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Tip leakage vortex flow (TLV) is a common flow phenomenon in the axial-flow hydraulic machinery. High-efficiency simulation of TLV is still not an easy task because of the complex turbulent vortex-cavitation interactions. As an important basis of CFD, turbulence model directly affects the efficient computation of TLV. The purpose of this paper is to evaluate the newly developed MST turbulence model in predicting the TLV flows.

By using the MST turbulence model and the ZGB cavitation model, numerical simulations of the TLV generated by a NACA0009 hydrofoil were performed under the cavitation-free and cavitation conditions, and the results were compared with the available experimental data.

The important features of TLV are well captured by the MST-based simulation scheme, and the problem of under-predicting the cavitating TLV tube is well solved. Turbulent viscosity is reasonably adjusted in the TLV core regions, and the LES-like mode is activated, which is beneficial to obtain more turbulent information on the same URANS grids. The requirements of grid size and time step of the MST model are much lower than that of the LES method, thereby weighing a good balance between the simulation accuracy and computation cost.

The MST turbulence model is suitable for the high-efficiency simulation of the TLV flows, which can lay a good foundation for efficient engineering computations of the cavitating TLV in the axial-flow hydraulic machinery.

As one of the omnichannel sales models, “buy online and pick up in store” (BOPS) not only is used in the commercial field but also has gradually attracted many scholars’ interests. However, although there are numerous research ideas, most of the current work is still limited to theoretical and empirical research, and few scholars study BOPS through models. This paper aims to discuss the best market conditions and opportunities for the implementation of BOPS against the backdrop of omnichannel by means of mathematical models and data simulations and discuss the optimal price–service strategies under different sales models.

First, from the perspective of different consumer shopping types, this paper separately divides consumers into different groups in traditional “dual channel” and BOPS models. Then, the authors analyze the impact of company market size, consumer service sensitivity and the scale of BOPS on companies’ strategies and the profit of the supply chain. Subsequently, they conduct an empirical analysis through specific values. Finally, the authors further expand the model on the basis of the original research, and discuss the retailer’s fairness concerns and unit compensation strategy to ensure that the research content is more rigorous.

It is observed that whether companies adopt BOPS depends on consumers’ service sensitivity degree and the scale of BOPS consumers and online retailers: when the sensitivity and the proportion of online consumers are high or the number of BOPS consumers is large, it is more advantageous for companies to implement BOPS. Moreover, companies should not only consider the market scale and production cost but also have a precise orientation of consumers’ experience sensitivity and willingness to engage in extra consumption when making price and service strategies. At the same time, the compensation strategy of companies and the peer-regarding fairness concern behavior of offline retailers will affect the optimal price and service strategy in the BOPS model.

These results provide managerial insights for companies preparing to implement BOPS and promote the development of relevant theories in the channel field.

At present, most of the research on BOPS is based on empirical reviews. However, this paper analyzes the applicability and feasibility of implementing BOPS by using specific models, and it will provide some reference for companies preparing to implement BOPS. In addition, this paper also discusses the unit compensation strategy and peer-regarding fairness concern behavior in the BOPS model, which have not been studied by relevant scholars.

The objective of this paper is to provide a better understanding of the effect of irregular columnar jointed structure on the permeability and flow characteristics of rock masses.

An efficient numerical procedure is proposed to investigate the permeability and fluid flow in columnar jointed rock masses (CJRMs), of which the columnar jointed networks are generated by a modified constrained centroid Voronoi algorithm according to the field statistical results. The fractures are represented explicitly by using the lower-dimensional zero thickness elements. And the modeling scheme is validated by a benchmark test for flow in fractured porous media. The effective permeability and representative elementary volume (REV) size of CJRMs are estimated using finite element method (FEM). The influences of joint density and variation coefficient of columnar joint structure on the permeability of the rock mass are discussed.

The simulation results indicate that the permeability is scale-dependent and tends to be stable with increase of model size. The hydraulic REV size is determined as 3.5 m for CJRMs in the present study. Moreover, the joint density is a dominant factor affecting the permeability of CJRMs. The average permeability of columnar jointed structures increases linearly with the joint density under the same REV size, while the influence from the coefficient of variation can be neglected.

The present paper investigates the REV size of the CJRMs and the effect of joint parameters on the permeability. The proposed method and the results obtained are useful on understanding the hydraulic characteristic of the irregular CJRMs in engineering projects.