Quasi-steady Regime Research Articles

Yield-stress effects on spontaneous imbibition in paper-based kits

The classic Richards equation is a good model for predicting imbibition of viscous fluids in porous materials such as dry soils or filter papers. It cannot, in principle, be used for physiological fluids such as blood simply because such fluids often exhibit a variety of non-Newtonian behavior such as a yield stress. In the present work, we have theoretically extended the classic Richards equation to viscoplastic fluids obeying the Bingham model using the concept of the effective viscosity together with the bundle-of-tube model. The new imbibition model could partly resolve the discrepancy reported in the literature between the predictions of the classic Richards equation for the stain growth of sessile blood droplets in a typical filter paper. A better fit, however, requires considering other non-Newtonian effects of the blood such as its viscoelasticity. Using the Bingham-modified Richards equation, it is demonstrated that yield stress in a test fluid has a retarding effect on the imbibition phenomenon, so that such fluids may not necessarily reach the test line of a paper-based diagnostic kit. But yield stress is predicted to extend the duration of the quasi-steady regime on the test line of diagnostic kits, which is a desirable effect. The results suggest that inducing (or elevating) the level of yield stress in a test liquid such as blood can be used as a passive means to control imbibition characteristics in paper-based systems.

Experimental investigation of three-dimensional Rayleigh–Taylor instability of a gaseous interface

Validating the theoretical work on Rayleigh–Taylor instability (RTI) through experiments with an exceptionally clean and well-characterized initial condition has been a long-standing challenge. Experiments were conducted to study the three-dimensional RTI of an SF $_6$ –air interface at moderate Atwood numbers. A novel soap film technique was developed to create a discontinuous gaseous interface with controllable initial conditions. Spectrum analysis revealed that the initial perturbation of the soap film interface is half the size of an entire single-mode perturbation. The correlation between the initial interface perturbation and Atwood numbers was determined. Due to the steep and highly curved feature of the initial soap film interface, the early-time evolution of RTI exhibits significant nonlinearity. In the quasi-steady regime, various potential flow models accurately predict the late-time bubble velocities by considering the channel width as the perturbation wavelength. Differently, the late-time spike velocities are described by these potential flow models using the wavelength of the entire single-mode perturbation. These findings indicate that the bubble evolution is influenced primarily by the spatial constraint imposed by walls, while the spike evolution is influenced mainly by the initial curvature of the spike tip. Consequently, a recent potential flow model was adopted to describe the time-varying amplitude growth induced by RTI. Furthermore, the self-similar growth factors for bubbles and spikes were determined from experiments and compared with existing studies, revealing that a large amplitude in the initial soap film interface promotes the spike development.

Turbulent Pulsating Convective Flow in the Quasi-Steady and Low-Frequency Regimes

Abstract The instantaneous and time-averaged dynamics of turbulent pulsating convective pipe flow is investigated experimentally over Strouhal number, St=3.3×10−4−0.12 that falls in the quasi-steady and low-frequency regimes, pulsation amplitude, βb=0.05−0.2, and bulk Reynolds numbers, Reb=7528−10,920. The analytical expressions for pulsation amplitudes of centerline velocity, bulk velocity, and Nusselt number are derived. The time series of oscillating components of centerline velocity (Uc˜), cross-sectionally averaged bulk velocity (Ub˜), and Nusselt number (Nu˜) depicts that the phase differences between Uc˜, and Ub˜, and between Ub˜, and Nu˜ increase with St nonmonotonically with near zero phase difference at St→0. The time-averaged pulsating Nusselt number Nu¯ is invariant of St for St > 0.01. Nu¯ depends marginally on βb. The relative mean Nusselt number, Nur=Nu¯/Nus<1 for Reb≥8885 and Nur>1 for Reb = 7528. The general observations from this study is that, in the quasi-steady and low-frequency regimes, turbulent pulsating flows leads to marginal changes in the time-averaged Nusselt number Nu¯ compared to the time-averaged Nusselt number Nus in steady flow condition at any Reb.

