Similitude Theory Research Articles

Overview of the innovative heat exchangers technologies

The current paper analyzed the new trends and challenges in heat exchanger technologies. The progress of the studies on mini and micro devices used in industry are presented. Particular attention is paid to the heat exchangers used in marine and chemical industries where the resistance to heat transfer increases due to the fouling or scaling. In the industry, there are very important the reduction in the size of devices, and the micro heat exchangers, due to its variety of advantages offered, are well recognized for their higher performance. The applications of them are ranging from process control to military applications. New engineering approaches for modeling the heat and fluid flow processes in micro heat exchangers are analyzed in the present paper. One of these is based on the dimensional analysis and principles of similitude theory that allow the modeling of microscale systems using a physical system at the mini scale. There are identified constant relationships between dimensions permitting the analysis of the fluid flow through micro channels.

Energy Similitude Correction Method for Free Vibration of Cylinders

Similitude theory has been applied to design scale models in many fields of engineering. As for free vibration of cylinders, the wall thickness is too thin to manufacture scale model, which leads to similitude distortion. The aim of this study is to correct the similitude distortion and establish the distorted similitude relationship for free vibration of cylinders. First, the complete and partial similitude relationships are deduced while the similitude distortion of wall thickness is discussed. Then, with analysis of similitude for energy, an equation with prediction of modal frequencies for prototype is established and the energy similitude correction method is proposed. Finally, through numerical examples, this method is verified and the influence of wall thickness variation on the accuracy of the proposed method is analyzed.

A Finite Similitude Approach to Scaled Impact Mechanics

The response characteristics of large-scale structures subjected to impact loading can in principle be determined by scaled experiments. Unfortunately, scaling suffers from scale effects and for impact mechanics, the non-scalability of strain rate and strain hardening can diminish the effectiveness of scaled trials. To resolve this difficulty, a new scaling method has recently appeared in the open literature called finite similitude. The theory is founded on the metaphysical concept of space scaling, where the idea is that by expanding or contracting space, changes in the governing mechanics can be assessed.In this paper the finite-similitude theory is further developed, where it is demonstrated how the constraints imposed by dimensional analysis can be broken. A new form of similarity is introduced but at the cost of requiring two scaled experiments at distinct scales. It is shown however, how the theory is able to combine the information from the two scaled trials to predict outcomes that can be markedly superior to what can be achieved with experiments at a single scale. All scale dependencies are accounted by the theory and consequently the new formulation attempts to capture scale effects, so provides a more realistic approach to scaled experimentation.Unlike dimensional analysis, the new first-order finite similitude theory can simultaneously target two independent physical properties of common dimension (e.g. initial-yield stress and linear strain hardening). The advantage offered by this feature is demonstrated analytically and numerically in the paper with a focus on axisymmetrical tube buckling and energy absorption. The analytical model serves to expound the theory and the numerical highlights its capabilities and the kinds of accuracy achievable with the new approach.

Design of scaled down model of a tower crane mast by using similitude theory

In this study, a tower crane mast which is very sensitive to the dynamic effects that will occur due to its delicate structure was scaled by similitude theory for the purpose of using in experimental studies. The variables that describe the structure in terms of dynamic were determined and pi groups were created by using the Buckingham Pi Theorem. A finite element model that is able to calculate the natural frequencies, mass participation factors, and draw the mode shapes of a structure composed of space frame elements was developed. The mast was scaled down to use in the laboratory environment with two different scale factors as 30 and 40. The most suitable model which represents the dynamic behavior of the real-size tower crane mast for the experimental studies was determined by comparing the modal analysis results of the real-size and scale models.

A partial similitude method considering variable powers in scaling laws and applied to rotor-bearing systems

Similitude theory is used to establish the necessary conditions between the enlarged or reduced model and the original structure, and has been widely applied to vibration and impact tests of large structures. However, several limitations and difficulties still persist in partial similitude for complex structures. In this paper, a partial similitude method to obtain scaling laws is proposed. The powers in scaling laws are variables against the scaling factors, and the coupling effect among design parameters is considered in the powers. The accuracy and applicability of the proposed method are demonstrated in two case studies. The first case study discusses the partial similitude of a single rotor-bearing system. The single rotor-bearing system is scaled with distortion in the geometrical dimension and boundary conditions. It is found that the proposed method predicts the critical speeds and unbalance responses with good accuracy. Furthermore, the proposed method can improve the prediction accuracy by comparing with the methods in current literatures. The second case study comprises a dual-rotor system to demonstrate the accuracy and applicability of the proposed method for more complex rotor-bearing system. The speed ratio, excitation position, co-rotation, and counter-rotation are discussed in predicting the critical speeds as well as unbalance responses. It is also found that the proposed method can improve the prediction accuracy.

