Compensator Designed for Electro-Hydraulic Servo System in Laminar State

The study researched the orifice flow equation when the flow state of the orifice is laminar. Based on the novel flow equation and the expected linear flow equation, a compensator is designed to compensate the non-linearity and make the flow characteristics linear. The characteris-tics experiment result shows that the flow after compensa-tion control is close to the expected flow, in which the pres-sure difference was increased from 0.5MPa to 4MPa, and the error is less than 20%. When the compensator is used as feed forward control in the EHSS and compound with proportional (P) control, the sinusoidal response error with frequency of 0.5Hz and amplitude of 5mm is within 0.4mm under large external load. While the error of the uncompensated system is up to 0.8mm. The compensator can be used into the electro-hydraulic system with larger load disturbance and improve the control performance compounded with the simplest proportional (P) controller.

Flow visualization and skin friction determination in transitional channel flow

The present study experimentally determines the transitional Reynolds number range for plane channel flow and characterizes its transitional state. The pressure along the channel is measured to determine the skin friction coefficient as function of Reynolds number from the laminar state, through the transitional region into the fully turbulent state. The flow structure was studied through flow visualisation which shows that as the Reynolds number increases from the laminar state the transitional region starts showing randomly occurring turbulent spots. With increasing Reynolds number the spots shift into oblique patches and bands of small scale turbulence that form across the channel width, together with large-scale streaky structures found in areas between the turbulent regions. An image analysing technique was used to determine the intermittency factor, i.e. the turbulence fraction in the flow, as function of Reynolds number. It is found that the skin friction coefficient reaches its turbulent value before the flow is fully turbulent (the intermittency factor is still below one). This suggests that the observed streaky structures in non-turbulent regions contribute to the enhancement of the wall-normal transfer of momentum. Also above the Reynolds numbers where the turbulent skin friction coefficient has been established large-scale features consisting of irregular streaky structures are found. They have an oblique shape similar to the non-turbulent and turbulent patches in the transitional flow indicating that the transition process is not fully complete even above the Reynolds number where the skin friction reaches its turbulent level. Graphic abstract

Experimental Analysis of The Effect of Hydrophobic Coating on Pressure Drop in Small Pipes

In this paper, experimental results are reported to quantify the effect of hydrophobic coating LT-8 on frictional drag of water flow in pipes of 450 mm length. Five pipes of 1, 2, 3, 4, and 5 mm inner diameter were tested. The results from 1, 2 and 3 mm diameter pipes demonstrated an average frictional drag reduction of 9%, 11.5% and 3%, respectively, while the results from 4mm and 5mm pipes showed an increase in frictional drag of 12% and 10%, respectively. The 2mm and 4mm pipes were also tested with a half application of hydrophobic coating. The half coated 2mm pipe showed decrease in drag while 4mm pipe showed increase in drag. The results indicate a relationship between drag reduction/ increase within the percentage of coated surface. The main conclusions are, the flow changed from laminar state to the liquid-air wetting surface condition (Cassie-Baxter wetting state) at the pipe surface and then destabilized by the turbulent boundary layer and entered the liquid wetting surface (Wenzel wetting state) will be appeared. This transition lead to a reduction in friction drag for laminar flow condition and increase in drag for turbulent flow condition.

Computational Fluid Dynamics modelling of sedimentation on Mars

<p>Gravity affects sedimentation of particles suspended in water and gases in two ways: directly by the gravitational force that pulls a particle towards the surface and indirectly by the flow conditions of water or gas around the particles. The latter create a drag which is affected by the settling velocity. Consequently, drag coefficients observed on Earth sand-sized particles cannot be used on Mars because they are likely to overestimate the drag generated by the turbulent flow around the particle on Earth may shift into a more laminar state that generates lower drag. The effect of gravity on settling velocity is not linearly related to particle size, which may affect the sorting of the sand grains deposited from running water.  Experiments carried out during parabolic flights at reduced gravity indicate that the potential error in particle settling and sorting is significant, i.e. leading to wrong interpretations of the flow velocities at the time of deposition. This in turn has implications for reconstruction of Martian environmental conditions from rock textures determined from close-up imagery. This study uses computational fluid dynamics (CFD) modelling to independently assess the effect of gravity on sediment settling velocities and sediment sorting. The CFD modelling also offers a wide capability for reconstruction sedimentation on Mars and thus supports the reconstruction of it’s environmental past, as well as the search for traces of life. </p>

