8.16 Real Gas Models

Some engineering problems involve fluids that do not behave as ideal gases. For example, at very high-pressure or very low-temperature conditions (e.g., the flow of a refrigerant through a compressor) the flow cannot typically be modeled accurately using the ideal-gas assumption. Therefore, the real gas model allows you to solve accurately for the fluid flow and heat transfer problems where the working fluid behavior deviate from the ideal-gas assumption.

ANSYS FLUENT provides three real gas options for solving these types of flows:

• Section  8.16.1: The Aungier-Redlich-Kwong Real Gas Model

• Section  8.16.2: The NIST Real Gas Model

• Section  8.16.3: The User-Defined Real Gas Model

All the models allow the user to solve for either a single-species fluid flow or a multiple-species mixture fluid flow.

Introduction

The states at which a pure material can exist can be graphically represented in diagrams of pressure vs. temperature (PT diagrams) and pressure vs. molecular or specific volume (PV diagrams). Homogeneous fluids are normally divided into two classes, liquids and gases. However the distinction cannot always be sharply drawn, because the two phases become indistinguishable at what is called the critical point. A typical pressure-temperature (PT) diagram of a pure material is shown in Figure  8.16.1.

Figure 8.16.1: Typical PT Diagram of a Pure Material

This diagram shows the single phase regions, as well as the conditions of P and T where two phases coexist. Thus the solid and the gas region are divided by the sublimation curve, the liquid and gas regions by the vaporization curve, and the solid and liquid regions by the fusion curve. The three curves meet at the triple point, where all three phases coexist in equilibrium. Although the fusion curve continues upward indefinitely, the vaporization curve terminates at the critical point. The coordinates of this point are called the critical pressure $P_c$ and critical temperature $T_c$. These represent the highest temperature and pressure at which a pure material can exist in vapor-liquid equilibrium. At temperatures and pressures above the critical point, the physical property differences that differentiate the liquid phase from the gas phase become less defined. This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable. This new phase, which has some properties that are similar to a liquid and some properties that are similar to a gas, is called a supercritical fluid.

Figure 8.16.2: Typical PV Diagram of a Pure Material

Figure  8.16.2 presents a typical diagram of pressure versus molar or specific volume (PV diagram) of a pure material. The dome shaped curve ACD is called the saturation dome and separates the single phase regions in the diagram; curve AC represents the saturated liquid and curve CD the saturated vapor. The area under the saturation dome ACD is the two-phase region and represents all possible mixtures of vapor and liquid in equilibrium. Curve ECB is the critical isotherm and exhibits a horizontal inflection at point C at the top of the dome. This is the critical point. The specific volume corresponding to the critical point, is called the critical specific volume $V_c$. The conditions to the right of the critical isotherm ECB correspond to supercritical fluid.

Choosing a Real Gas Model

The equation of state is the mathematical expression that relates pressure, molar or specific volume, and temperature for any pure homogeneous fluid in equilibrium states.

The simplest equation of state is the ideal gas law, which is approximately valid for the low pressure gas region of the PT and PV diagrams. Ideal gas behavior can be expected when

or

If your flow conditions correspond to either of those cases, you may use the ideal gas law in your simulation.

Another idealization, that of the incompressible fluid, can be employed for the low pressure region of the liquid phase. A constant density option is the appropriate selection in that case.

However, both of these approaches are not good approximations for flow conditions close to and beyond the critical point, where the fluid behavior cannot be described by the ideal gas, or the incompressible liquid assumptions. We refer to a fluid under those conditions as a real fluid, or a real gas and more complex relations are used for the determination of its physical and thermodynamic properties.

ANSYS FLUENT provides the following options for solving real fluid problems:

• The Aungier-Redlich-Kwong real gas model can be used to solve problems in the gas and supercritical fluid regimes. The model is not available for the liquid state and the two-phase region under the phase dome. For further details see Section  8.16.1.

• The NIST real gas model can be used to solve problems in the liquid, or gas and supercritical fluid regimes. The model does not allow modeling of the two-phase region. For further details see Section  8.16.2.

• The User-Defined real gas model allows you to solve problems in all regimes, as long as appropriate relationships are provided through the User-Defined real gas functions. For further details see Section  8.16.3 and the UDF manual.

The concepts presented in this section for pure materials are also extended to multi-component mixtures with the introduction of appropriate composition dependent parameters in the real gas equations of state and the material property models. All the real-gas modeling options above allow for either single-species or multi-component flow modeling. In addition, you may solve reacting flow problems with the Aungier-Redlich-Kwong model and the User-Defined real gas functions.