Large-scale Friction Research Articles

Asymptotic ultimate regime of homogeneous Rayleigh–Bénard convection on logarithmic lattices

We investigate how the heat flux $Nu$ scales with the imposed temperature gradient $Ra$ in homogeneous Rayleigh–Bénard convection using one-, two- and three-dimensional simulations on logarithmic lattices. Logarithmic lattices are a new spectral decimation framework which enables us to span an unprecedented range of parameters ( $Ra$ , $Re$ , $\Pr$ ) and test existing theories using little computational power. We first show that known diverging solutions can be suppressed with a large-scale friction. In the turbulent regime, for $\Pr \approx 1$ , the heat flux becomes independent of viscous processes (‘asymptotic ultimate regime’, $Nu\sim Ra ^{1/2}$ with no logarithmic correction). We recover scalings coherent with the theory developed by Grossmann and Lohse, for all situations where the large-scale frictions keep a constant magnitude with respect to viscous and diffusive dissipation. We also identify another turbulent friction-dominated regime at $\Pr \ll 1$ , where deviations from the Grossmann and Lohse prediction are observed. These two friction-dominated regimes may be relevant in some geophysical or astrophysical situations, where large-scale friction arises due to rotation, stratification or magnetic field.

Conformal Invariance of Characteristic Lines in a Class of Hydrodynamic Models

This paper addresses the problem of the existence of conformal invariance in a class of hydrodynamic models. For this we analyse an underlying transport equation for the one-point probability density function, subject to zero-scalar constraint. We account for the presence of non-zero viscosity and large-scale friction. It is shown analytically, that zero-scalar characteristics of this equation are invariant under conformal transformations in the presence of large-scale friction. However, the non-zero molecular diffusivity breaks the conformal group (CG). This connects our study with previous observations where CG invariance of zero-vorticity isolines of the 2D Navier–Stokes equation was analysed numerically and confirmed only for large scales in the inverse energy cascade. In this paper, an example of CG is analysed and possible interpretations of the analytical results are discussed.

Non-universal transitions to two-dimensional turbulence

The occurrence of system-scale coherent structures, so-called condensates, is a well-known phenomenon in two-dimensional turbulence and is a consequence of the inverse energy cascade – the energy transfer from small to large scales that is a characteristic of two-dimensional turbulence. Here, the onset of the inverse energy cascade and the ensuing condensate formation are investigated as a function of the magnitude of the force and for different types of forcing. Random forces with constant mean energy input lead to a supercritical transition, while forcing through a small-scale linear instability results in a subcritical transition with bistability and hysteresis. That is, the transition to two-dimensional turbulence is non-universal. For the supercritical case we quantify the effect of large-scale friction on the value of the critical exponent and the location of the critical point.

Design and Strength Verification of LNG Cargo Enclosure System FSP Type

The demand for natural gas in the world is increasing day by day. The efficient and flexible LNG becomes the preferred method for natural gas storage and transportation and has gradually entered people’s daily life. The enclosure system is the key core of LNG transport and storage vessels for storage of LNG at -163°C for isolation and thermal insulation. A new type of flat half-film prismatic LNG enclosure system has been developed for the shortcomings of the existing LNG cargo enclosure system. Through the breakthrough and mastery of key core technologies such as the overall layout and integration of the system, anti-leakage technology, liquid tank fixing technology, and large-scale friction stir welding (P-FSW) flat-line pipeline development technology, we’ll strive to fill the gap in the intelligent construction technology of large aluminum alloy tanks in China. The tank was subjected to water vapor test and numerical simulation. The results show that the structural strength of the FSP-LNG tank meets the strength check standard of IGC Code.

Hollow spherical and nanosheet-base BN nanoparticles as perspective additives to oil lubricants: Correlation between large-scale friction behavior and in situ TEM compression testing

In the present study we utilized h-BN nanoparticles (NPs) with different morphologies (hollow NPs with smooth surface (H-BNNPs), solid NPs with “pompon”-like or petalled structure (P-BNNPs), and globular NPs formed by numerous thin h-BN nanosheets (N-BNNPs)) as additives to PAO6 oil. Two sliding 100Cr6 surfaces were tested in the presence of PAO6+BNNP lubricants with 0.1% and 0.01% of BNNPs. The positive effect of BNNP additives increased along the row P-BNNPs → H-BNNPs → N-BNNPs. Utilization of N-BNNPs permitted to decrease noticeably the friction coefficient from 0.1 to 0.06 and reduce significantly the wear rate. In situ mechanical TEM tests were also performed to visualize and correlate the mechanical properties of individual h-BN NPs to their large-scale friction behavior.

