Energy Characteristics of Full Tubular Pump Device with Different Backflow Clearances Based on Entropy Production

In this study, the entropy theory was used as the evaluation standard of energy dissipation, and the effect of backflow clearance (the gap between motor rotor and motor shell) on energy characteristics of a full tubular pump was investigated by 3D unsteady flow simulation. The calculated results validated through testing shows that backflow clearance produces additional head loss and the rotation of the motor rotor requires more shaft power. The additional energy losses lead to a significant decline in the efficiency of tubular pump device. Under design conditions, the total dissipation of backflow clearance, rear guide vane, and outlet passage decreases with the increase of clearance radius, but that of the impeller decreases first and then rises with the increase of clearance radius. In addition, the increase of the clearance radius leads to disorderly flow pattern in the impeller. The total dissipation rate on the impeller suction side and near the impeller inlet increases with the increase of backflow clearance radius, but that on the impeller suction side decreases with the increase of backflow clearance radius. The total dissipation rate of the suction side of the guide vane and the wall of the outlet passage decreases with the increase of backflow clearance radius. This work can provide an intuitive analysis of the energy dissipation caused by backflow clearance and reference for engineering applications of full tubular pump.

Lagrange crisis and generalized variational principle for 3D unsteady flow

Purpose A three-dimensional (3D) unsteady potential flow might admit a variational principle. The purpose of this paper is to adopt a semi-inverse method to search for the variational formulation from the governing equations. Design/methodology/approach A suitable trial functional with a possible unknown function is constructed, and the identification of the unknown function is given in detail. The Lagrange multiplier method is used to establish a generalized variational principle, but in vain. Findings Some new variational principles are obtained, and the semi-inverse method can easily overcome the Lagrange crisis. Practical implications The semi-inverse method sheds a promising light on variational theory, and it can replace the Lagrange multiplier method for the establishment of a generalized variational principle. It can be used for the establishment of a variational principle for fractal and fractional calculus. Originality/value This paper establishes some new variational principles for the 3D unsteady flow and suggests an effective method to eliminate the Lagrange crisis.

Numerical Simulation of Deep Thermal Groundwater Exploitation in the Beijing Plain Area

Thermal groundwater is relatively abundant in the deep-seated bedrock underlying the Beijing plain area. The main geothermal reservoir is composed of dolomites of the Wumishan Group of the Meso–Neoproterozic Jixian System. The thermal groundwater has been developed and utilized since the 1970s and significant declines in groundwater levels were observed. A 3D unsteady flow model of an anisotropic karst-fissure aquifer based on the equivalent continuum is used to describe the flow of thermal groundwater and heat transport. The heat transportation is described by the governing equation including convection and dispersion. The simulation of this paper aims to solve such problems as uneven distribution and thinness of the aquifer, insufficient initial monitoring data, and poor knowledge of the properties of the horizontal boundary. They are solved by considering vertical stratification of the aquifer with equal thickness, replacing initial water level data by surface elevation, and choosing natural boundary far away from the exploitation areas. Through a trial–error procedure, the simulated and measured groundwater level and temperature in the simulation period are well fitted. Three exploitation schemes are proposed to predict the spatial and temporal changes in groundwater level and temperature of the thermal groundwater in the study area. The prediction results show that the reinjection can effectively slow the decline in the thermal groundwater levels. Except for the Dongnanchengqu, Xiaotangshan, and Liangxiang subgeothermal fields, the other six subgeothermal fields have the potential for further development of thermal groundwater.

Prediction of 3D Unsteady Flow and Heat Transfer in Rotating Cavity by Discontinuous Galerkin Method and Transition Model

Rotating cavities with axial throughflow are found inside the compressor rotors of turbo-machines. The flow pattern and heat transfer in the cavities are known as sophisticated problems. Because of the numerical errors and model errors, as well as the stiffness introduced by low-Ma number, prediction of 3D unsteady flow and heat transfer in rotating cavity is still a challenge for modern CFD technology. An in-house 3D unsteady CFD code was developed in this study. The discontinuous galerkin method, which can fulfill any high-order accuracy on the unstructured grid, was applied to reduce the discretization errors. The SST-γ-Reθ transition model proposed by Menter was applied to reduce the model errors. To overcome the stiffness and achieve good convergence characteristics and solution quality, the preconditioning matrix technique combined with DG method was introduced for low-Ma number viscous flow. First, natural convection of air in a square cavity was studied to test the code. The feasibility and credibility, of applying the DG method and the preconditioned matrix technique for buoyancy–induced Rayleigh-Bénard like flow, were further verified. Second, the 3D compressible flow field in a rotating cavity was investigated numerically using the FV method, DG method and laminar/SA/SST-transition turbulence model. It is demonstrated that the whole flow structure of all calculated cases was similar after comparing the calculated results with the available experimental data. But, the transition turbulence model fitted the experimental data better. On the other hand, the performance of high-order method was much better for both the rotating cavity flow and natural convection, in terms of heat transfer. To better understand this phenomenon, an accuracy analysis of heat flux using DG method and FV method was performed. It showed the DG method could realize arbitrary precision of viscous stress and heat fluxes on irregular unstructured grids, while the FV method could only realize the first-order accuracy of the heat fluxes at the boundary faces and may exhibit erroneous behaviors. It also demonstrated that the high-order accuracy of gradients was needed to decrease errors of heat fluxes and viscous stresses, and that DG method was a promising method.

Performance Investigation Into Supersonic Diffuser for a High Pressure Centrifugal Compressor

In high pressure centrifugal compressors, the overall stage performance is greatly influenced by its diffuser performance. Extremely complicated non-uniform and unsteady flow exists in the region between the impeller exit and the diffuser inlet. Furthermore, in the case of supersonic diffuser, shock waves can be observed near the diffuser inlet. These can cause aerodynamic losses. Therefore, it is essential to recognize such complicated flow to realize an appropriate diffuser design. An investigation into the performance of supersonic diffuser was carried out using a high pressure compressor test rig for a small industrial gas turbine with a high back swept impeller and a quasi pipe-shaped channel diffuser. In addition, 3D quasi-unsteady flow analyses of the entire compressor by a RANS code with Non Linear Harmonic method at several operating conditions between surge and choke were conducted to investigate the details of unsteady flow between the impeller exit and the diffuser exit. The results of the performance test and that of the 3D unsteady flow analyses have shown good agreement in the pressure rise and the isentropic efficiency at several operating conditions. These support high accuracy of the flow analyses and the performance measurements.