These simulations use the Atmospheric Cloud Physics Laboratory (APCL) simulator (Plooster, 1985). Conditions are typical for the CFD chamber, flow 9.5 LPM, pressure (840mb). Starting from plug flow, a symmetric Poiseuille velocity profile develops. The model is not exactly the same as the CFD chamber. The model has flat parallel plates, not concentric cylinders, and gravity is not included.
For these calculations, the walls are at -13°C and -27°C, and the air is +10°C when it enters the chamber. At a distance of 2.6cm from the start, the sample air is injected in the midplane of the flow. Here are two figures showing the temperature profiles between the walls at 5 cm intervals from the inlet. In the first figure, temperature is plotted versus distance from the warm wall. As expected, the air temperature adjusts much more rapidly when the gap between the walls is small.
The second figure shows temperature versus scaled distance (0 to 1) from the warm wall. It is a different view of the same information as the first plot. For the 1.12cm standard gap, after 20cm travel the central temperature is within 0.5C of the final value.
These figures indicated that if the overall chamber length must be limited, then the gap between the walls should be kept as small as possible in order to reach the steady-state profiles as quickly as possible. On the other hand, you have to allow some elbow room for the structure that injects a lamina of air between two sheath flows. However, if you have a clever idea for a small injection method, please let me know.
Plooster, M.N., 1985: Computer models for simulation of experiments in the Atmospheric Cloud Physics Laboratory (ACPL). Report 5-31701, Denver Research Institute, Univ. Denver, Denver, CO, 78pp.