Simple advecting structures and the edge of chaos in subcritical tokamak plasmas

In tokamak plasmas, sheared flows perpendicular to the driving temperature gradients can strongly stabilise linear modes. While the system is linearly stable, regimes with persistent nonlinear turbulence may develop, i.e. the system is subcritical. A perturbation with small but finite amplitude may be sufficient to push the plasma into a regime where nonlinear effects are dominant and thus allow sustained turbulence. The minimum threshold for nonlinear instability to be triggered provides a criterion for assessing whether a tokamak is likely to stay in the quiescent (laminar) regime. At the critical amplitude, instead of transitioning to the turbulent regime or decaying to a laminar state, the trajectory will map out the edge of chaos. Surprisingly, a quasi-travelling-wave solution is found as an attractor on this edge manifold. This simple advecting solution is qualitatively similar to, but simpler than, the avalanche-like bursts seen in earlier turbulent simulations and provides an insight into how turbulence is sustained in subcritical plasma systems. For large flow shearing rate, the system is only convectively unstable, and given a localised initial perturbation, will eventually return to a laminar state at a fixed spatial location.

Transition in the asymptotic suction boundary layer over a heated plate

The asymptotic suction boundary layer (ASBL) is a parallel shear flow that becomes turbulent in a bypass transition in parameter regions where the laminar profile is stable. We here add a temperature gradient perpendicular to the plate and explore the interaction between convection and shear in determining the transition. We find that the laminar state becomes unstable in a subcritical bifurcation and that the critical Rayleigh number and wavenumber depend strongly on the Prandtl number. We also track several secondary bifurcations and identify states that are localized in two directions, showing different symmetries. In the subcritical regime, transient turbulent states which are connected to exact coherent states and follow the same transition scenario as found in linearly stable shear flows are identified and analysed. The study extends the bypass transition scenario from shear flows to thermal boundary layers and highlights the intricate interactions between thermal and shear forces.

Disruption of states by a stable stratification

We identify ‘minimal seeds’ for turbulence, i.e. initial conditions of the smallest possible total perturbation energy density $E_{c}$ that trigger turbulence from the laminar state, in stratified plane Couette flow, the flow between two horizontal plates of separation $2H$, moving with relative velocity $2{\rm\Delta}U$, across which a constant density difference $2{\rm\Delta}{\it\rho}$ from a reference density ${\it\rho}_{r}$ is maintained. To find minimal seeds, we use the ‘direct-adjoint-looping’ (DAL) method for finding nonlinear optimal perturbations that optimise the time-averaged total dissipation of energy in the flow. These minimal seeds are located adjacent to the edge manifold, the manifold in state space that separates trajectories which transition to turbulence from those which eventually decay to the laminar state. The edge manifold is also the stable manifold of the system’s ‘edge state’. Therefore, the trajectories from the minimal seed initial conditions spend a large amount of time in the vicinity of some states: the edge state; another state contained within the edge manifold; or even in dynamically slowly varying regions of the edge manifold, allowing us to investigate the effects of a stable stratification on any coherent structures associated with such states. In unstratified plane Couette flow, these coherent structures are manifestations of the self-sustaining process (SSP) deduced on physical grounds by Waleffe (Phys. Fluids, vol. 9, 1997, pp. 883–900), or equivalently finite Reynolds number solutions of the vortex–wave interaction (VWI) asymptotic equations initially derived mathematically by Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666). The stratified coherent states we identify at moderate Reynolds number display an altered form from their unstratified counterparts for bulk Richardson numbers $\mathit{Ri}_{B}=g{\rm\Delta}{\it\rho}H/({\it\rho}_{r}{\rm\Delta}U^{2})=O(\mathit{Re}^{-1})$, and exhibit chaotic motion for larger $\mathit{Ri}_{B}$. We demonstrate that at hith Reynolds number the suppression of vertical motions by stratification strongly disrupts input from the waves to the roll velocity structures, thus preventing the waves from reinforcing the viscously decaying roll structures adequately, when $\mathit{Ri}_{B}=O(\mathit{Re}^{-2})$.

