Range Of Froude Numbers Research Articles

Extension of a Non-Oscillatory Forward-in-Time Scheme to Detached Eddy Simulation of Stratified Turbulent Flows With Unstructured Meshes

A detached eddy simulation algorithm is developed based on the non-oscillatory forward-in-time (NFT) multidimensional positive definite advection transport algorithm (MPDATA) scheme for stratified turbulent flows with low or moderate Reynolds numbers on unstructured meshes. NFT MPDATA is extended to viscous turbulent flows for the first time. Viscous diffusion terms and an explicit sub-grid-scale model are included. The working viscosity of the modified Spalart-Allmaras one equation model is transported by an algorithm based on the NFT MPDATA template. The scheme is semi-implicit which solves the linear equation system once per time step. The advantage of the scheme is efficiency and second-order accuracy. Furthermore, an edge-based data structure is adopted such that our scheme is suitable for both structured and unstructured meshes. The linear equation system is solved by an efficient algebraic multigrid (AMG) method. The algorithm is validated using test cases with Reynolds numbers 200 and 5000 over a range of Froude numbers. The flow patterns and dynamic drag coefficients are analysed and compared to numerical and experimental data in literature.

An Investigation of the Pentamaran Resistance Characteristic with Variance in Hull Combination and Configuration

Pentamaran model with Wigley-hull form have been investigated with four main configurations along with two variants of hull separation; 2 of the main configurations have dissimilar hull combination. The model was tested in calm water condition and constant Froude number ranging from 0.55 to 0.85 for configuration A and B, and from 0.4 to 0.6 for configuration C and D. Difference in hull combination indicates no similarity for Ct characteristic but close in magnitude. Hull separation indicates a slight noticeable change of Ct for the same configuration. The greater-Sa configurations (B and D) have negative magnitude of IF properties (minus) on the whole Froude number regime. The study expresses a specific approach of pentamaran resistance characteristic in limited Froude number range.

Direct measurement of bed shear stress using adjustable shear plate over a wide range of Froude numbers

The objective of this study is to extend reliability and applicability of the advanced measuring device for bottom shear stress introduced in the previous paper (Park et al., 2016) so that it could be deployed in the field. The high-speed open-channel flume used for the previous study has been renovated to accommodate even higher flow velocity (up to 6 m s−1). Then we adapted a non-intrusive velocity field measurement technique to such challenging flow conditions of interest. The specific experimental conditions required high degree of adaptation and subsequent development of analysis technique. The experimental results are used to reliably estimate bottom shear stress which is then compared to the measured value using the shear plate. It is shown that the shear plate can be applied to wide range of flow conditions by adjusting elastic shear modulus of the restoring mechanism.

Influence of interceptors, stern flaps, and their combinations on the hydrodynamic performance of a deep-vee ship

A study of the hydrodynamic performance of a deep-vee ship was performed to determine the influence of the use of stern flaps and interceptors on drag-resistance, trim, and sinkage properties of the said ship. Factors leading to changes in the resistance and attitude of the ship were analyzed in terms of the stern pressure distribution and transom flow fields. Analysis results demonstrate that both the stern flap and interceptor serve to reduce the amount of drag resistance, running trim, and sinkage of the ship, and that the drag reduction rate attained was of the order of 3–9% in the Froude number (Fr) range of 0.334–0.584. Further, resistance performance of the deep-vee ship equipped with stern flaps was observed to be better in the Fr range of 0.334–0.5; however, when Fr value exceeded 0.5, ship equipped with interceptors demonstrated an superior drag-reduction effect. The study focused on evaluation of the combined effect of the use of stern flaps and interceptors in an attempt to enhance the energy-saving capacity of ships. Results obtained via experimental and numerical analyses demonstrate that deployment of a reasonable combination of stern appendages causes significant improvement in the drag-reduction effect and trim optimization.

Experimental investigation of the dissipation rate in a chute aerator flow

Although chute aerator flows have been experimentally investigated in several studies, there is a paucity of information on the air–water flow properties such as bubble size distribution, dissipation rate, and bubble breakup frequency. Herein, experiments are conducted to investigate the aforementioned microcosmic characteristics for a wide range of Froude numbers (3.3 < F0 < 7.4) at relatively large Reynolds numbers (5 × 105 < R < 10.4 × 105). Observations indicate the development of bubble variation processes in terms of the range of probability for bubble chord lengths along the chute. The dissipation rate increases from the lower surface to the inner flow in the cavity zone and decreases from the bottom to the upper surface in the impact and equilibrium zones. The critical bubble diameter, dc = (σ/2ρ)3/5ε−2/5, exhibits good agreement with the observed change in power–law scaling of the bubble distribution and exceeds the corresponding mean bubble size. With respect to bubbles exceeding the critical bubble diameter that are subject to fragmentation, they exhibit –5/3 power–law scaling with respect to the diameter, and the breakup frequency increases and reaches a maximum when dab = 1.6dc. However, for bubbles with sizes exceeding 1.6dc, the frequency monotonically decreases relative to the bubble diameter.

