Increase downloads for free app on App Store

You need to consider good, old fashion SEO. Do some basic keyword research to understand how people might be searching for your app - or what it offers - and adjust or develop web content targeted for that search. If you're able to get rankings for these searches, you'll begin to see the increases and I would even recommend setting up a direct link to the store with analytics tracking to see how many leads that you're sending.

Also, it's not free, but advertising is something you should also consider. Apple launched a simple platform - http://advertising.apple.com/tools/iad-workbench/ - a few months back and there are several other app networks that you can use.

Best,

Clark

-Please get you active users to propagate your app through asking them for reviews in App Store , prompting for Facebook like , share on what's app with friend . With change in AppStore ranking algorithm reviews will help you generate good ranking and place higher in search results.
-If the economics allows gratify them with some offer for referrals ( may excess to any premium feature for a limited time , or points , discounts etc whatever is possible )
- rebuilt you visibility through a campaign where you do 1or burst activities towards weekend starting Thursday evening and sustain with normal activity ( 1/5th of burst) for few days .
- also you must see you LTV per active user and basis that work on activating the dormant users or put this data to use to acquire new user with above mentioned tactics

If you are trying to shift traffic from existing website to app use interstitial blocking pages. While somewhat annoying for users that just want to view content on the web they are very effective at directing traffic to apps. They're far more effective than the default iOS smart banners that are easily ignored. We found this for both iPhone & iPad use cases at Diapers.com (I also saw similar data from zappos) also once users dismiss interstitials or smart banner adding contextual links like "view XXXX page in the app" can prompt users when they're more committed as opposed to on first view.

I actually wrote a blog post last year on "81 Different ways to promote your Mobile App / Games" the link is http://blog.tapgage.com/2012/10/81-different-ways-to-promote-your-mobile-app-game/. Hopefully it helps. I will be releasing another updated version of this post very soon.

Generally speaking, people would check app reviews before downloading an app, and 88% people give much trust to app reviews. Then you should increase positive app reviews to increase the download rates.

Bestreviewapp(https://www.bestreviewapp.com/?from=cr-chris) provides this kind of service, which supports multiple countries for you to choose from, get your app targeted precisely, highly recommend.

With 1600 downloads/day you are in the "Fly Stage" (see our growth stages categorization: https://www.slideshare.net/christianpuricelli/mobile-app-marketing-presentation-81456295). To growth from there ASO, PR, App Review websites will not help you any more to growth significantly. At this point you could try to reinvest the cash flow you are generating for paid acquisition, an influencer campaign. Also at this point it makes sense to start optimizing all conversions.