Effects of Fluid Inertia Forces on the Performance of a Plane Inclined Sector Pad for an Annular Thrust Bearing Under Laminar Condition

1985 ◽  
Vol 107 (1) ◽  
pp. 46-52 ◽  
Author(s):  
Atsunobu Mori ◽  
Katsuyuki Tanaka ◽  
Haruo Mori
Keyword(s):  
Stokes Equations ◽  
Ambient Pressure ◽  
Dynamic Performance ◽  
Leading Edge ◽  
Navier Stokes ◽  
Frictional Torque ◽  
Fluid Inertia ◽  
Thin Film Lubrication ◽  
Navier Stokes Equations ◽  
Inertia Forces

The hydrodynamic wedge of a plane inclined sector pad is analyzed in relation to the lubricant inertia forces under incompressible laminar conditions. Based on the usual assumptions of thin film lubrication theory without the thermal effects, modified Reynolds equations are derived by averaging out all the inertia terms of the Navier-Stokes equations across the film thickness. The equations are linearized with respect to the inertia parameter, and solved numerically for a plane inclined, sectorial configuration. The boundary value of the film pressure at the leading edge is set at the ambient pressure, under the assumption of a negligibly small rampressure thereat. The inertial effects on the static and dynamic performance such as the load carrying capacity, flow rate, frictional torque, position of pressure center, film stiffness, and damping coefficient are discussed, in which the effects of the centrifugal force and those of the other convective inertia forces are compared with each other.

Numerical Simulation of Clocking Effect on Wake Transportation and Interaction in a 1.5-Stage Axial Turbine

2010 ◽  
Author(s):  
Wei Li ◽  
Hua Ouyang ◽  
Zhao-hui Du
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Navier Stokes ◽  
Maximum Efficiency ◽  
Suction Surface ◽  
Navier Stokes Equations ◽  
Pressure Surface ◽  
Turbine Efficiency ◽  
Small Influence

To give insight into the clocking effect and its influence on the wake transportation and its interaction, the unsteady three-dimensional flow through a 1.5-stage axial low pressure turbine is simulated numerically using a density-correction based, Reynolds-Averaged Navier-Stokes equations commercial CFD code. The 2nd stator clocking is applied over ten equal tangential positions. The results show that the harmonic blade number ratio is an important factor affecting the clocking effect. The clocking effect has a very small influence on the turbine efficiency in this investigation. The efficiency difference between the maximum and minimum configuration is nearly 0.1%. The maximum efficiency can be achieved when the 1st stator wake enters the 2nd stator passage near blade suction surface and its adjacent wake passes through the 2nd stator passage close to blade pressure surface. The minimum efficiency appears if the 1st stator wake impinges upon the leading edge of the 2nd stator and its adjacent wake of the 1st stator passed through the mid-channel in the 2nd stator.

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.

Boundary layer leading-edge receptivity to sound at incidence angles

2001 ◽  
Vol 444 ◽  
pp. 383-407 ◽  
Author(s):  
ERCAN ERTURK ◽  
THOMAS C. CORKE
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Incidence Angle ◽  
Leading Edge ◽  
Quantitative Agreement ◽  
Navier Stokes ◽  
Angle Of Incidence ◽  
Sound Waves ◽  
Nose Radius ◽  
Navier Stokes Equations

The leading-edge receptivity to acoustic waves of two-dimensional parabolic bodies was investigated using a spatial solution of the Navier–Stokes equations in vorticity/streamfunction form in parabolic coordinates. The free stream is composed of a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998) in which the solution for the basic flow and linearized perturbation flow are solved separately. We primarily investigated the effect of frequency and angle of incidence (−180° [les ] α2 [les ] 180°) of the acoustic waves on the leading-edge receptivity. The results at α2 = 0° were found to be in quantitative agreement with those of Haddad & Corke (1998), and substantiated the Strouhal number scaling based on the nose radius. The results with sound waves at angles of incidence agreed qualitatively with the analysis of Hammerton & Kerschen (1996). These included a maximum receptivity at α2 = 90°, and an asymmetric variation in the receptivity with sound incidence angle, with minima at angles which were slightly less than α2 = 0° and α2 = 180°.

