Outflow Conditions Research Articles

Sensitivity analysis of turbine stage aerothermal characteristics and blade cooling performance considering combustor swirl and hot spot

This paper investigates the global sensitivity of high-pressure-turbine (HPT) first stage cascades aerothermal characteristics and blade cooling performance under the influence of combustor swirl and hot spot. The combustor outflow conditions impact on turbine working performance and robustness. This paper is focused on the influence of uncertain combustor swirling flow and hot spot, rather than deterministic working conditions. A simplified combustor outflow simulation method is firstly proposed, and the effects of combustor outflow are quantified by combining chaos polynomial expansion with Sobol’ decomposition method. The results show that different rotating directions of the swirl lead to restricted influences on the averaged aerothermal performance of the turbine stage, but significantly affects its robustness. The positive swirl increases the total pressure loss generated by the lower passage vortex of the stator cascade, and the high uncertainty region of the stator cascade total pressure loss profile is the combined products of the residual swirl and the interaction between the passage vortex and mainstream. The total pressure loss of the rotor cascade due to leakage vortex has low sensitivity to the hot spot and swirl strength, while the total pressure loss generated by the passage vortex is affected by hot spot temperature. Temperature distribution affected by the passage vortex is sensitive to swirl strength. Generally, uncertainty variance of stage aerothermal parameters with positive swirl is about 30% larger than that of the negative case, since the positive swirl has stronger interactions with the blades, leading to more significant uncertainty. However, the averaged heat transfer coefficients with positive swirl are 37% less sensitive, compared to the negative swirl case. The results give better understanding on the influence mechanisms of turbine inflow conditions, emphasize the meaning of investigating uncertain characteristics of the turbine cascades. Investigations of this article provide reference for robust turbine blade cooling design.

Hydrogen in the Natural Gas Network—Relevance for Existing Fire Precautions

Power-to-gas technology can be used to convert excess power from renewable energies to hydrogen by means of water electrolysis. This hydrogen can serve as “chemical energy storage” and be converted back to electricity or fed into the natural gas grid. In the presented study, a leak in a household pipe in a single-family house with a 13 kW heating device was experimentally investigated. An admixture of up to 40% hydrogen was set up to produce a scenario of burning leakage. Due to the outflow and mixing conditions, a lifted, turbulent diffusion flame was formed. This led to an additional examination point and expanded the aim and novelty of the experimental investigation. In addition to the fire safety experimental simulation of a burning leakage, the resulting complex properties of the flame, namely the lift-off height, flame length, shape and thermal radiation, have also been investigated. The obtained results of this show clearly that, as a consequence of the hydrogen addition, the main properties of the flame, such as lifting height, flame temperature, thermal radiation and total heat flux densities along the flame, have been changed. To supplement the measurements with thermocouples, imaging methods based on the Sobel gradient were used to determine the lifting height and the flame length. In order to analyze the determined values, a probability density function was created.

Can Urinary Bladder Innervation Be Restored After Outlet Obstruction and Denervation?

Transurethral resection of the prostate, or other methods to decrease outlet resistance usually leads to relief of symptoms in patients with bladder outlet obstruction (BOO). If symptoms of underactivity persist after normalization of outflow conditions, treatment options are limited. In this review, we hypothesize, based on results from basic research, what might become treatment options for such patients in the future. The primary local treatment will still aim at reducing outlet obstruction. We speculate that local secondary treatment in the future might include transplantation of stem cells or mature bladder ganglion cells into the bladder wall. There has been some success in transplanting ganglion cells into the rat bladder. The ganglion cells will sprout into the surrounding tissue but functional connections between the axons of the transplanted neurons, and the detrusor smooth muscle have so far not been demonstrated. Neurotrophins or neurotrimin might be injected into the bladder wall to increase the sprouting of existing or transplanted neurons. Stem cell transplantation has been performed and improves detrusor function, but it has so far, been difficult to demonstrate transplanted stem cells. BOO, persisting detrusor underactivity, and decreased nerve density are often combined with inflammatory activity of the lower urinary tract. NLR family pyrin domain containing 3 (NLRP3) and its messenger RNA (mRNA) as well as cyclooxygenase-2 (Cox-2) mRNA are increased in obstructed bladders. Systemic treatment with the NLRP3 inhibitor glyburide normalized nerve density in rat bladder, and, to some extent, bladder function. It is unclear whether Cox-2 is involved in the decreased nerve density following obstruction, but Cox-2 mRNA increases 5-fold in obstructed bladder. Future therapy against bladder underactivity remaining following relief of obstruction includes either systemic treatment, perhaps by anti-inflammatory drugs, or local treatment by injection of stem cells, mature ganglion cells, and/or neurotrophins or neurotrimin into the bladder wall.

