Why did Imam Hussain go to karbala knowing what was going to happen to him & his family? He ran away from the tyrants in Mecca, why didn't he just run away again?

First Imam Hussain tried to avoid fighting as much as possible. He left Madeenah and Mecca to avoid fighting. The people of Iraq told him to come to them and they will be on his side, on his way there the army of Yazeed intercepted him. He asked for them to let him go to Turkey or Yemen and avoid fighting but they said no, either you pay allegiance to Yazeed or we will kill you. As far as the Imam knowing what tragedies are going to happen, that is the way all the Imams died. The fact that they know their death beforehand does not mean that they sought death or killed themselves. However, the knowledge of the Imam is separated into apparent knowledge( knowledge seen by everyone) and given knowledge ( special knowledge from Allah). The Imam makes his decisions in this life based on apparent knowledge and based on the apparent knowledge that the people of Iraq are on his side, going there was the best move. Also this shows the patience of the Imams and their submission to the will of Allah. Even though they know they are going to die they move forward with bravery and courage because that is what Allah chose. One last note with regard to this specific instance. Imam Hussain had a mission and in order for the mission to be accomplished, he had to die. His sacrifice is what was needed, not his physical victory. The goal was to show that the position of "khaleefah" at the time was completely separate from Islam. If it was not for Imam Hussain we would be saying Imam Yazeed today because the Muslims at the time were so ignorant that they believed yazeed to be the representative of Allah and the leader of the Muslims. When he killed the grandson of the Prophet and the master of the youth of heaven by the agreement of all Muslims, he lost that description and there was a "separation between church and state" if you will. The topic is rather deep and requires getting into many different aspects of the knowledge of the Imam and the way they make their actions but I hope this brief answer satisfies your curiosity for now and we will tackle the topic more deeply when we can.