Modeling Reference - Discharge To Atmosphere

Product(s): HAMMER
Version(s): V8i, CONNECT Edition
Area:  Modeling

Overview

This technote explains how the Discharge to Atmosphere (D2A) element works and its typical application in HAMMER. It also provides an example model file for demonstration purposes.

How it Works

The "discharge to Atmosphere" element encompasses a valve to atmosphere, orifice to atmosphere and head vs. flow rating table. It is used to model an opening / orifice that allows flow to leave the pipe network and discharge to the atmosphere. You can model it as a fixed orifice that is always open, or a valve that is either initially open or closed, then opens or closes during the transient simulation. It can be placed in series with the main water line or at a "T" 

 

 

Note: it is important to understand that this element discharges to atmosphere, not between the adjacent pipes. So in the above case of an in-line orientation, flow still passes through the pipeline beneath the valve, regardless of if the valve is opened or closed. 

 

In the calculation engine, it is essentially modeled as a demand point located a hydraulically short distance from its node coordinates (based on the wave speeds of the pipes connected to it). The initial pressure and flow (entered by the user) are used to automatically calculate a flow emitter (orifice) coefficient (the term CA in the orifice equation below), which will be used during the simulation to calculate transient outflows as the pressure changes. This applies to both the initial conditions (steady state) solver as well as the transient solver (they both use the same resulting pressure/flow relationship) Basically HAMMER uses that coefficient (CA term) to calculate other flows and their corresponding pressure drop: 

Q = C A (2 g P)^0.5

Q - Discharge (cfs, cms)
C - A 'discharge coefficient' (distinct from CV used elsewhere in HAMMER) which will be computed based on the typical flow/pressure
A - The cross-sectional area of the opening (ft, m) - this is combined with the "C" as a single term
g - gravitational acceleration
P - Pressure head (ft, m)

As you can see, once the "C A" is calculated from the initial head/flow, HAMMER can solve for other flows, as the pressure head changes during the simulation.

Example:

Let's take a look at an example, where the "Pressure Drop (typical)" is set to 1 m and the "Flow (typical)" is set to 0.5 m^3/s  :

Q = CA (2*g*P)^0.5
0.5 = CA (19.6)^0.5
0.5 = CA * 4.4272
CA = 0.1129

If the pressure at the D2A is example 1 m, then the outflow is exactly 0.5 m:

Now, say the pressure changes (due to system conditions) from 1 m to 10 m:

Q = CA (2*g*P)^0.5
Q = (0.1129) * (2*g*10)^0.5
Q = (0.1129) * 196^0.5
Q = 1.58 m^3/s

This is the flow you see when the pressure in the model is 10 m:

Air Pocket Formation

If the pressure drops below zero (subatmospheric) at the D2A element during the transient simulation, the D2A allows air into the system. When this happens, the air enters the pipeline freely on the assumption that the opening for the liquid is infinite for air. In this case, the node acts like a reservoir at zero pressure and the air pocket respectively expands or contracts accordingly as the liquid flows away from or towards the node, but the air remains at the branch end point(s) located at the D2A. The rate of change of the air volume is based on the water flow rate of the adjacent water column in the pipe. See further below for details on the application of a D2A for simulating an "inrush" or pipe filling/emptying.

Please also note the following: Assumptions and limitations of tracking air or vapor pockets in HAMMER

When to Use it

Common applications of the D2A acting as a valve

  1. Opening or closing of a hydrant, blowoff, sprinkler or other discharge - Select "Valve" as the Discharge Element type and specify the initial status. If the valve is initially closed at the start of the transient simulation, it will open and vice versa. Set the time to start operating and the time to be fully open; the valve opening increases linearly. Set the emitter value for the element by specifying the pressure drop at some flow rate. 
  2. Modeling a main break - The discharge element type is also "valve" in this case, but the "time to Fully Open or Close" would be zero. This is because it is conservative (for a design scenario) to model the rupture occuring quickly and producing a large opening. Essentially the initial conditions describe the normal pipe and appropriately conservative flow conditions just before the break, then the transient simulation instantly opens the 'valve', to initiate transition to a ruptured condition. To represent the opening's size, it is recommended that the user set the "Pressure drop (typical)" to the steady-state pressure (observed prior to the break), and only vary the "flow (typical)" according to the equation further above.
A sensitivity analysis wherein the cross sectional area, A is varied would illustrate the consequences of a range of breaks, with an upper limit to A being the diameter of the incoming pipe(s).
The analysis should also consider different locations of the break(s). Depending on the pipe network's topology, a sudden break can lead to the formation of vapor pockets with ensuing collapses and pressure spikes.



