Function Of Froude Number Research Articles

Experimental Study on Flow and Sediment Distribution at Off-Take Channel

River off-take is one of the complex features in fluvial systems and the distribution of flow, and sediments along the branches are still a matter of research. This paper deals with a physical simulation on an off-take channel for understanding the flow and sediment distribution in the vicinity. Laboratory-based test runs have been carried out by changing the discharges and the angles off-take. A total of eighteen test runs have been conducted for three discharge conditions with three off-take angles. Two equations for predicting water and sediment discharge ratios have been proposed as a function of Froude number, channel geometry and off-take angel. Flow visualizations have also been carried out in the vicinity of the off-take for understanding erosion and sedimentation pattern. Flow and sediment movement patterns were carefully observed during the simulation and four distinguished zone formations have been noted in the vicinity. Finally, validations of the developed equations have been done with the field data from selected river off-take systems of Bangladesh. Validation results of field data show mean discrepancy ratios of 0.83 for the discharge equation and 0.89 for sediment equation during low flow.

Evanescent to propagating internal waves in experiments, simulations, and linear theory

Experiments, numerical simulations, and linear theory are used to explore the kinetic energy density of waves generated by oscillating topography in a nonlinear stratification. Initially, generated waves are evanescent but then pass through a turning depth and into a propagating region. A technique for calculating kinetic energy density indirectly via the density perturbation field measured using synthetic schlieren is tested to assess the validity of the calculation. To establish the indirect calculation’s range of validity, numerical simulations were performed to compare the indirect calculation to an estimate of kinetic energy calculated from local velocity components (referred to here as the standard calculation). In addition, the standard calculation is applied to the velocity field determined via linear theory, which defines the fluid velocity using similar assumptions to the indirect calculation of kinetic energy. Both calculation methods show similar trends in the average kinetic energy density present in propagating waves as a function of Froude number, topography height, and distance from topography to the turning depth. Local comparisons of kinetic energy density from the indirect and standard calculations identify regions where the two methods compare well. Additionally, a correlation between linear theory and numerical simulations is presented to evaluate the range of applicability of the linear theory.

Scale and structure dependent drag in gas–solid flows

AbstractDrag plays a crucial role in hydrodynamic modeling and simulations of gas–solid flows, which is significantly affected by particle Reynolds number, solid volume fraction, heterogeneity, granular temperature, particle‐fluid density ratio, and so on. To clarify and quantify the multiscale effects of these factors, large‐scale particle‐resolved direct numerical simulations of gas–solid flows with up to 115,200 freely moving particles are conducted. Both domain‐averaged kinetic properties and local averaged dimensionless drag are sampled and analyzed. It is revealed that the complex scale‐dependence of drag is attributed to the multiscale effects of heterogeneous structures and particle fluctuating velocity. The granular temperature and the scalar variance of solid volume fraction are also found to be scale‐dependent. On account of these, a new drag correlation as the function of Froude number is proposed with consideration of scale‐dependence.

Experimental study of the local scouring around sloped piers and its estimation using statistical tools

Local scouring around sloped bridge piers in steady currents was studied both experimentally and mathematically. The effects of different inclination angles, flow intensities, flow depths, and pier size on local scouring were investigated. The experimental results show that the scouring depth increases with an increase in the values of discharge and pier width. The scouring depth for the sloped piers is smaller than the vertical piers one and the maximum scouring depth continuously decreases as the pier inclination angle increases. Prediction of the scouring depth around bridge piers using analytical models can be utilized in the feasibility studies of different models, and evaluations of the parametric analytical. Therefore, it was tried to model the scouring depth as a function of Froude number, flow intensity, and relative roughness parameters using non-dimensional analysis. The regression analysis based models were introduced to determine the scouring depth at upstream side of the pier using experimental tests data. Step-wise linear regression showed that the value of relative scouring depth has considerably good correlation only with two non-dimensionless parameters of inclination angle and normalized approaching flow depth. In this regard, some linear and nonlinear regression tools were utilized to establish functional relationships between these variables. Statistical indices and residual analyses of the models revealed the suitability of the models. Comparison of the experimental and predicted value of relative scouring depth illustrates that the suggested models can reasonably predict this parameter.

Laboratory investigation for development of local scour depth model for varying shapes of obstruction

This paper reports the effect of the shape of obstruction on local scour depth. Laboratory experiments were conducted on a tilting glass flume to study scour phenomenon around five obstructions of different shapes. Obstructions studied were chosen keeping in view not only the bridge piers but also some other structures, like obstructions in the flow channels, e.g., a jetty, big boulder, any building in the coastal area, etc. Maximum local equilibrium scour, a dependent parameter, was studied as a function of flow parameters and shape parameters of the obstruction. A model was developed for the maximum local scour depth estimation in which maximum local scour depth (ds) is a function of Froude number (Fr), flow depth (y) and shape factor (Sf). The experimental findings depict a considerable effect of the shape of obstruction on the local scour depth.

