Supercritical Flow Regimes Research Articles

On the effect of flow regime and slope of the channel bed on the hydraulic performance of the sharp-crested rectangular side weir: a numerical simulation

The aim of this study is to numerically investigate the effect of bed slope on the hydraulic performance of side weirs in supercritical and subcritical flow regimes. Increasing the bed slope decreases the weir efficiency and discharge coefficient in the subcritical flow regime up to 14.54% and in the supercritical flow regime up to 9.26%. By examining the longitudinal velocity distribution, it was observed that in the subcritical flow regime, the maximum longitudinal velocity occurs at the beginning of the upstream of the side weir, and by moving towards the downstream of the weir, the flow velocity decreases and increases again after leaving the length of the weir. In the supercritical flow regime, it has an increasing trend when the flow enters from the upstream of the side weir. The increase in discharge coefficient with the increase of the weir height varied between 4.6% and 7.8%. With increase of the slope of the channel bed, the velocity along the length of the weir increases by 10.88% and 6.17%, respectively, in the subcritical and supercritical regimes, and the transverse velocity along the transverse direction for the subcritical and supercritical flow regimes decreased by 22.23% and 4.80%, respectively.

Nonlinear gravity waves in the channel covered by broken ice

The two-dimensional nonlinear problem of a steady flow in a channel covered by broken ice with an arbitrary bottom topography including a semi-circular obstruction is considered. The mathematical model is based on the velocity potential theory accounting for nonlinear boundary conditions on the bottom of the channel and at the interface between the liquid and the layer of the broken ice, which are coupled through a numerical procedure. A mass loading model together with a viscous layer model is used to model the ice cover. The integral hodograph method is employed to derive the complex velocity potential of the flow, which contains the velocity magnitude at the interface in explicit form. The coupled problem is reduced to a system of integral equations in the unknown velocity magnitude at the interface, which is solved numerically using a collocation method. Case studies are conducted both for the subcritical and for the supercritical flow regimes in the channel. For subcritical flows, it is found that the ice cover allows for generating waves with amplitudes larger than those that may exist in the free surface case; the ice cover prevents the formation of a cusp and extends the solution to larger obstruction heights on the bottom. For supercritical flow regimes, the broken ice significantly affects the waveform of the soliton wave making it gentler. The viscosity factor of the model apparently governs the wave attenuation.

Flutter in a simplified blade cascade: Limits of the quasi-steady approximation

Flow-induced vibration in turbomachinery represents a major and persistent concern, especially in modern turbine and compressor designs with long and slender blades operating in transonic flow conditions. There is a wide range of computational and experimental methods for blade flutter prediction and analysis. In certain situations, the quasi-steady approximation can be utilized, considering the unsteady flow as a sequence of steady flow fields for each position of the oscillation cycle. The study is focused on experimental investigation of the limits of applicability of the quasisteady approximation in the case of a simplified linear five-blade cascade with the middle blade undergoing high-frequency torsional oscillation due to kinematic excitation. A measurement campaign of more than 100 wind tunnel runs was carried out for flow velocities ranging from high subsonic to transonic regimes (M = 0, 0.529, 0.777 and 1.018), frequency ratios 0 - 0.75 and reduced frequencies k = 0 – 0.41. A comparison of quasi-steady and time-resolved blade surface pressure measurements is reported, and the degree of unsteadiness of the airflow is quantified. For low reduced frequencies the stationary distributions match almost perfectly the time-resolved profiles. The degree of unsteadiness remains below 2% up to k = 0.1 for the subsonic and supercritical flow regimes. For reduced frequencies above 0.2, the global degree of unsteadiness increases quickly up to 10%, with local differences between the stationary and time-resolved pressure profiles up to 40%. In the case of transonic flow regime, the flow unsteadiness is generally higher and further complicated by intermittency — stochastic transition from supersonic to subsonic flow in the aft part of the blade.

