  For an immortal Ricci flow on an $m$-dimensional $(m\ge 3)$ closed manifold,
we show the following convergence results: (1) if the curvature and diameter
are uniformly bounded, then any unbounded sequence of time slices sub-converges
to a Riemannian orbifold; (2) if the flow is type-III with diameter growth
controlled by $t^{\frac{1}{2}}$, then any blowdown limit is an $m$-dimensional
negative Einstein manifold, provided that Feldman-Ilmanen-Ni's
$\boldsymbol{\mu}_+$-functional satisfies $\lim_{t\to \infty}
t\boldsymbol{\mu}_+'(t)=0$.
