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Non-Condensable Gas Model: It's Not Just a Phase

Our Development Note this issue highlights the Non-Condensable Gas Model: Enhancement of the Phase Change Model to be released in FLOW-3D Version 9.3.

Non-Condensable Gas Model: Enhancement of the Phase Change Model

A non-condensable gas includes any component of the gas phase that will not condense to liquid in the particular system of interest (i.e. the temperature & pressure range expected is above the boiling and/or critical point of the gas).

FLOW-3D's existing phase change model is a powerful tool that predicts the formation and interactions of vapor bubbles and the surrounding liquid – the bubbles can respond dynamically to liquid motion, and can grow or shrink depending on the temperature and pressure of their surroundings. However, it has not yet been possible to include the effects of a non-condensable gas that may be present along with the vapor inside the bubble or other vapor space.

This can be important, for instance, in the dynamics of an air/water/steam system, where bubbles containing both water vapor and air can exist at conditions cooler or at lower pressure than would the vapor alone. FLOW-3D Version 9.3 removes this limitation by allowing users to model non-condensable gases.

Highlights

Model Basics

This model must be used with FLOW-3D’s compressible two-fluid flow option, along with sharp interface tracking. A new quantity that tracks the local concentration of the non-condensable gas allows the model to predict the gas's effect within the gas/vapor phase: adjustments to the gas constant and heat capacity alter the pressure-density relationship. The computation of the vapor pressure of the condensable phase in the gas/vapor mixture is therefore changed as well: it is the volume fraction of the vapor times the local absolute pressure. Thus, the basis of the model is the calculation of the mass transfer rate:

Sample Results Using Experimental and Simulation Data

Work based on this model was recently presented at the American Institute of Aeronautics and Astronautics conference[1]. This work included a comparison between actual test data and computational simulations of cryogenic tanks containing liquefied gases in combination with a second, non-condensable gas (typically helium). The example below is for a tank containing liquid nitrogen with a gas space containing nitrogen vapor and helium gas. In the example, the walls of the tank are gradually heated until the tank pressure reaches 25 psi, at which point a spray of cool liquid nitrogen is introduced to rapidly cool (and thus depressurize) the tank. This process is then repeated. The simulation data shows good agreement with actual test data; the errors are typically of the order of ~10%. Errors between the FLOW-3D model and the test data can be partly attributed to the fact that the rate of heat transfer in the model is assumed to be constant, as the heat transfer coefficient is difficult to measure, and the liquid spray injected into the tanks is held at a constant temperature.

Plot of pressure within the cryogenic tank: comparison between test data and FLOW-3D model.
Plot of pressure within the cryogenic tank: comparison between test data (red) and FLOW-3D model (blue). The pressure rises due to gradual heating through the tank walls and then rapidly decreases due to introduction of a cool nitrogen spray.

 

Image of temperature profile inside the tank during FLOW-3D simulation
Image of temperature profile during FLOW-3D simulation. This plot shows the temperature profile immediately prior to initiation of the spray bar (centerline).

Summary

With the addition of non-condensable gas to the already powerful two-fluid phase change model, FLOW-3D users will be able to simulate a broader range of multiphase flow problems. This is just one of a long line of multiphase flow capabilities added to FLOW-3D, with more to come in the future.

[1] PDF icon Gary Grayson, Alfredo Lopez, Frank Chandler, Leon Hastings, Ali Hedayat, and James Brethour, CFD Modeling of Helium Pressurant Effects on Cryogenic Tank Pressure Rise Rates in Normal Gravity, 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, © 2007 by The Boeing Company. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. AIAA 2007-5524, 8 – 11 July 2007