Inverse Flux Research Articles

Phase fraction measurement of gas-liquid flow based on cyclonic capacitive sensor (CCS) and inverse drift flux method

Abstract As the demand for clean energy sources like natural gas increases, the need for methods to measure the phase fraction of gas-liquid two-phase flows, which have complex and variable flow patterns, becomes more pronounced. This study introduces a phase fraction measurement method based on a cyclonic capacitive sensor. An effective phase fraction prediction model for the gas-liquid flow measurement section is established based on the capacitive signals. Using the drift flux principle, the dimensionless drift velocity of the spiral annular flow is analyzed, and a volume gas fraction (GVF) prediction model based on the ‘inverse drift flux method’ is established. Experimental results show that this method is suitable for a wide range of phase fraction measurements and is highly accurate. When the liquid volume fraction (LVF) is less than 10%, the average relative error of the predicted GVF is 0.3%; for the LVF from 10% to 30%, the average relative error is 1.4%.

Eddy–Internal Wave Interactions: Stimulated Cascades in Cross-Scale Kinetic Energy and Enstrophy Fluxes

Abstract The interactions between oceanic mesoscale eddies, submesoscale currents, and internal gravity waves (IWs) are investigated in submesoscale-resolving realistic simulations in the North Atlantic Ocean. Using a novel analysis framework that couples the coarse-graining method in space with temporal filtering and a Helmholtz decomposition, we quantify the effects of the interactions on the cross-scale kinetic energy (KE) and enstrophy fluxes. By systematically comparing solutions with and without IW forcing, we show that externally forced IWs stimulate a reduction in the KE inverse cascade associated with mesoscale rotational motions and an enhancement in the KE forward cascade associated with divergent submesoscale currents, i.e., a “stimulated cascade” process. The corresponding IW effects on the enstrophy fluxes are seasonally dependent, with a stimulated reduction (enhancement) in the forward enstrophy cascade during summer (winter). Direct KE and enstrophy transfers from currents to IWs are also found, albeit with weaker magnitudes compared with the stimulated cascades. We further find that the forward KE and enstrophy fluxes associated with IW motions are almost entirely driven by the scattering of the waves by the rotational eddy field, rather than by wave–wave interactions. This process is investigated in detail in a companion manuscript. Finally, we demonstrate that the stimulated cascades are spatially localized in coherent structures. Specifically, the magnitude and direction of the bidirectional KE fluxes at submesoscales are highly correlated with, and inversely proportional to, divergence-dominated circulations, and the inverse KE fluxes at mesoscales are highly correlated with strain-dominated circulations. The predominantly forward enstrophy fluxes in both seasons are also correlated with strain-dominated flow structures.

Study on formation mechanism of mud-inclusion-type underground debris flows using natural caving method

This study aimed to investigate the formation mechanism of the mud-inclusion-type underground debris flows of natural caving underground mines. The characteristics of fine moraine particles flowing through the coarse-grained ore bed were used to analyze the formation process of mud inclusions in the caving ore bed through a physical model test. Based on the movement behavior of the mud inclusions of moraine in the caving ore bed, a formation-mechanism generalized model of underground debris flows with mud inclusions was established. The model was used to examine the formation mechanism of mud-inclusion-type underground debris flows in natural caving. The results showed that the fine moraine particles had good cross-flow characteristics in the process of drawing coarse-grained ore. The accumulation of fine moraine in the ore bed was a prerequisite for the formation of mud inclusions, and the fluid inclusions were formed by a mixture of the particles with the infiltrated water. When mud inclusions in moraine are affected by many factors, such as ore-drawing vibrations, blasting vibrations, and groundwater, the inclusions undergo multiple migration–stop–migration cycles, resulting in separation or fusion. However, the inclusions are released along the optimal random pore path to the outlet, forming a certain scale of underground debris flows accidents. The accuracy and reliability of the formation mechanism were verified through geophysical explorations based on the equivalent inverse flux transient electromagnetic method. This study not only broadens the research on debris flow, but also provides theoretical guidance for the prevention and control of underground debris flows.

