Showing papers on "Slip ratio published in 2014"

An analytical model of pneumatic tyres for vehicle dynamic simulations. Part 2: Comprehensive slips

Abstract: This is the second paper in a three–part study presenting an analytical approach for determining tyre dynamic properties. In this study analytical formulations are derived for the tyre dynamic properties as functions of the slip ratio, slip angle, camber angle and other tyre dynamic parameters. There formulae can be used for the general vehicle simultaneous in braking/traction and steering manoeuvres with a varying camber angle are regular or irregular terrains. In this paper the lateral force and self–aligning torque due to both slip and camber angles are first studied. The longitudinal, lateral forces and self–aligning torque during braking/traction and steering without any camber angle or with a varying camber angle are also analysed. Also, both the friction eclipse concept and the friction circle concept are investigated.

Extremum-Seeking Control of ABS Braking in Road Vehicles With Lateral Force Improvement

Abstract: An ABS control algorithm based on extremum seeking is presented in this brief. The optimum slip ratio between the tire patch and the road is searched online without having to estimate road friction conditions. This is achieved by adapting the extremum-seeking algorithm as a self-optimization routine that seeks the peak point of the tire force-slip curve. As an additional novelty, the proposed algorithm incorporates driver steering input into the optimization procedure to determine the operating region of the tires on the “tire force”-“slip ratio” characteristic-curve. The algorithm operates the tires near the peak point of the force-slip curve during straight line braking. When the driver demands lateral motion in addition to braking, the operating regions of the tires are modified automatically, for improving the lateral stability of the vehicle by increasing the tire lateral forces. A validated, full vehicle model is presented and used in a simulation study to demonstrate the effectiveness of the proposed approach. Simulation results show the benefits of the proposed ABS controller.

Shear viscosity and wall slip behavior of a viscoplastic hydrogel

Abstract: The coupled apparent slip and viscoplastic behavior of a hydrogel consisting of 0.2 wt. % aqueous solution of poly(acrylic acid) was analyzed employing steady torsional and circular tube (capillary) flows. Transparent disks and capillaries fabricated out of borosilicate glass were used to allow velocity measurements. The steady torsional flow of the hydrogel was dominated by wall slip which gave rise to plug flow over the apparent shear rate range of 0.1 to 1 s−1, in agreement with the plug flow observed in the capillary under similar shear stresses. The transition from plug flow provided the yield stress of the hydrogel, which was found to be consistent with velocity data collected over the 0.1–200 s−1 apparent shear rate range of steady torsional and capillary flows. The availability of both pressure drop versus flow rate and wall slip velocity data enabled the validation of correction procedures proposed earlier for the determination of the slip-corrected wall shear rate [Yilmazer and Kalyon, “Dilatancy of concentrated suspensions with Newtonian matrices,” Polym. Compos. 12, 226–232 (1991); D. Kalyon, “Apparent slip and viscoplasticity of concentrated suspensions,” J. Rheol. 49, 621–640 (2005)] and the determination of the shear viscosity parameters. The apparent slip layer thicknesses were found to be consistent with the elastohydrodynamic mechanism proposed by Martin et al. [“Wetting transitions at soft, sliding interfaces,” Phys. Rev. E 65, 031605 (2002)] and Meeker et al. [“Slip and flow in pastes of soft particles: Direct observation and rheology,” J. Rheol. 48, 1295–1320 (2004)] for steady torsional flow but not for capillary flow, emphasizing the role the applied pressure plays in shaping the apparent slip behavior.

Flow rate through microfilters: Influence of the pore size distribution, hydrodynamic interactions, wall slip, and inertia

Abstract: We examine the fluid mechanics of viscous flow through filters consisting of perforated thin plates. We classify the effects that contribute to the hydraulic resistance of the filter. Classical analyses assume a single pore size and account only for filter thickness. We extend these results to obtain an analytical formula for the pressure drop across the microfilter versus the flow rate that accounts for the non-uniform distribution of pore sizes, the hydrodynamic interactions between the pores given their layout pattern, and wall slip. Further, we discuss inertial effects and their order of scaling.