Laboratory investigation for development of local scour depth model for varying shapes of obstruction

This paper reports the effect of the shape of obstruction on local scour depth. Laboratory experiments were conducted on a tilting glass flume to study scour phenomenon around five obstructions of different shapes. Obstructions studied were chosen keeping in view not only the bridge piers but also some other structures, like obstructions in the flow channels, e.g., a jetty, big boulder, any building in the coastal area, etc. Maximum local equilibrium scour, a dependent parameter, was studied as a function of flow parameters and shape parameters of the obstruction. A model was developed for the maximum local scour depth estimation in which maximum local scour depth (ds) is a function of Froude number (Fr), flow depth (y) and shape factor (Sf). The experimental findings depict a considerable effect of the shape of obstruction on the local scour depth.

Effects of river width changes on flow characteristics based on flume experiment

The rapid changes in flow pattern due to varying channel widths will make significantly impact on the hydraulic structures and evolutions of open channel. To better understand the impact of varying width, a flume experiment with adjustable width and a depth-averaged two-dimension numerical model were used to analyze the variations of flow parameters. Our experimental results showed that flow velocity gradually increased with decreasing water depth in converging region, and decreased with increasing water depth in diverging zones. It was also found that the turbulence intensity laws in three directions were not agreed with the theoretical relationships proposed by Nezu and Nakagawa in 1993 in straight open channel flows. The flow in the channel with varying width may change from the supercritical flow to the subcritical flow as a function of Froude number. Our numerical simulations with different flow rates showed that most of the hydraulic jumps in diverging region were submerged jump and the degree of submergence increased with increasing flow rate in gradual channel transition. When the flow rate increased, the range of supercritical flow rapidly decreased and the flow changed from the supercritical condition to the subcritical condition in diverging sections.

Flow resistance of gravel bed channels

Existing resistance formulas produce a wide range of friction-factor estimates for gravel bed streams. The purpose of this paper is to develop a reliable resistance formula in terms of the Darcy-Weisbach friction factor f. Published data were screened and used to establish the formula. The existing formulas have considered that f is a function of relative roughness D84/R only, where R is the hydraulic radius and D84 is the particle size referred to the intermediate diameter that equals or exceeds that of 84 percent of bed sediments. In this paper, f is considered as a function of Froude number in addition to the relative roughness. f for D84/R>1 displays a different trend than that for D84/R<1 perhaps due to the invalid assumption of a logarithmic velocity distribution for D84/R>1. An f formula for D84/R<1 has been established.

Comparison of Model-Scale and Full-scale Deceleration of a Fully Skirted Air Cushion Vehicle in Sideslip

This article provides experimental results and shows comparisons of 90° sideslip performance of a fully skirted air cushion vehicle using theoretical predictions, 1/12th model-scale data, and full-scale data. The goal is to establish a relation among the three data sets and draw conclusions for use in future predictions. First, this article presents results and analysis of tow tank data obtained in late 2008. Then, the Froude scaled data are used to obtain an empirical drag coefficient. A comparison is made between this approach and a theoretical prediction proposed in previous work. An iterative, one-dimensional deceleration algorithm is then constructed using the coefficients to predict the deceleration of a full-scale craft having similar skirt characteristics. The predictions are performed for three craft weights and the resulting deceleration rates as a function of Froude number are presented. Data obtained from full-scale testing are then compared with the results of both the model-based algorithm and the theoretical prediction. In general, the model-based simulation overpredicts the deceleration rate for a full-scale craft, whereas the theoretical prediction is more accurate. The model simulation is recomputed using a developed correction factor and is plotted against the theoretical and full-scale deceleration, revealing favorable results. Lastly, a review of the technique is described and recommendations for improvements and following work are provided.

Comparison of Model-Scale and Full-scale Deceleration of a Fully Skirted Air Cushion Vehicle in Sideslip

This article provides experimental results and shows comparisons of 90 sideslip performance of a fully skirted air cushion vehicle using theoretical predictions, 1/12th model scale data, and full-scale data. The goal is to establish a relation among the three data sets and draw conclusions for use in future predictions. First, this article presents results and analysis of tow tank data obtained in late 2008. Then, the Froude scaled data are used to obtain an empirical drag coefficient. A comparison is made between this approach and a theoretical prediction proposed in previous work. An iterative, one dimensional deceleration algorithm is then constructed using the coefficients to predict the deceleration of a full-scale craft having similar skirt characteristics. The predictions are performed for three craft weights and the resulting deceleration rates as a function of Froude number are presented. Data obtained from full-scale testing are then compared with the results of both the model-based algorithm and the theoretical prediction. In general, the model-based simulation overpredicts the deceleration rate for a full-scale craft, whereas the theoretical prediction is more accurate. The model simulation is recomputed using a developed correction factor and is plotted against the theoretical and full-scale deceleration, revealing favorable results. Lastly, a review of the technique is described and recommendations for improvements and following work are provided.

