Critical Flow Research Articles

THE COOLING EFFECT OF COMBUSTOR EXIT LOUVER SCHEME ON A TRANSONIC NOZZLE GUIDE VANE ENDWALL

Abstract The ever-increasing combustor exit temperature in modern turbine engine designs raises challenges for the nozzle guide vane cooling. Due to the complexity of NGV cooling design, the cooling effect from the upstream combustor cooling features can prove valuable. This study investigates, experimentally and numerically, the cooling effect of a louver cooling scheme near the combustor exit on the NGV endwall. The wind tunnel testing and CFD simulation are carried out with engine-representative conditions of an exit Mach number of 0.85, an exit Reynolds number of 1.5 × 106, an inlet turbulence intensity of 16%, and a density ratio of 2.1. Various coolant mass flow ratios from 1% to 4% are tested to demonstrate the effect of the coolant rate. For the geometry studied, the results found a critical mass flow ratio between 1%~2%. The coolant forms a uniform film only by exceeding this value to provide good coverage upstream of the NGV passage inlet. As for the cooling of the NGV passage, the mass flow ratio of the range investigated is insufficient for desirable cooling performance. The pressure side endwall proves most difficult for the coolant to reach. In addition, the fishmouth cavity at the combustor-NGV passage causes a three-dimensional cavity vortex that transports the coolant in the pitch-wise direction. The transport pattern is dependent on the coolant mass flow ratio. Therefore, the authors propose combining this louver scheme with the upstream jump cooling scheme for a desirable NGV cooling system.

Vibration characteristics of piezoelectric pipe conveying fluid subjected to fluid-structure-electrical interaction

This paper mainly investigates the vibration characteristics of piezoelectric pipe conveying fluid subjected to fluid-structure-electrical interaction. Based on the Hamilton’s principle, the dynamic equations of the cantilever piezoelectric pipe subjected to the weight and fluid-structure-electrical interaction are established and solved by using the Galerkin method. Ultimately, complex frequency and critical flow velocity are obtained. The main discussion focused on the influence of electromechanical coupling, resistive load, and dimensionless capacitance on the critical flow velocity under different lengths of piezoelectric materials. It also examined the dynamic trajectories of the real and imaginary parts of the complex frequency under various mass ratios and resistive loads. Furthermore, it explored the impact of parameters representing voltage on the stability of the system. The results indicate various stability evolutions under different lengths of piezoelectric materials, flow velocities, and parameters representing voltage. The stability of the system pipe is influenced by factors such as the length of the piezoelectric material and resistive load.

Supercritical Carbon Dioxide Critical Flow Model based on a Physics-informed Neural Network

Supercritical Carbon Dioxide Critical Flow Model based on a Physics-informed Neural Network

Effects of surface roughness on the drag coefficient of finite-span cylinders freely rolling on an inclined plane

We present an experimental investigation aimed at understanding the effects of surface roughness on the time-mean drag coefficient ( $\bar {C}_{D}$ ) of finite-span cylinders ( $\text {span/diameter} = \text {aspect ratio}$ , $0.51 \le AR \le 6.02$ ) freely rolling without slip on an inclined plane. While lubrication theory predicts an infinite drag force for ideally smooth cylinders in contact with a smooth surface, experiments yield finite drag coefficients. We propose that surface roughness introduces an effective gap ( $G_{eff}$ ) resulting in a finite drag force while allowing physical contact between the cylinder and the plane. This study combines measurements of surface roughness for both the cylinder and the plane panel to determine a total relative roughness ( $\xi$ ) that can effectively describe $G_{eff}$ at the point of contact. It is observed that the measured $\bar {C}_{D}$ increases as $\xi$ decreases, aligning with predictions of lubrication theory. Furthermore, the measured $\bar {C}_{D}$ approximately matches combined analytical and numerical predictions for a smooth cylinder and plane when the imposed gap is approximately equal to the mean peak roughness ( $R_p$ ) for rough cylinders, and one standard deviation peak roughness ( $R_{p, 1\sigma }$ ) for relatively smooth cylinders. As the time-mean Reynolds number ( $\overline {Re}$ ) increases, the influence of surface roughness on $\bar {C}_{D}$ decreases, indicating that wake drag becomes dominant at higher $\overline {Re}$ . The cylinder aspect ratio ( $AR$ ) is found to have only a minor effect on $\bar {C}_{D}$ . Flow visualisations are also conducted to identify critical flow transitions and these are compared with visualisations previously obtained numerically. Variations in $\xi$ have little effect on the cylinder wake. Instead, $AR$ was observed to have a more pronounced effect on the flow structures observed. The Strouhal number ( $St$ ) associated with the cylinder wake shedding was observed to increase with $\overline {Re}$ , while demonstrating little dependence on $AR$ .

