Critical Flow State Research Articles

Effect of different underlying surfaces on hydraulic parameters of overland flow

The estimation of hydraulic parameters is the basis for establishing soil erosion models. However, the underlying surfaces greatly influence the hydraulic parameters of the overland flow. Since sediment flow and slope surface resistance interact, exploring the mechanism of overland flow movement in relation to different underlying surfaces is essential. A potential relationship between hydrodynamic parameters and slope gradient and flow discharge was investigated by carrying out overland flow experiments, which used four types of non-erosion slope surfaces (stem cover, brown soil, frozen soil, and organic glass), four slope gradients (3°, 6°, 9°, and 12°), and four flow discharges (0.35, 0.45, 0.55, and 0.65 L s–1). The results showed that the hydraulic parameters (i.e., mean flow velocity, flow depth, Froude number, Reynolds number, shear stress, drag coefficient, stream power, and unit stream power) differed with the increased slope gradients and flow discharges. The mean flow velocity of the stem cover slope was lower than that of the frozen soil slope, brown soil slope, and organic glass slope by 33%, 40%, and 50%, respectively. The stem cover slope drag coefficient was higher than the frozen soil slope, brown soil slope, and organic glass slope by 201%, 323%, and 630%, respectively. The critical flow states of the underlying surface were different under different slope gradients and flow discharge conditions. The flow on frozen soil slopes was mainly laminar and transitional, while the other three were transitional. These results help us understand the hydrodynamic mechanisms of the sediment transport process during overland flow. The results of the study provide a scientific basis for understanding the hydrodynamic mechanism of the dynamic changes of the sediment transport on the slope, deepening the understanding of the soil erosion mechanism and improving the prediction accuracy of the soil erosion process model.

Real-time polymer flow state monitoring during fused filament fabrication based on acoustic emission

Fused filament fabrication (FFF) has been widely used in various manufacturing situations and has shown that it is flexible and convenient in complex customize manufacturing scenarios. It is worth noting that the flow state of polymer melt inside the nozzle of the FFF process is closely related to the quality of the printed product, however, it is an unsolved problem to obtain effective information about this critical flow state by an in-situ and nondestructive method. In this work we proposed a strategy for identifying the polymer melt flow state inside the nozzle in the FFF process. Firstly, we summarized three types of printing products of different quality which was drawn by three different flow state, specifically an acoustic emission sensor was adopted to collect the information of flow state due to its real-time and nondestructive capability, the experiment of collecting acoustic emission (AE) signals under three different flow conditions was established, then an deep learning based pattern recognize model named AETCN was adopted to identify difference flow state without complex data preprocessing, and the accuracy rate is more than 98%. Results of our works can provide a novel perspective for FFF quality monitoring and benefit to the development of an FFF advanced monitoring system.

A performance comparison of the most commonly used minimally invasive monitors of cardiac output.

