Frictional Heat Flux Research Articles

Study on Temperature Field Distribution of a High-Speed Double-Helical Gear Pair with Oil Injection Lubrication

The temperature field distribution of high-speed double-helical gears under oil injection lubrication is investigated by obtaining heat flux density and convective heat transfer coefficients through theoretical calculations and CFD (computational fluid dynamics) simulations. Based on the CFD method, fluid simulations are performed to obtain the distribution of lubricating oil on the surface of the double-helical gears, the velocity streamline diagram of the lubricating oil, and the convective heat transfer coefficients of different surfaces of the gears. The friction heat flux density is calculated using Hertzian contact theory and theoretical formula of heat generation. The double-helical gears’ steady-state temperature field simulation uses this heat flux density as a boundary condition. The correctness of the calculation method is verified through experiments. The study shows that increasing the jet velocity allows the jet to reach the tooth surface more effectively, improving the cooling effect and reducing the maximum gear temperature. However, the relationship between the jet velocity and the minimum gear temperature is non-linear. Within a certain range, increasing the jet diameter makes the jet wider, and the area covered by the lubricating oil becomes larger as the jet spreads around the gear teeth, enhancing the cooling effect. An increase in gear speed leads to an increase in frictional heat flux density; moreover, the high-velocity airflow generated by the increased speed reduces the amount of lubricant entering the mesh zone, which in turn causes the maximum temperature of the gears to continue to rise.

Elastohydrodynamic lubrication analysis and temperature field simulation of gear system

Abstract The gearbox is one of the key components in the aero engine. In the process of high-speed operation, the internal temperature of the gearbox rises significantly, which seriously affects the service performance of transmission equipment. Based on the meshing principle and Herz contact theory, the basic meshing parameters are analyzed, and the comprehensive friction coefficient and heat flux are solved. According to the principle of convective heat transfer in a rotating disc and the frictional heat diffusion model, the CHTC (convective heat transfer coefficient) is analyzed. The FE model of the gear system is built based on ANSYS software, and the temperature distribution is analyzed by loading thermal boundary conditions with the APDL program. The calculation results indicate that the middle of the tooth tip or root of the gear has the maximum temperature. The research provides some reference values for the calculation method of the temperature field of the gear system under elastohydrodynamic lubrication.

Elucidating the in-process interfacial friction regime and thermal responses during inertia friction welding of dissimilar superalloys

Inertia friction welding (IFW) is a robust joining technique, particularly for hybrid structures composed of similar or dissimilar alloys. The highly transient thermal responses during friction heating produce variations in heat generation and temperature distribution, which are crucial for designing and controlling the IFW process. This study establishes a finite element (FE) model of the IFW process for dissimilar superalloys and investigates the transition of the interfacial friction regime and its impact on the transient thermal responses. The in-process state variables, including the frictional stress and heat flux, along with their spatial distributions at the welding interface, are obtained through FE simulations. The predicted results indicate that the transient transition of the friction regime produces two Coulomb friction zones accompanied by a shear friction zone. To capture the transient evolution of the friction regime, a novel phenomenological formula is developed. This model accurately predicts the shrinkage and disappearance of the two Coulomb friction zones and the enhancement of the shear friction zone from the initial 0.42 R0–0.87 R0 (where R0 is the workpiece radius) to the entire interface during the IFW process. The variations in interfacial heat flux, frictional stress, and temperature caused by the transition of the friction regime are comprehensively analyzed. Our results reveal that the transition from the Coulomb friction regime to shear friction regime at the interface is beneficial for temperature homogenization at the welding interface. The FE simulation results are validated against published experimental measurements, which confirms the accuracy and reliability of the FE model.

Frictional heat accumulation at cyclically rolling-sliding contacts with consideration to time-dependent contact pressure

A finite element model is proposed for analyzing the frictional heat accumulation at high-speed rolling-sliding contacts. The moving frictional heat flux as a function of the time-dependent contact pressure is applied cyclically on the contact surface. The convectional heat boundary is considered in non-contact region. The transient temperature changes on the contact surface are calculated, which is validated against analytical calculation results by employing the Fourier transform method. The frictional heat accumulation effect and equilibrium-state temperature are obtained during cyclically rolling-sliding contacts.

