Why not try an easier approach? Select opens when you hit enter when it has focus on it, so basically you need only to autofocus when the page load. Example:

<select id="dropdown" autofocus class="" name="">
 <option value="">Opt1</option>
 <option value="">Opt2</option>
 <option value="">Opt3</option>
</select>

If you still want to trigger the event EVERY time enter is hitted, you can do this:

window.addEventListener('keypress', function (e) {
 if (e.keyCode == 13) {
  document.getElementById("dropdown").focus();
 }
}, false);

Basically, select gain focus when you hit enter, then you can hit again to open it.

To answer my own question, the options are opened by using either the up/down arrow keys once the field is in focus. Its something that is build in the html, so no need to create separate listeners for it