On the effectiveness of Reynolds-averaged and subgrid scale models in predicting flows inside car cabins

The aim of the present study is to analyze the performances of unsteady Reynolds-averaged Navier–Stokes (URANS) and large eddy simulation (LES) approaches in predicting the airflow patterns inside car cabins and to give insight in the design of computational fluid dynamics simulations of a real car cabin. For this purpose, one eddy viscosity-based turbulence model (shear stress transport k–ω) and two subgrid scale models (wall-adapting local eddy-viscosity and dynamic kinetic energy) were tested, and numerical results were compared with particle image velocimetry measurements carried out on a commercial car. The URANS model exhibited great accuracy in predicting the mean flow behavior and was appreciably outperformed by the LES models only far from the inlet sections. For this reason, it was deemed suitable for conducting further analyses, aimed at characterizing the airflow patterns in winter and summer conditions and performing a thermal comfort analysis. The thermal regime was found to have a very little effect on the air flow patterns, once the quasi-steady state regime is achieved; in fact, both in winter and in summer, the temperature field is fairly uniform within the car cabin, making the contribution of buoyancy negligible and velocity fields to be very similar in the two seasons. Findings also reveal that thermal comfort sensation can be different for passengers sharing the same car but sitting on different seats; this aspect should be considered when designing and operating the ventilation system, since the minimum comfort requirements should be met for all the occupants.

Hydrodynamic damping in laminar, transient and turbulent regimes: Analytical and computational study

A study of oscillating flow over a flat plate using RANS modeling was conducted to investigate hydrodynamic damping and its correlation with the unsteady and oscillating boundary layer. It is found that the predictions with the γ SST turbulence model was more consistent with the experimental results compared to the SST turbulence models. Two distinct damping behaviors were observed in the flow. For Reδ<400, the damping remained constant and matched the laminar solution of Stokes’ second problem. In this scenario, the flow regime was quasi-laminar, and an increase in free-stream velocity did not lead to a rise in the fluid damping coefficient. Conversely, for Reδ>400, the increase in Reδ induced turbulence during the deceleration phase, resulting in an amplification of the phase difference between displacement and wall shear stress, consequently increasing damping. This trend continued at higher values of Reδ and during the quasi-steady regime. The results indicated that the existence of different damping regions, as reported in previous studies, occurred within a range similar to that of Stokes’ second problem. A transition in the boundary layer regime at higher Reδ could be a contributing factor to the variations in damping behavior.

The alarming state of Central Chile's groundwater resources: A paradigmatic case of a lasting overexploitation

Ensuring water supply under climate change scenarios is a global concern, and groundwater resources play a crucial role. Aquifer depletion is a worldwide trend, and Chile is no exception. Through a statistical approach with strong hydrogeological criteria, the groundwater overexploitation phenomenon is studied in Central Chile, the most populated region in this mountainous country. With this purpose, we assess the evolution of groundwater levels and pumping between 1970 and 2020 by analysing 26,065 groundwater rights and 222 observation wells. Withdrawals increased from 498 hm3 in 1970 to 8883 hm3 in 2020. We recognised two general trends in groundwater levels: a quasi-steady state hydrodynamic regime pre-1988 and sustained decline post-1988, exacerbated since 2010 with the start of the Megadrought. Although groundwater recharge is expected to decrease during this severe drought, the declining trend strongly correlates with pumping but not with precipitation changes. Climate forcing is usually invoked to warrant the dramatic depletion of groundwater resources, but we demonstrated that all analysed aquifers have been overexploited since much earlier than 2010. Finally, the Chilean aquifers' overexploitation is a clear example of the consequences of prioritising the water offer over the water demand regulation, which hinders the United Nations' sustainable development goals accomplishment.

The interaction of gravity currents in a porous layer with a finite edge

The interactions of upper (lighter) and lower (heavier) gravity currents are closely related to fluid-phase resource recovery in porous layers and cleaning of confined spaces. The addition of a second current increases the sweep efficiency of fluid displacement. In this paper, we first derive two ordinary differential equations to describe the interaction of gravity currents in the quasi-steady regime. Two asymptotic regimes are identified, characterised by whether or not the two currents attach to each other, depending on whether the source fluxes are large enough. In the attached regime, a symmetry condition is also identified that describes whether or not the pumping and buoyancy forces balance each other. The model also leads to analytical solutions for the interface shape of the interacting currents in both the detached and attached regimes and for both symmetric and asymmetric currents. For symmetric currents, analytical solutions can also be obtained for the pressure distribution along cap rocks and the sweep efficiency of flooding processes. A particularly interesting aspect is that the displaced fluid remains quiescent at any steady state, regardless of whether the currents attach to each other. Correspondingly, the interface shape of the currents can be described by relatively simple equations and solutions, as if the currents propagate independently in unconfined porous layers. Time transition towards quasi-steady solutions is provided, employing time-dependent numerical solutions of two coupled partial differential equations for dynamic current interaction.

