link at manholes”, which is specified in the network Simulation Parameters (see Figure 1).

Figure 1: The new '‘Inflow-based link at manholes’ simulation parameter.

Figure 1: The new ‘‘Inflow-based link at manholes’ simulation parameter.

This method sets the maximum water flow that can be exchanged from the 2d domain into the 1d system in a 2d manhole driven by a head-discharge table in a different manner from the original method implemented in the software. This new method is the default linking method for 2d manholes of the following types from ICM 6.0 onwards as well as 2D outfalls:-

  •  Flood type: Inlet 2D, Inlet input type: HeadD
  •  Flood type: Gully 2D

The new method is intended to be extended to other types of 2d manholes in future releases of the software.

The linking method can be reverted to the original Volume type method by unticking the “Inflow-based link at manholes” option in the simulation parameters of the network.

Previously the linking method to estimate the maximum flow to be passed from a 2d mesh element towards a 1d manhole was based only on the water volume in the element and the major time step set by the user in the run dialog to link the 1d and 2d engines. This approach had a weakness due to its dependency on the time step set by the user. Changing the time step meant changing the maximum flow available to be exchanged between engines and thus changing the results of the simulation. Increasing the time step meant decreasing the maximum flow to be exchanged between engines.

The time step dependency is particularly evident in the case of 1d-2d manhole connections driven by head-discharge relationships, where for a given depth (in the case of free discharge manhole) the user would expect to see a specific discharge determined by the H-Q curve. Nevertheless, as the user increases the time step the results become divergent from the discharge in the H-Q curve.

In order to avoid the time step dependency, the “Inflow-based link at manholes” approach uses the net inflow into an element instead of the volume in the element as the basis to set the maximum flow that can be exchanged between engines. The net inflow is estimated by adding up all the inflows into the element (inflow from neighbour elements, rainfall, etc) minus the outflows from the element (outflow towards neighbour elements, infiltration, etc, except the outflow towards the 1d system). Once equilibrium conditions are achieved, the net inflow in the element should be equal to the flow towards the 1d system. The methodology monitors the error between the head in the mesh element (measured head) and the corresponding head in the H-Q curve given by the net inflow in the mesh element (equilibrium head). By using a PID (proportional-integral-derivative) controller, the algorithm attempts to minimize the error by adjusting the maximum flow that can be exchanged between engines in order to make the equilibrium depth converge towards the actual depth in the mesh element. The PID controller sets a corrected maximum flow based on the proportional error (present error), integral error (accumulation of error during time) and derivative error (rate of error change and future predicted error). Once equilibrium conditions are achieved, the measured and equilibrium heads should tend to the same value and the flow towards the manhole should also tend to the one dictated in the H-Q table. The parameters of the PID controller are fixed and are constant for all manholes. They are based on satisfactory results obtained in typical flow examples and have been obtained by heuristic methods.

3      Results comparison

The following graphs show the effect of applying the new “Inflow-based link at manholes” method in the results obtained in manhole BV-1271 using an example model, running the simulation with a 20s time step.

Figure 2: Comparison of depths (m) in element 1635 and flows (m3/s) in manhole BV-1271 using the original volume based method (blue lines) and the new "Inflow-based link at manholes" method (green lines).

Figure 2: Comparison of depths (m) in element 1635 and flows (m3/s) in manhole BV-1271 using the original volume based method (blue lines) and the new “Inflow-based link at manholes” method (green lines).

The graph on the left of Figure 2 shows the depth in the 2d element 1635, which sits on top of manhole BV-1271, and the graph on the right shows the flow towards the 1d system at manhole BV-1271. The blue line represents the results obtained with the original volume based method and the green lines the results obtained with the new “Inflow-based link at manholes” method.

As it can be clearly seen in these graphs, the maximum depth reached in the element 1635 has decreased from almost 15cm to less than 4.6cm after applying the new method. On the other hand, the right graph shows how the maximum flow has increased from about 0.02m3/s to 0.215m3/s after applying the new linking method.

Figure 3 shows the head discharge table provided for manhole BV-1271. It can be observed there that the flow in the manhole with the new method “Inflow-based link at manholes” matches approximately the one provided in the head-discharge table. The head-discharge table specifies a discharge of 0.2124m3/s for a head of 4.57 cm, and the results of the model produces approximately 0.215m3/s for a head of 4.6cm, as seen in the graphs in Figure 2.

Figure 3. Head discharge table for manhole BV-1271. The head and discharge that matches the one produced by the model has been highlighted.

Figure 3. Head discharge table for manhole BV-1271. The head and discharge that matches the one produced by the model has been highlighted.

4      Other suggested considerations

  • The head discharge tables entered at 1d-2d manholes should be consistent with the wet-dry tolerance specified in the 2d model. In other words, if the wet/dry threshold is set to 1mm in the simulation, the head discharge table should start positive discharges above this head. This avoids overshooting and oscillations at low depth scenarios. This approach also introduces some tolerance when the flow is calculated under submerged manhole conditions, but this is considered to be a benign effect, which should not degrade simulation results significantly.
  • The “Inflow-based link at manholes” approach works better if the discharges are low for low heads. High discharges at low depths can produce oscillations and overshooting.

5      Summary

The blog summarises a new approach to the simulation of the transfer of flow between the 1D and 2D domain of the model. This new approach was added to version 6 of the software and will be the new default approach for transfer of flow between 1D and 2D for new networks. However, this can be overridden in the simulation parameters.

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    About Duncan Kitts

    Duncan Kitts is a Senior Support Engineer with Innovyze in the United Kingdom, specializing in River modelling and 2D modelling. He has over 9 years experience of modeling the key hydraulic processes involved in both fluvial systems and urban drainage environments. Duncan is responsible for providing support of both infoworks ICM and Infoworks RS.
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