Effects of vegetation stem coverage on the hydraulic characteristics and on-wall and jet flow proportions at the gully head

Vegetation in the upstream area played a critical role in influencing runoff processes and subsequent headcut erosion at the gully head. However, it remains unclear how the vegetation stem coverage affects the hydraulic parameters and the on-wall and jet flow characteristics at the gully head. A simulation flow scouring experiment was performed to explore the influences of the vegetation stem coverage (5 levels) on the hydraulic parameters and on-wall and jet flow proportions at the gully head under inflow discharges ranging from 3.6–9.6 m3 h−1. The results indicated that the runoff in the upstream area occurred in the supercritical turbulent flow regime, and its velocity decreased while the Manning roughness coefficient and Darcy–Weisbach coefficient increased with increasing vegetation stem diameter. The runoff velocity at the gully brink decreased with increasing vegetation stem diameter and increased as a linear function of the inflow discharge (R2 = 0.849–0.997). With increasing vegetation stem diameter, the proportion of on-wall flow increased, and the proportion of jet flow decreased. The on-wall and jet flow proportions ranged from 7% to 92% and 8% to 93%, respectively, under inflow discharges from 3.6–9.6 m3 h−1, thereby attaining the highest correlation with the runoff velocity, Reynolds number, and runoff kinetic energy and following a significant logarithmic function. The vegetation stem influences the hydraulic parameters of the upstream area and gully head and thus influences the on-wall/jet flow proportion. This study could help elucidate the effect of vegetation on the hydraulic mechanism of headcut erosion and provide a theoretical foundation for improving gully headcut erosion models.

Experimental Establishing of Moving Hydraulic Jump in a Trapezoidal Channel

This research was prepared as a preliminary laboratory study to achieve a moving hydraulic jump with controlled discharges. It is an initial part of the study that is being prepared to treat the salt tide occurring in the Shatt al-Arab due to the lack of water imports that were coming from the Karun and Karkheh rivers from Iranian territory, as this scarcity caused a salt tide that affected significantly the environmental reality of the city of Basra and the agricultural lands surrounding the Shatt al-Arab, such as the Shatt al-Arab district and the Siba orchards. As part of the proposed solutions, a moving hydraulic jump is created that pushes the salt tongue into the Persian Gulf; the results were promising. A moving hydraulic leap is a good example of unstable super- and sub-critical flow regimes and is regarded as a specific case of unsteady flow in a channel. There aren't many published experiments on this particular flow type, and the quantitative simulation of such a flow state has some inherent complexity. An experimental setup was created for this work in order to assess the hydraulic performance of a moving hydraulic jump in a trapezoidal flume. A sluice gate was installed at the flume's upstream edge to provide an unstable supercritical flow regime, movable hydraulic jumps along the channel, and temporal water stages at the gate's upstream side for the various downstream end boundary situations. Several flow factors, including energy head, pressure head, and flow depth, were estimated from the recorded data. The study found connections between discharge and shifting hydraulic jump variables. By employing relatively stable momentum and energy formulas, simple and time-independent formulas were developed that accurately predicted the pressure head in the subcritical region of an unstable mixed flow. As a result, the moving hydraulic jump factor can be correctly predicted using time-independent correlations by using the discharge variation as a boundary scenario. Doi: 10.28991/CEJ-2023-09-04-08 Full Text: PDF

On the cylinder noise and drag reductions in different Reynolds number ranges using surface pattern fabrics

This study experimentally investigates the potential of using surface pattern fabrics for the cylinder noise and drag control in different Reynolds number ranges. The aerodynamic and aeroacoustic effects were evaluated through the noise and force measurements in an anechoic wind tunnel. It was observed that the noise and drag reductions take place simultaneously but in different Reynolds number ranges, corresponding to the cylinder flow in different flow regimes, e.g., sub-critical, critical, and supercritical flow regimes. Microphone arc array measurements reveal that the suppression of the Aeolian tone in the critical regime is the major cause of noise reductions, and the noise directivity gradually loses dipole features in the critical and supercritical flow regimes, which is probably related to the reduced lift fluctuation coefficient and the spanwise segment of the sound sources. Further hotwire wake survey revealed significant changes in flow dynamics, which explain the variations of noise and drag in different flow regimes. We have shown for the first time that fabric with different surface patterns can effectively reduce cylinder drag and noise in different Reynolds number ranges. Since the Reynolds number is a key factor that determines the flow state in practical engineering applications, e.g., cycling aerodynamics, this study suggests that optimal drag and noise reductions can be realized by employing the combinations of different surface pattern fabrics to account for the Reynolds number effects.