Assessment of the Choked Flow Model of RELAP5 for Application of Inverse Quantification Methods

In the framework of deterministic safety analysis, best estimate plus uncertainty methodologies can provide a more informative detailed analysis of transients than conservative approaches. However, one important step in the application of such methodologies is derivation of uncertainty of the physical models. Probability density functions of the physical model parameters are obtained by applying inverse uncertainty quantification (IUQ) methods to experimental data. The present work deals with evaluation of the experimental database and assessment of the simulation model, which are required steps prior to the application of IUQ methods. The U.S. Nuclear Regulatory Commission system code RELAP5 has been applied for simulation of three experimental databases on choked/critical flow: Sozzi-Sutherland, Super MobyDick, and Marviken Critical Flow Tests. First, the adequacy of the experimental data to the specific target domain is carried out, to then proceed to calibration of the input model parameters by combining the use of Gaussian Process metamodels and optimization schemes. The assessment of the simulation models is performed by evaluating independently accuracy, precision, and consistency through four statistical indicators, including a novel indicator to evaluate the consistency of the results. The final results indicate that the model is capable of reproducing the selected experimental database and overall average accuracy, precision, and consistency below the 10% threshold and can be used for application of IUQ methods.

Gravity-driven flow of liquid bridges between vertical fibres

Liquid bridges are formed when a flowing liquid interacts with multiple parallel fibres, as relevant to heat and mass transfer applications that utilize flow down fibre arrays. We perform a comprehensive experimental study of flowing liquid bridges between two vertical fibres whose spacing is controlled dynamically in our experimental apparatus. The bridge patterns exhibit a regular periodic spacing typical of absolute instability for low flow rates, but become spatially inhomogeneous above a critical flow rate where the base flow is convectively unstable. The shapes of individual bridges and their associated dynamics are measured, as they depend upon the liquid properties, and fibre geometry/spacing. The bridge length scales similarly to static bridges between parallel fibres. The bridge dynamics exhibits a dependence on viscosity and scale with the impedance. A simple energy balance is used to derive a scaling relationship for the bridge velocity that captures the general trend of our experimental data. Finally, we demonstrate that these scalings similarly apply when the fibres are dynamically separated or brought together.

Shortening a mixed salt and mobile shale system: A case study from East Breaks, northwest Gulf of Mexico

The coexistence of two low-shear strength layers in a continental margin, such as salt and shales, conditions the resulting structural style and also constitutes a challenge for seismic imaging and energy resource exploration. We have analyzed the 3D structure of a mixed salt-shale system in the western Gulf of Mexico, in the East Breaks foldbelt, by interpreting a depth-migrated seismic data set. Overlying the allochthonous Sigsbee canopy and pierced by isolated salt diapirs, the Oligocene shale-prone sequences were shortened during the Miocene through pervasive deformations, developing a major suprasalt detachment system associated with duplexes below and different fold and thrust systems above. Oligocene shales locally reach a critical state and flow, resulting in: (1) inflated shale-cored detachment anticlines, with the stacking of allochthonous mobile shale domains; (2) detached lift-off anticlines with shale bulbs and fishtail thrusted welds; (3) allochthonous shale sheets at the upper tip of thrusts, fed by fluidized material migrating along associated fault zones; (4) hourglass shale diapirs; and (5) Christmas trees and vertical mud pipes connected to small mud volcanoes. The salt diapirs deformed simultaneously, as did the shales. Salt accommodated the shortening through localized subvertical welds that isolated them from the allochthonous Sigsbee canopy and through weld thrusts formed by fault-bounded blocks with highly sheared salt and mobile shales. Mobile shale structures wrap around the squeezed salt diapirs, presenting a unique pattern that has not yet been documented in experimental models with precursor salt diapirs deformed under contraction. Mixed salt-shale systems are a new challenge for structural analysis and experimental models, as well as for seismic model building in situations where there is a high dispersion of seismic energy due to the unique properties of mobile shales.