Analysis of fluid force and flow fields during gliding in swimming using smoothed particle hydrodynamics method

Gliding is a crucial phase in swimming, yet the understanding of fluid force and flow fields during gliding remains incomplete. This study analyzes gliding through Computational Fluid Dynamics simulations. Specifically, a numerical model based on the Smoothed Particle Hydrodynamics (SPH) method for flow-object interactions is established. Fluid motion is governed by continuity, Navier-Stokes, state, and displacement equations. Modified dynamic boundary particles are used to implement solid boundaries, and steady and uniform flows are generated with inflow and outflow conditions. The reliability of the SPH model is validated by replicating a documented laboratory experiment on a circular cylinder advancing steadily beneath a free surface. Reasonable agreement is observed between the numerical and experimental drag force and lift force. After the validation, the SPH model is employed to analyze the passive drag, vertical force, and pitching moment acting on a streamlined gliding 2D swimmer model as well as the surrounding velocity and vorticity fields, spanning gliding velocities from 1 m/s to 2.5 m/s, submergence depths from 0.2 m to 1 m, and attack angles from −10° to 10°. The results indicate that with the increasing gliding velocity, passive drag and pitching moment increase whereas vertical force decreases. The wake flow and free surface demonstrate signs of instability. Conversely, as the submergence depth increases, there is a decrease in passive drag and pitching moment, accompanied by an increase in vertical force. The undulation of the free surface and its interference in flow fields diminish. With the increase in the attack angle, passive drag and vertical force decrease whereas pitching moment increases, along with the alteration in wake direction and the increasing complexity of the free surface. These outcomes offer valuable insights into gliding dynamics, furnishing swimmers with a scientific basis for selecting appropriate submergence depth and attack angle.

Experimental study of simple flumes with converging triangular walls

For water management, the accurate measurement of discharge in irrigation channels is essential. Static flow measuring devices such as weirs and flumes play a significant role in discharge measurement in open channels. Flumes are one of the most commonly used devices for flow measurement. Many researchers have focused on application of simple flumes in irrigation networks. This investigation aims to study the flow discharge through a simple flume with converging triangular walls under free-flow conditions. The flume is constructed by placing two right-angled triangular plates on either side of a rectangular open channel. The channel cross section is rectangular while height of the converging walls reaches to zero at the end of the flume opening. The proposed flume is inexpensive, its operation is simple, its installation is easy and does not require high maintenance (maintenance free). The present study is designed to determine the effect of different variables on flow discharge of this kind of flumes. For this, an experimental program was conducted under upstream subcritical flow regime and under free outflow conditions to formulate the flow discharge of the flume. Flume discharge relationship was deduced using dimensional analysis method and then calibrated using the experimental data collected in this study (318 runs). The proposed discharge equation has an average absolute relative error of 1.66 %, and for 96.5 % of the measured discharge values, the relative errors are within ±5 %. To reliably estimate the flume discharge, free-flow and submerged-flow conditions should be distinguished. For this, suitable equation with an average absolute relative error less than 3.44 % was presented to estimate the submergence threshold. This flume is suitable for the rectangular channel for accurate measurement of free flow at any location on field. This particular device has considerable advantages over the other devices, as it can be quickly installed and removed for use in irrigation channels. The findings and results of this study will be of interest for practical applications.

