He did ghusl just to be clean, and he did not realize that he was junub. Should he repeat his ghusl?

I woke up and made ghusl and prayed as I usually do every morning. Two hours later I found out that I was junub. Should I repeat my ghusl in this case or the first ghusl is enough? Bearing in mind that I did not intend to clear the janaba while making ghusl.

Praise be to Allaah.
Firstly: 
If a person prays then realizes that he was junub, he must do ghusl and repeat the prayer; his first ghusl does not count that he did as a habit or to keep clean, without the intention to remove janaabah, because the Prophet (peace and blessings of Allaah be upon him) said: “Actions are but by intentions and each person will have but that which he intended.” Narrated by al-Bukhaari (1) and Muslim (1907). 
Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (1/158): If he intended to do an act of purification for something for which purification is not prescribed, such as to cool down, and he did not intend the purification that is prescribed in sharee’ah, then the impurity is not removed because he did not have the intention of purification, so it does not count as anything.
End quote.