Unsteady laminar flows of a Carbopol® gel in the presence of wall slip

Abstract: We present a comparative experimental study of unsteady laminar flows of a yield stress shear thinning fluid (Carbopol ® 980) in two distinct configurations: a parallel plate rheometric flow and a pressure driven pipe flow. Consistently with the observations in the case of the rheometric flow, the in situ characterisation of the unsteady pipe flow reveals three distinct flow regimes: solid (plug-like) , solid–fluid and fluid . In both configurations and as the flow forcing is gradually increased, the yielding emerges via an irreversible transition. The irreversibility of the deformation states is coupled to the wall slip phenomenon. Particularly, the presence of wall slip nearly suppresses the scaling of the deformation power deficit associated to the rheological hysteresis with the rate at which the material is forced. An universal scaling of the slip velocity with the wall velocity gradients and a slip length which is independent on the degree of the flow steadiness is observed in the pipe flow.

Cessation of viscoplastic Poiseuille flow with wall slip

Abstract: We solve numerically the cessation of axisymmetric Poiseuille flow of a Herschel–Bulkley fluid under the assumption that slip occurs along the wall. The Papanastasiou regularization of the constitutive equation is employed. As for the slip equation, a power-law expression is used to relate the wall shear stress to the slip velocity, assuming that slip occurs only above a critical wall shear stress, known as the slip yield stress. It is shown that, when the latter is zero, the fluid slips at all times, the velocity becomes and remains uniform before complete cessation, and the stopping time is finite only when the slip exponent s 1, the decay is much slower. Analytical expressions of the decay of the flat velocity for any value of s and of the stopping time for s < 1 are also derived. Using a discontinuous slip equation with slip yield stress poses numerical difficulties even in one dimensional time-dependent flows, since the transition times from slip to no-slip and vice versa are not known a priori. This difficulty is overcome by regularizing the slip equation. The numerical results showed that when the slip yield stress is non-zero, slip ceases at a finite critical time, the velocity becomes flat only in complete cessation, and the stopping times are finite, in agreement with theoretical estimates.

Adaptive motion control of wheeled mobile robot with unknown slippage

Abstract: As a major representative nonholonomic system, wheeled mobile robot (WMR) is often used to travel across off-road environments that could be unstructured environments. Slippage often occurs when WMR moves in slopes or uneven terrain, and the slippage generates large accumulated position errors in the vehicle, compared with conventional wheeled mobile robots. An estimation of the wheel slip ratio is essential to improve the accuracy of locomotion control. In this paper, we propose an improved adaptive controller to allow WMR to track the desired trajectory under unknown longitudinal slip, where the stabilisation of the closed-loop tracking system is guaranteed by the Lyapunov theory. All system states use neural network online weight tuning algorithms, which ensure small tracking errors and no loss of stability in robot motion with bounded input signals. We demonstrate superior tracking results using the proposed control method in various Matlab simulations.

Isoflux Nusselt Number and Slip Length Formulae for Superhydrophobic Microchannels

Abstract: We analytically and numerically consider the hydrodynamic and thermal transport behavior of fully developed laminar flow through a superhydrophobic (SH) parallel-plate channel. Hydrodynamic slip length, thermal slip length and heat flux are prescribed at each surface. We first develop a general expression for the Nusselt number valid for asymmetric velocity profiles. Next, we demonstrate that, in the limit of Stokes flow near the surface and an adiabatic and shear-free liquid–gas interface, both thermal and hydrodynamic slip lengths can be found by redefining existing solutions for conduction spreading resistances. Expressions for the thermal slip length for pillar and ridge surface topographies are determined. Comparison of fundamental half-space solutions for the Laplace and Stokes equations facilitate the development of expressions for hydrodynamic slip length over pillar-structured surfaces based on existing solutions for the conduction spreading resistance from an isothermal source. Numerical validation is performed and an analysis of the idealized thermal transport behavior suggests conditions under which superhydrophobic microchannels may enhance heat transfer.

Slip velocity of rigid fibers in turbulent channel flow

Abstract: In this study, the slip velocity between rigid fibers and a viscous carrier fluid is investigated for the reference case of turbulent channel flow. The statistical moments of the slip velocity are evaluated modelling fibers as prolate spheroids with Stokes number, St, ranging from 1 to 100 and aspect ratio, λ, ranging from 3 to 50. Statistics are compared one-to-one with those obtained for spherical particles (λ = 1) to highlight effects due to fiber elongation. Comparison is also made at different Reynolds numbers (Reτ =150, 180, and 300 based on the fluid shear velocity) to discuss effects due to an increase of turbulent fluctuations. Results show that elongation has a quantitative effect on slip velocity statistics, particularly evident for fibers with small St. As St increases, differences due to the aspect ratio tend to vanish and the relative translational motion between individual fibers and surrounding fluid is controlled by fiber inertia through preferential concentration. A clear manifestation o...

