Flow through a Cone Valve

The 3D cone valve experimental data is taken from Ref. 27 (the same in Ref. 14). The cone valve has a complex flow passage geometry combining sudden 3D contractions and expansions at different turning angles φ (Figure 1). Following the Ref. 14 and Ref. 27 recommendations on determining a valve’s hydraulic resistance correctly, i.e. to avoid any valve-generated flow disturbances at the places of measuring the flow total pressures upstream and downstream of the valve, the inlet and outlet straight pipes of the same diameter D and of enough length (we take 7D and 17D) are connected to the valve, so constituting the experimental rig model (see Figure 2). As in Ref. 27, a water flows through this model. Its temperature of 293.2 K and fully developed turbulent inlet profile (see Ref. 21) with mass-average velocity U ≈ 0.5 m/s (to yield the turbulent flow’s Reynolds number based on the pipe diameter ReD = 105) are specified at the model inlet, and static pressure of 1 atm is specified at the model outlet.

The corresponding model used for these predictions is shown in Figure 2. The valve’s turning angle φ is varied in the range of 0…55° (the valve opening diminishes to zero at φ = 82°30´).

The flow predictions performed with Flow Simulation are validated by comparing the valve’s hydraulic resistance ζv, and the dimensionless coefficient of torque M (see Figure 1) acting on the valve, m, to the experimental data of Ref. 27 (Ref. 14).

Since Ref. 27 presents the valve’s hydraulic resistance (i.e. the resistance due to the flow obstacle, which is the valve) ζv, whereas the flow calculations in the model (as well as the experiments on the rig) yield the total hydraulic resistance including both ζv and the tubes’ hydraulic resistance due to friction, ζf, i.e. ζ = ζv + ζf, then, to obtain ζv from the flow predictions (as well as from the experiments), ζf is calculated (measured in the experiments) separately, at the fully open valve (φ = 0); then ζv = ζ – ζf.

In accordance with Ref. 27, both ζ and ζf are defined as (Po inlet – Po outlet)/(ρU2/2), where

Po inlet and Po outlet are the flow total pressures at the model’s inlet and outlet, accordingly, ρ is the fluid density. The torque coefficient is defined as m = M/[D3·(ρU2/2)·(1 + ζv)], where M is the torque trying to slew the valve around its axis (vertical in the left picture in Figure 1) due to a non-uniform pressure distribution over the valve’s inner passage (naturally, the valve’s outer surface pressure cannot contribute to this torque). M is measured directly in the experiments and is integrated by Flow Simulation over the valve’s inner passage.

The Flow Simulation predictions have been performed at result resolution level of 5 with manual setting of the minimum gap size to the valve’s minimum passage in the Y = 0 plane and the minimum wall thickness to 3 mm (to resolve the valve’s sharp edges).

Flow Simulation has predicted ζf = 0.455, ζv shown in Figure 3, and m shown in Figure 4 It is seen that the Flow Simulation predictions well agree with the experimental data of Ref. 27.

This cone valve's 3D vortex flow pattern at φ = 45° is shown in Figure 5 by flow trajectories colored by total pressure. The corresponding velocity contours and vectors at the Y = 0 plane are shown in Figure 6.