Numerical Modeling of Fluid-Induced Rotordynamic Forces in Seals With Large Aspect Ratio

2012 ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Costin D. Untaroiu ◽  
Houston G. Wood ◽  
Paul E. Allaire
Keyword(s):  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Dynamic Properties ◽  
Bulk Flow ◽  
Large Aspect Ratio ◽  
Flow Method ◽  
Dynamic Coefficients ◽  
Aspect Ratios

Traditional annular seal models are based on bulk flow theory. While these methods are computationally efficient and can predict dynamic properties fairly well for short seals, they lack accuracy in cases of seals with complex geometry or with large aspect ratios (above 1.0). In this paper, the linearized rotordynamic coefficients for a seal with large aspect ratio are calculated by means of a three dimensional CFD analysis performed to predict the fluid-induced forces acting on the rotor. For comparison, the dynamic coefficients were also calculated using two other codes: one developed on the bulk flow method and one based on finite difference method. These two sets of dynamic coefficients were compared with those obtained from CFD. Results show a reasonable correlation for the direct stiffness estimates, with largest value predicted by CFD. In terms of cross-coupled stiffness, which is known to be directly related to cross-coupled forces that contribute to rotor instability, the CFD predicts also the highest value; however a much larger discrepancy can be observed for this term (73% higher than value predicted by finite difference method and 79% higher than bulk flow code prediction). Similar large differences in predictions one can see in the estimates for damping and direct mass coefficients, where highest values are predicted by the bulk flow method. These large variations in damping and mass coefficients, and most importantly the large difference in the cross-coupled stiffness predictions, may be attributed to the large difference in seal geometry (i.e. the large aspect ratio AR>1.0 of this seal model vs. the short seal configuration the bulk flow code is usually calibrated for, using an empirical friction factor).

Numerical Modeling of Fluid-Induced Rotordynamic Forces in Seals With Large Aspect Ratios

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Costin D. Untaroiu ◽  
Houston G. Wood ◽  
Paul E. Allaire
Keyword(s):  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Dynamic Properties ◽  
Bulk Flow ◽  
Large Aspect Ratio ◽  
Flow Method ◽  
Dynamic Coefficients ◽  
Aspect Ratios

Traditional annular seal models are based on bulk flow theory. While these methods are computationally efficient and can predict dynamic properties fairly well for short seals, they lack accuracy in cases of seals with complex geometry or with large aspect ratios (above 1.0). In this paper, the linearized rotordynamic coefficients for a seal with a large aspect ratio are calculated by means of a three-dimensional CFD analysis performed to predict the fluid-induced forces acting on the rotor. For comparison, the dynamic coefficients were also calculated using two other codes: one developed on the bulk flow method and one based on finite difference method. These two sets of dynamic coefficients were compared with those obtained from CFD. Results show a reasonable correlation for the direct stiffness estimates, with largest value predicted by CFD. In terms of cross-coupled stiffness, which is known to be directly related to cross-coupled forces that contribute to rotor instability, the CFD also predicts the highest value; however, a much larger discrepancy can be observed for this term (73% higher than the value predicted by the finite difference method and 79% higher than the bulk flow code prediction). One can see similar large differences in predictions in the estimates for damping and direct mass coefficients, where the highest values are predicted by the bulk flow method. These large variations in damping and mass coefficients, and most importantly the large difference in the cross-coupled stiffness predictions, may be attributed to the large difference in seal geometry (i.e., the large aspect ratio AR > 1.0 of this seal model versus the short seal configuration the bulk flow code is usually calibrated for using an empirical friction factor).

Fluid-Induced Forces in Pump Liquid Seals With Large Aspect Ratio

2011 ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Vahe Hayrapetian ◽  
Costin D. Untaroiu ◽  
Paul E. Allaire ◽  
Houston G. Wood ◽  
...  
Keyword(s):  
Shear Stress ◽  
Fluid Flow ◽  
Aspect Ratio ◽  
Stokes Equations ◽  
Complex Geometry ◽  
Dynamic Properties ◽  
Fluid Velocity ◽  
Bulk Flow ◽  
Large Aspect Ratio ◽  
Aspect Ratios

The instability due to fluid flow in seals is a known phenomenon that can occur in pumps and compressors as well as in steam turbines. Traditional annular seal models are based on bulk flow theory. While these methods are computationally efficient and can predict dynamic properties fairly well for short seals, they lack accuracy in cases of seals with complex geometry or with large aspect ratios (above 1.0). Unlike the bulk flow models, computational fluid dynamics (CFD) makes no simplifying assumption on the seal geometry, shear stress at the wall, relationship between wall shear stress and mean fluid velocity, or characterization of interfaces between control volumes through empirical friction factors. This paper presents a method to calculate the linearized rotor-dynamic coefficients for a liquid seal with large aspect ratio (balance drum) subjected to incompressible turbulent flow by means of a three dimensional CFD analysis to calculate the fluid-induced forces acting on the rotor. The Reynolds-averaged Navier-Stokes equations for fluid flow are solved by dividing the volume of fluid into a discrete number of points at which unknown variables are computed. As a result, all the details of the flow field, including the fluid forces with potential destabilizing effects, are calculated. A 2nd order curve fit is then used to express the fluid-induced forces in terms of equivalent linearized stiffness, damping, and fluid inertia coefficients.

