About the operational determination of the state and parameters of flowing moist air

The presented paper deals with the solution of moist air parameters for the needs of aerodynamic research or design. From the thermodynamic theory of moist air, a p-t diagram of moist air is designed to allow the operative expression of the process and state of the moist air. Using this diagram, it is possible to illustratively describe the course of parameters at various state changes in moist air such as isentropic expansion and compression, isothermal expansion and compression, isobaric state change, isochoric state change, or general polytrophic state change. The initial state of moist air is determined by the pressure, temperature and moisture of the air. In the p-t diagram, the process is expressed by the applicable curve; the identification of the parameters in which the phase transformation occurs in moist air is significant. Uncertainty analysis is performed.


Introduction
For quick determination of state of moist air, a Mollier's diagram of moist air is commonly used, it is a diagram that has a specific moisture of moist air on one axis (oriented from the vertical direction by 135°) and moist air enthalpy on the other axis (vertical). However, since the condition of moist air is determined by three parameters, one of the parameters (moist air pressure) must be fixed in the Mollier's diagram -that means, Mollier's moist air diagram is always designed for one concrete value of total pressure. In determining the condition of atmospheric moist air (when the pressure is always about 100 kPa), no problems occur. However, if it is necessary to solve changes of moist air that occur at other than atmospheric pressure, it should be noted that in the Mollier's diagram constructed for a different pressure value, all curves of constant relative moisture (and hence the saturation curve too) will be shifted. If it is necessary to solve such changes of moist air in which pressure changes, the Mollier's diagram is absolutely unusable. The aim of this paper is to construct such a diagram of moist air in which it would be possible to search the properties of moist air corresponding to different temperatures, moisture, but also to various pressures.

Fundamentals of moist air thermodynamics
Moist air is a mixture of dry air and water. The moisture (water) contained in the moist air is always in the form of steam, but in addition (in the case of a heterogeneous mixture), part of the moisture in moist air may also be in a liquid or solid state. [1] The moist air temperature   C  MA t is equal to the temperature of its components (1) The moist air pressure   Pa MA p is, according to Dalton's law, equal the sum of the partial pressures of dry air and water vapor (2) The saturated water vapor pressure   Pa V p   is a significant variable for moist air, determining the moisture content limit in the air for the existence of a homogeneous mixture: , the moist air is unsaturated and the mixture is homogeneous; , the moist air is saturated and the mixture is homogeneous. If there is more moisture in moist air than corresponds to the state of saturated moist air, excreted moisture condenses in liquid or solid form and moist air, as a heterogeneous mixture, is then formed by saturated moist air and by excreted condensate. Pressure of saturated water vapor is an unambiguous function of temperature (3) For pressure of saturated water vapor, the International Association for Water Vapor Properties has published relationships on temperature for equilibrium between liquid water and steam [2] and between solid phase of water and steam [3].
Relative moisture is defined only for a homogeneous mixture, and can be at a given temperature in the range In the case of a homogeneous mixture in which moisture is contained only in the form of steam, it is possible to write If the moist air forms a homogeneous mixture and its components (dry air and steam) can be described by the ideal gas model, it is possible to derive the relationship between specific and relative moisture For the specific moisture of a saturated homogeneous mixture   (10)

Curves of saturated moist air in equilibrium p -t diagram
For a given value of specific moisture of moist air can be calculated for each temperature from equation (10) the pressure of moist air, in which there would be exclude the moisture from the moist air. By plotting this dependence in the equilibrium p -t diagram, we get a curve of saturated moist air (it is a curve 1   ) for given specific moisture. If we plot the dependence of the pressure of saturated moist air on the temperature for different values of the specific moisture (it means with the parameter of the specific moisture x) in the equilibrium diagram, we obtained the moist air saturation curves (see Figure 1) [4]. In the diagram, the triple point -trDA and the critical point -crDA are indicated for dry air. For water vapor, the liquid-vapor saturation curve with the triple point -trV and the critical point -crV is indicated. For selected values of specific moisture x, the curves of pressure of saturated moist air are plotted.
Saturation lines for x = const.

Curves of constant relative moisture in equilibrium p -t diagram
If we wanted to use the diagram not only to determine the saturation limit, but also to determine the state of unsaturated moist air at different pressures and temperatures, it would be necessary to plot into the equilibrium p -t diagram not only the curves of the dependence of the saturated moist air pressure on the temperature (it is the curves 1   ), but also curves of dependences of moist air pressure on the temperature x = 0.001  Fig. 3 would be in the diagram several curves corresponding to a constant value of relative moisture . konst   (usually, the displayed curves of constant relative moisture are graded by 0.1, it is for each constant x, it would be further 9 curves) -see Figure 3a, respectively Figure 3b.
The diagram would be easy to use for the values of the specific moisture x for which curves are plotted, but for other values of the specific moisture x, the estimation of state of moist air from the diagram would be very complicated.
If we, however, in equation (8), respectively (9) neglect partial vapor pressure V p against the total moist air pressure MA p , it would be possible to express the total moist air pressure MA p as a function of temperature t (which is uniquely determined by the partial pressure of saturated vapors) and ratio of specific and relative moisture This dependence could then be plotted in the equilibrium p -t diagram as a set of curves with a parameter -see Figure 4a respectively Figure 4b.

Use of the equilibrium p -t moist air diagram with curves of a constant ratio of specific and relative moisture
The method of reading in such a diagram is very simplesee detail of p -t diagram - Figure 5: For moist air, its pressure MA p , temperature t and relative moisture  are usually specified. By the pressure and temperature, the point is determined in the equilibrium diagram (for example point A:  In addition, if we plot constant entropy lines in p -t diagram [4], diagram can also be used to solve isentropic changes of the state; for example from a previous state C -isentropic compression to twice pressure (point D:

Polytrophic change of state of moist air
The general reversible change of state of ideal gas (polytrophic state change) can be described by the equation [5] .

Relative uncertainty of the used approximation
The relative uncertainty  of such approximations when calculating the pressure of moist air (see 12) is equal to

Conclusion
Assuming the ideal behavior of gaseous components of moist air (dry air and water vapor), an equilibrium p -t diagram was constructed with a set of curves of a constant ratio of specific and relative moisture, enabling to determine the state of moist air at different pressures and to solve even such thermodynamic processes occurring in moist air, where the pressure changes. The second author, P.Šafařík, expresses thanks for support from the Project No. CZ.2.16/3.100/21569 Centre 3D Volumetric Anemometry.