Statistical analysis of vortex condensate motion in two-dimensional turbulence

An inverse turbulent cascade in a periodic square box produces a coherent system-sized vortex dipole. We study the statistics of its motion by carrying out direct numerical simulations performed for various bottom friction α, pumping intensity ε, and fluid hyperviscosity ν. In the main approximation, coherent vortices can be considered as point vortices, and within this model, they drift at the same dipole velocity, which is determined by their circulation and mutual arrangement. The characteristic value of the dipole velocity is more than an order of magnitude smaller than the polar velocity inside coherent vortices. Turbulent fluctuations give rise to a relative velocity between the vortices, which changes the distance between them. We found that for a strong condensate, the probability density function of the vector ρ, describing the difference in the mutual arrangement of coherent vortices from half the diagonal of the computational domain, has the form of a ring. The radius of the ring weakly depends on control parameters and its width is proportional to parameter δ=ϵ−1/3L2/3α, where ϵ is the inverse energy flux and L is the system size. The random walk around the ring, caused by turbulent fluctuations, has superdiffusion behavior at intermediate times. It results in a finite correlation time of the dipole velocity, which is of the order of turnover time τK=L2/3ϵ−1/3 of system-size eddies produced by an inverse turbulent cascade. The results obtained deepen the understanding of the processes governing the motion of coherent vortices.

An experimental study on monitoring of marine sediment transport by using a 3D sediment trap

The observation and analysis of sediment transport in oceans is an important means for the protection of the marine environment, resource development, construction engineering, and element cycling. However, traditional methods of observing sediment transport are either limited by the range of the instruments used or their own observational attributes, such that they cannot be used to accurately detect and analyze the process of transport of marine sediment. A 3D sediment trap has been proposed to compensate for the shortcomings of the various monitoring tools in our team, but no mature method for the analytical inversion of the data obtained from this device has been developed to date. In this paper, we developed analytical methods to invert sediment transport processes using corrected capture efficiency, sample inversion, and transport flux analysis. Through an annular flume test, we measured the turbidity, pressure, and particle size of the water stream and substituted them into the proposed analytical equations, thus verifying the applicability of the analytical methods. We used the slice experiment of the time series of the sediment samples, to determine the validity of the sample inversion, and establish the relationship between the particle size and concentration of the captured samples. We performed restoration tests on the process of sediment transport to establish a set of methods of flux analysis based on the velocity and turbidity of flow. And finally corrected for capture efficiency by particle size. The combination of analytical methods and 3D sediment trap could provide technological support for investigating the evolution of the sea, ecological cycle, and marine engineering.

An empirical firebrand pile heat flux model

Firebrand exposure has been identified as a leading cause of structure losses during wildfires. However, only a limited number of studies have attempted to quantify the incident firebrand heat flux to a target substrate surface. In this study, a bench-scale wind tunnel retrofitted with an IR thermal imaging system was used to generate high-resolution temperature data for the back surface of a thin, non-combustible insulation board exposed to a glowing firebrand pile at 0.9–2.7 m s−1 air flow velocities and 0.06 and 0.16 g cm−2 firebrand coverage densities. An inverse heat flux modelling technique utilizing a solid-phase pyrolysis solver, ThermaKin, was employed to determine transient firebrand pile heat flux profiles underneath and directly in front of a glowing firebrand pile. The inverse modelling technique used both the experimental back surface temperature data and the insulation's thermophysical properties. Average incident firebrand pile heat flux values obtained for all testing conditions ranged between 28 and 80 kW m−2. For the first time, an empirical model capturing the firebrand pile incident heat flux dependence on time, air flow velocity and firebrand coverage density was developed.