Wavelet analysis of the flow field around an oscillating airfoil undergoing pure pitching motion at low Reynolds number

This paper investigates the flow field around a NACA (National Advisory Committee for Aeronautics) 0012 airfoil undergoing pure pitching motion using continuous wavelet transform. Wind tunnel experiments were performed with a test-stand that provides a wide range of oscillation frequencies (f = 0–10 Hz). Sinusoidal pure pitching motion was considered with respect to the quarter chord for five reduced frequencies (K = 0.05, 0.1, 0.15, 0.2, and 0.3) at a Reynolds number of Re = 6 × 104. Mean angle of attack and pitch amplitude for all the cases were considered 0° and 6°, respectively. Unsteady surface pressure measurement was conducted, and the lift coefficient was calculated based on the phase-averaged surface pressure coefficient. The unsteady velocity distributions in the airfoil wake have been measured employing a pressure rake. The results indicate that the maximum value of the lift coefficient decreases by increasing the reduced frequency due to the “apparent mass” effects. For K = 0.05, close to the quasi-steady regime, the cl-α loop approximately follows the trend of the static case. Wavelet transform was used as a tool to examine the surface and wake pressure time series. Surface pressure wavelet transform plots indicate the presence of oscillation frequency and its superharmonics. Moreover, surface pressure wavelet analysis shows that the third and higher superharmonic frequencies are sensitive to the airfoil pitch angle during the oscillation cycle. Wavelet transform on wake reveals that the effective wake width gets smaller by increasing the reduced frequency. Furthermore, the trailing edge vortices get weaker by increasing the reduced frequency.

Natural convection due to surface cooling in sloping water bodies with vegetation

Natural convection induced by surface cooling in sloping water bodies with vegetation is investigated numerically. The sloping water body consists of a vegetated region with a bottom slope equal to 0.1 and a deep region with a horizontal bottom. The volume-averaged Navier–Stokes equations together with the volume-averaged energy equation are solved numerically in the vegetated region. Submerged vegetation has an equivalent porosity of 0.85. The vegetation length is either equal to the total or half the sloping region. A differential cooling is applied at the top free surface with a varying heat loss rate between the two regions. The non-vegetated sloping water body is also considered for validation purposes. The results indicate that, when cooling is reduced in the vegetated region (a) there is a time delay for the establishment of the quasi-steady regime and (b) the exchange flow rate and the gravity current's velocity decreases with increasing vegetation length. When cooling is completely blocked, different circulation patterns are developed.

Applying reinforcement learning to mitigate wake-induced lift fluctuation of a wall-confined circular cylinder in tandem configuration

The flow around two tandem circular cylinders leads to significant lift fluctuation in the downstream cylinder owing to periodic vortex shedding. To address such research issues, we present herein a numerical study that uses deep reinforcement learning to perform active flow control (AFC) on two tandem cylinders with a low Reynolds number of 100, where the actuator causes the rotation of the downstream cylinder. First, the cylinder center spacing ratio L* varies from 1.5 to 9.0, and the variation of L* leads to the quasi-steady reattachment regime (L*≤3.5) and the co-shedding regime (L*≥4.0). The fluctuating lift of the downstream cylinder is maximum when L*=4.5. Next, we train an optimal AFC strategy that suppresses 75% of the lift fluctuation in the downstream cylinder. This approach differs from using direct-opposition control to change the vortex-shedding frequency or strength, as reported in previous studies. This strategy modifies the phase difference between the lift fluctuations of the two cylinders by delaying the merging with the upstream cylinder wake and accelerating the formation of recirculating bubbles after the vortex merging. With the new phase difference, the effect of the additional lift from the upstream cylinder is significantly mitigated. The results of the dynamic mode decomposition show that the vortices surrounding the downstream cylinder in mode 1 that contribute to the lift fluctuation are weakened. To the best of our knowledge, this investigation can provide new ideas and physical insights into the problem of AFC under disturbed incoming flow.

