Stratified Flow Research Articles

Thermal Characterization of Subcooled Flow Boiling in a Pin-Fin Coldplate With Non-Uniform Heating

Abstract Coldplates are a crucial component in various cooling applications, such as cooling data center servers and power electronics. The unprecedented growth in electronics power density, along with the resulting ultrahigh heat fluxes, demands a transition from single-phase forced convection to two-phase flow boiling heat transfer. The majority of studies in the literature have focused on flow boiling in fin-enhanced silicon microgaps and microchannels, with only a few addressing flow boiling in millimeter-scale heat sinks. In the present study, flow boiling of HFE-7200 dielectric fluid in a millimeter-scale pin-fin coldplate is experimentally investigated under nonuniform heating conditions. Four background heaters represent the low-dissipating-power devices. On the other hand, five hotspot heaters mimic the high-heat-flux devices and generate heat fluxes ranging from 50 W/cm2 to 1000 W/cm2, corresponding to hotspot heat inputs ranging from 62.5 W to 1.25 kW, respectively. The coldplate's thermohydraulic performance is investigated for various flow rates and inlet temperature ranging from 0.5 L/min to 1.5 L/min and from 25 °C to 60 °C, respectively. A high-speed camera is utilized for a narrow field of view (FOV) flow visualization at a frame rate of 2229 fps while a digital camera is used for a wider FOV at 60 fps. Flow visualization demonstrated the transition between bubbly, slug/churn, and stratified two-phase flow regimes.

Large-scale self-organization in dry turbulent atmospheres.

How turbulent convective fluctuations organize to form larger-scale structures in planetary atmospheres remains a question that eludes quantitative answers. The assumption that this process is the result of an inverse cascade was suggested half a century ago in two-dimensional fluids, but its applicability to atmospheric and oceanic flows remains heavily debated, hampering our understanding of the energy balance in planetary systems. We show using direct numerical simulations with spatial resolutions of 122882 × 384 points that rotating and stratified flows can support a bidirectional cascade of energy, in three dimensions, with a ratio of Rossby to Froude numbers comparable to that of Earth's atmosphere. Our results establish that, in dry atmospheres, spontaneous order can arise through an inverse cascade to the largest spatial scales.

Mixing of the Connecticut River Plume During Ambient Flood Tides: Spatial Heterogeneity and Contributions of Bottom‐Generated and Interfacial Mixing

AbstractThe Connecticut River plume is influenced by energetic ambient tides in the Long Island Sound receiving waters. The objectives of this modeling study are (a) characterizing the spatial heterogeneity of turbulent buoyancy fluxes, (b) partitioning turbulent buoyancy fluxes into bottom‐generated and interfacial shear contributions, and (c) quantifying contributions to plume‐integrated mixing within the tidal plume. The plume formed during ambient flood tides under low river discharge, spring tides, and no winds is analyzed. Turbulent buoyancy fluxes (B) and depth‐integrated B through the plume (Bd) are characterized by pronounced spatial heterogeneity. Strong mixing (Bd ∼ 10−5‐10−4 m3/s3) occurs near the mouth, in the nearfield plume turning region, over shoals, and nearshore shallow areas. Low to moderate mixing (Bd ∼ 10−8‐10−6 m3/s3) occupies half the plume. Buoyancy fluxes are first partitioned based on the depth of the shear stress minimum between plume‐generated and bottom‐generated shear maxima. Four other tested partitioning methods are based on open channel flow and stratified shear flow parameterizations. Interfacial and bottom‐generated shear contribute to different areas of intense and moderate mixing. All methods indicate a significant plume mixing role for bottom‐generated mixing, but interfacial mixing is a bigger contributor. Plume‐integrated total and interfacial mixing peak at max ambient flood and the timing of peak bottom‐generated mixing varies among partitioning methods. Two‐thirds of the mixing occurs in concentrated intense mixing areas. A parameter space with the ambient tidal Froude number and plume thickness to depth ratio as axes indicates many tidally modulated plumes are moderately to dominantly influenced by bottom‐generated tidal mixing.

