Scaled Models Research Articles

Effect of scale factor on the dynamic response of frame foundations

Abstract In geotechnical engineering, a scale factor “n” is a numerical ratio that relates the physical properties of a physical model to those of a prototype. The effect of scale factor on the dynamic response of a frame foundation used for high-speed turbo machines is examined through numerical analyses to clarify the influence of scaling dimensions, frequency, static and dynamic loads, and scaled models’ material on the dynamic responses of the frame foundation. The static and dynamic analyses were conducted using Ansys Workbench software. The total number of analyses used to investigate the scale factor effect was 28. Both modal and harmonic analyses were performed to calculate the natural frequencies and displacement responses of the scaled and prototype models under the scaled dynamic loading. Five scale factors were used in this study for concrete models (1, 20, 25, 32, and 40), and two additional analyses on steel models of scale (1 and 20) were used to study the material scaling. The prototype results were first verified, and then the models were investigated after scaling the dynamic loads and dimensions. The results of this study revealed the importance of scaling the frequency when studying the high-speed turbo machine foundation models to reflect the correct responses of the prototype foundation.

Robustness of reinforced concrete frames with elements experiencing bending with torsion

The article presents the results of experimental and theoretical studies of deformation, cracking and fracture of frame structural systems under accidental impacts. The elements of frame structures may exhibit bending with torque as a consequence of the occurrence of an abnormal event. The study provides an energy-based approach to determining internal forces in such structural systems under a scenario in which a column is removed. It also presents a computational model that evaluates the robustness of a reinforced concrete frame of a multi-story building. The model permits the determination of dynamic effects within a structural system, at varying levels of static loads acting within it, and enables the investigation of deformation patterns within the spatial cross-section, including those experiencing bending and torsion. It also allows for the calculation of the robustness parameter of frame systems. In order to validate the proposed computational model, the study employs the outcomes of tests conducted on scale models of reinforced concrete frames with beams subjected to bending and torsion. The experimental frames were loaded in two stages. In the initial stage, the frame structures were subjected to static loading. At the second stage, scaled models were exposed to dynamic loading, which was caused by the sudden removal of columns. A comparison of calculated and experimental results for the investigated structures demonstrates the reliability and efficiency of the proposed calculation model. Consequently, it can be used to calculate the progressive collapse resistance of reinforced concrete frames of multi-storey buildings.

Scale effect on wave planing performance of amphibious aircraft at constant speed

Scaled model testing is commonly recognized as a valuable approach for predicting aircraft performance in the aeronautical applications. However, challenges arise in the case of wave planing events for amphibious aircraft due to difficulties in satisfying the scaling laws of Reynolds number and Froude number simultaneously in a water tank. Therefore, it is important to evaluate the scale effect of regular wave planing process for amphibious aircraft. In this study, by fixing the Froude number, five geosim cases with different scale factors (1/1, 1/2, 1/4, 1/8 and 1/16) are carried out based on the Reynolds-Averaged Navier–Stokes equations (RANS) framework. The hydrodynamic and aerodynamic characteristics at different scales are respectively examined in detail through several physical results, including acceleration, pressure, shear force, velocity and free surface elevation. Comparative analyses among all scaled models reveal that the aerodynamic and hydrodynamic performance both monotonously change with the scale factor, yet the proportion of aerodynamic and hydrodynamic loads remains within a reasonably small range. Furthermore, the results indicate that the scale effect primarily stems from the lack of similarity in Reynolds number, thus resulting in the discrepancies of boundary layer, wave surface elevation and flow separation between the scale model and prototype.

An ML-based wind turbine blade design method considering multi-objective aerodynamic similarity and its experimental validation

Model test is an essential technique to study the aerodynamic performance of wind turbines. To overcome the poor aerodynamic performance of scaled models caused by the scaling effect, this study proposes an innovative blade design method for scaled model testing based on machine learning (ML). The method achieves satisfactory similarity between the thrust and power coefficients under multiple operating conditions of the model and prototype. Furthermore, a case study of the NREL 5-MW wind turbine is carried out with wind tunnel tests to validate the effectiveness of the proposed method. Obtained results suggest that the aerodynamic performance of redesigned blade closely mirrors that of the prototype under multiple operating conditions, reaching 97.59 % (thrust) and 97.87 % (power) coefficients of the prototype at the rated operating condition, respectively. With this technique, aerodynamic performance similarities between the redesigned blade and the prototype can be enhanced, contributing to more accurate scale model testing.

