Thermohydrodynamic Models Research Articles

Effect of loaded-pad thickness on the static behaviors of five-pad hydrodynamic journal bearings

The use of tilting pad journal bearings (TPJBs) has increased in the recent past due to their stabilizing effects on the rotor bearing system. Most of the studies about steady state and dynamic behaviors of TPJBs are usually evaluated by means of thermohydrodynamic models assuming nominal dimensions for the bearing. However, machining errors could lead to actual bearing geometry and dimensions different from the nominal ones. In particular, for TPJB the asymmetry of the bearing geometry leads to unexpected behavior of the bearing. In this paper, effects of non-uniform clearance on TPJBs’ performances such as clearance profile, shaft locus, power loss, pad tilt angle, and pressure distribution are evaluated using an analytical model. The results show that effects of non-uniform clearance on static characteristics of TPJBs are considerable when evaluating the efficiency of the bearing in particular and system in general.

Kriging Approach Dedicated to Represent Hydrodynamic Bearings

Abstract The mathematical modeling of journal bearings has advanced significantly since the Reynolds equation was first proposed. Advances in the processing capacity of computers and numerical techniques led to multiphysical models that are able to describe the behavior of hydrodynamic bearings. However, many researchers prefer to apply simple models of these components in rotor-bearing analyses due to the computational effort that complex models require. Surrogate modeling techniques are statistical procedures that can be applied to represent complex models. In this work, Kriging models are formulated to substitute the thermohydrodynamic (THD) models of three different bearings found in a Francis hydropower unit, namely, a cylindrical journal (CJ) bearing, a tilting-pad journal (TPJ) bearing, and a tilting-pad thrust (TPT) bearing. The results determined by using the proposed approach reveal that Kriging models can be satisfactorily used as surrogate THD models of hydrodynamic bearings.

Thermo-elasto-hydrodynamic analysis of triangular textured mechanical face seals

A 3D thermo-elasto-hydrodynamic (TEHD) model is presented to study the effects of triangular dimples on the loadcarrying capacity, leakage and friction of a mechanical seal operated under mixed or full film lubrication conditions. The model is solved by the finite element method (FEM), which takes into account the effects of the Jakobsson-Floberg-Olsson (JFO) cavitation boundary condition, surface roughness, elastic-plastic contact, thermo-elastic deformation, and the temperature-viscosity relation. The numerical results of the TEHD model are quite different from those of the hydrodynamic (HD) and thermo-hydrodynamic (THD) models, especially at high speeds. In order to obtain the optimum shape and distribution of the triangular dimples, a comparative study is conducted to investigate different distributions of equilateral triangles and isosceles right triangles. The results show that a surface textured mechanical seal with isosceles right triangular dimples has the most significant hydrodynamic and pumping effects which, in turn, are beneficial to sealing face opening behavior and leakage limitation. The theoretical results are in good agreement with the experimental ones, and offer new guidance for the future design and development of high-speed mechanical seals for aviation piston pumps.

Evaluation of Transient Response of Turbochargers and Turbines Using Database Method for the Nonlinear Forces of Journal Bearings

The paper extents the fluid film bearing database method to arbitrary fixed bearing profiles including floating ring bearings. The method is applied to evaluate rotordynamic response of an automotive turbocharger, modeled as rigid rotor, and of a turbine-generator shaft train for power generation modeled as flexible rotor through the transient transfer matrix method. The methodology claims to render drastically faster evaluation of transient response of rotating systems with nonlinear bearings regardless the complexity of the bearing models implemented. The computational time of transient response is similar to this when short bearing expressions are used. Turbocharger rotordynamic simulation considers the use of nonlinear bearing models as mandatory, and several case studies have to be performed for the definition of key design parameters of floating ring bearings. The bearing database method offers the tool for a severe total time reduction in rotordynamic calculations, with the possibility to implement advanced thermohydrodynamic bearing models to the rotordynamic algorithm as fast as short bearing approximation formulas. Furthermore, the rotordynamic design of large turbine shaft trains is still based on linear harmonic analysis which leads to conservative designs. The database method aims to include the transient response of nonlinear rotor models as a standard procedure in the rotordynamic design of large shaft trains, which nowadays is avoided due to high time cost and complexity.

Role of electric discharges in the generation of atmospheric vortices

The existing thermohydrodynamic and hydroelectromagnetic models of tornado are considered. The potentialities of the humid atmosphere as a heat engine generating air vortices are analyzed in detail. The ability of long-term atmospheric electric discharges to form a tornado funnel and create an initial twist of up to 10–3–10–2 s–1 in it are estimated. The possible effect of a lightning discharge on the initiation and evolution of the tornado is discussed. It is shown that the electric current flowing along the lightning channel can lead to helical instability and generation of a weak primary vortex. The channel formed in the atmosphere by a lightning discharge and the vortex motion of the parent thundercloud can enhance the primary vortex and promote its transformation into a tornado. Possible mechanisms of enhancement of the primary vortex created by a lightning discharge and the possibility of its transformation into a tornado in the postdischarge stage are discussed.