Investigation of flow patterns in two-phase carbon dioxide in horizontal and vertical pipes

Modern particle detectors crucially depend on efficient cooling systems. Two-phase carbon dioxide (CO2) is a suitable solution as a cooling agent. This publication presents the observations and results of investigations of horizontal and vertical flow of two-phase CO_2 at a temperature of T = -15 °C and a pressure of approximately 23 bar. Heat fluxes between 98.5 kW/m2 and 200 kW/m2 were applied to the CO2, covering the range expected to occur in the future ATLAS Pixel detector being built for the high-luminosity phase of the Large Hadron Collider. Flow speeds ranged from 11.8 m/s to 28.1 m/s. Dedicated sensors measured the temperature and the pressure before and after heating the CO2. Two-phase flow patterns occuring in the pipe after heating the CO2 were recorded with a high-speed camera. Stratified, wavy and slug flow are found to be the predominant patterns for horizontal flow, while upward vertical flow is mainly found to be slug or churn. Based on the recorded images the void fraction of the CO2 after heating is determined and compared for the different setups. The results are summarised in a flow-pattern map. A clear distinction between vertical and horizontal flow is found, with horizontal flow exhibiting a significantly higher void fraction than vertical flow. Based on the pressure measurements, the pressure drop after heating the CO2 is measured and the corresponding Euler number is computed. While the pressure drop increases with the heat flux for horizontal flow, the pressure drop reduces with the heat flux in the case of upward vertical flow.

Angular momentum and chemical transport by azimuthal magnetorotational instability in radiative stellar interiors

Context. The transport of angular momentum and chemical elements within evolving stars remains poorly understood. Asteroseismic and spectroscopic observations of low-mass main sequence stars and red giants reveal that their radiative cores rotate orders of magnitude slower than classical predictions from stellar evolution models and that the abundances of their surface light elements are too small. Magnetohydrodynamic (MHD) turbulence is considered a primary mechanism to enhance the transport in radiative stellar interiors but its efficiency is still largely uncertain. Aims. We explore the transport of angular momentum and chemical elements due to azimuthal magnetorotational instability, one of the dominant instabilities expected in differentially rotating radiative stellar interiors. Methods. We employed 3D MHD direct numerical simulations in a spherical shell of unstratified and stably stratified flows under the Boussinesq approximation. The background differential rotation was maintained by a volumetric body force. We examined the transport of chemical elements using a passive scalar. Results. We provide evidence of magnetorotational instability for purely azimuthal magnetic fields in the parameter regime expected from local and global linear stability analyses. Without stratification and when the Reynolds number Re and the background azimuthal field strength are large enough, we observed dynamo action driven by the instability at values of the magnetic Prandtl number Pm in the range 0.6 − 1, which is the smallest ever reported in a global setup. When considering stable stratification at Pm = 1, the turbulence is transitional and becomes less homogeneous and isotropic upon increasing buoyancy effects. The transport of angular momentum occurs radially outward and is dominated by the Maxwell stresses when stratification is large enough. We find that the turbulent viscosity decreases when buoyancy effects strengthen and scales with the square root of the ratio of the reference rotation rate Ωa to the Brunt–Väisälä frequency N. The chemical turbulent diffusion coefficient scales with stratification similarly to the turbulent viscosity, but is lower in amplitude so that the transport of chemicals is slower than the one of angular momentum, in agreement with recent stellar evolution models of low-mass stars. Conclusions. We show that the transport induced by azimuthal magnetorotational instability scales somewhat slowly with stratification and may enforce rigid rotations of red giant cores on a timescale of a few thousand years. In agreement with recent stellar evolution models of low-mass stars, the instability transports chemical elements less efficiently than angular momentum.