Nonlinear deterministic dynamic analysis of a GPL micropipe conveying pulsating laminar flow

In several industries, the handling of fluid-filled micropipes is common. New-brand structures are increasingly being manufactured using advanced materials. This article tackles one of the crucial dynamic analyses that an advanced fluid-filled micropipe encounters. The dynamics of a graphene nanoplatelets-reinforced micropipe (GPL micropipe) under pulsating laminar flow for the first time is examined. The Euler-Bernoulli beam model follows the modified couple stress theory (MCST) and von-Karman’s nonlinear strain to formulate the problem. The impression of the flow profile exerted by a real flow as a consequence of fluid viscosity, is taken into account. The plug flow model results are compared to those regarding real flow consideration. Using the method of multiple scales (MMS), we determine the instability area and the steady state response of the GPL micropipe subjected to the principal parametric resonance of one of its modes due to pulsating laminar flow by applying this method to the discretized couple nonlinear gyroscopic governing equations. The Floquet theory treats the linear equations and fourth-order Runge–Kutta (RK4) method attacks nonlinear ones to validate MMS findings. It is confirmed that the 0.3 % addition of the GPL to matrix phase significantly enhances its advanced attributes, making it a highly effective material. The GPL reinforcement phase in the FGO pattern increases the critical flow velocity that exhibits the micropipe to static instability by 37.98 % , and critical flow stimulation amplitude fraction by 152.19 % , while declines instability area bandwidth by 36.95 % , and steady state response by 67.17 % relative to a non-reinforced micropipe. A denser flow degrades the corresponding values by 18.40 % , 42.59 % , 41.67 % , and 227.28 % in comparison to a lighter fluid. The declared findings provide crucial insights into the key design elements affecting significantly the functioning of fluid-filled GPL micropipes system, and regulate future research and expand openings for industry applications.

Targeted opportunities to mitigate water scarcity, inequality, and inequity embedded in international food trade for vulnerable countries

International food trade reshapes regional water scarcity through virtual water transfers (VWT), influencing water use equality and equity. This study examines eight populous yet impoverished countries in Africa and Asia, representing 30 % of the global poor population and contributing 20 % to agricultural VWT. Despite their significant role, these countries have been understudied due to a lack of data or attention. By integrating multiple datasets and models, we assess how international food trade impacts water scarcity, inequality, and inequity within these countries and identify the driving factors. Our findings reveal varied outcomes: Uganda and Ethiopia benefit from reduced water scarcity (∼40 % and ∼7 %) and improved equality and equity (∼90 % and ∼68 %), while India and Pakistan face exacerbated scarcity (∼4 % and ∼2 %) and widening inequality and inequity (∼4 % and ∼7 %). The effects are largely driven by critical trade flows of staple and cash crops like rice, sugar cane, and cotton among developing countries, propelled by comparative advantages in agricultural production, econo-geography, food demand, and water endowment between importers and exporters. Addressing these water challenges involves diversifying import channels to reduce reliance on detrimental trade flows, such as India's rice exports to Iran, while promoting beneficial flows, like Bangladesh's cotton imports from India, through trade agreements. Additionally, implementing pro-poor water policies (e.g., providing water subsidies) and water-saving techniques (e.g., adopting drip irrigation) is crucial, though caution is needed to avoid unintendedly marginalizing vulnerable groups through large-scale water projects.

Blowup dynamics for smooth equivariant solutions to energy critical Landau-Lifschitz flow

In this paper, we study the energy critical 1-equivariant Landau-Lifschitz flow mapping R2 to S2 with arbitrary given coefficients ρ1∈R,ρ2>0. We prove that there exists a codimension one smooth well-localized set of initial data arbitrarily close to the ground state which generates type-II finite-time blowup solutions, and give a precise description of the corresponding singularity formation. In our proof, both the Schrödinger part and the heat part play important roles in the construction of approximate solutions and the mixed energy/Morawetz functional. However, the blowup rate is independent of the coefficients.