Shock is common in critically ill and injured patients. Survival during shock is highly dependent on rapid restoration of tissue oxygenation with therapeutic goals based on cardiac output (CO) optimization. Despite the clinical availability of numerous minimally invasive monitors of CO, limited supporting performance data are available. Following approval of the University of Saskatchewan Animal Research Ethics Board, we assessed the performance and trending ability of PiCCOplus™, FloTrac™, and CardioQ-ODM™ across a range of CO states in pigs. In addition, we assessed the ability of invasive mean arterial blood pressure (iMAP) to follow changes in CO using a periaortic transit-time flow probe as the reference method. Statistical analysis was performed with function-fail, bias and precision, percent error, and linear regression at all flow, low-flow (> 1 standard deviation [SD] below the mean), and high-flow (> 1 SD above the mean) CO conditions. We made a total of 116,957 paired CO measurements. The non-invasive CO monitors often failed to provide a CO value (CardioQ-ODM: 40.6% failed measurements; 99% confidence interval [CI], 38.5 to 42.6; FloTrac: 9.6% failed measurements; 99% CI, 8.7 to 10.5; PiCCOplus: 4.7% failed measurements; 99% CI, 4.5 to 4.9; all comparisons, P < 0.001). The invasive mean arterial pressure provided zero failures, failingless often than any of the tested CO monitors (all comparisons, P < 0.001). The PiCCOplus was most interchangeable with the flow probe at all flow states: PiCCOplus (20% error; 99% CI, 19 to 22), CardioQ-ODM (25% error; 99% CI, 23 to 27), FloTrac (34% error; 99% CI, 32 to 38) (all comparisons, P < 0.001). At low-flow states, CardioQ-ODM (43% error; 99% CI, 32 to 63) and Flotrac (45% error; 99% CI, 33 to 70) had similar interchangeability (P = 0.07), both superior to PiCCOplus (48% error; 99% CI, 42 to 60) (P < 0.001). Regarding CO trending, the CardioQ-ODM (correlation coefficient, 0.82; 99% CI, 0.81 to 0.83) was statistically superior to other monitors including iMAP, but at low flows iMAP (correlation coefficient, 0.58; 99% CI, 0.58 to 0.60) was superior to all minimally invasive CO monitors (all comparisons P < 0.001). None of the minimally invasive monitors of CO performed well at all tested flows. Invasive mean arterial blood pressure most closely tracked CO change at critical flow states.

Experiment Study of Outburst Pulverized Coal-Gas Two-Phase Flow and Characteristic Analysis of Outburst Wave

Coal and gas outburst is still a major safety problem in the process of coal production in China. Correctly understanding of the migration law of outburst high gas and pulverized coal is an important basis for accurately predicting the occurrence time and possible scope of outburst. To reveal the airflow disturbance characteristics and coal-gas flow rule in coal and gas outburst process, outburst coal-gas migration simulations under different gas pressures were conducted using a self-developed visual outburst dynamic effect test device. The results showed that coal-gas flow state at the outburst port is divided into subcritical flow, critical flow, and supercritical flow state. The pulverized coal-gas flow migration in the roadway space can be divided into coal gas two-phase flow area, air compression area, and undisturbed area. Under the experimental conditions, the maximum propagation velocities of wave are 342.22~359.21 m/s, and the coal gas two-phase flow is far less than the propagation velocities of outburst wave, just 3.68~33.33 m/s. When the outburst energy is large, multiple compression waves can superimpose to form shock waves. The peak value of the wave does not necessarily appear in the first boosting range. The presence of pulverized coal leads to a faster attenuation of shock wave, but it makes a greater dynamic destructive force at the same speed.

Experimental investigation on the combined effects of surface roughness and corner radius for square cylinders at high Reynolds numbers up to 107

In this study, the aerodynamics of 2D, slightly rough, square-section cylinders with rounded corners is experimentally investigated for Reynolds numbers up to about 12 × 106. The cylinders have a mean relative surface roughness of k/D = 1 × 10−3, a corner radius of either r/D = 0.16 or 0.29 and are positioned at an angle of incidence of 0° or −45° in cross-flow direction. The results show that a larger corner radius induces lower drag coefficients and higher vortex shedding frequencies for all flow regimes, but at lower shedding intensities. Changing the angle of incidence from 0° to −45° results in all coefficients and the wake profile to become nearly independent of the Reynolds number. The critical flow state furthermore shifts to higher Reynolds numbers and decreases in length, whereas the supercritical flow state reduces to a single point. An increase of the surface roughness height from k/D = 5 × 10−6 to k/D = 1 × 10−3 induces a shift of the flow regimes towards significantly lower Reynolds numbers. The values of the coefficients show a lower dependency on the Reynolds number in all flow regimes, whereas in the upper transition a strong recovery of all coefficients towards subcritical values takes place.