New insights into experimental stratified flows obtained through physics-informed neural networks

We develop a physics-informed neural network (PINN) to significantly augment state-of-the-art experimental data of stratified flows. A fully connected deep neural network is trained using time-resolved experimental data in a salt-stratified inclined duct experiment, consisting of three-component velocity fields and density fields measured simultaneously in three dimensions at Reynolds number $= O(10^3)$ and at Prandtl or Schmidt number $=700$ . The PINN enforces incompressibility, the governing equations for momentum and buoyancy, and the boundary conditions at the duct walls. These physics-constrained, augmented data are output at an increased spatio-temporal resolution and demonstrate five key results: (i) the elimination of measurement noise; (ii) the correction of distortion caused by the scanning measurement technique; (iii) the identification of weak but dynamically important three-dimensional vortices of Holmboe waves; (iv) the revision of turbulent energy budgets and mixing efficiency; and (v) the prediction of the latent pressure field and its role in the observed asymmetric Holmboe wave dynamics. These results mark a significant step forward in furthering the reach of experiments, especially in the context of stratified turbulence, where accurately computing three-dimensional gradients and resolving small scales remain enduring challenges.

Experimental Study on Gas-Liquid Two-Phase Stratified Flow at High Pressure in a Horizontal Pipe

This study investigates wave-stratified flow in a horizontal pipe at high pressure, and flow characteristics are obtained, such as flow pattern map, liquid film thickness, and pressure drop. Compared with a flow pattern map of a gas-liquid two-phase flow carried out at atmosphere, stratified flow zone is depressed with increasing system pressure and the critical gas superficial velocity decreases for smooth-wave-stratified flow transition, while the critical liquid superficial velocity increases for stratified-intermittent transition. On one hand, the compressed air results in an increase in momentum transfer between gas and liquid phases, which accounts for the smaller gas superficial velocity that is encountered in both smooth-wave and stratified-annular flow transition at higher pressure. One the other hand, it slows down the liquid below the crest, and it makes the interface wave crest unstable and split for the vortex shedding behind the wave crest, which accounts for flow regime transition in gas-liquid two-phase flows in pipelines. As a result, stratified-intermittent flow transition is depressed and delayed. The pressure influence on the liquid film profile is analyzed, and relationships between film thickness and dimensionless numbers are studied, such as liquid Weber number and gas Weber number. Friction factors on different interfaces at high pressure are studied, and new empirical formulas are deduced.

The effect of flow stratification on ship performance: a numerical study

ABSTRACT If a layer of low-density water settles on top of higher density water, such as fresh water melting from a glacier and settling on top of colder seawater, a body of water can stratify into stable, distinct layers. A vessel advancing in such a stratified fluid can generate internal waves between these layers. The generation of internal waves requires energy and thus increases the resistance experienced by the vessel, a phenomenon known as the dead water effect which can result in a severe reduction in speed and loss of steering power. This study uses Computational Fluid Dynamics (CFD) to investigate the increase in ship resistance caused by the dead water effect. The results show that the presence of a stratified flow can increase total resistance approximately sixfold in extreme conditions. At standard operating conditions, total resistance may increase by approximately 6% as a result of flow stratification.

Gas-Liquid Hydrodynamics during Liquid Displacement by Gas in Up-Hill Pipeline

Mobile pipelines are the most efficient and reliable way to transport large quantities of oil over long distances in warfare, rescue and disaster relief. The oil in the pipe must be discharged and recovered when the oil transfer task is completed, usually via gas cap evacuation. Gas cap evacuation is the main method to evacuate mobile pipelines. During evacuation, due to the influence of topography, working conditions and gravitational forces, the oil in an up-hill pipeline is gradually deposited in the low-lying part of the pipeline to form a liquid, resulting in the incomplete emptying of the pipeline which directly affects the recovery efficiency of the pipeline. Focusing on the analysis of the gas carrying oil flow process in an up-hill pipeline during the evacuation of gas displacing oil in the mobile pipeline, the tail and head of the liquid accumulation were analyzed, and the liquid accumulation flow model was established based on the gas–liquid two-phase stratified flow theory. This model was used to analyze the flow law of the accumulated liquid under different pipe inclination angles, initial accumulation thicknesses and pipe diameters. It was found that the stagnant oil in the pipeline is carried by the gas flow into the upward tilting pipeline due to the influence of the axial gravity force of the pipeline. The gas flow can be divided into three phases: the initial discharge stage, the oscillation stage and the final discharge (reflux) stage.