ワンド水表面における浮遊物質の主流部への輸送速度に関する研究

Recently, maintaining biodiversity in rivers is required as a part of nature-oriented river works. Wandos made artificially in rivers are one of the measures to secure biodiversity. Transport of suspended solids at the water surface of wandos to river stream is known to be controlled by large scale vortices.In this study, firstly transport rates of expanded polystyrene particles as uspended solids at the water surface of a wando in a rectangular channel were examined. The results of experiments in the rectangular channel indicate that the transport rate of expanded polystyrene particles decreases with the increase in Froude number. Secondly, a formula on the transport of expanded polystyrene particles was proposed as a function of Froude number and the ratio between the length and the width of wando.

Numerical and experimental investigation of vortex breaker effectiveness on the improvement in launch vehicle ballistic parameters

The focus of the present study is to investigate the effectiveness of installing vortex breakers at the outlet of launch vehicle tanks on postponing vortex formation and decreasing the critical height of propellants while discharging. Analytical results in the absence of a vortex breaker show that the effects of the Weber and Reynolds numbers in the flow field can be ignored for values greater than 720 and 1.1 × 105, respectively; and critical height can be considered as a function of Froude number under aforementioned conditions. The analytical criteria are verified by two-dimensional, axis symmetrical, transient and two-phase numerical model. Eventually, some experiments are conducted to examine the effectiveness of the applied vortex breakers in reduction of the critical height of propellant. Experimental results show that a 30% decrease can be achieved in critical height by using a particular type of vortex breaker. Additionally, the carried out simulations for an existing two-stage launch vehicle indicate a 13% increase in orbital altitude, which in turn proves the considerable improvement in launch vehicle mass/energetic capabilities.

Investigation of Combustion Characteristics of Biodiesel and Its Blends

Experiments employing porous sphere technique are carried out to investigate the combustion characteristics of biodiesel produced from karanja oil and its blends with diesel and gasoline. Biodiesel or its blend is transpired to porous sphere surfaces, where it burns. Porous spheres are placed in an air stream blowing with a uniform velocity at atmospheric pressure and temperature under normal gravity conditions. At low air velocities, a flame envelops the entire sphere. Fuel feed rates are recorded for various sphere sizes and air velocities. Overall, the visible flame shape is analyzed with the help of digital flame image. At a particular air velocity, the flame will not envelope the sphere, but establish near the rear region of the sphere and the same is recorded for different sphere sizes. Theoretical correlations are proposed for burning rate as a function of effective Reynolds number and for Damköhler number as a function of Froude number.

Vorticity determination in a hydraulic jump by application of method of characteristics

The method of characteristics for solving systems of partial differential equations coupled with jump conditions is used in analysing flow downstream of a hydraulic jump instead of the normal analytical approach adopted in Hornung [1]. It is shown that the method of characteristics together with the jump conditions can correctly be used as an alternative method to determine the mean vorticity downstream of the hydraulic jump as a function of the Froude number and height ratio. The mean vorticity does not increase from zero as a function of Froude number minus one but, however, it approaches a constant value at large Froude number. The present work extends the model of Hornung [1] to include non linear velocity profile used in calculating the torque with a view to determining the mean vorticity. The result obtained by this method generalizes that of [1]. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 239-248

Study of Flow Over Side Weirs Under Supercritical Conditions

The present study focuses on the application of momentum principle to the analysis of spatially varied flow under supercritical conditions. Experimental studies were conducted on rectangular side weirs of different lengths and sill heights fitted in the test section of a rectangular aluminium channel that was built in a tilting flume. Measurements of discharges in the main channel and through the side weir were done separately. A pitot tube with direction finder was used to determine the velocities and angle of spill flow with the side weir. Depths of flow were measured both in longitudinal and transverse directions at regular intervals and their profiles were studied. Experiments were conducted with different test plates and flow conditions in the main channel. Coefficients of discharge were computed using momentum principle for different Froude numbers (between 1.5 and 3). The variation of discharge coefficient of the side weir as a function of Froude number was found to exhibit a non-linear relationship. Discharges over side weirs were computed using the computed coefficients of discharge for different Froude numbers and it was verified with the observed discharges. Coefficients of discharge were also computed using energy principle for different Froude numbers. Chi-square test was done between observed discharges over side weirs and discharges computed using momentum and energy principles, it was found that momentum principle is fitting better. Variation of the ratios of longitudinal components of velocity vector of spill flow to the mean velocity of the main channel flow at upstream end of the side weir with Froude number was found to exhibit a non-linear relationship. Variation of the discharge ratios of spill flow and main channel discharges with Froude number was also studied.