Electronic stability control for electric vehicle with four in-wheel motors

Abstract: The electric vehicle with four direct-driven in-wheel motors is an over actuated system. A three-level control strategy of electronic stability control (ESC) is proposed to achieve optimal torque distribution for four in-wheel motors. The first level is a gain-scheduled linear quadratic regulator which is designed to generate the desired yaw moment command for ESC. Control allocation is the second level which is used to distribute the desired longitudinal tire forces according to the yaw moment command while satisfying the driver’s intent for acceleration and deceleration. The associated weighting matrix is designed using the work load ratio at each wheel to prevent saturating the tire. The third level is slip ratio control (SRC) which is employed at each wheel to generate the desired longitudinal tire force based on a combined-slip tire model. Simulation results show that the proposed method can enhance the ESC performance for the test maneuvers. Since the tire model is often unknown for practical implementation, the effectiveness of the SRC is studied using the sine with dwell test. It is found that the SRC is not crucial for achieving performance similar to the proposed method with SRC, if the slip ratio can be maintained in the stable region using traction control system/anti-lock braking system.

Linear stability analysis of miscible two-fluid flow in a channel with velocity slip at the walls

Abstract: The linear stability characteristics of pressure-driven miscible two-fluid flow with same density and varying viscosities in a channel with velocity slip at the wall are examined. A prominent feature of the instability is that only a band of wave numbers is unstable whatever the Reynolds number is, whereas shorter wavelengths and smaller wave numbers are observed to be stable. The stability characteristics are different from both the limiting cases of interface dominated flows and continuously stratified flows in a channel with velocity slip at the wall. The flow system is destabilizing when a more viscous fluid occupies the region closer to the wall with slip. For this configuration a new mode of instability, namely the overlap mode, appears for high mass diffusivity of the two fluids. This mode arises due to the overlap of critical layer of dominant instability with the mixed layer of varying viscosity. The critical layer contains a location in the flow domain at which the base flow velocity equals the phase speed of the most unstable disturbance. Such a mode also occurs in the corresponding flow in a rigid channel, but absent in either of the above limiting cases of flow in a channel with slip. The flow is unstable at low Reynolds numbers for a wide range of wave numbers for low mass diffusivity, mimicking the interfacial instability of the immiscible flows. A configuration with less viscous fluid adjacent to the wall is more stable at moderate miscibility and this is also in contrast with the result for the limiting case of interface dominated flows in a channel with slip, where the above configuration is more unstable. It is possible to achieve stabilization or destabilization of miscible two-fluid flow in a channel with wall slip by appropriately choosing the viscosity of the fluid layer adjacent to the wall. In addition, the velocity slip at the wall has a dual role in the stability of flow system and the trend is influenced by the location of the mixed layer, the location of more viscous fluid and the mass diffusivity of the two fluids. It is well known that creating a viscosity contrast in a particular way in a rigid channel delays the occurrence of turbulence in a rigid channel. The results of the present study show that the flow system can be either stabilized or destabilized by designing the walls of the channel as hydrophobic surfaces, modeled by velocity slip at the walls. The study provides another effective strategy to control the flow system.

Effects of chemical reaction and thermal radiation on mhd flow over an inclined permeable stretching surface with non-uniform heat source/sink: an application to the dynamics of blood flow

Abstract: An analysis is performed to study the unsteady hydromagnetic heat and mass transfer of blood in a time-dependent porous narrow blood vessel over a permeable inclined stretching surface under slip conditions. The unsteadiness in the flow, temperature and concentration fields is caused by the time dependence of the stretching velocity, surface temperature and the surface concentration. Thermal radiation, chemical reaction, velocity slip, thermal slip and concentration slips are considered. Similarity transformations are used to convert the governing time-dependent non-linear boundary layer equations for momentum, heat equation and species equations into a system of ordinary differential equations. The resulting non-linear coupled differential equations are solved numerically by using fourth order Runge–Kutta scheme together with shooting method. The influence of pertinent parameters on velocity, temperature, concentration, skin-friction coefficient, Nusselt number and Sherwood number has been studied and nu...

