Mass-conserving Boundary Condition Research Articles

Thermal fluid lubrication analysis of hydrodynamic journal bearing based on mass conservation boundary conditions

The thermal-hydrodynamic lubrication analysis of bearing with different bearing speed and eccentricity was carried out under Reynolds boundary conditions and mass conservation boundary conditions, and the variation of performance parameters such as oil film carrying capacity with speed and eccentricity were analyzed in detail for the calculated results, and the calculation results under the two different boundary conditions were compared and analyzed. The results show that the boundary conditions have a greater influence on the lubrication flow calculation results, the Reynolds boundary conditions have a faster calculation process, and the mass conservation boundary conditions are recommended when focusing on the analysis of lubrication flow.

Effect of texture on hydrodynamic journal bearing performance under starvation lubrication

The effect of texture on tribological properties of journal bearings operating under starvation lubrication conditions is studied in this paper. The P-θ model with mass conservation boundary conditions is used to accurately predict the oil film distribution in the full oil film/starvation region of the textured bearing. The effects of various degrees of starvation lubrication on the tribological performance parameters, such as eccentricity, attitude angle, full film area, and friction coefficient, are discussed in textured bearings. The results show that the effect of texture on the bearing performance is affected by starvation lubrication conditions: (1) The effect severity varied with starvation levels; (2) The texturing still improved the operating performance of the journal bearing in the case of weak starvation; (3) Texturing increased the bearing load carrying capacity and reduced the friction coefficient, improving safety and preventing safety accidents due to oil supply problems.

Influence of the mass conservation cavitation boundary on the tribo-dynamic responses of the micro-groove water-lubricated bearing

This study aims to reveal the role of the mass conversation cavitation boundary on the tribo-dynamic responses of five kinds of micro-groove water-lubricated bearing under mixed lubrication. By introducing the mass conservation boundary, the tribo-dynamic model of the water-lubricated micro-groove bearing is established and numerically solved by the control volume method. The accuracy of the developed model is verified by comparing the calculated results with the existing experimental and simulation results. The effects of cavitation under Reynolds and mass conservation boundary conditions on different micro-groove bearings were analyzed using the model, and the rotational speed and microgroove depth parameters were analyzed. The simulation results show that , regardless of the shape of the bottom of the microgroove, cavitation can stabilize the journal movement and enhance the dynamic pressure effect of the micro-grooves. The parameter analysis of rotational speed and micro-groove depth proves that rotational speed significantly influences the micro-groove cavitation zone and the dynamic pressure effect. Moreover, the greater the micro-groove depth, the smaller the enhancement effect of cavitation to dynamic pressure. The water-lubricated micro-groove bearing with the bottom shape of the left-triangle has the best lubricating performance during the whole analysis process.

Lubrication and stability enhancement by attaching superconducting magnetic force on non-contacting mechanical seals for reusable rocket turbopump

The purpose of this paper is to investigate the lubrication performance and stability improvement of rocket turbopump mechanical seals by attaching superconducting magnetic force. A comprehensive multiphysics numerical model is presented including microscale clearance flow, magnetic field, as well as three degrees of freedom dynamic motion. The Maxwell equation and modified Reynolds equation considering mass-conserving boundary conditions and turbulence flow were solved simultaneously at each time step to obtain the transient response of sealing parameters. Results indicate that the mechanical seal attaching superconducting magnetic force could dramatically improve carrying capacity and lubrication characteristics under heavy loading conditions, and it also has an appreciable effect on dynamic stability. It is worth exploring the application of superconducting magnetic force in reusable rockets and cryogenic equipment combined with its unique advantages.

Influence of squeezing behavior on cavitation characteristics and performance parameters of mechanical seals with an efficient mass-conserving algorithm

The purpose of this paper is to investigate the influence of squeezing and traction effects on the sealing performance of spiral groove mechanical seals. Firstly, a modified algorithm is proposed to solve the Reynolds equation with squeeze term and mass-conserving boundary conditions, which could effectively improve the calculation efficiency with high accuracy. Then, squeeze effect is put forward to analyze the cavitation characteristic at different boundary conditions and pressure distribution with various squeeze velocities. Finally, the squeeze effect on seal performance, i.e., fluid bearing capacity, clearance flow and cavitation region, under different operating conditions and structural parameters, is discussed. Results indicate that the traction effect has relatively apparent impact than squeeze effect on pressure and flow rate variation. Squeeze effect becomes less visible when the rotational speed exceeds 3000 r/min and film thickness or groove depth exceeds 20 μm. This result would contribute to revealing the feature of transient flow and dynamic response during unsteady conditions.

