While reading the answers and comments of When is "Y" a vowel? I thought of a few other words that seem to have "w" as a vowel but am not sure. In addition to "cwm" there is also "crwth" and "hwyl." My question is specifically about "hwyl." Is the "y" or the "w" in "hwyl" the vowel or both?
The linked-to post asks about when Y should be considered a vowel. The top answer there looks at words like why, where it arguably is, and words like yes, where it isn't. The very reasonable stance taken in that post is that letters represent sounds, and we can establish in a given word whether a particular sound should be considered a vowel or a consonant. This is true. Well, kind of.
Phonetically, vowels are sounds that do not contain friction or turbulence in the air flow. There is also no obstruction in the mouth restricting or diverting this airflow as it passes through the vocal tract. However, whether we consider such a sound a vowel or a consonant depends more on its position in the syllable structure than on its phonetic quality. It's primarily a matter of phonology (you can think of phonology as a kind of sound-grammar in a language), not sound quality.
English syllables are split into two parts. There's the Onset and the Rhyme. The rhyme is obligatory, but the onset is an optional feature. The onset is usually a consonant or group of consonants at the beginning of the word before the vowel, the rhyme is everything else. So in the word cat /kæt/, the onset is /k/ and the rhyme is /æt/.
Now the rhyme is further split into two parts. It has the most sonorous musical and vowellish part, the Nucleus, which is obligatory. It can also have a Coda, which involves the syllable getting both quieter and less sonorant. Codas are usually consonants or consonant clusters. So in /kæt/ the nucleus is /æ/ and the coda is /t/. So the syllable itself represents a peak in sonority. If it has an onset and a coda, then these will represent the dips in sonority at either end of the syllable.
Notice that I said that nucleuses are usually vowels. This is because we can, in special circumstances, have a syllabic consonant. This is when the nucleus of a syllable is a consonant. For example, in the word criticism /krɪtɪsɪzm/, the last syllable just consists of an /m/ sound. The consonants /r, l/ and /n/ also frequently occur as syllabic consonants in English.
I also said that onsets and codas are usually consonants. In actual fact we can get sounds that are phonemically vowels such as /w/, found at the beginning of the word wok, which occur in onsets. Generally, when we get a sound like this which only occurs in onsets, we regard it as a consonant, at least in terms of the phonology. This is despite the fact that phonetically, in terms of the quality of the sound, it's technically a vowel.
Now the letter Y can represent several different sounds. It can be a /j/, which is the sound at the beginning of yes /jes/, or it can be an /ɪ/, which is the sound in crypt /krɪpt/; it can be an /i:/ as in silly /sɪli/; it can be an /aɪ/ as in my /maɪ/. In the word yes /j/ occurs in the onset of the syllable and so would therefore be regarded as a consonant (at least in terms of the phonology). In the other words these sounds occur in the nucleus, so we would regard Y as representing a vowel in those words.
The word hwyl represents an interesting case. It can be pronounced with two syllables: hu: ɪl or hu: əl. But it can also be pronounced with a single vowel, a diphthong (a single vowel that changes quality), like this: huɪl. In the first instance the nucleus of the first syllable would be /u:/; the nucleus of the second would be /ɪ/. So there in the orthography we'd want to say that W represented one vowel and Y another. But in the pronunciation with one syllable, we might be inclined to say there was one vowel /uɪ/. So in this case we might consider WY to be a single vowel.
[Different scholars may have different views on whether a diphthong is a single vowel or not. If they think it isn't they might not put both vowels in the nucleus here.]