A Physical Model for the Observed Inverse Energy Cascade in Typhoon Boundary Layers

AbstractThe knowledge of the observed inverse energy cascade in typhoon boundary layers holds significant implications for understanding the formation, enhancement, and deformation of typhoons. This study reveals that the observed inverse energy cascade originates from the rapid rotation of typhoons. The transition from the direct energy cascade regime to the inverse energy cascade regime can be characterized by the Zeman length scale. The turbulence structures behave as two dimensional above the Zeman length scale. Through symmetry analysis, it is discovered that the ratio of the inverse energy cascade flux to the direct energy cascade flux is proportional to the turbulence Rossby number with a power of −2. These findings offer a framework for incorporating the inverse energy cascade into the turbulence parameterizations and improving typhoon modeling.

Upscale transfer of waves in one-dimensional rotating shallow water

We study the inverse flux of waves in one of the simplest geophysical fluid dynamics models: one-dimensional rotating shallow water equations. Based on direct numerical integration of the governing equations, we find that waves injected at small scales get transferred upscale predominantly via resonant quartic interactions between wave modes. The waves’ upscale transfer is non-local and involves turbulent transfer between disparate scales of the flow. Our analysis reveals that the upscale transfer of waves is extremely intermittent and is a result of localized-in-time bursts in wave action flux. These intermittent events of flux bursts lead to shallower waves’ spectrum and relatively higher amplitude wave fields in physical space. On examining statistics of the flow fields, we find that low-energy high wavenumbers more or less comply with the assumptions used in wave turbulence theory, such as uniformly distributed wave phases and the Gaussian distribution of fields, while non-uniform distribution of wave phases and non-Gaussian statistics dominate at large scales or low wavenumbers that contain a major share of the flow energy. Our findings point out that the one-dimensional rotating shallow water equations, despite being a simple geophysical fluid dynamic model, harbour complex and intricate features associated with the upscale transfer of waves that have not been recognized in the past.

A heat flux-corrected experimental inverse technique for simultaneously estimating the thermal properties of a metallic medium as functions of temperature

ABSTRACT This paper presents an experimental inverse approach to simultaneously estimate the temperature-dependent thermal properties of AISI 316 stainless steel. The heat flux conducted to the sample was corrected by using a transducer, evaluating contact resistance at microscopic level, and performing experiments under vacuum. Estimates were severely biased when heat flux correction was not applied. Metaheuristics were used to enlarge the search space, which can cover the thermal properties of all known metallic materials, thereby taking advantage of better thermal modeling adequacy. The estimation reliability was shown by comparison with literature data, statistical significance, uncertainty analysis, and inverse heat flux retrieval.

Origin of Quasi-periodic Pulsation at the Base of a Kink-unstable Jet

We studied a blowout jet that occurred at the west limb of the Sun on 2014 August 29 using high-resolution imaging/spectroscopic observations provided by the Solar Dynamics Observatory/Atmospheric Imaging Assembly and the Interface Region Imaging Spectrograph. An inverse γ-shaped flux rope appeared before the jet–morphological indication of the onset of kink instability. The twisted field lines of the kink-unstable flux rope reconnected at its bright knot and launched the blowout jet at ≈06:30:43 UT with an average speed of 234 km s−1. Just after the launch, the northern leg of the flux rope erupted completely. The time–distance diagrams show multiple spikes or bright dots, which is the result of periodic fluctuations, i.e., quasi-periodic fluctuations (QPPs). The wavelet analysis confirms that QPPs have a dominant period of ≈3 minutes. IRIS spectra (Si iv, C ii, and Mg ii) may also indicate the occurrence of magnetic reconnection through the existence of broad and complex profiles and bidirectional flows in the jet. Further, we found that line broadening is periodic with a period of ≈3 minutes, and plasma upflow always occurs when the line width is high, i.e., multiple reconnection may produce periodic line broadening. The emission measure (EM) curves also show the same period of ≈3 minutes in different temperature bins. The images and EM show that this jet spire is mainly cool (chromospheric/transition region) rather than hot (coronal) material. Further, line broadening, intensity, and EM curves have a period of ≈3 minutes, which strongly supports the fact that multiple magnetic reconnection triggers QPPs in the blowout jet.