Thermal and solutal stratified Heimanz flow of AA7072-deionized water over a wedge in the presence of bioconvection

The bioconvective Heimanz flow of nanofluid across a wedge with thermal stratification is analyzed in this article. The wedges are often seen in glider aircraft, rocket climbing frames, etc. The nanofluid considered in this study is composed of aluminum alloys of AA7072 and deionized water. The AA7072 alloys are specially manufactured materials composed of Aluminum and Zinc in the ratio of 98 : 1 along with metals like silicon, ferrous, and copper so that they possess enhanced heat transfer features. The mathematical model is formed using the modified Buongiorno’s model that includes the discussions related to slip mechanisms and volumetric analysis in terms of the weight of the nanoparticle. The model is in the form of partial differential equations and is later converted to ordinary differential equations with the assistance of similarity transformation. This set of equations is solved by the Differential Transformation Method (DTM) and the outcomes are discussed through graphs. ,

Experimental study on leakage characteristics of gas-liquid two-phase flow in a horizontal pipe

Oil and gas pipeline leakage accidents caused by aging and third-party damage have increased, resulting in polluting the ecological environment and jeopardizing life and property safety. A detailed and systematic investigation on the leak characteristics of oil and gas two-phase pipelines is significantly urgent. The leak experiments were performed on a horizontal tube with a diameter of 32 mm. There was a 3 mm round leakage hole at the bottom of the tube. The distance of the leakage hole from the pipe inlet was 4.8 m. Three inlet flow patterns, including stratified flow, slug flow, and annular flow via adjusting the gas superficial velocity (1.73 m/s ≤ USG ≤ 24.19 m/s) and liquid superficial velocity (0.017 m/s ≤ USL ≤ 0.415 m/s), were obtained. The conclusions point out that the type of leakage, whether it is mainly liquid or both gas and liquid, depends on the USG. The degree of phase separation in stratified flow is the greatest among the three inlet flow patterns, with a maximal phase separation efficiency (η) of 0.403. Slug flow has the least phase separation degree. Interestingly, the η is directly proportional to the inlet mass fraction only for slug flow. The harmonic frequency that appeared in the power spectral density curves for the pressure difference of leakage hole in slug flow, indicates that leakage is not a standard periodic event. The liquid velocity loss is primarily related to the gas leakage mechanism. These findings can provide new insights into two-phase pipeline leak detection and accident consequence prediction.

Characterization of a liquid jet from a stratified or full flow in a pipe and injected into a steam crossflow

This study presents the physical analysis of the injection jet based on the two-phase CFD simulation of no water level and co-current steam flow pressurized thermal shock (PTS) COSI experiments. In a first step, the physical analysis deals with various aspects related to the flow characteristics at the injection outlet, such as flow configuration (stratified or full), water level, jet trajectory or breakup length in the quiescent gas. In a second step, the analysis is completed by studying the influence of steam crossflow on the jet, resulting in modifications to the jet regime, jet trajectory, breakup height and deformation, which is characterized by the jet width and angle spread. It is observed that at low flow rates, the flow in the injection is stratified. Correlations from the literature are used to characterize this flow, consistent with the simulations carried out. Analysis shows that the liquid jet remains continuous in the cold leg. The liquid jet simulated for stratified or full flow in the injection is compared satisfactorily with correlations for jets injected in a quiescent gas or in a gas crossflow. Steam crossflow strongly modifies the trajectory and shape of the jet.