Study on Sealing Performance of Oil Seal with Micro-pores Textured in Rotary Shaft Surface

In order to improve the reliability and the long life cycle of the lip seals, comprehensive consideration of the liquid film cavitation and JFO mass conservation boundary conditions, the geometry model of the oil seal with micro-diamonds textured on the shaft surface is given, and its mathematical model is built, the relevant numerical calculation method is used, eventually that the film pressure distribution and the micro diamond pores structure parameters effect on the seal performance are obtained under the different operating conditions. The results showed that the dynamic pressure effect caused by the diamond pores can make the oil film pressure field between the axial surface and the lip produced regular axial and radial wave change. At the same time, the change of working conditions strengthen or weaken the change law of the oil film pressure field, so which make the reliability of the liquid pressure, lubricating property and pump suction effect also change accordingly. The size, shape and pores direction of the micro-diamonds texture have great influence on the oil seal performance and lubrication characteristics, which can help to reduce the leakage rate, control the pump suction direction, stable the liquid pressure and reduce the friction. In order to improve the stability of the liquid film and pump suction effect, reduce the leakage rate, friction and wear, the axial surface micro-diamond pores texture of which the cone width ratio is 0.4-0.6, the pores depth is 1.5-4.5μm and the tilt angle is 40°-50° shall be selected for the oil seals.

Hydrodynamic lubrication of textured infinitely long slider with cross-hatched texture

An analytical model for the textured infinitely long slider is developed to study the influence of cross-hatched texture on hydrodynamic lubrication by considering the mass-conserving boundary condition. The three-dimensional morphology of the cross-hatched texture is characterized by a series of mathematical formulas. By using multigrid method and Gauss–Seidel iteration, the hydrodynamic pressure distribution of textured surface can be obtained to analyze the influence of width, depth, spacing, cross-hatched angle and overlapping coefficient of the cross-hatched texture on the hydrodynamic lubrication. The results show that hydrodynamic lubrication can be generated between two parallel plane surfaces with cross-hatched texture. Moreover, the geometrical parameters of the cross-hatched texture have prominent effect on hydrodynamic pressure distribution and load carrying capacity.

A free boundary model of epithelial dynamics

In this work we analyse a one-dimensional, cell-based model of an epithelial sheet. In the model, cells interact with their nearest neighbouring cells and move deterministically. Cells also proliferate stochastically, with the rate of proliferation specified as a function of the cell length. This mechanical model of cell dynamics gives rise to a free boundary problem. We construct a corresponding continuum-limit description where the variables in the continuum limit description are expanded in powers of the small parameter 1/N, where N is the number of cells in the population. By carefully constructing the continuum limit description we obtain a free boundary partial differential equation description governing the density of the cells within the evolving domain, as well as a free boundary condition that governs the evolution of the domain. We show that care must be taken to arrive at a free boundary condition that conserves mass. By comparing averaged realisations of the cell-based model with the numerical solution of the free boundary partial differential equation, we show that the new mass-conserving boundary condition enables the coarse-grained partial differential equation model to provide very accurate predictions of the behaviour of the cell-based model, including both evolution of the cell density, and the position of the free boundary, across a range of interaction potentials and proliferation functions in the cell based model.

Analysis of metal extrusion by the Finite Volume Method

Abstract Present work examines and validates the novel numerical scheme to calculate the velocity, stress, strain, pressure and strain rate fields of metal plastic flow in direct extrusion processes by employing the finite volume method, FVM. Traditionally, the classical methods such as the upper-bound, slab, slip-line and more recently the Finite Element Method have been largely applied in metal extrusion analysis. However, recently the FVM has been applied and published by the authors for analysis of metal plastic flow, concluding that direct extrusion of metals could be mathematically modelled by the plastic flow formulation similar to an incompressible non-linear viscous fluid. Tannehill et al. suggested that viscous fluid flow can be numerically simulated by FVM, obeying the mass, momentum and energy conservation equations and boundary conditions. Hence, the governing equations of metal plastic flow in Euler approach were discretized by FVM, using the Explicit MacCormack Method in structured, fixed and collocated mesh. SIMPLE method was applied to attain the necessary pressure-velocity coupling. These new numerical scheme was applied to the analysis of direct hot extrusion process of Al 6351 and Al 6060 aluminium alloys. The velocity and other variables fields achieved fast convergence and a good agreement with experimental results from visioplasticity tests by the grid stripe pattern technique and Forge 2008 software. The MacCormack Method applied to metal extrusion revealed consistent results without the need of artificial viscosity as required by the compressible fluid flow simulation approaches. Therefore, present numerical results confirm that FVM with MacCormack method together with Euler formulation approach and SIMPLE method can be applied satisfactory in the solution of metal forming processes.

