Thermohydrodynamic Model Research Articles

Study of the sealing performance of a high-speed deep groove mechanical seal thermodynamic lubrication model

PurposeThe purpose of this study is to investigate the sealing performance of different deep groove mechanical seals by considering the changing law of dynamic pressure effect and temperature gradient caused by high speed and high pressure.Design/methodology/approachA thermohydrodynamic lubrication model (THD) of the mechanical seal was constructed and solved using the commercial software FLUENT. The pressure and temperature distributions of the fluid under different groove types, as well as the sealing performance under different pressures, rotational speeds and sealing gaps, are obtained.FindingsThe annular groove (AG) can effectively reduce the temperature, and the T-type spiral groove (STG) can effectively inhibit the leakage. The increase of pressure and rotational speed leads to the enhancement of dynamic pressure effect and the increase of leakage, while the sealing gap increases and the leakage increases while taking away more heat. The choice of groove type is very important to the impact of sealing performance.Originality/valueIn consideration of the beneficial effect of deep grooves on cooling performance, the viscous temperature equation and the impact of the thermodynamic lubrication model are evaluated in conjunction with the sealing performance of four distinct groove types. This approach provides a theoretical basis for the optimal design of mechanical seals.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2024-0184/

Study on rotor-bearing dynamic performance of a novel motorized spindle supported by water-lubricated hydrodynamic spiral grooved bearings

The water-lubricated hydrodynamic spiral grooved bearings have been utilized to support the high-speed motorized spindle. However, the viscous damping effect of water is much weaker than that of the oil, so the dynamic behavior and the stability of the motorized spindle with the water-lubricated spiral grooved bearings need to be studied thoroughly. This paper established an improved rotor-bearing dynamic model for the motorized spindle by incorporating both the distributed effect of journal bearing and the tilting effect of thrust bearing into a turbulent thermohydrodynamic lubrication model. An experimental setup for the motorized spindle was developed to measure the spindle dynamic behaviors and verify the established dynamic model. The critical speeds, the transient dynamics and the stability of the motorized spindle are studied theoretically and experimentally. The results show that the motorized spindle with the water-lubricated spiral grooved bearings can operate at high speeds with a satisfactory supporting stiffness and exhibits an excellent operational stability.

Phase transformation and powder densification behavior of the polyamide-12 during powder bed fusion process

The phase transformation and densification behaviors are two critical research topics in the semi-crystalline polymer Laser Powder Bed Fusion (L-PBF) process. This study first introduces a thermal model incorporating crystallization kinetics to study the temperature evolution and phase transformation behavior during the L-PBF of polyamide-12 (PA12). The model highlights the delayed solidification behavior represented by the overall degree of crystallization compared with the temperature evolution during the cooling stage. A thermo-hydrodynamic model is then developed based on the thermal model to predict densification behavior and investigate the contraction under various processing conditions, incorporating powder densification kinetics. Numerical studies reveal that the contraction of the melt pool lags behind the movement of the laser beam significantly because the densification is not a transient but a continuing process accompanied by the fusion phase transformation. The model is validated by comparing the melt pool contraction obtained by experimental measurement and numerical simulation on single-track sintering. The reasonable thermal interaction during multiple-track simulations is proven to improve the final density noticeably. Finally, a two-laser scanning strategy is proposed to enhance the density of polymer L-PBF components.

Thermal stratification characteristics and cooling water shortage risks for pumped storage reservoir–green data centers under extreme climates

