Turbulent Water Flow Research Articles

IMPROVEMENT OF APPROACHES AND METHODS OF TURBULENT FLOW THEORY IN THE PIPES

Abstract. The article consideres the analysis of the literature about the development of the water turbulent flow theory in the pipes. According to the results of analysis and theoretical studies, we obtained mathematical models. These models described the kinematic structure of the water turbulent flow in the pipes for different regions of turbulence. For the first time, the hypothesis was accepted that the dependence obtained from the Navier-Stokes differential equation for constructing the velocity profile in the laminar regime is suitable for calculating the average velocities in the turbulent regime of flow, but for this, it is necessary to replace the molecular kinematic viscosity with the total turbulent kinematic viscosity, which includes kinematic viscosity on the inner surface of the pipe and turbulent kinematic viscosity , which occurs due to the movement of masses from one layer into another, as recommended in J.V. Boussinesq. Based on experimental data I. Nikuradze and F.O. Shevelev, we obtained a distribution of the total kinematic viscosity in the pipes, including the kinematic viscosity on the pipe inner surface and the kinematic turbulent viscosity. For the first time, we used the kinematic viscosity distribution equation in the pipes and obtained the averaged velocity profile equation. This equation corresponds to the boundary conditions on the pipe inner surface and on the axis of the pipe. The equation of maximum averaged velocity, the equation of distance from the axis of the pipe to the points having average velocity, the equation of the ratio of maximum velocity to average velocity was obtained. For the first time, the equation of the tangent stresses components ( , ) and the tangent stresses equation in radial coordinates ( ) were obtained. The equation of the maximum value of the tangent stresses located on the inner surface of the pipe was obtained. The tangent stresses assume a zero value on the pipe axis. The equation of the vortex components ( , ) was obtained. We have shown that vortex lines are concentric circles whose centers are located on the pipe axis. The equation of angular velocity of flow particles rotation relative to the vortex lines was obtained. The maximum value of the particle rotation angular velocity on the pipe inner surface is determined. It decreases monotonically to zero on the axis of the pipeline. It is zero on the pipe axis. In this article, all equations reveal the kinematic structure of the water flow. We described these equations by the Reynolds number and the pipe friction factor. Such equations are adopted to show the dependencies between the regimes and the flow kinematic structure. These equations make it possible to calculate the distribution profile of the total kinematic viscosity, averaged velocity, tangential stresses and angular velocity of flow particle rotation.

МЕТОД РЕШЕНИЯ ЗАДАЧИ СВОБОДНОГО РАСТЕКАНИЯ БУРНОГО ПОТЕНЦИАЛЬНОГО ПОТОКА ЗА БЕЗНАПОРНОЙ ТРУБОЙ

The paper substantiates the design scheme and General formulation of the method for solving the problem of coupling various flows necessary in the practice of hydraulic engineering construction of GTS.
 In the scheme given in the article, when solving the problem of free spreading of a turbulent two-dimensional water flow with a uniform flow, a simple wave borders, and not a General flow, such as a radial flow. The analysis of the three characteristic zones of the flow. It is proved that a turbulent flow under free spreading transforms into a radial one, and the elements of the radial expansion of the flow are determined. The equations for determining the geometric shape and flow parameters for all three sections of the flow with its free spreading are obtained. The research results in this paper are obtained for the first time and complete the research started in the works of other authors.

Optimization of tire tread pattern based on flow characteristics to improve hydroplaning resistance

Tire tread pattern is a crucial parameter to prevent hydroplaning. In this study, numerical modeling was used to investigate tire hydroplaning based on flow–structure interaction. The empirical model of hydroplaning speed published in the literature was used to validate the computational model. Analysis of water flow velocity and turbulent flow energy revealed that lateral grooves of the tire significantly influenced water drainage capacity. Based on the relationship between water flow vector and lateral groove shape, a combination of Kriging surrogate model and simulated annealing algorithm was used to optimize lateral groove design to minimize hydrodynamic lift force. Four geometry parameters of lateral grooves were selected as the design variables. Based on design of experiment principle, 12 simulation cases based on the optimal Latin hypercube design method were used to analyze the influence of design variables on hydrodynamic lift force. The surrogate model was optimized by the simulated annealing algorithm to optimize tire tread pattern. The results indicated that at the same water flow speed, the optimized lateral grooves can reduce hydrodynamic lift force by 14.05% and thus greatly improve safety performance of the tire. This study proves the validity and applicability of using numerical modeling for solving the complex design of tire tread pattern and optimization problem.

