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The purpose of this study is to explore the transient characteristics of mixed-flow pumps during startup process.

This study uses a full-flow field transient calculation method of mixed-flow pump based on a closed-loop model.

The findings show the hydraulic losses and internal flow characteristics of the piping system during the start-up process.

Large computational cost.

Improve the accuracy of current numerical simulation results in transient process of mixed-flow pump.

Simplify the setting of boundary conditions in the transient calculation.

This study aims to investigate the noise-inducing characteristics during the start-up process of a mixed-flow pump and the impact of different start-up schemes on pump noise.

This study conducted numerical simulations on the mixed-flow pump under different start-up schemes and investigated the flow characteristics and noise distribution under these schemes.

The results reveal that the dipole noise is mainly caused by pressure fluctuations, while the quadrupole noise is mainly generated by the generation, development and breakdown of vortices. Additionally, the noise evolution characteristics during the start-up process of the mixed-flow pump can be divided into the initial stage, stable growth stage, impulse stage and stable operation stage.

The findings of this study can provide a theoretical basis for the selection of start-up schemes for mixed-flow pumps, reducing flow noise and improving the operational stability of mixed-flow pumps.

This paper aims to study the transient flow characteristics in a mixed-flow pump during the start-up period.

In this study, numerical calculation of the internal flow field in a mixed-flow pump using the sliding mesh method was carried out. The regulation of the pressure, streamline and the relative speed during the start-up period was analyzed.

The trend of the simulated head is consistent with the experimental results, and the calculated head is around 0.3 m higher than the experimental head when the rotation speed reached the stable stage, indicating that the numerical method for the start-up process simulation of the mixed-flow pump has a high accuracy. At the beginning, the velocity inside the impeller changes little along the radius direction and the flow rate increases slowly during the start-up process. As the rotation speed reached the stable stage, the flow inside the impeller became steady, the vortex reduced and transient effects disappeared gradually.

The study results have significant value for revealing the internal unsteady flow characteristics of the mixed-flow pump and providing the reference for the design optimization of the mixed-flow pump.

Friction and wear are very important factors in predicting the performance of journal bearings, particularly under heavy load in start-up processes. However, there are few relevant studies on the numerical model. This study aims to establish a transient-mixed lubrication model to predict the performance of journal bearings, focusing on the friction and wear behavior under heavy load during start-up.

The average Reynold equation, three-dimensional energy equation, shear stress model for friction and Archard model for wear are coupled in the transient model by finite difference method. The linear wear simulation method is bought out to reduce the update times and the calculation time.

The different start-up accelerations and linear wear times set are compared and discussed, which indicates a reasonable start-up acceleration is necessary for journal bearings under heavy load during start-up, and setting linear wear times is an effective method to reduce the simulation time significantly. Furthermore, the wear profile in the start-up process spreads in both the clearance and circumferential directions, but mainly in the clearance direction, which increases the minimum film thickness and affects the friction performance.

This study is of great significance for the numerical prediction of the transient performance of journal bearings during start-up considering friction and wear.

The purpose of this paper is to reveal the transient thermo-elasto-hydrodynamic lubrication mechanism of a bidirectional thrust bearing in a pumped-storage unit, and to propose the transient simulation method of two-way fluid-solid-thermal interaction of thrust bearing.

The transient fluid-solid-thermal interaction method is used to simulate the three-dimensional lubrication of the thrust bearing, during the start-up and shutdown process of a pumped storage unit. A pad including an oil hole is modelled to analyze the temporal variation of lubrication characteristics, such as the film pressure, thickness and temperature, during the transient operation process.

The injection of the high-pressure oil sufficiently affects the lubrication characteristics on film, in which the hysteresis phenomena were found between the start-up and shutdown possess.

This paper reveals the transient lubrication mechanism of tilting pad in a thrust bearing, by means of transient fluid-solid-thermal interaction method. Lubrication characteristics are simulated without assuming the temperature relationship between the oil film inlet and the outlet and the heat transfer on the pad free surface. This paper provides a theoretical basis for the safe design and stable operation of thrust bearings.

This study aims to present a numerical solution for the analysis of the influence of surface roughness as presented by a sinusoidal ripple of different amplitude and wavelength on the performance of transient elastohydrodynamic lubrication at motion start-up under different operational parameters of entraining speed and load as well as different acceleration rates.

A statistical asperity micro-contact model represented by a sinusoidal ripple expressed by two parameters (wavelength and undeformed amplitude) is considered. The ball equation of motion is used to calculate the force on the ball as it starts to move. The time-dependent Reynolds equation is solved together with surface deformation and statistical asperity models using the Newton–Raphson technique with the Gauss–Seidel iteration method.

The behaviour of the film thickness was found to be strongly influenced by the acceleration rate for different ripple amplitude and wavelength parameters. The effect of increasing the final entraining speed will eventually lead to rapid film thickness build-up and increase the film thickness jump at the moment of motion start-up. The effect of increasing applied load is to reduce the deviation of the minimum film thickness jump at the start-up of motion, making its value approximately equal to the steady-state value over the entire run-time period.

Influence of surface roughness for various wavelength and undeformed amplitude on the performance of transient elastohydrodynamic lubrication at motion start-up is presented at different acceleration rates as well as for different operating parameters of entraining speed and load. Ball equation of motion is used to calculate the force on the ball as it starts to move.

This paper aims to investigate the lubrication performance of cam/tappet contact during start up. Especially, the thermal insulation effects of coating on the lubrication performance during cold start up process and warm start up process are studied.

