4.3. Hydraulic nodes¶

4.3.1. General¶

An H-node connects two or more H-components which each other. In the diagram this H-node is represented by a connection line, connected to the hydraulic connect point of a H-component (blue dot). In case more than two connect points have to be connected the H-node is compounded of a master and one or more slave connection lines, thus forming a tree. For more information about the connection line, see “Connecting components” on page 34.

4.3.2. Pressure definition for H-node¶

In the H-node the main variable H (Head) is calculated from a set of equations as explained in “Implementation” on page 157. The pressure P is derived from this head according Bernouilli (see “Bernoulli’s theorem” on page 148).

The total pressure is derived from this total head, according to:

(4.3.1)¶\[P_{\text {Total}}=\rho_g(H-z)\]

with

Variable	Description	Units
\(P_{\text{total}}\)	Total pressure	N/m²
\(\rho_g\)	Fluid density	kg/m³
\(H\)	Total head	m
\(z\)	Elevation of H-node	m

The pressure in the connect points of the adjacent H-components are derived from the pressure of the H-node. If the adjacent H-component has a diameter property (e.g: VALVE, PIPE), the velocity v can be determined and thus, the velocity head can be taken into account. Please note that only the velocity head of pipes which are flowing into the node is taken into account, according:

(4.3.2)¶\[P=\rho_g\left(H-z-\frac{v^{2}}{2 g}\right)\]

Because the diameters of the adjacent H-components may differ or the elevation of the centreline (in case of PIPE) may differ, the local pressure in the individual connect points may differ. From a mathematical view the connect points and the H-node is the same location.

The H-node model knows the elevation and diameters of the adjacent H-components. For all adjacent components the lowest pressure is computed at the soffit.

The pressure shown for the H-node is the lowest connect point pressure.

Example:

In the system below the discharge (Q) is 884 m³/h. In the Mode & Options menu the pressure output reference (only used for PIPE output) is set to “centreline”.

../_images/image334.png — Fig. 4.3.1 Example to explain the parameters of (4.3.1).¶

Consider H-node C and adjacent H-components:

Table 4.3.1 Derived parameters for the example system¶
Property	Value
The energy head (or total head)	11.17 m
Elevation of H-node and elevation begin of pipe	5 m
Velocity head of Valve	\(\frac{v^{2}}{2 g}=\frac{5 \times 5}{2 \times 9.81}=1.27 m\)
Velocity head in Pipe	\(\frac{v^{2}}{2 g}=\frac{2.5 \times 2.5}{2 \times 9.81}=0.32 \mathrm{~m}\)
Pressure downstream side Valve	\(P=1000 \times 9.81 \times(11.17-5.00-1.27)=0.480\) barg
Pressure upstream side Pipe at C_L	\(P=1000 \times 9.81 \times(11.17-5.00-0.32)=0.574\) barg
Total Pressure in H-node C	\(P=1000 \times 9.81 \times(11.17-5.00)=0.605\)
Lowest pressure in H-node C based on soffit location: Valve	\(P=1000 \times 9.81 \times(11.17-5.00-1.27-0.125)=0.468\) barg
Pipe	\(P=1000 \times 9.81 \times(11.17-5.00-0.32-0.177)=0.556\) barg

Lowest pressure at Valve is shown in the property window

4.3.3. Cavitation in H-node¶

If the pressure drops below the vapour pressure, cavitation occurs(see “Cavitation” on page 176). Cavitation in an H-node is only taken into account if the H-node is connected to a PIPE.

The H-node model knows the elevation and diameters of the adjacent H-components. For all adjacent components the lowest pressure is computed at the soffit. If this lowest pressure drops below the vapour pressure, cavitation occurs.

The lowest pressure in an H-node is computed according:

(4.3.3)¶\[P_{\text {lowest }}=\operatorname{MIN}_{i}\left(\rho g\left(H-z_{\text {soffit } i}-\frac{v_{i}^{2}}{2 g}\right)\right)\]

with:

Variable	Description	Units
\(P_{\text{lowest}}\)	Total pressure	N/m²
\(\rho\)	Fluid density	kg/m³
\(g\)	Gravitational acceleration	m/s²
\(H\)	Total head	m
\(Z_{\text{soffit}, i}\)	Soffit of “diameter-defined” H-component i	m
\(v_{i}\)	Velocity at begion or end of H-component i	m/s

The void fraction is expressed as the cavitation vapour volume divided by the sum of the half-element volumes of the adjacent pipes.

4.3.4. Standard output of H-node types¶

Standard output for each type of H-node is:

Head [m]
Pressure [N/m²] (the lowest pressure of the connected H-components)

Node specific output for the H-node is:

Total Pressure [N/m²]
Void fraction [-]

4.3.5. Available H-node types¶

The following types of H-nodes are available and are described in next sections:

H-node
H-node with initial head
H-node with conditional initial head

4.3.6. H-node¶

This H-node is the standard hydraulic node, by default generated after connecting of two H-components.

The output (H and P) can be calculated if the H-node is part of a fully connected (“open”) hydraulic network with one or more a boundary conditions for the Head (e.g. BOUNDH, TANK). “Open” means that each H-component has a certain relation between head and discharge and that there is at least one component prescribing the head or pressure.

