Jet liquid-liquid pump

Pumps and Motors

The Jet Pump block represents a jet liquid-liquid pump consisting of a nozzle, throat, and diffuser, as shown in the following illustration.

The model is based on the following equations, described in [1]:

$${q}_{1}=\frac{{A}_{n}}{\sqrt{1+{K}_{n}}}\sqrt{\frac{2}{\rho}\left({p}_{1}-{p}_{0}\right)}$$ | (1) |

$${q}_{2}=\frac{{A}_{n}\cdot c}{\sqrt{1+{K}_{en}}}\sqrt{\frac{2}{\rho}\left({p}_{2}-{p}_{0}\right)}$$ | (2) |

$${p}_{d}-{p}_{0}=Z{b}^{2}\left(\frac{2}{b}+\frac{2}{1-b}{M}^{2}-{\left(1+M\right)}^{2}\cdot \left(1+{K}_{th}+{K}_{di}+{a}^{2}\right)\right)$$ | (3) |

$$b=\frac{{A}_{n}}{{A}_{th}}$$

$$c=\frac{1-b}{b}$$

$$Z=\rho \frac{{V}_{n}^{2}}{2}=\rho \frac{{q}_{1}^{2}}{2{A}_{n}^{2}}$$

$$M=\frac{{q}_{2}}{{q}_{1}}$$

where

q_{1} | Primary flow rate pumped through the nozzle |

q_{2} | Secondary flow rate |

q_{d} | Output flow rate |

p_{1} | Pressure at the nozzle inlet |

p_{2} | Pressure at the secondary flow rate inlet |

p_{0} | Pressure at the throat inlet |

p_{d} | Pressure at the pump outlet |

A_{n} | Nozzle area |

A_{th} | Throat area |

a | Diffuser area ratio, A / _{th}A_{d} |

A_{d} | Diffuser outlet area |

K_{n} | Nozzle hydraulic loss coefficient |

K_{en} | Throat entry hydraulic loss coefficient |

K_{th} | Throat hydraulic loss coefficient |

K_{di} | Diffuser hydraulic loss coefficient |

ρ | Fluid density |

Equation 1 describes the nozzle, Equation 2 – throat entry, and Equation 3 – the combination of the throat and the diffuser. The equations correspond to a standard configuration of the pump, where all the longitudinal dimensions conform to established, empirically determined values. For more details, see [1].

The pump parameters are closely related to each other, and the methodology described in [1] is recommended to determine their initial values.

The model is based on the one-dimensional theory.

The primary and secondary flows enter the mixing throat with uniform velocity distribution, and the mixed flow leaves the diffuser with uniform velocity distribution.

The fluid in the primary and secondary flows is the same.

The fluid is assumed to be incompressible and containing no gas.

**Nozzle area**Cross-sectional area of the nozzle. The parameter must be greater than zero. The default value is

`1`

cm^2.**Throat area**Cross-sectional area of the throat. The throat area is usually two to four times larger than the nozzle area. The default value is

`4`

cm^2.**Diffuser inlet/outlet area ratio**The ratio between the inlet and outlet diffuser areas. For a standard pump with a 5° – 7° included-angle diffuser, the ratio is close to 0.2. The parameter must be greater or equal to zero. The default value is

`0.224`

.**Nozzle loss coefficient**The hydraulic friction loss coefficient in the nozzle. The parameter must be greater than zero. The default value is

`0.05`

.**Throat entry loss coefficient**The hydraulic friction loss coefficient in the throat entry. The parameter must be greater than zero. The default value is

`0.005`

.**Throat loss coefficient**The hydraulic friction loss coefficient in the throat. The parameter must be greater than zero. The default value is

`0.1`

.**Diffuser loss coefficient**The hydraulic friction loss coefficient in the diffuser. The parameter must be greater than zero. The default value is

`0.1`

.

Parameters determined by the type of working fluid:

**Fluid density**

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

The block has the following ports:

`A`

Hydraulic conserving port associated with the nozzle entry (primary flow entry).

`S`

Hydraulic conserving port associated with the pump suction (secondary flow entry).

`P`

Hydraulic conserving port associated with the pump outlet.

`N`

Internal nonvisible hydraulic conserving port associated with the throat entry section of the pump. You can view the variables associated with the port by logging simulation data. For more information, see Data Logging (Simscape).

The Well with Jet Pump example represents a well jet pump installation, consisting of a surface-mounted centrifugal pump and a jet pump installed in the well below water level.

[1] I.J. Karassic, J.P. Messina, P. Cooper, C.C. Heald, *Pump
Handbook*, Fourth edition, McGraw-Hill, NY, 2008

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