Minimal-energy perturbations rapidly approaching the edge state in Couette flow

Transition to turbulence in shear flows is often subcritical, thus the dynamics of the flow strongly depends on the shape and amplitude of the perturbation of the laminar state. In the state space, initial perturbations which directly relaminarize are separated from those that go through a chaotic trajectory by a hypersurface having a very small number of unstable dimensions, known as the edge of chaos. Even for the simple case of plane Couette flow in a small domain, the edge of chaos is characterized by a fractal, folded structure. Thus, the problem of determining the threshold energy to trigger subcritical transition consists in finding the states on this complex hypersurface with minimal distance (in the energy norm) from the laminar state. In this work we have investigated the minimal-energy regions of the edge of chaos, by developing a minimization method looking for the minimal-energy perturbations capable of approaching the edge state (within a prescribed tolerance) in a finite target time $T$. For sufficiently small target times, the value of the minimal energy has been found to vary with $T$ following a power law, whose best fit is given by $E_{min}\propto T^{-1.75}$. For large values of $T$, the minimal energy achieves a constant value which corresponds to the energy of the minimal seed, namely the perturbation of minimal energy asymptotically approaching the edge state (Rabin et al., J. Fluid Mech., vol. 738, 2012, R1). For $T\geqslant 40$, all of the symmetries of the edge state are broken and the minimal perturbation appears to be localized in space with a basic structure composed of scattered patches of streamwise velocity with inclined streamwise vortices on their flanks. Finally, we have found that minimal perturbations originate in a small low-energy zone of the state space and follow very fast similar trajectories towards the edge state. Such trajectories are very different from those of linear optimal disturbances, which need much higher initial amplitudes to approach the edge state. The time evolution of these minimal perturbations represents the most efficient path to subcritical transition for Couette flow.

Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow

The present work provides an optimal control strategy, based on the nonlinear Navier–Stokes equations, aimed at hampering the rapid growth of unsteady finite-amplitude perturbations in a Blasius boundary-layer flow. A variational procedure is used to find the blowing and suction control law at the wall providing the maximum damping of the energy of a given perturbation at a given target time, with the final aim of leading the flow back to the laminar state. Two optimally growing finite-amplitude initial perturbations capable of leading very rapidly to transition have been used to initialize the flow. The nonlinear control procedure has been found able to drive such perturbations back to the laminar state, provided that the target time of the minimization and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier–Stokes equations has been found much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered. Regions of strong sensitivity to blowing and suction have been also identified for the given initial perturbations: when the control is actuated in such regions, laminarization is also observed for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternating wall-normal velocity perturbations, which appear to modify the core flow structures by means of two distinct mechanisms: (i) a wall-normal velocity compensation at small times; (ii) a rotation-counterbalancing effect al larger times. Similar control laws have been observed for different target times, values of the cost parameter, and streamwise extents of the blowing and suction zone, meaning that these two mechanisms are robust features of the optimal control strategy, provided that the nonlinear effects are taken into account.

RANS Modelling of Accelerating Boundary Layers

A numerical investigation of accelerated boundary layers (BL) has been performed using linear and non-linear eddy viscosity models (EVM). The acceleration parameters (KS) investigated range between 1.5×10−6 and 3.0×10−6. The one equation (k-l), Spalart Allmaras (SA) and the two-equation Menter SST and Chien models in their standard forms are found to be insensitive to acceleration. Nevertheless, proposed modifications for the SA, Chien and the k-l models significantly improved predictions. The major improvement was achieved by modifying the damping functions in these models and also an analogous source term, E, for the Chien model. Encouraging agreement with measurements is found using the Launder Sharma (LS), Cubic and Explicit Algebraic Stress Models (EASM) in their standard forms. The cubic model best predicted the turbulence quantities. Investigations confirm that it is practical for Reynolds Average Navier-Stokes (RANS) models to capture reversion from the turbulent to laminar state albeit for equilibrium sink type flows.