Penetrative magneto-convection of a rotating Boussinesq flow in f-planes

In this study, we conducted linear instability analysis of penetrative magneto-convection in rapidly rotating Boussinesq flows within tilted f-planes, under the influence of a uniform background magnetic field. We integrated wave theory and convection theory to elucidate the penetration dynamics in rotating magneto-convection. Our findings suggest that efficient penetration in rapidly rotating flows with weakly stratified stable layers at low latitudes can be attributed to the resonance of wave transmission near the interface between unstable and stable layers. In the context of strongly stratified flows, we derived the scaling relationships of penetrative distances Δ with the stability parameter δ. Our calculation shows that, for both rotation-dominated and magnetism-dominated flows, Δ obeys a scaling of Δ∼O(δ−1/2). In rotation-dominated flows, we noted a general decrease in penetrative distance with an increased rotational effect, and a minor decrease in a penetrative distance with an increased latitude. When a background magnetic field is introduced, we observed a significant shift in the penetrative distance as the Elsasser number Λ approaches one. The penetrative distance tends to decrease when Λ≪1 and increase when Λ≫1 with the rotational effect, indicating a transition from rotation-dominated to magnetism-dominated flow. We have further investigated the impact of the background magnetic field when it is not aligned with the rotational axis. This presents a notable contrast to the case where the magnetic field is parallel to the rotational axis.

Modal and nonmodal stability analysis of turbulent stratified channel flows

Modal and nonmodal stability analysis of turbulent stratified channel flows

Direct numerical simulation of temporally evolving stratified wakes with ensemble average

Direct numerical simulations are conducted for temporally evolving stratified wake flows at Reynolds numbers from $10\,000$ to $50\,000$ and Froude numbers from $2$ to 50. Unlike previous studies that obtained statistics from a single realization, we take ensemble averages among 80–100 realizations. Our analysis shows that data from one realization incur large convergence errors. These errors reduce quickly as the number of statistical samples increases, with the benefit of ensemble average diminishing beyond 40–60 realizations. The data with ensemble average allow us to test the previously established scalings and arrive at new scaling estimates. Specifically, the data do not support power-law scaling in the centreline velocity deficit $U_0$ beyond the near wake. Its decay rate increases continuously from 0.1 at the onset of the non-equilibrium regime until the end of our calculations without reaching any asymptote. Additionally, while no power-law scalings could be found in the wake width ( $L_H$ ) and wake height ( $L_V$ ) in the late wake, $L_H\sim (Nt)^{1/3}$ is a good working approximation of the wake's horizontal size, where $N$ is buoyancy frequency and $t$ is time. Besides the low-order statistics, we also report the transverse integrated terms and the vertically integrated terms in the turbulent kinetic energy budget equation as a function of the vertical and transverse coordinates. The data indicate that there are two peaks in the vertically integrated production and transport terms, and one peak when the two terms are integrated horizontally.

Quantifying and predicting near-wall global intermittency in stably stratified channel flow

Quantifying and predicting near-wall global intermittency in stably stratified channel flow

Volumetric thermo-convective and stratified prandtl fluid magnetized flow over an extended convectively inclined surface with chemically reactive species

Substantive applications of stratified flows have been observed in various industrial operating systems. Stratified flows driven by gravity differences possess pervasive significance in the performance of nuclear reactors along with the management of safety problems due to pressurized thermal shock and induced water condensation. In addition, thermos-gravitational stratified regimes also play an exclusive role in multiphase processes in diversified engineering disciplines. Therefore, this artifact investigates the thermal and solutally stratified Prandtl fluid flow over an inclined extendable surface with magnetic field aspects. Convective boundary constraints are prescribed at the surface of the sheet and chemical reaction of first-order is also accounted. Firstly, problem formulation is conceded in the form of PDEs which are later transformed into ODEs by employing a similar set of variables. Then these ODEs are solved by employing the shooting method in collaboration with the Runge–Kutta scheme. A comparison of results in a restrictive sense with outcomes attained from an analytical approach to analyze the robustness and accuracy of currently employed schemes is also executed. The results expressing the behavior of the involved parameters on flow distributions are revealed in graphical and tabular formats. It is revealed that the heat and mass flux coefficients increase by up to 41% and 22%, respectively, in the presence of stratification in comparison to the situation when it is absent. The velocity of the fluid is accelerated by uplifting the angle of inclination and buoyancy ratio parameters. By increasing the magnitude of the model flow parameters, the fluid velocity increased. The Prandtl number tends to reduce the temperature and elevate the heat-flux coefficient. The velocity distribution showed a positive trend with the change in the angle of inclination.