Boundary Condition Options for Carotid Bifurcation Analysis, Using Doppler Velocity Measurements

The Common Carotid Artery plays a vital role in supplying the brain, and its bifurcation is susceptible to vascular diseases. It is often analyzed using computational fluid dynamics (CFD) simulations, but it is challenging to prescribe boundary conditions that approach patient-specific flow conditions. We examined six boundary condition (BC) groups to determine the most accurate flow conditions aligning with available measured data. We conducted CFD simulations on a stenotic carotid bifurcation, using patient-specific Doppler ultrasound sonography velocity measurements at the inlet and both outlets. Three BC methods used defined inlet flow rate and either constant pressure (Basic), Windkessel model, or constant flow ratio (Murray) at the outlets. Three other methods were defined with flow rates at two boundaries and constant pressure at the third one. Defining two boundary flow rates shows the closest results to physiologically valid data. However, the difficult Doppler measurements on the outlet branches can inaccurately amplify velocity amplitudes and may detect a false flow direction. Therefore, cross-sectional corrections were implemented to fit the outlet and inlet flow rates, while keeping the measured velocity histories.Our results show that the Murray and Basic methods, while easily available, exclude carotid-specific flow conditions by disregarding downstream flow resistances. We conclude that a Windkessel-method can produce the most accurate results without forcing outflow conditions. However, usually unavailable measurements are necessary for its application. Simulations with outlet-defined volume flow can also produce physiologically valid solutions but require the application of cross-sectional geometry correction.

Production of p Nuclei from r -Process Seeds: The νr Process

We present a nucleosynthesis process that may take place on neutron-rich ejecta experiencing an intensive neutrino flux. The nucleosynthesis proceeds similarly to the standard r process, a sequence of neutron captures and beta decays with, however, charged-current neutrino absorption reactions on nuclei operating much faster than beta decays. Once neutron-capture reactions freeze out the produced r process, neutron-rich nuclei undergo a fast conversion of neutrons into protons and are pushed even beyond the β stability line, producing the neutron-deficient p nuclei. This scenario, which we denote as the νr process, provides an alternative channel for the production of p nuclei and the short-lived nucleus Nb92. We discuss the necessary conditions posed on the astrophysical site for the νr process to be realized in nature. While these conditions are not fulfilled by current neutrino-hydrodynamic models of r-process sites, future models, including more complex physics and a larger variety of outflow conditions, may achieve the necessary conditions in some regions of the ejecta. Published by the American Physical Society 2024

Mixed convection flow over a horizontal plate and the horizontal wake far downstream

The laminar mixed convection flow over a heated or cooled horizontal plate of finite length is a surprisingly intriguing problem. The hydrostatic pressure jump at the trailing edge and across the wake is to be compensated by induced circulation in the outer potential flow, similar to a plate at a non-zero angle of attack. The mixed convection flows over semi-infinite and finite horizontal plates, respectively, are thus substantially different. As the hydrostatic pressure jump remains finite along the infinitely extended wake, the induced outer potential flow around the plate would grow beyond bounds in a domain extending to infinity. Thus, boundary conditions must be imposed at the boundaries of a finite domain. However, the numerical solution of the Navier-Stokes equations remains a challenging problem due to the lack of appropriate outflow conditions. The traditional outflow condition cannot comply with the finite hydrostatic pressure jump across the wake. Thus, an asymptotic expansion for the wake far downstream from the plate is performed. Remarkably, the perturbation of the flow does not decay with increasing distance from the plate as in a classical wake. The asymptotic solution is implemented as an outflow boundary condition for the numerical solution of the Navier-Stokes equations. The results are compared with a boundary-layer solution obtained in previous work for the limiting case of vanishing Prandtl number.