Experiments on the aerodynamic behaviour of square cylinders with rounded corners at Reynolds numbers up to 12 million

The influence of the angle of incidence and corner radius on the aerodynamics of square-section cylinders is studied by means of wind tunnel experiments. Two different corner radii (r∕D=0.16 and 0.29) were investigated at three angles of incidence (α=0°, −22.5° and −45°). Steady and unsteady global forces and local surface pressures were measured in the high-pressure wind tunnel in Göttingen. The Reynolds number was varied up to values as high as 12×106, thereby spanning the known flow state regimes up to high transcritical. The results demonstrated that a decrease of the cylinder’s bluffness induced lower maximum drag coefficients and r.m.s. values, as well as higher Strouhal numbers in all flow state regimes. Furthermore, the critical Reynolds numbers shifted to significantly lower values. For the cylinder configurations at α=0° no upper transition or transcritical flow state was present up to ReD=12 million. A decrease in the angle of incidence resulted in a significant reduction of the length of the supercritical flow state, a shift of the drag force, Strouhal number and base pressure to higher values and an increase of the critical Reynolds numbers. The cylinders at non-zero angles of incidence all displayed a clear critical flow state, at which two discontinuous transitions were observed, accompanied by jumps in the CD and CL values and the Strouhal number. Only three out of six studied configurations experienced hysteresis, where for the high corner radius configuration at α=0° a particularly broad hysteresis effect was measured.

Aerodynamic forces and galloping instability for a skewed elliptical cylinder in a flow at the critical Reynolds number

The mechanism of large-amplitude aeroelastic vibrations of cylindrical bodies in the critical Reynolds number range are still unclear. This study concerns the aerodynamic forces acting on elliptical cylinders and the induced galloping instability resulting from skew flows (i.e., the direction of the flow is angled 0°–45° with respect to the central axis of the cylinder) for Reynolds numbers in the range of 37–235 k. The effects of the critical Reynolds number and the skew angle on the aerodynamic forces and the galloping instability are investigated with pressure wind tunnel tests. In all of the cases investigated in the present study, a sharp decrease in the lift coefficient with increasing angle of attack and a reduction in the drag coefficient at the critical Reynolds number could be responsible for the galloping instability. Variations in the torque coefficient leads to a torsional aerodynamic instability at the critical Reynolds number. Furthermore, the skew flow cause a critical flow state at lower Reynolds numbers. One possible reason for this behavior is that the longer effective cross section allows the flow to reattach.

Effect of the Reynolds number on the aerodynamic forces and galloping instability of a cylinder with semi-elliptical cross sections

The effects of the Reynolds number on the aerodynamic forces and galloping instability of a semi-elliptical cross-section, which are used to simulate the shape of the iced conductors, have not been fully studied. Simultaneous multi-pressure wind tunnel experiments were conducted to explore the aerodynamic forces on cylinder with semi-elliptical cross-sections; the Reynolds number was in the sub-critical and critical regimes. A unified single-degree-of-freedom (SDOF) approach and a three-degree-of-freedom (3-DOF) model were used to analyze the galloping instability with the Reynolds number in the following regime: Re=34k–175k. The variation in the aerodynamic force with the angle of attack is sensitive at the critical Reynolds number; at this critical regime, the sudden decrease in the lift coefficient value with an increasing angle of attack is sufficient to create negative aerodynamic damping. The galloping instability analysis shows that the occurrence of negative aerodynamic damping strongly depends on the critical flow state. In all cases considered in the present work, the critical Reynolds number effects are shown to include aerodynamic forces that could well be responsible for the whole range of translational galloping instabilities and part range of torsional flutter and 3-DOF galloping instabilities for semi-elliptical cylinders.