Numerical simulation of stratified waxy crude oil and water flows across horizontal pipes in the presence of wall heating

In the present work, a 3D numerical study was carried out to investigate the stratified flow of waxy crude oil-water through a horizontal pipe with a contraction-expansion placed in its midsection. Moreover, a uniform heat flux was applied to the pipeline wall to investigate its effect on the overall pressure drop across the pipeline and the two-phase flow pattern. Waxy crude oils are highly viscous fluids, and they exhibit non-Newtonian viscoplastic flow behavior. The governing equations of such non-Newtonian multiphase flows were discretized and solved using the finite volume method on a structured numerical grid. The volume of fluid (VOF) method was utilized to capture the oil-water interface. Waxy crude oil flowed in the laminar regime while a turbulent water flow field was assumed, and it was modeled using the well-known SST k-ω turbulence model. The effect of several parameters, such as heat flux, wax content of the crude oil, and oil inlet velocity, have been studied comprehensively. The results revealed that the overall pressure drop was extremely sensitive to the wax content. Moreover, the simulation results indicated that using a relatively low uniform heat flux can reduce the pressure drop, up to 25%. Finally, it is shown that by increasing oil velocity at the inlet, pressure drop monotonically increased.

A novel and effective optimization algorithm for global optimization and its engineering applications: Turbulent Flow of Water-based Optimization (TFWO)

In this study we present a new and effective grouping optimization algorithm (namely, the Turbulent Flow of Water-based Optimization (TFWO)), inspired from a nature search phenomenon, i.e. whirlpools created in turbulent flow of water, for global real-world optimization problems. In the proposed algorithm, the problem of selecting control parameters is eliminated, the convergence power is increased and the algorithm have a fixed structure. The proposed algorithm is used to find the global solutions of real-parameter benchmark functions with different dimensions. Besides, in order to further investigate the effectiveness of TFWO, it was used to solve various types of nonlinear Economic Load Dispatch (ELD) optimization problems in power systems and Reliability–RedundancyAllocation Optimization (RRAO) for the overspeed protection system of a gas turbine, as two real-world engineering optimization problems. The results of TFWO are compared with other algorithms, which provide evidence for efficient performance with superior solution quality of the proposed TFWO algorithm in solving a great range of real-parameter benchmark and real-world engineering problems. Also, the results prove the competitive performance and robustness of TFWO algorithm compared to other state-of-the-art optimization algorithms in this study. The source codes of the TFWO algorithm are publicly available at https://github.com/ebrahimakbary/TFWO.

On the Green's function emergence from interferometry of seismic wave fields generated in high-melt glaciers: implications for passive imaging and monitoring

Abstract. Ambient noise seismology has revolutionized seismic characterization of the Earth's crust from local to global scales. The estimate of Green's function (GF) between two receivers, representing the impulse response of elastic media, can be reconstructed via cross-correlation of the ambient noise seismograms. A homogenized wave field illuminating the propagation medium in all directions is a prerequisite for obtaining an accurate GF. For seismic data recorded on glaciers, this condition imposes strong limitations on GF convergence because of minimal seismic scattering in homogeneous ice and limitations in network coverage. We address this difficulty by investigating three patterns of seismic wave fields: a favorable distribution of icequakes and noise sources recorded on a dense array of 98 sensors on Glacier d'Argentière (France), a dominant noise source constituted by a moulin within a smaller seismic array on the Greenland Ice Sheet, and crevasse-generated scattering at Gornergletscher (Switzerland). In Glacier d'Argentière, surface melt routing through englacial channels produces turbulent water flow, creating sustained ambient seismic sources and thus favorable conditions for GF estimates. Analysis of the cross-correlation functions reveals non-equally distributed noise sources outside and within the recording network. The dense sampling of sensors allows for spatial averaging and accurate GF estimates when stacked on lines of receivers. The averaged GFs contain high-frequency (>30 Hz) direct and refracted P waves in addition to the fundamental mode of dispersive Rayleigh waves above 1 Hz. From seismic velocity measurements, we invert bed properties and depth profiles and map seismic anisotropy, which is likely introduced by crevassing. In Greenland, we employ an advanced preprocessing scheme which includes match-field processing and eigenspectral equalization of the cross spectra to remove the moulin source signature and reduce the effect of inhomogeneous wave fields on the GFs. At Gornergletscher, cross-correlations of icequake coda waves show evidence for homogenized incident directions of the scattered wave field. Optimization of coda correlation windows via a Bayesian inversion based on the GF cross coherency and symmetry further promotes the GF estimate convergence. This study presents new processing schemes on suitable array geometries for passive seismic imaging and monitoring of glaciers and ice sheets.