Experimental and Numerical Investigations of Structural Performance of Slab Track under Hygrothermal Environment

The coupled heat and moisture actions could easily cause deformation, cracking and corrosion problems in the slab ballastless track under operational conditions via China Railway Track System (CRTS) Ⅱ. In this paper, two one-quarter-scaled models of CRTS Ⅱ slab ballastless track under hygro-thermal environment were tested in a testing chamber, respectively. To study the effect of constrained conditions on the structural performance of track structure, temperature distribution, stress and displacement of two scaled models with constrained and free boundary conditions were also compared. Then, the temperature and stress field of the track structure was investigated by establishing a finite-element model. The results showed that the temperature transfer between layers has a temperature-lag effect. The positive and negative temperature gradients between the lower part of the track slab and the cement asphalt (CA) mortar layer of the constrained specimen are smaller than those of the free specimen. The longitudinal displacement of the track slab for the free specimen is significantly affected under the hygro-thermal environment and the longitudinal displacement of the concrete base and the track slab forms a displacement difference. Numerical-analysis results showed that the bottom of the concrete base is prone to produce a high-temperature core and that the temperature inside the track structure forms an agglomeration effect. KEYWORDS: Slab track, Hygro-thermal environment, Structural performance, Scale model, Finiteelement model.

A study of scale effects in experiments of monopile scour protection stability

Small scale hydraulic experiments are widely used to model the stability of a scour protection around an offshore monopile foundation. Knowing the associated scale effects is important for evaluating the validity of the obtained experimental and design results. This paper provides a quantification analysis of scale effects that exist in monopile scour protection experiments, with a focus on the shear damage of a dynamically stable scour protection. Large scale models (scale ratio 1:8.33 and 1:16.67) and similar small scale models (scale ratio 1:50) have been adopted in the experiments with waves against current hydrodynamic conditions applied. For the waves and current conditions, the Froude scaling rule is used; for the armour stones, the so-called Best Model scaling rule suggested by Hughes (1993) is used. The scaling scheme achieves similarities between large and small scale models with regard to Shields number, relative density, geometry and settling velocity of particle. The scour protection damage patterns are measured and the three dimensional damage numbers are analysed. For better comparing the small and large scale test results, the small scale tests are performed repeatedly to obtain reliable damage results with associated range of deviation. Visual assessment of the damage patterns shows some agreements between small and large scale tests with regard to the damage and accretion locations. However, detailed analysis shows that the small scale tests introduce higher global and subarea damage numbers compared to large scale tests. The damage areas in small scale tests are larger than that in large scale tests. Significant lee-side damage due to the presence of lee-wake vortices is found in small scale tests. The dissimilarities of pile Reynolds number ( R e , D P ), ratio between Shields numbers ( θ m a x / θ c r ) and vortex shedding frequency in the different scaled models are believed to be the primary reasons of obtained scale effects. • Scale effects in monopile scour protection experiments are investigated quantitatively. • Large scale (1:8.33 and 1:16.67) and small scale (1:50) experiments are performed under wave opposing current conditions. • Repeated small scale experiments are carried out to obtain reliable mean damage numbers and 95% confidence intervals. • Scour protection damages are analyzed and compared between small and large scale experiments. • Time scale of scour protection progressive damage development is investigated. • Different Reynolds numbers ( R e , D P ) and ratios between Shields numbers ( θ m a x / θ c r ) are the main reasons for the scale effects.

Dynamic Scaling of a Wing Structure Model Using Topology Optimization

In this paper, a dynamic scaling methodology is introduced to devise reduced scaled models of aircraft with the objectives of minimizing the development cost and exploring the design space. A promising way to accomplish this is using Topology Optimization (TO) for Additive Manufacturing (AM). Here, TO is employed to design a reduce scale model by matching its natural frequencies and mode shapes to those of a full scale model. Different TO strategies based on density approach are tested with the goal of achieving a dynamically scaled structure that can be manufactured. To achieve this goal, the TO solution should be free from intermediate densities, which is observed for some TO strategies but not all. When no penalization factor is applied: (i) the relative difference between natural frequencies is less than 1% and (ii) the estimated Modal Assurance Criteria (MAC) metric to evaluate the correlation between mode shapes is close to the ideal identity matrix. These results demonstrate the effectiveness of the dynamic scaling methodology. However, when using a penalization factor to avoid intermediate densities, the dynamic behavior correlation between full and scaled models degrades. This trend is more visible in the MAC metric, where off-diagonal terms above 20% and diagonal terms below 90% appear.