Research on the Fault-Transient Characteristics of a DC Power System Considering the Cooperative Action of a Flexible Current-Limiting Device and a Circuit Breaker

As an effective carrier of a new energy collection, the DC power grid has low inertia and weak damping characteristics, making it essential to limit fault current and isolate the DC system. To quickly and effectively suppress fault current, a flexible current-limiting device (FCLD) is proposed, which can realize transient fault self-recovery without circuit breaker action and permanent and quick isolation of a fault. It improves the operational ability of the DC system under an asymmetric condition. First, a rectifier provides a set-slope current to each cascade inductor, so the voltage of the inductor can be clamped. Second, a controlled current source (CCS) is applied to generate inverse flux to prevent the inductor from magnetic saturation. The protection action time of the DC circuit breaker is reformulated. Finally, by considering the synergistic action of the current-limiting device, the circuit breaker, and the transient characteristics of the DC grid fault, the protection scheme of the multi-terminal flexible DC system can be formulated. To verify the validity of the proposed flexible current-limiting device, a multi-terminal flexible DC simulation platform is established, and the faults of DC lines are simulated and analyzed.

Real-time identification of severe heat loads over external interface of lightweight thermal protection system

The lightweight thermal protection system (LTPS) is typically employed on the exterior surface of high-speed aircraft to prevent the penetration of high-temperature heat flux. The sequential function specification method (SFSM) is exploited in this study to solve the inverse issue in anticipation of the external-surface heating conditions of a lightweight thermal protection system by entering temperature data at a single measurement station. The results show that the inversion accuracy is significantly dependent on the temperature acquisition position as well as the forecast time step. Adding noise to the temperature data reveals that temperature noise aggravates the volatility of the inverse heat flux, necessitating an increase in the forecast time step to enhance the inverse accuracy. The experiment of a light thermal protection system demonstrates that the approach can efficiently and correctly recover the boundary heat flux by employing the inner wall temperature of the thermal protection structure.

A Forward Energy Flux at Submesoscales Driven by Frontogenesis

Abstract Submesoscale currents, comprising fronts and mixed-layer eddies, exhibit a dual cascade of kinetic energy: a forward cascade to dissipation scales at fronts and an inverse cascade from mixed-layer eddies to mesoscale eddies. Within a coarse-graining framework using both spatial and temporal filters, we show that this dual cascade can be captured in simple mathematical form obtained by writing the cross-scale energy flux in the local principal strain coordinate system, wherein the flux reduces to the sum of two terms, one proportional to the convergence and the other proportional to the strain. The strain term is found to cause the inverse energy flux to larger scales while an approximate equipartition of the convergent and strain terms captures the forward energy flux, demonstrated through model-based analysis and asymptotic theory. A consequence of this equipartition is that the frontal forward energy flux is simply proportional to the frontal convergence. In a recent study, it was shown that the Lagrangian rate of change of quantities like the divergence, vorticity, and horizontal buoyancy gradient are proportional to convergence at fronts, implying that horizontal convergence drives frontogenesis. We show that these two results imply that the primary mechanism for the forward energy flux at fronts is frontogenesis. We also analyze the energy flux through a Helmholtz decomposition and show that the rotational components are primarily responsible for the inverse cascade while a mix of the divergent and rotational components cause the forward cascade, consistent with our asymptotic analysis based on the principal strain framework.

