Jet Pump (IL)

Liquid-liquid jet pump in an isothermal liquid network

Since R2020a

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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 $$p_B-p_{N,\min },$$ 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

A — Liquid port

isothermal liquid

Motive liquid inlet port.

S — Liquid port

isothermal liquid

Suction liquid inlet port.

B — Liquid port

isothermal liquid

Mixed fluid outlet port.

Parameters

Nozzle area — Nozzle inlet area

1e-4 m^2 (default) | positive scalar

Cross-sectional area of the inlet nozzle at its widest section. The motive liquid enters the jet pump through the nozzle.

Nozzle to throat area ratio — Nozzle outlet to throat area

0.25 (default) | positive scalar

Characteristic ratio of the nozzle outlet and throat cross-sectional areas.

Diffuser inlet to outlet area ratio — Diffuser geometry ratio

0.25 (default) | positive scalar

Characteristic ratio of the diffuser inlet and outlet cross-sectional areas.

Primary flow nozzle loss coefficient — Friction loss coefficient

0.05 (default) | positive scalar

Characterizes the losses in pressure due to nozzle friction in the motive flow.

Secondary flow entry loss coefficient — Friction loss coefficient

0.005 (default) | positive scalar

Characterizes the losses in pressure in the suction flow due to the suction inlet friction.

Throat loss coefficient — Friction loss coefficient

0.1 (default) | positive scalar

Characterizes the losses in pressure in the mixture due to throat friction.

Diffuser loss coefficient — Friction loss coefficient

0.1 (default) | positive scalar

Characterizes the losses in pressure due in the mixed flow due to friction in the diffuser.

Minimum nozzle pressure — Minimum pressure at the nozzle outlet

0.1 Pa (default) | positive scalar

Sets the maximum allowed pressure change in the jet pump. If pressures at the nozzle exit fall below this value, the block simulates the effect of cavitation by restricting the fluid velocity to the velocity at the minimum nozzle pressure.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a