Examples of non-K\"ahler Calabi-Yau manifolds with arbitrarily large $b_2$

We construct non-K"ahler Calabi-Yau manifolds of dimension $\ge$ 4 with arbitrarily large 2nd Betti numbers by smoothing normal crossing varieties. The examples have K3 fibrations over smooth projective varieties and their algebraic dimensions are of codimension 2.