Dynamic Similitude Research Articles

Shake table model testing and its application

AbstractThis paper presents a study of shake table testing for aseismic design of structure systems. Two reinforced concrete structure models of different scales were used first to implement and demonstrate the similitude concept using available testing equipment. This concept was then applied to a 33‐story reinforced concrete building's scaled model, using multidirectional simulated seismic excitations. The test results were used to evaluate and modify the original design. Some of these results were also verified using field testing after the building's construction was completed. Comparison of the results between the model test and the full‐scale test shows that testing based on dynamic similitude using shake table are useful although not perfect and can provide supplementary data for decision making in engineering design. Copyright © 2007 John Wiley & Sons, Ltd.

Dunes, turbulent eddies, and interfacial exchange with permeable sediments

Interfaces between a water column and underlying porous media are ubiquitous in nature. Turbulent flow over an irregular interface separating a water column and underlying porous media drives advective‐fluid exchange between the two domains. We investigate the dynamics of this coupled system for unidirectional flow in the water column and a triangular interface modeled on dunes. Numerical simulations solve the Reynolds‐averaged Navier‐Stokes equations for the water column and then Darcy's Law and the continuity equation for the porous media. The two sets of equations are coupled via the pressure distribution along the interface. The pressure maximum and minimum along the interface, which are tied to the presence of an eddy, dominantly control the configuration of and flux through the interfacial exchange zone (IEZ) in the porous media. Since the length of eddies for fully developed turbulent flow is insensitive to the Reynolds numbers (Re), the configuration of the IEZ remains stable across a range ofRe, although flux through the IEZ is strongly dependent on theRe. The flux is a power function ofReand a linear function of the current‐topography induced pressure gradient along the interface. Mean residence times for fluids in the IEZ follow an inverse‐power relationship withResince the volume of the IEZ is insensitive toRe. The IEZ depths and fluxes can be predicted via equations fitted to the simulated IEZ depths and fluxes, scaled by the dune steepness, for differentRe, granted that other systems maintain close dynamic similitude with those studied here.

CANDU-6 원자로 감속재 열수력 개별영향실험을 위한 축소화 기법에 따른 1/8 축소형 HU-KINS 설계

To investigate the moderator coolability for CANDU-6 reactors, a test facility (HU-KINS) has been manufactured as a 1/8 scaled-down of a calandria tank. In the design of the test facility, a scaling law was developed in such a way to consider the thermal-hydraulic characteristics of a CANDU-6 moderator. The proposed scaling law takes into consideration of the energy conservation, the dynamic similitude such as dimensionless numbers, Archimedes number (Ar) and Reynolds number (Re), and thermal-hydraulic properties similitude. Using this proposed scaling law, the thermal-hydraulic scaling analyses of similar test facilities such as the SPEL (1/10 scale) and the STERN (1/4 scale), have been identified. As a result, in the case of the SPEL, while the energy conservation is well defined, the similarities of Ar and the heat density are not well considered. As for the similarity of the STERN, while both the energy conservation and the characteristics of Ar are well defined, the heat density is not. In the meanwhile, the HU-KINS test facility with 1/8 length scaled-down is well similitude in compliance with all similarities of the energy conservation, the fluid dynamics and thermal-hydraulic properties. To verify the adequacy of the similarities in terms of thermal-hydraulics, a computational fluid dynamic (CFD) analysis has been conducted using the CFX-5 code. As the results of the CFD analyses, the predicted flow patterns and variation of axial properties inside the calandria tank are well consistant with those of previous studies performed with FLUENT and this implies that the present scaling method is acceptable.

