Application of an Efficient Pressure-Temperature Coupled Solver to Industrial Hydrodynamic Bearings in Conjunction With Multi-Objective Evolutionary Optimization

2011 ◽  
Author(s):  
V. Indriolo ◽  
G. Melina ◽  
G. Ottino ◽  
G. Romanelli ◽  
S. Minniti ◽  
...  
Keyword(s):  
Gas Turbines ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Oil Viscosity ◽  
Hydrodynamic Bearings ◽  
Hydrodynamic Bearing ◽  
Vibration Absorption ◽  
Multi Objective

Hydrodynamic bearings have a key role in the functioning of heavy duty gas turbines: they join a great vibration absorption with an efficient power dissipation by means of a film oil inserted between the turbo machine axes and the bearing case. A classical approach for studying the functioning and the performance of this kind of bearings is to solve the so called Reynolds’ equation, which is obtained from the Navier-Stokes equations under simplifying assumptions. As a result the pressure field is derived, the fluid film being considered isothermal: dissipation effects have to be estimated a posteriori in a postprocessing procedure. On the other hand a fluid environment having to be taken into account, a direct approach is carried out by the time consuming CFD analysis. After defining an appropriate mesh and choosing the appropriate solver, an almost exact solution of the entire flow field is obtained, that is pressure, velocity and temperature distributions. The main drawback is that the required time is several order greater than that required for the solution of the Reynolds’ equation. In the present work an alternative strategy is proposed, which consists of an iterative procedure: at each step the Reynolds’ equation is solved in order to obtain the pressure field; a 1D energy balance is then applied along the length of the bearing for computing the temperature field. In this way the close relationship between pressure and temperature is modelled, the former depending on the oil viscosity locally changing with temperature, and the latter depending on the local oil mass flow and on dissipated power strictly correlated to the pressure distribution. The upgrading of both the entities ends when the convergence is reached. Comparisons with literature test cases reveal the efficiency of the proposed technique: treating the interaction between pressure and temperature gives a solution which is very close to industrial configurations investigated, and at the same time the computational load is as light as that needed for the solution of the only Reynolds’ equation. The performance of the above coupled solver can be greatly emphasised applying it to the bearing design. An integration with a multi-objective genetic optimization process is proposed, taking as objects to be optimized both geometrical and environmental variables. Application examples are shown about an industrial Ansaldo Energia lemon bore hydrodynamic bearing: given a currently applied configuration, possible improvements are suggested. Results are presented.

scholarly journals Performance investigation of a volute porous tongue of a turbocharger turbine

2020 ◽  
Vol 40 (1) ◽  
pp. 59-66
Author(s):  
Abderrahmane Chachoua ◽  
Mohamed Kamal Hamidou ◽  
Mohammed Hamel
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Gas Turbines ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Recirculation Flow ◽  
Recirculating Flow ◽  
Show Evidence ◽  
The Right

The design for better performance of the spiral housing volute used commonly in radial and mixed inflow gas turbines is of prime importance as it affects the machine stage at both design and off design conditions. The tongue of the scroll divides the flow into two streams, and represents a severe source of disturbances, in terms of thermodynamic parameter uniformity, maximum kinetic energy, the right angle of attack to the rotor and minimum losses. Besides, the volute suffers an undesirable effect due to the recirculating mass flow rate in near bottom vicinity of the tongue. The present project is an attempt to design a tongue fitted with cylindrical holes traversing normal to the stream wise direction, where on account of the large pressure difference between the top and the bottom sides of the tongue will force the recirculating flow to go through the rotor inlet. This possibility with its limitations has not yet been explored. A numerical simulation is performed which might provide our suitable objectives. To achieve this goal the ANSYS code is used to build the geometry, generate the mesh, and to simulate the flow by solving numerically the averaged Navier Stokes equations. Apparently, the numerical results show evidence of favorable impact in using porous tongue. The realization of a contact between the main and recirculation flow by drilled holes on the tongue surface leads to a flow field uniformity, a reduction in the magnitude of the loss coefficient, and a 20 % reduction in the recirculating mass flow rate.

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.

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.

scholarly journals SPH modelling of hydrodynamic lubrication: laminar fluid flow–structure interaction with no-slip conditions for slider bearings

2020 ◽  
Author(s):  
Marco Paggi ◽  
Andrea Amicarelli ◽  
Pietro Lenarda
Keyword(s):  
Reynolds Equation ◽  
Stokes Equations ◽  
Hydrodynamic Lubrication ◽  
Flow Direction ◽  
Navier Stokes ◽  
Slider Bearing ◽  
Fluid Films ◽  
Slip Conditions ◽  
Application Fields ◽  
New Research