Molecular dynamics simulations of unsteady evaporation of thin liquid argon layer into a vacuum

The unsteady evaporation of liquid argon layer into a vacuum was studied based on molecular dynamics technique using the LAMMPS package. The comparison of the mass flow rate with the known kinetic theory analytical equations was carried out for several temperatures of the liquid layer. It was obtained that after short relaxation time mass flow rate ceases to depend on time for some period. The relaxation time for mass flow rate was estimated. It turned out that this time depends on the temperature of the liquid layer and decreases with increase of its temperature. The mass flow rate values predicted by molecular dynamics simulation are found to be well described by some analytical formulas from kinetic theory. The temporal dynamics of the liquid layer was investigated. The linear dependence between film thinning rate and mass flow rate values was obtained both in the quasi-steady regime and out of it. It was found that liquid interface temperature depends on liquid thickness by power law with an exponent independent of initial liquid film temperature.

Quasi-steady imbibition of physiological liquids in paper-based microfluidic kits: Effect of shear-thinning

In the present work, spontaneous imbibition of shear-dependent fluids is numerically investigated in a two-layered, rectangular/fan-shaped, paper-based diagnostic kit using the modified Richards equation. It is shown that the average velocity at the test line of the kit is strongly influenced by the absorbent pad's microstructure with its contact angle playing a predominant role. Assuming that the test fluid is shear-thinning, a generalized version of the Richards equation, valid for power-law fluids, was used to investigate the effect of shear-thinning on the quasi-steady regime. The shear-thinning behavior of the test fluid is predicted to shorten the duration of the constant-velocity regime on the nitrocellulose membrane used as the test cell. By manipulating the contact angle and/or choosing appropriate microstructure for the absorbent pad, it is still possible to establish a constant velocity regime at the test line for nearly five minutes even for such fluids. A comparison between our numerical results and published numerical results obtained using simplistic theories has revealed the key role played by the transition, partially saturated zone near the advancing front during the liquid imbibition. The general conclusion is that use should preferably be made of robust models such as Richards equation for the design of lateral-flow, paper-based assays.

Resonant growth of inertial oscillations from lee waves in the deep ocean

The interactions between inertial oscillations (IO) and lee waves (LW) close to the bottom of the ocean and the role of IO in energy dissipation are addressed for a range of physical parameters typical of Southern Ocean conditions. Idealized numerical simulations in a vertical plane and resonant interaction theory are combined for this purpose. The lee waves are emitted by a uniform geostrophic flow over a sinusoidal topography for a constant buoyancy frequency at mid-latitude. We show that IO can grow by triadic resonant interactions with the LW. Two triads are dominant, which involve waves with frequency , f and , where is the intrinsic frequency of the LW and f the Coriolis frequency (assumed positive). These triads differ by the sign and value of the IO vertical wavenumber. Results from the numerical simulations show that the triad associated with the upward phase propagation of the IO is selected, consistent with oceanic observations, that a good agreement is obtained with the IO growth rate predicted theoretically and that the IO develop in a bottom layer of height less than 1000 m. A quasi-steady flow regime is eventually reached, with the IO amplitude being of the same order as the geostrophic flow speed. During this regime, depending upon the flow parameters, the IO kinetic energy is equal to 30–70% of the LW energy flux during one inertial period. This large range of values is not reflected in the turbulent kinetic energy (TKE) dissipation rate, which is comprised between 10 and 30% of the LW energy flux, whatever the IO amplitude, even if vanishingly small. Therefore, for the set of parameters we consider, the TKE dissipation rate cannot be inferred from the IO amplitude. Yet, the nonlinear interactions between the lee waves and the IO are critical in setting the energy spectrum, and similarly for the internal tide and the IO at low latitudes according to the literature. This implies that IO should be taken into account in the parameterisation of mixing in the ocean.