Stiffness and Atomic-Scale Friction in Superlubricant MoS2 Bilayers.

Molecular dynamics simulations, performed with chemically accurate ab initio machine-learning force fields, are used to demonstrate that layer stiffness has profound effects on the superlubricant state of two-dimensional van der Waals heterostructures. We engineer bilayers of different rigidity but identical interlayer sliding energy surface and show that a 2-fold increase in the intralayer stiffness reduces the friction by a factor of ∼6. Two sliding regimes as a function of the sliding velocity are found. At a low velocity, the heat generated by the motion is efficiently exchanged between the layers and the friction is independent of the layer order. In contrast, at a high velocity, the friction heat flux cannot be exchanged fast enough and a buildup of significant temperature gradients between the layers is observed. In this situation, the temperature profile depends on whether the slider is softer than the substrate.

Unsteady nanofluid flow over a cone featuring mixed convection and variable viscosity

This article addresses unsteady nanofluid flow over a cone with MHD and mixed convection effects. Effects of variable viscosity and viscous dissipation are also considered. The resulting system of equations is tackled through the Homotopy Analysis Method (HAM). The impact of different influential variables on skin friction coefficient, heat and mass flux are discovered through numerical tables and graphs. It is noted that the surface drag force in x and y directions increases against the buoyancy force parameter. Also, it is observed that the tangential and azimuthal velocity decrease against the variable viscosity parameter. Furthermore, the temperature of fluid is observed to decay against the unsteady parameter but it increases against the Eckert number.

Angular momentum and moment of total enthalpy integral equations for high-speed boundary layers

Angular momentum and moment of total enthalpy integral (AMI and MTEI) equations provide a quantitative mapping between flow phenomena such as turbulence on skin friction and surface heat flux for high-speed boundary layers relative to laminar flows. Using the AMI equation, the effect of edge Mach number (Ma) and wall-cooling are measured on the turbulent torque that enhances the skin friction coefficient. Moreover, the AMI equation introduces stress-weighted density that yields a more robust collapse of the dataset with different configurations. The MTEI equation distinguishes the impact of Ma and wall-cooling on the turbulent flux of mean kinetic energy and enthalpy, respectively.

Numerical examination of wall properties for the magnetohydrodynamics stagnation point flow of micro-rotating fluid subject to weak concentration

In this investigation, stagnation point flow of non-Newtonian fluid is considered under the impact of magnetohydrodynamics, porous medium, and mixed convection effects. Additionally, angular momentum and energy transport constitutive equations are also taken into account in order to explore the fluid micro-rotational effects. The fluid motion develops by virtue of linear stretching and slip factors. Furthermore, the energy transport equation is raised with the effect of viscous dissipation and heat source phenomena. Mathematical formulations lead to a set of ordinary differential equations by introducing similarity variables. The proposed model has been solved numerically using fourth-order Runge–Kutta method with shooting technique. Influence of pertinent flow parameters for the case of weak concentration of micro-elements on velocity, temperature, skin friction, and local heat flux at the surface is computed and discussed. Different ranges are chosen for the flow parameters, for example; magnetic field variation is taken [0, 0.9], micro-rotation [0,1], stretching ratio [0,0.2], surface condition [0,1], the Prandtl number [3, 12], and the Eckert number [3, 11]. The fluid velocity slows down when the magnetic number varies from 0.0 to 0.5 in the presence of weak concentration (m = 0.5) of micro-elements. In addition, the maximum increasing percentage of skin friction is obtained when the porosity parameter varies from 0.0 to 0.6. The maximum decreasing percentage of the Nusselt number is obtained when the thermal slip parameter varies from 0.0 to 0.8. The current study has multiple fascinating applications in polymeric solutions, bio-medical functions like magnetic drug targeting, heat conduction in tissues, surface roughness, and squeeze film lubrication problems between conical bearings.