Oxygen evolution and its drivers in a stratified reservoir: A supply-side perspective for informing hypoxia alleviation strategies

Hypoxia in stratified waters greatly threatens aquatic ecology and societal development owing to enhanced nutrient discharge and increasing global temperature. Current research predominantly alleviates hypoxia by reducing dissolved oxygen (DO) consumption or conducting hypolimnetic oxygenation, yet their implementation has encountered bottlenecks. Therefore, this study explores the potential of increasing the inherent DO supplies in stratified reservoirs to mitigate hypoxia. High-frequency in situ observations and massive modeling experiments are integrated to discern the DO supply mode and the dominant driver of DO evolution. Results indicate that periodic thermodynamic conditions determine the DO supply relationships between oxygen sources (inflow carriage, reaeration, and photosynthesis) for different water layers. Thermal stratification causes the hypolimnion to rely mostly on the inflow for DO supply, leading to a fragile budget prone to hypoxia. However, episodic hydrodynamic events (turnover, wind stir, density current, and flood) can promote DO supply and inhibit hypoxia. Temperature and DO regimes are primarily driven by outflow conditions, followed by inflow and meteorology conditions. Furthermore, hypolimnetic hypoxia can be regulated by altering inflow volume, outflow volume, and outlet elevation. These findings highlight the importance of longitudinal solute exchange in DO evolution in stratified reservoirs, providing a basis for alleviating hypoxia through cascade reservoir operations.

Years of Drought and Salt: Decreasing Flows Determine the Distribution of Zooplankton Resources in the San Francisco Estuary

The San Francisco Estuary (estuary) and the Sacramento–San Joaquin Delta (the Delta) in California face significant challenges in managing water resources during extended droughts. Zooplankton are a vital trophic link between phytoplankton producers and higher-level consumers such as predatory zooplankton and fish. However, there is still much to be learned about what drives zooplankton abundance and how they respond to drastic changes in environmental conditions, such as droughts. We found that during drought years zooplankton abundance and distribution changes varied for examined taxa. Significant declines in the abundance of Daphnia spp. and the copepod Pseudodiaptomus forbesi occurred in the Suisun Marsh and Suisun Bay regions. In contrast, abundance of the non-native copepod Limnoithona tetraspina increased in Suisun Marsh and the South-Central Delta during those same drought conditions. Salinity is a strong determinant of the presence and abundance of the studied taxa, and we showed that changes in the distribution of salinity low outflow conditions were an important factor in the regional abundance of zooplankton. Because of the expected increase in the frequency and severity of regional droughts, understanding how these conditions affect zooplankton in the estuary will benefit scientists and resource managers who aim to improve conditions for native fishes.

International tax competition as an element of the country’s marketing strategy

In the conditions of permanent capital outflow and business registration by residents in other jurisdictions, the issue of developing a country’s marketing strategies for doing business and identifying the most effective mechanisms for increasing international tax attractiveness is urgent. The prerequisite of these processes should be the determination of the level of international tax competitiveness followed by identifying the most significant factors of its growth. The purpose of the study is to assess the level of international tax competitiveness as an element of marketing strategies of Ukraine and some EU countries during 2011–2021. The methodological tools are correlation-regression analysis, the Fisher method, and the multiplicative convolution method. The paper assessed the level of international tax competitiveness as a comprehensive indicator that considers procedural, institutional, moral-ethical, and economic components. The calculations showed that the most competitive are the tax systems of Estonia, Latvia, Lithuania, Croatia, Finland, the Czech Republic, and Hungary. Based on hierarchical and non-hierarchical (k-means method) clustering, 3 clusters of regions were identified. For each of them, based on an analysis of the features of the tax system construction and the comparison of marginal and average values, the criteria for the identification of competing countries and those with common development trends were formed. This makes it possible to determine the most effective mechanisms for the implementation of marketing strategies reforming tax policy from the point of view of increasing its international tax attractiveness. AcknowledgmentThe study is funded by the EU NextGenerationEU through the Recovery and Resilience Plan for Slovakia under the project No. 09I03-03-V01-00042.The authors are grateful to the participants of projects “National security of Ukraine through the prevention of financial fraud and money laundering: war and post-war challenges” (2023–2025, state registration number: 0123U101945) and “De-shadowing and regulatory efficiency of environmental taxation: optimization modelling to ensure national security and rational use of nature” (2022–2024, registration number 0122U000777) for numerous discussions and comments.