DYNAMIC CRACK PROPAGATION IN FIVE-FOLD SYMMETRY QUASICRYSTALS

2009 ◽  
Vol 23 (12) ◽  
pp. 1509-1518
Author(s):  
ZHI-HUA YIN ◽  
TIAN-YOU FAN ◽  
AI-YU ZHU
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Crack Propagation ◽  
Difference Method ◽  
Coupling Effect ◽  
Dynamic Properties ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Point Groups ◽  
The Finite Difference Method

Based on the elasto-/hydro-dynamic model the dynamic properties of the five-fold symmetry quasicrystals with point groups 5, [Formula: see text] are investigated, by using the finite difference method. The problems including dynamic initiation of crack growth and fast crack propagation of this material are studied. The results show that the phonon–phason coupling effect plays an important role to the dynamic properties of the quasicrystals.

On the Dynamic Properties of Pump Liquid Seals

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Vahe Hayrapetian ◽  
Costin D. Untaroiu ◽  
Houston G. Wood ◽  
Bruno Schiavello ◽  
...  
Keyword(s):  
Complex Geometry ◽  
Dynamic Properties ◽  
Bulk Flow ◽  
Damping Factor ◽  
Steam Turbines ◽  
Fluid Inertia ◽  
Flow Equations ◽  
Dynamic Coefficients ◽  
Aspect Ratios ◽  
Rotor Dynamic

Rotordynamic instability due to fluid flow in seals is a well known phenomenon that can occur in pumps as well as in steam turbines and air compressors. While analysis methods using bulk-flow equations are computationally efficient and can predict dynamic properties fairly well for short seals, they often lack accuracy in cases of seals with complex geometry or with large aspect ratios (L/D above 1.0). This paper presents the linearized rotordynamic coefficients for a liquid seal with large aspect ratio subjected to incompressible turbulent flow. The fluid-induced forces acting on the rotor are calculated by means of a three-dimensional computational fluid dynamics (3D-CFD) analysis, and are then expressed in terms of equivalent linearized stiffness, damping, and fluid inertia coefficients. For comparison, the seal dynamic coefficients were calculated using two other codes: one developed with the bulk flow method and one based on the finite difference method. The three sets of dynamic coefficients calculated in this study were used then to predict the rotor dynamic behavior of an industrial pump. These estimations were then compared to the vibration characteristic measured during the pump shop test, results indicating that the closest agreement was achieved utilizing the CFD generated coefficients. The results of rotor dynamic analysis using the coefficients derived from CFD approach, improved the prediction of both damped natural frequency and damping factor for the first mode, showing substantially smaller damping factor which is consistent with the experimentally observed instability of the rotor-bearing system. As result of continuously increasing computational power, it is believed that the CFD approach for calculating fluid excitation forces will become the standard in industry.

Natural convection inside a C-shaped nanofluid-filled enclosure with localized heat sources

2014 ◽  
Vol 24 (8) ◽  
pp. 1954-1978 ◽  
Author(s):  
M.A. Mansour ◽  
M.A. Bakeir ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Volume Fraction ◽  
Cu Nanoparticles ◽  
Content Type ◽  
The Finite Difference Method

Purpose – The purpose of this paper is to investigate natural convection fluid flow and heat transfer inside C-shaped enclosures filled with Cu-Water nanofluid numerically using the finite difference method. Design/methodology/approach – In this investigation, the finite difference method is employed to solve the governing equations with the boundary conditions. Central difference quotients were used to approximate the second derivatives in both the X and Y directions. Then, the obtained discretized equations are solved using a Gauss-Seidel iteration technique. Findings – It was found from the obtained results that the mean Nusselt number increased with increase in Rayleigh number and volume fraction of Cu nanoparticles regardless aspect ratio of the enclosure. Moreover the obtained results showed that the rate of heat transfer increased with decreasing the aspect ratio of the cavity. Also, it was found that the rate of heat transfer increased with increase in nanoparticles volume fraction. Also at low Rayleigh numbers, the effect of Cu nanoparticles on enhancement of heat transfer for narrow enclosures was more than that for wide enclosures. Originality/value – This paper is relatively original for considering C-shaped cavity with nanofluids.

Effect of Turbulence and Offset Loading on the Performance of a Single Pad Externally Adjustable Fluid Film Bearing

2012 ◽  
Author(s):  
B. Satish Shenoy ◽  
Rammohan S. Pai B. ◽  
Raghuvir Pai B. ◽  
Shrikanth Rao D.
Keyword(s):  
Steady State ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Fluid Film ◽  
Wide Range ◽  
Steady State Performance

Paper deals with the effect of turbulence on steady state performance characteristics of an eccentrically loaded 120° single pad externally adjustable fluid film bearing. The bearing has an aspect ratio of one and operates over a wide range of eccentricity ratios and adjustments. Two load-offset positions (β/χ) of 0.45 and 0.55 are considered in the present analysis. Reynolds equation incorporated with the Linearized turbulence model of Ng and Pan is solved numerically using finite difference method. A comparative study predicts that, load capacity of a bearing operating with β/χ = 0.55 and Re = 16000 is superior for negative radial and tilt adjustment configuration of the pad.

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