A New Approach to Generalization of Experimental Data on Heat Transfer to Fluids in Supercritical Region

Abstract The paper contains the results of analysis of heat transfer regimes in the case of forced turbulent flow of water and modeling fluids in channels of various configurations at supercritical pressures. Two new complex criteria were proposed for describing heat transfer in the pseudo-phase transition region. A system of equations suitable for the engineering calculation of heat transfer in fuel assemblies of nuclear supercritical water reactors is presented. A comparison of the calculations of heat transfer coefficient (HTC) with experimental data for the regimes of normal, deteriorated and mixed heat transfer is made.

Laser ranging measurements of turbulent water surfaces

Laser ranging is a measurement method, applied in a wide range of applications. In this study, laser ranging is used to measure the height of turbulent water flows. Measurements were performed in three cross sections of a confluence where a tributary flow meets the main flow. Both flows exhibited high Reynolds and Froude numbers where the free-water surface profiles were turbulent, non-stationary and non-homogeneous. Measurements were taken using a commercial LIDAR and a high-speed camera. The high-speed camera was operated on the principle of laser triangulation, using only the illumination from the LIDAR laser beam. Since, no other state-of-the-art method for measuring instantaneous water surface profiles exists, LIDAR and triangulation methods could only be compared with each other. The results show good agreement between both methods for the average turbulent water profile and fair agreement for instantaneous profiles. Presented herein is an explanation of these results.

Here Determination of the Free Flow Maximum Expansion into a Wide Diversion Channel of Turbulent Water Flow Behind the Non-Pressure Water Throughput Hole

In the work proposed a calculating method for the β, up, hp, lp flow parameters, and the way of determining the geometric shape of the flow region (i. e., the geometry of the current extreme line). And determined of specific areas in the flow spreading petal from the edge of the feed pipe to the cross section of the p-p maximum flow spread; obtained the most convenient type of flow equations; an algorithms for determining parameters of the β, up, hp, lp of the flow are developed p; The evaluation of the model (method) results in comparison with the experimental results are given.

Glaciohydraulic seismic tremors on an Alpine glacier

Abstract. Hydraulic processes impact viscous and brittle ice deformation. Water-driven fracturing as well as turbulent water flow within and beneath glaciers radiate seismic waves which provide insights into otherwise hard-to-access englacial and subglacial environments. In this study, we analyze glaciohydraulic tremors recorded by four seismic arrays installed in different parts of Glacier de la Plaine Morte, Switzerland. Data were recorded during the 2016 melt season including the sudden subglacial drainage of an ice-marginal lake. Together with our seismic data, discharge, lake level, and ice flow measurements provide constraints on glacier hydraulics. We find that the tremors are generated by subglacial water flow, in moulins, and by icequake bursts. The dominating process can vary on sub-kilometer and sub-daily scales. Consistent with field observations, continuous source tracking via matched-field processing suggests a gradual up-glacier progression of an efficient drainage system as the melt season progresses. The ice-marginal lake likely connects to this drainage system via hydrofracturing, which is indicated by sustained icequake signals emitted from the proximity of the lake basin and starting roughly 24 h prior to the lake drainage. To estimate the hydraulics associated with the drainage, we use tremor–discharge scaling relationships. Our analysis suggests a pressurization of the subglacial environment at the drainage onset, followed by an increase in the hydraulic radii of the conduits and a subsequent decrease in the subglacial water pressure as the capacity of the drainage system increases. The pressurization is in phase with the drop in the lake level, and its retrieved maximum coincides with ice uplift measured via GPS. Our results highlight the use of cryo-seismology for monitoring glacier hydraulics.