Scaling an Artificial Neural Network-Based Water Quality Index Model from Small to Large Catchments

Scaling models is one of the challenges for water resource planning and management, with the aim of bringing the developed models into practice by applying them to predict water quality and quantity for catchments that lack sufficient data. For this study, we evaluated artificial neural network (ANN) training algorithms to predict the water quality index in a source catchment. Then, multiple linear regression (MLR) models were developed, using the predicted water quality index of the ANN training algorithms and water quality variables, as dependent and independent variables, respectively. The most appropriate MLR model has been selected on the basis of the Akaike information criterion, sensitivity and uncertainty analyses. The performance of the MLR model was then evaluated by a variable aggregation and disaggregation approach, for upscaling and downscaling proposes, using the data from four very large- and three large-sized catchments and from eight medium-, three small- and seven very small-sized catchments, where they are located in the southern basin of the Caspian Sea. The performance of seven artificial neural network training algorithms, including Quick Propagation, Conjugate Gradient Descent, Quasi-Newton, Limited Memory Quasi-Newton, Levenberg–Marquardt, Online Back Propagation, and Batch Back Propagation, has been evaluated to predict the water quality index. The results show that the highest mean absolute error was observed in the WQI, as predicted by the ANN LM training algorithm; the lowest error values were for the ANN LMQN and CGD training algorithms. Our findings also indicate that for upscaling, the aggregated MLR model could provide reliable performance to predict the water quality index, since the r2 coefficient of the models varies from 0.73 ± 0.2 for large catchments, to 0.85 ± 0.15 for very large catchments, and for downscaling, the r2 coefficient of the disaggregated MLR model ranges from 0.93 ± 0.05 for very large catchments, to 0.97 ± 0.02 for medium catchments. Therefore, scaled models could be applied to catchments that lack sufficient data to perform a rapid assessment of the water quality index in the study area.

The effect of model scale, acceleration history, and soil condition on closed-ended pipe pile response under coupled static-dynamic loads

This paper analyzes the effect of scaling-up model and acceleration history on seismic response of closed-ended pipe pile using a finite element modeling approach and the findings of 1g shaking table tests of a pile embedded in dry and saturated soils. A number of scaling laws were used to create the numerical modeling according to the data obtained from 1g shake table tests performed in the laboratory. The current study found that the behaviors of the scaled models, in general have similar trends. From numerical modeling on both the dry and saturated sands, the normalized lateral displacement, bending moment, and vertical displacement of piles with scale factors of 2 and 35 are less than those of the pile with a scale factor of 1 and the shaking table test. In general, the pile deformation factor was higher in saturated sand models than the dry sand models. Liquefaction ratios were increased by increasing the seismic intensity; hence the maximum liquefaction ratio was observed with the model of scale 1 under the effect of the Kobe earthquake (0.82g). In another full-scale model, the liquefaction ratio decreased significantly; i.e., it was decreased from 1.64% (λ=1) to 1.04% (λ=35) in the same mentioned model. Pile frictional resistance was numerically investigated and the overall results were compared with previous studies in the literature. In general, the frictional resistance at the pile tip was slightly higher than the frictional resistance around the pile body, and the frictional resistance factor on the ground surface of dry soil models was slightly higher than those of saturated soil models.

Use of scaled discrete element model of rubber tyre loader buckets for draft prediction

The work applies discrete element modelling (DEM) and similitude theory to predict draft on a rubber tyre loader bucket. A DEM model is calibrated and validated using a 1:16 scale model of a rubber tyre loader, followed by simulations at three different speeds (60 mm s −1 , 70 mm s −1 , and 80 mm s −1 ) and two different rake angles (5° and 7.5°). The work hypothesised that the simulated peak draft on the 1:16 DEM model should be able to predict the peak draft on a 1:8 scaled model. A 1:8 scaled model was used to verify the predictions from DEM model. The results show that the predicted peak draft based on DEM results are reasonable when compared to the peak draft observed during the physical experiments on bigger scaled models. The slope of the regression line between the predicted and measured values was 0.9708 and the correlation coefficient 0.5524. There was under-prediction at lower speeds and over-prediction at a higher speeds of operation indicating that the DEM model is sensitive to loading rate. A complete methodology to help original equipment manufacturers (OEMs) in mining, construction and agriculture develop valid and computationally efficient DEM models that can help predict draft for rubber tyre loader design and analysis. Similar techniques can be applied to other ground-engaging tools. • Valid scaled DEM can be used to predict draft on larger or full-size RTL models. • There is slight under prediction at lower speed, and over prediction at higher speed. • Discrete element models are more sensitive to loading rate (speed). • Valid and computationally efficient DEM models can help product design and analysis.

