A CFD Study on the Dynamic Coefficients of Labyrinth Seals

Labyrinth seals are widely used in gas compressors to reduce internal leakage and increase the compressor efficiency. Due to the eccentricity between the rotating impeller and the stationary part as *well as the shaft whirling motion, forces are generated when the leakage flow passing through the cavities and the seals. For a lot of applications with high speed and pressure, these forces can drive the system unstable. Thus, predicting the forces accurately become a very important for compressor rotordynamic designs. A lot of research and studies has been done to the seals itself, including bulk flow method, computational fluid dynamic (CFD) and test measurement. The seal and leakage flow interaction forces can be predicted relatively accurate. But very few research treat the seal and cavities as one component interacting with the leakage flow and produce the forces. This paper presents results of CFD investigations on the dynamic coefficients of one typical impeller eye seal and front cavity. The CFD results show that large forces are generated in the front cavity due to circumferential uniform pressure distribution, which caused by the downstream labyrinth seal. The forces generated in the front cavity are more than in the front seal. It was found that the inertia, damping, and stiffness are proportional to average pressure. The cross-coupling stiffness increases with speed with power of 2 while the direct stiffness increases with speed with power of about 1.7.

Unsteady Flow Analysis and Vibratory Stress Predictions for a High Work Single Stage Turbine Blade

The flow field in High-Work Single-Stage (HWSS) turbines differs from traditional turbine flow fields. Operating at increased pressure ratios, wakes and trailing edge shocks at the exit of the vane are more likely to cause a vibratory response in the rotating blade. This flow field can produce increased excitation at harmonics that correspond to the vane passing frequency and harmonics higher than the vane passing frequency. In this paper, blade vibratory stresses in a HWSS gas turbine stage are predicted using unsteady pressures from two Rolls-Royce in-house flow codes that employ different phase lagged unsteady approaches. Hydra uses a harmonic storage approach, and the Vane/Blade Interaction (VBI) code uses a direct storage approach. Harmonic storage reduces memory requirements considerably. The predicted stress for four modes at two engine speeds are presented and are compared with rig test strain gauge data to assess and validate the predictive capability of the codes for forced response. Strain gauge data showed the need to consider harmonics higher than the fundamental vane passing frequency for the max power shaft speed and operating at the conditions. Because of this, it was a good case for validation and for comparing the two codes. Overall, it was found that, stress predictions using the Hydra flow code compare better with data. To the best of the authors’ knowledge, this paper is a first in comparing two different phase lagged unsteady approaches, in the context of forced response, to engine rig data for a High-Work Single Stage turbine.

Effect of Cooling Flow on the Operation of a Hot Rotor-Gas Foil Bearing System

Gas foil bearings (GFBs) operating at high temperature rely on thermal management procedures that supply needed cooling flow streams to keep the bearing and rotor from overheating. Poor thermal management not only makes systems inefficient and costly to operate but could also cause bearing seizure and premature system destruction. This paper presents comprehensive measurements of bearing temperatures and shaft dynamics conducted on a hollow rotor supported on two first generation GFBs. The hollow rotor (1.36 kg, 36.51 mm OD and 17.9 mm ID) is heated from inside to reach an outer surface temperature of 120°C. Experiments are conducted with rotor speeds to 30 krpm and with forced streams of air cooling the bearings and rotor. Air pressurization in an enclosure at the rotor mid span forces cooling air through the test GFBs. The cooling effect of the forced external flows is most distinct when the rotor is hottest and operating at the highest speed. The temperature drop per unit cooling flow rate significantly decreases as the cooling flow rate increases. Further measurements at thermal steady state conditions and at constant rotor speeds show that the cooling flows do not affect the amplitude and frequency contents of the rotor motions. Other tests while the rotor decelerates from 30 krpm to rest show that the test system (rigid-mode) critical speeds and modal damping ratio remain nearly invariant for operation with increasing rotor temperatures and with increasing cooling flow rates. Computational model predictions reproduce the test data with accuracy. The work adds to the body of knowledge on GFB performance and operation and provides empirically derived guidance for successful rotor-GFB system integration.

Crack Propagation Prediction Using Haensel Damage Model

The Haensel damage model correlates lifetime of a component until crack initiation to the dissipated and stored energy in the material during cyclic loading. The crack initiation is influenced by mean stresses. The Haensel damage model considers the mean stress effect by including compressive and tensile stresses in calculations of elastic strain energy during cyclic loading conditions. The goal of the paper is to extend the above model to predict crack propagation under large cyclic plasticity and non-proportional loading conditions. After voids initiation onset of necking, voids growth and linking takes place among them. During this process a mesocrack is created. This stage of fracture involves the same amount of released energy for new crack surface creation as dissipated energy for mesocrack initiation. The amount of dissipated and stored energy is related to the process zone size and to the number of cycles. Ilyushin’s postulate is used to calculate the amount of dissipated energy. In order to consider a contribution of tensile stresses only during loading to crack propagation, tensile/compressive split is performed for the stress tensor. One of the key drivers of this paper is to provide a straightforward engineering approach, which does not require explicit modelling of cracks. The proposed mathematical approach accounts for redistribution of stresses, strains and energy during crack propagation. This allows to approximate the observed effect of distribution of dissipated energy on the front of a crack tip. The developed approach is validated through FE (Finite Element) simulations of the Dowling and Begley experiment. The Haensel lifetime prediction of Dowling’s experiment is in good agreement with the experimental data and the explicit FE results. Finally, the proposed mathematical approach simplifies significantly the engineering effort for Nonlinear Fracture Mechanics lifetime prediction by avoiding the requirement to simulate real crack propagation using node base release methods, XFEM or remeshing procedures.

