Froude Similarity Research Articles

Evaluation of scale effects in physical modeling of combined ogee and sharp-crested weir flow using a 3D CFD model

Research on scale effects on flows over weirs has been conducted on a limited basis, primarily focusing on flows upstream of a single-type weir, such as ogee, broad-crested, and sharp-crested (linear and non-linear) weirs. However, the scale effects downstream of these single-type weirs have not been thoroughly investigated. This study examined the scale effects on flows over a combined weir system consisting of an ogee weir and a sharp-crested weir, both upstream and downstream, utilizing physical modeling at a 1:33.33 scale based on Froude similarity and three-dimensional (3D) computational fluid dynamics (CFD) modeling. The sharp-crested weir in this study was represented by two sluice gates that remain closed and submerged during flood events. The experimental data confirmed that the equivalent discharge coefficients of the combined weir system behaved similarly to those of a sharp-crested weir across various H/P (where H is the total head, and P is the weir height) values. However, scale effects on the discharge rating curve due to surface tension and viscosity could only be minimized when H/P > 0.4, Re > 26 959, and We > 240 (where Re and We are the Reynolds and Weber numbers, respectively), provided that the water depth exceeded 0.042 m above the crest. Additionally, Re greater than 4 × 104 was necessary to minimize scale effects caused by viscosity in flows in the spillway channel and stilling basin (with baffle blocks). The limiting criteria aligned closely with existing literature. This study offers valuable insights for practical applications in hydraulic engineering in the future.

Prediction of impulse waves generated by the potential failure of large deposits in the Rumei Reservoir, Lancang River, China

The impulse wave generated by the reservoir landslide seriously endangers the surrounding safety. In this paper, the failure mode of a large deposit in Rumei Reservoir, China was first explored by centrifuge test. Thereafter, a physical model based on Froude similarity (scale 1:200) and a numerical model based on fluid‒solid coupling were constructed. The failure motion process and the generated impulse waves of the deposits at high (2895 m) and low (2750 m) water levels are studied in detail. The results of the two models are similar. The velocity and wave height of the deposits at the 2750 m water level are greater than those at the 2895 m water level. The maximum wave heights generated in the river under both conditions exceed 46 m and 22 m, respectively, and the maximum run-ups formed on the opposite bank are 71 m and 30 m, respectively. This also suggests that landslides in the near field area are dangerous. Waves at both water levels will not overtop the dam, but attention should be given to the effect of the first wave at the 2895 m water level on the dynamic water pressure in the key area of the dam.

SPH study of scale effects of perforated caissons

The hydrodynamic characteristics of perforated caissons are significantly influenced by the viscous fluid motion near the perforations on the front wall. Consequently, models designed in accordance with the Froude similarity suffer from the scale effects. To investigate the scale effects, a Smoothed Particle Hydrodynamics (SPH) model is established, in which fluid motion is governed by the continuity and Navier-Stokes equations, and the solid boundaries are represented by the dynamic boundary particles. The convergence and reliability of the SPH model are examined by employing it to replicate two laboratory experiments. Subsequently, the SPH model is applied to the study of interactions between regular waves and perforated caissons with different length scales, porosities, and chamber length to wavelength ratios. This enables an analysis of the scale effects on the vorticity and velocity fields, wave reflection, and wave force. The findings indicate that a scaled-down model tends to underestimate flow field intensity and wave force amplitude, while overestimate the wave reflection coefficient.

Experimental Validation of Power Output and Efficiency for an Oscillating Water Column (OWC)

