Theory Versus Experiment for the Effects of Pressure Ratio on the Performance of an Orifice-Compensated Hybrid Bearing

1995 ◽  
Author(s):  
Phillip Mosher ◽  
Dara W. Childs
Keyword(s):  
Stokes Equations ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Pressure Ratio ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rotordynamic Coefficients ◽  
Wide Range ◽  
Bearing Load ◽  
Hybrid Bearing

Abstract This research investigates the effect of varying the concentric recess pressure ratio of hybrid (combination hydrostatic and hydrodynamic) bearings to be used in highspeed, high-pressure applications. Bearing flowrate, load capacity, torque, rotordynamic coefficients, and whirl frequency ratio are examined to determine the concentric, recess-pressure ratio which yields optimum bearing load capacity and dynamic stiffness. An analytical model, using two-dimensional bulk-flow Navier-Stokes equations and anchored by experimental test results, is used to examine bearing performance over a wide range of concentric recess pressure ratios. Typically, a concentric recess pressure ratio of 0.50 is used to obtain maximum bearing load capacity. This analysis reveals that theoretical optimum bearing performance occurs for a pressure ratio near 0.40, while experimental results indicate the optimum value to be somewhat higher than 0.45. This research demonstrates the ability to analytically investigate hybrid bearings and shows the need for more hybrid-bearing experimental data.

Theory Versus Experiment for the Effects of Pressure Ratio on the Performance of an Orifice-Compensated Hybrid Bearing

1998 ◽  
Vol 120 (4) ◽  
pp. 930-936 ◽  
Author(s):  
P. Mosher ◽  
D. W. Childs
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Pressure Ratio ◽  
Navier Stokes ◽  
Rotordynamic Coefficients ◽  
Wide Range ◽  
Bearing Load ◽  
Hybrid Bearing

This research investigates the effect of varying the concentric recess pressure ratio of hybrid (combination hydrostatic and hydrodynamic) bearings to be used in high-speed, high-pressure applications. Bearing flowrate, load capacity, torque, rotordynamic coefficients, and whirl frequency ratio are examined to determine the concentric, recess-pressure ratio which yields optimum bearing load capacity and dynamic stiffness. An analytical model, using two-dimensional bulk-flow Navier-Stokes equations and anchored by experimental test results, is used to examine bearing performance over a wide range of concentric recess pressure ratios. Typically, a concentric recess pressure ratio of 0.50 is used to obtain maximum bearing load capacity. This analysis reveals that theoretical optimum bearing performance occurs for a pressure ratio near 0.40, while experimental results indicate the optimum value to he somewhat higher than 0.45. This research demonstrates the ability to analytically investigate hybrid bearings and shows the need for more hybrid-bearing experimental data.

Entrance Effects in Annular Seal Flows

1995 ◽  
Author(s):  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Stokes Equations ◽  
Dynamic Stiffness ◽  
Turbulence Models ◽  
Radial Force ◽  
Navier Stokes ◽  
Test Case ◽  
Navier Stokes Equations ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Thin Fluid Film

Abstract The paper presents the theoretical results for a test case proposed by Staubli (1993) that allows testing the procedures for predicting rotordynamic coefficients of plain annular seals. The calculations were made using the time averaged Navier-Stokes equations. The results underline the weaknesses of the traditional turbulence models. Comparisons with a thin fluid film based procedure show that the entrance zone in the seal, where the flow is not a parallel one, influences the radial force and so the direct dynamic stiffness coefficient.

Rotordynamic Coefficients of Labseals for Turbines: Comparing CFD Results With Experimental Data on a Comb-Grooved Labyrinth

2005 ◽  
Author(s):  
Joachim Schettel ◽  
Martin Deckner ◽  
Klaus Kwanka ◽  
Bernd Lu¨neburg ◽  
Rainer Nordmann
Keyword(s):  
Stokes Equations ◽  
Labyrinth Seal ◽  
Navier Stokes ◽  
Test Rig ◽  
Navier Stokes Equations ◽  
Detailed Model ◽  
Identification Methods ◽  
Rotating Speed ◽  
Flow Models ◽  
Rotordynamic Coefficients

The main goal of this paper is to improve identification methods for rotordynamic coefficients of labseals for turbines. This aim was achieved in joint effort of the Technische Universita¨t Mu¨nchen, working on experimental identification methods for rotordynamic coefficients, the University of Technology, Darmstadt, working on prediction methods, and Siemens AG, realizing the results. The paper focuses on a short comb-grooved labyrinth seal. Short labseals, amongst others the above mentioned comb-grooved labyrinth, were examined. by means of a very accurately measuring test rig. The rotor was brought into statically eccentric positions relative to the stator, in order to measure the circumferential pressure distribution as a function of pressure, rotating speed and entrance swirl. The data collected were used to validate results obtained with a numerical method. The theoretical approach is based on a commercial CFD tool, which solves the Navier Stokes equations using numerical methods. As a result, a detailed model of the flow within the test rig is produced. The efforts of computation here are greater than when compared with the likewise wide-spread Bulk flow models, however improved accuracy and flexibility is expected. As the validation of the model is successful, it could then be used to gain further insight in the flow within the seal, and to understand the results better. This showed that rotordynamic coefficients of labseals gained from different test rigs are not necessarily comparable.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

Numerical Simulations of Onset of Volute Stall Inside a Centrifugal Compressor

2008 ◽  
Author(s):  
Hua Chen ◽  
Strong Guo ◽  
Xiao-Cheng Zhu ◽  
Zhao-Hui Du ◽  
Stone Zhao
Keyword(s):  
Centrifugal Compressor ◽  
Peak Pressure ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Pressure Rise ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Navier Stokes Equations ◽  
Mass Flow Rates ◽  
Discharge Section