Effect of the flow regime on the hydraulic features governing the operation of vortex drop shafts with spiral inlets.

If the operation of existing vortex drop shafts should be verified, then it is essential to know the hydraulic performance of these special structures under both subcritical and supercritical flow regimes. The purpose of the present research consisted of providing practical guidelines and recommendations for managing the hydraulic design and verification of subcritical and supercritical vortex drop shafts. The examination of various experimental results from physical model investigations allowed to show that the inlet channel and the spiral inlet behaved differently depending on the energy approach flow content. The main dissimilarity lay, however, in the functioning of the vertical shaft and the dissipation chamber. The rotation of the falling flow along the vertical shaft was more evident for approaching supercritical flows. Severe flow conditions in terms of water depths and bottom pressures could be observed in the dissipation chamber under a supercritical flow regime. The design of this special component must be carried with prudence compared with the subcritical flow regime because failure events as the chamber submergence and the crash of the bottom surface just under the shaft outlet may occur for approaching supercritical flows.

Machine learning modeling for the near-wake mean velocity deficit profiles behind a rough circular cylinder

This study proposes a machine-learning framework to model the near-wake mean velocity profile, illustrating the similarity in the near wake of a circular cylinder. A dataset comprising the near-wake velocity field and wall pressure of the rough circular cylinder, ranging from the subcritical to supercritical flow regimes, is obtained via the wind tunnel test. Then, singular value decomposition of the mean velocity deficit matrixes is performed to obtain the left- and right-singular vectors. The generalized basis and coordinate are finalized by analyzing the scatter of the singular vectors, the correlation of the singular vectors with inputs, and the energy distribution of different generalized basis and coordinates. Next, the random forests (RF) algorithm is applied with the asymmetry of the wall pressure coefficient, drag force coefficient, Reynolds number, and spatial coordinate as inputs, and outputs the generalized coordinates. Finally, the importance of inputs is investigated through Shapley Additive Explanation (SHAP), which enhances the interpretability of the model. The test results show that the RF model can accurately predict the near-wake mean velocity deficit profiles at various Reynolds numbers. The SHAP evaluation indicates that the asymmetry of the pressure coefficient is crucial for modeling the velocity fields among different regimes.

San Felipe and Caracol tuffaceous sandstones, NE Mexico – Late Cretaceous continental arc petrogenetic link: Petrographic, geochemical, and geochronological evidence