Experimental study of the dynamic stall noise on an oscillating airfoil

In this paper, the noise emitted by an oscillating NACA0012 airfoil at Reynolds number Rec=2.1×105 is studied. Combined far-field noise and surface pressure measurements are performed in order to investigate the effect of the amplitude of motion α1 and reduced frequency k on the emitted far-field noise. These two parameters can be combined using the reduced pitch rate k⋆=α1k that is shown to be the most relevant parameter in this study. The dynamic stall noise is characterized by an increase of the noise amplitude at frequencies below 700 Hz and takes place each time the airfoil incidence increases over the critical dynamic stall angle. For a low reduced pitch rate (k⋆=1.2×10−3), a quasi-steady regime is obtained, with the light-stall and deep-stall regimes commonly observed for a static airfoil taking place during the pitching motion. For a higher pitch rate (k⋆=13.1×10−3), an increase of the duration and amplitude of the broadband noise occurring at the stall onset is identified. For all the reduced pitch rates investigated, a delay in the apparition of the stall noise is observed in comparison with the static stall noise, leading to a hysteresis of the stall noise as a function of the angle of attack.

Quasi-steady circulation regimes in the Baltic Sea

Abstract. Circulation plays an essential role in the creation of physical and biogeochemical fluxes in the Baltic Sea. The main aim of the work was to study the quasi-steady circulation patterns under prevailing forcing conditions. A total of 6 months of continuous vertical profiling and fixed-point measurements of currents, two month-long underwater glider surveys, and numerical modeling were applied in the central Baltic Sea. The vertical structure of currents was strongly linked to the location of the two pycnoclines: the seasonal thermocline and the halocline. The vertical movements of pycnoclines and velocity shear maxima were synchronous. The quasi-steady circulation patterns were in geostrophic balance and highly persistent. The persistent patterns included circulation features such as upwelling, downwelling, and boundary currents, as well as a sub-halocline gravity current. The patterns had a prevailing zonal scale of 5–60 km as well as considerably higher magnitude and different direction than the long-term mean circulation pattern. A northward (southward) geostrophic boundary current in the upper layer was observed along the eastern coast of the central Baltic in the case of southwesterly (northerly) wind. The geostrophic current at the boundary was often a consequence of wind-driven, across-shore advection. The sub-halocline quasi-permanent gravity current with a width of 10–30 km from the Gotland Deep to the north over the narrow sill separating the Fårö Deep and Nothern Deep was detected in the simulation, and it was confirmed by an Argo float trajectory. According to the simulation, a strong flow, mostly to the north, with a zonal scale of 5 km occurred at the sill. This current is an important deeper limb of the overturning circulation of the Baltic Sea. The current was stronger with northerly winds and restricted by the southwesterly winds. The circulation regime had an annual cycle due to seasonality in the forcing. The boundary current was stronger and more frequent northward during the winter period. The sub-halocline current towards the north was strongest in March–May and weakest in November–December.

Effect of new overhead phase change material enclosure designs on thermo-electric performance of a photovoltaic panel

Photovoltaic (PV) panel harvests solar energy into electric energy; however, its electric conversion efficiency is very low and most of incoming radiation is wasted as heat to the surroundings. Electric performance of PV panel is badly affected by increased PV cell temperature as result of this wasted heat. A new design concept of overhead phase change material (PCM) enclosure design attached with a photovoltaic panel has been investigated. Various design configurations studied and based on the melting front characteristics, an optimum final design is proposed. The new design enhances the solar radiation gain (ratio of utilized to unutilized radiation) by about 17 times the conventional PV system. Higher solar radiation utilization manifests in about 10% increase in energy storage density. With strategic distribution of PCM, duration of quasi-steady regime where convection dominates, has been increased that manifested into higher melting rates of PCM compared to the conventional rectangular design. The study revealed that electrical conversion efficiency of PV panel can approach to about 12% if suitable strategies are adopted as demonstrated in this paper. This study would be useful in developing efficient PV technologies to meet the ever-growing energy needs. The findings of this investigation are reported from an experimentally validated numerical model that accurately captures the melting behavior of PCM and other thermal characteristics of the system.

