Generating a multidimensional crystalline beam in a storage ring has been known to be difficult without a special cooling force, i.e., tapered cooling, because of the momentum dispersion induced by bending magnets. It is, however, possible to eliminate the dispersion all around the ring by adding an electric dipole field in each magnetic bending region. A storage ring with such unique deflectors should enable us to reach multidimensional crystalline states with an ordinary untapered cooling force. In order to verify this expectation, molecular dynamics simulations are performed to study beam crystallization in several dispersion-free storage rings including the S-LSR at Kyoto University. The present results show that various crystalline states can be established without relying on the tapered force.