A Multiscale Method Modeling Surface Texture Effects

2006 ◽  
Vol 129 (2) ◽  
pp. 221-230 ◽  
Author(s):  
Alex de Kraker ◽  
Ron A. J. van Ostayen ◽  
A. van Beek ◽  
Daniel J. Rixen
Keyword(s):  
Surface Texture ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Multiscale Method ◽  
Operating Conditions ◽  
Contact Load ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Inertia Effects

In this paper a multiscale method is presented that includes surface texture in a mixed lubrication journal bearing model. Recent publications have shown that the pressure generating effect of surface texture in bearings that operate in full film conditions may be the result of micro-cavitation and/or convective inertia. To include inertia effects, the Navier–Stokes equations have to be used instead of the Reynolds equation. It has been shown in earlier work (de Kraker et al., 2006, Tribol. Trans., in press) that the coupled two-dimensional (2D) Reynolds and 3D structure deformation problem with partial contact resulting from the soft EHL journal bearing model is not easy to solve due to the strong nonlinear coupling, especially for soft surfaces. Therefore, replacing the 2D Reynolds equation by the 3D Navier–Stokes equations in this coupled problem will need an enormous amount of computing power that is not readily available nowadays. In this paper, the development of a micro–macro multiscale method is described. The local (micro) flow effects for a single surface pocket are analyzed using the Navier–Stokes equations and compared to the Reynolds solution for a similar smooth piece of surface. It is shown how flow factors can be derived and added to the macroscopic smooth flow problem, that is modeled by the 2D Reynolds equation. The flow factors are a function of the operating conditions such as the ratio between the film height and the pocket dimensions, the surface velocity, and the pressure gradient over a surface texture unit cell. To account for an additional pressure buildup in the texture cell due to inertia effects, a pressure gain is introduced at macroscopic level. The method also allows for microcavitation. Microcavitation occurs when the pressure variation due to surface texture is larger than the average pressure level at that particular bearing location. In contrast with the work of Patir and Cheng (1978, J. Lubrication Technol., 78, pp. 1–10), where the microlevel is solved by the Reynolds equation, and the Navier–Stokes equations are used at the microlevel. Depending on the texture geometry and film height, the Reynolds equation may become invalid. A second pocket effect occurs when the pocket is located in the moving surface. In mixed lubrication, fluid can become trapped inside a pocket and squeezed out when the pocket is running into an area with higher contact load. To include this effect, an additional source term that represents the average fluid inflow due to the deformation of the surface around the pocket is added to the Reynolds equation at macrolevel. The additional inflow is computed at microlevel by numerical solution of the surface deformation for a single pocket that is subject to a contact load. The pocket volume is a function of the contact pressure. It must be emphasized that before ready-to-use results can be presented, a large number of simulations to determine the flow factors and pressure gain as a function of the texture parameters and operating conditions have yet to be done. Before conclusions can be drawn, regarding the dominanant mechanism(s), the flow factors and pressure gain have to be added to the macrobearing model. In this paper, only a limited number of preliminary illustrative simulation results, calculating the flow factors for a single 2D texture geometry, are shown to give insight into the method.

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.

The Validity of the Compressible Reynolds Equation for Gas Lubricated Textured Parallel Slider Bearings

2012 ◽  
Author(s):  
Mingfeng Qiu ◽  
Brian Bailey ◽  
Rob Stoll ◽  
Bart Raeymaekers
Keyword(s):  
Gas Flow ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Hydrodynamic Lubrication ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slider Bearings ◽  
Simplifying Assumptions ◽  
Simulation Results

The Navier-Stokes and compressible Reynolds equations are solved for gas lubricated textured parallel slider bearings under hydrodynamic lubrication for a range of realistic texture geometry parameters and operating conditions. The simplifying assumptions inherent in the Reynolds equation are validated by comparing simulation results to the solution of the Navier-Stokes equations. Using the Reynolds equation to describe shear driven gas flow in textured parallel slider bearings is justified for the range of parameters considered.

Numerical analysis of textured piston compression ring conjunction using two-dimensional-computational fluid dynamics and Reynolds methods

2018 ◽  
Vol 232 (11) ◽  
pp. 1467-1485 ◽  
Author(s):  
Chengwei Wen ◽  
Xianghui Meng ◽  
Wenxiang Li
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Compression Ring ◽  
Dynamics Method

The Reynolds equation, in which some items have been omitted, is a simplified form of the Navier–Stokes equations. When surface texturing exists, it may unreasonably reveal the tribological effects in some cases. In this paper, both the two-dimensional computational fluid dynamics method, which is based on the Navier–Stokes equations, and the corresponding one-dimensional Reynolds method are adopted to analyze the performance of the textured piston compression ring conjunction. To conduct a comparison between these two methods, the modified Elrod algorithm for Jakobsson–Floberg–Olsson cavitation model is chosen to solve the Reynolds equation. The results show that the Reynolds method is somewhat different from the computational fluid dynamics method in the minimum oil film thickness, pressure distribution, and cavitation at given operating conditions. Moreover, for a low ratio of texture depth to length, the Reynolds equation is still suitable to predict the overall effects of the designed groove textures. The simulation results also reveal that it is not always beneficial for the tribological performance and sometimes may increase the total friction force when the ring is textured.