Hydrodynamic and thermal analysis of water, ethylene glycol and water-ethylene glycol as base fluids dispersed by aluminum oxide nano-sized solid particles

PurposeThe purpose of this paper is to carry out a hydrodynamic and thermal analysis of turbulent forced-convection flows of pure water, pure ethylene glycol and water-ethylene glycol mixture, as base fluids dispersed by Al2O3 nano-sized solid particles, through a constant temperature-surfaced rectangular cross-section channel with detached and attached obstacles, using a computational fluid dynamics (CFD) technique. Effects of various base fluids and different Al2O3 nano-sized solid particle solid volume fractions with Reynolds numbers ranging from 5,000 to 50,000 were analyzed. The contour plots of dynamic pressure, stream-function, velocity-magnitude, axial velocity, transverse velocity, turbulent intensity, turbulent kinetic energy, turbulent viscosity and temperature fields, the axial velocity profiles, the local and average Nusselt numbers, as well as the local and average coefficients of skin friction, were obtained and investigated numerically.Design/methodology/approachThe fluid flow and temperature fields were simulated using the Commercial CFD Software FLUENT. The same package included a preprocessor GAMBIT which was used to create the mesh needed for the solver. The RANS equations, along with the standard k-epsilon turbulence model and the energy equation were used to control the channel flow model. All the equations were discretized by the finite volume method using a two-dimensional formulation, using the semi-implicit method for pressure-linked equations pressure-velocity coupling algorithm. With regard to the flow characteristics, the interpolation QUICK scheme was applied, and a second-order upwind scheme was used for the pressure terms. The under-relaxation was changed between the values 0.3 and 1.0 to control the update of the computed variables at each iteration. Moreover, various grid systems were tested to analyze the effect of the grid size on the numerical solution. Then, the solutions are said to be converging when the normalized residuals are smaller than 10-12 and 10-9 for the energy equation and the other variables, respectively. The equations were iterated by the solver till it reached the needed residuals or when it stabilized at a fixed value.FindingsThe result analysis showed that the pure ethylene glycol with Al2O3 nanoparticles showed a significant heat transfer enhancement, in terms of local and average Nusselt numbers, compared with other pure or mixed fluid-based nanofluids, with low-pressure losses in terms of local and average skin friction coefficients.Originality/valueThe present research ended up at interesting results which constitute a valuable contribution to the improvement of the knowledge basis of professional work through research related to turbulent flow forced-convection within channels supplied with obstacles, and especially inside heat exchangers and solar flat plate collectors.

Effect of Particle Size and Surface Properties on the Sandbed Erosion with Water Flow in a Horizontal Pipe

Summary An experimental study was conducted to investigate the transport of sand particles over the sand bed deposited in a horizontal conduit by using turbulent flow of water. The main objectives were to determine the near-wall turbulence characteristics at the onset of bed erosion (i.e., near-wall velocity profile, Reynolds shear stresses, and axial-turbulent intensity); to determine critical velocity required for particle removal from the bed deposits; and more specifically, to determine how the sand-particle size and surface characteristics would influence the critical velocity required for the onset of bed erosion and the near-wall turbulence characteristics. A large-scale horizontal flow loop equipped with a nonintrusive laser-based particle-image velocimetry (PIV) system has been used for the experiments. The effect of sand-particle surface characteristics (i.e., wettability) on the critical velocity and the near-wall turbulence characteristics were investigated by using treated and untreated industrial sands of four different mesh sizes (i.e., 20/40, 30/50, 40/70, 100). The PIV technique was used to determine instantaneous local velocity distribution near the stationary sandbed fluid interface under subcritical and critical flow conditions. The near-wall velocity distribution measured directly at the sand bed/fluid interface together with the measured frictional pressure-loss values were then used for the evaluation of the Reynolds shear stresses and axial turbulent intensities acting at the bed/fluid interface. The results indicated that critical velocity for the onset of particle removal from sand beds increased with the increasing particle size. When sands with special surface treatment were used, it was observed that the critical velocity required for the onset of the bed erosion was significantly lower than that of required for the untreated sands. The degree of reduction in critical velocity varied between 14 and 40% depending on the particle size. In this study, by conducting experiments under controlled conditions, we provided much-needed fundamental data that can be used for the development of improved solid-transport design criteria and suitable mitigation technologies. In particular, we have shown the proof of concept that the surface-treated sand particles might have great potential for improving the transport efficiency of proppants used for hydraulic-fracturing operations.