Reynolds number dependence of large-scale friction control in turbulent channel flow

The present work investigates the effectiveness of the control strategy introduced by Schoppa and Hussain [Phys. Fluids 10, 1049 (1998)] as a function of Reynolds number (Re). The skin-friction dra ...

Apparent Dependence of Rate- and State-Dependent Friction Parameters on Loading Velocity and Cumulative Displacement Inferred from Large-Scale Biaxial Friction Experiments

We investigated the constitutive parameters in the rate- and state-dependent friction (RSF) law by conducting numerical simulations, using the friction data from large-scale biaxial rock friction experiments for Indian metagabbro. The sliding surface area was 1.5 m long and 0.5 m wide, slid for 400 s under a normal stress of 1.33 MPa at a loading velocity of either 0.1 or 1.0 mm/s. During the experiments, many stick–slips were observed and those features were as follows. (1) The friction drop and recurrence time of the stick–slip events increased with cumulative slip displacement in an experiment before which the gouges on the surface were removed, but they became almost constant throughout an experiment conducted after several experiments without gouge removal. (2) The friction drop was larger and the recurrence time was shorter in the experiments with faster loading velocity. We applied a one-degree-of-freedom spring-slider model with mass to estimate the RSF parameters by fitting the stick–slip intervals and slip-weakening curves measured based on spring force and acceleration of the specimens. We developed an efficient algorithm for the numerical time integration, and we conducted forward modeling for evolution parameters (b) and the state-evolution distances (L_{text{c}}), keeping the direct effect parameter (a) constant. We then identified the confident range of b and L_{text{c}} values. Comparison between the results of the experiments and our simulations suggests that both b and L_{text{c}} increase as the cumulative slip displacement increases, and b increases and L_{text{c}} decreases as the loading velocity increases. Conventional RSF laws could not explain the large-scale friction data, and more complex state evolution laws are needed.

Stationary two-dimensional turbulence statistics using a Markovian forcing scheme

In this study we investigate the statistics of two-dimensional stationary turbulence using a Markovian forcing scheme, which correlates the forcing process in the current time step to the previous time step according to a defined memory coefficient. In addition to the Markovian forcing mechanism, the hyperviscous dissipation mechanism for small scales and the Ekman friction type of linear damping mechanism for the large scales are included in the model. We examine the effects of various dissipation and forcing parameters on the turbulence statistics in both wave space and physical space. Our analysis includes the effects of the effective forcing scale, the bandwidth of the forcing, the memory correlation coefficient, and the forcing amplitude, along with the large scale friction and small scale dissipation coefficients. Scaling exponents of structure functions and energy spectra are calculated, and the role of the parameters associated with the Markovian forcing is discussed. We found that the scaling exponents are approximately invariant and show a universal behavior for the various forms of forcing schemes used. We found, however, that the final states strongly depend on the large scale friction mechanism considered. When the large scale friction mechanism is included in the model with a high friction coefficient, we demonstrate that the behavior is no longer universal. Our analysis also shows that the second-order vorticity structure function has an asymptotic scaling exponent for larger dissipation. Additionally, we confirmed that vorticity behaves as a passive scalar when the dissipation mechanism becomes less effective. Finally, although turbulence is not believed to have a separation of time scales in the dynamics of the velocity field, we conjectured that a separation of time scales exists in the dynamics of the energy spectrum.

On the Arrest of Inverse Energy Cascade and the Rhines Scale

Abstract The notion of the cascade arrest in a β-plane turbulence in the context of continuously forced flows is revised in this paper using both theoretical analysis and numerical simulations. It is demonstrated that the upscale energy propagation cannot be stopped by a β effect and can only be absorbed by friction. A fundamental dimensional parameter in flows with a β effect, the Rhines scale, LR, has traditionally been associated with the cascade arrest or with the scale that separates turbulence and Rossby wave–dominated spectral ranges. It is shown that rather than being a measure of the inverse cascade arrest, LR is a characteristic of different processes in different flow regimes. In unsteady flows, LR can be identified with the moving energy front propagating toward the decreasing wavenumbers. When large-scale energy sink is present, β-plane turbulence may attain several steady-state regimes. Two of these regimes are highlighted: friction-dominated and zonostrophic. In the former, LR does not have any particular significance, while in the latter, the Rhines scale nearly coincides with the characteristic length associated with the large-scale friction. Spectral analysis in the frequency domain demonstrates that Rossby waves coexist with turbulence on scales smaller than LR thus indicating that the Rhines scale cannot be viewed as a crossover between turbulence and Rossby wave ranges.