Utilizing the thermal stratification of reservoirs to obtain cold water for cooling green data centers (GDCs) is a new mode of energy conservation and emission reduction. However, global warming is expected to alter this phenomenon in deep reservoirs and thus may affect the digitalization process. While the frequency and intensity of extreme climate (EC) events are increasing under a changing climate, the impacts of these highly destructive events on thermal stratification and the related cascading effects on GDC cold-water supplies are still unclear. A two-lateral-dimensional thermohydrodynamic model was established to determine the characteristics of reservoir thermal stratification changes and its potential water environment impacts based on the heat extreme experienced by the Jinshuitan Reservoir, a large, pumped storage power station (PSPS) with a GDC in southeastern China. Fourteen different PSPS inlet/outlet schemes under 2 climate scenarios were designed, and two new indexes, namely, the risk index of cold-water shortage and the index of thermal stratification, were proposed to explore the impact of extreme climates on GDC water extraction. The results showed that compared to the present climate conditions, the reservoir experienced stronger thermal stratification with a 20.6 % average increase in thermal stability, a longer thermal stratification duration with a transitional trend from seasonal to permanent stratification, and a thinner cold-water layer with a 15-m average decrease. Changes in the thermal stratification of reservoirs under EC conditions will benefit some species, such as diatoms (except for early July and the period from mid-August to early October), green algae and cyanobacteria and the migration of warm-water fish, but adversely impact dissolved oxygen, diatoms and cold-water fish. Furthermore, the risk of cold-water shortages under EC conditions was consistently greater than that under average climate (AC) conditions (traditional assessment) when the elevation of pumped storage intake/outlet was less than 145 m. According to the traditional assessment method, the intake/outlet elevation of pumped storage reservoirs resulted in a 60.27 % increase in the risk of cold-water shortages during climate extremes. Furthermore, the demand for green cold-water withdrawal and optimal pumped storage power generation benefits were met when the PSPS intake/outlet elevation was 145 m. Beyond solving this specific case, this study elucidates the importance of linking the thermal stratification and data center of cold-water withdrawal to ECs. These findings provide new insights for increasing climate change resilience.

Thermo-hydrodynamic lubrication and energy dissipation mechanism of a pump-turbine thrust bearing in load-rejection process

The dynamic behavior of the pump-turbine thrust bearing is important to the safety operation of the unit. This paper analyzed the lubrication and energy dissipation mechanism of pump-turbine thrust bearing during load-rejection based on the thermo-hydrodynamic model. The results show that the variation of the axial force and the maximum pad surface pressure is basically consistent with that of the inclination of the pad surface. The change of the friction loss is consistent with the change of rotational speed, while the change of pad surface temperature is affected by the combination of pad inclination and rotational speed. The chaotic flow in the oil tank is accompanied by different forms of vortices, such as Taylor vortices, vortex pairs, and Karman vortices, and results in a significant asymmetry in the pressure distribution. The flow in the bearing pad groove has an effect on the energy dissipation in the oil film. This paper provides a theoretical basis for the design and optimization of thrust bearings, and provides a reference for solving the problems of wear, oil mist, and other related problems of thrust bearings in engineering.

DETERMINATION OF A TORSIONAL VIBRATION VISCOUS DAMPER’S OPERATING TEMPERATURE USING A NEW THERMOHYDRODYNAMIC MODEL

This article presents an innovative algorithm and mathematical model of a torsional vibration viscous damper. The problem of torsional vibrations damping in a multicylinder internal combustion engine is extremely important for the reliable operation of a drive unit. The effective reduction of the vibration amplitude extends the service life and prevents failures that generate logistic and transport problems. One of the key parameters used to assess the quality of vibration damper operation is the temperature. This criterion is so important that it is the main indicator for the possible replacement of dampers installed in trucks, locomotives, and ships. Despite the importance of this parameter, the literature lacks mathematical models that describe the thermodynamics of damper operation. Therefore, the authors of this paper developed and presented an innovative thermohydrodynamic model of a torsional vibrations viscous damper, which was used to determine the operating parameters.

The effects of bubble evolution and oil shear thinning on the static behavior of bubbly oil lubricated bearing

Bubble evolution and shear thinning effect are main factors affecting lubrication behavior of bubbly oil. In this study, a thermohydrodynamic lubrication model for the bubbly oil considering the bubble evolution and the shear thinning effect was established based on the multiphase mixtures theory. The influence of bubble evolution and shear thinning effect on the static behavior of bubbly oil lubricated bearing was analyzed, and an experimental study was conducted to verify the model. The result shows that the bubble radius is mainly dependent on the liquid pressure; the bearing static behavior is affected by the bubble evolution through the interface effect; the shear thinning effect of the pure oil can be enhanced with regarding the bubble evolution effect.