Simulation of 2-Way Fluid Structure Interaction in a 3D Model Combustor

The liner of a gas turbine combustor is a very flexible structure that is exposed to the pressure oscillations that occur in the combustor. These pressure oscillations can be of very high amplitude due to thermoacoustic instability, when the fluctuations of the rate of heat release and the acoustic pressure waves amplify each other. The liner structure is a dynamic mechanical system that vibrates at its eigenfrequencies and at the frequencies by which it is forced by the pressure oscillations to which it is exposed. On the other hand the liner vibrations force a displacement of the flue gas near the wall in the combustor. The displacement is very small but this acts like a distributed acoustic source which is proportional to the liner wall acceleration. Hence liner and combustor are a coupled elasto-acoustic system. When this is exposed to a limit cycle oscillation the liner may fail due to fatigue. In this paper the method and the results will be presented of the partitioned simulation of the coupled acousto-elastic system composed of the liner and the flue gas domain in the combustor. The partitioned simulation uses separate solvers for the flow domain and the structural domain, that operate in a coupled way. In this work 2-way fluid structure interaction is studied for the case of a model combustor for the operating conditions 40–60 kW with equivalence ratio of 0.625. This is done in the framework of the LIMOUSINE project. Computational fluid dynamics analysis is performed to obtain the thermal loading of the combustor liner and finite element analysis renders the temperature, stress distribution and deformation in the liner. The software used is ANSYS workbench V13.0 software, in which the information (pressure and displacement) is also exchanged between fluid and structural domain transiently.

A System Identification Method for Excitation-Frequency Dependent Rotordynamic Coefficients

Experimental identification of rotordynamic systems presents unique challenges. Gyroscopics, generally damped systems, and non-self-adjoint systems due to fluid structure interaction forces mean that symmetry cannot be used to reduce the number of parameters to be identified. Rotordynamic system experimental measurements are often noisy, which complicates comparisons with theory. When linearized, the resulting dynamic coefficients are also often a function of excitation frequency, as distinct from operating speed. In this paper, a frequency domain system identification technique is presented that addresses these issues for rigid-rotor test rigs. The method employs power spectral density functions and forward and backward whirl orbits to obtain the excitation frequency dependent effective stiffness and damping. The method is highly suited for use with experiments that employ active magnetic exciters that can perturb the rotor in the forward and backward whirl directions. Simulation examples are provided for excitation-frequency reduced tilting pad bearing dynamic coefficients. In the simulations, 20 and 50 percent Gaussian output noise was considered. Based on ensemble averages of the coefficient estimates, the 95 percent confidence intervals due to noise effects were within 1.2% of the identified value. The method is suitable for identification of linear dynamic coefficients for rotordynamic system components referenced to shaft motion. The method can be used to reduce the effect of noise on measurement uncertainty. The statistical framework can also be used to make decisions about experimental run times and acceptable levels of measurement uncertainty. The data obtained from such an experimental design can be used to verify component models and give rotordynamicists greater confidence in the design of turbomachinery.

Development and Validation of a Three-Dimensional Multiphase Flow CFD Analysis for Journal Bearings in Steam and Heavy Duty Gas Turbines

The traditional method for hydrodynamic journal bearing analysis usually applies the lubrication theory based on the Reynolds equation and suitable empirical modifications to cover turbulence, heat transfer, and cavitation. In cases of complex bearing geometries for steam and heavy-duty gas turbines this approach has its obvious restrictions in regard to detail flow recirculation, mixing, mass balance, and filling level phenomena. These limitations could be circumvented by applying a computational fluid dynamics (CFD) approach resting closer to the fundamental physical laws. The present contribution reports about the state of the art of such a fully three-dimensional multiphase-flow CFD approach including cavitation and air entrainment for high-speed turbo-machinery journal bearings. It has been developed and validated using experimental data. Due to the high ambient shear rates in bearings, the multiphase-flow model for journal bearings requires substantial modifications in comparison to common two-phase flow simulations. Based on experimental data, it is found, that particular cavitation phenomena are essential for the understanding of steam and heavy-duty type gas turbine journal bearings.

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

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).

Tilting Pad Journal Bearings: A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot Flexibility

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency dependent stiffness and damping. Measured hot bearing clearances are approximately 30% smaller than measured cold bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.

Strain Rate and Loading Waveform Effects on an Energy-Based Fatigue Life Prediction for AL6061-T6

The energy-based lifing method is based on the theory that the cumulative energy in all hysteresis loops of a specimens’ lifetime is equal to the energy in a monotonic tension test. Based on this theory, fatigue life can be calculated by dividing monotonic strain energy by a hysteresis energy model, which is a function of stress amplitude. Recent studies have focused on developing this method for a sine wave loading pattern — a variable strain rate. In order to remove the effects of a variable strain rate throughout the fatigue cycle, a constant strain rate triangle wave loading pattern was tested. The testing was conducted at various frequencies to evaluate the effects of multiple constant strain rates. Hysteresis loops created with sine wave loading and triangle loading were compared. The effects of variable and constant strain rate loading patterns on hysteresis loops throughout a specimens’ fatigue life are examined.