Numerical Method for Pressure Distribution Calculation on Spherical Distribution Pair of IHT

2011 ◽  
Vol 52-54 ◽  
pp. 1427-1432
Author(s):  
Shi Hua Yuan ◽  
Ding Hua Liu ◽  
Chao Wei
Keyword(s):  
Pressure Distribution ◽  
Reynolds Equation ◽  
Thickness Distribution ◽  
Transformation Method ◽  
Physical Domain ◽  
Spherical Distribution ◽  
Distribution Calculation ◽  
Curvilinear Grid ◽  
Control Equation ◽  
Flux Conservation

To calculate the pressure distribution of oil film on spherical port plate of Innas hydraulic transformer (IHT), finite difference method (FDM) based on boundary fitted coordinate (BFC) technique is presented. Spherical curvilinear grid system was obtained with a coincident boundary of irregular physical area. The flux conservation form of Reynolds’ equation was applied as control equation. By FDM, the thickness distribution and pressure distribution of distribution pair were calculated. It shows that BFC transformation method is advantaged to closely simulate the physical domain with complex geometrical boundaries.

scholarly journals An Assessment of Quantitative Predictions of Deterministic Mixed Lubrication Solvers

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Yuechang Wang ◽  
Abdel Dorgham ◽  
Ying Liu ◽  
Chun Wang ◽  
Mark C. T. Wilson ◽  
...  
Keyword(s):  
Reynolds Equation ◽  
Thickness Distribution ◽  
Computation Time ◽  
Simulation Method ◽  
Coefficient Matrix ◽  
Mixed Lubrication ◽  
Contact Ratio ◽  
Lubricated Contacts ◽  
Discretization Schemes ◽  
Parametric Studies

Abstract The ability to simulate mixed lubrication problems has greatly improved, especially in concentrated lubricated contacts. A mixed lubrication simulation method was developed by utilizing the semi-system approach which has been proven to be highly useful for improving stability and robustness of mixed lubrication simulations. Then different variants of the model were developed by varying the discretization schemes used to treat the Couette flow terms in the Reynolds equation, varying the evaluation of density derivatives and varying the contribution of terms in the coefficient matrix. The resulting pressure distribution, film thickness distribution, lambda ratio, contact ratio, and the computation time were compared and found to be strongly influenced by the choice of solution scheme. This indicates that the output from mixed lubrication solvers can be readily used for qualitative and parametric studies, but care should be taken when making quantitative predictions.

The pressure distribution on dihedral wings at supersonic speed

1959 ◽  
Vol 6 (2) ◽  
pp. 302-312 ◽  
Author(s):  
Lu Ting
Keyword(s):  
Wave Equation ◽  
Pressure Distribution ◽  
Elementary Function ◽  
Thickness Distribution ◽  
Normal Velocity ◽  
Supersonic Speed ◽  
Integral Relationship

For wings with supersonic edges and with arbitrary dihedral, twist, camber and thickness distribution, the pressure distribution on the wing exterior to and along the two Mach lines emanating from the vertex of the wing is equal to the corresponding pressure distribution for a planar wing. The problem is to find the pressure distribution inside the two Mach lines. In the present paper, the unknown pressure distribution is approximated by an elementary function of the two surface variables. The (as yet undetermined) constants in the function are then found by the conditions: (i) that the function takes on the corresponding planar values along the two Mach lines, (ii) that it fulfils certain generalized integral relationships (Ting 1959), and (iii) that it satisfies the averaging property of solutions of the wave equation to be developed in this paper. The generalized integral relationship relates the integral of the pressure distribution along the line of intersection of a Mach plane with the wing to the integral along the same line of the prescribed normal velocity. The averaging property relates the pressure distribution along the line of intersection of the surface of the dihedral wing to that on a planar wing.

Hydrodynamic Analysis of the Flow in a Rotary Lip Seal Using Flow Factors

2004 ◽  
Vol 126 (1) ◽  
pp. 156-161 ◽  
Author(s):  
Richard F. Salant ◽  
Ann H. Rocke
Keyword(s):  
Flow Field ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Present Approach ◽  
Operating Parameters ◽  
Pumping Rate ◽  
Hydrodynamic Analysis ◽  
Lip Seal ◽  
Lubricating Film ◽  
Computationally Intensive

The flow field in the lubricating film of a rotary lip seal is analyzed numerically by solving the Reynolds equation with flow factors. The behavior of such a flow field is dominated by the asperities on the lip surface. Since previous analyses treated those asperities deterministically, they required very large computation times. The present approach is much less computationally intensive because the asperities are treated statistically. Since cavitation and asperity orientation play important roles, these are taken into account in the computation of the flow factors. Results of the analysis show how the operating parameters of the seal and the characteristics of the asperities affect such seal characteristics as the pressure distribution in the film, the pumping rate and the load support.

