  We present a simple way to construct 3D initial conditions for relativistic
heavy-ion collisions based on the Glauber collision geometry. Local energy and
momentum conservation conditions are imposed to set non-trivial constraints on
our parameterizations of longitudinal profiles for the system's initial energy
density and flow velocity. After calibrating parameters with charged hadron
rapidity distributions in central Au+Au collisions, we test model predictions
for particle rapidity distributions in d+Au and peripheral Au+Au collisions in
the Beam Energy Scan (BES) program at Relativistic Heavy-Ion Collider (RHIC).
Simulations and comparisons with measurements are also made for Pb+Pb
collisions at Super Proton Synchrotron (SPS) energies. We demonstrate that
elliptic flow measurements in heavy-ion collisions at $\sqrt{s} \sim 10$ GeV
can set strong constraints on the dependence of Quark-Gluon Plasma shear
viscosity on temperature and net baryon chemical potential.
