A NONHOMOGENEOUS BULK FLOW MODEL FOR GAS IN LIQUID FLOW ANNULAR SEALS: AN EFFORT TO PRODUCE ENGINEERING RESULTS

Seals in multiple phase rotordynamic pumps must operate without compromising system efficiency and stability. Both field operation and laboratory experiments show that seals supplied with a gas in liquid mixture (bubbly flow) can produce rotordynamic instability and excessive rotor vibrations. This paper advances a nonhomogeneous bulk flow model (NHBFM) for the prediction of the leakage and dynamic force coefficients of uniform clearance annular seals lubricated with gas in liquid mixtures. Compared to a homogeneous BFM (HBFM), the current model includes diffusion coefficients in the momentum transport equations and a field equation for the transport of the gas volume fraction (GVF). Published experimental leakage and dynamic force coefficients for two seals supplied with an air in oil mixture whose GVF varies from 0 (pure liquid) to 20% serve to validate the novel model as well as to benchmark it against predictions from a HBFM. The first seal withstands a large pressure drop (~ 38 bar) and the shaft speed equals 7.5 krpm. The second seal restricts a small pressure drop (1.6 bar) as the shaft turns at 3.5 krpm. The first seal is typical as a balance piston whereas the second seal is found as a neck-ring seal in an impeller. For the high pressure seal and inlet GVF = 0.1, the flow is mostly homogeneous as the maximum diffusion velocity at the seal exit plane is just ~0.1% of the liquid flow velocity. Thus, both the NHBFM and HBFM predict similar flow fields, leakage (mass flow rate) and drag torque. The difference between the predicted leakage and measurement is less than 5%. The NHBFM direct stiffness (K) agrees with the experimental results and reduces faster with inlet GVF than the HBFM K. Both direct damping (C) and cross-coupled stiffness (k) increase with inlet GVF < 0.1.Compared to the test data, the two models generally under predict C and k by ~ 25%. Both models deliver a whirl frequency ratio (fw) ~ 0.3 for the pure liquid seal, hence closely matching the test data. fw raises to ~0.35 as the GVF approaches 0.1. For the low pressure seal the flow is laminar, the experimental results and both NHBFM and HBFM predict a null direct stiffness (K). At an inlet GVF = 0.2, the NHBFM predicted added mass (M) is ~30 % below the experimental result while the HBFM predicts a null M. C and k predicted by both models are within the uncertainty of the experimental results. For operation with either a pure liquid or a mixture (GVF = 0.2), both models deliver fw = 0.5 and equal to the experimental finding. The comparisons of predictions against experimental data demonstrate the NHBFM offers a marked improvement, in particular for the direct stiffness (K). The predictions reveal the fluid flow maintains the homogeneous character known at the inlet condition.

Effect of Pad Material, Copper Vs. Steel, On the Performance of a Tilting Pad Journal Bearing: Measurements and Predictions

The paper presents measurements of performance conducted on a copper pads bearing (C-PB) and a steel-pads bearing (S-PB). Both bearings have the same geometry and differ on the pads' backing material, copper vs. steel. The journal diameter D=102 mm, and a bearing has five pads with length L=0.4D, nominal radial clearance 0.064 mm. The bearings operate at four shaft speeds ranging from 6 krpm to 14 krpm and under multiple specific loads ranging from 0.17 MPa to 2.1 MPa. At the highest load (on pad) and low speed, the S-PB static eccentricity is up to 37% higher than that for the C-PB. The oil exit temperature rise is similar for both bearings, the maximum difference reaches 6 °C. For all operating conditions, the pads' peak temperature rise, having a maximum difference of 5 °C to 16 °C, is larger for the S-PB. The S-PB produces a ~ 5% lower drag power loss than that in the C-PB. From dynamic load test results, the C-PB direct stiffness KYY (along the load direction) is up to 30% higher than the S-PB stiffness, while the difference in KXX between the C-PB and the S-PB ranges from 60% to 90%. Similar to the stiffness results, the C-PB produces larger direct damping coefficients; CYY and CXX are up to 25% and 40% larger than those for the S-PB.

Exact Dynamic Characteristic Analysis of Steel-Concrete Composite Continuous Beams

The free vibration characteristics of steel-concrete composite continuous beams (SCCCBs) are analyzed based on the Euler–Bernoulli beam theory. A modified dynamic direct stiffness method has been developed, which can be used to analyze the SCCCBs with some lumped masses and elastic boundary conditions. The results obtained by the proposed method are exact due to the elimination of approximated displacement and force fields in derivation. The proposed method is verified by comparing its results with those obtained by ANSYS software and laboratory tests. Then, the influencing factors on the reduction of natural frequency are analyzed and discussed in detail using the proposed method. The results show that stronger interfacial interaction results in higher values of natural frequency as well as larger steel subbeam and thinner concrete slab. The smaller the natural frequency of the SCCCBs is, the more significant effect the interfacial interaction on the natural frequency is. The reduction of natural frequency is not affected by the different numbers of spans but the equal single-span length and various ratios of the side span to the main span but equal total length, but it is influenced by the extra single-span length and different ratios of the side span to the main span but equal main span length. And it is only affected by bending stiffness. Furthermore, the reasonable ratio of the side span to the main span is 0.9∼1.0.

Comparing Leg Quasi-Stiffness Methods Across Running Velocities

This study investigated the differences between 5 commonly used methods to calculate leg stiffness over a range of running velocities. Thirteen male, habitually rearfoot, recreational runners ran on a force instrumented treadmill for a 5-minute running session. Each session consisted of 30-second intervals at 6 progressively faster speeds from 2.5 m·s−1 through 5.0 m·s−1 with each interval speed increasing by 0.5 m·s−1. Two-way within-factors repeated-measures analyses of variance were used to evaluate leg stiffness and length. A one-way repeated-measures analysis of variance was used to evaluate the slope of each trend line of each model across speeds. Pearson correlations were used to compare the relationship between the different computational methods. The results indicated that the direct stiffness methods increased with speed whereas the indirect stiffness methods did not. The direct methods were strongly correlated with each other as were the indirect methods. However, there were no strong correlations between the direct and indirect methods. These differences can be mostly attributed to how each individual stiffness method calculated leg length. It is important for researchers to understand these differences when conducting future studies and comparing past studies.