  In this paper, we consider certain union $X(\mu,b)$ of affine Deligne-Lusztig
varieties in the affine flag variety that arises in the study of mod-$p$
reduction of Rapoport-Zink spaces and moduli spaces of shtukas associated to a
connected reductive group. Under a mild hypothesis on $\mu$, but no further
restrictions on the group, we compute its dimension in the case where $b$ is
the maximal neutrally acceptable element.