Numerical Simulation of Partial Cavitating Flow of 2-D Hydrofoil in Viscous Flow

2012 ◽  
Vol 214 ◽  
pp. 102-107
Author(s):  
Xiao Hui He ◽  
Lei Gao ◽  
Hong Bing Liu ◽  
Zhi Gang Li
Keyword(s):  
Numerical Simulation ◽  
Numerical Calculation ◽  
Flow Field ◽  
Viscous Flow ◽  
Reynolds Equation ◽  
Cavitating Flow ◽  
Partial Cavitation ◽  
Calculation Results ◽  
Control Equation ◽  
Precise Degree

This paper has studied the partial cavitation of 2-D hydrofoil based on the theory of viscous flow. The numerical calculation sets forth from the complete N-S equation and adopts the two-equation turbulence model closed Reynolds equation. As the basic control equation, the cavitating flow adopts the Rayleigh plesset model and calculates the zero angle of attack. At the same time, it calculates the influences of different ship speeds on the hydrofoil partial cavitating flow and analyzes the flow field of the hydrofoil. In addition, it makes comparisons on the calculation results and the published test conclusions. The results have shown that the calculation method in this paper has relatively good calculation precise degree.

Modelling and Analysis of the Dynamic Behavior of an Active Journal Bearing

1994 ◽  
Author(s):  
Linxiang Sun ◽  
Janusz M. Krodkiewski ◽  
Nong Zhang
Keyword(s):  
Pressure Distribution ◽  
Reynolds Equation ◽  
Hydrodynamic Pressure ◽  
Chamber Pressure ◽  
Oil Film ◽  
Simulation Based ◽  
Rotor Bearing ◽  
New Type ◽  
The Stability ◽  
Bearing System

Modelling and analysis of a rotor-bearing system with a new type of active oil bearing are presented. The active bearing basically consists of a flexible sleeve and a pressure chamber. The deformation of the sleeve can be controlled by the chamber pressure during the operation, and so can the pressure distribution of the oil film. Finite Element Methods (FEMs) and the Guyan condensation technique were utilised to create mathematical models for both the rotor and the flexible sleeve. The hydrodynamic pressure distribution of the oil film, for the instantaneous positions and velocities of the flexible sleeve and rotor, was approximated by Reynolds equation. The influence of the chamber pressure on the stability of the rotor system was investigated by numerical simulation based on the nonlinear model. The results showed that the stability of the rotor-bearing system can be improved effectively by implementation of the active bearing.

scholarly journals Pressure Distribution in a Porous Squeeze Film Bearing Lubricated with a Herschel-Bulkley Fluid

2016 ◽  
Vol 21 (4) ◽  
pp. 951-965
Author(s):  
A. Walicka ◽  
P. Jurczak
Keyword(s):  
Pressure Distribution ◽  
Successive Approximation ◽  
Porous Layer ◽  
Reynolds Equation ◽  
Viscoplastic Fluid ◽  
Squeeze Film ◽  
Bearing Clearance ◽  
Parallel Disks ◽  
Modified Reynolds Equation

Abstract The influence of a wall porosity on the pressure distribution in a curvilinear squeeze film bearing lubricated with a lubricant being a viscoplastic fluid of a Herschel-Bulkley type is considered. After general considerations on the flow of the viscoplastic fluid (lubricant) in a bearing clearance and in a porous layer the modified Reynolds equation for the curvilinear squeeze film bearing with a Herschel-Bulkley lubricant is given. The solution of this equation is obtained by a method of successive approximation. As a result one obtains a formula expressing the pressure distribution. The example of squeeze films in a step bearing (modeled by two parallel disks) is discussed in detail.