Effect of interaction strength on recovery downstream of incident shock interactions

Direct numerical simulations of a supersonic turbulent boundary layer on a flat plate interacting with an impinging shock wave are carried out with two different incident shock angles at Mach 2.25. The effect of the interaction strength on the recovery process in the downstream region is systematically studied, including the turbulence evolution, the statistical and structural properties of wall pressure fluctuations, and the generation of mean skin friction and wall heat flux. The variations of the Reynolds stress components, the anisotropy tensor, and the turbulent kinetic energy budget in the two flow cases highlight a slow reversal tendency and an increasingly pronounced importance of the outer-layer large-scale structures in the relaxation region of the strong interaction. We find that the effect of increasing the interaction strength on the fluctuating wall pressure is reflected by a decrease in the characteristic frequencies, an increase in the spatial extent, and a decrease in the convection velocity. We decompose the mean skin friction and wall heat flux into different physically informed contributions and reveal that the mean wall heat flux generation is the same regardless of the interaction strength; in contrast, the generation mechanism of mean skin friction is found to be fundamentally changed. A novel scale-decomposition method is used to quantify the effect of the increased interaction strength on the leading components, and it is demonstrated that the energetic outer-layer large-scale structures are the dominant contributor in the recovery process as the interaction strength is increased.

Dry sliding wear and heat flux mapping of closed-cell Mg-2Zn-2Ca foam fabricated by stir casting route

Dry sliding wear mechanisms and of closed-cell Mg-2Zn-2Ca foam fabricated by stir-casting were investigated using pin-on-disc tribometer. Wear tests were conducted in wide range of varying load of 5–100 N and sliding velocities of 2,3 and 4 m/s at constant sliding distance of 1000 m to develop wear and heat flux mapping plots. Transition of mild to severe wear by establishing different wear mechanisms, its comparative study with solid alloy and microstructure characterization were carried out for potential sustainability of Mg-alloy foam in automotive and biomedical applications. Wear rate was reduced while increasing the effects of work hardening and decreasing the effects of thermal softening occurred during frictional heat flux generation due to competition between work hardening and thermal softening. The results were concluded that Mg-2Zn-2Ca foam exhibited good wear resistance at load up to 25 N, sliding velocity up to 2 m/s and recommended for low load bearing light-weight tribological applications.

Modular Method for Estimation of Velocity and Temperature Profiles in High-Speed Boundary Layers

The fluid property variation caused by viscous heating affects the mean velocity and Reynolds stresses in compressible turbulent boundary layers, and as a result also affects the resulting skin friction and wall heat transfer. We present a method based on the work of Huang et al. (AIAA Journal, Vol. 31, No. 9, 1993, pp. 1600–1604) that estimates the mean velocity and temperature profiles, and therefore also the friction and heat transfer coefficients, for a given Mach number, Reynolds number, and wall thermal condition. The method is modular in the sense that it works with multiple variable-property scaling formulas (or “transformations”), velocity–temperature relationships, viscosity–temperature relationships, and equations-of-state. The method is validated against multiple Direct Numerical Simulation (DNS) cases and was found to predict the skin friction and wall heat flux to within 8 and 11% compared to the current state-of-the-art (the Van Driest II method), which is within 16 and 13% for the same data.

Thermal behavior of friction discs in dry clutches based on a non-uniform pressure model

To investigate the thermal behavior of friction discs in dry clutches during long-term slipping, a two-dimensional transient thermal model was established using the finite element method. Because the pressure distribution on the friction interface is important, a dimensionless non-uniform pressure model was proposed based on measured data using Fuji Prescale pressure-sensitive films arranged on the friction disc. Subsequently, the frictional heat flux, which varied nonlinearly with the radius, was determined. The heat conduction processes of the friction pairs were analyzed in detail. The results of the temperature distribution calculated using the non-uniform pressure model agree well with those obtained from dynamometer experiments. The results reveal that high temperatures exist near the high-pressure region on the friction interface. Compared to the results of two conventional models, those of the non-uniform pressure model are closer to the experimental data. The maximum temperature error is reduced by 23.23% and 34.03% relative to the uniform pressure and uniform wear models, respectively, after a 15 s slipping period. Therefore, by using the non-uniform pressure model, the thermal analysis can be more effective in avoiding excessive wear and prolonging the service life of dry clutches.