Changes in phosphorus turnover when soils under long-term P management are amended with bio-based fertiliser

Understanding available phosphorus (P) turnover could improve sustainable P management. An isotope tracing 33P was used to measure daily P turnover rates and exchangeable P (E) in P deficient, balanced, and excess P soils from a long-term P site. Turnover under P deficient conditions was characterised by the lowest P flux predominantly from the available into the exchangeable P pools (P efflux). The P efflux in the P deficient soil was 3.7 ± 0.6 mg P/L day−1 and the inverse flux (P influx) was 1.6 ± 0.4 mg P/L day−1. Turnover rates were more than twofold higher under P balanced and surplus conditions, exhibiting an equilibrium between influx and efflux rates. The contribution of abiotic processes to P turnover was predominant in the excess P soil, whereas biotic processes dominated turnover rates under P deficient conditions.Changes in P turnover were measured following application of single superphosphate (SSP) and dairy processing sludge (DPS). Both fertiliser types increased P turnover rates and availability across all soils. After SSP application, E values plateaued between 238 and 297 mg P/L regardless of initial P status. Slower P release from DPS was evidenced by a wider range of E values (97–160 mg P/L) with slower turnover.

Turbulent Transition of a Flow from Small to O(1) Rossby Numbers

Abstract Oceanic flows are energetically dominated by low vertical modes. However, disturbances in the form of atmospheric storms, eddy interactions with various forms of boundaries, or spontaneous emission by coherent structures can generate weak high-baroclinic modes. The feedback of the low-energy high-baroclinic modes on large-scale energetically dominant low modes may be weak or strong depending on the flow Rossby number. In this paper we study this interaction using an idealized setup by constraining the flow dynamics to a high-energy barotropic mode and a single low-energy high-baroclinic mode. Our investigation points out that at low Rossby numbers the barotropic flow organizes into large-scale coherent vortices via an inverse energy flux while the baroclinic flow accumulates predominantly in anticyclonic barotropic vortices. In contrast, with increasing Rossby number, the baroclinic flow catalyzes a forward flux of barotropic energy. The barotropic coherent vortices decrease in size and number, with a strong preference for cyclonic coherent vortices at higher Rossby numbers. On partitioning the flow domain into strain-dominant and vorticity-dominant regions based on the barotropic flow, we find that at higher Rossby numbers baroclinic flow accumulates in strain-dominant regions, away from vortex cores. Additionally, a major fraction of the forward energy flux of the flow takes place in strain-dominant regions. Overall, one of the key outcomes of this study is the finding that even a low-energy high-baroclinic flow can deplete and dissipate large-scale coherent structures at O(1) Rossby numbers.

Profile of a two-dimensional vortex condensate beyond the universal limit.

It is well known that an inverse turbulent cascade in a finite (2π×2π) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly correlated in time, random in space, and had a correlation length l_{f}=2π/k_{f} with k_{f} ranging from 100 to 12.5. Previously, it was found that in the asymptotic limit of small-scale forcing, the vorticity exhibits the power-law behavior Ω(r)=(3ε/α)^{1/2}r^{-1}, where r is the distance to the vortex center, α is the bottom friction coefficient, and ε is the inverse energy flux. Now we show that for a spatially homogeneous forcing with finite k_{f} the vorticity profile becomes steeper, with the difference increasing with the pumping scale but decreasing with the Reynolds number at the forcing scale. Qualitatively, this behavior is related to a decrease in the effective pumping of the coherent vortex with distance from its center. To support this statement, we perform an additional simulation with spatially localized forcing, in which the effective pumping of the coherent vortex, on the contrary, increases with r, and show that in this case the vorticity profile can be flatter than the asymptotic limit.

Indirect inverse flux mapping of a concentrated solar source using infrared imaging.

With the growing interest in high-flux solar sources, a need exists for simple, accurate, and inexpensive strategies to characterize their output radiative flux. In this paper, the irradiation output from a 10 kWe xenon lamp solar simulator is characterized by an inverse mapping technique that uses a custom radiometer and infrared camera, validated by a direct characterization method (heat flux gauge). The heat flux distribution is determined in a vacuum chamber using an easily obtainable graphite target and an inverse heat transfer model. The solar simulator produces peak fluxes in the range of 1.5-4.5 MW/m2 as measured directly by a heat flux gauge, and its output can be controlled using a variable power supply. Spectral measurements indicate that minor variations in the simulator's output with respect to its current supply occur in the spectral range of 450-800nm. The radiometer presented in this work allows for characterizing solar irradiation under practical conditions (e.g., inside a solar reactor) and thus accounts for deviations due to additional components, such as viewport effects. Additionally, it provides an inexpensive and efficient means of monitoring any deterioration in the performance of solar sources over time without the need for complex recalibration.