Sedimentological and provenance (petrography, whole-rock geochemistry, zircon geochemistry, and ages documented by other authors) analysis carried out in San Felipe Formation and provenance (petrography and zircon geochemistry) analysis established for this unit and the Caracol Formation have allowed inferring the depositional environment for the San Felipe Formation, source area composition, and a possible relationship with the Laramide continental arc system during the Late Cretaceous in Northeast Mexico for both units. San Felipe Formation is constituted by two facies that are characterized by (a) intercalations of shales, tuffaceous sandstones that have Bouma sequence-like structures, ash tuffs and lapilli that develop supercritical and critical flow regime structures (e.g., low-angle parallel lamination), and (b) limestones with mudstone, wackestone, and packstone texture, that show Cruziana and Zoophycos ichnofacies. These features can be interpreted as a mixed ramp system in open sea conditions developed in the foredeep, forebulge, and back-bulge depozones. The San Felipe tuffaceous sandstones are lithic-feldspatho-quartzose to feldspatho-lithic-quartzose rocks (Q54F22L24; n = 13; mean value), rich in microlithic and lathwork tuffaceous volcanic fragments (Lvf40LvMic + Lvlt15LvTob45; felsitic volcanic grains-microlithic volcanic fragments + lathwork lithic fragment-tuffaceous fragments), with abundant volcanic glass. Tuffaceous sandstones from the Caracol Formation, a facial variant of the San Felipe unit, are lithic feldspatho-quartzose to feldspatho-lithic-quartzose rocks (Q46F26L28; n = 12; mean value) rich in felsitic (Lvf79LvMic + Lvlt4LvTob17) and plutonic lithics with subordinate metamorphic fragments and abundant volcanic glass. A predominance of felsitic tuffaceous volcanic lithics and plutonic fragments with low weathering degree (CIA = 41 ± 7; PIA = 38 ± 9) in the San Felipe volcaniclastic strata and magmatic zircons with chemistry linked mostly from continental arcs (log of U/Yb and Nb/Yb ratios) in both formations suggest that the volcaniclastic rocks of the San Felipe and the Caracol Formations have an origin related to the Cretaceous-Eocene Mexican Magmatic Arc. After a relatively fast transport, the volcanic tuffs were deposited in the foredeep, forebulge, and back-bulge depocenters distributed in Northeast Mexico.

Air‐Water Mixing in Vegetated Supercritical Flow: Effects of Vegetation Roughness and Water Temperature on Flow Self‐Aeration

AbstractVegetated flow is rarely investigated for supercritical flow regime, in which self‐aeration occurs and modifies the flow dynamics, energy dissipation, and mass transfer between the water body and ambient air environment. In this study, natural river water was used at two flow rates in combination with six bottom vegetation conditions to investigate the air‐water flow development in an 18‐m‐long sloping chute. The vegetation configurations included two artificial turfs with different grass lengths and three flexible plant covers with different canopy densities, in addition to a reference case of smooth solid boundary, providing flow resistance and turbulent disturbance with different orders of equivalent roughness heights. Physical measurements were focused on the air concentration, free‐surface splashing, turbulent velocity, bubble count frequency, and bubble size distributions from the upstream non‐aerated flow to the far‐field fully developed aeration region. Compared to the velocity developing to uniform equilibrium shortly downstream the inception of aeration, the flow self‐aeration reached air‐concentration equilibrium at further downstream positions, while the bubble count and air‐water interfacial area kept increasing. The vegetation roughness conditions affected the inception location, equivalent bubble rise velocity, superfacial splashing height, velocity gradient, and maximum bubble count near the free surface, whereas the equilibrium air concentration in the fully developed region depended only upon the slope. The vegetation type influenced the percentage of submillimetre bubbles. Little differences were shown in the air‐water flow characteristics by repeating the summer experiments in winter with a 25.5°C drop in water temperature, despite the variation in fluid viscosity thus the Reynolds number under identical discharge.

Overland flow resistance and its components for slope surfaces covered with gravel and grass

Overland flow resistance plays an important role in predicting hillslope hydrological and erosion processes on hillslopes. Soil surfaces covered with grass and/or gravel may increase hydraulic resistance to overland flow, but there is little information on the determination on these resistance components in a composite slopeland. In this study, the smooth and sand-bed surfaces covered with different gravel or/and grass (cover degree = 2.5%, 5%, 10%, 15%, 20%) under five slope gradients (3°, 6°, 9°, 12°, 15°) were subjected to inflows to investigate the hydraulic resistance and validate the sum law of resistance components. The results showed that, the overland flow mainly belonged to transition or turbulent and supercritical flow regime with 150 < Re < 2050 and 0.4 < Fr < 6.9. As the gravel or grass cover increased, Darcy-Weisbach resistance coefficient (f) significantly increased. The resistance can be well predicted by flow discharge, gravel or grass cover using a power equation. The flow discharge had a greater influence on flow resistance than gravel or grass cover, and the impact of flow discharge weakened with the increasing bed slopes. The total resistance was generally greater than the sum of resistance components, and there existed a positive additional resistance for the composite surfaces. The additional resistance accounted for 37.4%, 4.2% and 16.6% to the total resistance for the sand surfaces covered with gravel, grass and both of them, respectively. These results can help to understand the rainfall-runoff processes and improve the design of soil and water conservation measures in the rocky and mountainous areas.