The Effect of Infill Steel Plate Thickness on the Cycle Behavior of Steel Plate Shear Walls

The effect of changing in the bed slope of stilling basins produces changing in characteristics of the hydraulic jump such as sequent depth ratio, length of jump ratio, length of the roller and energy dissipation ratio, consequently the dimensions of stilling basin changed. In this study hydraulic jump investigated on smooth bed (without any appurtenances) for three adverse slopes (- 0.03, - 0.045, - 0.06) in addition to horizontal bed slope, the experiments were applied for the range of Froude number (Fr1) between 3.99 and 7.48. The results showed a reduction about10 % in sequent depth ratio, 22.1 % in length of jump ratio, 20.51 % in length of roller ratio and 13.87% in the energy dissipation ratio when the adverse slope (- 0.06) used instead of horizontal bed for the same Froude numbers. Empirical equations for the sequent depth ratio, length of roller ratio and the energy dissipation ratio were obtained from the experimental data

An investigation on HOBEM in evaluating ship wave of high speed displacement ship

A practical numerical tool is developed to evaluate ship waves of high speed displacement ships on the basis of potential flow theory, in which high order boundary element method (HOBEM) based on biquadratic shape functions is applied to solve the boundary value problem. Since the sinkage and trim of ship at high speeds are notable, influences of ship attitude on wave drag are investigated and three kinds of models are used to evaluate them. To make the numerical approach highly efficient, an incomplete LU factorization preconditioner is adopted and incorporated with the restarted generalized minimal residual method GMRES (m) to solve the boundary integral equation. A corresponding Fortran code is developed and applied to evaluate ship waves of the Wigley hull and 4a model, a transom stern ship. Computations are performed for both monohulls and catamarans over a wide range of Froude numbers (Fr = 0.10 - 1.00) . Numerical issues including mesh convergence and computational efficiency are investigated at first. Computed results of the wave drag, sinkage and trim show generally good agreement with experimental data. Reasonable wave patterns are obtained and physical phenomena that wake angle φmax, where the largest waves occur, would become narrow at high speeds is also captured by the present computations. Numerical results indicate the proposed method would be accurate and efficient to evaluate resistance for hull design of high speed displacement ship.

Analytical relations for filtering negligible short ship waves

The important basic practical problem of filtering inconsequential short waves that have no significant influence upon the wave drag, the sinkage and the trim experienced by a ship that travels at a constant speed in calm water of large depth is considered. This problem is an essential and nontrivial element of the prediction of ship waves via the use of a Green function that satisfies the linearized boundary condition at the free surface. Simple analytical relations that explicitly determine the wavenumber of insignificant short waves in terms of the Froude number and three main parameters that broadly characterize the ship hull shape are given for ships with bow, midship and stern regions and for ships with wide transoms. These relations are obtained via a parametric numerical analysis, based on the classical Hogner potential flow model, for a wide range of Froude numbers and a large number of hull forms associated with a broad range of hull-shape parameters. The relations provide an effective way of filtering negligible short waves that have no appreciable influence upon the wave drag, the sinkage and the trim of a ship.

Vertical drafts and mixing in stratified turbulence: Sharp transition with Froude number

We investigate the large-scale intermittency of vertical velocity and temperature, and the mixing properties of stably stratified turbulent flows using both Lagrangian and Eulerian fields from direct numerical simulations of the Boussinesq equations with periodic boundary conditions, in a parameter space relevant for the atmosphere and the oceans. Over a range of Froude numbers of geophysical interest we observe very large fluctuations of the vertical components of the velocity and the potential temperature, localized in space and time, with a sharp transition leading to non-Gaussian wings of the probability distribution functions. This behavior is captured by a simple model representing the competition between gravity waves on a fast time scale and nonlinear steepening on a slower time scale. The existence of a resonant regime characterized by enhanced large-scale intermittency, as understood within the framework of the proposed model, is then linked to the emergence of structures in the velocity and potential temperature fields, localized overturning and mixing. Finally, in the same regime we observe a linear scaling of the mixing efficiency with the Froude number and an increase of its value of roughly one order of magnitude.