In a previous publication (Guo & Chen et al., 2007), the authors solved the unsteady, 3-D Navier-Stokes equations with the k-ε turbulence model using CFX software to show that there is a volute stall coincided with the stage stall of a turbocharger centrifugal compressor operated at 423m/s tip speed and the stage stall frequency is dictated by a volute standing wave. This paper presents the flow condition at the vaneless diffuser and volute from the same simulation at various mass flow rates from stage peak efficiency to deep stage stall. Time averaged flow conditions show that (1) the influence of exducer blade passing at the volute inlet rapidly diminishes at the compressor peak pressure ratio point and the influence vanishes when the stage is in stall; (2) only at the peak pressure ratio point, circumferentially averaged, spanwise distribution of radial velocity at the volute inlet has an inflection point and the distribution meets the requirement of the Fjo̸rtoft instability theorem; (3) in the volute discharge section, the flow stalls after the stage stalls and the vortex core at the cross sectional center of the section breaks down; (4) impeller total pressure rise curve has a flat region in the middle before the stage stalls and (5) diffuser stall triggers the stage stall and drives the volute into stall.

Complex dynamics in a stratified lid-driven square cavity flow

2018 ◽  
Vol 855 ◽  
pp. 43-66 ◽  
Author(s):  
Ke Wu ◽  
Bruno D. Welfert ◽  
Juan M. Lopez
Keyword(s):  
Stokes Equations ◽  
Complex Dynamics ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Square Cavity ◽  
Navier Stokes Equations ◽  
Stable Temperature ◽  
Wide Range ◽  
Side Walls ◽  
Steady State Solutions

The dynamic response to shear of a fluid-filled square cavity with stable temperature stratification is investigated numerically. The shear is imposed by the constant translation of the top lid, and is quantified by the associated Reynolds number. The stratification, quantified by a Richardson number, is imposed by maintaining the temperature of the top lid at a higher constant temperature than that of the bottom, and the side walls are insulating. The Navier–Stokes equations under the Boussinesq approximation are solved, using a pseudospectral approximation, over a wide range of Reynolds and Richardson numbers. Particular attention is paid to the dynamical mechanisms associated with the onset of instability of steady state solutions, and to the complex and rich dynamics occurring beyond.

Analysis of Three-Lobe Bearings Having Non-Newtonian Lubricants by a Finite Element Method

1983 ◽  
Vol 7 (1) ◽  
pp. 7-11 ◽  
Author(s):  
D.V. Singh ◽  
R. Sinhasan ◽  
S.P. Tayal
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Load Capacity ◽  
Navier Stokes ◽  
Shear Strain Rate ◽  
Navier Stokes Equations ◽  
Viscosity Term ◽  
Static Performance ◽  
Iteration Technique ◽  
Element Method

Additives are extensively used in the commercial lubricants to improve their specific qualities. These lubricants are therefore non-Newtonian and their nonlinear relations between shear stress and shear strain rate are generally represented by cubic shear stress laws. The Navier-Stokes equations and the continuity equation in clindrical coordinates, representing the flow-field in the clearance space of each lobe of the three-lobe hydrodynamic journal bearings having Newtonian fluids, are solved by the finie element method using Galerkin’s technique. The solution for non-Newtonian lubricants is obtained by an iteration technique modifying the viscosity term in each iteration. The static performance characteristics have been obtained for both Newtonian and the non-Newtonian lubricants. The load capacity and friction of the bearing decrease with increase in the nonlinearity of the lubricant whereas the end flow is relatively unaffected.

Heat Transfer From a Circular Cylinder at Low Reynolds Numbers

1998 ◽  
Vol 120 (1) ◽  
pp. 72-75 ◽  
Author(s):  
V. N. Kurdyumov ◽  
E. Ferna´ndez
Keyword(s):  
Circular Cylinder ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Degree

A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

Design and Experimental Study on the Surge Performance Improvement by the Effects of Bleed Slot Casing of a Centrifugal Compressor

2014 ◽  
Author(s):  
Hong Won Kim ◽  
Jae Hoon Chung ◽  
Hyo Seong Lee ◽  
Min Ouk Choi
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Design Parameters ◽  
Navier Stokes Equations ◽  
Operating Range ◽  
Surge Margin ◽  
Commercial Code

The primary design goal of a compressor is focused on improving efficiency. Secondary objective is to widen the compressor’s operating range. This paper presents a numerical and experimental investigation of the influence of the bleed slot to enlarge operating range for the 1.2MW class centrifugal compressor installed in a turbocharger. The main design parameters of the bleed slot casing are upstream slot position, inlet pipe slope, downstream slot position and width. The DOE (design of experiment) method was carried out to optimize the casing design. Numerical analyses were done by the commercial code ANSYS-CFX based on the three dimensional Reynolds-averaged Navier-Stokes equations. From the analysis, as the downstream slot position and width are smaller and upstream position is located away from impeller inlet, efficiency and pressure ratio are increased. Experimental works were done with and without the bleed slot casing. The simulation results were in good agreement with the test data. In case without the bleed slot casing, the surge margin value came out to be only 11.8% but with the optimized bleed slot design, the surge margin reached 23%. Therefore, the surge margin increase of 11.2% was achieved.

scholarly journals Calculating Rotordynamic Coefficients of Seals by Finite-Difference Techniques

1987 ◽  
Vol 109 (3) ◽  
pp. 388-394 ◽  
Author(s):  
F. J. Dietzen ◽  
R. Nordmann
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Flow Field ◽  
Pressure Distribution ◽  
Difference Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rotordynamic Coefficients ◽  
Finite Difference Techniques

For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence model (k-ε-model) are solved by a finite-difference method. A motion of the shaft around the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotordynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs [1] and with experimental results.

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