In this problem, a circular jet impacts on a spring-loaded flat plate. The flow
changes direction when it reaches the plate, resulting in an analytical force
of:(1)
Where,
Is fluid density.
Is volumetric flowrate.
Is the jet velocity.
Volumetric flow of a jet of diameter d is Q = πd2/4, where d is jet
diameter. Assuming a spring with a stiffness of k, the above force will displace the
plate by Δx = F/k.
To reduce the oscillations, the plate motion is critically damped using a linear
damper. The damping coefficient is set to c = 2(kM)1/2, so the plate of
mass M approaches its equilibrium position without overshooting.
Table 1 shows the parameters used for the simulation here.
Based on these values, the analytical plate displacement in the jet direction is
0.01m.
Table 1. Simulation Parameters for Jet Impinging on a Plate
ρ [kg/m3]
µ [Pa.s]
V [m/s]
k [N/m]
c [N.s/m]
d [m]
M [kg]
1000
0.001
10
7068.58
531.74
0.03
10
Numerical Setup
The square plate of side length w = 0.09m is placed in the middle of a cubic
computational domain with a side length of h = 0.12m. Discretized by 30 particles
across diameter (dx = 0.001m), only the jet fluid phase is simulated. Figure 1 shows a schematic of the problem. Figure 1. Jet, Plate and Spring-Damper Configuration Schematic
Results
In Figure 2, the plate reaches a constant displacement of 0.0989m
between 0.4s and 0.5s, very close to the analytical value of 0.01m. While the force
applied to the plate has some oscillations, the time averaged force on the plate in
0.1s to 0.5s interval is equal to 69.94N. The analytical value of the impact force
is equal to 70.68N. Figure 2. Results of Jet Impingement on the Spring-Loaded Plate. left: shows the plate displacement versus time. right: shows the fluid
force on the plate due to jet impact. The dashed line is the average
force.