Optimizing flow regime for the Four Major Chinese Carps by integrating habitat suitability within reservoir operation

The construction of dams has brought many benefits to human society. However, it has also altered the natural hydrological regime, affected aquatic organisms’ habitat conditions and decreased important fishery resources. In the post-dam construction era, it has become crucial to evaluate the ecological flow requirements for all stages of fish life and ensure the provision of dynamic flow pulsation, particularly during the spawning stage. Here, we proposed a Reservoir Operation Model for Fish Habitat across Life Stages (ROM-FHLS) to reconcile the apparent contradiction between fish habitat preservation and hydropower generation in the Yangtze River Basin. Compared with the conventional outflow conditions, our model demonstrated significant improvements in power generation and suitable habitat area during the migration, spawning and incubation, and juvenile periods. Specifically, we observed average increases of 15.2%, 13.1%, and 6.7% in power generation, and enhancements of 16.5%, 17.3%, and 1.8% in suitable habitat area, respectively. Our approach advocates for the comprehensive protection of fish throughout their entire life cycle while highlighting the feasibility of enhancing fish habitats without compromising power generation. Furthermore, we proposed an outflow scheme that incorporates pulsation patterns into reservoir operations to effectively stimulate fish spawning activities. This study presents a fresh perspective on comprehending the intricate interplay among dam-controlled hydrological processes, river hydrodynamic environment, and fish behavior. The findings have the potential to enhance fish spontaneous reproduction and aid in the recovery of aquatic populations in large dammed rivers.

Numerical modeling of turbulent puffs evolution

The results of numerical simulation of the formation and motion of turbulent puffs resulting from the blowing of pulsed jets with different initial velocities and durations are presented. A model of an axisymmetric turbulent flow described by non-stationary Reynolds equations is adopted. It is shown that, regardless of the initial conditions, after the same dimensionless time interval from the instant the jet outflow begins, a vortex cloud appears, which has a spherical shape of vortex. The vortex-induced flow in the rest of the space is close to potential. It has been established that the velocity profiles in vortices in the axial and transverse directions are close to self-similar and are similar for different conditions of the outflow of pulsed jets. Time dependences of the geometric and kinematic characteristics of puffs are presented and analyzed: the position of the cloud center (points with maximum velocity) and the radius of a sphere equivalent in volume to a puff, as well as maximum and average velocities. For the studied jet outflow conditions, the characteristics of puffs turn out to be similar.

The splitting-based semi-implicit finite-difference schemes for simulation of blood flow in arteries

This paper is devoted to construction and analysis of splitting-based finite-difference schemes for simulation of blood flow in applications of one-dimensional models. Proposed schemes are constructed for inviscid and viscid models of blood. The proposed approach is based on the modification of averaged incompressibility condition, rewritten for the square root of a cross-sectional area. It is approximated by an absolutely stable scheme with a skew-symmetric operator. The constructed schemes can be classified as semi-implicit. The stability of proposed schemes is analyzed by the method of energy inequalities. Sufficient stability conditions are obtained. For the problems with analytical solutions, it is demonstrated that a second-order convergence rate is achieved in practice.The proposed schemes are compared with the widely used explicit finite-difference schemes, such as Lax–Wendroff, Lax–Friedrichs and McCormack schemes. The benchmark problems for simulation of flows in the following vascular systems are considered: human carotid artery, human aorta with bifurcation, vessel with bifurcation and absorbing outflow conditions, and networks with 31, 63, and 127 vessels. It is demonstrated that the computations based on the splitting-based semi-implicit schemes can be performed much faster than for the explicit schemes with close values of relative errors.