Static, Dynamic, and Thermal Properties of Compressible Fluid Film Journal Bearings

Modern turbo-machinery applications, high-speed machine tools, and laboratory equipment require ever-growing rotational speeds and high degree of precision and reliability. Gas journal bearings are often employed because they meet the demands of high-speed performance, in a clean environment, and work great efficiency. A great deal of literature has concentrated on the analysis and prediction of the static and dynamic performance of gas bearings, assuming isothermal conditions. The present contribution presents a detailed mathematical modeling for nonisothermal lubrication of a compressible fluid film journal bearing, in order to identify when this type of analysis should be of concern. Load capacity, stiffness, and damping coefficients are determined by the solution of the standard Reynolds equation coupled to the energy equation. Numerical investigations show how bearing geometry, rotational speed and load influence the bearing performance. Comparisons between isothermal and thermohydrodynamic models and discrepancies are quantified for three different types of bearing geometries.

Dynamical stability of journal-bearing devices through numerical simulation of thermohydrodynamic models

This paper considers the numerical solution of a transient thermo-hydrodynamical model for a journal-bearing device is considered. The hydrodynamical model assumes that both bush and shaft are rigid bodies and it considers dynamical phenomena in the shaft-lubricant film system through a transient two-dimensional Elrod–Adams model. The proposed model also takes into account thermal effects in the lubricant film, bush and shaft. The dynamical model is solved by a combination of different techniques for spatial discretization (including finite element, finite volume and boundary element methods) and the resulting DAE-like system is integrated with implicit schemes. The developed algorithm is then applied to analyze the stability of steady solutions of the thermo-hydrodynamical model. Existing results based on analytical solutions for simplified configurations are revisited in order to extend stability predictions to more general conditions. This analysis allows to elucidate the role of different parameters on stability, including oil supply and thermal transfer conditions in finite width journal-bearing devices.

Lattice Boltzmann method with self-consistent thermo-hydrodynamic equilibria

Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria are placed within the framework of continuum kinetic theory. The mathematical treatment reveals that in order to be consistent with the correct thermo-hydrodynamical description, temperature must also be shifted, besides momentum. New perspectives for the formulation of thermo-hydrodynamic lattice kinetic models of non-ideal fluids are then envisaged. It is also shown that on the lattice, the definition of the macroscopic temperature requires the inclusion of new terms directly related to discrete effects. The theoretical treatment is tested against a controlled case with a non-ideal equation of state.

Analyse numérique du régime THD dans un patin échelon

A lack of thermohydrodynamic (THD) models adapted to discontinuous fluid film geometries can be noted in the lubrication-related literature. The finite differences method, largely used in THD analysis, cannot be easily applied to discontinuous flow domains. This article proposes two finite volumes based models, suitable for discontinuous domains. The first model, based on Reynolds generalized equation, lacks in accuracy near the discontinuity line, but gains in computing speed. The second model, based on Navier-Stokes equations, is more accurate but also significantly more demanding in terms of computing requirements. The two models are applied and compared on the simple geometry of a bi-dimensional Rayleigh step bearing. Different configurations are analyzed, allowing the validation of the Reynolds model for most of the cases encountered in fluid film lubrication.

Turbulent thermohydrodynamic lubrication models compared with measurements

The authors derived a three-dimensional turbulent thermohydrodynamic lubrication (THL) model (model A), based on the isothermal turbulent lubrication model developed in 1971 by Aoki and Harada. The Aoki-Harada theory is characterized by its modified definition of mixing length which enables its velocity profile in the lubricating oil film to agree very well with measurements not only in the log region (full turbulent layer) but also in the viscous sublayer and the buffer layer. On the other hand, Taniguchi et al. derived a three-dimensional turbulent THL model (model B), based on the isothermal turbulent lubrication model developed in 1965 by Ng and Pan, and Mikami et al. derived a two-dimensional turbulent THL model (model C), based on the Aoki-Harada model. The present authors coded and used these three different turbulent THL models to predict the static performance of a four-pad tilting pad journal bearing of a real size and to compare the predictions with measurements. The theoretical results given by model A were found to be in better agreement with measurements obtained in a test rig of the bearing, compared with those given by models B and C.

Experiments on thermal effects in a hydrodynamic thrust bearing

The objective of this work is to analyse the characteristics of a fixed-geometry thrust bearing in typical operating conditions and to give experimental results in order to validate future thermohydrodynamic models. The influence of the applied load, the rotational speed and the feeding temperature on the thrust bearing performance is presented and discussed.

