The healthcare industry faces serious problems with health data. Firstly, health data is fragmented and its quality needs to be improved. Data fragmentation means that it is difficult to integrate the patient data stored by multiple health service providers. The quality of these heterogeneous data also needs to be improved for better utilization. Secondly, data sharing among patients, healthcare service providers and medical researchers is inadequate. Thirdly, while sharing health data, patients' right to privacy must be protected, and patients should have authority over who can access their data. In traditional health data sharing system, because of centralized management, data can easily be stolen, manipulated. These systems also ignore patient's authority and privacy. Researchers have proposed some blockchain-based health data sharing solutions where blockchain is used for consensus management. Blockchain enables multiple parties who do not fully trust each other to exchange their data. However, the practice of smart contracts supporting these solutions has not been studied in detail. We propose CrowdMed-II, a health data management framework based on blockchain, which could address the above-mentioned problems of health data. We study the design of major smart contracts in our framework and propose two smart contract structures. We also introduce a novel search contract for searching patients in the framework. We evaluate their efficiency based on the execution costs on Ethereum. Our design improves on those previously proposed, lowering the computational costs of the framework. This allows the framework to operate at scale and is more feasible for widespread adoption.