Investigation of G4-73 Centrifugal Fan Airfoil Stall Characteristics

2011 ◽  
Vol 383-390 ◽  
pp. 4221-4226
Author(s):  
Song Ling Wang ◽  
Zhe Liu ◽  
Lei Zhang
Keyword(s):  
Stokes Equations ◽  
Incidence Angle ◽  
Leading Edge ◽  
Suction Side ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Reliable Operation ◽  
Safe Operation ◽  
Navier Stokes Equations ◽  
Strong Vortex

It’s of great significance for safe and reliable operation of fan to research on the stall characteristics of the airfoil. The 2D non-compressible Reynolds-Averaged Navier-Stokes equations was built to simulate the flow around the airfoil of G4-73No.8D centrifugal fan, a detailed numerical simulation under different angles has been carried out which based on the Realizable turbulence model with Fluent. The numerical results show that the smaller of the flow rate, the bigger incidence angle is, when the incidence angle is bigger than the critical incidence angle, the suction side stall appears. According simulation the airfoil stall appears when the incidence angle is -28°, with the increasing of the negative incidence angle, the separation point gradually moves to the leading edge. There is a strong vortex which locates at suction side =0.5,the alternating stress on the blade which caused by vortex will make the blade fatigue. If the incidence angle is less than -20°,there is no flow separation, therefore, to ensure the safe operation of the fan, the incidence angle should be less than -20°.

Laminar incompressible flow past a semi-infinite flat plate

1967 ◽  
Vol 27 (4) ◽  
pp. 691-704 ◽  
Author(s):  
R. T. Davis
Keyword(s):  
Flat Plate ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Local Similarity ◽  
Approximate Methods ◽  
Navier Stokes Equations ◽  
Flow Past

Laminar incompressible flow past a semi-infinite flat plate is examined by using the method of series truncation (or local similarity) on the full Navier-Stokes equations. The first and second truncations are calculated at points on the plate away from the leading edge, while only the first truncation is calculated at the leading edge. The solutions are compared with the results from other approximate methods.

Finite-Reynolds-Number Effects in Steady, Three-Dimensional Airway Reopening

2006 ◽  
Vol 128 (4) ◽  
pp. 573-578 ◽  
Author(s):  
Andrew L. Hazel ◽  
Matthias Heil
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Elastic Tube ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Navier Stokes Equations ◽  
Airway Reopening ◽  
Reynolds Number Effects ◽  
Steady Propagation

Motivated by the physiological problem of pulmonary airway reopening, we study the steady propagation of an air finger into a buckled elastic tube, initially filled with viscous fluid. The system is modeled using geometrically non-linear, Kirchhoff-Love shell theory, coupled to the free-surface Navier-Stokes equations. The resulting three-dimensional, fluid-structure-interaction problem is solved numerically by a fully coupled finite element method. Our study focuses on the effects of fluid inertia, which has been neglected in most previous studies. The importance of inertial forces is characterized by the ratio of the Reynolds and capillary numbers, Re∕Ca, a material parameter. Fluid inertia has a significant effect on the system’s behavior, even at relatively small values of Re∕Ca. In particular, compared to the case of zero Reynolds number, fluid inertia causes a significant increase in the pressure required to drive the air finger at a given speed.

scholarly journals Coriolis effect and the attachment of the leading edge vortex

2017 ◽  
Vol 820 ◽  
pp. 312-340 ◽  
Author(s):  
T. Jardin
Keyword(s):  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Coriolis Effect ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Leading Edge Vortex ◽  
Edge Vortex ◽  
Vorticity Transport ◽  
Rotating Wing