Simple Models for Turbulent Self‐Regulation in Galaxy Disks

We propose that turbulent heating, wave pressure and gas exchanges between different regions of disks play a dominant role in determining the preferred, quasi-equilibrium, self-similar states of gas disks on large-scales. We present simple families of analytic, thermohydrodynamic models for these global states, which include terms for turbulent pressure and Reynolds stresses. Star formation rates, phase balances, and hydrodynamic forces are all tightly coupled and balanced. The models have stratified radial flows, with the cold gas slowly flowing inward in the midplane of the disk, and with the warm/hot phases that surround the midplane flowing outward. The models suggest a number of results that are in accord with observation, as well as some novel predictions, including the following. 1) The large-scale gas density and thermal phase distributions in galaxy disks can be explained as the result of turbulent heating and spatial couplings. 2) The turbulent pressures and stresses that drive radial outflows in the warm gas also allow a reduced circular velocity there. This effect was observed by Swaters, Sancisi and van der Hulst in NGC 891, a particularly turbulent edge-on disk. The models predict that the effect should be universal in such disks. 3) They suggest that a star formation rate like the phenomenological Schmidt Law is the natural result of global thermohydrodynamical balance, and may not obtain in disks far from equilibrium. (Abridged)

Thermoélastohydrodynamique des paliers à patins oscillants en régime transitoire

The aim of this work is to study the thermal effects of tilting-pad journal bearings during start-up. A four-shoe tilting-pad journal bearing is tested on an original device. Two theoretical approaches permit us to take into account the heat flux generated by viscous dissipation, the transient heat transfer and the viscosity variation across the film thickness: these are the thermohydrodynamic (THD) and thermoelastohydrodynamic (TEHD) models. The relevance of thermoelastic deformations is emphasized by a comparison with theoretical THD and TEHD results: a decrease in radial bearing clearance is observed. The minimum transient period is about 1 or 2 min. A very good agreement between theoretical predictions and experimental data is obtained when both the solid deformations and heat transfer in the bearing elements are considered.

Thermohydrodynamic models of the interaction of pulse-periodic radiation with matter

Experimental and theoretical investigations were made of the processes of drilling and deep melting of metals by pulsed and pulse-periodic laser radiation. Direct photography of the surface revealed molten metal splashing due to interaction with single CO2 laser pulses. A proposed thermohydrodynamic model was used to account for the experimental results and to calculate the optimal parameters of pulse-periodic radiation needed for deep melting. The melt splashing processes were simulated numerically.

Assessment of Core Thermo-Hydrodynamic Models of REFLA-1D Code with CCTF Data for Reflood Phase of PWR-LOCA

The REFLA-1D is a computer code for the one-dimensional best-estimate analysis of the thermo-hydrodynamic behavior during the reflood phase of a PWR-LOCA. The core thermo-hydrodynamic models of the code were developed using the experimental data of the small scale facilities, whose scaling ratios to a 1,000MWe class PWR are 1/2,500 and 1/370. In order to assess these models with a large scale reflood experiment data, REFLA-1D calculation were performed for the CCTF tests. The CCTF is a 1/21-scaled large scale reflood test facility with four primary loops. The height of each section of the CCTF is almost the same as that of a 1,000MWe class PWR and the radial dimension is scaled down by 1/4.6. The calculated CCTF tests simulated the reflooding behavior during a PWR-LOCA under 200% cold leg large break conditions. The calculated results indicate that the turnaround temperature and the quench time at the midplane level of the average power rod are predicted within 10% difference from the test data under various conditions. It is also shown that the transients of the rod surface temperature are predicted well qualitatively with REFLA-1D code.

Assessment of core thermo-hydrodynamic models of REFLA-1D code with CCTF data for reflood phase of PWR-LOCA.

The REFLA-1D is a computer code for the one-dimensional best-estimate analysis of the thermo-hydrodynamic behavior during the reflood phase of a PWR-LOCA. The core thermo-hydrodynamic models of the code were developed using the experimental data of the small scale facilities, whose scaling ratios to a 1,000MWe class PWR are 1/2,500 and 1/370. In order to assess these models with a large scale reflood experiment data, REFLA-1D calculation were performed for the CCTF tests. The CCTF is a 1/21-scaled large scale reflood test facility with four primary loops. The height of each section of the CCTF is almost the same as that of a 1,000MWe class PWR and the radial dimension is scaled down by 1/4.6. The calculated CCTF tests simulated the reflooding behavior during a PWR-LOCA under 200% cold leg large break conditions. The calculated results indicate that the turnaround temperature and the quench time at the midplane level of the average power rod are predicted within 10% difference from the test data under vari...