Similarity Laws
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2021 ◽  
Vol 11 (3) ◽  
pp. 1314
Mohamed Murshid Shamsuddeen ◽  
Sang-Bum Ma ◽  
Sung Kim ◽  
Ji-Hoon Yoon ◽  
Kwang-Hee Lee ◽  

A multistage centrifugal pump is designed for pumping low-viscosity, highly volatile and flammable chemicals, including hydrocarbons, for high head requirements. The five-stage centrifugal pump consists of a double-suction impeller at the first stage followed by a twin volute. The impellers for stages two through five are single-suction impellers followed by diffuser vanes and return channel vanes. The analytical performance is calculated initially in the design stage by applying similarity laws to an existing scaled-down pump model designed for low flow rate applications. The proposed pump design is investigated using computational fluid dynamics tools to study its performance in design and off-design conditions for water as the base fluid. The design feasibility of the centrifugal pump is tested for other fluids, such as water at a high temperature and pressure, diesel and debutanized diesel. The pump design is found to be suitable for a variety of fluids and operating ranges. The losses in the pump are analyzed in each stage at the best efficiency point. The losses in efficiency and head are observed to be higher in the second stage than in other stages. The detailed flow behavior at the second stage is studied to identify the root cause of the losses. Design modifications are recommended to diminish the losses and improve the overall performance of the pump.

2021 ◽  
Vol 22 (1) ◽  
pp. 35-46
Syed Muzzamil Hussain Shah ◽  
Zahiraniza Mustaffa ◽  
Shabir Hussain Khahro ◽  
Khamaruzaman Wan Yusof ◽  
Aminuddin Ab Ghani ◽  

In terms of stability, the response of static cars in floodwaters has been widely investigated. However, the hydrodynamics of a non-static vehicle exposed to such events are less explored. Herein the study ponders the assessment of the hydrodynamic forces experienced by a non-static vehicle attempting to cross a low-lying flooded street. With that regards, a Perodua Viva was modeled (1:10) and tested in the Hydraulics Laboratory under partial submergence and sub-critical flows, fulfilling the similarity laws. Since the Froude number could best analyze the flow conditions, the behavior of the hydrodynamic forces and the Froude number have been the focus of this investigation. From the study of outcomes, an inverse relation of the Froude number with respect to the buoyancy force, along with positive trends relating to drag, frictional, and rolling resistance, were noticed. ABSTRAK: Dari segi kestabilan, tindak balas kereta statik dalam air banjir telah banyak dikaji. Walau bagaimanapun, hidrodinamik kenderaan tidak statik yang terdedah kepada kejadian seperti itu kurang diterokai. Kajian ini menilai daya hidrodinamik kenderaan tidak statik yang cuba melintas jalan raya yang banjir. Sehubungan itu, sebuah Perodua Viva dimodelkan (1:10) dan diuji dalam Makmal Hidraulik di bawah perendaman separa dan didedahkan kepada aliran sub-kritikal, seperti ketika kejadian. Manakala nombor Froude adalah terbaik dalam menganalisa keadaan aliran air. Oleh itu, tindak balas daya hidrodinamik dan nombor Froude menjadi fokus penyelidikan ini. Dapatan kajian menunjukkan kaitan terbalik nombor Froude pada daya apungan, sedangkan tren positif yang berkaitan dengan daya tarik, geseran dan rintangan guling diperhatikan.

V. Vanin ◽  
M. Kruhol

The work is devoted to the study of thermal power plants auxiliary energy efficiency. The main mechanisms in the auxiliary systems are centrifugal mechanisms that work in complex hydraulic networks with variable productivity. The main ways to adjust the parameters of the centrifugal mechanisms are to change the speed of rotor rotation, change the guide vane angle and throttle. The operation mode of a complex hydraulic network which includes a group of centrifugal mechanisms with a mixed connection scheme is analyzed. The system of equations which characterize the hydraulic system has been obtained on the basis of Kirchhoff's laws. The centrifugal mechanisms' operating characteristics are given by approximation dependences obtained with the method of least squares and similarity laws. To analyze efficiency of different methods of centrifugal mechanisms parameters regulation, optimal control problems were set and solved. The constraints for the problems are a system of equations that describe the hydraulic system operation and technical constraints that depend on the control method. Through solving the problems, values of the optimal parameters and weighted average efficiency of the group mechanisms were obtained. Studies have shown that the most effective way to regulate the centrifugal mechanisms parameters is to use an individual frequency drive, the least effective is to use only changing angle of centrifugal mechanism's guide vane. Utilization of group control is highly efficient and not inferior to individual frequency drive. However, this statement is correct under condition of the operating characteristics agreement with the centrifugal mechanisms’ operating modes similarity.

