I've read that Gavin Menzies claims that Zheng He's voyages were not afflicted by scurvy, because they had good vitamin C sources (such as sprouting stored soybeans throughout the voyage). It seems to me that this would be feasible prima facie, but Gavin Menzies isn't a credible source.
I can look at bits of Avoiding the Dire Straits: An inquiry into Food Provisions and Scurvy in Maritime and Military History of China and wider East Asia, by Mathieu Torck on Google Books, but it’s fragmentary unless I actually put down, like, $60 for the real thing.
The soy-bean sprout solution seems to be the generally accepted consensus, though allowing the beans to sprout (and thus produce Vitamin C) seems to have been a fallback solution, if and when their main vegetable supplies of bamboo shoots, cabbage, and turnips ran low. But that was a much lower danger than, say, European voyages across the Atlantic, both since making landfall was much more frequent since the fleets tended to hug the coast rather than venture into the open sea, and since the Bao Chuan fleet specifically travelled with their own armadas of grain and supply ships, which meant they could bring much more.
Moreover, even though seafaring in a real sense was a pretty new thing for the Ming, the Chinese were by no means strangers to the nutritional dangers of long journeys through hostile places. Though it was on land, the Tarim Basin and especially the Gobi and Taklamakan Deserts had given them ample experience of what could happen to men if they ran out of specific sources of food/nutrients. From Erik T. Patterson:
All of this would have required a considerable degree of knowledgeable foresight and organization. This could hardly have been developed de nouveau for these specific fleets. The Chinese must have known about the prevention of scurvy long before 1421.
As such "Enough citrus fruits – limes, lemons, oranges, pomelos and coconuts – were taken aboard to give every man protection against the disease." At least some of the rice, according to Ding, Shi, and Weintrit (2007), was left with-husk, for instance, specifically because it was know that the husks contained Vitamin B1 - which staved off the equally dangerous nervous degenerative disease beriberi - even if the sailors themselves couldn't have explained "why" such conditions happened, or "what" about brown rice seemed to stave it off.
Ding, Jin, Chaojian Shi, and Adam Weintrit (2007). "Zheng He’s sailing to West Ocean" in Coordinates Vol. III, No. 9. Article. <-- (This one has a bunch of other academic references in its cited list, so that might be of use to you for further reading at a potentially lower price-point.)
Paterson, Erik T. (2005). "James Lind, Zheng He and the Prevention of Scurvy" in Journal of Orthomolecular Medicine Vol. 20, No. 4. PDF (Though he acknowledges that Menzies' 1421 is controversial, he nevertheless seems to take much of it at face-value, including Bao Huan's "supposedly" making it all the way down to Kerguelen Island and South Shetland Islands, which... y'know... take that for what it's worth)
