# Jet Pump (IL)

**Libraries:**

Simscape /
Fluids /
Isothermal Liquid /
Pumps & Motors

## Description

The Jet Pump (IL) block models a liquid-liquid jet pump in an isothermal liquid
network with the same motive and suction fluids. The motive enters the primary nozzle at
port **A**, which draws in the suction fluid through input port
**S**. After mixing in the throat, the combined flow expands
through the diffuser and is discharged at port **B**. The total
pressure change over the pump is the sum of the individual contributions of friction and
area change in each section of the pump and momentum changes in the throat. The sign
convention for the equations below correspond to positive flow into the throat.

**Jet Pump Schematic**

### Changes in Pressure Due to Area Changes

The mass flow rate is conserved in the pump:

$${\dot{m}}_{A}+{\dot{m}}_{S}+{\dot{m}}_{B}=0,$$

where $$\dot{m}$$_{A} is the mass flow rate through port
**A**, $$\dot{m}$$_{S} is the mass flow rate through port
**S**, and $$\dot{m}$$_{A} is the mass flow rate through port
**B**.

Using mass conservation and the Bernoulli Principle, the area changes over the pump segments can be expressed in terms of pressure change. The pressure change associated with the nozzle is:

$$\Delta {p}_{a,}{}_{Nozzle}=\frac{{\dot{m}}_{A}}{4\rho {A}_{N}^{2}},$$

or 0, whichever is greater. The formulation depends on:

*A*_{N}, the**Nozzle area**, taken at its widest section.*ρ*, the fluid density.

It is assumed that the nozzle inlet is much larger than the nozzle outlet.

Although the geometry of a typical suction inlet is not shaped like a nozzle, it effectively experiences the same type of area reduction as it enters the throat around the nozzle outlet. This annulus is assumed to be much smaller than the suction inlet. The pressure change due to this area reduction is:

$$\Delta {p}_{a,}{}_{Annulus}=\frac{{\dot{m}}_{S}}{4\rho {\left({A}_{T}-{A}_{N}\right)}^{2}},$$

or 0, whichever is greater.
*A*_{T} is the cross-sectional area of the
throat. The pressure change over the diffuser expansion is:

$$\Delta {p}_{a,}{}_{Diffuser}=-\frac{{\dot{m}}_{B}{}^{2}}{2\rho {A}_{T}^{2}}\left(1-{a}^{2}\right),$$

where *a* is the **Diffuser inlet to
outlet area ratio**.

**Reversed Flows**

In the case of reversed flow, the effect of the nozzle area on pressure change is not modeled, and therefore flow traveling from the throat through the nozzle will not undergo any pressure gain. This ensures the numerical stability of the block during simulation of reversed flows.

### Changes in Pressure Due to Mixing

Mixing between the motive and suction flows occurs in the throat. This change in momentum is associated with a change in pressure:

$$\Delta {p}_{mixing}=\frac{\frac{{\dot{m}}_{A}^{2}}{b}+\frac{{\dot{m}}_{S}^{2}}{1-b}-{\dot{m}}_{B}^{2}}{\rho {A}_{T}},$$

where *b* is the **Nozzle to throat area
ratio**, which is defined between the largest and smallest
cross-sectional areas of the nozzle.

### Pressure Losses Due to Friction

The flow experiences losses due to friction in the nozzle, secondary suction inlet, throat, and diffuser. These losses are calculated based on a coefficient defined for each section and the area, or area ratio, between different sections of the pump. Note that friction incurs pressure losses, irrespective of flow direction. The pressure loss in the nozzle due to friction is:

$$\Delta {p}_{f,Nozzle}={K}_{N}\frac{{\dot{m}}_{A}\left|{\dot{m}}_{A}\right|}{2\rho {A}_{N}^{2}},$$

where *K*_{N} is the
**Primary flow nozzle loss coefficient**. The pressure loss due
to friction in the suction flow through the annulus is:

$$\Delta {p}_{f,Annulus}={K}_{S}\frac{{\dot{m}}_{S}\left|{\dot{m}}_{S}\right|}{2\rho {\left({A}_{T}-{A}_{N}\right)}^{2}},$$

where *K*_{S} is the
**Secondary flow entry loss coefficient**. The pressure loss in
the throat due to friction is:

$$\Delta {p}_{f,Throat}={K}_{T}\frac{{\dot{m}}_{B}\left|{\dot{m}}_{B}\right|}{2\rho {A}_{T}^{2}},$$

where *K*_{T} is the
**Throat loss coefficient**. The pressure loss in the diffuser
due to friction is:

$$\Delta {p}_{f,Diffuser}={K}_{D}\frac{{\dot{m}}_{B}\left|{\dot{m}}_{B}\right|}{2\rho {A}_{T}^{2}},$$

where *K*_{D} is the
**Diffuser loss coefficient**. Note that the sign corresponds
to negative flow from the throat toward port **B**. Losses are
defined for the regions of highest velocity in the flow. For this reason, the throat
area, which is equal to the diffuser inlet area, is used in the diffuser loss
equation.

### Saturation Pressure in the Nozzle

Cavitation occurs when a region of low pressure in the flow falls below the vapor
saturation pressure. This creates pockets of vapor in the liquid and impedes any
further increase in flow through the pump. You can model this flow rate limit by
specifying a **Minimum nozzle pressure**, beyond which the fluid
velocity will remain constant. The total pressure change over the pump depends on
this pressure threshold at the nozzle outlet. Between the nozzle and the diffuser,
the pressure change is either

$${p}_{B}-{p}_{N}=\Delta {p}_{mixing}+\Delta {p}_{f,Throat}+\Delta {p}_{f,Diffuser}-\Delta {p}_{a,Diffuser}$$

or $${p}_{B}-{p}_{N,\mathrm{min}},$$ whichever is smaller.

The total pressure change in the nozzle is:

$${p}_{A}-{p}_{N}=\Delta {p}_{a,Nozzle}+\Delta {p}_{f,Nozzle}.$$

The total pressure change in the annulus is:

$${p}_{S}-{p}_{N}=\Delta {p}_{a,Annulus}+\Delta {p}_{f,Annulus}.$$

### Assumptions and Limitations

The motive and suction liquids are the same.

Mixing in the throat is assumed to be uniform and complete.

The nozzle inlet is much larger than the nozzle outlet, and the suction jet annulus is much smaller than the suction inlet.

The change in pressure due to the nozzle is not modeled for reversed flows.

Any effect of cavitation is modeled as a maximum limit on the flow rate in the throat.

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2020a**