## Jet Pumps and Steam/Gas Ejectors

**Jet Pumps and Steam/Gas Ejectors**

In this network five different approaches are described in order to model Jet Pumps and Steam or Gas Ejectors in Flownex.

**Momentum addition from a Pipe element**

This first case has momentum addition from the sidepipe into the main stream – check the pipe sizes. It is specified on the downstream pipe, as indicated by the “M” below right from that pipe element. See the Flownex Theory Manual section 5.3.5 for information.

The pressures were chosen such that there is no choking.

This case solved with no relaxation.

**Momentum addition from a Restrictor with Discharge Coefficient into the main stream**

The pressures were chosen such that there is no choking.

For this case to solve the options are:

1. relax pressure < 0.65 && relax mass =1

2. relax pressure = 0.7 && relax mass < 0.5

Remember that the RD element assumes total velocity term pressure loss, i.e. K=1.

**Momentum addition from the Restrictor with Loss Coefficient into the main stream**

The pressures were chosen such that there is no choking.

For this case to solve the options are:

1. Relax pressure < 0.65 && relax mass =1

2. Relax pressure = 0.7 && relax mass < 0.5

It does not seem to make any difference that the loss factor for the Restricor with Loss Coefficient element can be set to much less than the Restrictor with Discharge Coefficient element.

**Using a Jet Pump element**

See the Flownex Library Manual: Chapter 8-2 for information.

As shown in the Library Manual, the loss factor for the Jet pump is dependent on volume flow rates (which, with pressure boundaries, are dependent on the losses), therefore this case requires more iterations than some of the other momentum addition cases to get the loss factor and the mass flow rates converged.

Reducing the pressure and mass relaxation only caused an increase in iterations.

However, the number of iterations required with this component is very sensitive to the “junction relaxation”.

For the case on the right, it required 72 iterations to converge with default junction relaxation, which should be 0.4 (see the Flownex General User Manual: Chapter 3-102, section 3.3.2.7 Relaxation parameters).

Keep in mind that the loss factors for this components were analytically derived assuming incompressible flow.

**Using a Turbine coupled to a Compressor component in Flownex**

While all the cases above apply specifically to incompressible or low-Mach number cases, an appropriate method to simulate a compressible flow jet pump or steam ejector is presented in this network. The fact that there are no data transfer links that passes around mass flow or pressure ensures complete mass, momentum and energy conservation and is therefore safe and stable to use in a network.

Conceptually in a steam or gas ejector, the motive fluid/high pressure stream drives a turbine that drives an isentropic pump on the low-pressure side.

The pump speed have to be iterated until its power consumption matches the turbine power production.

The motive fluid/high pressure stream flow relationship is taken care off correctly by setting the simple turbine to use a restrictor characteristic, which takes choking into account.

The low-pressure fluid flow is also taken into account in the right way by the Restrictor with Loss coefficient, which will also limit the flow with a choked throat.

The downstream fluid pressure drop is through an incremented pipe, which will also add an appropriate pressure drop by means of choking.

Furthermore it does not require any underrelaxation but it does sometimes require more iterations than default because of the iterative script.

The performance of the iterative script is quite dependent on its relaxation parameter. Vary it by an order of 10 larger or smaller when in doubt and do check the convergence behaviour very closely to get the right relaxation parameter.

Appropriate values for the turbine isentropic efficiency can be obtained from the research papers by McGovern, Bulusu, Antar and Lienhard.

Typical values are between 5% and 30%, dependent on the various pressure ratios.

Apply for Internship