Similitude Criteria for a Two-dimensional Wall Jet in an Isothermal Mechanically Ventilated Enclosure

A scale model experiment is an important method to study ventilation airflow pattern inside buildings that affects indoor air quality. The similitude criteria are the decision factors to guarantee using the result of model study to predict actual airflow of prototype. It is important to decide the similitude criteria between scale model and prototype. The aim of this project focuses on deciding the similitude criteria of a two-dimensional wall jet between the model and prototype to establish same airflow pattern in an isothermal mechanically ventilated enclosure. The parameters of the Reynolds number, Euler number, and jet momentum ratio proposed by previous researchers are investigated to find which parameter is the similitude criterion for a two-dimensional wall jet in isothermal condition. Experiments were conducted in two geometrically similar scale models. The similitude criteria were verified by comparing latent parameters with airspeed distribution following the kinematic similitude, whereas the airflow pattern following the dynamic similitude between the model and prototype. Experimental results indicate that the Euler number is not the similitude criterion, but the jet momentum ratio related to inlet airspeed is the similitude criterion of a two-dimensional wall jet in an isothermal mechanically ventilated enclosure. Reynolds number may be used as the similitude criterion only for flows at low Reynolds numbers. Our results are useful for the researcher to decide the parameters and boundary conditions of scale model study for the prediction of prototype performance of a two-dimensional wall jet in an isothermal mechanically ventilated enclosure.

Scaled vehicle tire characteristics: dimensionless analysis

This article demonstrates the use of dimensional analysis for scaled vehicle tires. The motivation for this approach is the understanding of realistic nonlinear tire behavior in scaled vehicle control studies. By examining the behavior of vehicle tires within a dimensionless framework, several key tire parameters are developed that allow for an appropriate relationship between full-sized tires and scaled tires. Introducing these scalings into vehicle dynamics studies allows for the development of scaled vehicles that have a high degree of dynamic similitude with full-sized vehicles, but are safer and more economical testbeds on which to develop experimental control strategies. Experimental data are used to compare the nonlinear characteristics for sets of scaled and full-sized tires. Finally, design of a scaled vehicle based on tire characteristics is demonstrated.

Scale Effects in Flume Experiments on Flow around a Spur Dike in Flatbed Channel

This paper presents the findings from a series of flume experiments conducted to determine scale effects in small-scale models of flow around a single spur dike ~wing-dam, groyne, or abutment! placed in a channel whose bed is fixed and flat. The flow features of primary interest are flow-thalweg alignment ~line of maximum streamwise velocity! around a dike, and area extent of the flow-separation region ~wake! immediately downstream of the dike. Those features are of practical concern in the deployment of dikes for various channel control purposes. The scale effects of concern herein are those attributable to use small length scales together with a bed-shear stress parameter ~e.g., Shields parameter! as the primary criterion for dynamic similitude. Small-scale models, especially micromodels, often are used for investigating channel-control issues. Also, the shear-stress criterion is commonly used for models of flow in loose-bed channels, whereas Froude number commonly is the primary similitude criterion for models of fixed-bed open-channel flows. The experiments show that use of a shear-stress parameter as the primary criterion for dynamic similitude influences the flow thalweg and flow separation region at a dike. It does so by distorting pressure gradients around the model dike and by affecting turbulence generated by the dike. It also is shown that, for a range of small models, thalweg alignment and extent of separation region do not scale with model length scales. These findings are important for interpreting results from small hydraulic models, especially micromodels, of flow in loose-bed channels.

Experimental Investigation of a Small-Scale Bridge Model under a Moving Mass

The dynamic response of a small-scale bridge model under a moving mass is investigated. The analysis is based on the continuous Euler–Bernoulli beam theory. By expanding the unknown structural response in a series of the beam eigenfunctions, the given problem is reduced to the solution of a set of second order linear differential equations with time varying coefficients. The analytical solution is validated through a series of experiments. A small-scale model is designed to satisfy both static and dynamic similitude with a selected prototype bridge structure, and a set of necessary similitude conditions for the given problem is provided. Attention is paid, in particular, to satisfaction of the mass similitude requirement, often constituting one of the main difficulties in the design of small-scale dynamic models. It is shown that experimental results are in good agreement with theoretical predictions, thus validating the analytical procedure.