Large-scale friction and wear tests on a hybrid UHMWPE-pad/primer coating combination used as bearing element in an extremely high-loaded ball-joint

The surfaces of a heavily loaded ball-joint were initially covered with a sliding spray and suffer wear. A solution is found by incorporating UHMWPE pads (Ultra high molecular weight polyethylene) with a carbon fibre/epoxy reinforced ring as sliding material into the chairs of the structure, while the steel ball-side is covered with a Zn-phosphate primer coating, protecting against corrosion. The local static and dynamic behaviour of the hybrid UHMWPE pads in contact with steel or Zn-coated counterfaces has been large-scale tested on loading capacity, low friction and wear resistance. For protection of the sliding counterface against wear, a polymer lip covering the carbon ring has been experimentally designed to flow over the carbon ring under high contact pressures, assuming the retained polymer disc under hydrostatic conditions. As such, the soft coating resists extremely high contact pressures (150 MPa) with good adhesion to the steel ball. However the application method should be carefully selected, sprayed coatings are the most favourable for low initial static friction. Calculated bulk and flashtemperatures revealed that the UHMWPE melting temperature is not exceeded, although softening of the coating under high contact pressures may be favourable for a ‘self-repairing’ ability. Pre-sliding creep and intermediate wear paths as manifesting in the ball-joint were simulated, indicating that the maximum design coefficient of friction is not exceeded. Test results are compared to FEM-calculations to verify the practical applicability of the modified sliding system.

Dispersive and friction-induced stabilization of the Cahn–Hilliard inverse cascade

We discuss the stabilization of the inverse cascade in the large-scale instability of the Kolmogorov flow described by the complete Cahn–Hilliard equation with inclusion of β effect, large-scale friction and deformation radius. The friction and the β values halting the inverse cascade at the various possible intermediate states are calculated by means of singular perturbation techniques and compared to the values resulting from numerical simulation of the complete Cahn–Hilliard equation. The excellent agreement validates the theory. Our main result is that the critical values of friction or β halting the inverse cascade scale exponentially as a function of the jet separation in the final flow, contrary to previous theories and phenomenological approach.

Universal n−5 spectrum of zonal flows on giant planets

The energy spectra of the observed zonal flows on Jupiter and Saturn are shown to obey the scaling law EZ(n)=CZ(Ω/R)2n−5 in the range of total wave numbers n not affected by large scale friction (here, Ω and R are the rotation rate and the radius of the planet, and CZ is an order-one constant). These spectra broadly resemble their counterpart in recent simulations of turbulent flows on the surface of a rotating sphere [Huang et al., Phys. Fluids 13, 225 (2001)] that represents a strongly anisotropic flow regime evoked by the planetary vorticity gradient. It is conjectured that this regime governs the large scale circulations and the multiple zonal jets on giant planets. The observed strong equatorial jets that were not produced in the nearly inviscid simulations by Huang et al. are attributed to the combined effect of the energy condensation in the lowest zonal modes and the large scale friction.

Phase transition in the passive scalar advection

The paper studies the behavior of the trajectories of fluid particles in a compressible generalization of the Kraichnan ensemble of turbulent velocities. We show that, depending on the degree of compressibility, the trajectories either explosively separate or implosively collapse. The two behaviors are shown to result in drastically different statistical properties of scalar quantities passively advected by the flow. At weak compressibility, the explosive separation of trajectories induces a familiar direct cascade of the energy of a scalar tracer with a short-distance intermittency and dissipative anomaly. At strong compressibility, the implosive collapse of trajectories leads to an inverse cascade of the tracer energy with suppressed intermittency and with the energy evacuated by large-scale friction. A scalar density whose advection preserves mass exhibits in the two regimes opposite cascades of the total mass squared. We expect that the explosive separation and collapse of Lagrangian trajectories occur also in more realistic high Reynolds number velocity ensembles and that the two phenomena play a crucial role in fully developed turbulence.

Preseismic slip in a large scale friction experiment : Dieterich, J H; Barber, D W; Conrad, G Proc 19th US Symposium on Rock Mechanics, Stateline, Nevada, 1–3 May 1978, V1, P110–117. Publ Reno: University of Nevada, 1978

Preseismic slip in a large scale friction experiment : Dieterich, J H; Barber, D W; Conrad, G Proc 19th US Symposium on Rock Mechanics, Stateline, Nevada, 1–3 May 1978, V1, P110–117. Publ Reno: University of Nevada, 1978