• Tribology and Lubricants
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• v.28 no.5
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• pp.218-232
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• 2012

In a spool valve analysis, the Reynolds equation is commonly used to investigate the lubrication characteristics. However, the validity of the Reynolds equation is questionable in a spool valve analysis because cavitation often occurs in the groove and the depth of the groove is much higher than the clearance in most cases. Therefore, the validity of the Reynolds equation in a spool valve analysis is investigated by comparing the results obtained from the Reynolds equation and the Navier-Stokes equation. Dimensionless parameters are determined from a nondimensional form of the governing equations. The differences between the lateral force, friction force, and volume flow rate (leakage) obtained by the Reynolds equation and those obtained by the Navier-Stokes equation are discussed. It is shown that there is little difference (less than 10%), except in the case of a spool valve with many grooves where no cavitation occurs in the grooves. In most cases, the Reynolds equation is effective for a spool valve analysis under a no cavitation condition.

• Tribology and Lubricants
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• v.29 no.5
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• pp.275-285
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• 2013

The Reynolds equation is commonly used to investigate the lubrication characteristics of a spool valve. However, the applicability of the Reynolds equation is questionable for analyzing a spool valve because cavitation often occurs in the grooves of the valve and the depth of a groove is much higher than the clearance in most cases. In this study, the validity of the Reynolds equation in the spool valve analysis is investigated by comparing the results obtained from the Reynolds equation and those obtained from the Navier-Stokes equation. The results are compared in terms of the lateral forces, friction forces, and volume flow rates (leakages). A significant difference of more than 20% is found in the lateral forces in cases where cavitation occurs and there are many grooves. Therefore, the Navier-Stokes equation should be used to investigate the lubrication characteristics of a spool valve when cavitation occurs and when the spool valve contains many grooves.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.599-605
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• 2003

For practical calculations, the Reynolds equation is frequently used to analyze the lubricating flow. The full Navier-Stokes Equations are used to find validity limits of Reynolds equation in a lubricating flow regime by result comparison. As the amplitude of wavy upper wall increased at a given average channel height, the difference between Navier-Stokes and lubrication theory decreased slightly : however, as the minimum distance in channel throat increased, the differences in the maximum pressure between Navier-Stokes and lubrication theory became large.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.5
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• pp.1203-1217
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• 1994

In the present study, in order to analyze a turbulent flow in a square sectiond 180.deg. bend, Kim's low Reynolds number second moment turbulence closure is adopted. In this model, turbulence model constants in the wall region are modified as functions of turbulent Reynolds number by use of near wall turbulent universal properties based on Laufer's experimental results of Reynolds stress distriburions. Algebraic stress model and Reynolds stress equation model are used to verify the low Reynolds number second moment closure. The application of the present low Reynolds number algebraic stress model to the prediction of a square sectioned 180.deg. bend flow gives improved velocities and Reynolds stresses profiles compared with those obtained by using the van Driest mixing length model and present low Reynolds number Reynolds stress equation model.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.473-478
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• 2010

In this study, the Ergun's equation has been verified in order to calculate pressure drop of the two phase flow. The equation had been used in the high Reynolds number region for interior ballistic analysis in spite of being verified in the low Reynolds number region. Therefore additional verification seems to be inevitable. Thus, the validity of the equation has been verified using CFD in the high Reynolds number cases of the diameter-particle ratio 10, 13 and 16.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.760-767
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• 2014

This paper proposes a method to calculate pressure and flow of the fluid dynamic bearings (FDBs) with a recirculation channel (RC) by solving the Reynolds and the Hagen-Poiseuille equations at the same time. The Hagen-Poiseuille equation is one-dimensional equation which describes the flow in a circular pipe such as the RC. This research developed a finite element program to solve the Reynolds and the Hagen-Poiseuille equation together. The proposed method was applied to calculate the pressure and flow of the FDBs which are composed of grooved or plain journal and thrust bearings, and RC. To verify the proposed method, it also developed a finite volume model of the FDBs, and pressure and flow were calculated by the commercial CFD solver. They agree well with the pressure and flow calculated by the proposed method. Finally, this research investigated the characteristics of the FDBs due to the radius change of the RC.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.172-177
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• 2004

In the present work, we have interests on the modification of parallel implemented with MPI(Message Passing Interface) programming method, 3-Dimensional, unsteady, incompressible Navier-Stokes equation solver to analyze the low-Reynolds number flow In order to accurate calculation aerodynamic coefficients in low-Reynolds number flow field, we modified the two-equation turbulence model. This paper describes the development and validation of a new two-equation model for the prediction of flow transition. It is based on Mentor's low Reynolds $\kappa-\omega$ model with modifications to include Total Stresses Limitation (TSL) and Separation Transition Trigger (STT)

• Journal of computational fluids engineering
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• v.2 no.2
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• pp.9-17
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• 1997

The performance of several turbulence models in computing an axisymmetric supersonic base flow is investigated. A compressible Navier-Stokes code, which incorporates k-ε, k-ω model and Reynolds stress closure with three kinds of pressure-strain correlation model, has been developed using implicit LU-SGS algorithm with second-order upwind TVD scheme. Numerical computations have been carried out for Herrin and Dutton's base flow. It is observed that the two-equation models give large backward axial velocity approaching to the base and somewhat larger variation of base pressure distribution than the Reynolds stress model. It is also found that the Reynolds stress model with third order pressure-strain model in the anisotropy tensor predicts most accurate mean flow field.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.404-408
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• 2005

The Reynolds strss equation with turbulent energy-length scales was simplified in the nearly homogeneous turbulent equilibrium flow and a modified Reynolds stress model was proposed. Tn the model proposed in the present study, Reynolds stresses can be expressed in the form of algebraic equation, so that the turbulent stresses and related quantities are calculated through relatively simple procedures. The model predicted well the turbulent shear stresses of homogeneous flow in local equilibrium state obtained from experimental results published earlier Constants used In the model was determined universally and its validity was discussed briefly.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.6
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• pp.55-68
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• 1995

Approximately 30 to 70 % of the mechanical losses in a reciprocating engine are contributed by the friction at the piston ring-cylinder interface. The friction characteristics of the piston ring during engine operation is known to as mixed lubrication experimentally. The mixed lubrication models based on the Average Reynolds Equation have been used by this time in order to study the tribological performance of the ring. However, the Average Reynolds Equation contains the expected value term(${\bar{h}}_r$) of local film thickness as well as nominal film thickness(h), so that the work of numerically solving ${\bar{h}}_r$ must be included to obtain the pressure in the oil film. The process of solving ${\bar{h}}_T$ causes a greater multiplying in the numerical solution. In this paper the mixed lubrication analysis using the Simplified Average Reynolds Equation in the piston ring is presented. This equation has only h as oil film thickness term. Therefore the tedious numerical procedure required to obtain ${\bar{h}}_T$ is not needed, and also, computation time can be reduced.