Effect of changing geometrical characteristics for different shapes of a single ridge passing through elastohydrodynamic of point contacts

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohamed Abd Alsamieh
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
Time Step ◽  
Content Type ◽  
Geometrical Characteristics ◽  
Different Shapes

Purpose The purpose of this paper is to study the behavior of a single ridge passing through elastohydrodynamic lubrication of point contacts problem for different ridge shapes and sizes, including flat-top, triangular and cosine wave pattern to get an optimal ridge profile. Design/methodology/approach The time-dependent Reynolds’ equation is solved using Newton–Raphson technique. Several shapes of surface feature are simulated and the film thickness and pressure distribution are obtained at every time step by simultaneous solution of the Reynolds’ equation and film thickness equation, including elastic deformation. Film thickness and pressure distribution are chosen to be the criteria in the comparisons. Findings The geometrical characteristics of the ridge play an important role in the formation of lubricant film thickness profile and the pressure distribution through the contact zone. To minimize wear, friction and fatigue life, an optimal ridge profile should have smooth shape with small ridge size. Obtained results are compared with other published numerical results and show a good agreement. Originality/value The study evaluates the performance of different surface features of a single ridge with different shapes and sizes passing through elastohydrodynamic of point contact problem in relation to film thickness and pressure profile.

Modelling a New Three-Pad Active Bearing

2004 ◽  
Author(s):  
Janusz M. Krodkiewski ◽  
Gregory J. Davies
Keyword(s):  
Pressure Distribution ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Oil Film ◽  
Active Devices ◽  
System Of Matrix Equations ◽  
Stiffness Matrices ◽  
Oil Flow ◽  
Lower Chamber ◽  
Non Linear System

This paper describes investigations into a new type of active bearing to be implemented in the field of rotating machinery. Active bearings are based on the concept that journal oil flow can be modified during operation by active devices. Here, the concepts of the flexible pads and the oil-filled chambers that control their deflection are used. Three active pads are positioned around the journal with three oil-filled chambers positioned behind them. One of them, the load-bearing pad located at the bottom of the bearing, acts as a passive device and is equipped with a very thin film chamber, which acts as a source of damping. Such a damper was found in previous work to be effective in dissipating energy. Here, in a departure from previous work, two additional small pads with deep oil-filled chambers have been added in order to allow control theory to be implemented. They are located in the upper part of the active bearing. A non-linear system model is developed for the rotor-bearing system that includes the described active bearing. The flow inside the upper chambers that control motion of the active pads was neglected due to their large volume. It results in a uniform pressure distribution along the upper pads. The pressure distribution within the damper oil film (inside the lower chamber) and the journal oil film was modeled with the aid of the Reynolds equation. They were solved by means of the finite difference method and Gauss-Seidel technique. The same mesh used for solution of the Reynolds equation was used for the division of the flexible pads into the finite elements. The same approach was adopted for the modelling of the dynamic properties of the rotor. The mass and stiffness matrices for the pads and rotor were condensed down to 12 master generalized coordinates using Guyan condensation. The obtained system of matrix equations was converted to a system of first order equations and solved via the Runge-Kutta method. Some results of the numerical testing of the mathematical model developed are provided.

Determination of Dynamic Coefficients in a Hydrodynamic Journal Bearing Based on the 3-D Navier-Stokes Equations and Considering Cavitation Effects

2012 ◽  
Author(s):  
Changhu Xing ◽  
Minel J. Braun
Keyword(s):  
Pressure Distribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Maximum Magnitude ◽  
Navier Stokes Equations ◽  
Dynamic Coefficients ◽  
Finite Perturbation ◽  
Hydrodynamic Journal Bearing

Dynamic coefficients are very important for the stability of a hydrodynamic journal bearing and therefore for its design. In order to determine the stiffness, damping and added mass coefficients of the hydrodynamic bearing, the finite perturbation method around its stabilization position was employed. Based on the Reynolds equation with Gumbel cavitation algorithm, the maximum magnitude of the perturbation was judged by comparing results from finite perturbation (numerical way) to those from infinitesimal perturbation (additional analytical equations need to be derived based on order analysis), as well as theoretical analysis. Using the determined perturbation amplitude, the full three-dimensional Navier-Stokes equations in CFD-ACE+ were used to evaluate coefficients from an actual lubricant and compare to those obtained with Reynolds equation. Finally, a homogeneous gaseous cavitation algorithm is coupled with the Navier-Stokes equation to establish the pressure distribution in the bearing. When gas concentration was varied, the pressure distribution as well as the dynamic coefficients changed significantly.

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