Bilateral Sudden Expansion

It is known from hydrodynamics that channels with a sudden expansion generate hydraulic resistance to the flow due to a loss of flow energy caused by vortices in the vortex region downstream of the sudden expansion.

In accordance with Ref. 14, the local hydraulic loss coefficient of a bilateral sudden expansion (the so-called total pressure loss due to flow) for a turbulent (Re > 104) flow with a uniform inlet velocity profile depends only on the expansion area ratio and is determined from the following formula:

where A0 and A1 are the inlet and outlet cross sectional areas respectively, P0 and P1 are the inlet and outlet total pressures, and ρu02/2 is the inlet dynamic head.

In a real sudden expansion the flow hydraulic loss coefficient is equal to ξ = ξf + ξs, where ξf is the friction loss coefficient. In order to exclude ξf from our comparative analysis, we have imposed the ideal wall boundary condition on all of the channel walls.

In this validation example the channel expansion area ratios under consideration are: 1.5, 2.0, 3.0, and 6.0. To avoid disturbances at the outlet due to the sudden expansion, the channel length is 10 times longer than its height. The 1 atm static pressure is specified at the channel outlet.

The ξs values predicted by Flow Simulation at result resolution level 8 for different channel expansion area ratios A0/A1 are compared to theory (Ref. 14) in Figure 1

From Figure 1, one can see that Flow Simulation overpredicts ξs by about 4.5...7.9 %.

Figure 1. Comparison of Flow Simulation calculations to the theoretical values for the sudden expansion hydraulic loss coefficient versus the channel expansion area ratio.