Development of overturning circulation in sloping waterbodies due to surface cooling

Cooling the surface of freshwater bodies, whose temperatures are above the temperature of maximum density, can generate differential cooling between shallow and deep regions. When surface cooling occurs over a long enough period, the thermally induced cross-shore pressure gradient may drive an overturning circulation, a phenomenon called ‘thermal siphon’. However, the conditions under which this process begins are not yet fully characterised. Here, we examine the development of thermal siphons driven by a uniform loss of heat at the air–water interface in sloping, stratified basins. For a two-dimensional framework, we derive theoretical time and velocity scales associated with the transition from Rayleigh–Bénard type convection to a horizontal overturning circulation across the shallower sloping basin. This transition is characterised by a three-way horizontal momentum balance, in which the cross-shore pressure gradient balances the inertial terms before reaching a quasi-steady regime. We performed numerical and field experiments to test and show the robustness of the analytical scaling, describe the convective regimes and quantify the cross-shore transport induced by thermal siphons. Our results are relevant for understanding the nearshore fluid dynamics induced by nighttime or seasonal surface cooling in lakes and reservoirs.

Episodic deluges in simulated hothouse climates.

Earth's distant past and potentially its future include extremely warm 'hothouse'1 climate states, but little is known about how the atmosphere behaves in such states. One distinguishing characteristic of hothouse climates is that they feature lower-tropospheric radiative heating, rather than cooling, due to the closing of the water vapour infrared window regions2. Previous work has suggested that this could lead to temperature inversions and substantial changes in cloud cover3-6, but no previous modelling of the hothouse regime has resolved convective-scale turbulent air motions and cloud cover directly, thus leaving many questions about hothouse radiative heating unanswered. Here we conduct simulations that explicitly resolve convection and find that lower-tropospheric radiative heating in hothouse climates causes the hydrologic cycle to shift from a quasi-steady regime to a 'relaxation oscillator' regime, in which precipitation occurs in short and intense outbursts separated by multi-day dry spells. The transition to the oscillatory regime is accompanied by strongly enhanced local precipitation fluxes, a substantial increase in cloud cover, and a transiently positive (unstable) climate feedback parameter. Our results indicate that hothouse climates may feature a novel form of 'temporal' convective self-organization, with implications for both cloud coverage and erosion processes.

Experimental Study of Transient Flow Regimes in a Model Hydroturbine Draft Tube

Swirling flow with the formation of a precessing vortex core (PVC) in the draft tube model of a hydroturbine was studied. Experiments were performed on an aerodynamic setup under transient operating conditions of the hydroturbine. The turbine operating conditions were varied by continuously changing the flow rate at a constant runner speed. The transition from the partial load regime, when a precessing vortex core is formed, to the best efficiency point without a core is considered. Applied to this task, a comparison of the windowed Fourier transform with wavelet analysis is given. The dependence of the PVC lifetime in the transient regime correlates with the transient time. It is shown that the velocity profiles and the spectrum of pressure pulsations in transient regimes change quasistatically between part-load operation and the best efficiency point of the turbine. The phase-averaged velocity distributions in the transient regimes show that a transient regime is a sequence of quasisteady regimes.

Scaling of buoyancy-driven flows on a horizontal plate subject to a ramp heating of a finite time

Buoyancy-driven flows on a horizontal plate subject to a ramp heating of finite time are studied in this paper. The dynamics of the thermal boundary layer and the subsequent starting plume on the heated horizontal plate are revealed and the scaling laws for different scenarios and regimes are obtained using a scaling analysis, which are further verified against results of direct numerical simulations (DNS) at the Rayleigh number of 5 × 102 ~ 5 × 104, the Prandtl number of 7 and the non-dimensional time of ramp heating from 0.072 to 0.143. A distinct sequential development of the thermal boundary layer, thermal bulges and starting plume is observed in the DNS and characterised by the scaling laws. The thicknesses of the thermal boundary layer and plume are found to decrease as the Rayleigh number increases because the convection intensifies. In addition, the scaling analysis suggests that the development of the starting plume may undergo five scenarios, each of which has a series of different regimes, depending on the Rayleigh number, the Prandtl number and the time of ramp heating. In a typical scenario, the starting plume may ascend under an unsteady viscosity conduction regime, a quasi-steady viscosity conduction regime or a steady viscosity conduction regime.