Jet Impinging on a Spring-Loaded Plate
Problem Description
ρ is fluid density. Q is volumetric flowrate. V 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.
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

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.