Modeling of the internal wave wake of a self-propelled body for radar scattering cross sections

The motion of a self-propelled body excites internal waves that modulate wind-induced microscale waves and affect the radar scattering cross section of rough sea surfaces. This process is closely related to factors such as stratification, propulsion effect, and radar parameters. Based on this, this study establishes and partially verifies a computational model for the scattering cross section of the internal wave wake left by an underwater self-propelled body. The model incorporates the first-order resonant internal waves of the stratified flow field as the dominant component of the wake-effect internal waves and determines the equivalent source size using the wake evolution model, thereby effectively simulating the characteristics of the surface flow field when the net momentum of the underwater vessel is nonzero. By solving the wave-action conservation equations, the wave spectrum of the modulated surface is derived, and the tilt and convergence/divergence effects caused by internal waves are comprehensively considered through the facet scattering model to assess their impact on the synthetic aperture radar (SAR) scattering cross section. Overall, this study systematically elucidates the correlation mechanism between the flow field and the radar system.

Experiments on capacitance based liquid flow meter with parallel channels used in two-phase

A new flow meter has been proposed to measure liquid mass flow rate in a two-phase system. Irrespective of the input flow, the proposed system transforms incoming stream into laminar stratified flow. This configuration offers a promising avenue for assessing liquid flow rates in a two-phase system by leveraging measurements of liquid column height. Extensive performance assessments have been conducted for different vapour and liquid flows. Since the fluid properties are taken into consideration for designing the system, the temperature dependence on the performance of the flow meter also has been studied. The outcome of these studies has yielded a robust correlation between the actual liquid flow rate and the value deduced from the observed liquid column height. The correlation developed between the actual liquid flow rate and that determined from the height of fluid was accurate with an error of ± 3.8 %. It is also found that this flow meter is capable enough to determine the changes in flow conditions with temperature and would provide flow measurements within an error of ± 4 %. This novel two-phase flow meter not only advances the precision of liquid mass flow rate measurements but also demonstrates its adaptability in accommodating changing flow conditions, particularly those driven by temperature dynamics. The findings presented herein underscore the potential of this innovative flow meter as a reliable tool for accurate flow rate determination in diverse industrial applications such as cryogenics, superconductivity, etc.

Weakly nonlinear stability analysis of non-isothermal parallel flow in a vertical porous annulus

The study examines the stability of parallel airflow within a tall vertical coaxial circular annulus filled with a highly permeable porous medium under stable stratification. The linear stability theory predicts that the least unstable mode can be either axisymmetric or non-axisymmetric, depending on the values of the governing parameters. The curvature parameter, defined as the gap between coaxial circular cylinders, contributes to the stabilization of the flow. Depending on various controlling parameter values, the stably stratified non-isothermal annular parallel flow (SNAPF) can manifest three instability modes: thermal-shear, thermal-buoyant, and mixed or interactive. The instability type can change abruptly with Reynolds number, curvature parameter, and media permeability. A finite-amplitude instability analysis is examined using weakly nonlinear stability theory. The analysis demonstrates both subcritical and supercritical bifurcations near the instability boundary. The range of Reynolds numbers for subcritical bifurcation expands when switching from axisymmetric to non-axisymmetric disturbance. Bifurcation transitions between supercritical and subcritical occur due to changes in the least stable azimuthal mode. The study also investigates the equilibrium/threshold amplitude within the supercritical/subcritical instability regime, and it verifies the existence of subcritical/supercritical bifurcation through nonlinear kinetic energy balance. Furthermore, the finite-amplitude analysis anticipates that the lower critical Rayleigh number increases as the Reynolds number, curvature parameter, or media permeability decreases. An increase in the Reynolds number shifts the point of inflection in the velocity profile toward the inner cylinder, which subsequently leads to a reduction in the size of the core vortex region. In the subcritical instability regime, the radius of the primary vortex cell decreased significantly as the Rayleigh number increased. When the curvature is altered, a structural transition occurs in the isotherms from multicellular to unicellular.