Input properties

Description	Input	unit	remarks
Elevation	Real	[m]

Messages

Message	Message	Explanation
Cavitation in steady state not allowed	error	The lowest pressure in the H-node is less than the vapour pressure
Pressure < Pvapour; Cavitation not supported for H-node without PIPE connections	warning	In this H-node there is no PIPE component connected. The cavitation model needs at least 1 PIPE to compute the vapour volume. This warning is only given the first time the pressure condition is true; the rest of the simulation is physically invalid.
Cavitates	informative	H-node starts cavitating; that means that the lowest pressure becomes less than the vapour pressure
Cavitation collapses	informative	Void fraction becomes 0
Change Type to Hydraulic node with initial head	error	H-node is part of an isolated part of the network in which no information is available for the head; the user must define the head in this part of the model. See “H-node with initial head” on page 198.

4.3.7. H-node with initial head¶

If the H-node is part of a “closed” or “”isolated” hydraulic network, there is no connection with a boundary condition like a BOUNDH and the actual head in the steady state computation can not be determined.

This is explained in the figure below: the head in the H-nodes U1, U2 and U3 can not be calculated.

../_images/image343.png — Fig. 4.3.2 Schematic overview of a Wanda model with a closed section.¶

It is therefore necessary to define the head for this area in one of the H-nodes. It is up to the user which H-node head will be prescribed (changed into the type: H-node with initial head).

Note: if this “isolated network” occurs during the transient computation, the head of the previous time step will be used.

The type of the H-node can be changed via the property window (drop down list in “Type” field)

Input properties

Description	Input	unit	remarks
Elevation	Real	[m]
Initial head	Real	[m]

Messages

Message	Message	Explanation
Cavitation in steady state not allowed	error	The lowest pressure in the H-node is less than the vapour pressure
Pressure < Pvapour; Cavitation not supported for H-node without PIPE connections	warning	In this H-node there is no PIPE component connected. The cavitation model needs at least 1 PIPE to compute the vapour volume. This warning is only given the first time the pressure condition is true; the rest of the simulation is physically invalid.
Cavitates	informative	H-node starts cavitating; that means that the lowest pressure becomes less than the vapour pressure
Cavitation collapses	informative	Void fraction becomes 0

4.3.8. H-node with conditional initial head¶

If the H-node is part of a “closed” or “”isolated” hydraulic network, there is no connection with a boundary condition like a BOUNDH and the actual head in the steady state computation cannot be determined.

Fig. 4.3.3 shows that the head in the H-nodes U1, U2 and U3 cannot be calculated.

It is therefore necessary to define the head for this area in one of the H-nodes. It is up to the user which H-node head will be prescribed (changed into the type: H-node with initial head). However when using for example the parameter script is can be useful that the node only describes the pressure and temperature when they are part of an isolated system. For this purpose the conditional init H node can be used. This node only pre describes its head when it is part of an isolated system. Note: if this “isolated network” occurs during the transient computation, the head of the previous time step will be used. The type of the H-node can be changed via the property window (drop down list in “Type” field)

Input properties

Description	Input	unit	remarks
Elevation	Real	[m]
Initial head	Real	[m]

Messages

Message	Message	Explanation
Cavitation in steady state not allowed	error	The lowest pressure in the H-node is less than the vapour pressure
Pressure < Pvapour; Cavitation not supported for H-node without PIPE connections	warning	In this H-node there is no PIPE component connected. The cavitation model needs at least 1 PIPE to compute the vapour volume. This warning is only given the first time the pressure condition is true; the rest of the simulation is physically invalid.
Cavitates	informative	H-node starts cavitating; that means that the lowest pressure becomes less than the vapour pressure
Cavitation collapses	informative	Void fraction becomes 0

4.3.9. H-node with demand¶

If the H-node is part of a “closed” or “”isolated” hydraulic network, there is no connection with a boundary condition like a BOUNDH and the actual head in the steady state computation can not be determined.

This is explained in the figure below: the head in the H-nodes U1, U2 and U3 can not be calculated.

It is therefore necessary to define the head for this area in one of the H-nodes. It is up to the user which H-node head will be prescribed (changed into the type: H-node with initial head).

Note: if this “isolated network” occurs during the transient computation, the head of the previous time step will be used.

The type of the H-node can be changed via the property window (drop down list in “Type” field)

Input properties

Description	Input	unit	remarks
Elevation	Real	[m]
Base demand	Real	[m3/h]

Messages

Message	Message	Explanation
Cavitation in steady state not allowed	error	The lowest pressure in the H-node is less than the vapour pressure
Pressure < Pvapour; Cavitation not supported for H-node without PIPE connections	warning	In this H-node there is no PIPE component connected. The cavitation model needs at least 1 PIPE to compute the vapour volume. This warning is only given the first time the pressure condition is true; the rest of the simulation is physically invalid.
Cavitates	informative	H-node starts cavitating; that means that the lowest pressure becomes less than the vapour pressure
Cavitation collapses	informative	Void fraction becomes 0