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Nowadays Practical Byzantine Fault Tolerance (PBFT) algorithm has become the most extensive consensus algorithm in the alliance chain. However, the PBFT algorithm is usually only applicable to small networks due to high communication complexity and poor scalability. Although there have been many improved algorithms for PBFT in recent years, they ignore fault tolerance and democracy. Therefore, to meet the requirements of a high degree of decentralization and fault tolerance of blockchainbased scenarios. This paper proposes a high fault tolerance consensus algorithm NBFT, which follows the principle of decentralization and democratization of blockchain and ensures the improvement of performance in fault tolerance upper limit and scalability. First, we use the consistent hash algorithm to group the consensus nodes to avoid much communication between nodes, reduce the communication complexity of the network, and improve the scalability of the network. Second, to ensure the fault-tolerant ability of the grouping consensus, the nodal decision broadcast model and threshold vote-counting model are proposed first. Combined with the proposed two models, the joint fault analysis of nodes is carried out, and the fault tolerance upper limit is more than 1/3. Then, the Faulty Number Determined(FND) model is introduced to simulate the experiment, and the results are verified.INDEX TERMS high fault tolerance; group consensus; scalability I. INTRODUCTION

The consensus algorithm is very critical in any blockchain system, because it directly affects the performance and security of the blockchain system. At present, the classic Practical Byzantine Fault Tolerance Algorithm (PBFT), which is mainly used in the consortium chain, will lead to system communication congestion and reduced throughput when the number of nodes increases, so the PBFT algorithm is not suitable for large-scale consortium chains. In response to the above problems, this paper proposes a new clustering-based sharding consensus algorithm (KBFT), which aims to ensure that the consortium chain takes into account decentralization, security and scalability. The KBFT algorithm first uses the K-prototype clustering algorithm to shard the nodes in the network according to mixed attributes, and second, disjoint transactions are used to reach consensus in parallel in different shards. Concurrently, the KBFT algorithm introduces a supervision mechanism and a node credit mechanism, which is used to supervise and score the behavior of the nodes and select the proxy nodes, which improves security. We discuss the choice of shard size with the help of the binomial probability distribution and analyze the probability that the system can successfully form a global block under different node failure probabilities. Finally, the proposed algorithm is evaluated through theoretical analysis and simulation experiments. Results show that the proposed algorithm achieves a marked improvement in scalability and throughput along with a marked reduction in communication complexity compared with the classic baseline algorithm PBFT in this field of study, which improves the operating efficiency of the system and simultaneously guarantees the security and robustness of the system.

Numerical simulations have been performed to study the effect of the circumferential single-grooved casing treatment (CT) at multiple locations on the tip-flow stability and the corresponding control mechanism at three tip-clearance-size (TCS) schemes in a transonic axial flow compressor rotor. The results show that the CT is more efficient when its groove is located from 10% to 40% tip axial chord, and G2 (located at near 20% tip axial chord) is the best CT scheme in terms of stall-margin improvement for the three TCS schemes. For effective CTs, the tip-leakage-flow (TLF) intensity, entropy generation and tip-flow blockage are reduced, which makes the interface between TLF and mainstream move downstream. A quantitative analysis of the relative inlet flow angle indicates that the reduction of flow incidence angle is not necessary to improve the flow stability for this transonic rotor. The control mechanism may be different for different TCS schemes due to the distinction of the stall inception process. For a better application of CT, the blade tip profile should be further modified by using an optimization method to adjust the shock position and strength during the design of a more efficient CT.

To explain the effect of tip leakage flow on the performance of an axial-flow transonic compressor, the compressors with different rotor tip clearances were studied numerically. The results show that as the rotor tip clearance increases, the leakage flow intensity is increased, the shock wave position is moved backward, and the interaction between the tip leakage vortex and shock wave is intensified, while that between the boundary layer and shock wave is weakened. Most of all, the stall mechanisms of the compressors with varying rotor tip clearances are different. The clearance leakage flow is the main cause of the rotating stall under large rotor tip clearance. However, the stall form for the compressor with half of the designed tip clearance is caused by the joint action of the rotor tip stall caused by the leakage flow spillage at the blade leading edge and the whole blade span stall caused by the separation of the boundary layer of the rotor and the stator passage. Within the investigated varied range, when the rotor tip clearance size is half of the design, the compressor performance is improved best, and the peak efficiency and stall margin are increased by 0.2% and 3.5%, respectively.