Session doesn't expire after close browser

The session doesn't expire even Allow persistent logins is set or not.
My authentication method is set to Db

Follow includes/Session.php (line 387) is call to non exist function validate_session_db().

$method = 'validate_session_' . $method;
if (function_exists($method))
{
if (!$method($this->data))

{ $session_expired = true; }

}

My solution is add this function at the end of includes/auth/auth_db.php file. The result is working well on myside.

function validate_session_db(&$user)
{
if ($user['session_id'] != $_COOKIE["PHPSESSID"] && !isset($_COOKIE["PHPSESSID"]) && !$user['session_autologin'])

{ return false; }

else

{ return true; }

}