Vibration of damaged beams under a moving mass: theory and experimental validation

A theoretical and experimental study of the response of a damaged Euler–Bernoulli beam traversed by a moving mass is presented. Damage is modelled through rotational springs whose compliance is evaluated using linear elastic fracture mechanics. The analytical solution is based on the series expansion of the unknown deflection in a basis of the beam eigenfunctions. The latter are calculated using the transfer matrix method, taking into account the effective mass distribution of the beam. The convective acceleration terms, often omitted in similar studies, are considered here for a correct evaluation of the beam–moving mass interaction force. The analytical solution is then validated through a series of experimental tests. An adequate small-scale model is designed to satisfy both static and dynamic similitude with a prototype bridge structure, thus providing data of practical engineering relevance. It is shown that experimental results are in good agreement with the theoretical predictions. Moreover, it is observed that the percentages of variation in the beam response due to damage are, generally, larger than those induced in the structural natural frequencies; that is, an increase in structural damage sensitivity is noticed under the effect of a moving interacting load.

Dimensional hydrodynamic similitude in three-phase fluidized beds

This study tests the scaling approach for three-phase fluidized bed hydrodynamics proposed by Safoniuk, Grace, Hackman, & McKnight (Chem. Eng. Sci. 54 (1999) 4961) based on geometric and dynamic similitude with a limited number (5) of dimensionless groups. Experiments were carried out in two systems in which all five dimensionless groups were matched: an aqueous glycerol solution with glass beads (system 1) and silicone oil with porous alumina particles (system 2), with air as the gas in both cases. Although bed expansions were similar for the two systems, trends differed. Gas holdups were always slightly higher for system 1. The dimensionless transition velocities from dispersed to coalesced flow were similar. The minimum liquid fluidization velocity Reynolds number was slightly higher for system 1 without gas, but somewhat lower with gas present. Differences between the systems are statistically significant, but generally less than 12%, so the dimensional similitude approach gives a reasonable basis for estimating global hydrodynamic parameters under the present operating conditions. The differences between the two systems are attributed to the complex coalescence behavior of liquid mixtures, suggesting that additional dimensionless groups are needed to fully characterize the local dynamic bed behavior.

Use of pressure fluctuations to validate hydrodynamic similitude in fluidized media: bubbling beds

Principles of dynamic similitude have been used over the last few years to develop hydrodynamic scaling laws for fluidized beds. The present study is a comprehensive evaluation of dynamic scaling in bubbling fluidized beds using pressure fluctuation data from model and prototype beds for 27 distinct operating conditions. Pressure spectra were quantitatively compared by presenting the data as Bode plots and analyzing the plots as linear, dynamical systems. Characteristic frequencies and damping constants for up to three oscillatory phenomena were determined from the Bode plots and compared between model and prototype beds. Comparison of pressure fluctuations between model and prototype bubbling fluidized beds suggest that hydrodynamic similitude can be achieved for a wide range of operating conditions. However, measurements should be made away from the surface of the bed and caution should be exercised in using very small diameter tubes for the model bed.

Using a scale testbed: Controller design and evaluation

To circumvent the cost and inherent danger in testing aggressive vehicle controllers using full-sized vehicles, a scale vehicle testbed has been developed for use as an evaluation tool to bridge the design gap between simulation studies and full-sized hardware. We describe vehicle dynamic models of the IRS simulation system, along with experimental verification using frequency response and parameter measurements. The next section provides a detailed discussion of dynamic similitude via the Buckingham pi theorem (1914), as well as a graphical comparison between distributions of dynamic scale parameters of scaled and full-sized vehicles. Following that, a yaw rate vehicle controller is introduced to exemplify the type of investigations that can be conducted with the IRS. The controller uses differential torque and brake inputs to assist the driver to control the yaw rate of the vehicle and is designed to achieve model tracking while allowing the driver to maintain control over the front wheels of the vehicle.