Nonlinear flexural-gravity waves due to a body submerged in the uniform stream

The two-dimensional nonlinear problem of steady flow past a body submerged beneath an elastic sheet is considered. The mathematical model is based on the velocity potential theory with fully nonlinear boundary conditions on the fluid boundary and the elastic sheet, which are coupled throughout the numerical procedure. The integral hodograph method is employed to derive the complex velocity potential of the flow which contains the velocity magnitude on the interface in explicit form. The coupled problem has been reduced to a system of nonlinear equations with respect to the unknown magnitude of the velocity on the interface, which is solved using a collocation method. Case studies are undertaken for both subcritical and supercritical flow regimes. Results for interface shape, bending moment, and pressure distribution are presented for the wide ranges of Froude numbers and depths of submergence. According to the dispersion equation, two waves on the interface may exist. The first longest wave is that caused by gravity, and the second shorter wave is that caused by the elastic sheet. The obtained solution exhibits a strongly nonlinear interaction of these waves above the submerged body. It is found that near the critical Froude number, there is a range of submergences in which the solution does not converge.

Study of Surface Roughness Effect on a Bluff Body—The Formation of Asymmetric Separation Bubbles

Turbulent flows around bluff bodies are present in a large number of aeronautical, civil, mechanical, naval and oceanic engineering problems and still need comprehension. This paper provides a detailed investigation of turbulent boundary layer flows past a bluff body. The flows are disturbed by superficial roughness effect, one of the most influencing parameters present in engineering applications. A roughness model, recently developed by the authors, is here employed in order to capture the main features of these complex flows. Starting from subcritical Reynolds number simulations (Re = 1.0 × 105), typical phenomena found on critical and supercritical flow regimes are successfully captured, like non-zero lift force and its direction change, drag crisis followed by a gradual increase on this force, and separation and stagnation points displacement. The main contribution of this paper is to present a wide discussion related with the temporal history of aerodynamic loads of a single rough circular cylinder capturing the occurrence of asymmetric separation bubbles generation. The formation of asymmetric separation bubbles is an intrinsic phenomenon of the physical problem, which is successfully reported by our work. Unfortunately, there is a lack of numerical results available in the literature discussing the problem, which has also motivated the present paper. Previous study of our research group has only discussed the drag crisis, without to investigate its gradual increase and the change on lift force direction. Our results again confirm that the Lagrangian vortex method in association with Large-Eddy Simulation (LES) theory enables the development of two-dimensional roughness models.

Flow Regimes and Föhn Types Characterize the Local Climate of Southern Patagonia

The local climate in Southern Patagonia is strongly influenced by the interaction between the topography and persistent westerlies, which can generate föhn events, dry and warm downslope winds. The upstream flow regime influences different föhn types which dictate the lee-side atmospheric response regarding the strength, spatial extent and phenomenology. We use a combination of observations from four automatic weather stations (AWSs) and high-resolution numerical modeling with the Weather Research and Forecasting (WRF) model for a region in Southern Patagonia (48° S–52° S, 72° W–76.5° W) including the Southern Patagonian Icefield (SPI). The application of a föhn identification algorithm to a 10-month study period (June 2018–March 2019) reveals 81 föhn events in total. A simulation of three events of differing flow regimes (supercritical, subcritical, transition) suggests that a supercritical flow regime leads to a linear föhn event with a large spatial extent but moderate intensity. In contrast, a spatially limited but locally strong föhn response is induced by a subcritical regime with upstream blocking and by a transition regime with a hydraulic jump present. Our results imply that the hydraulic jump-type föhn event (transition case) is the most critical for glacier mass balances since it shows the strongest warming, drying, wind velocities and solar radiation over the SPI. The consideration of flow regimes over the last 40 years shows that subcritical flow occurs most frequently (78%), however transitional flow occurs 14% of the time, implying the potential impact on Patagonian glaciers.

