I'm not sure I understand your intention - do you want to refresh the page the user is on, once he/she has sent a new comment ?
If so - if you're using a normal form post/get, then you can redirect the user request to which ever page you want, and show a notice, using the code @Seb wrote above.
If you're using ajax to send the comment, you can return a response from the ajax call, notifying the javascript function that created the ajax call that the page needs to refresh, and then set the location.href variable to what ever url you want.
However - if you want to refresh the page for all users seeing the comments page, once another user has sent a comment, you will need to have a repeated ajax call every few seconds/minutes, that checks if something has changed in the server, and if so use the location.href variable to redirect the user to a different.
You can't do this if you're relying only on the session variable saved on the computer of the commenter, as it is only accessible when the original commenter is using your site.