Stability analysis of a vertical cantilever pipe with lumped masses conveying two-phase flow

This study investigates the vibration behavior of a vertical cantilever pipe conveying gas-liquid two-phase flow, focusing on the influence of lumped masses attached to the vertical cantilevered pipe. The governing motion equation based on small deflection Euler–Bernoulli beam theory is solved by using the generalized integral transforms technique. The proposed solution approach was first validated against available numerical and experimental results in the literature. The effects of the mass ratios, number and position of lumped masses on the stability of the pipe are investigated. Numerical results show that the parameters of the lumped masses affect significantly the stability of the pipe conveying two-phase flow, by altering the fluid–structure interaction dynamics and impacting natural frequencies and vibration modes of the pipe. Specifically, as the position of a single lumped mass moves downward from the fixed end to the free end, the critical flow velocity initially increases and subsequently decreases, thereby reducing the stability of pipe. Moreover, increasing the number of lumped masses significantly impacts the critical flow velocity due to the mass ratios and locations. Notably, modal “jumping” phenomena are observed, which demonstrate continuous shifts between equilibrium and non-equilibrium states in the cantilever pipes. These findings are crucial for ensuring the safe operation of pipes with discrete masses across various engineering applications.

Coupled Modeling of Computational Fluid Dynamics and Granular Mechanics of Sand Production in Multiple Fluid Flow

Summary Sand production is a significant issue in oil and gas fields with poorly consolidated formations, often involving the multiphase flow of reservoir fluids and solid particles. The multiscale mechanisms of sand production, particularly fluid flow and particle movement, remain poorly understood. This study investigates these mechanisms using a coupled computational fluid dynamics and discrete element method (CFD-DEM) modeling approach. Single and multiple fluid flows of water and heavy oil were simulated with increasing fluid injection velocities, leading to different sand production patterns. The simulation results were compared with experimental results from a large cylindrical specimen of weak artificial sandstone under similar loading conditions. The multiphase conditions created various localized flow and deformation patterns that influenced both fluid and solid production, resulting in shorter transient sand production periods. Microstructures and phenomena such as fingering and water coning were observed, associated with a critical flow rate below which oil displacement was uniform and no water breakthrough occurred. Higher fluid injection velocities and fluid viscosities resulted in greater drag forces, leading to progressive damage zones and explaining the occurrence of single or multiple staged sand production events. The evolution of the microscopic granular structure was visualized under the effect of transient sand production.

Exact closed-form solution for buckling and free vibration of pipes conveying fluid with intermediate elastic supports

In this paper, the exact closed-form solution is given to investigate the influence of the intermediate elastic support on the buckling and free vibration of an elastically supported pipe. According to the Euler–Bernoulli beam theory, the mechanical model of the pipe is established. The exact equilibrium configuration is derived using the generalised function method without enforcing continuity conditions. A simple solution to the eigenvalue problem is formulated using the methods of complex mode superposition and Laplace transformation. The comparative study shows the differences in the supercritical vibration characteristics and highlights the limitations of previous studies. Parametric studies are carried out to investigate the influence of elastic support and intermediate support conditions on the equilibrium configuration, critical flow velocity, and natural frequency. The results demonstrate that the proposed closed-form solution can determine the support conditions that lead to the maximum critical flow velocity and natural frequency of a pipe with multiple intermediate supports. The maximum values are required to adjust the support conditions leading to the nodes of higher-order equilibrium configurations and complex modes. Furthermore, the natural frequencies of the pipe conveying supercritical fluid no longer satisfy the monotonicity for the support stiffness, the symmetry for the support position, and the ‘zero-point’ property for the support number.