Transport processes in the Kara Sea

Field data from late summer cruises in 1993–1996 and results from a rotating laboratory model study are used to infer transport routes for contaminants in the Kara Sea on the western Siberian coast. The data show a circulation pattern that differs significantly from published concepts and contains a richer structure. Both the inflowing coastal water from the west and the modified Atlantic Water from the Barents Sea and the Arctic Ocean in the north affect the water properties of the East Novaya Zemlya Trough through mixing, intrusion, and possible transformation during winter convection. Much of the current structure can be explained as a result of topographical steering of the throughflows. Weak summer winds of variable direction affect only the upper layer, whereas persistent strong winds may affect long‐term circulation patterns and transports. The main outflow routes are north to the Santa Anna Trough and northeast to the Voronin Trough. The outflowing surface water and ice to the north are expected to join the inflowing Polar Water from the Arctic Ocean that forms the Persey Current into the Barents Sea. Deeper outflows are expected to follow the continental slope to the east in the Arctic Ocean. The laboratory model has been validated to earlier current measurements to the north and south of Novaya Zemlya and shows several of the features observed in the newer field measurements. This suggests that the dynamic similitude and boundary forcing of the model are good. Two notable exceptions are the westward transport of drifting buoys to the north of Novaya Zemlya and the late winter hydrography to the north of the Ob and Yenisey estuaries. Both are probably due to persistent winds. The conclusions from the measured and modeled currents are supported by measurements of 137Cs in the seawater and sediments.

Beneficial residual stress from the cold expansion of large holes in thick light alloy plate

Beneficial residual compressive stress is induced around fastener holes by the process of cold expansion in civil aircraft. Fatigue performance is enhanced by increasing the allowable fatigue stress levels which are accounted for in the design. Much work exists that explains both the cold-expansion process and its effects when applied to smaller diameter holes and smaller plate thicknesses, i.e. 12mm or less. Since the introduction of larger diameter holes and larger plate thicknesses of 25mm and greater to current large civil aircraft, investigations have revealed that the cold-expansion process has several unique features that are attributable to the larger size. While superficially the two scales of component may appear to have both static and dynamic similitude, in fact the scaling is not total when the complete manufacturing system is considered. All the dimensions are scaled up with the important exception of the flat portion of the mandrel; it is this easily missed feature that gives rise to the significant three-dimensional effect under investigation. This paper is written from an industrial perspective and reviews the result of experimental stress analyses that demonstrate the difference in the process between small and large holes. Strains were measured in the time domain and the strain progression against time indicates definite three-dimensional effects in the process which are compared with a closed-form solution and a three-dimensional finite element analysis.

The Illinois Roadway Simulator: a mechatronic testbed for vehicle dynamics and control

The Illinois Roadway Simulator (IRS) is a novel, mechatronic, scaled testbed used to study vehicle dynamics and controls. An overview of this system is presented, and individual hardware issues are addressed. System modeling results on the vehicles and hardware are introduced, and comparisons of the resulting dynamics are made with full-sized vehicles. Comparisons are made between dynamic responses of full-scale and IRS-scale vehicles. The method of dynamic similitude is a key to gaining confidence in the scaled testbed as an accurate representation of actual vehicles to a first approximation. The IRS is then used in a vehicle control case study to demonstrate the potential benefits of scaled investigations. The idea of driver-assisted control is formulated as a yaw-rate model-following problem based on the representation of the driver as a known disturbance model. The controller is designed and implemented to show that the vehicle's dynamics can be changed to match a prescribed reference model.

Emergency Gate Vibration of the Pipe-Turbine Model

The vibration behavior of an emergency gate situated on a horizontal-shaft Kaplan turbine is studied. The analysis and transfer of the dynamic movements of the gate are quite complex. In particular the behavior is examined of the emergency gate for the case when the power unit is disconnected from the system or there is a breakdown of the guide vane system at the moment when the maximal head and capacity are achieved. Experimental-numerical methods both in the time domain and in the frequency domain are employed. Natural vibrations characterize a first zone, corresponding to relatively small gate openings. As the gate opening increases, the vibration behavior of the gate becomes increasingly dependent on the swirl pulsations in the draft tube of the turbine. Finally, the data transfer from the model to the prototype by use of the dynamic similitude law is discussed.

Use of dimensional similitude for scale-up of hydrodynamics in three-phase fluidized beds

A new method of scaling three-phase fluidized beds is presented based upon achieving geometric and dynamic similitude with the aid of the Buckingham Pi theorem. This results in five dimensionless groups that must be matched to ensure hydrodynamic similarity between separate units. Experiments have been carried out to validate this technique by comparing gas hold-up and bed expansion in two different columns operating with significantly different fluid and solids properties, but where efforts have been made to match the five dimensionless groups. These comparisons show mostly favourable agreement between the two units.