Thermohydrodynamic Analysis of a Controllable Stiffness Foil Bearing With Shape Memory Alloy Springs: Experimental Tests and Theoretical Predictions

Abstract Shape memory alloy (SMA)-gas foil bearings (SMA-GFBs) are novel gas bearings comprising top foil, SMA springs, and housing. The radial clearance, stiffness, and damping coefficients of SMA-GFBs can be regulated by the bearing temperature which is determined by the electric heating of SMA springs and the cooling flow. A 3D thermohydrodynamic model (THD) considering the conduction and convection of the top foil, bearing housing, and hollow rotor, and the heat energy of heated SMA springs is presented to simulate the temperature distribution of SMA-GFBs at different rotational speeds, heating powers, and cooling flows. Centrifugal growth of the rotor and thermal expansions of the rotor, SMA springs, and bearing housing are also considered. A test rig is built to measure the bearing temperature and to validate the effectiveness of the theoretical model and circumferential cooling mode. Parametric studies are conducted with different speeds, heating powers, and cooling flows. The heat transfer ratios of the rotor and substructure are also compared. Compared to the temperature differences of the bearing temperature in the circumferential or axial directions, the effects of rotational speed and cooling flow on the bearing temperature are more apparent. The phase transition process of SMA spring can be controlled by adjusting the rotor speed and the cooling flow reasonably, and then the temperature characteristics of SMA-GFB can be changed. The temperature depending on the compressed gas film and heated SMA springs and cooling flow can be adjusted to confirm the feasibility of actively altering the performance of the bearing-rotor system.

Machine Learning-Based Optimizer for Tilting Pad Journal Bearing Inlet Flowrate

Abstract In view of the green economy and energy transition, the reduction of the environmental impact of the power generation sector plays a key role. Fluid film bearings are the most common bearing for industrial turbomachinery and new design requirements have a direct impact on bearings operation. In fact, to achieve higher levels of efficiency, bearings must support higher specific loads and higher peripheral speeds. Furthermore, there is great interest in reducing the oil flowrate required for the bearing operation as much as possible. In this work, an optimization strategy for reducing the flowrate fed to tilting pad journal bearings (TPJBs) is proposed. An artificial neural network (ANN) is trained to estimate the static and dynamic performance of the bearings. The training dataset is built with a Reynolds-based thermo-hydrodynamic model. The trained ANN is then used in a constrained optimization that has the goal of minimizing the oil flowrate while ensuring safe bearing operation. Predictions are compared with experimental data from compressor mechanical running tests. The proposed model is an effective tool that can help industry achieve the goals required by the energy transition and can help in the development of optimized fluid film bearings.

METHOD OF CREATION AND ADAPTATION THERMOHYDRODYNAMIC MODELS OF DEVELOPMENT TURONIAN GAS DEPOSITS BASED ON HYDRODYNAMIC MODELS OF ISOTHERMAL FILTRATION FOR PREDICTION THERMOBARIC CONDITIONS OF HYDROCARBON RAW MATERIALS DURING THEIR DEVELOPMENT

The current high rates of exploration and involvement in thedevelopment of hard-to-recover natural gas reserves associated with theTuronian deposits require an increase in the level of digitalization ofdevelopment, including the development of means to ensure integratedintegrated design and forecasting of development processes. The articledescribes the developed methodology for the creation and adaptation ofthermohydrodynamic models for the development of Turonian gasdeposits based on hydrodynamic models of isothermal filtration to predictthe thermobaric conditions of hydrocarbon raw materials duringtheir development. The main advantages of the thermohydrodynamicmodel include the ability to use it to solve applied and practical tasks forthe design of development and monitoring of its implementation. Inparticular, it is possible to assess the impact of the hydrate formationprocess on changes in the productivity of producing wells, develop proposalsfor optimizing the applied methods of gas-dynamic studies andinterpreting data taking into account the risk of hydrate precipitation inunacceptable operating modes, justify the maximum and maximumdepressions during the entire development period for existing and projectwells to control the thermobaric conditions of hydrate formation andprevent the formation of hydrates in well completion system. Taking intoaccount the urgency of the issue of import substitution, the developedmethodology was implemented and tested using the domestic tNavigatorhydrodynamic simulator. The stage of analysis of initial data (fluid data,core research data, geological and field data on wells) is described, thebasic concepts of thermohydrodynamic modeling of development (thermalconductivity, Fourier law, enthalpy, internal energy, entropy, Joule-Thomson effect) are given, the stage of integration of the thermal optioninto the isothermal filtration model is described, approaches are presentedto adapt the thermohydrodynamic model to the actual geologicaland field data, the evaluation and analysis of the results obtained werecarried out.