Abstract The FOSS CFD-SPH code SPHERA v.9.0.0 (RSE SpA) is improved to deal with “fluid–solid body” interactions under no-slip conditions and laminar regimes for the simulation of hydrodynamic lubrication. The code is herein validated in relation to a uniform slider bearing (i.e. for a constant lubricant film depth) and a linear slider bearing (i.e. for a film depth with a linear profile variation along the main flow direction). Validations refer to comparisons with analytical solutions, herein generalized to consider any Dirichlet boundary condition. Further, this study allows a first code validation of the “fluid–fixed frontier” interactions under no-slip conditions. With respect to the most state-of-the-art models (2D codes based on Reynolds’ equation for fluid films), the following distinctive features are highlighted: (1) 3D formulation on all the terms of the Navier–Stokes equations for incompressible fluids with uniform viscosity; (2) validations on both local and global quantities (pressure and velocity profiles; load-bearing capacity); (3) possibility to simulate any 3D topology. This study also shows the advantages of using a CFD-SPH code in simulating the inertia and 3D effects close to the slider edges, and it opens new research directions overcoming the limitations of the codes for hydrodynamic lubrication based on the Reynolds’ equation for fluid films. This study finally allows SPHERA to deal with hydrodynamic lubrication and improves the code for other relevant application fields involving fluid–structure interactions (e.g. transport of solid bodies by floods and earth landslides; rock landslides). SPHERA is developed and distributed on a GitHub public repository.

Numerical Analysis of Unstable Flow in Last-Stage Blades of Steam Turbines

2006 ◽  
Author(s):  
J. C. Garci´a ◽  
J. Kubiak ◽  
F. Sierra ◽  
G. Gonza´lez ◽  
G. Urquiza
Keyword(s):  
Steady State ◽  
Pressure Field ◽  
Stokes Equations ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Steam Turbines ◽  
Unstable Flow ◽  
Geometry Model ◽  
Last Stage ◽  
Exit Edge

As well known steam turbines are strongly affected because of vibrations. Unstable vibrations can appear together with steady-state vibrations. We present the results of numerical computations about unstable flow and its interaction on blades of steam turbines, which can lead to unstable modes of vibration. Unstable phenomena appear as a result of interaction of blades with the stream of steam flow where the pressure field provides the force. The analysis centers particularly in the last stage or L-0 of a 110 MW turbine. Navier-Stokes equations are resolved in two dimensions using a commercial program called Fluent based on finite-volume method. A 2-D geometry model was built in order to represent the dimensional aspects of the diaphragm as well as the rotor located in the last stage of the turbine. Periodic boundary conditions were applied to both sides of the blade with the purpose of simplifying the computation avoiding resolve for the whole wheel. The computations were conducted in both modes, steady state and time dependent. The results show the distribution of pressure fields as a function of the distance to the exit edge of the diaphragm blades. Also, the pressure and velocity fields are shown through contours along the flow channel between the diaphragm blades. The paper includes the time-dependence behavior of pressure field. A Fourier analysis is used to determine the characteristic frequencies of the system, based on numerical results.

A PRIORI PRESSURE FIELD CONSTRUCTION ITERATIVE METHOD FOR THE SOLUTION OF THE STEADY-STATE NAVIER–STOKES EQUATIONS USING GENERAL FINITE-VOLUME CO-LOCATED GRIDS

2007 ◽  
Vol 04 (04) ◽  
pp. 567-601
Author(s):  
JOSE A. LAMAS
Keyword(s):  
Iterative Method ◽  
Pressure Field ◽  
Stokes Equations ◽  
A Priori ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Navier Stokes ◽  
Pressure Equation ◽  
Navier Stokes Equations ◽  
Correction Equations

An iterative method has been developed for the solution of the Navier–Stokes equations and implemented using finite volumes with co-located variable arrangement. A pressure equation is obtained combining algebraic momentum and mass conservation equations resulting in a self-consistent set of equations. An iterative procedure solves the pressure equation consistently with mass conservation and then updates velocities based on momentum equations without introducing velocity or pressure correction equations. The process is repeated until velocities satisfy both mass and momentum conservation. Tests demonstrate a priori pressure field solution consistent with mass conservation, and solution of hydrostatic problems in one iteration.

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.

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.

scholarly journals Multi-objective aerodynamic optimization of flying-wing configuration based on adjoint method

2021 ◽  
Vol 39 (4) ◽  
pp. 753-760
Author(s):  
Xiaodong Liu ◽  
Peiliang Zhang ◽  
Guanghong He ◽  
Yongen Wang ◽  
Xudong Yang
Keyword(s):  
Optimization Design ◽  
Adjoint Method ◽  
Stokes Equations ◽  
Design Method ◽  
Adjoint Equation ◽  
Geometric Constraints ◽  
Navier Stokes ◽  
Aerodynamic Design ◽  
Aerodynamic Optimization ◽  
Multi Objective

In order to solve the multi-objective multi-constraint design in aerodynamic design of flying wing, the aerodynamic optimization design based on the adjoint method is studied. In terms of the principle of the adjoint equation, the boundary conditions and the gradient equations are derived. The Navier-Stokes equations and adjoint aerodynamic optimization design method are adopted, the optimization design of the transonic drag reduction for the two different aspect ratio of the flying wing configurations is carried out. The results of the optimization design are as follows: Under the condition of satisfying the aerodynamic and geometric constraints, the transonic shock resistance of the flying wing is weakened to a great extent, which proves that the developed method has high optimization efficiency and good optimization effect in the multi-objective multi-constraint aerodynamic design of the flying wing.

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.

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