  We apply a quark combination model with equal-velocity combination (EVC)
approximation to study the elliptic flow ($v_{2}$) of hadrons in heavy-ion
collisions in a wide collision energy range ($\sqrt{s_{NN}}=$ 27 - 5020 GeV).
Utilizing the simple relationship between $v_{2}$ of hadrons and those of
quarks under EVC, we find that $v_{2}$ of up/down quarks obtained by
experimental data of proton is consistent with that obtained by data of
$\Lambda$ and $\Xi$. $v_{2}$ of strange quarks obtained by data of $\Omega$ is
consistent with that obtained by data of $\Lambda$ and $\Xi$, and at RHIC
energies it is also consistent with that obtained by data of $\phi$. This means
that $v_{2}$ of these hadrons have a common quark-level source. Using data of
$D^0$, we obtain $v_{2}$ of charm quarks with $p_T\lesssim 6$ GeV/c. We find
that under EVC charm quark dominates $v_{2}$ of $D$ mesons at low $p_{T}$ but
light-flavor quarks significantly contribute to $v_{2}$ of $D$ mesons in the
range $3\lesssim p_{T}\lesssim8$ GeV/c. We predict $v_{2}$ of charmed baryons
$\Lambda_{c}^{+}$ and $\Xi_{c}^{0}$ which show a significant enhancement at
intermediate $p_{T}$ due to the double contribution of light-flavor quarks. The
properties of the obtained quark $v_{2}$ under EVC are studied and a regularity
for $v_{2}$ of quarks as the function of $p_{T}/m$ is found.
