Analytical Model for the Deformation of Viscoelastic Non-Newtonian Drops Undergoing Secondary Atomization

2016 ◽  
Author(s):  
Sharon E. Snyder ◽  
Varun Kulkarni ◽  
Paul E. Sojka
Keyword(s):  
Analytical Model ◽  
Xanthan Gum ◽  
Experimental Results ◽  
Analytical Models ◽  
Drop Diameter ◽  
Droplet Deformation ◽  
Secondary Atomization ◽  
Starting Point ◽  
Breakup Model ◽  
Xanthan Gum Solution

While there is no single analytical model that accurately predicts all stages and modes of secondary atomization, many groups have developed models that predict deformation and oscillation of a single, isolated drop. The TAB (Taylor Analogy Breakup) model was chosen for this investigation, mainly due to its widespread use by Liu and Reitz [1], Hwang et al. [2], Tanner [3], and Lee and Reitz [4], among others. Since the TAB model is also the foundation for many other analytical models, it will also be used here as a starting point for the development of a viscoelastic non-Newtonian model to predict droplet deformed radii, droplet deformation time, and velocity at deformation time for viscoelastic xanthan gum - DI water solutions. Three additional improvements are made to this viscoelastic TAB model: the first is a change to a TAB coefficient; the second to the equation for the drag coefficient, and the third modification is to the breakup criterion. This model uses Carreau rheology and Zimm relaxation time. Non-dimensional drop diameter and initiation times are plotted against We; model results are compared to experimental results for a range of xanthan gum solution concentrations. Results show fair agreement between experimental results and model results for non-dimensional drop diameter, with the best match at low XG concentration and low-to-medium We (10–30). It was also noted that increased viscoelasticity seems to increase this drop diameter. Good agreement between experimental data and model results has been seen for initiation time, with increased viscoelasticity increasing this parameter as well.

Analytical Model of Post-Impact Droplet Spreading on a Micro-Patterned Superhydrophobic Surface With Surface Slip

2014 ◽  
Author(s):  
Cristian E. Clavijo ◽  
Julie Crockett ◽  
Daniel Maynes
Keyword(s):  
Analytical Model ◽  
Contact Angles ◽  
Superhydrophobic Surfaces ◽  
Analytical Models ◽  
Impact Behavior ◽  
Droplet Deformation ◽  
Droplet Spreading ◽  
Surface Slip ◽  
Classical Energy ◽  
Dynamical Parameters

Several analytical models exist to predict droplet impact behavior on superhydrophobic surfaces. However, no previous model has rigorously considered the effect of surface slip on droplet spreading and recoiling that is inherent in many superhydrophobic surfaces. This paper presents an analytical model that takes into account surface slip at the solid-fluid interface during droplet deformation. The effects of slip are captured in terms that model the kinetic energy and viscous dissipation and are compared to a classical energy conservation model given by Attane et al. and experimental data from Pearson et al. A range of slip lengths, Weber numbers, Ohnesorge numbers, and contact angles are investigated to characterize the effects of slip over the entire range of realizable conditions. We find that surface slip does not influence normalized maximum spread diameter for low We but can cause a significant increase for We > 100. Surface slip affects dynamical parameters more profoundly for low Oh numbers (0.002–0.01). Normalized residence time and rebound velocity increase as slip increases for the same range of We and Oh. The influence of slip is more significantly manifested on normalized rebound velocity than normalized maximum spread diameter. Contact angles in the range of 150°–180° do not affect impact dynamics significantly.

Comparison of Analytical Models of Force Prediction during Dynamic Bending Stage for 3-Roller Conical Bending Process

2014 ◽  
Vol 1016 ◽  
pp. 150-155
Author(s):  
Mahesh Chudasama ◽  
Harit K. Raval
Keyword(s):  
Shear Stress ◽  
Analytical Model ◽  
Optimum Design ◽  
Experimental Results ◽  
Analytical Models ◽  
Force Prediction ◽  
Bending Force ◽  
Bending Process ◽  
Dynamic Bending ◽  
Bottom Roller

Conical bending process using three rollers with different configurations is a widely used process for manufacturing conical sections and shells in the industries. The process involves static as well dynamic stages. For optimum design of the machine, accurate analytical model of the force prediction is required for static as well dynamic bending stages. In this paper the analytical models considering three different stress conditions have been compared with the experimental results. The observations of the comparison have been reported. It is concluded that for higher bottom roller inclination, the shear stress has to be considered for evaluation of bending force whereas for lower bottom roller inclination it can be neglected.

scholarly journals Modeling the Effect of Imperfections in Glassblown Micro-Wineglass Fused Quartz Resonators

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Yusheng Wang ◽  
Mohammad H. Asadian ◽  
Andrei M. Shkel
Keyword(s):  
Analytical Model ◽  
Mechanical Quality Factor ◽  
Experimental Results ◽  
Analytical Models ◽  
Thin Shells ◽  
Frequency Mismatch ◽  
Fused Quartz ◽  
Mechanical Quality ◽  
Quartz Resonators ◽  
Thermal Reflow