Exact Analytical Solution for the Peristaltic Flow of Nanofluids in an Asymmetric Channel with Slip Effect of the Velocity, Temperature and Concentration

Abstract: The peristaltic flow of nanofluids under the effect of slip conditions was theoretically investigated. The mathematical model was governed by a system of linear and non-linear partial differential equations with prescribed boundary conditions. Then, the exact solutions were successfully obtained and reported for the first time in the present work. These exact solutions were then used for studying the effects of the slip, thermophoresis, Brownian motion parameters and many others on the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and pressure gradient. In addition, it is proved that the obtained exact solutions are reduced to the literature results in the special cases.In the general case, it was found that on comparing the current solutions with the approximate ones obtained using the homotopy perturbation method in literature, remarkable differences have been detected for behaviour of the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and finally the pressure gradient. An example of these differences is about effect of the Brownian motion parameter on the velocity profile; where it was shown in this paper that the small values of this parameter have not a significant effect on the velocity, while this situation was completely different in the published work. Many other significant differences have been also discussed. Therefore, these observed differences recommend the necessity of including the convergence issue when applying the homotopy perturbation method or any other series solution method to solve a physical model. In conclusion. The current results may be considered as a base for any future analysis and/or comparisons.

Thermal and velocity slip effects on the MHD peristaltic flow with carbon nanotubes in an asymmetric channel: application of radiation therapy

Abstract: Peristaltic flow is used to study the flow and heat transfer of carbon nanotubes in an asymmetric channel with thermal and velocity slip effects. Two types of carbon nanotubes, namely, single- and multi-wall carbon nanotubes are utilized to see the analysis with water as base fluids. Empirical correlations are used for the thermo-physical properties of carbon nanotubes (CNTs) in terms of solid volume fraction of CNTs. The governing equations are simplified using long wavelength and low Reynolds number approximation. Exact solutions have been evaluated for velocity, pressure gradient, the solid volume fraction of CNTs and temperature profile. The effects of various flow parameters, i.e. Hatmann number M, the solid volume fraction of the nanoparticles ϕ, Grashof number G, velocity slip parameter β, thermal slip parameter γ and Prandtl number P r are presented graphically for both single- (SWCNT) and multi-wall carbon nanotubes (MWCNT).

Viscoplastic Poiseuille flow in a rectangular duct with wall slip

Abstract: We solve numerically the Poiseuille flow of a Herschel–Bulkley fluid in a duct of rectangular cross section under the assumption that slip occurs along the wall following a slip law involving a non-zero slip yield stress. The constitutive equation is regularized as proposed by Papanastasiou. In addition, we propose a new regularized slip equation which is valid uniformly at any wall shear stress level by means of another regularization parameter. Four different flow regimes are observed defined by three critical values of the pressure gradient. Initially no slip occurs, in the second regime slip occurs only in the middle of the wider wall, in the third regime slip occurs partially at both walls, and eventually variable slip occurs everywhere. The performance of the regularized slip equation in the two intermediate regimes in which wall slip is partial has been tested for both Newtonian and Bingham flows. The convergence of the results with the Papanastasiou regularization parameter has been also studied. The combined effects of viscoplasticity and slip are then investigated. Results are presented for wide ranges of the Bingham and slip numbers and for various values of the power-law exponent and the duct aspect ratio. These compare favorably with available theoretical results and with numerical results in the literature obtained with both regularization and augmented Lagrangian methods.

Slip behavior of liquid flow in rough nanochannels

Abstract: The molecular dynamics simulation is applied to investigate the liquid flow in rough nanochannels with a focus on interfacial velocity slip via three-dimensional Couette flow system. The typical liquid spatial distribution, velocity profile and slip length for liquid flow in rough nanochannels are evaluated and compared with smooth nanochannel. The effects of liquid–solid interaction, surface roughness and shear flow orientation on slip behavior of liquid flow in rough nanochannels are all investigated and discussed. The results indicate that, regardless of whether the liquid flow in transverse or longitudinal flow configuration, the rough surface induces extra energy losses and contributes to the reduction of interfacial velocity in nanochannel when compared with smooth surface. A larger roughness size introduces a more irregular near-wall flow, which results in a smaller interfacial velocity slip. In addition, irrespective of surface condition, increases in liquid–solid interaction strength lead to small interfacial velocity slip and expand the extent of velocity nonlinearity in wall-neighboring region. In particular, the slip behavior of liquid flow in rough nanochannels is also influenced by the shear flow orientation. Interestingly, we find that interfacial velocity slip at the rough solid surface in transverse flow configuration is smaller than that in longitudinal flow configuration.

Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis

Abstract: The effect of velocity slip at the walls on the linear stability characteristics of two-fluid three-layer channel flow (the equivalent core-annular configuration in case of pipe) is investigated in the presence of double diffusive (DD) phenomenon. The fluids are miscible and consist of two solute species having different rates of diffusion. The fluids are assumed to be of the same density, but varying viscosity, which depends on the concentration of the solute species. It is found that the flow stabilizes when the less viscous fluid is present in the region adjacent to the slippery channel walls in the single-component (SC) system but becomes unstable at low Reynolds numbers in the presence of DD effect. As the mixed region of the fluids moves towards the channel walls, a new unstable mode (DD mode), distinct from the Tollman Schlichting (TS) mode, arises at Reynolds numbers smaller than the critical Reynolds number for the TS mode. We also found that this mode becomes more prominent when the mixed layer overlaps with the critical layer. It is shown that the slip parameter has nonmonotonic effect on the stability characteristics in this system. Through energy budget analysis, the dual role of slip is explained. The effect of slip is influenced by the location of mixed layer, the log-mobility ratio of the faster diffusing scalar, diffusivity, and the ratio of diffusion coefficients of the two species. Increasing the value of the slip parameter delays the first occurrence of the DD-mode. It is possible to achieve stabilization or destabilization by controlling the various physical parameters in the flow system. In the present study, we suggest an effective and realistic way to control three-layer miscible channel flow with viscosity stratification.

Jet impingement and the hydraulic jump on horizontal surfaces with anisotropic slip

Abstract: This paper presents an analysis that describes the dynamics of laminar liquid jet impingement on horizontal surfaces with anisotropic slip. Due to slip at the surface and the anisotropy of its magnitude, the overall behavior departs notably from classical results. For the scenario considered the slip length varies as a function of the azimuthal coordinate and describes superhydrophobic surfaces micropatterned with alternating ribs and cavities. The thin film dynamics are modeled by a radial momentum analysis for a given jet Reynolds number and specified slip length and the influence of slip on the entire flow field is significant. In an average sense the thin film dynamics exhibit similarities to behavior that exists for a surface with isotropic slip. However, there are also important deviations that are a direct result of the azimuthally varying slip and these become more pronounced at higher Reynolds numbers and at greater slip lengths. The analysis also allows determination of the azimuthally varying radial location of the hydraulic jump that forms due to an imposed downstream depth. Departure from the no slip case and from the scenario of isotropic slip is characterized over a range of jet Reynolds numbers and realistic slip length values. The results show that for all cases the hydraulic jump is elliptical, with eccentricity increasing as the Reynolds number or slip length increases, or as the downstream depth decreases. The radial location of the hydraulic jump is greatest in the direction of greatest slip (parallel to the microribs), while it is a minimum in the direction transverse to the rib/cavity structures. The model results for the hydraulic jump radial position are compared to experimental measurements with good agreement.

Numerical study of the load-carrying capacity of lubricated parallel sliding textured surfaces including wall slip

Abstract: This article analyzes the combined effect of surface texturing and wall slip on the load-carrying capacity of parallel sliding systems. A new modified Reynolds equation with slip is proposed, based on the critical shear stress model, to reveal the hydrodynamic load-carrying capacity. A range of parameters such as texturing zone, texture cell aspect ratio, critical shear stress, and slip length are analyzed. It is shown that the optimal texturing zone length oscillates around 75% of the slider length. A slight shift of the optimized texturing zone toward the inlet of the contact is observed when the critical shear stress is increased. The numerical analysis also shows that there is a unique threshold value of the critical shear stress for every texture cell aspect ratio. When this ratio is increased, the threshold value increases, thus influencing the slip considerably. Slip has a positive effect on the load-carrying capacity for critical shear stress lower than the threshold value, whereas it has no effect on higher values. It is also found that in comparison with a solely textured surface, the load-carrying capacity of the combined textured/wall slip pattern can be increased by around 300% using the optimized slip parameters.