Modeling and optimization of cavitation on a textured cylinder surface coupled with the wedge effect

Based on the mass-conservation boundary conditions, in this paper, the mass flow parameters are selected as the conservation parameters to derive an improved Reynolds formulation. The paper establishes an analytic mathematic model to describe a uniformly distributed micro-texture cavitation to address the variable density, the pressure distribution, the cavitation situation, the vapor volume fraction prediction, the friction and the support force of the friction pair textured unit cell model. The results from the proposed model and the computational fluid dynamics (CFD) simulation are consistent. Finally, the analytic solution of piston cavitation characteristics is calculated coupled with the wedge effect, and the optimization results provide a reference for the gas-liquid mixed flow that can improve the performance of hydraulic components.

An EHD-mixed lubrication analysis of main bearings for diesel engine based on coupling between flexible whole engine block and crankshaft

Purpose – The purpose of this paper is to develop a good calculation model to accurately predict the lubrication characteristic of main bearings of diesel engine and improve the service life. Design/methodology/approach – Based on the coupling of the whole flexible engine block and the flexible crankshaft reduced by the Component Mode Synthesis (CMS) method, considering mass-conserving boundary conditions, the average flow model equation and Greenwood/Tripp asperity contact theory, an elastohydrodynamic (EHD)-mixed lubrication model of the main bearings for the diesel engine is developed and researched with the finite volume method and the finite element method. Findings – Obviously, the mixed lubrication of bearings is normal, while full hydrodynamic lubrication is transient. The results show that under the whole flexible block model, maximum oil film pressure, maximum asperity contact pressure and radial shell deformation decrease, while minimum oil film thickness increases. Oil flow over edge decreases, and so does friction loss. Therefore, coordination deformation ability of whole engine block is favorable to mean load. In the whole block model, friction contact happens on both upper shell and lower shell positions. In addition, average oil film fill ratio at the key position becomes smaller in the whole engine block model, and consequently increases the chances of cavitations erosion more. So, wearing resistance of both upper and lower shells and anti-cavitations erosion ability must be enhanced simultaneously. Originality/value – Based on the coupling of the whole flexible engine block and the flexible crankshaft reduced by the CMS method, considering mass-conserving boundary conditions, the average flow model equation and Greenwood/Tripp asperity contact theory, an EHD-mixed lubrication model of the main bearings for the diesel engine is built, which can predict the lubrication of journal bearings more accurately.

Performance Analysis of Spiral-groove Rotary Seals Considering Mass Conserving Boundary Condition

Performance Analysis of Spiral-groove Rotary Seals Considering Mass Conserving Boundary Condition

Thermo-elasto-hydrodynamic Mixed Lubrication of Main Bearings of Marine Diesel Engines, Based on Coupling between Flexible Engine Block and Crankshaft

Flexible whole engine block and flexible crankshaft are built by CMS method. Under coupling between them, based on the generalized Reynolds considering mass-conserving boundary condition and Greenwood/Tripp asperity contact theory, Thermo-elastic-hydrodynamic mixed lubrication model of main bearings of marine diesel engines is developed and validated indirectly. Simultaneously, calculation shows that mixed lubrication is normalcy, while full hydrodynamic film lubrication is transient. Cavitation erosion becomes a very real possibility only when cavitations, centripetal or centrifugal movement of crankshaft and suddent change of film pressure gradient occur simultaneously. As oil leakage dissipated power is more than 80 percent of the whole dissipated power, outlet film temperature can be a key parameter for monitoring journal bearing lubrication. 8 pieces of bearings meet the requirement of lubrication basically, but work condition of two of the bearings is worse and they need be optimized furthermore.

A mass conserving boundary condition for the lattice Boltzmann method for tangentially moving walls

Abstract In the present discussion a no-slip boundary condition for walls with a tangential movement is derived. The resulting closure is local, conserves mass exactly and is second order accurate with respect to the grid spacing. In addition it avoids the numerical instabilities observed for other types of boundary conditions. Therefore the resulting boundary condition is stable for relaxation frequencies close to two. The present boundary condition is verified for Couette flow, half Poiseuille flow, the second problem of Stokes and flow in a lid-driven square cavity.

