Spending on orphanages comes in two forms:

First: Personal needs: food, drink, clothes and the like.

Second: Building orphanages.

It is permissible to pay the Zakah (alms) funds for the first form since the orphans are poor and those entrusted by the ruler to take care of them, being minors, receive the funds on their behalf.

As for building orphanages from the Zakah funds, this isn`t permissible because Zakah is an act of worship that must meet certain conditions- stipulated in Sharia-to be considered valid. For example, the eligible recipients should receive the funds.  Allah, The Almighty, Says {What means}: "The alms are only for the poor and the needy, and those who collect them, and those whose hearts are to be reconciled, and to free the captives and the debtors, and for the Cause of Allah, and (for) the wayfarer; a duty imposed by Allah. Allah is Knower, Wise." {At-Tawbah, 60}.

As known to all, orphanages are state property and orphans leave them as soon as they become adults. Moreover, benefactors should be encouraged to build orphanages-as a continuous charity-from other funds. However, if a person borrowed money to build an orphanage, then it is permissible to give him from the Zakah funds under the pretext of being a debtor, even if he is rich.  In fact, the debtor who borrows money for common good is allowed to take from the Zakah money, even if he is rich. And Allah The Almighty Knows Best.