Compressive strength of reduced concrete specimens considering dimensional distortion of coarse aggregates

The present study investigates the mechanical behavior of small cylindrical specimens (∅50 × 100 mm) in relation to the minimum standard size (∅100 × 200 mm) recommended by ASTM and Brazilian codes. Statistical and dimensional analyses were performed for three different classes of compressive strength (20, 30, and 40 MPa), and four grades of coarse aggregates (Dmax 9.5, 12.5, 19, and 25 mm). To this purpose, the Student’s t-Test for two means and equations from the Similitude Theory were applied. The following evaluations were performed: a) influence of the dimensional distortion of aggregates on the compressive strength of small concrete specimens; b) analyses through hypothesis testing between strength means; c) the use of prediction coefficients with statistical reliability for correcting the dimensional distortion of aggregates; and d) influence of the wall effect for different specimen sizes and concrete mixes. The results showed that the reduced and the standard specimens have similar compressive strengths, despite the reduced ones having presented higher variability of results. Also, innovative quantitative results from Wall Effect analysis show agreement with the strength results and illustrate the phenomena from a new perspective.

Numerical and experimental analysis of thermal-flow characteristics in a pyrolysis reactor of a gas scrubber designed based on similitude theory

ABSTRACT With the continuous development of the semiconductor industry, interest in the technology for treating various pollutant gases in the semiconductor fabrication process has increased recently. Various gas scrubbers are being used to remove the pollutant gas from the processes. An efficient design of the pyrolysis reactor is crucial in a scrubber system due to the effective removal of pollutant sources and the overall operation stability. In this study, the thermal and flow characteristics in the reactor were examined through experiments and numerical analysis using a small-scale model of simplified pyrolysis reactor. Furthermore, a prototype model of pyrolysis reactor was designed through analysis result of small-scale model based on the similitude theory. The results of this study can be used as basic data for analyzing thermal and flow characteristics in a variety of scrubber systems. Implications: This study investigated and suggested a methodology for designing a pyrolysis reactor of the gas scrubber to overcome the design failure by using the concept of similarity, which can use the results from one system to explain phenomena in another system. We believe that our study makes a significant contribution to the literature because it provides a way to improve the performance of the gas scrubbers and test this performance with a smaller scalable model. And, we expect this study to be used as basic data when applying innovative and new design proposals in various industries.

An investigation into finite similitude for high-rate loading processes: Advantages in comparison to dimensional analysis and its practical implementation

Exploration of the behaviour of large-scale structures under impact and explosive loading can in principle be achieved by means of scaled experimentation. In practice however, scaled experiments can be unrepresentative of high-rate phenomena due to non-scalable strain-rate effects and altered material behaviours. Critical is proper experimental design but this is presently impeded by the inability of dimensional analysis to cater for the absence of exact similarity in high-rate loading scenarios.This paper re-examines the place of high-rate scaled experimentation in the light of a new similarity theory founded on the distortion of space (called finite similitude), which has recently appeared in the open literature. The advantage of finite similitude over dimensional-analysis based techniques is demonstrated in the paper, which is able cope (to some extent) with the breakdown in similarity with an approximate approach called inexact-finite similitude. It is shown to be independent of loading type (unlike competing methods), which is a feature demonstrated through the analysis of a scaled plate subject to a free-air explosion.The work presented here provides the first attempt to test the practical importance of the new theory through detailed experimental trials. The experimental investigations reaffirm the theoretical studies and reveal that the developed inexact-finite similitude theory can practically be used for predicting full-scale behaviour by conducting experimental tests on trial models of different sizes and even different materials. For this purpose, circular tubes subjected to high loading rate axial impact using a gas-gun apparatus are chosen as case studies. It is shown that in most cases, scaled experimentation provides superior predictions of buckling shapes, shortenings, temporal response of axial force and peak loads in comparison with numerical simulation. Analytical outputs for mean force and peak load are also shown to be significantly inferior to those returned through scaled experimentation.

