Scaling of the Transient Hydroelastic Response and Failure Mechanisms of Self-Adaptive Composite Marine Propellers

Table 1

Scaling ratios for critical parameters assuming geometric similarity and the following conditions to be true [27]: 𝜆_𝑔=𝜆_𝜌=𝜆_𝜈=𝜆_𝑎=𝜆_𝐽=𝜆_𝜎𝑛=𝜆_𝜌𝑠=1.

Parameter	Expression	Froude scale	Mach scale
Froude number	𝜆Fr	1	𝜆𝐷^−1
Reynolds number	𝜆Re	𝜆𝐷^3/2	𝜆𝐷
Mach number	𝜆Ma	𝜆𝐷^1/2	1
Axial velocity	𝜆𝑉	𝜆𝐷^1/2	1
Angular velocity	𝜆𝑛	𝜆𝐷^−1/2	𝜆𝐷^−1
Elastic modulus	𝜆𝐸𝑖	𝜆𝐷	1
Shear modulus	𝜆𝐺𝑖𝑗	𝜆𝐷	1
Poisson's ratio	𝜆𝜈𝑖𝑗	1	1
Elastic force	𝜆𝐹	𝜆^3𝐷	𝜆^2𝐷
Gravitational force	𝜆𝐺	𝜆^3𝐷	𝜆^3𝐷
Hydrodynamic inertial force	𝜆𝐻	𝜆^3𝐷	𝜆^2𝐷
Rotor inertial force	𝜆𝐼	𝜆^3𝐷	𝜆^2𝐷
Natural frequencies	𝜆𝜔	𝜆𝐷^−1/2	𝜆𝐷^−1