It is well established that when a turbulent flow is subjected to a non-uniform body force, the turbulence may be significantly suppressed in comparison with that of the flow of the same flow rate ...and hence the flow is said to be laminarised. This is the situation in buoyancy-aided mixed convection when severe heat transfer deterioration may occur. Here we report results of direct numerical simulations of flow with a linear or a step-change profile of body force. In contrast to the conventional view, we show that applying a body force to a turbulent flow while keeping the pressure force unchanged causes little changes to the key characteristics of the turbulence. In particular, the mixing characteristics of the turbulence represented by the turbulent viscosity remain largely unaffected. The so-called flow laminarisation due to a body force is in effect a reduction in the apparent Reynolds number of the flow, based on an apparent friction velocity associated with only the pressure force of the flow (i.e. excluding the contribution of the body force). The new understanding allows the level of the flow ‘laminarisation’ and when the full laminarisation occurs to be readily predicted. In terms of the near-wall turbulence structure, the numbers of ejections and sweeps are little influenced by the imposition of the body force, whereas the strength of each event may be enhanced if the coverage of the body force extends significantly away from the wall. The streamwise turbulent stress is usually increased in accordance with the observation of more and stronger elongated streaks, but the wall-normal and the circumferential turbulent stresses are largely unchanged.
It has previously been shown that the transient flow in a channel following a step increase of Reynolds number from 2800 to 7400 (based on channel half-height and bulk velocity) is effectively a ...laminar–turbulent bypass transition even though the initial flow is turbulent (He & Seddighi, J. Fluid Mech., vol. 715, 2013, pp. 60–102). In this paper, it is shown that the transient flow structures exhibit strong contrasting characteristics in large and small flow perturbation scenarios. When the increase of Reynolds number is large, the flow is characterized by strong elongated streaks during the initial period, followed by the occurrence and spreading of isolated turbulent spots, as shown before. By contrast, the flow appears to evolve progressively and the turbulence regeneration process remains largely unchanged during the flow transient when the Reynolds number ratio is low, and streaks do not appear to play a significant role. Despite the major apparent differences in flow structures, the transient flow under all conditions considered is unambiguously characterized by laminar–turbulent transition, which exhibits itself clearly in various flow statistics. During the pre-transition period, the time-developing boundary layers in all the cases show a strong similarity to each other and follow closely the Stokes solution for a transient laminar boundary layer. The streamwise fluctuating velocity also shows good similarity in the various cases, irrespective of the appearance of elongated streaks or not, and the maximum energy growth exhibits a linear rate similar to that in a spatially developing boundary layer. The onset of transition is clearly definable in all cases using the minimum friction factor, and the critical time thus defined is strongly correlated with the free-stream turbulence in a power-law form.
Direct numerical simulations (DNS) are performed of a transient channel flow following a rapid increase of flow rate from an initially turbulent flow. It is shown that a low-Reynolds-number turbulent ...flow can undergo a process of transition that resembles the laminar–turbulent transition. In response to the rapid increase of flow rate, the flow does not progressively evolve from the initial turbulent structure to a new one, but undergoes a process involving three distinct phases (pre-transition, transition and fully turbulent) that are equivalent to the three regions of the boundary layer bypass transition, namely, the buffeted laminar flow, the intermittent flow and the fully turbulent flow regions. This transient channel flow represents an alternative bypass transition scenario to the free-stream-turbulence (FST) induced transition, whereby the initial flow serving as the disturbance is a low-Reynolds-number turbulent wall shear flow with pre-existing streaky structures. The flow nevertheless undergoes a ‘receptivity’ process during which the initial structures are modulated by a time-developing boundary layer, forming streaks of apparently specific favourable spacing (of about double the new boundary layer thickness) which are elongated streamwise during the pre-transitional period. The structures are stable and the flow is laminar-like initially; but later in the transitional phase, localized turbulent spots are generated which grow spatially, merge with each other and eventually occupy the entire wall surfaces when the flow becomes fully turbulent. It appears that the presence of the initial turbulent structures does not promote early transition when compared with boundary layer transition of similar FST intensity. New turbulent structures first appear at high wavenumbers extending into a lower-wavenumber spectrum later as turbulent spots grow and join together. In line with the transient energy growth theory, the maximum turbulent kinetic energy in the pre-transitional phase grows linearly but only in terms of ${u}^{\ensuremath{\prime} } $, whilst ${v}^{\ensuremath{\prime} } $ and ${w}^{\ensuremath{\prime} } $ remain essentially unchanged. The energy production and dissipation rates are very low at this stage despite the high level of ${u}^{\ensuremath{\prime} } $. The pressure–strain term remains unchanged at that time, but increases rapidly later during transition along with the generation of turbulent spots, hence providing an unambiguous measure for the onset of transition.