Calculation of the parameters of the hydraulic transport of enrichment waste in polyethylene pipes

In the article, a new method is presented for calculating hydraulic slope and critical speed of cleaning reject hydrotransportation through the polyethylene pipelines, which is based on the Methodology for Calculating Hydrotransport Plants for Tailings Transporting and Inwashing at the Iron Ore Mining and Processing Enterprises. This methodology was approved by the State Construction Committee of the Ukrainian SSR in its Temporary Instructions on Technology of the Tailing Dump Arrangement and was used in the design of all of the waste storage facilities in the Krivyy Rih ore-dressing and processing enterprises. For the conditions of the experiments, it was shown that experimental multiplier in the formula for calculating critical speed of hydrotransportation was depended on the pipeline diameter, free fall acceleration, kinematic coefficient of water viscosity and absolute roughness of the pipe inner surface. The acknowledgement of these factors made an empirical constant in the considered formula dimensionless and close to average value of the constants in the formulas obtained by other similar methods. With the considered method, it is proved that experimental constant in the formula for calculating critical speed of hydrotransportation is inversely proportional to the cubic root of the roughness of the pipeline inner surface, while coefficient of proportionality is a universal constant, which does not depend on the properties of the pipeline material and is equal to 10.1. Therefore, for determining critical speed of hydrotransportation through the polymer pipes by using this method, it is necessary to multiply critical speed for steel pipe with a similar diameter by the cubic root of ratio of roughness of the inner surfaces of the steel and polymer pipelines. It is further shown that value of hydraulic slope significantly depends on the operating coefficient, which shows by how many times coefficient of friction hydraulic resistance in the polyethylene pipe operating in supercritical flow regime exceeds the same value in case of critical flow regime for the same pipe. The research results allowed finding formulas for calculating hydraulic slope and critical speed of the iron-ore cleaning reject hydrotransportation through the polyethylene pipelines, which are based on the dependencies obtained for the steel pipes and value of absolute roughness of the pipeline inner surface.

Effect of flow pulsations on chaos in nanotubes using nonlocal strain gradient theory

In this article, a chaos analysis is performed for the viscoelastic nonlinear coupled dynamics of perfectly straight nanotubes conveying pulsatile fluid for the first time. A size-dependent advanced elasticity model is developed with consideration of stress nonlocality as well as the gradient of strain components. After presenting the nonlinear motion equations using Hamilton's approach, they are numerically solved via application of a time-integration technique for a system with a large number of degrees of freedom. Chaos analysis is performed for the nanotube at both subcritical and supercritical flow regimes. Both mean fluid velocity and the amplitude of velocity pulsation are varied as the bifurcation parameter. The proposed size-dependent continuum modelling and numerical results would be useful in order to tailor the system parameters to avoid chaos in nanoelectromechanical devices using fluid-conveying nanotubes.

Application of Fawer Theory to End Depth in Trapezoidal Sloping Channel

AbstractThe Fawer assumption is applied to both energy and momentum equations to analyze free overfalls for a trapezoidal sloping channel in the supercritical flow regime under the assumption of ps...

On the flow around two circular cylinders in tandem arrangement at high Reynolds numbers