APPLICATION OF THE TEST-PARTICL STATISTICAL METHOD FOR THE SIMULATION OF RAREFIED PLUME FLOWS IN A VACUUM

The article substantiates the important role of the problem of the supersonic jet outflow into a vacuum to control the motion of the center of mass, orientation, and stabilization of the spacecraft’s position in space. The types of low-thrust engines and microrocket engines viewed have plumes that can pass through all regimes from continuum to free-molecular. In zones where motion is described at the molecular-kinetic level, statistical methods are most often used. The statistical Test Particle Method (TPM) has so far been used only in rarefied homogeneous flows. The aim of this work is to develop the TPM for numerical modelling plume flows. Below are the basic tenets of the TPM and changes in its algorithm. The initial drawing of the trajectories of molecules is carried out either from the nozzle exit (in the absence of a dense core) or from the initial surface, which is the virtual border of the continuity zone. Determining the distributions over the surface of the drawing of the coordinates of the start and the mass velocity of the plume flow is decisive for obtaining adequate results. Among the considered launch options, the most realistic one is uneven, with a concentration on the plume axis. The calculation of the mass velocity of the plume flow at the initial surface can be performed using numerical methods of continuum aerodynamics or using approximate methods. The testing of TPM in the far field of a rarefied nitrogen plume was carried out by comparing the relative density distribution with the data of the approximate method. The results obtained in the presence of the initial sphere and in its absence agree with each other. The TPM testing in the area adjacent to the nozzle was carried out by comparing the isolines of relative density and Mach numbers with the results of direct Monte Carlo simulation for the experimental conditions of helium outflow from a lowthrust engine into a vacuum. Satisfactory agreement has been obtained between the numerical simulation data of the TPM and the compared data

Estimation in jet deflection angle of deflector on the chutes

ABSTRACT Ski jumps are commonly used to discharge flow away from release structures into downstream rivers for energy dissipation. However, due to large intersection angles of jet and river flow or the jet impacting position unreasonable, the serious sour of riverbed or bank may occur, threatening the security of hydraulic structure. Hence, the impacting position and direction of jet from ski jump are pressing for research. For obtaining a controllable and desired outflow condition, adding rectangular tetrahedral deflector is a common and effective measure to change the flow direction. In this study, physical experiments and numerical simulation were conducted and the effect of the deflector contraction ratio on the flow deflection angle was revealed. The results indicate that the contraction ratio is a key parameter of the deflector, and a larger contraction ratio contributes to a larger jet deflection angle. Based on the data in the present and previous studies, a new empirical expression for estimating the deflection angle is proposed for rectangular tetrahedral deflector. By contrast with previous research, the calculated result from the expression presents a better agreement with the test data.

A non-intrusive approach for physics-constrained learning with application to fuel cell modeling

A data-driven model augmentation framework, referred to as weakly-coupled Integrated Inference and Machine Learning (IIML), is presented to improve the predictive accuracy of physical models. In contrast to parameter calibration, this work seeks corrections to the structure of the model by (a) inferring augmentation fields that are consistent with the underlying model, and (b) transforming these fields into corrective model forms. The proposed approach couples the inference and learning steps in a weak sense via an alternating optimization approach. This coupling ensures that the augmentation fields remain learnable and maintain consistent functional relationships with local modeled quantities across the training dataset. An iterative solution procedure is presented in this paper, removing the need to embed the augmentation function during the inference process. This framework is used to infer an augmentation introduced within a polymer electrolyte membrane fuel cell (PEMFC) model using a small amount of training data (from only 14 training cases). These training cases belong to a dataset consisting of high-fidelity simulation data obtained from a high-fidelity model of a first generation Toyota Mirai. All cases in this dataset are characterized by different inflow and outflow conditions on the same geometry. When tested on 1224 different configurations, the inferred augmentation significantly improves the predictive accuracy for a wide range of physical conditions. Predictions and available data for the current density distribution are also compared to demonstrate the predictive capability of the model for quantities of interest which were not involved in the inference process. The results demonstrate that the weakly-coupled IIML framework offers sophisticated and robust model augmentation capabilities without requiring extensive changes to the numerical solver.