Flow of magnetic shear thinning nano fluid under zero mass flux and hall current

In this research, the investigation of Hall and ion-slip effects on oblique stagnation point flow of magneto hydrodynamics Casson nanofluid have been discussed with Newtonian heating and zero heat and mass on an elastic surface. The mass concentration equation is also contemplated to examine the flow. By use of proper similarity transformation the governing equation of model are transformed into system of nonlinear ODEs. The numerical results are presented by using the Runge-Kutta (RK) Fehlberg method, accompanied by the shooting technique by converting the system of ODEs to first-order ODEs. The effect of all physical constraints on velocity, temperature, and nanoparticles' concentration is shown graphically. Skin friction quantities, heat and mass flux are the physical quantities which are to be measured numerically. Temperature and concentration of nanoparticles near the wall in negligibly small for magnetic field parameter but this have a dominant influence on temperature and concentration of nanoparticles far away from the surface. Also it is observed that mass flux at the surface is larger for Ion slip parameter and Hall parameter, while skin friction coefficient at surface rises for magnetic field parameter but decreases for Hall parameter.

Uncertainty Analysis of Parameters in SST Turbulence Model for Shock Wave-Boundary Layer Interaction

Shock wave-boundary layer interactions (SWBLIs) have a tremendous influence on the performance of hypersonic vehicles. For the numerical simulation of such engineering flows, Reynolds averaged Navier-Stokes (RANS) still occupies an irreplaceable role. However, parameters of turbulence models in RANS have substantial uncertainties, which impact the reliability of simulation results. Thus, the aim of the present study is to conduct an uncertainty analysis on parameters in the shear-stress transport (SST) turbulence model for the simulation of SWBLIs. In the current work, uncertainty quantification was performed first. A surrogate model was constructed by the non-intrusive polynomial chaos (NIPC) method to propagate uncertainties from model parameters to the quantities of interests (QoIs) and quantify them. In the subsequent sensitivity analysis, the key parameters were identified for such flow by calculating the Sobol index of each parameter for various QoIs. The results indicate that uncertainties of model parameters led to non-negligible uncertainties in those QoIs, particularly in skin friction and wall heat flux. The parameters α1, σω1, β1 were identified as primary contributors through the sensitivity analysis. Moreover, the specific effects of the three parameters on the flow prediction were analyzed by changing the parameters’ values separately.

Development of a 2D finite element model for the investigation of the tread braked railway wheels thermo-mechanical behaviour

The main drawback of tread braking is the rail wheel heating due to friction sliding. Thermal stresses and strains can lead to wheel surface damages while at the same time fast cooling from high temperature can cause microstructural changes, with possible local formation of brittle martensite. Nowadays, the investigation of the wheel and shoe thermomechanical interaction is typically performed using finite element (FE) codes. The paper shows the development, implementation and preliminary validation of a 2D plane FE model for the calculation of the thermal field produced in a tread braked wheel due to drag and stop braking operations. The model includes a structural contact module for the static calculation of the normal and tangential contact pressure at the wheel-shoe interface and a thermal transient module, which computes the wheel temperature considering the friction heat flux and the cooling due to air convection and rail chill.

Near-wall Taylor-series expansion solution for compressible Navier–Stokes–Fourier system

This paper presents the Taylor-series expansion solution of near-wall velocity and temperature for a compressible Navier–Stokes–Fourier system with a no-slip curved boundary surface. When the shear viscosity is a single-valued function of local fluid temperature, the near-wall velocity and temperature are explicitly expressed using the surface quantities including skin friction, surface pressure, surface dilatation, surface heat flux, surface temperature, surface curvature, and their relevant derivatives at the wall. In addition, the wall-normal pressure gradient at the wall is found to be contributed by three physical mechanisms including the skin friction divergence and surface dilatation effect as well as the coupled skin friction and surface heat flux with varying shear viscosity. Furthermore, without losing generality, we derive the near-wall Taylor-series expansion solution for the Lamb vector under the assumption of constant viscosities. Different physical mechanisms that are responsible for initial formation of the Lamb vector in the viscous sublayer are elucidated. The significance of the skin friction divergence and surface dilatation to the near-wall Lamb vector is highlighted.

