Using Two Control Curves in SWMM 5 to Simulate a Head Difference Rule

Using Two Control Curves in SWMM 5 to Simulate a Head Difference Rule

In SWMM 5, Real Time Control (RTC) rules can't directly use the head difference across an orifice as a control parameter. However, you can simulate this behavior by using node depths, which are available as control parameters. Here's how to set up a system where orifice operation is based on the head difference indirectly:

Methodology:

1. Setup with Two Orifices:
   • Instead of one orifice, use two orifices (as shown in Figure 1 of your example), one for each flow direction or condition.
2. Control Curves and Rules:
   • Define two control curves (RuleOrf1 and RuleOrf2) that dictate how each orifice's setting changes based on node depth. These curves control the opening/closing of each orifice.
3. Rules for Control:
   • Use two separate rules to govern the behavior of each orifice:
   • Rule for Orifice1:
     RULE Orifice1
     IF  NODE UPNode  Depth >= 0 
     THEN ORIFICE ORIFICE1 SETTING = Curve RuleOrf1
     PRIORITY 10

     • This rule means Orifice1 starts open but will close (or adjust) based on the depth at UPNode. The curve RuleOrf1 should define how the orifice setting decreases as the depth at UPNode increases, effectively closing when the head difference becomes negligible.
   • Rule for Orifice2:
     RULE Orifice2
     IF  NODE DNode  Depth >= 0
     THEN ORIFICE ORIFICE2 SETTING = Curve RuleOrf2
     PRIORITY 10

     • Here, Orifice2 starts closed but will open or adjust based on the depth at DNode. The curve RuleOrf2 should specify how the orifice setting increases with the depth at DNode, opening up when there's enough head difference to allow flow in the opposite direction.

Explanation:

• Orifice1 Control: This orifice is designed to allow flow from UPNode to DNode when there's a positive head difference. As the depth at UPNode increases (indicating a positive head difference), the orifice gradually closes according to RuleOrf1.
• Orifice2 Control: Conversely, this orifice facilitates flow from DNode back to UPNode when there's a negative head difference or when the head difference is close to zero but with flow from the downstream side. As the depth at DNode increases (indicating a potential backflow), Orifice2 opens according to RuleOrf2.

Variations:

• You could reverse the control nodes for each orifice, using DNode to control Orifice1 and UPNode for Orifice2, depending on your specific hydraulic needs or the behavior you wish to simulate.

This setup effectively mimics a head difference rule by using node depths as proxies, allowing for sophisticated control of flow through orifices based on dynamic head conditions in the system.

 

Figure 1.  Two Orifice Solution

 

Figure 2. Two Orifice solution to have control over the Orifice(s) at both the upstream and downstream nodes. 

 

Contrasting SWMM 4 and SWMM 5 St. Venant Solutions

Contrasting SWMM 4 and SWMM 5 St. Venant Solutions

Both SWMM 4 and SWMM 5 aim to solve for changes in flow (Q) and depth (H) over time using the St. Venant equations, but they do so in fundamentally different ways:

1. Compute Changes:
   • SWMM 4 & SWMM 5: Both models compute changes in flow (dQ/dt) for links and changes in depth (dH/dt) for nodes based on conditions at time t.
2. Iteration for Convergence:
   • SWMM 5: Uses an iterative method where:
     • Iteration: At least 2 iterations are performed, with up to a maximum of 8, aiming for convergence of all nodes and links.
     • Implicit Method: The solution is implicitly iterative, meaning that each new iteration uses the updated values of Q and H from the previous iteration within the same time step. This approach generally leads to faster convergence, especially for gradually varied flow conditions.
   • SWMM 4:
     • Explicit Method: Solves the equations explicitly, where:
       • Half and Full Step: The new values of Q and H are calculated based on the conditions at the beginning of the time step (t) plus adjustments made halfway through (t + delta t/2) and at the end (t + delta t).
       • No Iterative Convergence: Unlike SWMM 5, it doesn't iterate to convergence within each time step but computes directly from one step to the next.
3. Utilizing New Values:
   • SWMM 5: Once convergence is achieved or the maximum iteration limit reached, the values of Q and H at t + delta t are used for the next time step, ensuring that the new step starts with the most recent, converged values.
   • SWMM 4: Directly uses the new values calculated explicitly for the next time step without further iteration within that step.

Key Differences:

• Stability and Accuracy:
  • SWMM 5's implicit method tends to be more stable for a wider range of conditions, especially when dealing with rapidly changing or complex flow situations due to its iterative approach towards convergence.
  • SWMM 4's explicit method can be computationally faster for simple, stable flow conditions but might require smaller time steps to maintain accuracy and stability in more complex scenarios.
• Computational Approach:
  • SWMM 5's method involves more computational work per time step due to iteration but can handle more complex hydraulic behaviors like backwater effects or tidal influences more accurately.
  • SWMM 4's method, while simpler, might need careful setting of time steps to avoid numerical instability, especially in systems with significant backwater or when flows are changing rapidly.

In summary, SWMM 5 offers a more robust and adaptable solution for modeling urban drainage systems with its iterative, implicit approach, while SWMM 4 provides a simpler, direct computation method that's adequate for less complex or more stable hydraulic conditions.