Common applications of the D2A acting as an Orifice

  1. Demand/consumption points that can let air in. In HAMMER, any demand at a node (junction or hydrant) is called a consumption node and is treated as an orifice discharging to atmosphere that cannot allow air back into the system during periods of subatmospheric pressure. This is because the majority of water demands entered into hydraulic models are really the sum of several houses or demand points, each located at a significant distance from the point where their aggregate demand is being modeled. HAMMER assumes that any air allowed into the system at the individual demand points cannot reach the aggregate demand location. If this is not the case, you must model the demand using the Discharge To Atmosphere element, set as an orifice. This is because upon subatmospheric pressure, the discharge to atmosphere element allows air into the system. 
  2. Any free discharge point. For example, the end of a sewer force main that discharges to an unsubmerged manhole, or a free discharge into the top of an un-modeled tank (top-fill tank). You would need to decide how to compute the headloss through the pipe outlet (and thus the corresponding "typical flow" and "typical head drop"), but a decent estimate might be to use the standard headloss equation: headloss = k*v2/2g, where k is set to 1, v is the flow velocity and g is gravity. Alternatively, if the outlet orifice is smaller than the pipe diameter (unlikely) you might want to use the orifice equation, V = C*(2g*headloss)0.5 In either case, the headloss is essentially the pressure drop. These equations are very similar to each other. Basically you would select an approximate flow (and therefore velocity) and use one of the above approaches to solve for an appropriate "Pressure drop (typical)". In order to do this, you would need to estimate a value for C. There is some documentation available for reference for such estimates. For instance, Brater and King (1976) lists orifice coefficients for various heads and sizes of circular, square, rectangular, and triangular shapes, and the U.S. Soil Conservation Service (1986) provides a chart of orifice coefficients for orifice plates placed over pipe opening. 

    As an example, assume a case where you know the flow but not the pressure/head. Say for example the flow is 10 cfs through a 12 inch opening. The velocity in this case would be: V = Q/A = 10 / (pi*0.5^2) = 12.73 ft/s. If you assume C = 0.6, (a typical orifice coefficient, just for example purposes and may not reflect your orifice/opening) you could calculate the corresponding appropriate headloss using the orifice equation relationship: = (V/C)^2 / 2g = (12.73 / 0.6)^2 / (2 * 32.174) = 7 ft. In this example, the "Pressure Drop (Typical)" would be set as 7 ft H2O. HAMMER would then use the orifice equation (see above under "how it works") to compute a change in outflow as the pressure changes. If you already know the flow at a corresponding head, you would simply enter them in the D2A properties and HAMMER will calculate the discharge coefficient internally and use that during the transient simulation to vary outflow with pressure.

  3. Transients initiated by an 'inrush' event. When a pump turns back on in a sewer force main, it may expel some air from the downstream end. The headloss through the discharge opening causes a resistance that can result in a severe upsurge once the water column reaches the opening. For example, with a small orifice size, an upsurge occurs when the flow reaches it, because the water basically can't get out of the pipe fast enough. Modeling this situation can be done by using the Discharge to Atmosphere element, operating as an orifice. The initial conditions must describe the low head condition (zero pressure at the discharge to atmosphere element) and you must enter a volume of air in the "Gas Volume (initial)" field. You would then have the head increase during the transient simulation (pump turning on or periodic head element with head value increasing, for example.) The "Flow (typical)" and "Pressure drop (typical)" would be estimated similar to item 2. Basically the higher the "Pressure Drop (typical)", the smaller the orifice size, and the more resistance to flow, resulting in a higher upsurge after the air pocket is expelled. See further above for details and assumptions about air pockets.