Shuai Wang ◽  
Fei Xu ◽  
Xiaoyu Zhang ◽  
Leifeng Yang

When different strain hardening and strain rate sensitive materials are used for scaled model and prototype, the traditional pure geometrical similarity laws of solid mechanics will fail. Although correcting the basic scaling factors of velocity, density and geometry have been developed to compensate for the material distortion in recent non-geometric scaling works, it is difficult to be widely used because of its inherent indirect (depending on the structural strain and strain rate responses) and inexact (having significant prediction errors for prototype) defects. In this paper, a framework of material similarity, based on the new suggested material dimensionless numbers and the ‘Material number vs. strain/strain-rate’ function curves, are further developed, which represents the objective requirement of similarity theory for the basic mechanical properties of materials. It is demonstrated what is similitude materials of solid mechanics and how to use the best similitude materials to overcome the non-scalabilities of materials for identical or different materials. The direct and exact solution of the basic correction factors is further obtained and therefore overcomes the previous inherent indirect and inexact defects radically. Based on the similarity evaluation of different materials of the classical constitutive models, the impacted structures of circular plate and crooked plate with strain hardening and strain rate sensitive materials are verified numerically. The results show the completely different materials can be exact similitude for various structural behaviors (strain, strain rate, stress and displacement) of time and space fields after using the best similitude materials; and the basic correction factors do not depend on the structural strain and strain rate responses. As a contrast, when the non-similitude materials are used, the similarity results are very sensitive to the selection of strain/strain-rate and often leads to failed predictions. In addition, for the material elastic and temperature effects, the proposed method is also discussed to be valid.

Atmosphere ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 791
Nicolas Velasquez ◽  
Ricardo Mantilla

Regional Distributed Hydrological models are being adopted around the world for prediction of streamflow fluctuations and floods. However, the details of the hydraulic geometry of the channels in the river network (cross sectional geometry, slope, drag coefficients, etc.) are not always known, which imposes the need for simplifications based on scaling laws and their prescription. We use a distributed hydrological model forced with radar-derived rainfall fields to test the effect of spatial variations in the scaling parameters of Hydraulic Geometric (HG) relationships used to simplify routing equations. For our experimental setup, we create a virtual watershed that obeys local self-similarity laws for HG and attempt to predict the resulting hydrographs using a global self-similar HG parameterization. We find that the errors in the peak flow value and timing are consistent with the errors that are observed when trying to replicate actual observation of streamflow. Our results provide evidence that local self-similarity can be a more appropriate simplification of HG scaling laws than global self-similarity.

2020 ◽  
Vol 65 (5) ◽  
pp. 419
A. M. Hetalo ◽  
O. V. Khorolskyi ◽  
S. A. Stetsenko ◽  
S. O. Samoilenko ◽  
O. S. Svechnikova

On the basis of experimental data obtained for the viscosity, density, and refractive index of fluorinated alcohols and proceeding from the similarity laws, the structural features of molecules of the researched liquids are determined. A comparison of molecular refraction values determined for fluorinated and non-fluorinated alcohols made it possible to reveal a modification of the structure of fluorinated alcohol molecules. Namely, this is a probable minor change in the arrangement of fluorine atoms in the alcohol molecule, at which the structure of a molecule remains similar to the structure of molecules of aliphatic alcohols. A similarity in the behavior of the rheological properties of 2,2,3,3-tetrafluoropropan-1-ol and 1H,1H-pentafluoropropan-1-ol, on the one hand, and propan-1-ol, on the other hand, as well as 1H,1H,7H-dodecafluoroheptan-1-ol and 1H,1H-tridecafluoroheptan-1-ol, on the one hand, and heptan-1-ol, on the other hand, is found. A method for estimating the melting temperatures of halogenated molecular liquids, which is based on the similarity of the rheological properties of those liquids, is proposed. The melting temperatures for 1H,1H-pentafluoropropan-1-ol, Tm = (244.5 ± 1.0) K, and 1H,1H-tridecafluoroheptan-1-ol, Tm = (255.0 ± 1.0) K, which are not available in the literature, are evaluated.