The role of the Coriolis effect on the attachment of the leading edge vortex (LEV) is investigated. Toward that end, the Navier–Stokes equations are solved in the non-inertial reference frame of a high angle of attack $\unicode[STIX]{x1D6FC}$ rotating wing with the Coriolis term being artificially tuned. Reynolds numbers in the range $Re\in [100;750]$ are considered to identify the interplay between Coriolis and viscous effects. Similarly, artificial tuning of the centrifugal term is achieved to identify the interplay between Coriolis and centrifugal effects. It is shown that (i) the Coriolis effect is the key element in LEV stability for $Re>200$, (ii) viscous effects are the key element for $Re<200$ and (iii) centrifugal effects have a marginal role. The Coriolis effect is found to promote spanwise flow in the core and behind the LEV, which is known to promote outboard vorticity transport and presumably contributes to stabilizing the aft boundary layer. These mechanisms of LEV stabilization have increased authority as $\unicode[STIX]{x1D6FC}$ decreases.

The Influence of Fluid Inertia in Unsteady Lubrication Films

1982 ◽  
Vol 104 (2) ◽  
pp. 180-186 ◽  
Author(s):  
A. Sestieri ◽  
R. Piva
Keyword(s):  
Computational Model ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Geometrical Shape ◽  
Fluid Inertia ◽  
Navier Stokes Equations ◽  
Film Boundary ◽  
Simple Boundary ◽  
Complete Set

The influence of the inertial forces in steady and unsteady lubrication films has been analyzed by means of an accurate computational model of the complete set of Navier Stokes equations for incompressible flows. A coordinate transformation accounts for the geometrical shape of the film boundary and its variation in time, reducing the numerical integration to a rectangular constant domain in the transformed plane. A dimensional analysis of the equations, both in steady and unsteady conditions, is performed to deduce the most significant nondimensional variables and parameters to be considered for a proper evaluation of the inertial effects. The applications are restricted to two-dimensional fields and simple boundary conditions to test the simulation capabilities of the computational model, by comparison with analytical solutions available in literature. Several geometrical and kinematic conditions are discussed and the effect of the convective and time dependent inertial terms is quantitatively evaluated.

scholarly journals Effect of Leading-Edge Bulges on Aerodynamic Characteristics of Bionic Wingsail

2021 ◽  
Author(s):  
Chen Li ◽  
Peiting Sun ◽  
Hongming Wang
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Suction Surface ◽  
Ansys Fluent ◽  
Navier Stokes Equations ◽  
Extension Direction ◽  
Lift And Drag

The leading-edge bulges along the extension direction are designed on the marine wingsail. The height and the spanwise wavelength of the protuberances are 0.1c and 0.25c, respectively. At Reynolds number Re=5×105, the Reynolds Averaged Navier-Stokes equations are applied to the simulation of the wingsail with the bulges thanks to ANSYS Fluent finite-volume solver based on the SST K-ω models. The grid independence analysis is carried out with the lift and drag coefficients of the wingsail at AOA = 8° and AOA=20°. The results show that while the efficiency of the wingsail is reduced by devising the leading-edge bulges before stall, the bulges help to improve the lift coefficient of the wingsail when stalling. At AOA=22° under the action of the leading-edge tubercles, a convective vortex is formed on the suction surface of the modified wingsail, which reduces the flow loss. So the bulges of the wingsail can delay the stall.

Calculation of Transition in Adverse Pressure Gradient Flow by Conditioned Equations

1996 ◽  
Author(s):  
J. Steelant ◽  
E. Dick
Keyword(s):  
Pressure Gradient ◽  
Transport Equation ◽  
Stokes Equations ◽  
Growth Parameter ◽  
Gradient Flow ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations

Conditionally averaged Navier-Stokes equations are used to describe transitional flow in adverse pressure gradient combined with a transport equation for the intermittency factor γ. A transport equation developped in earlier work has been modified to eliminate the use of a distance along a streamline. An extension of the correlations is proposed to determine the spot growth parameter in adverse pressure gradient. This approach is verified against flows over a flat plate with an elliptical leading edge.

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