In this paper, we developed an analytical model, supported by experimental results, on the effect of imperfections in glassblown micro-wineglass fused quartz resonators. The analytical model predicting the frequency mismatch due to imperfections was derived based on a combination of the Rayleigh's energy method and the generalized collocation method. The analytically predicted frequency of the n = 2 wineglass mode shape was within 10% of the finite element modeling results and within 20% of the experimental results for thin shells, showing the fidelity of the predictive model. The postprocessing methods for improvement of the resonator surface quality were also studied. We concluded that the thermal reflow of fused quartz achieves the best result, followed in effectiveness by the RCA-1 surface treatment. All the analytical models developed in this paper are to guide the manufacturing methods to reduce the frequency and damping mismatch, and to increase the mechanical quality factor of the device.

scholarly journals Generalized analytical model based on harmonic coupling for hybrid plasmonic modes: comparison with numerical and experimental results

2015 ◽  
Vol 23 (21) ◽  
pp. 27376 ◽  
Author(s):  
Mitradeep Sarkar ◽  
Jean-François Bryche ◽  
Julien Moreau ◽  
Mondher Besbes ◽  
Grégory Barbillon ◽  
...  
Keyword(s):  
Analytical Model ◽  
Experimental Results ◽  
Model Based

scholarly journals Comparison of Experimental and Numerical Transient Drop Deformation during Transition through Orifices in High-Pressure Homogenizers

2021 ◽  
Vol 5 (3) ◽  
pp. 32
Author(s):  
Benedikt Mutsch ◽  
Peter Walzel ◽  
Christian J. Kähler
Keyword(s):  
High Pressure ◽  
Visual Analysis ◽  
Imaging Technique ◽  
Extensional Flow ◽  
Droplet Breakup ◽  
Experimental Results ◽  
Drop Deformation ◽  
Droplet Deformation ◽  
Shadow Imaging ◽  
Good Agreement

The droplet deformation in dispersing units of high-pressure homogenizers (HPH) is examined experimentally and numerically. Due to the small size of common homogenizer nozzles, the visual analysis of the transient droplet generation is usually not possible. Therefore, a scaled setup was used. The droplet deformation was determined quantitatively by using a shadow imaging technique. It is shown that the influence of transient stresses on the droplets caused by laminar extensional flow upstream the orifice is highly relevant for the droplet breakup behind the nozzle. Classical approaches based on an equilibrium assumption on the other side are not adequate to explain the observed droplet distributions. Based on the experimental results, a relationship from the literature with numerical simulations adopting different models are used to determine the transient droplet deformation during transition through orifices. It is shown that numerical and experimental results are in fairly good agreement at limited settings. It can be concluded that a scaled apparatus is well suited to estimate the transient droplet formation up to the outlet of the orifice.

scholarly journals Novel Structure and Thermal Design and Analysis for CubeSats in Formation Flying

Aerospace ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 150
Author(s):  
Yeon-Kyu Park ◽  
Geuk-Nam Kim ◽  
Sang-Young Park
Keyword(s):  
Analytical Model ◽  
Formation Flying ◽  
Thermal Environment ◽  
Thermal Analyses ◽  
Thermal Design ◽  
Analytical Models ◽  
Test Results ◽  
Solar Panels ◽  
Novel Structure ◽  
Micro Propulsion

The CANYVAL-C (CubeSat Astronomy by NASA and Yonsei using a virtual telescope alignment for coronagraph) is a space science demonstration mission that involves taking several images of the solar corona with two CubeSats—1U CubeSat (Timon) and 2U CubeSat (Pumbaa)—in formation flying. In this study, we developed and evaluated structural and thermal designs of the CubeSats Timon and Pumbaa through finite element analyses, considering the nonlinearity effects of the nylon wire of the deployable solar panels installed in Pumbaa. On-orbit thermal analyses were performed with an accurate analytical model for a visible camera on Timon and a micro propulsion system on Pumbaa, which has a narrow operating temperature range. Finally, the analytical models were correlated for enhancing the reliability of the numerical analysis. The test results indicated that the CubeSats are structurally safe with respect to the launch environment and can activate each component under the space thermal environment. The natural frequency of the nylon wire for the deployable solar panels was found to increase significantly as the wire was tightened strongly. The conditions of the thermal vacuum and cycling testing were implemented in the thermal analytical model, which reduced the differences between the analysis and testing.