A numerical model with nonuniform grids for the analysis of dynamic characteristics of scratched tilting-pad bearings

PurposeThe purpose of this study is to present a numerical model for scratched tilting-pad bearings (STPBs) with nonuniform grids. In addition, the model is used to reveal the effects of the structural parameters of bearings on the dynamic characteristics of STPBs under impact loading.Design/methodology/approachBy combining the Reynolds equation, the flow balance equation and the assumption of adiabatic bearings and shafts, a thermo-hydrodynamic model with nonuniform grids of scratched journal bearings was built. Describing the motion of the shaft using the Euler method and introducing the pad-tilting-angle modification equation, a dynamic model of STPBs was established.FindingsThe occurrence of scratches in tilting-pad bearings yields great sensitivity to impact loading. Less width-to-diameter ratio and larger clearance ratio reduce the minimum film thickness and enlarge the maximum film pressure, which may lead to bearing collision or abrasion. Moreover, STPBs with larger clearance ratios take longer to recover from impact loading.Originality/valueThis work is original and a valuable reference for the analysis of the dynamic characteristics of STPBs. The effects of other factors on the dynamic characteristics of STPBs can be further investigated based on this model.

Artificial neural network for tilting pad journal bearing characterization

Tilting pad journal bearings (TPJBs) are modeled with Reynold-based models or computational fluid dynamics (CFD) approach. In both cases, the estimation of the dynamic coefficients of the oil-film forces and the static characteristic, can be computationally expensive and time consuming. Artificial Intelligence (AI) is assuming a key role in engineering but is rarely applied in fluid film bearing analysis. A properly trained Deep Learning (DL) model can perform very fast predictions of TPJB behavior with accuracy comparable to more time-consuming models. In this case, the main drawback is the time required to build the training dataset. In this work, an Artificial Neural Network (ANN) is trained to predict the dynamic stiffness and damping coefficients along with the main static quantities of TPJBs, such as minimum oil-film thickness and inlet flowrate. At first, a design of experiment is performed to build an appropriate training dataset. Secondly, a Reynolds-based thermo-hydrodynamic (THD) model is used to populate the training dataset and an appropriate test dataset. Then, a feed-forward ANN is trained with Levenberg–Marquardt backpropagation and its architecture is optimized to increase accuracy. Finally, the accuracy of the ANN is tested using the test dataset and experimental data. The time and computational effort required by the ANN regression are much less than those required by the THD model. Therefore, the trained ANN is an effective and efficient tool for the characterization of TPJBs.

Dynamic Behavior of a Tilting-Pad Thrust Bearing Operating Under a Hybrid Lubrication Regime

Abstract The present contribution aims to evaluate the effects of the oil pressure injection on the dynamic behavior of a hybrid-lubricated tilting-pad thrust bearing. First, a thermohydrodynamic model is applied to determine the equilibrium position as dictated by pressure and temperature distributions resulting from both hydrodynamic and hybrid lubrication regimes. Subsequently, the perturbation and frequency reduction methods are applied to determine the stiffness and damping coefficients of the bearing for various operational conditions. The results show that the dynamic force coefficients are strongly dependent on the operational conditions of the bearing, such as static load and rotating speed, as well as the perturbation frequency, for both lubrication regimes. The quantification of the injection pressure influence on the force coefficients of hybrid-lubricated thrust bearings is the main original contribution of this work.