With the global energy demand escalating and concerns over the environmental impact of fossil fuels, there's a pressing need for cleaner, sustainable alternatives. This study highlights the potential contribution of wave energy to the power needs of coastal structures in the context of renewable energy. The research evaluates the power output and efficiency for an Oscillating Water Column (OWC) system that can be integrated into coastal structures to meet part of their power needs. Findings from both theoretical calculations and a 1:10 scale model experiment are presented. The mechanical power output and efficiency of the system for a full-scale prototype were calculated for deep water conditions with a wave height of 3m. The water surface oscillation inside the chamber is assumed to reflect the oscillation occurring outside the chamber. The maximum average mechanical power output for the full-scale prototype, corresponding to a wavelength of 22.5 m, was determined to be 64.8 kW, achieving a mechanical efficiency of 64.4%. The overall efficiency of the system is calculated as 55% by assuming the generator efficiency to be 85%, resulting in an average power output of approximately 55 kW. A 1:10 scale model of the OWC system with a Wells turbine was constructed and tested in a tank for deep water conditions. Froude similarity and Keulegan-Carpenter similarity were used, ensuring a seamless transition from the model to the prototype. The OWC model was subjected to controlled heaving motion with a period of T=1.2 s. The power generated by the OWC model illuminated four integrated 3.4V LEDs on the Wells turbine, which were used to measure the power output produced. The power output of the model was measured to be a minimum of 0.12 W for a rotational speed of 107 rpm, which corresponds to a power output of 12 kW for the scaled-up prototype. This system has the potential for further enhancement by incorporating multiple OWCs into coastal structures exposed to wave action. Such development could facilitate meeting the power requirements of coastal structures, thereby contributing to the promotion of both renewable energy generation and a sustainable environment. Future research will focus on optimizing OWC chamber sizes for specific sites and refining the model to better capture water surface oscillation dynamics. l

МОДЕЛИРОВАНИЕ И РАСЧЕТ КОНСТРУКТИВНЫХ И РЕЖИМНЫХ ПАРАМЕТРОВ ТУРБИННОЙ МЕШАЛКИ ДЛЯ ДИСПЕРГИРОВАНИЯ РАСТВОРОВ ПОЛИМЕРНЫХ КОМПОЗИТОВ

Mixers with technical characteristics established by GOST 20680-2002 are not suitable for mixing solutions of polymer nanocomposites when restoring bearing fits. The optimal design parameters of a multi-bladed turbine mixer with full-length inclined blades for mixing solutions of polymer nanocomposites were determined at the Lipetsk State Technical University. Formulas for calculating the pumping effect and power when designing multi-blade turbine mixers of various sizes are obtained using these parameters. The average value of the peripheral speed coefficient, which is k≈0.92, was determined experimentally. A formula for calculating power when designing multi-blade turbine mixers of various standard sizes with full-length inclined blades is proposed. The experiment showed a high convergence of calculated and actual values of power consumed by a turbine mixer when mixing nanocomposite solutions. An experiment was carried out to evaluate and select a similarity criterion for the design of multi-bladed turbine mixers of various standard sizes. Reynolds and Froude similarity criteria were studied. The light transmission coefficient of the solution after stirring at a rotation frequency determined by the Reynolds criterion is Kc=57%. A similar parameter of the solution after treatment in the mode determined by the Froude criterion is 2.2 times lower and amounts to Kc = 26%. A higher quality index according to the Froude criterion is confirmed by the fact that the strength of the samples is σ = 27.308 MPa, which is 1.24 times greater than the strength of samples obtained from nanocomposite solutions processed in the mode determined by the Reynolds criterion. A formula for calculating the power of multi-bladed turbine mixers with inclined blades was proposed as a result of the research. Modeling of the design and operating parameters of multi-blade turbine mixers of various standard sizes should be carried out according to the Froude criterion.

Physical Modelling Of A Caisson Breakwater Under Impulsive Cyclonic Waves : Case Of Port East (Reunion Island)

The GPMDLR (Port Authority of La Réunion Island, France) has requested ARTELIA to carry out the preliminary studies for the enlargement of the containers terminal in Port East. In this context, the laboratory of ARTELIA has performed 2D physical model testing to evaluate the behavior of caissons exposed to cyclonic conditions. The solution based on a vertical breakwater has been proposed as an alternative to a rubble mound breakwater given the lack of quarries suitable to provide big quantities of large rocks. Main objectives of the study were: the evaluation of overtopping rates (mean and max), the verification of the stability of foot protection blocks and stones, and the recording of wave pressures (gauges) and loads (scale) on the caissons. Given the fact that most of the waves broke violently upon the caisson, the nature of efforts was impulsive and the scaling to prototype by classical Froude similarity principles was not appropriate. Results were therefore amended following Cuomo’s correction factors for the Froude scaling law (Cuomo et al. 2010). Times series of efforts (forces and pressures) were used to feed numerical models (static and dynamic) allowing for the verification of caissons’ geotechnical stability and the design of concrete parts. This article collects the concerns, feedback and further questioning related to the conducted experiment.