Assessment of short-term supply disruption impacts for the Swiss mobility, energy and ICT sectors – Application of the SPOTTER approach

In this paper, supply disruption impacts along supply chains within the Swiss mobility, energy and ICT sectors are assessed in the short-term (i.e. the next 5 years) using the recently developed SPOTTER approach with the objective to identify hotspots and technologies associated with comparably low supply risks. SPOTTER has been chosen because, compared to other approaches, it is the only one that allows for an assessment along the full supply chain and it is integrated into the Life Cycle Sustainability Assessment framework. To decrease the respective data acquisition efforts for the here-performed supply risk analysis of entire sectors, in a first step, material/product flows that are most influential for an assessment with SPOTTER are identified and considered for the calculation of related impact scores. Our study analyzes critical material and product flows between trade partner countries along relevant supply chains. It thus identifies new hotspots and adds relevant country-specific information to current knowledge. In particular, the identified hotspots refer to volatile prices of solar panels, interrupted trade of oil and gas from Russia, Nigeria and Niger as well as disrupted imports of electronic devices from China. Suggestions for mitigation strategies comprise hedging and/or diversifying the supply chains. Other identified hotspots refer to the critical supply of cobalt and natural graphite along battery supply chains, which could for example be addressed by supporting and/or incentivizing the construction of a circular economy. A third category of identified hotspots indicates risks related to the trade of hafnium and nuclear power plant equipment that could be mitigated by shifting to less risky energy technologies. Our comparisons of overall impacts between relevant technologies suggest higher supply risks for conventional cars, solar panels and Chinese laptops compared to battery electric cars, wind turbines and German laptops. In these comparisons, more details regarding disruptions along full product and fuel supply chains are considered than in current studies.

Effect of Nonlinear Magnetic Forces on Transverse Galloping Dynamics of Square Cylinders

Under the influence of cross-fluid flow, a cylinder of a square cross-section may gallop. Galloping is a self-excited vibration mode that can be utilized for low-power harvesting applications. The harvested power depends on several factors, including upstream flow velocity and system dynamics. This study explores the potential of magnetically-induced nonlinear stiffness to improve the power output of galloping-based energy harvesters. In this experimental study, the vibration response of a square rod with a mass ratio of 10 is investigated at a Reynolds number of 200. The vibration behavior of two identical coaxial square rods with magnetic monopoles at opposite ends is analyzed. Results reveal that the magnets’ configuration and strength significantly affect vibration amplitude and the critical flow velocity necessary for the onset of galloping.

A Review of Numerical Methodologies for Predicting Rotating Stall and Surge in High-Speed Centrifugal Compressors

Abstract High-speed supersonic radial compressors are a critical enabling technology for meeting the requirements of future aviation- propulsion and thermal-management systems. These turbomachines must be designed to be both efficient and robust on the widest possible operating range. Flow instabilities in the form of rotating stall and surge are therefore phenomena that must be accurately predicted early in the design process. Unsteady full-annulus computational fluid dynamics can be used to get accurate information about the onset of instabilities, but at the expense of costly simulations. As a result, the design of new compressors continues to rely on existing correlations for the prediction of the critical mass flow rate. This approach, however, leads to sub-optimal compressor designs. This article provides a review of the numerical methodologies that can be used for the accurate prediction of the critical mass flow rate in high-speed centrifugal compressors. Methods of different fidelity level and computational cost are described. Two particularly promising models, namely those proposed by Spakovszky and Sun, are subsequently examined in more detail. Exemplary applications of these two models are finally discussed.

Circular orbits of accretion flow around charged black hole coupled with a nonlinear electrodynamics field

This study investigates the particle’s geodesic motion and accretion around the spherically symmetric Reissner–Nordström black hole coupled with a nonlinear electrodynamics field. The formation of the disc-like structure in the accretion process arises from the geodesic motion exhibited by particles near the black hole. In the equatorial plane, we analyze the circular orbits of particles and their stability in detail. The analysis of the fluid’s critical flow, maximum accretion rate, radiant flux energy, radioactive efficiency, and radiant temperature are also examined near the central object. We analyze the perturbations experienced by particles throughout, employing restoring forces and the oscillatory behavior of the particles around the black hole. Our results show that the NED parameter ζ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta $$\\end{document} affects the circular geodesics of particles and the maximum accretion rate of the Reissner–Nordström black hole coupled with nonlinear electrodynamics.