Influence of Inertia Terms on High Pressure Gap Flow Applications in Hydraulics

2019 ◽  
Author(s):  
Felix Fischer ◽  
Andreas Rhein ◽  
Katharina Schmitz
Keyword(s):  
High Pressure ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Fluid Phase ◽  
Simulation Models ◽  
Rigid Bodies ◽  
Navier Stokes ◽  
Dependent Manner ◽  
Fluid Inertia ◽  
Navier Stokes Equations

Abstract Hydraulic pumps, which reach pressures up to 3000 bar, are often realized as plunger-piston type pumps. In the case of a common-rail pump for diesel injection systems, the plunger is driven by a cam-tappet construction and the contact during suction stroke is maintained by a helical spring. Many hydraulic piston-based high pressure pumps include gap seals, which are formed by small clearances between the two surfaces of the piston and the bushing. Usually the gap height is in the magnitude of several micrometers. Typical radial gaps are between 0.5 and 1 per mil of the nominal diameter. These gap seals are used to allow and maintain pressure build up in the piston chamber. When the gap is pressurized, a special flow regime is reached. For the description of this particular flow the Reynolds equation, which is a simplification of the Navier-Stokes equations, can be used as done in the state of the art. Furthermore, if the pressure in the gap is high enough — 500 bar and above — fluid-structure interactions must be taken into account. Pressure levels above 1500 or 2000 bar indicate the necessity for solving the energy equation of the fluid phase and the rigid bodies surrounding it. In any case, the fluid properties such as density and viscosity, have to be modelled in a pressure dependent manner. This means, a compressible flow is described in the sealing gap. Viscosity changes in magnitudes while density remains in the same magnitude, but nevertheless changes about 30 %. These facts must be taken into account when solving the Reynolds equation. In this paper the authors work out that the Reynolds equation is not suitable for every piston-bushing gap seal in hydraulic applications. It will be shown that remarkable errors are made, when the inertia terms in the Navier-Stokes equations are neglected, especially in high pressure applications. To work out the influence of the inertia terms in these flows, two simulation models are built up and calculated for the physical problem. One calculates the compressible Reynolds equation neglecting the fluid inertia. The other model, taking the fluid inertia into account, calculates the coupled Navier-Stokes equations on the same geometrical boundaries. Here, the so called SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm is used. The discretization is realized with the Finite Volume Method. Afterwards, the solutions of both models are compared to investigate the influence of the inertia terms on the flow in these specific high pressure applications.

Assessing the Dynamic Stability of an Offshore Supply Vessel

2011 ◽  
Author(s):  
Vladimir Shigunov ◽  
Ould el Moctar ◽  
Thomas E. Schellin ◽  
Jan Kaufmann ◽  
Rasmus Stute
Keyword(s):  
Dynamic Stability ◽  
Stokes Equations ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Ship Motions ◽  
Navier Stokes Equations ◽  
Counter Measures ◽  
Seakeeping Analysis ◽  
Design Speed ◽  
Run Up

The dynamic stability was investigated of a typical offshore service vessel operating under stability critical operating conditions. Excessive roll motions and relative motions at the stern were studied for two loading conditions for ship speeds ranging from zero to the design speed. A linear frequency-domain seakeeping analysis was followed by nonlinear time-domain simulations of ship motions in waves. Based on results from these methods, critical scenarios were selected and simulated using finite-volume solvers of the Reynolds-averaged Navier-Stokes equations to understand the phenomena related to dynamically unstable ship motions as well as to confirm the results of the simpler analysis methods. Results revealed the possibility of excessive roll motions and water run-up on deck; counter measures such as a ship-specific operational guidance are discussed.

Inertial effect on gas squeeze film for large radius disc excited by standing waves with complex modal shapes

2019 ◽  
Vol 33 (24) ◽  
pp. 1950282 ◽  
Author(s):  
Yi Qiang Fan ◽  
M. Miyatake ◽  
S. Kawada ◽  
Bin Wei ◽  
S. Yoshimoto
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Standing Waves ◽  
Inertial Effect ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Large Radius ◽  
Navier Stokes Equations ◽  
Sinusoidal Functions

In order to investigate the gas inertial effect on bearing capacity of acoustic levitation on condition of complex exciting shapes, a new kind of numerical model including inertial effect in cylindrical coordinates was proposed. The inertial terms in Navier–Stokes equations are packaged to derive modified Reynolds equations. The amplitudes of standing waves were tested by distance probe in experiment and film thickness equation were reconstructed by sum of the sinusoidal functions. The theoretical and experimental results implied that the inertial effect is strongly related to the exciting modal shapes. It is concluded that the proposal of modified Reynolds equation can provide more optimized numerical solutions to solve the problems about the deviation between theoretical and experimental data.