Scale Effects Investigation in Physical Modeling of Recirculating Shallow Flow Using Large Eddy Simulation Technique

In this study, the Large Eddy Simulation (LES) model in OpenFOAM was used to investigate the scale effects in the physical modeling of recirculating shallow flow at low Froude numbers. A laboratory test of turbulent flow through a submerged conical island with a Reynolds number of 6,210 was selected. The lab prototype was scaled with factors of 3 and 10 for both undistorted and distorted models. Our study employed the Froude similarity as the gravitational force is more dominant than the others (viscous, drag, and cohesion forces). Because the fluid (water) used for the prototype and model is the same, it is impossible to match the Reynolds, Weber, and Froude numbers simultaneously, resulting in the scale effects. For a scale of 1:1, the LES model could simulate the experimental data by appropriately capturing the vortices behind the conical island. For the undistorted models with scales of 3 and 10, the numerical model captured weaker magnitudes of vortices than the 1:1 scale, indicated by the discrepancies in velocity. In fact, the magnitudes of vortices became weaker with the distorted models. We also observed a significant increment in energy loss behind the conical island (where recirculating flows exist) as the scale increased. However, no significant discrepancies in velocity were observed between the results of the 1:1 scale and the scaled models in front of the conical island, where vortices were absent. These results indicate that the scale effects due to the Froude similarity are quite significant provided that recirculating turbulent flow occurs.

On the Issue of Generation of Hydrodynamic Waves in the Shovi Gorge (Georgia) due to a Collapse on Glacier Tbilisa

The occurrence of a glacial mudflow in the Shovi gorge on August 3, 2023 was caused by a destructive process on the Tbilisa glacier. Based on the existing picture of the spread of the mudflow, it is possible to carry out an analysis regarding the rheological qualities of the water-saturated soil mass that forms its basis. It is also possible to approximately estimate the parameters of various types of hydrodynamic waves, the generation of which was probably possible during the propagation of the debris flow. It seems that such a problem can be satisfactorily solved only in the case of a correct assessment of the values of dimensionless criteria for the flow of debris flow, which are convenient quantitative characteristics that simplify the analysis of the qualitative consequences of applying the principle of hydrodynamic similarity. For example, in the case of approximating the bed of a debris flow with a rectangular channel, you can use the results of well-known analytical solutions obtained under simplifying assumptions that are valid for certain intervals of variation in the Reynolds and Froude similarity numbers. In particular, in the shallow water approximation, in the case of sufficiently large Reynolds numbers, when the fluid flow is highly turbulent, the Froude parameter allows one to fairly correctly simulate changes in the flow regime that occur as a result of the generation of hydrodynamic waves. The negative effects that often accompany the process of propagation of wave disturbances largely depend on the type of these waves. Therefore, in the case of a mudflow in the Shovi gorge, it seems quite realistic, for example, the generation of the so-called rolling hydrodynamic waves, which could well have been among the probable causes that determined the catastrophic scale of the tragic event.

A numerical study on the feasibility of predicting the resistance of a full-scale ship using a virtual fluid

In general, the resistance of a real ship is estimated using an extrapolation method after doing experimental tests or numerical simulations with a model scale ship. Since the only Froude similarity is applied in the model test and simulation, the flow characteristics between the model and real ships could be different due to the inconsistency of Reynolds number. However, in the Computational Fluid Dynamics (CFD), the Froude and Reynolds numbers can be satisfied simultaneously because a fluid with virtual properties can be applied. This study investigated the effect of turbulence models and scales for a flat plate. And then the hydrodynamic feasibility of using a virtual fluid was investigated through numerical analysis. The resistance performance and flow structure of the ship were analysed by applying the virtual fluid, and they were confirmed how well these values and flow characteristics simulate the full-scale with a real fluid. This study shows that the results of a full-scale can be obtained at model scale by applying a virtual fluid instead of full-scale numerical simulations that require more computational resources.

Classification and description of the drainage state of manholes in urban drainage systems.