Numerical investigation of aeroacoustic characteristics of a circular cylinder in cross-flow and in yaw

It is well known that aerodynamic noise becomes dominant when the speed of high-speed trains exceeds about 300 km/h. The pantograph is one of the main aerodynamic noise sources, particularly in the presence of noise barriers which shield the sources on the lower part of the train more effectively. The pantograph consists of a number of slender bodies with different cross-sections. In the current research, the aerodynamic characteristics of a circular cylinder have been investigated through computational fluid dynamics simulations using a Delayed Detached-Eddy Simulation model. Then the aeroacoustic behaviour has been predicted by using Ffowcs Williams-Hawkings equation. Simulations have been carried out for various speeds, resulting in a wide range of Reynolds number, which includes subcritical, critical, and supercritical flow states. The results have been compared with experiments and give good agreement. As the pantograph arms are inclined to the flow, the effect of yaw angle is analyzed in this paper and the effect on vortex-shedding frequency and noise level is determined. Moreover, it is demonstrated that the critical Reynolds number, which determines the beginning of the critical flow state, is affected by the yaw angle. In addition, considering the high turbulence intensity on the train roof, a turbulent inflow with different levels of intensity has been considered and the results will be presented.

Finite amplitude long-wave instability of a thin viscoelastic fluid during spin coating

This paper investigates the stability of a thin incompressible viscoelastic fluid designated as Walters’ liquid B″ during spin coating. The long-wave perturbation method is proposed to derive a generalized kinematic model of the film flow. The method of normal mode is applied to study the linear stability. The amplitude growth rates and the threshold conditions are characterized subsequently and summarized as the by-products of the linear solutions. Using the multiple scales method, the weakly nonlinear stability analysis is studied for the evolution equation of a film flow. The Ginzburg–Landau equation is determined to discuss the threshold conditions of the various critical flow states. The study reveals that the rotation number and the radius of the rotating circular disk generate the destabilizing effects. Moreover, the viscoelastic parameter k indeed plays a more significant role in destabilizing the film flow than a thin Newtonian fluid during spin coating [27].

Weakly Nonlinear Stability Analysis of a Thin Magnetic Fluid during Spin Coating

This paper investigates the stability of a thin electrically conductive fluid under an applied uniform magnetic filed during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. After linearizing the nonlinear evolution equation, the method of normal mode is applied to study the linear stability. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The Ginzburg-Landau equation is determined to discuss the necessary conditions of the various critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that the rotation number and the radius of the rotating circular disk generate similar destabilizing effects but the Hartmann number gives a stabilizing effect. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.

Critical Flow: A Historical Perspective

The dynamics of free surface flows are strongly influenced by the so-called critical flow state. The critical flow theory is relevant from an engineering standpoint, allowing for the computation of the head-discharge relationship for weirs and flumes, or the identification of control sections from which a free surface profile may be computed both in the up- and downstream directions Montes 1998; Hager 1999; Chanson 2004. In what follows, the origins of the critical flow concept are reviewed. Its evolution from perspectives of both the specific energy and the specific momentum is then highlighted, involving applications both in parallel- and curvilinear-streamline flows.

Weakly Nonlinear Stability Analysis of a Thin Liquid Film With Condensation Effects During Spin Coating

This paper investigates the stability of a thin liquid film with condensation effects during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. The weakly nonlinear dynamics of a film flow are studied by the multiple scales method. The Ginzburg–Landau equation is determined to discuss the necessary conditions of the various states of the critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that decreasing the rotation number and the radius of the rotating circular disk generally stabilizes the flow.

Influence of Downstream Control and Limited Depth on Flow Hydrodynamics of Impinging Buoyant Jets

Much study has been performed on the mixing properties of submerged, turbulent buoyant jets. It is safe to say that the problem of estimating dilution rates in vertical buoyant jets spreading in an `infinitely deep' ambient water has been more than adequately resolved by previous researchers. However, the majority of environmental applications involve discharges into ambient waters of finite depths in which a bounding surface serves to re-direct the impinging buoyant jet horizontally into a radial spreading layer. Previous research indicates that this impinging jet undergoes additional mixing before buoyancy stabilizes vertical mixing and confines the spreading layer to the vicinity of the bounding surface. Unfortunately, the conceptualization and subsequent mathematical modeling of this additional mixing phenomenon is surrounded by considerable amount of disagreement between researchers. The purpose of this study is to provide, by means of velocity and concentration profile measurements, independent experimental evidence for the existence of a critical flow state immediately downstream of the active mixing zone in the horizontally flowing, radial flow that forms after impingement. It is further shown that this critical flow state must be expressed in terms of a composite Froude Number that takes into account the possibility of a non-zero exchange layer flow. Finally, the influence of the presence of a sill-like topographic downstream control on the criticality of the radial flow immediately downstream of the active mixing zone is also investigated.

