How to while loop until the end of a file in Python without checking for empty line?

Don't loop through a file this way. Instead use a for loop.

for line in f:
    vowel += sum(ch.isvowel() for ch in line)

In fact your whole program is just:

VOWELS = {'A','E','I','O','U','a','e','i','o','u'}
# I'm assuming this is what isvowel checks, unless you're doing something
# fancy to check if 'y' is a vowel
with open('filename.txt') as f:
    vowel = sum(ch in VOWELS for line in f for ch in line.strip())

That said, if you really want to keep using a while loop for some misguided reason:

while True:
    line = f.readline().strip()
    if line == '':
        # either end of file or just a blank line.....
        # we'll assume EOF, because we don't have a choice with the while loop!
        break