Comparison of Microbubble and Air Layer Injection with Porous Media for Drag Reduction on a Self-propelled Barge Ship Model

Ship resistance issues are related to fuel economy, speed, and cost efficiency. Air lubrication is a promising technique for lowering hull frictional resistance as it is supposed to modify the energy in the turbulent boundary layer and thereby reduce hull friction. In this paper, the objective is to identify the optimum type of air lubrication using microbubble drag reduction (MBDR) and air layer drag reduction (ALDR) techniques to reduce the resistance of a 56-m Indonesian self-propelled barge (SPB). A model with the following dimensions was constructed: length L = 2000 mm, breadth B = 521.60 mm, and draft T = 52.50 mm. The ship model was towed using standard towing tank experimental parameters. The speed was varied over the Froude number range 0.11–0.31. The air layer flow rate was varied at 80, 85, and 90 standard liters per minute (SLPM) and the microbubble injection coefficient over the range 0.20–0.60. The results show that the ship model using the air layer had the highest drag reduction up to a maximum of 90%. Based on the characteristics of the SPB, which operates at low speed, the optimum air lubrication type to reduce resistance in this instance is ALDR.

Vortex Formation and Subsequent Air Entrainment inside a Liquid Pool

The origins of free surface vortex and gas entrainment are investigated within a liquid pool using a rotating cylindrical disc having longitudinal axis normal to the gas–liquid interface with varying submergence from 1.40 to 2.85 times the disc radius (20 mm). A generalized vortex profile is obtained by suitable scaling for a range of rotational Froude numbers (2.38–11.18). The transient evolution rate of the vortex tip followed logarithmic law and is correlated with experimental data of air and glycerin. The axial pull that holds the vortex against gravity is found to be linearly increasing with the rise of disc rotation. Asymmetric vortex profiles with increased extent of asymmetry are obtained upon increase of disc inclination (0–17.45°). Axial and radial circulations are revealed by following the trajectory of a solid particle in the flow field. Entrainment of discrete air volumes is observed from the vortex core at the corresponding Froude number and submergence ratio.

Evaluation and modeling scouring and sedimentation around downstream of large dams

Flip buckets are often used at the end of chute spillways to dissipate energy and direct flow to submergence plunge pool and especially in large dams. Flip buckets with central deviation also are a specific and new design of these buckets that have a transverse slope and are mixed in plan with a curvature. In this paper, the experimental and numerical simulation study of sediment scouring in such flip bucket has been targeted. Extensive experimental data are obtained from physical model studies conducted at Water Research Institute, Iran. The flow field with various flood discharges in a range of Froude numbers (Fr = $$V/\sqrt {gh}$$ : 3.5–7.5) in Flow3D model was compared to experimental results obtained from a similar model. Analyzing the simulated models in the Flow3D model and comparing the results with the experimental model, the hydraulic parameters of the pressure, velocity and depth of flow are determined. Considering the accuracy of the numerical model in simulating bed scouring, this model can be used for similar cases in large dams. The results of the simulation model compare well with the experimental results in parameters of the maximum scour depth, profile scouring and the ridge height which accumulates around downstream of the scour hole. This investigation improves the understanding of bed topography effects of downstream dams in high-velocity jet impact based on experimental observations and simulation analysis.

The role of periodically varying discharge on river plume structure and transport

We present results from laboratory experiments that simulate the effects of periodically varying discharge on buoyant coastal plumes. Freshwater is discharged into a two meter diameter tank filled with saltwater on a rotating table. The mean inflow rate, tank rotation period and density of the ambient salt water are varied to simulate a range of inflow Froude and Rossby numbers. The amplitude and the period of the inflow modulation are varied across a range that simulates variability due to tides and storms. Using the optical thickness method, we measure the width and depth of the plume, plume volume and freshwater retention rate in the plume. With constant discharge, freshwater is retained in a growing anticyclonic bulge circulation near the river mouth, as observed in previous studies. When the discharge is varied, the bulge geometry oscillates between a circular plume structure that extends mainly in the offshore direction, and a compressed plume structure that extends mainly in the alongshore direction. The oscillations result in periodic variations in the width and depth of the bulge and the incidence angle formed where the bulge flow re-attaches with the coastal wall. The oscillations are more pronounced for longer modulation periods, but are relatively insensitive to the modulation amplitude. A phase difference between the time varying transport within the bulge and bulge geometry determines the fraction of the bulge flow discharged into the coastal current. As a result, the modulation period determines the variations in amount of freshwater that returns to the bulge. Freshwater retention in the bulge is increased in longer modulation periods and more pronounced for larger modulation amplitudes.

