Jet pump (IH)#

The Jet pump (IH) block models a liquid-to-liquid pump with an additional inlet for the suction liquid in an isothermal liquid network.

Description of pump operation

The block has three hydraulic ports:

main input port A;
suction inlet port S;
output port B.

The main fluid flow moves from port A to port B, accelerating in the converging nozzle. After the nozzle, in the low-pressure region, additional fluid is drawn in through port S. The mixing of flows occurs in a neck (mixing chamber) of constant cross-section, after which the liquid enters the diffuser, at the outlet of which its pressure increases as the flow expands.

Block properties

The Nozzle area property specifies the narrowest cross-section of the main flow (from port A to port B) immediately before mixing.
The Nozzle to throat area ratio property allows you to calculate the cross-section in the throat where the flows mix.
The Inlet to outlet diffuser area ratio property allows you to calculate the flow cross-section at the diffuser outlet, assuming that at the inlet it is equal to the throat cross-section calculated above.
Properties:

allow you to set losses in the main and secondary inlets of the pump, as well as in the throat and diffuser.

The Minimum nozzle pressure property allows you to limit the pressure at the point where it is minimal along the path of fluid from inlet A to outlet B of the pump.

Changes in pressure due to changes in area

The mass flow is stored in the pump (1) :

(1)#\[M_a+M_b+M_s=0\]

where:

\(M_a\) — mass flow through port A, [kg/s];

\(M_b\) — mass flow through port B, [kg/s];

\(M_s\) — mass flow through port S, [kg/s].

Using the law of conservation of mass and Bernoulli’s principle, we can express changes in area across pump segments in terms of pressure changes. The pressure change associated with the nozzle is:

(2) :

(2)#\[\Delta p_{a,Nozzle}=\frac{\dot m_A}{4\cdot \rho \cdot A_N^2}\]

or 0, whichever is greater.

Here:

\(A_N\) — value of the parameter nozzle outlet cross-section area, [m\(^2\)];

\( ho\) is the density of the liquid, [kg/m\(^3\)].

The change in pressure due to the area at the suction opening is:

(3) :

(3)#\[\Delta p_{a,Annulus}=\frac{\dot m_S}{4\cdot \rho \cdot (A_T-A_N)^2}\]

or 0, whichever is greater.

Here \(A_T\) is the cross-sectional area of the throat (mixing chamber), [m\(^2\)].

The change in pressure during expansion of the diffuser is (4) :

(4)#\[\Delta p_{a,Diffuser}=-\frac{\dot m_B^2}{2\cdot \rho \cdot A_T^2}\cdot (1-a^2)\]

where \(a\) is the value of the parameter of the ratio of the inlet area to the outlet area of the diffuser.

Pressure changes due to mixing

The driving and suction flows mix in the throat. The pressure change from mixing is equal to (5):

(5)#\[\Delta p_{mixing}=\frac{\frac{\dot m_A^2}{b}+\frac{\dot m_S^2}{1-b}-\dot m_B^2}{\rho \cdot A_T}\]

where b is the value of the parameter of the ratio of the area of the nozzle outlet cross-section to the area of the throat, which is determined between the largest and smallest cross-sectional areas of the nozzle.

Pressure losses due to friction

The flow loses pressure due to friction in the nozzle, secondary suction, throat, and diffuser. The unit calculates these losses based on a coefficient for each section and the area or area ratio between the different pump sections. Friction causes pressure loss regardless of flow direction. The pressure loss in the nozzle due to friction is (6) :

(6)#\[\Delta p_{f, Nozzle}=K_N \cdot \frac{\dot m_A \cdot |\dot m_A|}{2 \cdot \rho \cdot A^2_N}\]

where \(K_N\) is the value of the loss coefficient parameter of the primary flow nozzle.

The pressure loss due to friction in the suction flow through the annular space is (7) :

(7)#\[\Delta p_{f, Annulus}=K_S \cdot \frac{\dot m_S \cdot |\dot m_S|}{2 \cdot \rho \cdot (A_T-A_N)^2}\]

where \(K_S\) is the value of the loss coefficient parameter at the input of the secondary flow.

The pressure loss in the throat due to friction is (8) :

(8)#\[\Delta p_{f, Throat}=K_T \cdot \frac{\dot m_B \cdot |\dot m_B|}{2 \cdot \rho \cdot A_T^2}\]

where \(K_T\) is the value of the loss coefficient parameter in the neck.

The pressure loss in the diffuser due to friction is (9) :

(9)#\[\Delta p_{f, Diffuser}=K_D \cdot \frac{\dot m_B \cdot |\dot m_B|}{2 \cdot \rho \cdot A_T^2}\]

where \(K_D\) is the value of the diffuser loss coefficient parameter. Since the block determines losses for areas of highest flow velocity, the block uses the throat area, which is equal to the diffuser inlet area, in the diffuser loss equation.

Saturation pressure in the nozzle

To avoid cavitation in the nozzle (the nozzle outlet is the point of lowest pressure in the pump), you can specify a minimum pressure in the nozzle.

Between the nozzle and the diffuser the pressure change is:

or (10) :

(10)#\[p_B-p_N=\Delta p_{mixing} + \Delta p_{f, Throat}+ \Delta p_{f, Diffuser}- \Delta p_{a, Diffuser}\]

or \(P_B-P_{Nmin}\) - whichever is smaller.

The total change in pressure in the nozzle is (11) :

(11)#\[p_A-p_N=\Delta p_{a, Nozzle}+ \Delta p_{f, Nozzle}\]

The total change in pressure in the annular space is (12) :

(12)#\[p_S-p_N=\Delta p_{a, Annulus}+ \Delta p_{f, Annulus}\]

1. Properties#

Property	Default Value	Description	Units of measurement
Nozzle area	0.01	-	m\(^2\)
Nozzle to throat area ratio	0.25	-	-
Inlet to outlet diffuser area ratio	0.25	-	-
Primary flow loss coefficient	0.05	-	-
Suction flow loss coefficient	0.005	-	-
Throat loss coefficient	0.1	-	-
Diffuser loss coefficient	0.1	-	-
Minimum nozzle pressure	0.1	-	Pa

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Inlet A (primary line)	Input	-	-	Isothermal hydraulics
Inlet S (suction line)	Input	-	-	Isothermal hydraulics
Output	Output	-	-	Isothermal hydraulics

In order to see the connection capabilities of the block, you need to go to page Description of block ports