2020 ◽  
Mariya Yurovskaya ◽  
Vladimir Kudryavtsev ◽  
Bertrand Chapron

<p>The study is based on a simple parametric model, which is an extension of the self-similarity theory for surface waves generated by a wind field. According to the original similarity concept, the development of wind waves can be fully described using the scale of the fetch length (or time) and wind velocity. The aim of the work is to develop a parametric model to describe the wave generation in arbitrary spatio-temporal wind field. We assume that in this case similarity laws are also fulfilled, i.e., the rate of spectral the peak frequency and wave energy change is completely determined by the wave age. The source function is written in a form providing the stationary solution that corresponds to the well-known fetch law, confirmed in numerous experiments.</p><p>In order to extend the equations to the two-dimensional case, when the wind change occurs in both directions, it is assumed that the relations stay valid if the wind speed is replaced by its component in spectral peak direction. In this case, the system of equations should be supplemented by an expression for the evolution of spectral peak direction, describing its adaptating to the direction of non-uniform wind.</p><p>The algorithm for solving the complete system of equations describing the evolution of wave height, spectral peak frequency, its propagation direction and focusing/defocusing of wave energy, is based on the method of characteristics. To simulate the evolution of waves in a hurricane, we use the calculation in a non-stationary reference system associated with the hurricane. Coordinates, wave peak frequency, energy and direction are calculated along ray trajectory at every discrete time moment. To increase the stability of the numerical scheme, an implicit 4th-order Runge-Kutta method is used.</p><p>Test calculations were carried out for the case of the wave development from the coast with a uniform wind and then for an inhomogeneous cyclonic wind field for different hurricane speeds. The calculations reproduce the anisotropy of the energy distribution inside the hurricane and the effect of wave trapping by a moving cyclone. A comparison of the results with available field measurements of wave parameters in tropical cyclones showed their good agreement. The proposed algorithm can be used in wave forecast models and can serve for deeper understanding the wave field formation in extreme conditions.</p><p>The work was supported by Russian Science Foundation via grant 17-77-30019 and the Ministry of Education and Science of the Russian Federation under the State Assignment No. 0827-2018-0003.</p>

Shuai Wang ◽  
Fei Xu ◽  
Xiaoyu Zhang ◽  
Zhen Dai

A framework of similarity laws, termed oriented-density-length-velocity (ODLV) framework, is suggested for the geometric distorted structures subjected to impact loading. The distinct feature of this framework is that the newly proposed oriented dimensions, dimensionless numbers and scaling factors for physical quantity are explicitly expressed by the characteristic lengths of three spatial directions, which overcome the inherent defects that traditional scalar dimensional analysis could not express the effects of structural geometric characteristics and spatial directions for similarity. The non-scalabilities of geometrical distortion as well as other distortions such as different materials and gravity could be compensated by the reasonable correction for the impact velocity, the geometrical thickness and the density, when the proposed dimensionless number of equivalent stress is used between scaled model and prototype. Three analytical models of beam, plate and shell subjected to impact mass or impulsive velocity are verified by equation analysis. And a numerical model of circular plate subjected to dynamic pressure pulse is verified in more detail, form the view of point of space deformation, deformation history and the components of displacement, strain and stress. The results show that the proposed dimensionless numbers have attractively perfect ability to express the dimensionless response equations of displacement, angle, time, strain and strain rate. When the proposed dimensionless numbers are used to regularize impact models, the structural responses of the geometrically distorted scaled models can behave the completely identical behaviors with those of the prototype on space and time —not only for the direction-independent equivalent stress, strain and strain rate but also for the direction-dependent displacement, stress and strain components.

2019 ◽  
Vol 15 (1) ◽  
Vidya Venkatesan ◽  
Lakshminarasimhan Mukundarajan ◽  
Anantharaman Narayanan

Abstract Eulerian-Eulerian approach and conventional Eulerian-Lagrangian model are computationally exhaustive for modelling circulating fluidized bed (CFB) riser which has wide particle size distribution and billions of particles Alternatively, the relatively recent Eulerian- Lagrangian computational particle fluid dynamics (CPFD) model enables simulation of the CFB system with lesser computational resources. Most of the published studies on CPFD simulations of CFB risers deal with single grate system. The present study aimed to investigate the performance of the CPFD model for predicting solids distribution in a CFB riser with pant-leg structure (dual grate) and characteristics similar to a commercial boiler. Experiments conducted in a scaled down 250 MWe CFB facility according to Glicksman’s simplified similarity laws for fluidized beds were simulated using commercial code Barracuda. The bottom dense bed, upper lean solid phase, increase in bottom bed voidage with increasing fluidizing velocity and reducing solids inventory, decrease in bottom bed solids concentration with decrease in particle size and exchange of solids between the legs typically occurring in a CFB with pant-leg structure were successfully captured by the CPFD calculations. Simulation results showed that the upper solids concentration is hardly influenced by the solids inventory level in line with the experimental observation, therefore the amount of solids inventory can be optimized during actual operation. The predicted pressures varied from the average experimental pressure data within the range –10 to 39 %.

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