Calculation Modeling of Adsorbed and Bulk-Phase Oil Resources Based on Molecular Dynamics Simulations

Summary Nanopores prevalent in shale reservoirs significantly impact shale oil occurrence characteristics due to the strong intermolecular forces between crude oil molecules and the pore walls. Unlike bulk-phase oil, which is more readily recoverable with current technologies, the behavior of oil within these small-scale environments presents unique challenges. This study utilizes molecular dynamics simulations (MDSs) to investigate the characteristics of shale oil in slit nanopores, with the goal of refining a model that estimates the quantities of both bulk and adsorbed oil in shale reservoirs. We constructed models for three types of nanopores—organic graphene, illite, and quartz—using n-hexane (n-C6H14) as a proxy for shale oil. Our analysis reveals that mineral composition significantly influences fluid adsorption capacity, ranked as graphene > illite > quartz. Unlike prior research, we found that the critical flow pore diameter, which dictates the transition from adsorbed to free-flowing oil, cannot be simplistically equated to the combined thickness of adsorption layers. Specifically, in graphene pores with a diameter of 3.8 nm, the fluid mass density at the pore center still exhibits adsorption layer characteristics, forming up to nine layers. Building on these insights, we revised the shale reservoir resource estimation model to account for adsorption variances across different pore types. Our findings highlight the significant role of adsorbed oil in nanopores within shale reservoirs. Data from the Gulong shale oil block in the Daqing oil field indicate that adsorbed oil constitutes 37.15% of geological reserves, while bulk-phase oil accounts for the remaining 62.85%. This research provides essential data for accurately calculating shale oil reserves in nanopores, which are crucial for the effective exploitation of shale oil reservoirs.

Regression prediction of critical exhaust volumetric flow rate in tunnel fire with two-point extraction ventilation based on neural network method

In this study, a Genetic Algorithm-Backpropagation Neural Network (GA-BPNN) model was developed to predict critical exhaust volumetric flow rate in tunnel fires with two-point extraction ventilation system. Seven influencing factors served as inputs for the model, while the critical exhaust volumetric flow rate was the output. Experimental data from two reduced-scale tunnels were utilized to both train and validate the GA-BPNN model. The results demonstrate a satisfactory prediction performance, with key metrics such as Mean Absolute Percentage Error (MAPE), Relation Coefficient (R2), and Root Mean Square Error (RMSE) achieving values of 0.0384, 0.9989, and 3.5258, respectively. Importantly, the model maintains a maximum Absolute Percentage Error (APE) below 10 %. In contrast, the traditional BPNN model exhibited an APE of approximately 18.9 %. Moreover, the predictive results of the GA-BPNN model were compared with those of a previously semi-empirical formula. It was observed that the semi-empirical predictions exhibited APE exceeding 20 % for certain data points. This further underscores the superiority of the GA-BPNN model in predicting critical exhaust volumetric flow rates in tunnel fires with two-point ventilation system. These findings affirm the feasibility and effectiveness of GA-BPNN regression model as a reliable method for predicting critical exhaust volumetric flow rates under multiple factors.

Combination of two-fluid model and delayed equilibrium model for the critical flow in a slit

Accurately predicting the mass flux, pressure profile, and velocity profile of the critical flow in a slit is essential for analyzing the breaking process of the liquid phase and calculating the aerosol source term for leak-before-break (LBB) monitoring and Loss of Coolant Accident (LOCA) risk analysis. A new critical flow model combining Two-fluid Model (TFM) and Delayed Equilibrium Model (DEM) is built to get accurate profiles while avoiding the same phase velocity in DEM and the arbitrary critical flow criterion in TFM. The new model is verified using past experiments of the critical flow in a slit. It proves to be accurate in mass flux but not in critical pressure, with maximum relative errors of around 25% in mass flux and around 80% in critical pressure. The new model is optimized for higher accuracy in critical pressure. The empirical equation of saturated phase mass flow rate fraction gradient is optimized by conducting approximate pressure profile calculation and regression analysis. The maximum relative error decreases little while the ratio of critical pressure relative errors lying in the range of ±40% increases after optimization. In contrast, the difference in the average abstract relative error of pressure between original TFM-DEM and DEM is much larger, for the maximum relative error of mass flux and critical pressure are around 25% and 110%. The comparison between the original and optimized TFM-DEM proves that the new critical flow model is accurate in mass flux and can be optimized to raise pressure calculation accuracy. The comparison between the original TFM-DEM and DEM proves that the phase velocity difference is the major source of accuracy improvement in the pressure profile.