All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
Scholars have unanimously agreed that the rich son is obliged to provide for his poor parent. Ibn Qudaamah wrote, "The scholars reached a consensus on the fact that the sustenance of the poor parents who have no source of income is an obligation in their child's money." [Al-Mughni]
An-Nawawi wrote, "The most likely correct view is that the person who receives sufficient financial maintenance from a relative or a husband is not considered poor." [Minhaaj At-Taalibeen]
Hence, if this grandfather has a son who takes care of him in terms of spending on his basic needs, then he is not considered poor, and paying zakah to him does not clear the liability of the payer from the obligation of zakah.
In case that the son is financially strained, then the grandchildren cannot pay their zakah to their poor grandfather because, according to some scholars, they are obliged to spend on him. Ar-Rawdh Al-Murbi‘ reads, "If a person has a poor father and grandfather, then he is obliged to support both of them financially (i.e. he is also obliged to support his grandfather), even if he is prevented from inheriting from his grandfather due to the existence of his poor father."
However, based on the scholarly view that the grandson is not obliged to spend on his poor grandfather in this case, which is also the view of many scholars, it is allowable to pay the zakah to one's grandfather if he is poor.
Allah knows best.