Note that it is easy to sell the dollar in Sudan and you can sell at the central bank but the exchange rate is very low against what you can get in the black market so tourists and expatriates prefer to deal with the black market.
What if it's the other way around: can you sell your SDG back to the central bank for dollars before you leave the country? I guess you can't, otherwise the black market sellers would get rich.
Just a hypothetical question, I'm not going to Sudan (or anywhere else) as a tourist any time soon.I never did that process before, but they'd probably request for your financial documents before you can exchange a substantial amount of SDG for dollars. I mean, they aren't going to just let people on the black market exchange a ton of SDG, those traders would get in deep trouble if they did that. But on the other hand there is a legitimate need for people to convert their SDG to other currencies for business purposes.
Probably the most feasible way to withdraw cash is if you get it from your bank account, and then exchange it for dollars p2p.
Al Baraka Bank let's you withdraw up to 2,000 SDG at once, five times a day (so ~$180 USD, you can't use it to siphon thousands of USD at once, which makes sense, because there is a shortage of dollars). I found no such web page for Bank of Khartoum you can wire cash via Western Union. I don't know the transfer limit of that though.