Entropy generation during the quasi-steady burning of spherical fuel particles

Entropy generation during the quasi-steady combustion of spherical liquid fuel particles has been presented in detail. The effects of freestream velocity, particle diameter, ambient temperature and gravity, on the entropy generation rate, have been discussed in detail. In the range of sub-critical freestream velocity, where an envelope flame is present, the entropy generation rate presents a minimum value. At a critical velocity, where the flame transition occurs, the entropy generation rate reaches a maximum value. Flame transition significantly affects the entropy generation rate, which suffers a sharp decrease in its value after the transition. Heat transfer and chemical reaction contribute almost equally to the total entropy generation rate. When normal gravity is considered in an upward flow configuration, there is an increase in the entropy generation rate as compared to the zero gravity case. The effect of gravity poses a complex variation pattern in the entropy generation rate, for a downward flow configuration. The entropy generation rate decreases with increasing ambient temperature. The entropy generation rate increases with the particle diameter. A correlation has been presented for the non-dimensional entropy generation number as a function of Froude number.

Spatial and radiative properties of an open-flame hydrogen plume

Considerable effort is being directed toward updating safety codes and standards in preparation for production, distribution, and retail of hydrogen as a consumer energy source. In the present study, measurements were performed in large-scale, vertical flames to characterize the dimensional and radiative properties of an ignited hydrogen jet. These data are relevant to the safety scenario of a sudden leak in a high-pressure hydrogen containment vessel. Specifically, the data will provide a technological basis for determining hazardous length scales associated with unintended releases at hydrogen storage and distribution centers. Visible and infrared video and ultraviolet flame luminescence imaging were used to evaluate flame length, diameter and structure. Radiometer measurements allowed determination of the radiant heat flux from the flame. The results show that flame length increases with total jet mass flow rate and jet nozzle diameter. When plotted as a function of Froude number, which measures the relative importance of jet momentum and buoyancy, the measured flame lengths for a range of operating conditions collapse onto the same curve. Good comparison with hydrocarbon jet flame lengths is found, demonstrating that the non-dimensional correlations are valid for a variety of fuel types. The radiative heat flux measurements for hydrogen flames show good agreement with non-dimensional correlations and scaling laws developed for a range of fuels and flame conditions. This result verifies that such correlations can be used to predict radiative heat flux from a wide variety of hydrogen flames and establishes a basis for predicting a priori the characteristics of flames resulting from accidental releases.

Effect of specific energy variation on lateral overflows

A numerical model was used to study the effect of change in specific energy height along a side weir on flow. Discharge coefficient was considered as a local variable that includes flow depth and the angle of the deflected water jet along side weir. Hydraulic profile on the weir plane and the hydraulic head on the weir were obtained using two dimensionless parameters ψ and m as a function of Froude number. Flow depths and flow rates were then computed and minimum standard errors were determined based upon these parameters. The agreement between computed values and observations was demonstrated. It was concluded that rates of flow are considerably affected by the variation of specific energy along the side weir when weir head is based on flow depth at the weir plane. Considerable deviations from the constant specific energy assumption may be observed in this case specially when a great change in flow rates exists along side weirs with zero end discharges.

A simple formula for estimating backwater at bridge constrictions

The past experimental studies to investigate the backwater effects due to bridge constrictions have been mostly performed in setups of single rectangular channels with fairly smooth surfaces. Therefore, there is a need to investigate more realistic cross-sectional shapes and roughness conditions. The most obvious case is to consider bridges in natural channels with floodplains. This paper reports the findings of model testing of arch and straight deck bridge constrictions in a compound channel flume with both smooth and roughened surfaces. Four different types of bridge models, namely single opening semicircular, multiple opening semicircular, single opening elliptic, and straight deck models with and without piers, were used in the testing program. An attempt was made to develop a simple formula for estimating bridge backwater as a function of Froude number and opening ratio.Key words: bridge backwater, hydraulic model testing, open channel flow, flood control.

Modeling of the Onset of Gas Entrainment Through a Finite-Side Branch

A theoretical investigation has been conducted for the prediction of the critical height at the onset of gas entrainment during single discharge from a stratified, two-phase region through a side branch with a finite diameter. Two different models have been developed, a simplified point-sink model and a three-dimensional finite-branch model. The two models are based on a new criterion for the onset of gas entrainment. The results of the predicted critical heights at the onset of gas entrainment showed that the finite-branch model approaches the physical limits at low Froude numbers. However, as the values of the Froude number increased, the predictions of both models eventually converged to the same value. Based on the results of the models, the critical height corresponding to the onset of gas entrainment was found to be a function of Froude number and fluid densities. The results of both models are compared with available experimental data. The comparisons illustrate a very good agreement between the measured and predicted values.