Data-driven model for improving wall-modeled large-eddy simulation of supersonic turbulent flows with separation

A machine learning algorithm is presented, serving as a data-driven modeling tool for wall-modeled large eddy simulations (WMLESs). The proposed model is formulated to address the problems of log layer mismatch and inaccurate prediction of skin friction, particularly for supersonic separated and reattached flows. This machine learning algorithm uses random forest regression to map the local mean flow fields to the discrepancies in the skin friction (heat flux) while complying with Galilean invariance as the flow features input is provided using relative velocities. The model is tested on two different supersonic flows, namely, flow over a flat plate and flow around an expansion-compression corner. The performance is evaluated by comparing the skin friction (heat flux) and flow properties with exact values. The ultimate goal is to build a robust and generalizable machine learning model to improve the prediction of WMLES of supersonic flows. To this end, the model is trained by a set of flows containing some essential flow physics to devise a generalizable model. Although the general machine learning model shows some advantages over the baseline WMLES model, it is concluded the data set is far from being representative of the rich flow physics model; therefore, the machine learning model should be trained and tested by a broader set of flows.

Aerothermodynamic characteristics of hypersonic curved compression ramp flows with bistable states

The aerothermodynamic characteristics (including wall friction Cf, pressure pw, and heat flux St) in curved compression ramp (CCR) flows with bistable states are studied numerically and theoretically. Direct numerical simulations of bistable states of separation/attachment induced by variation of the turning angle ϕ, as well as the influence of inflow Mach number and wall temperature on dual-solution interval, are carried out. Distributions of wall friction, pressure and heat flux are analyzed. Further, the emergence of the first and second minima of Cf in the separation bubble is interpreted, which are dominated by the adverse pressure gradient induced by separation and reattachment shock, respectively. The present results and analysis indicate that the reversed-flow singularity of F. T. Smith (Proc. R. Soc. London. A: Math. Phys. Sci. 420, 21–52 (1988)] is less likely to occur in CCR flows. The prediction of pressure peak ppk of separation states confirms the model based on the minimum viscous dissipation theorem [Hu et al., Phys. Fluids 32(10), 101702 (2020)]. While the pressure overshoot pos can be analyzed by shock-polars with pressure match of compression and expansion process. The correlation between heat flux peak and pressure peak of both separation and attachment states is also discussed in terms of the classical power relation.

Thermomechanical properties and frictional contact behavior of oxygen doped DLC film through molecular dynamics simulation

Using the MD simulation techniques, we investigated the effects of doped oxygen atoms on the thermomechanical properties and tribological performance of diamond like carbon (DLC). The atomic percentage of oxygen (at.% O) in DLC was varied from 0 to 20.0%. The mechanical stiffness of oxidized DLC samples was evaluated using the nanoindentation simulation, while the coefficient of friction (COF) and the frictional temperature rise were obtained from the sliding contact simulation. From the simulation results, it could be found that the mechanical stiffness and the COF decreased with the at.% O in DLC. The lower COF for the oxidized DLC could be explained by the less covalent interactions with the diamond tip surface. Due to the lower stiffness, the oxidized DLC showed larger surface displacement and wear during the sliding contact. Also, the frictional temperature rise was evaluated with respect to the at.% O in DLC. The higher at.% O in DLC, the lower surface temperature rise. This could be attributed to the lower frictional heat flux and the higher specific heat of the oxidized DLC samples.

Effects of operating and material parameters on the thermal characteristics of a wet clutch

Based on the frictional mechanism of a wet clutch, frictional models of wet clutch engagement were established using the modified Reynolds equation and the elastic contact model between frictional pairs. Then, the heat flux models for the viscous shear and asperity friction were built, and the two-dimensional transient thermal models for the separator plate, friction disk, and ATF heat convection model were deduced based on the heat transfer theory and conservation law of energy. Finally, the Runge–Kutta numerical method was used to solve the frictional and thermal models. The average temperature of the separator plate, friction disk, and ATF were calculated. The effects of operating and material parameters, such as applied pressure, initial angular velocity, friction lining permeability, surface combined roughness RMS, equivalent elastic modulus, and ATF flow, on the thermal characteristics of friction pairs and ATF during engagement, were studied. The simulation results show that the temperature characteristics of the separator plate, friction disk, and ATF depend mainly on the viscous shear and asperity friction heat flux, and that the operating and material parameters of the wet clutch also have significant impacts on the overall variation trend of the thermal characteristics of the separator plate, friction disk, and ATF.