Experimental thermal analysis of a turbulent nano enriched water flow in a circular tube

In the present study the effect of adding MgO nanoparticles to the water on the turbulent flow thermal properties in a counter-flow heat exchanger is investigated experimentally. Experiments have been done in Reynolds number of 6,000 to 32,000 and nanoparticles volume fraction of 0.005 to 0.02. In this investigation convective heat transfer coefficient, pressure drop, friction factor and Nusselt number are measured and discussed. According to experimental data convective heat transfer coefficient, average Nusselt number, and pressure drop have direct mathematical relation with nanoparticles volume fraction and Reynolds number (with maximum enhancement of 31.96% in nanoparticles volume fraction of 2%). However, at certain nanoparticle volume fractions and Reynolds numbers, increasing nanoparticle volume fraction led to a reduction of the flow friction factor (1.63% when φ=0.5%). Also, irrespective of the nanoparticle volume fraction, increasing the Reynolds numbers caused decreases of the flow friction factor. Considering high cost of experimental studies as a problem, a new mathematical and statistical based correlation is presented to predict the Nusselt number with independent variables of φ, Pr and Re.

Experimental and Numerical Investigation of Swirling Flow on Triple Elbow Pipe Layout

The secondary flow downstream of a triple elbow layout was studied experimentally and numerically to visualize the flow behavior under swirling inlet flow conditions. The inlet swirling condition was generated by a swirl generator, consisting of a rotary pipe and honeycomb assembly. The experiments were carried out in turbulent water flow condition at Reynolds number Re = 1 × 104 and inlet swirl intensity S = 1. Ultrasonic measurements were taken at four locations downstream of the third elbow. The two-dimensional velocity field of the flow field was measured using the phased array ultrasonic velocity profiler technique to evaluate the flow field with separation. Furthermore, a numerical simulation was performed and its results were compared with the experimental data. The numerical result was obtained by solving three-dimensional, Reynolds-averaged Navier-Stokes equations with the renormalization group k-ε turbulence model. The experimental results confirmed that the swirling flow condition modified the size of the separation region downstream of the third elbow. A qualitative comparison between the experimental and CFD simulation results of the averaged velocity field downstream of the third elbow showed similar tendency on reverse flow.

Applying PIV to study a fluid flow in the vicinity of a circular streamlined cylinder

The round cylinder streamlining by a turbulent water flow in a hydrodynamic pipe is investigated experimentally. Using the optical method of PIV (Particle Image Velocimetry) the averaged velocity fields near the cylinder are obtained and, on their basis, the geometric characteristics of the vortex zone of the near wake are calculated for the non-cavitation and cavitation flow regimes in the critical region of Reynolds numbers. The use of two mirrors, set at a certain angle to each other, allows obtaining a picture of the velocity fields around the entire cylinder, rather than around half of it, as it is done in most of the works. Using vector patterns of averaged velocity fields, the angles of the boundary layer separation from the cylinder surface along the reverse flow are determined in the considered flow regimes. An asymmetrical separation of the boundary layer from different sides of the streamlined cylinder was obtained. It is shown that the increase in the Reynolds number for the non-cavitation flow regimes leads to a more than two times decrease in the vortex zone behind the cylinder, and, accordingly, to a displacement of the separation angles downstream. Cavitation increases the vortex zone behind the cylinder and displaces the separation angles upstream.

Experiments on grain size segregation in bedload transport on a steep slope

Sediment transport in mountain and gravel-bed-rivers is characterized by bedload transport of a wide range of grain sizes. When the bed is moving, dynamic void openings permit downward infiltration of the smaller particles. This process, termed here ‘kinetic sieving’, has been studied in industrial contexts, but more rarely in fluvial sediment transport. We present an experimental study of two-size mixtures of coarse spherical glass beads entrained by turbulent and supercritical steady water flows down a steep channel with a mobile bed. The particle diameters were 4 mm and 6 mm, and the channel inclination 10%. The spatial and temporal evolution of the segregating smaller 4 mm diameter particles was studied through the introduction of the smaller particles at a low constant rate into the large particle bedload flow at transport equilibrium. Particle flows were filmed from the side by a high-speed camera. Using original particle tracking algorithms, the position and velocity of both small and large particles were determined. Results include the time evolution of the layer of segregating smaller beads, assessment of segregation velocity and particle depth profiles. Segregation resulted in the progressive establishment of a quasi-continuous region of small particles reaching a steady-state penetration depth. The segregation dynamics showed a logarithmic time decreasing trend. This evolution was demonstrated to be dependent on the particle streamwise shear rate which decays downwards exponentially. This result is comparable to theories initially developed for dry granular flows.