    Note: The "Gas Volume (Initial)" will impact the timing of the release of the air. The value you enter will be up to your engineering judgment, but a good starting point may be the volume of the "empty" pipe. A larger volume of air for the same size orifice will take longer to be expelled from the D2A. This, in turn, will impact the head increase at the source. The most important impact on the system will occur with the air is fully expelled, which is when the transient would occur. So while a large air volume will take longer to expel, the setup and size of the D2A may prove to the be most important part of the transient event. 

  4. Impulse turbine. The turbine element in HAMMER is not used to represent impulse turbines. Transients caused by impulse turbines can be approximated in HAMMER by using a Throttle Control Valve (TCV) or Discharge to Atmosphere element to represent the turbine nozzle.


 

Note: the "rating curve" discharge element type is used when the discharge out of your orifice does not follow a typical orifice-equation relationship. It allows you to explicitly define the flow released out of the system for certain pressures at the discharge location.

Attributes

The following attributes are available when the "discharge element type" is set to "Valve": 

"Valve Initial Status" - This specifies whether the valve is initially open or initially closed.

"Time to Start Operating" - The valve starts to operate after this time. (either starts to open or starts to closed, based on the initial status selection) It is measured from the start of the simulation. So a value of 5s means that the valve remains in a fixed position for the first 5 seconds, and then starts to operate. 

"Time to Fully Open or Close" - This is the time it takes for the valve to either fully open (if the initial status is closed) or fully close (if the initial status is open. It is measured from the "time to start operating". Meaning, if the "time to start operating" is set to 5s and the "time to fully open or close" is set to 10 seconds, then the valve closes linearly between time t=5 and t=15. (the valve is fully closed 10 seconds after it starts operating). 

"Flow (Typical)" - This is the typical discharge out of the valve when it is open. 

"Pressure Drop (Typical)" - This is the pressure corresponding to the typical flow through the valve. It is referred to as the "drop" because the pressure beyond the orifice is zero. The pressure and flow computed in the initial conditions will not necessarily be equal to these values, so you only need to enter any known pair. For example, if modeling a hydrant closure, you might enter the typical pressure and flow as the flow and pressure observed in a field test when the hydrant was opened.

You are basically defining an orifice size by way of the "typical" flow and pressure drop fields. By supplying one pair of pressure and flow, HAMMER can figure out the relationship based on the orifice equation that gives the pressure drop for any flow value. So, if unsure, you can use the orifice equation along with the size of your opening and an estimate of the "head" (pressure head drop) to solve for the typical flow. Selecting a pressure head drop close to a typical value you might see under normal operating conditions will yield the most accurate pressure/flow relationship during both the initial conditions and transient simulation. See further above under "How it works".

Note: a standard 2.5 in. (100 mm) hydrant outlet would have a pressure drop of roughly 10 psi at 500 gpm. 

When the Discharge Element type is set to "orifice", only the typical pressure drop and typical flow are available. When set to Rating Curve, only a rating curve table is available, where you would enter the table of head versus flow for your discharge. Initial conditions and transient head/flow is computed based on the values in this rating table. 

Example Model

The below model is an example of the use of the D2A element in HAMMER and has several scenarios for different configurations. Note:

  • This example is included in recent versions of HAMMER, in the "Samples" folder within the installation folder
  • The link below is to a version that can be opened in HAMMER V8i build 08.11.00.30 and above. 
  • Additional information can be found in the Project Properties
  • You must be signed in to download the file. The link will not work if you are not signed in.
  • This model is for illustrative purposes only

Click to Download

See Also

How do do WaterCAD/WaterGEMS treat the discharge to atmosphere element?

Product TechNotes and FAQs

OpenFlows Methods Product Tech Notes And FAQs

Protective Equipment FAQ

General HAMMER V8i FAQ

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