New Parent Flowfield for Streamline-Traced Intakes

The prespecified flowfield is essential in the inverse design method for generating inward-turning streamline-traced intakes, i.e., the parent flowfield. The internal conical flow C (ICFC) flowfield shows superiority over other parent flowfields in terms of performance and length. A drawback to the ICFC flowfield is the existence of the expansion zone, which creates a second reflected shock and decreases the flow uniformity. Hence, this paper proposes a new basic flowfield called the internal conical flow M (ICFM) to overcome the shortcoming of the ICFC flowfield. For the proposed basic flowfield, a new methodology has been devised for connecting the M-flow and truncated Busemann flowfields. This methodology merges the singular line of the M-flow with the truncated ray of Busemann flowfield in order to reduce the flow inclination angle difference effectively. The concept of the basic flowfield is reviewed, and the new ICFM basic flowfield is calculated using the Taylor–Maccoll equations. Complete details of the new merging procedure and calculation of the ICFM flowfield are presented. The characteristics of the new basic flowfield with design conditions of Mach 4.0, 5.0, 6.0, and 7.0 are examined at different outflow conditions. A comparison with the ICFC flowfield indicates that the new ICFM basic flowfield demonstrates better inviscid performance and a shorter length. Besides, the expansion region is significantly reduced, and the second reflected shock wave is eradicated.

Planar Stationary Solution to Outflow Problem for Compressible Heat Conducting Gas in \(\mathbb{R}^3_+\): Stability and Convergence Rate

We are concerned with the stability and convergence rate of planar stationary solution to the compressible heat conducting gas in half space under outflow condition. (1) It is shown that a corresponding planar stationary solution is time asymptotically stable in three cases (i.e., supersonic, subsonic, and transonic), respectively, provided the initial perturbation in a certain Sobolev space and the boundary strength are sufficiently small. (2) Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. Precisely, we obtain an algebraic decay rate provided that an initial perturbation decays in a tangential direction with the algebraic rate for a supersonic flow. The corresponding algebraic convergence rate is also obtained for a transonic flow, which is worse than that for the supersonic flow due to a degenerate property of the transonic flow. Each proof is given by deriving a priori estimates of the perturbation from the stationary wave by using a time and space weighted energy method.

Experimental study of simple flumes with trapezoidal contraction

There are different devices available for measuring the flow discharge. Static measuring devices such as weirs and flumes (without any moving parts) play a significant role in discharge measurement in open channels. Many researchers have focused on application of flumes in irrigation networks. This investigation set out to study the flow discharge through a trapezoidal cut-throated flume (TCTF). The flume is simply constructed by placing two triangular plates on either side of a rectangular open channel to form a trapezoidal throat. The channel cross section is rectangular while throat cross section of the flume is trapezoidal. The proposed flume is simple, low-cost, easy to install and does not require high maintenance. The present study was designed to determine the effect of different variables on the flume discharge. For this, an experimental study was carried out under free outflow conditions and under upstream subcritical flow regime to formulate the flume discharge. Three models are defined for flume discharge relation based on the Buckingham's theorem of dimensional analysis, and then calibrated using the experimental data collected during this study. The first discharge model has an average error of 1.81%, while the second and third improved models have average errors of 0.96% and 1.44% respectively. To reliably estimate the flume discharge, free-flow and submerged-flow conditions should be distinguished. For this, suitable equations with an average error less than 2.23% were presented to estimate the submergence threshold. The results of this study indicate that while the downstream wall slope influences the submergence threshold, the flume discharge is not influenced by this variable. The proposed models are simple and accurate and present appropriate estimation of discharge for flows through the TCTFs. The findings of this study will be of interest for practical hydraulic engineers.