Dynamic similarity analysis for a piezo-electromechanical system

Most research about using piezoelectric stacks to suppress vibration of mechanical structures didn’t involve the similarity problem for the piezoelectric stacks. The goal of this paper is to investigate the dynamic similarity between a prototype piezo stack and a scaled up or down piezo stack, whilst discussing the feasibility of predicting the vibration of prototype structure which use the piezoelectric stacks for vibration control. To illustrate this problem concisely, a single-DOF system consists of a proof mass and a piezo stack shunted with a series RL circuit is considered. Firstly, the governing equation of such piezo-electromechanical system in frequency domain is derived. Next the dynamic similarity of prototype and model stack is analyzed by similitude theory. After that the scaling laws are derived. Finally, a numerical simulation and relative error analysis are given to demonstrate the scaling laws.

A Study on Thermal-flow Characteristics in a Reaction Chamber of Gas Scrubber Designed Based on Similitude Theory

Objectives A gas scrubber which is normally composed of a reaction chamber and a scrubbing part is being used to purify the waste gases from the processes. An efficient design of the reaction chamber is essential in a scrubber system due to the overall operation stability and high destruction & removal efficiency (DRE). The purpose of the study was to obtain the basic design data of deriving the improved design by analyzing a small-scale model of the commercial reaction chamber. Methods In the present study, the small-scale model of the simplified the reaction chamber was designed and fabricated based on similitude theory, and the thermal-flow characteristics were numerically analyzed inside the chamber using commercial Computational Fluid Dynamics (CFD) code. Results and Discussion Based on two dimensionless numbers for the geometric similarity and three dimensionless numbers for the kinematic similarity, the small-scale model of the reaction chamber was designed and fabricated. From the numerical and experimental results, thermal-flow characteristics such as temperature gradient and thermal efficiency were evaluated. To validate the numerical method applied herein, the numerical results of the temperature at specific monitoring points were compared with the experimental data. The average error rates (2.5~9.8%) between them was shown and the numerical results of temperature distribution are in good agreement with the experimental data. Conclusions In this study, the small-scale model, which was designed and manufactured based on similarity theory was analyzed. From these results, the basic design data for drawing the improved design ideas were acquired The results of this study can be used as basic data for analyzing thermal and flow characteristics in a variety of scrubber systems. Key words: Semiconductor Industry, Gas Scrubber, Reaction Chamber, Similitude Theory, Computational Fluid Dynamics (CFD)

An experimental and numerical investigation on temperature profile of underground soil in the process of heat storage

A detailed understanding of soil temperature in underground energy engineering is a major concern in designing a high-efficient and less cost-operated underground soil energy system (e.g. ground source heat pump (GSHP) and ground energy pile system). In this paper, similitude theory is introduced as a methodology to design a small-scale thermal energy storage experiment setup for studying the heat transfer behavior in underground soil. Based on heat transfer governing equations and similitude analysis, the scaling laws and similarity conditions are derived, and a laboratory scaled-down thermal energy storage experiment model is designed and constructed. The proposed experiment can be used to study the heat transfer behavior of ground energy storage by reducing the time consumption substantially. A transient 3-D numerical model is proposed and validated with sandbox data set. The numerical model is applied to calculate the temperature variation of ground heat exchanger in full scale and used to estimate the accuracy using the p-linear distribution approximation to represent the vertical profile of fluid temperature. The comparison between the experiment model results (after scaling to prototype) and numerical results are given, and the coincidence between them is good, particularly at the late-time period. For implementing a design and optimization of the field-scale engineering underground energy storage system, by using the scaling factor, the experimental model results could be used to predict the temperature distribution of the full-scale underground energy storage system with different types of underground soil in different controlled working conditions. This work would provide more accurate reference data and foundation with less time-consuming for engineering application of underground energy storage system, such as GSHP, ground energy pile and etc..

Application of Structural Similitude for Scaling of a Pressure Vessel

Pressure vessels find their use in various fields, ranging from gas cylinders used in households for cooking, boilers for steam engines, fuselage of aircraft to solid rocket motors used in missiles and space shuttle. The design of such vessels is validated by performing tests on full scale prototypes. Mostly the testing of such vessels is cumbersome and expensive. This paper establishes the method to reduce the cost for testing the pressure vessels. The theory of similitude is studied to make the testing process easier by establishing structural similitude for a pressure vessel. Using similitude theory a scaled model of the prototype vessel is developed in such a way that when the scaled models’ responses are multiplied by a calculated scale factor, behaviour of the prototype could be predicted. By testing on the scaled down model, the cost of manufacturing is reduced. The pressure vessel considered here is representative of the pressures and materials used in high pressure applications. In this paper a 1/10th scaled model of the pressure vessel is developed using structural similitude theory. Buckingham pi-theorem technique has been used for dimensional analysis after studying parameters on which pressure vessel is designed and ANSYS software is used to validate the resulting pi-products. Complete similarity is achieved when predicted prototype results completely map on to prototype results.

