Mixing of air streams is a frequently occurring scenario in many engineering applications. For the purposes of this discussion, let the two incoming streams be A and B and the resulting (output) stream be C. Usually, we would know the conditions of A & B and the requirement would be to determine the conditions of C. However, sometimes the requirement would be to determine B, knowing A and C.
The properties of air that are relevant to the analysis of such situations are:
Temperature – measurable
Pressure – measurable
Density (or specific volume) – not measurable
Moisture Content (also indicated by specific humidity, relative humidity, percentage saturation, vapour pressure) – relative humidity is measurable.
Background to the Problem
One basic assumption is that energy losses due to flow behaviour can be ignored, thus leading to the premise that the energy (specific enthalpy * mass) of the output stream is equal to the sum of the energies of the input streams. It is also assumed that there is no mass loss during the mixing process.
Direct measurement of enthalpies is not feasible. Hence these have to be calculated using psychrometric relations. Mass flow rates may be derived from volumetric flow rates and the density. Density, not being directly measurable, has to be worked out from the pressure, temperature and relative humidity. So the measurable parameters are pressure, temperature and relative humidity and the parameters that need to be determined are the enthalpy, and mass flow rate. It is obvious that psychrometric relationships have to be utilised to solve such problems.
Variations of the Problem
1. A, B and C are at the same pressure (temperatures of A and B could be same or different)
2. A & B are at the same pressure, but C is at a different pressure (same or different temperatures)
3. A, B & C are all at different pressures. (same or different temperatures)
General Method of Solution
For Type 1 problems, knowing the temperature and relative humidities of the incoming streams (A & B) it is possible to mark points (say P & Q) corresponding to the conditions of A & B. Draw a line between P & Q and find the point X such that the distances between X and P and X and Q correspond to the mass flow rates of B & A. The psychrometric values at point X would then indicate the condition of the output stream. This type of situation is easily represented on the normal psychrometric chart because the pressures of all three streams are the same.
For Type 2 problems, where the input streams are at the same pressure, the procedure is identical to that of Type 1, up to the stage of finding point X. However, as the output stream is at a different pressure, the psychrometric properties at point X, as indicated on that psychrometric chart, would not be correct for the pressure of stream C. In this case the solution would be to superimpose a chart for the pressure of C over the previous chart and read off values from the new chart.
For Type 3 problems, we would need 3 charts, one each for the 3 pressures involved. The same approach could be used because enthalpy is not dependent on the pressure.
A graphical solution to deal with the issues of mixing streams, would be made much easier where the psychrometric relationships at all three pressures could be available from the same chart. While superimposing full psychrometric charts over another one will be so confusing as to render the scheme unfeasible, it is possible to draw just the relevant lines for each of the two or three pressures concerned on the same graph and use a dynamic readout mechanism to display the set of psychrometric property values of the three streams concerned.