Honestly, if you are trying to make money it seems that donations would not be the way to go. Since you already have a user base and you know how quickly you have picked up that user base you can create a pitch on how many project users you will have at certain milestones, and how many you currently have. Though those pitch idea are just ideas they will be tools for what I am going to suggest you do.
Your best option to create any nominal sort of income from this free application would be to either contact companies that you feel would find the user base to be potential clients for them. There are many sources that you could find on trying to sell advertising to companies, and how to price that advertising so I will not waste time trying to explain it here. I have had most success selling to companies that were based locally, and what I always would try to hammer home is their ROI, because in reality that is usually the driving factor with most decisions in a business. ROI will most likely navigate you toward the answer here that yields the largest one. To make a long story short your best option to make money on a free application(If you don't have any other products to advertise or in game items that you could sell using micro-transactions) would be to go out and sell advertising space yourself.