Corrected similarity laws of stiffened panels considering geometric distortion under low speed impact load

In the experiment of scaled models to dealing with the impact of large structures, the strain rate hardening effect can cause large differences between dynamic responses of prototype structure and scaled models. It is almost impossible to completely scale models due to manufacturing restrictions. In the present study, a corrected method based on VSG (V represented initial impact velocity, S represented dynamic flow stress and G represented impact mass) system is developed through Buckingham-Π theorem. The dimensionless analysis focus on factors related to energy absorption, in which the static moment of the cross-section is regarded as the dominant one. Through introducing the corrected velocity factor βv which considered the strain rate hardening effect and geometric distortion, experimental and numerical tests are established and consistent results show the method is effective to relate dynamic responses of scaled models even with distortion to the prototype structure. Additionally, as the distortion factor affects scaled models design greatly, the sensitivity of geometry distortion is discussed and it is shown that a more notable difference occurred when scaled models under the negative βD. Furthermore, it is confirmed in the paper that although exact similitude is not generally possible through the Cowper-Symonds constitutive model, good accuracy is nevertheless achievable regardless of structure facture.

Numerical simulations over a three body launch vehicle for incompressible flows

In the present work, three dimensional numerical simulations over a launch vehicle at 70 m/s are performed for 3 scale models. The vehicle has a cylindrical core body and two strap on boosters. The scaled models chosen so that they represent a wind tunnel blockage ratio of 3%, 4% and 5% respectively. Simulations are performed using commercial CFD software Ansys Fluent. Three dimensional structured mesh is generated using ICEMCFD software. The solver depends on finite volume technique, and SIMPLE calculation is utilized to address the couple continuity and energy conditions. K-w SST model is utilized for disturbance demonstration. The computed flow field is analyzed in terms of velocity, pressure and turbulent kinetic energy contours. Surface pressure acquired from the three simulation (relating to every blockage ratio) arrangements in balance plane is compared to understand the impact of blockage ratio on the stream field and drag coefficients. As the blockage is increased, it was observed that maximum velocity is increasing. Lowest blockage found to give highest drag coefficient.

Design of an aeroelastic physical model of the DTU 10MW wind turbine for a floating offshore multipurpose platform prototype

Multi-purpose offshore structures are very complex systems to be designed as many different requirements have to be taken into account simultaneously. Experimental tests on scaled models can be very useful to verify structural behavior and to validate numerical models. The definition of the scale can play a key role in performing tests as high scales, closer to full-scale, are generally related to more reliable results. The present paper concerns the design of a wind turbine model for a large-scale model of a Multi-purpose offshore Platform developed within the EU project H2020 Blue Growth Farm. This project aims at developing an offshore farm, based on a modular floating structure that integrates wave energy converters and a wind turbine with aquaculture. The scale model of the complete structure will be deployed at the Natural Ocean Engineering Laboratory (NOEL). The paper will focus on the strategies adopted to scale 1:15 the DTU 10 MW wind turbine in order to represent both the main aeroelastic features and all the functionalities of a real machine. The complete design of the machine and its control will be also provided.

An hybrid approach for the comparison of VAWT and HAWT performances for floating offshore wind turbines

This article describes the experimental comparison of the DTU 10MW HAWT with the WindQuest 10MW VAWT scaled models when both fitted on the Nautilus-10 semi-submersible. For the campaign in Ifremer Wind&Wave tank, different rotor representations are tested from inertia only to hybrid testing with propellers and a Software in the Loop. The hybrid testing uses a tabulated approach for thrust computation and is discussed in this article. The different thrust reproduction methods are compared to OpenFAST simulations calibrated during the Lifes50+ project and used as reference points. When quantifying the scale model’s fidelity to Open Fast, cross-correlation was increased up to 14% with the use of the SiL. Thanks to the validation of hydrodynamic simulations based on experimental responses of the floater, it is shown that the VAWT rotor can be upscaled to 13MW for the same platform.

Preliminary study on flutter scaling of high-aspect ratio wings

As a result of the increasing demand for aircraft performance, the high-aspect-ratio wing (HARW) becomes the primary structural type of the emerging aircraft as it improves the lift-to-drag ratio. However, HARWs result in higher deflections, leading to a geometrical nonlinear behavior and nonlinear aeroelastic problems. In this work, the preliminary study on aeroelastic behavior of two classic types of HARWs, namely, Goland wing and High Altitude Long Endurance (HALE) wing, are investigated. Aeroelastically scaled models using two scaling methods, called classic scaling method and modified scaling method, are applied and compared with each other. Froude number is considered in the modified scaling method. Both static aeroelastic and flutter analyses are conducted on each scaled model by using different scaling methods. The results show that the Froude number is important to the HALE wing, where both static deflects and flutter velocity obtained by the scaled model agree well with the full model when the Froude number similarity is met. Thus, the Froude number may be the key similar parameter for the HALE wing scaling model design. For the Goland wing scaling model, the Froude number could be ignored.