Stochastic bedload transport in mountain streams

Describing bedload transport as a stochastic process is an idea that emerged in the 1930s with the pioneering work of Einstein. For a long time, the stochastic approach attracted marginal attention, but the situation has radically changed over the last decade with the recent advances in the theory of bedload transport. In parallel, the implementation of bedload monitoring techniques at high temporal resolution has produced a wealth of interesting results showing, among other things, that classic empirical bedload transport equations do not capture neither the mean behavior of sediment transport rates qs nor its order of magnitude, especially at low sediment transport rates (a case that is most frequent in mountain streams). We have developed a stochastic model, which takes inspiration from population dynamics and provides a stochastic partial differential equation for the number of moving particles. Taking the ensemble average leads to a fairly simple advection diffusion equation for particle activity (i.e., the number of moving particles per unit streambed area). The model has a number of unique features. For instance, it yields the probability distribution of the bedload transport rate and predicts bedform formation for a wide range of Froude numbers.

Experimental investigation of ventilated supercavitation with gas jet cavitator

We conduct an experimental study of the ventilated supercavitation generated from gas jet cavitator [gas jet ventilated supercavitation (GJVS)] over a broad range of ventilation and flow conditions for two gas jet nozzle sizes. The experiments show that supercavity evolves across different cavity regimes with distinct patterns, i.e., bubbly flow, Stable Cavity (SC), Unstable Cavity (UC), and Jet Cavity (JC) with increasing ventilation rate. The supercavity transition is shown to be a result of the stagnation location of gas jet shifting from the potential core zone to the established turbulent flow zone of the jet as ventilation increases. The variation of supercavity regimes under a broad range of Froude numbers is compiled, and the map of supercavity regime transition shows similar trends for different Froude numbers and nozzle sizes. Compared to a disc cavitator, in the SC regime, the GJVS exhibits similar ventilation hysteresis with a significantly higher ventilation demand for the formation of a supercavity. The transitions from SC to UC and UC to JC are examined using the ratio of gas jet length to potential core length, which shows a variation across different Froude numbers and nozzle sizes. Moreover, the change of supercavity dimension upon increasing ventilation is examined for SC and JC regimes. In the SC regime, the maximum diameter of the supercavity and the corresponding cavitation number remain constant with increasing ventilation, similar to the case of a disc cavitator. In contrast, the maximum diameter and the cavitation number grow linearly upon an increase of ventilation in the JC regime.

Effect of baffle block configurations on characteristics of hydraulic jump in adverse stilling basins

The construction of stilling basin with adverse slope change the characteristics of hydraulic jump such as sequent depth ratio, length of jump ratio, length of roller and energy dissipation ratio, consequently the dimensions of stilling basin are changed, also using baffle blocks with different configurations develop these characteristics. In this study different shapes of baffle block (models (A), (B), (C) and (D)) installed in the stilling basins at adverse slopes (- 0.03, - 0.045, - 0.06) in addition to horizontal bed, all these models are tested in the stilling basin to show their effects on the characteristics of hydraulic jump, the experiments applied for the range of Froude number (Fr1) between 3.99 and 7.48. The baffle block model (D) showed good results when compared with models (B) and (C), therefore it used with arrangement of (single and double row) and compared with baffle block model (A) at slopes (0, - 0.03, - 0.045, - 0.06) to study the effects of baffle blocks on hydraulic jump when bed slopes are changed. In general using baffle block caused a reduction in sequent depth ratio, length of jump ratio and the length of the roller, but the energy dissipation ratio increased.

An investigation on the outer bank cell of secondary flow in channel bends

Beside the curvature-induced secondary flow in curved channels, often a counter-rotation secondary flow cell is observed near the outer bank, called outer-bank cell. In the current study, experiments were conducted for three low subcritical Froude numbers typical for natural streams that complement the Froude number range investigated in previous studies. It was found that for increasing Froude numbers, the main cell of secondary flow expanded and strengthened. Simultaneously, the outer-bank cell reduced in size and retreated towards the boundary. A term-by-term analysis of the energy production and the vorticity equations was performed to substantiate this observation. In the outer-bank zone, for increasing Froude numbers, a reduction of the energy flux from turbulence to the mean flow was discernible; which confirms that the turbulence-induced processes affect the outer-bank cell. The analysis of the vorticity equation showed the balance between generative and degenerative terms in the streamwise vorticity equation.