A Mixed Lubrication Deterministic Model of an Elastic Support Water-Lubricated Tilting Pad Thrust Bearing

In order to study the effect of surface roughness on lubrication performance of an elastic support water-lubricated tilting pad thrust bearing, a mixed lubrication (ML) deterministic model is hereby presented based on a unified Reynolds equation model. This very model incorporates the elastic–plastic deformation of asperities and polymer matrix of the thrust pad, as well as the elastic deformation of the rubber support. The randomly distributed surface roughness of the thrust pad is generated by a mathematical model and shares the same distribution characteristics as the measured surface roughness. The Greenwood and Williamson asperity contact model and thin plate deformation model are combined to solve the asperities contact stress and deformation. Meanwhile, the bearing ML performance is compared with the results calculated by a thermohydrodynamic (THD) lubrication model and a thermo-elasto-hydrodynamic (TEHD) lubrication model, while the film thickness is also compared with measurements. The results show that the water film thickness calculated by the ML model is smaller than that by the THD model and the TEHD model, but the water film temperature is higher. The roughness has a great influence on the contact area ratio and the lubrication state, but little effect on the average film thickness. A higher roughness indicates a higher rotational speed required for the bearing to achieve full hydrodynamic lubrication. The film thickness calculated by the mixed lubrication model is closer to the measured results. Overall, it is proved that the mixed lubrication model can more accurately predict the lubrication performance of bearings. Compared to the thin plate deformation model, the elastic deformation simulation based on the half-infinite space model severely overestimates the elastic deformation of the pad surface, making it unsuitable for calculating the elastic deformation of the polymer matrix of the thrust pad under contact force or water film pressure. This ML deterministic model provides an effective means for high-precision prediction of the lubrication performance of the elastic supported water-lubricated thrust bearings coupled with multi-layer soft materials.

Effect of direct injection and pivot stiffness on the static performance parameters of tilting pad journal bearings

This work presents a thermo-hydrodynamic model of a tilting pad journal bearing (TPJB) supported on flexible pivots and considering direct injection on the bearing gap. It initially investigates separately each effect on the static characteristics of a TPJB and after, the concomitant influence of both mechanisms on the bearing performance. The study reveals both mechanisms of direct injection and pivot deflection affect the lubricant pressure and temperature distribution. Direct injection is a local effect, mainly influencing the pressure around the injection orifice and the temperature downward it. Pivot flexibility reduces the lubricant pressure and the temperature rise, as the film thickness increases with pivot deflection. For soft pivots, direct injection may reduce even further the lubricant temperature. As the pivot stiffness reduces, the journal displacement increases, but the drag torque is reduced, indicating that bearing mechanical efficiency may be increased if the tilting pads are supported on flexible pivots, whether the journal displacement is within acceptable bounds. Each considered mechanism in a TPJB may affect its performance and should be modeled accordingly.

Thermal modeling of the respiratory turbinates in arctic and subtropical seals

Mammals possess complex structures in their nasal cavities known as respiratory turbinate bones, which help the animal to conserve body heat and water during respiratory gas exchange. We considered the function of the maxilloturbinates of two species of seals, one arctic (Erignathus barbatus), one subtropical (Monachus monachus). By means of a thermo-hydrodynamic model that describes the heat and water exchange in the turbinate region we are able to reproduce the measured values of expired air temperatures in grey seals (Halichoerus grypus), a species for which experimental data are available. At the lowest environmental temperatures, however, this is only possible in the arctic seal, and only if we allow for the possibility of ice forming on the outermost turbinate region. At the same time the model predicts that for the arctic seals, the inhaled air is brought to deep body temperature and humidity conditions in passing the maxilloturbinates. The modeling shows that heat and water conservation go together in the sense that one effect implies the other, and that the conservation is most efficient and most flexible in the typical environment of both species. By controlling the blood flow through the turbinates the arctic seal is able to vary the heat and water conservation substantially at its average habitat temperatures, but not at temperatures around −40 °C. The subtropical species has simpler maxilloturbinates, and our model predicts that it is unable to bring inhaled air to deep body conditions, even in its natural environment, without some congestion of the vascular mucosa covering the maxilloturbinates. Physiological control of both blood flow rate and mucosal congestion is expected to have profound effects on the heat exchange function of the maxilloturbinates in seals.