Manholes are important structures in urban storm drainage systems connecting roads and underground drainage networks, and they are also an important part of the research on improving urban resistance to storm flooding. Due to cost and space constraints, most of the existing experimental data on manholes come from scale model experiments obtained by scaling according to Froude's similarity criterion, and there is a lack of validation based on full-size experimental data. This also leads to inconsistencies in the form and parameter values of the manhole flow exchange equations derived from different experiments. To remedy this deficiency, a full-scale urban drainage engineering physics model was developed in this study with the aim of investigating the flow exchange of surface water as it flows through manholes into the sewer system. Experiments were conducted under steady flow conditions and compared with predictions from the existing models. The results show that the predictions of the existing model deviate significantly from the measured values when the flow is between free weir flow and submerged orifice flow. Therefore, we constructed a weighting equation based on weir and orifice flows and found that the weighting coefficients decayed exponentially during the transition from weir to orifice flow.

Froude Similarity and Flying Qualities Assessment in the Design of a Low-Speed BWB UAV

Froude Similarity and Flying Qualities Assessment in the Design of a Low-Speed BWB UAV

Design approach of thrust-matched rotor for basin model tests of floating straight-bladed vertical axis wind turbines

Rotor redesign approaches have been widely proposed to solve the thrust mismatch issue caused by scaling effects for basin model tests of horizontal axis floating wind turbines (FWTs). However, limited basin model tests utilized the thrust-matched rotor (TMR) to accurately evaluate the aerodynamic loads applying to the vertical axis FWTs. This paper described the detailed design approach of the TMR of floating straight-bladed vertical axis wind turbines (VAWTs) with a rated power of 5.3 MW. First, the AG455 airfoil was selected to replace the NACA0018 airfoil. AG455 airfoil can show a larger lift coefficient and a smaller drag coefficient at low Reynolds number. On this basis, the load distribution match algorithm was used to assign the blade pitch angle and chord length at each section of the blade. This method takes the spanwise load and load change rate of model-scaled blade and full-scaled blade as the constraint conditions. By adopting this method, the rotor thrust can be tailored to match the prototype values across a wide range of tip speed ratios. This design approach proves advantageous in assessing the aerodynamic performance of VAWTs under varying inflow wind speeds and unsteady wind conditions. The redesigned TMR model under low Reynolds number can meet Froude similarity criterion, which is helpful to improve the accuracy of vertical axis FWT model tests in the wave basin.

The impact of yaw motion on the wake interaction of adjacent floating tidal stream turbines under free surface condition

Several works put emphasis on the maturation of floating tidal stream turbine systems, deemed viable for sites at deep water depths. The objective of this research is to determine, through a CFD model, the yaw effect on the wake and functioning of a floating twin-turbine system under wave-induced motion. The simulation certainty is corroborated against experiments on a 1:7 piled twin-turbine system (Froude similarity). Collectively, the variation and deficiency of the power and thrust coefficients are amplified with the yaw frequency and amplitude. Whereas the individual wakes collide, depending on the yaw feature and turbine cross-current spacing, resembling a smoke-plume-type pattern. The larger cross-current spacing shortens the wakes and reduces near-wake deficit at mid-row due to the greater energy exchange from the ambient flow. Regardless of the yaw feature, the transversal wake deficits turn from double (majority symmetrical) at near wake into triple distributions thenceforth, before flattening at far wake. Importantly, the wake unsteadiness and recovery rate are more obvious with period, as opposed to amplitude effect. As yaw operation is imminent, contributed by flow skewness and platform yaw motion, it will be constructive to implement natural frequency analysis to prevent vortex-induced vibrations and mechanical weariness in the floating system.

EXPERIMENTAL EVALUATION OF THE PERFORMANCE OF A HYBRID ARTIFICIAL CORAL REEF WITH BRAIN AND STAGHORN CORALS

Considering that more than 40 percent of the world's population resides within 100 km of coastal areas [WRI, 2007], the protection of coastal communities is critical. Coral reefs provide a large variety of ecosystem services from fishing, recreation and tourism to coastal flood risk reduction to nearby populations. They act as a green, self-building and self-repairing breakwaters dissipating wave energy through wave breaking and bed friction [Beck, 2018]. However, coral reefs are not typically accounted for as a coastal infrastructure as their effects are not easy to quantify [Ferrario, 2014] as their interaction with waves depends on multiple parameters including the variable morphologies of the organisms that form the reef. In this study, the wave energy dissipation of a scaled reef model with two coral species (staghorn and brain corals) of variable cover was evaluated through a series of laboratory experiments at the University of Miami SUrge STructure Atmosphere INteraction (SUSTAIN) Facility, a wind/wave tank with hurricane capabilities. A scaled coral reef model was tested under the direct impact of swell and hurricane generated waves considering Froude similarity with a prototype reef in South Florida.

