I sent ... vs. I have sent ... vs. I had sent you an email already [closed]
They're different tenses.
sent - past simple tense
(for) something that happened once in the past
(for) something that happened again and again in the past
(for) something that was true for some time in the past
have sent - present perfect tense
for something that started in the past and continues in the present
for something we have done several times in the past and continue to do
(i.e. actions completed in the present)
had sent - past perfect tense
for something that started in the past and continued up to a given time in the past
for something we had done several times up to a point in the past and continued to do after that point
(i.e. actions completed in the past)
In all cases, the use of "already" jars, unless it's emphasising that the action had taken place by the time in question (definition 1):
I keep asking you, where's that report?
But I sent you the email already!
I am aware that it's more common in north American (east coast?) English to use it in the form of definition 2 as well - the exasperated "enough already!" use.
They are all grammatically correct, but have slightly different connotations (in my opinion).
The first two mean almost exactly the same thing; the only difference I infer between them is that the second is more likely to be in response to a person saying something like "why haven't you sent me an email yet?", with an emphasis on the word 'have' in the response. I would likely follow that sentence with something like "Have you checked your spam folder to make sure it didn't wind up there?"
The third one conveys the idea that I am recounting past events, rather than talking to you about a present situation.