  We take the experimental data for transverse momentum spectra of identified
charged hadrons in different centrality classes for nucleus-nucleus (A+A)
collisions at various Relativistic Heavy-Ion Collider (RHIC) energies measured
by the STAR collaboration. We analyse these data in the framework of color
string percolation model (CSPM) in order to extract various percolation
parameters at different centralities at RHIC energies to study the effect of
collision geometry and collision energy. We use these parameters to study the
centrality dependent behaviour of initial temperature of the percolation
cluster, energy density, average transverse momentum, shear viscosity to
entropy density ratio ($\eta/s$) and trace anomaly for different energies at
RHIC from $\sqrt{s_{\rm NN}}$ = 19.6 to 200 GeV. These observables are found to
strongly depend on centrality at various collision energies. The critical
percolation density, which is related to the deconfinement phase transition is
achieved in the most central nucleus-nucleus collisions, while it fails in the
peripheral collisions. A universal scaling is observed in color suppression
factor and initial temperatures when studied as a function of charged particle
pseudorapidity distribution scaled by nuclear overlap area at RHIC energies.
The minimum of $\eta/s$ is observed in the most central collisions at
$\sqrt{s_{\rm NN}}$ = 130 and 200 GeV.