Unsteady Flow Around an Elliptic Cylinder in the Critical Reynolds Number Regime.

Experimental investigation of the flow around an elliptic cylinder of axis ratio 3 : 1 was carried out for several angles of attack and a wide range of Reynolds numbers. The flow characteristics were studied by measuring the fluid force and the surface pressure fluctuation. In the critical Reynolds number regime, a discontinuous change of flow state was observed. This change was accompanied by the hysteresis effect. The fluid force and the pressure fluctuation decreased markedly in the critical flow state.

The critical cross-section of a vortex

This paper discusses the problem of critical-flow cross-sections in vortex flows. It is shown that there are two different types of vortex flows, A-type and B-type vortices (say). An A-type vortex approaches its critical flow state as its cross-sectional area increases and departs from the critical state as the cross-sectional area is decreased. This property is associated with the particular dependence of total pressure and circulation on the stream function, and it holds for both subcritical and supercritical A-type vortices. On the other hand, both subcritical and supercritical B-type vortices approach their critical flow states as their cross-sectional areas are decreased and depart from their critical states for increasing cross-sectional area. As was shown by Benjamin, setting the first variation of the flow force with respect to the stream function equal to zero leads to Euler's equation of motion. The second variation also vanishes if the corresponding flow state is critical. In this case the sign of the third variation decides whether the flow is an A-type or a B-type vortex. Within the framework of inviscid-fluid flow theory the type of a vortex is preserved unless vortex breakdown occurs. Making use of the knowledge that vortex flows are controlled by two different types of critical-flow cross-sections a variety of vortex flow phenomena are investigated, including the two types of inlet vortices that are observed upstream of jet engines, the behavior of vortex valves, the flow characteristics of liquid-fuel atomizers and the bath tub vortex.

Entrainment effects in vortex flows

Following recent work of the present author [Phys. Fluids 6, 1524 (1994)], the effects of entrainment of axisymmetric vortex flows are further investigated. Assuming self-similar flow, it is found that, under the influence of entrainment, vortex flows with jet-like cores always approach certain critical flow states, and self-similar solutions cease to exist afterward. It is argued that this apparent paradox can be resolved by accounting for the possibility of vortex breakdown. Furthermore, explanations are presented for the possible appearance of successive vortex breakdown transitions and for the increasingly jet-like character of certain subcritical vortex flows as they approach a cross section of critical flow.

On tornado-like vortex flows

In a first step, the problem of inviscid axisymmetric flow with buoyancy is investigated. It is found that both supercritical and subcritical vortex flows depart from their critical flow states if they are dominated by buoyancy. In a second step, the effects of entrainment are also taken into account. However, the investigation is restricted to nearly self-similar flows. Both supercritical and subcritical vortex flows approach their critical flow states if they are dominated by entrainment. However, the superimposed effects of buoyancy and entrainment may lead to an equilibrium close to the critical state. It is argued that the existence of such an equilibrium is the direct reason for the appearance of certain violent vortex flows in nature, including tornadoes and fire storms. The weather conditions that may lead to the appearance of tornadoes and the different forms of appearance are also discussed.