Organic chemistry lecture course and exercises based on true scale models

Abstract 3D models of chemical structures are an important tool for chemistry lectures and exercises. Usually, simplified models based on standard bond length and angles are used. These models allow for a visualized discussion of (stereo)chemical aspects, but they do not represent the true spatial conditions. 3D-printing technologies facilitate the production of scale models. Several protocols describe the process from X-ray structures, calculated geometries or virtual molecules to printable files. In contrast, only a few examples describe the integration of scaled models in lecture courses. True bond angles and scaled bond lengths allow for a detailed discussion of the geometry and parameters derived therefrom, for example double bond character, aromaticity and many more. Here, we report a complete organic chemistry/stereochemistry lecture course and exercise based on a set of 37 scale models made from poly(lactic acid) as sustainable material. All models have been derived from X-ray structures and quantum chemical calculations. Consequently, the models reflect the true structure as close as possible. A fixed scaling factor of 1 : 1.8·108 has been applied to all models. Hands-on measuring of bond angles and bond length leads to an interactive course. The course has been evaluated with a very positive feedback.

Similarity laws of structures under impact load: Geometric and material distortion

Recent developments of similarity laws in structural impact have focused on methods of altering the impact velocity to overcome strain-rate effects and differences in material mechanical properties. The present study shows a more comprehensive framework where density, material properties and small thickness distortion are all taken into account when relating scaled models to prototypes under impact loads. The procedure is applied to using theoretical solutions of impact loaded structures such as beams, circular plates and a double plate structure. In addition, numerical simulation is performed to assess the behaviour of a double plate structure, circular plates under impact and impulsive loading. Results have shown that differences in density, strength properties as well as thickness distortions can all be compensated by respecting dimensionless number based on plastic bending moment M0 and mass ratio. This allows one to predict the response of a large structure by testing a small scale model, even when they are made of different materials.

Development of a scale model of a Modular Multilevel Converters

Modular Multilevel Converters are now being introduced in the power grid. Control systems for these converters are complex with many degrees of freedom. Simulation models are useful for exploring control algorithms, but there is still a need for acquiring experience from real converters. As extensive experiments on full-scale converters are not always feasible due to the cost and potential consequences, reduced-scale models that correctly reproduce the salient characteristics of the original converters are necessary. This paper describes the development of 60 kVA scaled models of modular multilevel converters with 6 halfbridge, 12 fullbridge and 18 halfbridge cells per arm, respectively. Most parameters scale naturally, but the equivalent series resistance and therefore the per-unit losses due to load current tend to increase, giving more damping of oscillation than in the full-scale reference.

INCORPORATION OF UNRELIABLE INFORMATION INTO PHOTOGRAMMETRIC RECONSTRUCTION FOR RECOVERY OF SCALE USING NON-PARAMETRIC BELIEF PROPAGATION

Abstract. The creation of large photogrammetric models often encounter several difficulties in regards to geometric accuracy, scale and geolocation, especially when not using control points. Geometric accuracy can be a problem when encountering repetitive features, scale and geolocation can be challenging in GNSS denied or difficult to reach environments. Despite these challenges scale and location are often highly desirable even if only approximate, especially when the error bounds are known. Using non-parametric belief propagation we propose a method of fusing different sensor types to allow robust creation of scaled models without control points. Using this technique we scale models using only the sensor data sometimes to within 4% of their actual size even in the presence of poor GNSS coverage.

INCORPORATION OF UNRELIABLE INFORMATION INTO PHOTOGRAMMETRIC RECONSTRUCTION FOR RECOVERY OF SCALE USING NON-PARAMETRIC BELIEF PROPAGATION

The creation of large photogrammetric models often encounter several difficulties in regards to geometric accuracy, scale and geolocation, especially when not using control points. Geometric accuracy can be a problem when encountering repetitive features, scale and geolocation can be challenging in GNSS denied or difficult to reach environments. Despite these challenges scale and location are often highly desirable even if only approximate, especially when the error bounds are known. Using non-parametric belief propagation we propose a method of fusing different sensor types to allow robust creation of scaled models without control points. Using this technique we scale models using only the sensor data sometimes to within 4% of their actual size even in the presence of poor GNSS coverage.