Convective Losses From Cavity Solar Receivers—Comparisons Between Analytical Predictions and Experimental Results

1983 ◽  
Vol 105 (1) ◽  
pp. 29-33 ◽  
Author(s):  
A. M. Clausing
Keyword(s):  
Experimental Data ◽  
Experimental Evidence ◽  
Analytical Model ◽  
Excellent Agreement ◽  
Experimental Results ◽  
Simple Analytical Model ◽  
Refined Model ◽  
Wall Area

Cavity solar receivers are generally believed to have higher thermal efficiencies than external receivers due to reduced losses. A simple analytical model was presented by the author which indicated that the ability to heat the air inside the cavity often controls the convective loss from cavity receivers. Thus, if the receiver contains a large amount of inactive hot wall area, it can experience a large convective loss. Excellent experimental data from a variety of cavity configurations and orientations have recently become available. These data provided a means of testing and refining the analytical model. In this manuscript, a brief description of the refined model is presented. Emphasis is placed on using available experimental evidence to substantiate the hypothesized mechanisms and assumptions. Detailed comparisons are given between analytical predictions and experimental results. Excellent agreement is obtained, and the important mechanisms are more clearly delineated.

scholarly journals Development of Permeability Models for Saturated Fluid Flow across Arrays of Fibre Clusters

2002 ◽  
Vol 11 (3) ◽  
pp. 096369350201100
Author(s):  
E.M. Gravel ◽  
T.D. Papathanasiou
Keyword(s):  
Analytical Models ◽  
Dual Porosity ◽  
Hydraulic Permeability ◽  
Fibrous Media ◽  
Fibre Bundles ◽  
Hexagonal Packing ◽  
Composites Manufacturing ◽  
Starting Point ◽  
Wide Range ◽  
Flow Through

Dual porosity fibrous media are important in a number of applications, ranging from bioreactor design and transport in living systems to composites manufacturing. In the present study we are concerned with the development of predictive models for the hydraulic permeability ( Kp) of various arrays of fibre bundles. For this we carry out extensive computations for viscous flow through arrays of fibre bundles using the Boundary Element Method (BEM) implemented on a multi-processor computer. Up to 350 individual filaments, arranged in square or hexagonal packing within bundles, which are also arranged in square of hexagonal packing, are included in each simulation. These are simple but not trivial models for fibrous preforms used in composites manufacturing – dual porosity systems characterised by different inter- and intra-tow porosities. The way these porosities affect the hydraulic permeability of such media is currently unknown and is elucidated through our simulations. Following numerical solution of the governing equations, ( Kp) is calculated from the computed flowrate through Darcy's law and is expressed as function of the inter- and intra-tow porosities (φ, φt) and of the filament radius ( Rf). Numerical results are also compared to analytical models. The latter form the starting point in the development of a dimensionless correlation for the permeability of such dual porosity media. It is found that the numerically computed permeabilities follow that correlation for a wide range of φ i, φt and Rf.

The effects of geometric offsets on the dynamic responses of a Scott—Russell amplifying mechanism with flexible hinges

2009 ◽  
Vol 223 (10) ◽  
pp. 2413-2423 ◽  
Author(s):  
C-M Chen ◽  
R-F Fung
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Dynamic Responses ◽  
Analytical Models ◽  
Dynamic Equations ◽  
Magnification Factor ◽  
Flexure Hinges ◽  
Magnification Factors ◽  
Straight Line ◽  
Deviation Factor

The dynamic equations of a micro-positioning Scott—Russell (SR) mechanism associated with two flexible hinges and an offset are developed to calculate output responses. Both rigid and flexible hinges are considered to explore the results. The main features in the kinematics of the SR mechanism are its displacement amplification and straight-line motion, which are widely needed in practical industries. The manufacturing inaccuracy of the SR mechanism definitely causes geometric offsets of flexure hinges, and affects displacement amplification and straight-line output motion. Analytical models based on kinematics and Hamilton's principle are derived to explore the variation of linearity ratio, magnification factor, and deviation factor due to various offsets and link lengths. From numerical simulations for the SR mechanism with various offsets of flexible hinges in the conditions of different link lengths, it is found that offsets of flexure hinges obviously affect the amplifying factor and linearity ratio, and appear to dominate the changes of magnification factors. Moreover, an analytical model is also used to predict magnification factors due to various offsets. Finally, some conclusions concerning the effects of offset on the performance of the SR mechanism are drawn.

Modeling of residual stresses by correlating surface topography in machining of AISI 52100 steel

2021 ◽  
pp. 1-26
Author(s):  
Chao Liu ◽  
Yan He ◽  
Yufeng Li ◽  
Yulin Wang ◽  
Shilong Wang ◽  
...  
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Cutting Force ◽  
Surface Topography ◽  
Analytical Model ◽  
Analytical Models ◽  
Workpiece Surface ◽  
Dynamic Cutting Force ◽  
Intermittent Cutting ◽  
Effect Of Surface

Abstract The residual stresses could affect the ability of components to bear loading conditions and also the performance. The researchers considered workpiece surface as a plane and ignored the effect of surface topography induced by the intermittent cutting process when modeling residual stresses. The aim of this research develops an analytical model to predict workpiece residual stresses during intermittent machining by correlating the effect of surface topography. The relative motions of tool and workpiece are analyzed for modeling thermal-mechanical and surface topography. The influence of dynamic cutting force and thermal on different positions of surface topography is also considered in analytical model. Then the residual stresses model with the surface topography effect can be developed in intermittent cutting. The analytical models of dynamic cutting force, surface topography and residual stresses are verified by the experiments. The variation trend of evaluated values of the residual stress of workpiece is basically consistent with that of measured values. The compressive residual stress of workpiece surface in highest point of the surface topography are higher than that in the lowest point.

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