Physical Modelling and Numerical Simulation of the Deep Drawing Process of a Box-Shaped Product Focused on Material Limits Determination

Similitude theory helps engineers and scientists to accurately predict the behaviors of real systems through the application of scaling laws to the experimental results of a scale model related to the real system by similarity conditions. The theory was applied when studying the deep drawing process of a bathtub made from cold rolled low carbon aluminum-killed steel from the point of view of material limits. The bathtub model was created on the basis of geometric, physical, and mechanical similarity on a scale of 1:5. Thus, simulations and physical models were created. The simulation model was used to verify the combination yield locus/hardening law on the basis of comparing the thickness change. As a result, Hill 48/Krupkowski showed the minimal deviation by comparing data evaluated from numerical simulations and that measured on the physical model. Additionally, material anisotropy was modelled when virtual materials were defined from experimentally measured values of the plastic strain ratio. As an outcome, extra deep drawing quality steel with an average plastic strain ratio of rm ≥ 1.47 and an average strain hardening exponent of nm ≥ 0.23 must be used for the deep drawing of the bathtub.

EXPERIMENTAL STUDY ON PROPERTY OF DYNAMIC SIMILAR MATERIAL MADE OF DIFFERENT RAW MATERIALS

With the development of dynamic model test such as centrifuge and shaking table, the requirement for dynamic similar material is more detailed. On the basis of dynamic similitude theory of model test, how to select the ratio of raw materials accurately plays an important role in the model test. This paper selects river sand with different particle gradations, iron powder, barite powder and mica sheet as the raw materials, and jet cement as the cementing agent. It then studies the physical and mechanical property of the similar materials with the elastic wave speed simulation measurement and uniaxial compressive test. The results show the follows. (1)The density, dynamic and static elasticity modulus of the specimens with better particle gradation are bigger and the sand-blinder ratio has a greater influence on the density of similar material as the gap gradation enlarges. (2)The dynamic similar material can be obtained whose density is between 1.5-2.2g·cm-3, dynamic Poisson's ratio is between 0.2-0.4 and dynamic elasticity modulus is between 2.5-5.5Gpa if we choose the river sand as aggregate and cement as cementing agent. (3)Iron powder has better effect on gaining weight than the barite powder. The dynamic and static elasticity modulus of the barite specimen have no obvious changes with the change of barite powder content. Therefore, barite powder is an ideal raw material to make dynamic similar material with high-density and low-strength. (4)With the increase of mica sheet content, the dynamic Poisson's ratio, dynamic and static elasticity modulus of specimen can reduce evidently. As a result, the mica sheet is not suitable for similar material with high density but it can make similar material of weak intercalation or structural plane.

Dynamic plastic behaviour of strain rate sensitive tubes under axial impact

In this paper, the axisymmetric buckling of circular strain rate sensitive tubes subjected to axial impact is investigated theoretically and experimentally. The nonlinear governing equations are first derived in an incremental form. Then, the finite difference method is employed to solve the obtained equations implicitly for the case when a stationary tube is impacted by a striking mass. Experimental tests are performed by using a gas gun. The effect of linear and multi-linear approximation for strain hardening and strain rate on the shortening, buckling shape and axial force of steel tubes are investigated in which the strain rate is considered as a function of time. By applying the strain rate effect and using the multi-linear approximation for strain hardening, we showed there is a significant association between theoretical and experimental results of steel tubes. Also, using the nonlinear dynamic equations and newly developed inexact finite similitude theory it is revealed that the response characteristics of full-scale strain rate sensitive tubes can be predicted using small-scale strain rate insensitive tubes.

A Review of Similitude Methods for Structural Engineering

Similitude theory allows engineers, through a set of tools known as similitude methods, to establish the necessary conditions to design a scaled (up or down) model of a full-scale prototype structure. In recent years, to overcome the obstacles associated with full-scale testing, such as cost and setup, research on similitude methods has grown and their application has expanded into many branches of engineering. The aim of this paper is to provide as comprehensive a review as possible about similitude methods applied to structural engineering and their limitations due to size effects, rate sensitivity phenomena, etc. After a brief historical introduction and a more in-depth analysis of the main methods, the paper focuses on similitude applications classified, first, by test article, then by engineering fields.