The effect of three closures on critical conditions in two-phase flow with unequal phase velocities

The paper develops an analytic approach to assess the effect of three closure conditions on the critical-flow state in two-phase flow. The approach is based on the geometrical-topological analysis of dynamical systems. The details of the analysis are developed in relation to a “general slip” model which is completed by three closure conditions: homogeneous flow, Bankoff's hypothesis and the drift-flux model. For the sake of simplicity, the study is restricted to adiabatic flows and thermodynamic equilibrium. These make it possible to reduce the model to a single quasi-linear differential equation and to parametrize the problem with respect to the mass-flow rate m ̇ and the total stagnation enthalpy h. The phase space is thus reduced to the P, z diagram. Detailed results are given for the flow of water/steam through a convergent-divergent nozzle discharging from a stagnation reservoir. All three closures lead to the same topological structure of the “potrait” of solutions in the phase space which incorporates a saddle point. The numerical results are summarized in table 1. This shows that the location of the critical cross-section (saddle point) is essentially unaffected by the closure chosen for the model; it is situated very close to the throat and downstream from it. The most significant critical-flow characteristics, such as mass-flow rate, critical pressure, critical velocity, critical void fraction and critical slip velocity differ markedly from those predicted by the homogeneous-flow assumption when the effects of slip are included. The differences between the two closures with the slip are significant but much smaller than between either of them and the no-slip model. All models calculate a very large increase in the void fraction as the critical state near the throat is approached. This is interpreted to mean that none of the three closures should be used to analyze critical flows, because their validity has been tested only for much lower values of void fraction. The critical velocity is a sole function of the local thermodynamic state. The two slip closures lead to considerable differences in this relationship when compared with the sound velocity under homogeneous-flow conditions.

Wellbore and Near-Surface Hydraulics of a Blown-Out Oil Well

Summary A method is presented for calculating the critical flow velocity, pressure, and temperature at the exit of a blown-out oil well. The calculation depends on the wellbore geometry, the thermal properties of the wellbore and its surroundings, and an a priori knowledge or estimate of the well productivity index (PI) and gas/oil ratio (GOR). A procedure is also given for estimating the flow conditions at the end of the two-phase pressure transition region that forms above the well exit. Introduction Among the primary concerns associated with a blown-out oil well are the environmental effects of the expelled fluids. In addition to the obvious pollution hazards, there is the danger of gas/oil combustion. If the gas plume ignites, various additional problems are created. Heating effects of a burning well can damage nearby equipment and neighboring wellheads. To analyze and predict such effects, estimates of certain flow parameters at the discharge of the well are needed.The primary mechanism governing the hydraulics of a blown-out oil well is the rapid, near-surface liberation and subsequent expansion of large amounts of dissolved gas. As the accelerating fluids rise to the surface, their speed is limited by the available flowing pressure. For typical GOR'S, it has been found that the two-phase pressure drop limits the speed and, hence, the maximum rate of flow. As the speed of the fluids approaches the critical (sonic) speed of the mixture, the pressure drop increases dramatically. Corresponding to the two-phase sonic discharge velocity is the critical (minimum possible) discharge pressure. The critical flow state depends strongly on the relative volumes of oil and free gas present at the surface. As the critical pressure decreases, the volumetric fraction of free gas increases, causing an increase in the two-phase critical speed for typical GOR's.It is possible for a blowout flow rate to be less than critical because of partial blockage of the well exit. In such cases the surface pressure will stabilize at a value greater than the critical pressure. Whatever the nature of the well exit, however, there is a region of pressure transition between the underexpanded pipe flow and its associated two-phase atmospheric plume. The flow conditions at the end of this region are important for analyzing the subsequent interaction between the expelled wellbore fluids and the atmosphere.The analysis of the wellbore and discharge jet hydraulics has been coupled with the formation characteristics and the reservoir pressure. Knowledge of the well PI, bottomhole temperature, and GOR then fixes the critical flow conditions for a given well. A method has been developed for calculating the critical flow from an uncontrolled oil well. The discharge pressure, temperature, and speed are calculated interatively until the two-phase pressure drop limitation is established at the surface. Once the critical discharge conditions are determined, the next step is to calculate the flow at the end of the two-phase pressure transition region outside the wellbore. These calculations then serve to establish the starting point for analyzing the subsequent interaction between the expelled wellbore fluids and the atmosphere. Results obtained for the pressure transition region appear to be in good agreement with published predictions and photographs of supersonic underexpanded gas jets. JPT P. 2181^