New Nondimensional Parameters in Fluid Mechanics and Their Application to Turbine Flowmeter Data Analysis

Dimensional analysis has been used in experimental fluid mechanics for over a hundred years. Controllable and uncontrollable variables in an experiment can be efficiently organized into nondimensional groups or parameters. Such nondimensional parameters are used for geometric scaling, and for developing dynamic similitude in experimental processes. Commonly used nondimensional parameters in fluid mechanics include Reynolds number, Mach number, Froude number, Weber number, Strouhal number, etc. Most modern text books and technical papers discuss the use of Buckingham Pi theorem for developing the nondimensionalization process. An often ignored and somewhat older technique is the Rayleigh method. Both the Pi theorem and the Rayleigh method are founded on the principle of dimensional homogeneity, and require some experience in the grouping of physical variables. The present paper uses the Rayleigh method to develop two new nondimensional parameters. A discussion is presented about the use of the parameters in the application of turbine flowmeter calibration and test data analysis. It is shown that data analysis for turbine flowmeters is considerably simplified by the use of the new parameters.

Scale Effect in Pier-Scour Experiments

Presented here are the results of an enquiry into the effects of pier width on local scour depth. The results show that scour depth does not scale linearly with pier width unless there is more-or-less complete geometric similitude of pier, flow, and loose-bed particles—a condition that is rare. Geometric similitude is an important prerequisite to dynamic similitude in replicating local energy gradients for flow around piers. The implications for laboratory experiments on local scour and for design estimation of scour depth are discussed.

EFFECT OF MODELLING ASSUMPTIONS AND INPUT MOTION CHARACTERISTICS ON SEISMIC DESIGN PARAMETERS OF RC BRIDGE PIERS

Modelling assumptions, boundary and loading conditions have a significant effect on analytical assessment of ductility supply and demand measures for RC bridges, a structural form which had suffered extensively in recent earthquakes. In recognition of the important role played by analysis in advancing seismic design of bridges, this paper is concerned with assessing the effect of model characteristics and earthquake strong-motion selection on analytical action and deformation seismic design parameters. This is of particular significance when viewed in the light of the large capital investment and problems with the satisfaction of dynamic similitude encountered in physical testing of piers and pier-deck assemblies. The models studied range between simple fixed-base cantilever and inclusion of both soil and deck effects, represented by assemblies of springs in translational and rotational degrees of freedom. Moreover, two sets of earthquake records are used in dynamic analysis, each comprising six records covering low, intermediate and high a/v, where a and v are the peak ground acceleration and velocity, respectively. The two sets differ in the scaling procedure employed to bring them to a common level of severity; the first set is obtained by direct acceleration scaling whilst the second utilizes the concept of velocity spectral intensity. The results from static and dynamic analysis, using advanced material characterization and solution procedures, are assessed and discussed. Subject to the limitations of the study, outlined in the paper, the results indicate that the inclusion of deck stiffness and/or soil representation is essential to avail of accurate seismic response parameters. However, the effect of variations in soil stiffness and/or deck torsional rigidity applied in the analysis is rather small, compared to the inclusion/exclusion of the model feature. Moreover, it is also observed that using acceleration scaling leads to much larger scatter in the results than when velocity spectral intensity scaling is used. Finally, the results from two particular earthquakes, Friuli and El Centro, highlight the peril of using a small number of records selected without due consideration to the relationship between their wave form, predominant periods and spectral shapes on the one hand and the response periods of the structure on the other.

Non-linear cable response and model testing in water

It is shown that the dynamics of an elastic cable submerged in a heavy fluid, such as water, are dominated by its elastic stiffness; hence dynamic similitude is ensured only if the elasticity of the line is properly modelled. The dynamic tension may reach large values, possibly exceeding the static tension, and then the free falling velocity of the cable becomes a critical parameter.