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ππ = ππ»ππππ βππ Eqn.3-49 ππ»ππππ + πΌπΏπππ + πΌπ πΆ + πΌπ·πΉ 3.3.6 Vaneless Space and Diffuser Calculations The vaneless space is modeled by assuming conservation of angular momentum and the expansion of the turbulent boundary layer along the walls of the vaneless space. By conservation of angular momentum, rVΞΈ is a constant and rVr is a constant. Thus, the flow angle with respect to the radial direction remains constant with the exception of changes in radial velocity resulting from narrowing or widening of the space. Figure 3.11 shows the flow path through the vaneless space. Due to the conservation requirements, the flow follows a curved path through the space. Figure 3.11: The flow path in the vaneless space (not to scale). The flow angle with respect to the radial direction, Ξ±, is a constant. In real compressors the velocity profile at the impeller outlet is highly non-uniform. For that reason the core flow and the flow near the walls will follow very different flow paths. Near the wall, flow can re-enter the impeller and therefore an additional surge condition is used. If the tangent of the absolute flow angle is above 4.0, then the flow is said to be surged. The subroutine VANELESS begins by setting a time step such that the flow will travel 1/500 of the distance to the vaned diffuser in the first time step. That same time step is then used throughout the vaneless space. The velocity and flow direction at the beginning of the time step are assigned to the entire time step. The position of a fluid particle at the end of that time step is then computed. The velocity is computed at the new position, based on conservation of angular momentum, and then the code continues until the position has reached the entrance to the vaned diffuser. Figure 3.11 is not accurate in that it shows a constant angle ΞΈ between time steps. In RGRC the angular distance traveled each step will actually decrease, as the velocity decreases. 67PDF Image | Supercritical Carbon Dioxide Cycle Analysis
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