An Adaptive Barrier-Mooring System for Coastal Floating Solar Farms

Floating solar farms in the coastal areas are subjected to more complex environmental loads of tides and waves than lakes or reservoirs with greater challenges to their mooring. At present, mooring systems based on elastic cables are prevalent for coastal floating solar farms, but these cables tend to be expensive and require periodic retuning with higher maintenance costs. In this study, we propose a new alternative of an adaptive barrier-mooring system which is consisted of perimeter pontoons, barriers, clump weights, mooring lines and anchors as a new alternative. The performance of the adaptive barrier-mooring system installed on the leading edge of a coastal floating solar farm is first examined through static analysis. The results showed that the new mooring system enables the floating solar farm to adapt up to 36% of water depth without introducing slack in the mooring cables. In addition, the resulting nonlinear mooring stiffness and lower pulling-out forces on the anchors are also both beneficial to the system design. Subsequently, a floating solar farm model with four different mooring systems, including adaptive barrier-mooring systems as well as elastic mooring cables, were tested for dynamic performance in a wave flume in the laboratory with Froude similarity under both incident waves as well as water level changes. The experimental results demonstrated the good performance of the adaptive barrier-mooring system in terms of higher platform stability over a large tidal range. Finally, the construction and maintenance costs of the adaptive barrier-mooring system should be lower compared to elastic mooring systems due to the use of common materials without the need for periodic tightening. We hope that the adaptive barrier-mooring system can further aid the development of coastal floating solar farms in the future.

Flame distortion and backwards heating behaviors of moving fires: A comparative study

Moving fires have been paid great attention by researchers in recent years, while the behavior of this special combustion phenomenon has not been fully investigated. In this paper, a 1:10 scale burning car was innovatively designed based on Froude similarity criterion, and a series of moving model experiments were conducted. The flame morphological characteristics and heating behaviors between the stationary and moving fires were thoroughly compared. The results manifest that the distorted flame of moving fires is 15.2%-45.7% more than that of stationary fires, while this behavior is not accurately predicted by current models for wind-blown and wall-attached flames, which suggests that the wind tunnel test has limitations in studying moving fires. Besides, compared with stationary fires, the temperature upstream of the fire source is considerably elevated, and the heat transfer from the flame to the top surface of the burning car is dramatically enhanced. A physical model is proposed to describe the flame distortion and backwards heating behaviors in moving fires, which reflects the important role of the air entrainment and the cool fuel-rich cone in the combustion process. This paper represents a first step toward understanding the behavior of moving fires, which can provide a framework to deeply investigate the combustion mechanism of moving fires in the future.

Experimental testing to determine stability thresholds for partially submerged vehicles at different flow orientations

Vehicles exposed to flooding and losing stability may be washed away, causing potential injuries and fatalities. Such vehicles cause additional disruption to traffic already affected by flooding, which may lead to significant indirect economic impacts, especially in urban areas. Therefore, it is important to analyze the stability of vehicles exposed to flooding to make decisions for reducing damage and hazards. In this study a series of experiments were conducted with a small passenger vehicle, Polo GTI, a large passenger vehicle, Audi A6L, and a large four-wheel drive (4WD) vehicle, Range Rover models with a scale of 1:18. The buoyancy forces of the model-scale vehicles were measured by buoyancy experiments, which allowed for the calculation of the buoyancy force as a function of the flow depth. The drag forces and transverse forces at different flow orientations were determined experimentally using a hydraulic flume, and the drag coefficients (1.22 ≤ CD ≤ 6.82) and transverse force coefficients (0 ≤ CT ≤ 2.40) of the three vehicles were determined by fitting data from all experiments at the same flow direction (from 0° to 180°). Corresponding forces on the full-scale (prototype) vehicles were computed based on the Froude similarity laws. Then stability thresholds and stability curved surfaces for prototype vehicles exposed to flooding were derived based on the experimental results and force analysis of vehicles exposed to flooding. The study results provide valuable information for decision-makers in the field of urban flood risk management to consider the impact of urban road runoff on vehicle stability thresholds.