A Novel Flexible Fault Current Limiter for DC Distribution Applications

As an effective carrier of new energy collection, DC power grid has characteristics of low inertia and weak damping, which makes DC fault propagate extremely fast. However, the existing protection and DC circuit breaker (DCCB) technique still could not match its fault propagation speed. Therefore, to solve this problem, a novel of flexible fault current limiter (NFFCL) is presented in this paper. Under normal operation condition, NFFCL is connected to DC line in series without negative influence. When a fault occurs to DC line, NFFCL’s rectifier circuit, according to the protection criterion, provides cascade inductor, which is connected to DC line in series, with a set-slope linear current. In this case, the voltage drop between both ends of inductor can be clamped flexibly, which can even completely isolate the fault area. A controlled voltage source (CCVS) is applied to generate inverse flux to prevent the cascading inductor from magnetic saturation. When the fault disappears, the energy of current-limit inductor can be released and transferred to AC power grid through NFFCL’s converter. Finally, simulation cases are carried out to verify the working principles and practicability of proposed NFFCL.

Subgrid-scale models of isotropic turbulence need not produce energy backscatter

This investigation questions the importance of inverse interscale energy fluxes, the so-called energy backscatter, for the modelling of the energy cascade in large-eddy simulations (LES) of turbulent flows. The invariance of the filtered Navier–Stokes equations to divergence-preserving transformations of the subgrid-scale (SGS) stress tensor is exploited here to explore alternative representations of the local SGS energy fluxes. Numerical optimisation procedures are applied to the SGS stress tensor – obtained by filtering isotropic turbulence flow fields – to find alternative stresses that satisfy the filtered Navier–Stokes equations, but that produce negligible backscatter. These alternative SGS stresses show that backscatter represents not a flux of energy from the subgrid to the resolved scales, but conservative spatial fluxes, and that it need not be modelled to reproduce the local energetic exchange between the resolved and the subgrid scales in LES. From the perspective of statistical mechanics, it is argued that this is a consequence of the strong statistical irreversibility of inertial-range dynamics, which precludes inverse energy cascades even in a local sense. These findings show that the energy cascade is strongly unidirectional locally, and that it can be modelled as an irreversible sink of energy, justifying the extended use of purely dissipative SGS models in LES.

λ-Navier-Stokes turbulence.

We investigate numerically the model proposed in Sahoo et al. (2017 Phys. Rev. Lett. 118, 164501) where a parameter λ is introduced in the Navier-Stokes equations such that the weight of homochiral to heterochiral interactions is varied while preserving all original scaling symmetries and inviscid invariants. Decreasing the value of λ leads to a change in the direction of the energy cascade at a critical value [Formula: see text]. In this work, we perform numerical simulations at varying λ in the forward energy cascade range and at changing the Reynolds number [Formula: see text]. We show that for a fixed injection rate, as [Formula: see text], the kinetic energy diverges with a scaling law [Formula: see text]. The energy spectrum is shown to display a larger bottleneck as λ is decreased. The forward heterochiral flux and the inverse homochiral flux both increase in amplitude as [Formula: see text] is approached while keeping their difference fixed and equal to the injection rate. As a result, very close to [Formula: see text] a stationary state is reached where the two opposite fluxes are of much higher amplitude than the mean flux and large fluctuations are observed. Furthermore, we show that intermittency as [Formula: see text] is approached is reduced. The possibility of obtaining a statistical description of regular Navier-Stokes turbulence as an expansion around this newly found critical point is discussed. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.