A Similitude Theory for Modeling Traffic Flow Dynamics

Similitude theory, particularly dimension analysis, is a common tool for testing scaled-down engineering models and is widely used in vehicle dynamics and other engineering fields. However, it is barely employed in scaling traffic flow dynamics. In this paper, dimension analysis is adopted to scale car-following dynamics. Under the guidance of the similitude theory, a scaled downvehicle test bed is built where seven cars are running on a circular track at a maximum speed initially and congestion emerges after a period of time. In other words, a phantom traffic jam appears in our similitude test bed without any bottlenecks. The fundamental diagrams drawn from the experimental results show that our test bed has the capability of generating traffic hysteresis that is commonly observed in the field. Therefore, the design of this test bed can be used to simulate traffic dynamics to a certain degree and will pave the way for scaled-down connected and automated vehicle systems development.

Scaled models for failure under impact loading

Small-scale experimentation is recognised to play an important role in the investigation of the behaviour of large-scale structures. Presently however, there exists no known procedure for analysing structures involving damage or failure by means of scaled experiments when high-rate impact loading is involved. The principal problem impeding the scaled approach is that similarity seldom exists for high-rate dissipative problems and consequently dimensional analysis provides an ineffective framework for experimental design and analysis.This paper is concerned with the application of the finite similitude theory which scales experiments by means of space distortion. Although finite similitude suffers many of the limitations of dimensional analysis it has one principal advantage, i.e. it is able to cater for inexact similitude where sources and effects of mismatch can be quantified. This feature is exploited in the work to answer the open question whether it is possible to determine the failure response of structures subjected to high rate loading by performing experimental tests on scaled structures manufactured with different materials.The efficacy of the proposed methodology for scaled experimentation is tested by means of numerical analysis on a number of well-known test cases, which are supported by experimental evidence. In particular the perforation of circular plates and the Taylor bar impacting on a rigid wall are analysed using the commercial finite element software package Abaqus. The Johnson–Cook thermo-viscoplastic constitutive equation together with the Johnson–Cook damage model are used to describe yielding, strain hardening, strain rate effects, thermal softening and material failure. It is revealed in the paper that although exact similitude is not achievable the results of the full-scale model can be predicted to good accuracy by means of scaled experimentation founded on finite similitude theory.

A force/stiffness equivalence method for the scaled modelling of a high-speed train head car

Research using a scaled model train is a fast and efficient method to study train collisions, and can shorten the product development cycle and reduce the test cost. Owing to the large number of thin-walled structures in high-speed train, the particularity determines that the high-speed train cannot be scaled simply according to the similitude theory. This study proposes a new method of force/stiffness equivalence-scaled modelling for high-speed trains, which can also be used for the scaled modelling of a prototype composed of thin-walled structures. An initial scaled model of a head car was established by scaling the energy absorbing part and undeforming part in a full-scale prototype. Numerical simulations indicated that the relationships among deformation, acceleration, and energy absorption are similar in the initial scaled model and prototype; however, a certain error occurs between the initial scaled model and prototype. Using a multi-objective genetic optimisation algorithm, a corrected scaled model was obtained based on the initial model. Finally, a numerical simulation and crash test of the corrected scaled model were performed. Compared to the results of the prototype test, the maximum error of the average acceleration in the corrected scaled model’s numerical simulation and crash test are 3.1% and 5.5%, respectively. The results indicate that this new method can be used for the scaled modelling of a prototype composed of thin-walled structures.

Metal Foam-Filled Tubes as Plastic Dissipaters in Earthquake-Resistant Steel Buildings

The aim of this paper is to investigate whether metal-foam-made devices can be effective to dissipate seismic energy in buildings during strong earthquakes. To this purpose, non-linear numerical analyses of concentrically braced steel buildings under recorded ground motions have been carried out, while some experimental tests on metal-foam specimens and metal-foam-filled tubes have been performed. Foam-based devices are assumed to be inserted within the diagonal braces of the considered steel frame to dissipate energy by plastic deformation during strong earthquakes. To apply the experimental data, a scaled numerical model of the prototype building has been implemented by means of the similitude theory and the Buckingham Π theorem. The results of the study provide a preliminary assessment of the potential of metal foam-based dissipaters to reduce the seismic effects in civil structures.