The flows around two tandem circular cylinders in the subcritical and supercritical flow regimes are studied through three-dimensional numerical simulations. Different spacing ratios L/D (where L is the center-to-center distance between the two cylinders with D being the diameter of the cylinders) from 2.0 to 5.0 is considered. The instantaneous flow structures, pressure distributions and hydrodynamic forces on two tandem cylinders are analyzed at subcritical (Re=2.2×104) and supercritical (Re=3.0×106) Reynolds numbers. The present numerical solutions demonstrated that at the two Re, for L/D<3.5, the shear layer from the upstream cylinder reattaches on the surface of the downstream cylinder and vortex street is only formed behind the downstream cylinder, while the shear layer from the upstream cylinder rolls up alternately for L/D≥3.5, and vortex shedding occurs from both upstream and downstream cylinders. Compared with the flow characteristics at Re=2.2×104, for Re=3.0×106, the flow separation positions on the upstream cylinder move backward and the width of the wake behind the upstream cylinder becomes narrower, which leads to forward movement of the reattachment position. At the supercritical Reynolds number, the mean drag and fluctuating lift coefficients of the upstream cylinder are nearly independent of L/D while the sharp increase of force coefficients of the downstream cylinder occurs for L/D=3.5. Comparing to the case at the subcritical Reynolds number, higher vortex-shedding frequencies from the upstream and downstream cylinders are identified. It is also revealed that the slope of the best fit line for φ (the phase lag of the fluctuating lift force between two cylinders) and L/D increases at the supercritical Reynolds number. In addition, for L/D=2.5, the mean drag coefficients of the upstream cylinder decrease sharply for Re>1.0×105, while those of the downstream cylinder rise slightly with the growing Re. Moreover, the fluctuating lift coefficients of the upstream cylinder are almost independent of Re, but those of downstream cylinder drop as Re increases.

Experimental investigation of the aerodynamic drag of roof-mounted insulators for trains

This paper presents the results of experimental investigations on the aerodynamic drag of roof-mounted insulators for use on low- and high-speed trains. Wind tunnel investigations at different Reynolds numbers in the subcritical, critical, and supercritical flow regime were performed, in addition to investigations using wall-mounted cylinders. Furthermore, the impact of insulator sheds made of flexible material was analyzed. For a better understanding of the aerodynamic behavior of the insulators when mounted on trains, different boundary conditions representing realistic configurations as found on the roof of trains were simulated. From the measured drag, the energy demand to overcome the aerodynamic resistance of different types of insulators was calculated. Depending on the above mentioned boundary conditions, a noticeable contribution of the insulators to the entire train's aerodynamic drag could be observed. With flexible insulator sheds, a further increased air resistance was observed with the onset of fluttering. Similar to the cylinder, the aerodynamic behavior of the insulators depends on the respective Reynolds number.

Real‐time monitoring and estimation of the discharge of flash floods in a steep mountain catchment

AbstractSynchronously and accurately estimating the flood discharges and dynamic changes in the fluid density is essential for hydraulic analysis and forecasting of flash floods, as well as for risk assessment. However, such information is rare for steep mountain catchments, especially in regions that are hotspots for earthquakes. Therefore, six hydrological monitoring sites were established in the main stream and tributaries of the 78.3‐km2 Longxi River catchment, an affected region of the Wenchuan earthquake region in China. Direct real‐time monitoring equipment was installed to measure the flow depths, velocities, and fluid total pressures of the flood hydrographs. On the basis of field measurements, real‐time mean cross‐sectional velocities during the flood hydrographs could be derived from easily obtainable parameters: cross‐sectional maximum velocities and the calibrated dimensionless parameter Kh. Real‐time discharges were determined on the basis of a noncontact method to establish the effective rating curves of this mountainous stream, ranging from 1.46 to 386.34 m3/s with the root mean square errors of ≤10.22 m3/s. Compared with the traditional point‐velocity method and empirical Manning's formula, the proposed noncontact method was reliable and safe for monitoring whole flood hydrographs. Additionally, the real‐time fluid density during the flood hydrographs was calculated on the basis of the direct monitoring parameters for fluid total pressures and water depths. During the flood hydrograph, transient flow behaviour with higher fluid density generally occurred downstream during the flood peak periods when the flow was in the supercritical flow regime. The observed behaviour greatly increased the threat of damage to infrastructure and human life near the river. Thus, it is important to accurately estimate flood discharge and identify for fluid densities so that people at risk from an impending flash flood are given reliable, advanced warning.