R. Nordmann

Bio: R. Nordmann is an academic researcher from Kaiserslautern University of Technology. The author has contributed to research in topics: K-epsilon turbulence model & Finite difference method. The author has an hindex of 5, co-authored 5 publications receiving 122 citations.

Calculating Rotordynamic Coefficients of Seals by Finite-Difference Techniques

Abstract: For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence (kappa-epsilon) model are solved by a finite-difference method. A motion of the shaft round the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotor-dynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs and with experimental results.

Calculation of Rotordynamic Coefficients and Leakage for Annular Gas Seals by Means of Finite Difference Techniques

Abstract: The compressible flow in a seal can be described by the Navier-Stokes equations in connection with a turbulence model (k–e model) and an energy equation. By introducing a perturbation analysis in these differential equations we obtain zeroth order equations for the centered position and first order equations for small motions of the shaft about the centered position. These equations are solved by a finite difference technique. The zeroth order equations describe the leakage flow. Integrating the pressure solution of the first order equations yields the fluid forces and the rotordynamic coefficients, respectively.

Finite difference analysis of rotordynamic seal coefficients for an eccentric shaft position

Abstract: The dynamic coefficients of seals are calculated for shaft movements around an eccentric position. The turbulent flow is described by the Navier-Stokes equations in connection with a turbulence model. The equations are solved by a finite-difference procedure.

Rotordynamic coefficients and leakage flow of parallel grooved seals and smooth seals

Abstract: Based on Childs finite length solution for annular plain seals an extension of the bulk flow theory is derived to calculate the rotordynamic coefficients and the leakage flow of seals with parallel grooves in the stator. Hirs turbulent lubricant equations are modified to account for the different friction factors in circumferential and axial direction. Furthermore an average groove depth is introduced to consider the additional circumferential flow in the grooves. Theoretical and experimental results are compared for the smooth constant clearance seal and the corresponding seal with parallel grooves. Compared to the smooth seal the direct and cross-coupled stiffness coefficients as well as the direct damping coefficients are lower in the grooved seal configuration. Leakage is reduced by the grooving pattern.

A 3-dimensional finite-difference method for calculating the dynamic coefficients of seals

Abstract: A method to calculate the dynamic coefficients of seals with arbitrary geometry is presented. The Navier-Stokes equations are used in conjunction with the k-e turbulence model to describe the turbulent flow. These equations are solved by a full 3-dimensional finite-difference procedure instead of the normally used perturbation analysis. The time dependence of the equations is introduced by working with a coordinate system rotating with the precession frequency of the shaft. The results of this theory are compared with coefficients calculated by a perturbation analysis and with experimental results.

Rotating Machinery Vibration: From Analysis to Troubleshooting

Abstract: Part I: Primer on Rotor Vibration Vibration Concepts and Methods One-Degree-of-Freedom Model Multi-DOF Models Modes, Excitation, and Stability of Multi-DOF Models Lateral Rotor Vibration Analysis Models Simple Linear Models Formulations for RDA Software Insights into Linear LRVs Nonlinear Effects in Rotor Dynamical Systems Torsional Rotor Vibration Analysis Models Rotor-Based Spinning Reference Frames Single Uncoupled Rotor Coupled Rotors Semidefinite Systems Part II: Rotor Dynamic Analyses RDA Code for Lateral Rotor Vibration Analyses Unbalance Steady-State Response Computations Instability Self-Excited-Vibration Threshold Computations Additional Sample Problems Bearing and Seal Rotor Dynamics Liquid-Lubricated Fluid-Film Journal Bearings Experiments to Measure Dynamic Coefficients Annular Seals Rolling Contact Bearings Squeeze-Film Dampers Magnetic Bearings Compliance Surface Foil Gas Bearings Turbo-Machinery Impeller and Blade Effects Centrifugal Pumps Centrifugal Compressors High-Pressure Steam Turbines and Gas Turbines Axial Flow Compressors Part III Monitoring and Diagnostics Rotor Vibration Measurement and Acquisition Introduction to Monitoring and Diagnostics Measured Vibration Signals and Associated Sensors Vibration Data Acquisition Signal Conditioning Vibration Severity Guidelines Casing and Bearing Cap Vibration Displacement Guidelines Standards, Guidelines, and Acceptance Criteria Shaft Displacement Criteria Signal Analysis and Identification of Vibration Causes Vibration Trending and Baselines FFT Spectrum Rotor Orbit Trajectories Bode, Polar, and Spectrum Cascade Plots Wavelet Analysis Tools Chaos Analysis Tools Symptoms and Identification of Vibration Causes Part IV Trouble-Shooting Case Studies Forced Vibration and Critical Speed Case Studies HP Steam Turbine Passage through First Critical Speed HP-IP Turbine Second Critical Speed through Power Cycling Boiler Feed Pumps: Critical Speeds at Operating Speed Nuclear Feed Water Pump Cyclic Thermal Rotor Bow Power Plant Boiler Circulating Pumps Nuclear Plant Cooling Tower Circulating Pump Resonance Generator Exciter Collector Shaft Critical Speeds Self-Excited Rotor Vibration Case Studies Swirl Brakes Cure Steam Whirl in a 1300 MW Unit Bearing Unloaded by Nozzle Forces Allows Steam Whirl Misalignment Causes Oil Whip/Steam Whirl "Duet" Additional Rotor Vibration Cases and Topics Vertical Rotor Machines Vector Turning from Synchronously Modulated Rubs Air Preheater Drive Structural Resonances Aircraft Auxiliary Power Unit Commutator Vibration-Caused Uneven Wear Impact Tests for Vibration Problem Diagnoses Bearing Looseness Effects Tilting-Pad versus Fixed-Surface Journal Bearings Base-Motion Excitations from Earthquake and Shock Parametric Excitation: Nonaxisymmetric Shaft Stiffness Rotor Balancing Index