A new modified boundary slip model for thrust bearing performance under fluid–thermal–structure interaction regime

PurposeThis study aims to investigate the thermohydrodynamic (THD) and thermoelastohydrodynamic (TEHD) performance of an air-lubricated thrust bearing under different slip conditions, especially the slip length effect.Design/methodology/approachIn this study, a new modified boundary slip model was established to investigate thrust bearing performance. The THD and TEHD bearing characteristic distribution was analyzed with fluid–thermal–structure interaction approach. The effect of the slip length on the bearing performance was studied using various bearing structure parameters.FindingsThe increased slip length changed the classical feature distribution of the film pressure and temperature. The sacrifice of the bearing load capacity effectively compensated for the aerodynamic thermal effect and friction torque under the slip condition. The TEHD model has a lower film pressure and load capacity than the THD model. However, it also has lower film temperature, lower friction torque and smaller Knudsen number (Kn).Originality/valueThe bearing THD and TEHD performances of the modified boundary slip model were compared with those of a traditional no-slip bearing. The results help to guide the selection of the bearing surface materials and processing technology of rotor and foil, so as to fully control the degree of slip and make use of it.

Effect of thermal boundary conditions on dynamic characteristics of multi-lobed bearings

This work presents a three-dimensional, variable viscosity, thermo-hydrodynamic model of multi-lobed journal bearings, capable to estimate the pressure and temperature distributions of the lubricant flowing between a rotating shaft and the partial arcs composing the multi-lobed bearing configuration, that must support the external applied load. The thermal model estimates the lubricant temperature increase and its effect on the pressure distribution, the bearing hydrodynamic forces and its equivalent stiffness and damping coefficients. Estimation of the temperature increase requires numerical solution of the energy equation, which depends on the assumed thermal boundary conditions. Consequently, the model must take into account the shaft and bush surfaces either isothermal or adiabatic. This work investigates the effect of such cases on the predictions of the pressure, temperature, locus, stiffness and damping coefficients on two and three lobed bearings. It shows that if both surfaces are isothermal, the lubricant temperature increase is smaller. If both surfaces are adiabatic, temperature increase is higher. The effect of lobe preload is also investigated, showing that the bearing coefficients increase with preload.

A simplified thermohydrodynamic lubrication model for application to the design of cylindrical journal bearings with two-axial oil grooves

A simplified thermohydrodynamic lubrication model for application to the design of cylindrical journal bearings with two-axial oil grooves

Thermohydrodynamic behavior of partially coated plain journal bearings with/without considering wall slip

A thermohydrodynamic model was used to study the influence of partial composite coatings on the behavior of plain journal bearings, considering solid elastic deformations and wall slip occurring at the oil film–polytetrafluoroethylene coating interface, and heat conduction between film, coating, interlayer and basement. The purpose is to design partial polytetrafluoroethylene coating to obtain improved bearing behavior based on analyzing the maximum temperature and minimum film thickness in different coating positions (or slip zones). The influences of coating thickness and coating materials (polytetrafluoroethylene, graphite and diamond-like carbon coatings) at different coating positions are also presented. Results show that polytetrafluoroethylene coatings that are completely located in the film convergent region have a small influence on thermal behavior in both nonslip and slip cases. Without slip, a full polytetrafluoroethylene coating can increase the maximum temperature; however, wall slip occurring on a full polytetrafluoroethylene coating surface is helpful in decreasing the maximum temperature when accompanied by a lower minimum film thickness. A thicker polytetrafluoroethylene coating causes bearing seizures more readily. Unlike polytetrafluoroethylene, graphite and diamond-like carbon coatings improve the thermal behavior.