The turbulence behaviour of current-dominated pulsating flows has been investigated. Direct numerical simulations have been carried out for Stokes lengths over a range of $l_s^+=5\unicode{x2013}26$, ...and amplitudes spanning 90 % of the current-dominated regime, about a mean flow of $\overline {Re}=6275$. The results show that the turbulence response in intermediate and low-frequency pulsations is governed by a multistage turbulent–turbulent transition process, which bears a strong similarity to the multistage response of non-periodic acceleration. During the early acceleration period, the flow enters a pretransition stage, in which a new laminar perturbation boundary layer forms at the wall, and the streamwise velocity streaks are stretched. If the low-speed streaks destabilise prior to the deceleration period, then the flow enters a transition stage in which the perturbation boundary layer undergoes a bypass-like transition process. A unique feature of pulsating flows is the ongoing mechanism of turbulence decay, which initiates during the deceleration period and constitutes the main transient turbulence mechanism for much of the cycle. For high-frequency pulsations, the perturbation boundary layer fails to reach the pretransition stage prior to the deceleration period. Instead, the flow alternates between two inertial stages which are characterised by two layers of amplified viscous force; one growing at the wall, and one detached and moving towards the core.
In this work, a green and efficient procedure is reported for the preparation of N,N'-diarylformamidines, benzoxazoles, benzothiazoles, and benzimidazoles using nanoporous TiO2 containing an ionic ...liquid bridge. This reagent is prepared via the modification of nanoporous TiO2 with bis-3-(trimethoxysilylpropyl)-ammonium hydrogen sulfate (TiO2-bip-NH2+ HSO4−). The procedure gave the products in excellent yields in very short reaction times under solvent-free conditions. The reusability of the catalyst is the other important feature of the reported method.
We report new laboratory experiments of a flow accelerating from an initially turbulent state following the opening of a valve, together with large eddy simulations of the experiments and extended ...Stokes first problem solutions for the early stages of the flow. The results show that the transient flow closely resembles an accelerating laminar flow superimposed on the original steady turbulent flow. The primary consequence of the acceleration is the temporal growth of a boundary layer from the wall, gradually leading to a strong instability causing transition. This extends the findings of previous direct numerical simulations of transient flow following a near-step increase in flow rate. In this interpretation, the initial turbulence is not the primary characteristic of the resulting transient flow, but can be regarded as noise, the evolution of which is strongly influenced by the development of the boundary layer. We observe the spontaneous appearance of turbulent spots and discontinuities in the velocity signals in time and space, revealing rich detail of the transition process, including a striking contrast between streamwise and wall-normal fluctuating velocities.
•Results of DNS of transient flow in a pipe are compared with those in a channel.•The transient pipe flow is a laminar–turbulent bypass transition even the initial flow is turbulent.•Correlation ...between transition Re and free stream turbulence is the same in pipe and channel.•Responses in channel and pipe are the same near the wall but somewhat different in the core.
Direct numerical simulation (DNS) is conducted to study the transient flow in a pipe following a near-step increase of flow rate from an initial turbulent flow. The results are compared with those of the transient flow in a channel reported in He and Seddighi (2013). It is shown that the flow again exhibits a laminar–turbulent transition, similar to that in a channel. The behaviours of the flow in a pipe and a channel are the same in the near-wall region, but there are significant differences in the centre of the flow. The correlation between the critical Reynolds number and free stream turbulence previously established for a channel flow has been shown to be applicable to the pipe flow. The responses of turbulent viscosity, vorticity Reynolds number, and budget terms are analysed. Some significant differences have been found to exist between the developments of the vorticity Reynolds number in the pipe and channel flows.
•Major features of unsteady flow are identified from DNS results.•Performance of turbulence models are assessed against these features.•Launder and Sharma (1974) 36 and Langtry and Menter’s (2009) ...transition SST are best models.•Chang et al. (1995) 28 is also good but can be unstable sometimes.