Computational Fluid Dynamics Study of the Dead Water Problem

The dead water problem, in which under certain conditions a vessel advancing in a stratified fluid experiences a considerable increase in resistance respect to the equivalent case without stratification, was studied using computational fluid dynamics (CFD). The advance of a vessel in presence of a density interface (pycnocline) results in the generation of an internal wave that in the most adverse conditions can increase the total resistance coefficient by almost an order of magnitude. This paper analyses the effects of stratification on total and friction resistance, the near field wake, internal and free surface waves, and resistance dynamics. Some of these effects are reported for the first time, as limitations of previous efforts using potential flow are overcome by the use of a viscous, free surface CFD solver. A range of densimetric Froude numbers from subcritical to supercritical are evaluated changing both the ship speed and pycnocline depth, using as platform the research vessel athena. It was found that the presence of the internal wave causes a favorable pressure gradient, acceleration of the flow in the downstream of the hull, resulting in thinning of the boundary layer and increases of the friction resistance coefficient of up to 30%. The total resistance presents an unstable region that results in a hysteretic behavior, though the characteristic time to establish the speed–resistance curve, dominated by the formation of the internal waves, is very long and unlikely to cause problems in modern ship speed controllers.

Two-phase discharge from a stratified region through two horizontal branches with centerlines falling on an inclined plane

The main objective of this study was to obtain new experimental data for conditions not previously tested for discharging two-phase flow through two 6.35 mm diameter branches with centerlines falling in an inclined plane. The present results are relevant to many industrial applications including headers and manifolds, multichannel heat exchangers and small breaks in horizontal pipes. In the experimental investigation, the critical heights for the onsets of liquid and gas entrainment (OLE and OGE, respectively) were obtained, analyzed and correlated for two different branch spacings and two different angles between the branches. For each combination of branch spacing and angle between the branches, a wide range of Froude numbers was used. Two-phase mass flow rate and quality results were also obtained and analyzed for a range of interface heights for 16 different combinations of branch spacing, inclination angle, test section pressure and pressure drop across each branch. New empirical correlations were developed to predict the dimensionless mass flow rate and quality. The new correlations show good agreement with the present data and with previous correlations.

A comparative study of natural and ventilated supercavitation across two closed-wall water tunnel facilities

Despite half a century of experimental investigation into both natural and ventilated supercavitation, there are still significant discrepancies among the results, in terms of supercavity geometry and ventilation demand, etc., under approximately similar conditions from different water tunnel facilities. To understand the influences of the flow facilities on the supercavitation experiments, a systematic comparison is conducted using the results from two closed-wall water tunnels, i.e. the Saint Anthony Falls high-speed water tunnel and the Chuangnam National University Closed Tunnel. For both ventilated and natural supercavitation, the experimental conditions from the two facilities are designed to match over a wide range of Froude number and blockage ratio, etc. For the ventilated supercavitation, the cavitation number for generating a ventilated supercavity and the hysteresis process for sustaining a supercavity show a proper match across the two facilities while holding the Froude number and blockage ratio constant. However, the ventilation demand to form a supercavity shows a noteworthy difference across the facilities even under the same Froude number and blockage ratio. Such a difference in the ventilation requirement is attributed to the mismatch of Reynolds number, the detailed geometry of the cavitator models as well as the test section which influences the pressure distribution along the span of the supercavity. Similarly, for natural supercavitation, both facilities yield a similar vaporous cavitation number for the supercavity formation under the same Froude number and blockage ratio, as well as similar choking behavior, i.e. cavitation number stays constant despite the decrease of test section pressure once a natural supercavity forms. The theoretical analysis of the choking phenomenon explains the trend of cavitation number under choking and its dependence on cavitator geometry, Froude number as well as the pressure loss in the water tunnel. A geometry comparison is conducted for both natural and ventilated supercavities in the two facilities under the same Froude number, blockage ratio and cavitation number. The comparison results show differences in the normalized cavity total length across different facilities as well as supercavity types despite the similarities in the supercavity maximum diameter and half-length. These differences were attributed to the variance in the pressure and flow distributions from the different facilities and across ventilated and natural supercavitation. The natural supercavities from the two facilities are further compared with the estimated natural supercavitation in unbounded flow under the same cavitation conditions. The comparison result highlights the limitation of the conventional theory in capturing the cavity geometries in actual experiments.