Analysis of bearing lubrication under dynamic loading considering micropolar and cavitating effects

Numerical computation of the dynamically loaded journal bearings lubricated with micropolar fluids is undertaken based on the improved Elord cavitation algorithm and over-relaxation method. The results show that the average inflow and average outflow based on the mass conservation boundary conditions are almost equal, which is in accordance with the fact. However, under the Reynolds boundary conditions, large difference is shown between the average inflow and outflow. It is also demonstrated that with the micropolar fluids lubrication, the minimum film thickness, bearing capacity and friction power loss are increased while the maximum film pressure is decreased.

Performance of Dynamically Loaded Journal Bearing with Couple Stress Fluids Considering Mass-conserving Boundary Condition

Based on the couple stress fluid theory and the modified Elrod’s cavitation algorithm, the lubrication performance of dynamically-loaded journal bearings is numerically simulated. With the mass conserving boundary condition ,the Reynolds equation under dynamic loads is solved. Comparisons are made between the average inflow and the average leak flow. The results show that the average inflow and average leak flow based on the mass conserving boundary condition are equal, which is more agreeable with the fact. Comparisons are made between the Newtonian fluids and couple stress fluids for the effects on the oil film pressure, the minimum oil film thickness and the leak flow. It can be found that the couple stress fluids yield an obvious increase in the oil film thickness and the load capacity, but a decrease in the oil film pressure and the leak flow.

A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation

A numerical algorithm for fully dynamical lubrication problems based on the Elrod–Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmark’s scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm.

Numerical Approach for Solving Reynolds Equation With JFO Boundary Conditions Incorporating ALE Techniques

Calculating the fluid flow and pressure field in thin fluid films, lubrication theory can be applied, and Reynolds fluid film equation has to be solved. Therefore, boundary conditions have to be formulated. Well-established mass-conserving boundary conditions are the Jakobsson–Floberg–Olsson (JFO) boundary conditions. A number of numerical techniques, which have certain advantages and certain disadvantages, have been developed to solve the Reynolds equation in combination with JFO boundary conditions. In the current paper, a further method is outlined, which may be a useful alternative to well-known techniques. The main idea is to rewrite the boundary value problem consisting of the Reynolds equation and the JFO boundary conditions as an arbitrary Lagrangian–Eulerian (ALE) problem. In the following, an ALE formulation of the Reynolds equation with JFO boundary conditions is derived. Based on a finite element implementation of the governing boundary value problem, numerical examples are presented, and pressure fields are calculated for a plain hydrodynamic journal bearing with an axial oil groove.

A mass conserving boundary condition for the lattice Boltzmann equation method

In lattice Boltzmann (LB) simulations, the widely used wall boundary conditions (BCs) proposed by Filipova and Hänel (FH) and Mei, Luo and Shyy (MLS) result in constant mass leakage in certain circumstances. In this paper, we have analyzed the source of the leakage. Based on this analysis, we propose a second-order accurate mass conserving wall BC. In our BC, the distribution function at a wall node is decomposed into its equilibrium and non-equilibrium parts. The mass conservation is guaranteed by enforcing a mass conserving rule in the construction of the fictitious equilibrium distribution part. We have shown through several benchmark test problems involving steady and unsteady flows that our new BC not only eliminates the constant mass leakage, but also has many other advantages over the FH and MLS BCs.

HISTORY MOVING OF CAVITATION FOR DYNAMICALLY LOADED JOURNAL BEARING

On the base of the Elrod algorithm, a generalized equation is derived to describe the lubrication in full film region and in cavitation region of dynamically loaded journal bearing, which is nominated as the incompressible mass-conserving cavitation algorithm. A numerical technique with this algorithm has been solved. By the definition of a switch function g and a variable ξ, which have different meaning in different zone, a generalized equation is derived to integrate the Reynolds equation in full film region with the lubrication equation in cavitation region. This algorithm can predict the moving oil boundary automatically and make the mass conserving boundary condition (JFO theory) more easily and precisely to be applied in actual analysis. It is found that the analysis results with the incompressible mass-conserving cavitation algorithm have good agreement with the existing experiment data. The incompressible cavitation algorithm can predict the history moving of cavitation well. And it is also shown that the pressure value in the cavitation has great effect on the analysis results.