A numerical model for the analysis of thermal elastohydrodynamic lubrication of coated cam/tappet contact is presented. In this model, the Reynolds equation and the energy equations are discretized by the finite difference method and solved jointly.

During start up, the contact force at cam nose-to-tappet contact decreases with increasing time, while the absolute entrainment velocity has the upward trend. The minimum film thickness, maximum average temperature and friction power loss increase with increasing time, while the coefficient of friction decreases during start up. Because of the thermal insulation effect, the coating can significantly increase the degree of temperature rise. Compared with the uncoated case, the coated cam/tappet results in a lower friction power loss. Generally, the friction power loss in the cold start up process is much higher than that in the warm start up process.

By this study, the lubrication performance and the kinematics and the dynamics of the cam/tappet during start up process are investigated. Meanwhile, the thermal insulation effect of coating is also illustrated. The difference of lubrication performance between cold start up process and warm start up process is analyzed. The results and thermal elastohydrodynamic lubrication method presented in this study can be a guidance in the design of the coated cam/tappet.

The capability to predict and evaluate the motor pressure during each phase by means of a numerical analysis can significantly increase the efficiency of the preliminary design process with a reduction of both the motor development and operational costs. This paper aims to perform numerical simulation to analyze the ignition transient in solid rocket motor by solving Euler equation coupled with some semi-empirical correlations. These relations take into account the main phenomena affecting the ignition transient. Coupling relationships include the heat transfer of the gas to the propellant and erosive burning rate relationship.

The current research effort divides motor into series of control volumes along the port axis, and the variation of port area, burning surface and burning rate along the port are taken into account. A set of governing equations are then solved using explicit, time-dependent, predictor-corrector finite difference method. The numerical model helps to capture and embed shock wave associated with igniter flow within the solution. Second-order artificial viscosity dampens out the numerical oscillations due to sharp gradient within the flow field. The developed computer code predicts the start-up characteristics of motor. The study also provides comparison of simulation results with in-house experimental motor.

Simulations are performed with and without erosive burning to demonstrate that the flow model is a good physical approximation of motor. Numerical results calculated by this model without erosive burning are not in good agreement with experimental results. This minor discrepancy has motivated the inclusion of erosive burning in numerical model. The simulated results are then compared with the experimental data for head-end and rear-end pressure. The agreement between simulation and experiment is remarkable. In summary, major finding of this study is that unsteady quasi-one-dimensional gas dynamic model can capture the flow field in the motor during ignition transient effectively.

Unsteady quasi-one-dimensional gas dynamic model can capture the flow field in the motor during ignition transient effectively. However, in systems where two- and three-dimensional effects are pre-dominant, one would require to develop a more elaborate, multi-dimensional model which will allow for further understanding of the flow behavior and eventually lead to modeling of rocket motors with more complex geometries.

The close agreement between experimental and simulation results can be considered as forced to some degree, because the general mathematical model of erosive burning contains a free variable erosive burning exponent. However, in future, this variable can be established a priori by erosive burning tests.

The solid propellant ignition process consists of series of rapid events and must be completed in a fraction of a second. An understanding of the dynamics of ignition has become increasingly vital with the development of larger and more sophisticated solid propellant rocket motors. This research effort provides the simulation framework to predict and evaluate the motor pressure during each phase by means of a numerical analysis, thus significantly increasing the efficiency of the preliminary design process with a reduction of both the motor development and operational costs.

This aim of this paper has been to investigate the squeeze effect of a water-lubricated tilting-pad thrust bearing during start-up and shut-down periods.

In this paper a numerical model with a squeeze and slippage effect was adopted to analyse the asymmetry characteristic of a tilting-pad thrust bearing during start-up and shut-down periods. A test rig was built to verify numerical results, which were a combined measurement method in which acceleration sensor and torque sensor were used simultaneously to determine the angle change of the thrust pad.

It was found that as the velocity gradient increased, the difference of the minimum dimensionless film H_min could be ignored in the start-up process. But in the shut-down process, as the velocity gradient increased, the value of H_min also increased, which showed that there was an asymmetry characteristic of the tilting bearing in two processes. This phenomenon was verified by measuring the friction torque curve in the test.

The results of the studies demonstrated that the velocity gradient could be designed to reduce the friction of the thrust bearing, which would be beneficial to the working life of the tilting-pad thrust bearing.

The classical integer derivative diffusionmodels for fluid flow within a channel of parallel walls, for heat transfer within a rectangular fin and for impulsive acceleration of a quiescent Newtonian fluid within a circular pipe are initially generalized by introducing fractional derivatives. The purpose of this paper is to represent solutions as steady and transient parts. Afterward, making use of separation of variables, a fractional Sturm–Liouville eigenvalue task is posed whose eigenvalues and eigenfunctions enable us to write down the transient solution in the Fourier series involving also Mittag–Leffler function. An alternative solution based on the Laplace transform method is also provided.

In this work, an analytical formulation is presented concerning the transient and passage to steady state in fluid flow and heat transfer within the diffusion fractional models.

From the closed-form solutions, it is clear to visualize the start-up process of physical diffusion phenomena in fractional order models. In particular, impacts of fractional derivative in different time regimes are clarified, namely, the early time zone of acceleration, the transition zone and the late time regime of deceleration.

With the newly developing field of fractional calculus, the classical heat and mass transfer analysis has been modified to account for the fractional order derivative concept.