Bubbly drag reduction using a hydrophobic inner cylinder in Taylor–Couette turbulence

In this study we experimentally investigate bubbly drag reduction in a highly turbulent flow of water with dispersed air at $5.0 \times 10^{5} \leq \text{Re} \leq 1.7 \times 10^{6}$ over a non-wetting surface containing micro-scale roughness. To do so, the Taylor-Couette geometry is used, allowing for both accurate global drag and local flow measurements. The inner cylinder - coated with a rough, hydrophobic material - is rotating, whereas the smooth outer cylinder is kept stationary. The crucial control parameter is the air volume fraction $\alpha$ present in the working fluid. For small volume fractions ($\alpha < {4}\,\%$), we observe that the surface roughness from the coating increases the drag. For large volume fractions of air ($\alpha \geq 4\,\%$), the drag decreases compared to the case with both the inner and outer cylinders uncoated, i.e. smooth and hydrophilic, using the same volume fraction of air. This suggests that two competing mechanisms are at place: on the one hand the roughness invokes an extension of the log-layer - resulting in an increase in drag - and on the other hand there is a drag-reducing mechanism of the hydrophobic surface interacting with the bubbly liquid. The balance between these two effects determines whether there is overall drag reduction or drag enhancement. For further increased bubble concentration $\alpha = {6}\,\%$ we find a saturation of the drag reduction effect. Our study gives guidelines for industrial applications of bubbly drag reduction in hydrophobic wall-bounded turbulent flows.

Horns of subaqueous barchan dunes: A study at the grain scale.

Many complex aspects are involved in the morphodynamics of crescent-shaped dunes, known as barchans. One of them concerns the trajectories of individual grains over the dune and how they affect its shape. In the case of subaqueous barchans, we proposed [C. A. Alvarez and E. M. Franklin, Phys. Rev. Lett. 121, 164503 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.164503] that their extremities, called horns, are formed mainly by grains migrating from upstream regions of the initial pile, and that they exhibit significant transverse displacements. Here, we extend our previous work to address the dynamics of grains migrating to horns after the dune has reached its crescentic shape and present new aspects of the problem. In our experiments, single barchans evolve, under the action of a turbulent water flow, from heaps of conical shape formed from glass beads poured on the bottom wall of a rectangular channel. Both for evolving and for developed barchans, the horns are fed up with grains coming from upstream regions of the bedform and traveling with significant transverse components, differently from the dynamics usually described for the aeolian case. For these grains, irrespective of their size and the strength of the water flow, the distributions of transverse and streamwise components of velocities are well described by exponential functions, with the probability density functions of their magnitudes being similar to results obtained from previous studies on flat beds. Focusing on moving grains whose initial positions were on the horns, we show that their residence time and traveled distance are related following a quasilinear relation. Our results provide new insights into the physical mechanisms underlying the shape of barchan dunes.

A quantification of penetration length of steam jet condensation in turbulent water flow in a vertical pipe

An experimental research is performed to investigate the penetration length of steam jet condensation in turbulent water flow in a vertical pipe. The penetration length of the condensing jet, with steam mass velocities ranging from subsonic to supersonic, was measured via utilizing a visualization window and a high-speed camera. At low steam flow rate a steam bubble plume forms, while at relatively high flow rate the bubbles in the plume coalesce and a steam jet is produced. Quantitative analyses of the interface behavior of the condensing jet are performed by exploring the transient and statistical characteristics of the jet penetration length. The waveforms of the transient jet penetration length exhibit that in the bubbling regime the period is approximately constant, while in the jetting regime the period varies a lot. The statistical analysis of the transient jet penetration length confirms that significant variations of the power distribution function (PDF) and power spectrum density (PSD) between the bubbling and jetting regimes occur at the transonic condition. The ratio of steam mass flux to critical steam mass flux at ambient pressure is found to have good linearity with the mean of the jet penetration length. And a linear correlation is fitted with a maximum absolute deviation of 5.5% between the measured and predicted values of mean of the jet penetration length. The relative unsteadiness of jet penetration length, defined as the ratio of the standard deviation to mean of transient penetration length, is approximately invariable in the bubbling and jetting regime. The bubbling regime contains more relative unsteadiness, while the jetting regime yield less relative unsteadiness. Because absolute instability exists in the subsonic region while no absolute instability occurs in the supersonic region, the transition from the bubbling to jetting regime occurs in the transonic region.

Hybrid Artificial Viscosity–Central-Upwind Scheme for Recirculating Turbulent Shallow Water Flows

AbstractIn this paper, a hybrid artificial viscosity–central-upwind (AV-CU) scheme is proposed for simulating recirculating turbulent shallow water flows by combining the artificial viscosity (AV) ...