Study on simulation of real‐time hybrid model test for offshore wind turbines

AbstractAs an emerging energy source with great potential, offshore wind power is supported by development policies in an increasing number of countries. However, the performance evaluation of floating offshore wind turbine (FOWT) structures is challenging due to the complexity of wind and wave loads and the difficulty in reproducing such loading conditions for downscaled FOWTs in laboratories. In physical model tests of FOWTs, the Froude's similarity law is adopted for the foundation, while the Reynolds similarity law is adopted for the blades, thus there is an issue with uncoordinated scaling laws. The FOWTs real‐time hybrid test uses loading device to simulate air loads, offering a new way to avoid scaling issues and reduce cost barriers. In this study, taking the 5 MW Braceless FOWT as the research object, a conceptual design of a real‐time hybrid model test system for Braceless offshore wind turbines is proposed. Six sets of working conditions are set for simulation to study the motion and force performances of the hybrid system. The performance requirements of the Braceless structure for the loading device in the real‐time hybrid test are quantified. Simulate different errors in the test to analyse the sensitivity of the response of the Braceless offshore wind turbine to various errors. The results show that the Braceless FOWT is relatively sensitive to motion and force errors. Due to the low‐frequency characteristics of offshore wind turbines and external load, the delay error has relatively little effect. The method results in this paper can provide theoretical support and design information support for the implementation of real‐time hybrid model tests in the future.

Development of a Three-Dimensional CFD Model and OpenCV Code by Comparing with Experimental Data for Spillway Model Studies

This article presents a three-dimensional CFD model and OpenCV code by comparing the flow over the spillway with the experimental data for use in spillway studies. A 1/200-scale experimental model of a real dam spillway was created according to Froude similarity. In the experimental studies, velocity and water depth were measured in four different sections determined in the spillway model. A three-dimensional ANSYS Fluent model of the spillway was created and the simulations of the flows occurring during the flood were obtained. In the numerical model, the two-phase VOF model and k-epsilon turbulence model are used. As a result of the numerical analysis, velocity, depth, pressure, and cavitation index values were examined. The velocity and depth values obtained with models were compared and a good agreement was found between the results. In addition, in this study, a different technique based on image processing is developed to calculate water velocity and depth. A floating object was placed in the spillway channel during the experiment and the movement of the object on the water was recorded with cameras placed at different angles. By using the object tracking method, which is an image processing technique, the position of the floating object was determined in each video frame in the video recordings. Based on this position, the velocity of the floating object and its perpendicular distance to the bottom of the channel was determined. Thus, an OpenCV-Python code has been developed that determines the velocity and water depth of the floating object depending on its position. The floating object velocity values obtained by the algorithm were compared with the velocity values measured during the experimental model, and new velocity correction coefficients were obtained for the chute spillways.

Power fluctuation and wake characteristics of tidal stream turbine subjected to wave and current interaction

Turbulence and waves interactions are present in tidal streams ensuing the poorly comprehended unsteady state. To clarify several aspects of the wave influence on the flow and turbine power output, the 1:60 scale rotor experiments (Froude similarity) are carried out: current only and with parallel waves. Compared to steady predictions, the mean power in current and with waves against a range of rotor speeds are analogous. The power spectrum under wave conditions is almost a superposition of current and additional components, including wave frequency, rotation frequency, and their mixing frequency. The waves distort significantly the operating flow, by augmenting the turbulent intensity, wake rotation, anisotropy, and Reynold stresses, both in large proportion with the wave energy flux. The mean wake recovery was analogous, with deficits following symmetrical distributions of diminishing height longitudinally. Strikingly, the turbulence in the undisturbed flow resembles mostly near the pancake shape. This transitions towards the cigar-shaped in both most of the stream tube due to the turbine obstruction, and of the channel with the wave introduction. Further studies are required to validate these findings on non-isotropy and non-homogeneous effects in other wave conditions, such as a range of frequencies, heights and incident directions.