Three-Dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals

Abstract: Labyrinth seals are utilized inside turbomachinery to provide noncontacting control of internal leakage. These seals can also play an important role in determining the rotordynamic stability of the machine. Traditional labyrinth seal models are based on bulk-flow assumptions where the fluid is assumed to behave as a rigid body affected by shear stress at the interfaces. To model the labyrinth seal cavity, a single, driven vortex is assumed and relationships for the shear stress and divergence angle of the through flow jet are developed. These models, while efficient to compute, typically show poor prediction for seals with small clearances, high running speed, and high pressure.* In an effort to improve the prediction of these components, this work utilizes three-dimensional computational fluid dynamics (CFD) to model the labyrinth seal flow path by solving the Reynolds Averaged Navier Stokes equations. Unlike bulk-flow techniques, CFD makes no fundamental assumptions on geometry, shear stress at the walls, as well as internal flow structure. The method allows modeling of any arbitrarily shaped domain including stepped and interlocking labyrinths with straight or angled teeth. When only leakage prediction is required, an axisymmetric model is created. To calculate rotordynamic forces, a full 3D, eccentric model is solved. The results demonstrate improved leakage anti rotordynamic prediction over bulk-flow approaches compared to experimental measurements.

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

Abstract: 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 10) 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 (ie, the large aspect ratio AR >10 of this seal model versus the short seal configuration the bulk flow code is usually calibrated for using an empirical friction factor) [DOI: 101115/14007341]

Rotordynamic Force Prediction of Whirling Centrifugal Impeller Shroud Passages Using Computational Fluid Dynamic Techniques

Abstract: The demand for higher efficiencies and performance of modern centrifugal turbomachinery requires improved knowledge of critical design factors in strength of materials, aerodynamics, and rotordynamics. While tremendous strides in finite element stress analysis and computational fluid dynamics (CFD) have addressed the first two areas, the lack of accurate prediction tools for centrifugal impellers typically leaves rotordynamics out of the design loop. While several authors have analyzed the rotordynamic forces arising from shrouded centrifugal impellers, there has been no study to couple the secondary shroud passage with the three-dimensional primary flow model. The strong interaction between these domains makes this approach advantageous. The current study utilizes CFD techniques to analyze the full three-dimensional viscous, primary/secondary flow field in a centrifugal pump impeller to determine rotordynamic forces. Multiple quasisteady solutions of an eccentric three-dimensional model at different precessional frequency ratios yield the rotordynamic impedance forces. Performing a second order least-squares analysis generates the skew-symmetric stiffness, damping, and mass matrices. The results show good correlation with experiment for both performance and rotordynamic forces.

Prediction of Rotordynamic Coefficients for Short Labyrinth Gas Seals Using Computational Fluid Dynamics

Abstract: The analysis is presented for the computational fluid dynamics (CFD)-based modeling of short labyrinth gas seals. Seal leakage performance can be reliably predicted with CFD for a wide operating range and various sealing configurations. Prediction of seal influence on the rotordynamic stability, however, is a challenging task requiring relatively high computer processing power. A full 3D eccentric CFD model of a short staggered three-tooth-on-stator labyrinth seal is built in ANSYS CFX. An extensive grid independence study is carried out showing influence of the grid refinement on the stiffness coefficients. Three methods for the prediction of stiffness and damping coefficients as well as the effect of turbulence modeling, boundary conditions, and solver parameters are presented. The rest of the paper shows the results of a parameter variation (inlet pressure, preswirl, and shaft rotational speed) for two labyrinth seals with a tooth radial clearance of 0.5 mm and 0.27 mm, respectively. The latter was compared with experimental data in Pugachev and Deckner, 2010, textquotelefttextquoteleftAnalysis of the Experimental and CFD-Based Theoretical Methods for Studying Rotordynamic Characteristics of Labyrinth Gas Seals,textquoterighttextquoteright Proceedings of ASME Turbo Expo 2010, Paper No. GT2010-22058.