The performance of a number of low-Reynolds number turbulence models is evaluated against direct numerical simulations (DNS). All models are applied to an unsteady flow comprising a ramp-type excursion of flow rate inside a closed channel. The flow rate is increased linearly with time from an initial Reynolds number of 9308 (based on hydraulic diameter and bulk velocity) to a final Reynolds number of 29,650. The acceleration rate is varied to cover low, intermediate and high accelerations. It is shown that among the models investigated, the k–ε models of Launder and Sharma (1974) and Chang et al. (1995) 28 and the γ–Reθ transition model of Langtry and Menter (2009) 38 capture well the key flow features of these unsteady turbulent flows. For the cases of low and intermediate acceleration rates, these three models yield predictions of wall shear stress that agree well with the corresponding DNS data. For the case of high acceleration, the γ–Reθ model of Langtry and Menter (2009) 38 and the k–ε model of Launder and Sharma (1974) yield reasonable predictions of wall shear stress.
A direct numerical simulation investigation of a transient flow in a channel with a smooth top wall and a roughened bottom wall made of close-packed pyramids is presented. An initially stationary ...turbulent flow is accelerated rapidly to a new flow rate and the transient flow behaviour after the acceleration is studied. The equivalent roughness heights of the initial and final flows are
$k_{s}^{+}=14.5$
and 41.5, respectively. Immediately after the acceleration ends, the induced change behaves in a ‘plug-flow’ manner. Above the roughness crests, the additional velocity due to the perturbation flow is uniform; below the crest, it reduces approximately linearly to zero at the bottom of the roughness elements. The interaction of the perturbation flow with the rough wall is characterised by a series of events that resemble those observed in roughness-induced laminar–turbulent transitions. The process has two broad stages. In the first of these, large-scale vortices, comparable in extent to the roughness wavelength, develop around each roughness element and high-speed streaks form along the ridge lines of the elements. After a short time, each vortex splits into two, namely (i) a standing vortex in front of the element and (ii) a counter-rotating hairpin vortex behind it. The former is largely inactive, but the latter advects downstream with increasing strength, and later lifts away from the wall. These hairpin vortices wrap around strong low-speed streaks. The second stage of the overall process is the breakdown of the hairpin vortices into many smaller multi-scale vortices distributed randomly in space, leading eventually to a state of conventional turbulence. Shortly after the beginning of the first stage, the three components of the r.m.s of the velocity fluctuation all increase significantly in the near-wall region as a result of the vortical structures, and their spectra bear strong signatures of the surface topology. During the second stage, the overall turbulence energy in this region varies only slightly, but the spectrum evolves significantly, eventually approaching that of conventional turbulence. The direct effect of roughness on the flow is confined to a region up to approximately three element heights above the roughness crests. Turbulence in the core region does not begin to increase until after the transition near the wall is largely complete. The processes of transition over the smooth and rough walls of the channel are practically independent of each other. The flow over the smooth wall follows a laminar–turbulent transition and, as known from previous work, resembles a free-stream turbulence-induced boundary layer bypass transition.
OBJECTIVE To determine the minimum infusion rate (MIR) of propofol required to prevent movement in response to a noxious stimulus in dogs anesthetized with propofol alone or propofol in combination ...with a constant rate infusion (CRI) of ketamine. ANIMALS 6 male Beagles. PROCEDURES Dogs were anesthetized on 3 occasions, at weekly intervals, with propofol alone (loading dose, 6 mg/kg; initial CRI, 0.45 mg/kg/min), propofol (loading dose, 5 mg/kg; initial CRI, 0.35 mg/kg/min) and a low dose of ketamine (loading dose, 2 mg/kg; CRI, 0.025 mg/kg/min), or propofol (loading dose, 4 mg/kg; initial CRI, 0.3 mg/kg/min) and a high dose of ketamine (loading dose, 3 mg/kg; CRI, 0.05 mg/kg/min). After 60 minutes, the propofol MIR required to prevent movement in response to a noxious electrical stimulus was determined in duplicate. RESULTS Least squares mean ± SEM propofol MIRs required to prevent movement in response to the noxious stimulus were 0.76 ± 0.1 mg/kg/min, 0.60 ± 0.1 mg/kg/min, and 0.41 ± 0.1 mg/kg/min when dogs were anesthetized with propofol alone, propofol and low-dose ketamine, and propofol and high-dose ketamine, respectively. There were significant decreases in the propofol MIR required to prevent movement in response to the noxious stimulus when dogs were anesthetized with propofol and low-dose ketamine (27 ± 10%) or with propofol and high-dose ketamine (30 ± 10%). CONCLUSIONS AND CLINICAL RELEVANCE Ketamine, at the doses studied, significantly decreased the propofol MIR required to prevent movement in response to a noxious stimulus in dogs.
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