Numerical Characterisation of Jet-Vane based Thrust Vector Control Systems

2015 ◽  
Vol 65 (4) ◽  
pp. 261 ◽  
Author(s):  
M.S.R. Chandra Murthy ◽  
Debasis Chakraborty
Keyword(s):  
Vector Control ◽  
Control Systems ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Static Tests ◽  
Thrust Vector Control ◽  
Thrust Vector

<p>Computational fluid dynamics methodology was used in characterising jet vane based thrust vector control systems of tactical missiles. Three-dimensional Reynolds Averaged Navier-Stokes equations were solved along with two-equation turbulence model for different operating conditions. Nonlinear regression analysis was applied to the detailed CFD database to evolve a mathematical model for the thrust vector control system. The developed model was validated with series of ground based 6-Component static tests. The proven methodology is applied toa new configuration.</p><p><strong>Defence Science Journal, Vol. 65, No. 4, July 2015, pp. 261-264, DOI: http://dx.doi.org/10.14429/dsj.65.7960</strong></p>

3-D Numerical Simulation for Fuel Cell Performance

2002 ◽  
Author(s):  
Tien-Chien Jen ◽  
S. H. Chan ◽  
T. Z. Yan
Keyword(s):  
Fluid Flow ◽  
Fuel Cell ◽  
Stokes Equations ◽  
Current Density Distribution ◽  
Mass Transfer Process ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fuel Cell Performance ◽  
Gas Channel

A 3-D mathematical model for the PEM fuel cell including gas channel has been developed to simulate fluid flow, current density distribution, and multi-component transport. In order to understand the developing fluid flow and mass transfer process inside the fuel cell channels, the conventional Navier-Stokes equations for gas channel, and volume-averaged Navier-Stokes equations for porous gas diffusers and catalyst layer are adopted individually in this study. A set of conservation equations and species concentration equations are solved numerically in a coupled gas channel and porous media domain using the vorticity-velocity method with power law scheme. Detailed development axial velocity and secondary flow fields at various axial positions in the entrance region are presented. Polarization curves under various operating conditions are demonstrated by solving the equations for electrochemical reactions and the membrane phase potential. Compared with experimental data from published literatures, numerical results of this model agree closely with experimental results. Finally, mass transport equations are solved at a preset condition of electrochemical reaction, and oxygen and hydrogen mole fraction distribution fields are displayed.

Solution of Reynolds Equation in Polar Coordinates Applicable to Nonsymmetric Entrainment Velocities

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Kurt Beschorner ◽  
C. Fred Higgs ◽  
Michael Lovell
Keyword(s):  
Reynolds Equation ◽  
Stokes Equations ◽  
Angular Position ◽  
Technical Note ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Polar Form ◽  
Fluid Films ◽  
Navier Stokes Equations ◽  
Cylindrical Polar Coordinates

Reynolds equation in polar cylindrical (polar) coordinates is used for numerous tribological applications that feature thin fluid films in sliding contacts, such as chemical mechanical polishing and pin-on-disk testing. Although unstated, tribology textbooks and literary resources that present Reynolds equation in polar coordinates often make assumptions that the radial and tangential entrainment velocities are independent of the radial and tangential directions, respectively. The form of polar Reynolds equation is thus typically presented, while neglecting additional terms crucial to obtaining accurate solutions when these assumptions are not met. In the present investigation, the polar Reynolds equation is derived from the cylindrical Navier–Stokes equations without the aforementioned assumptions, and the resulting form is compared with results obtained from more traditionally used forms of the polar Reynolds equation. The polar form of Reynolds equation derived in this manuscript yields results that agree with the commonly used Cartesian form of Reynolds equation but are drastically different from the typically published form of the polar Reynolds equation. It is therefore suggested that the polar form of Reynolds equation proposed in this technical note be utilized when entrainment velocities are known to vary with either radial or angular position.

Three-Dimensional Analysis of Turbine Rotor Flow Including Tip Clearance

1993 ◽  
Author(s):  
R. Heider ◽  
J. M. Duboue ◽  
B. Petot ◽  
G. Billonnet ◽  
V. Couaillier ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Turbine Rotor ◽  
Operating Conditions ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbine Rotor Blade ◽  
Calculation Results ◽  
Rotor Flow

A 3D Navier-Stokes investigation of a high pressure turbine rotor blade including tip clearance effects is presented. The 3D Navier-Stokes code developed at ONERA solves the three-dimensional unsteady set of mass-averaged Navier-Stokes equations by the finite volume technique. A one step Lax-Wendroff type scheme is used in a rotating frame of reference. An implicit residual smoothing technique has been implemented, which accelerates the convergence towards the steady state. A mixing length model adapted to 3D configurations is used. The turbine rotor flow is calculated at transonic operating conditions. The tip clearance effect is taken into account. The gap region is discretized using more than 55,000 points within a multi-domain approach. The solution accounts for the relative motion of the blade and casing surfaces. The total mesh is composed of five sub-domains and counts 710,000 discretization points. The effect of the tip clearance on the main flow is demonstrated. The calculation results are compared to a 3D inviscid calculation, without tip clearance.

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