Eulerian Multi-Fluid Model of Air Blast Atomization

2006 ◽  
Author(s):  
Srimani Bhamidipati ◽  
Mahesh Panchagnula ◽  
John Peddieson
Keyword(s):  
Closed Form ◽  
Recurrence Relations ◽  
Model Problem ◽  
Fluid Model ◽  
Closed Form Solution ◽  
Fluid Phase ◽  
Form Solution ◽  
Air Blast ◽  
Carrier Fluid ◽  
Selection Of

The application of fully Eulerian "multi-fluid" models to air blast atomization is discussed. Such models envision the system as consisting one carrier fluid phase and multiple drop phases, each having a discrete size. A model problem is formulated which allows a general closed form solution in terms of recurrence relations. This closed form solution is employed to produce representative results. A selection of these is used to illustrate interesting aspects of the predictions.

Stochastic Dynamic Response of a Simplified Nonlinear Fluid Model for Viscoelastic Materials

2012 ◽  
Vol 28 (2) ◽  
pp. 365-372 ◽  
Author(s):  
T.-P. Chang
Keyword(s):  
Dynamic Response ◽  
Closed Form ◽  
Fluid Model ◽  
Closed Form Solution ◽  
Mean Value ◽  
Form Solution ◽  
Stochastic Dynamic ◽  
Viscoelastic Materials ◽  
Viscoelastic Modeling ◽  
Nonlinear Fluid

AbstractIn the present study, we propose a simplified nonlinear fluid model to characterize the complex nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been utilized by many researchers to simulate some parts of human body in bioengineering and to represent many material properties in mechanical engineering, electronic engineering and construction engineering. Occasionally it is almost impossible to evaluate the constant parameters in the model in the deterministic sense, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to model the stochastic properties of the viscoelastic materials. After some transformations, the closed-form solution can be obtained for the mean value of the displacement of the simplified nonlinear fluid model, subjected to constant rate of displacement. Based on the closed-form solution, the proposed method generates the stochastic dynamic response of the simplified nonlinear model, which plays an important role in performing the reliability analysis of the nonlinear system.

scholarly journals Acoustic Wave Propagation in a Trifurcated Lined Waveguide

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Ayub ◽  
M. H. Tiwana ◽  
A. B. Mann ◽  
H. Zaman
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Closed Form ◽  
Integral Transform ◽  
Closed Form Solution ◽  
Form Solution ◽  
Kernel Functions ◽  
Acoustic Wave Propagation ◽  
Proper Selection ◽  
Selection Of

The diffraction of sound from a semi-infinite soft duct is investigated. The soft duct is symmetrically located inside an acoustically lined but infinite duct. A closed-form solution is obtained using integral transform and Jones' method based on Wiener-Hopf technique. The graphical results are presented, which show how effectively the unwanted noise can be reduced by proper selection of different parameters. The kernel functions are factorized with different approaches. The results may be used to design acoustic barriers and noise reduction devices.

Analytical Study of Reachable Workspace for 2-RPR Planar Parallel Mechanisms

2012 ◽  
Author(s):  
Mahdi Agheli ◽  
Stephen S. Nestinger ◽  
Robert L. Norton
Keyword(s):  
Closed Form ◽  
Analytical Study ◽  
Structural Parameters ◽  
Closed Form Solution ◽  
High Accuracy ◽  
Form Solution ◽  
Parallel Mechanisms ◽  
Design And Optimization ◽  
Reachable Workspace ◽  
Selection Of

In both planar and spatial parallel mechanisms, selection of the structural parameters for a desired workspace generally employs the use of numerical methods. However, using the closed-form solution, if it exists, facilitates workspace-based design and optimization of the mechanism, and may significantly reduce the required time and calculation for finding the workspace of the mechanism. This paper presents a general and comprehensive closed-form solution for the reachable workspace of a 2-RPR planar parallel mechanism. The workspace of the mechanism is analyzed step-by-step in detail and its boundary is derived analytically. Since the solution is closed-form, it has high accuracy and reliability. Furthermore, the provided solution can be employed to solve the workspace of similar mechanisms in a closed-form manner including other n-RPR planar parallel mechanisms.

scholarly journals A Designer’s Approach for Estimation of Nuclear-Air-Blast-Induced Ground Motion

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Shashank Pathak ◽  
G. V. Ramana
Keyword(s):  
Closed Form ◽  
Stress Wave ◽  
Field Data ◽  
Wave Attenuation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Ground Displacement ◽  
Air Blast ◽  
Proposed Model ◽  
Stress Dependent

A reliable estimate of free-field ground displacement induced by nuclear-air-blast is required for design of underground strategic structures. A generalized pseudostatic formulation is proposed to estimate nuclear-air-blast-induced ground displacement that takes into account nonlinear stress-strain behaviour of geomaterials, stress-dependent wave propagation velocity, and stress wave attenuation. This proposed formulation is utilized to develop a closed-form solution for linearly decaying blast load applied on a layered ground medium with bilinear hysteretic behaviour. Parametric studies of closed-form solution indicated that selection of appropriate constrained modulus consistent with the overpressure is necessary for an accurate estimation of peak ground displacement. Stress wave attenuation affects the computed displacement under low overpressure, and stress-dependent wave velocity affects mainly the occurrence time of peak displacement and not its magnitude. Further, peak displacements are estimated using the proposed model as well as the UFC manual and compared against the field data of atmospheric nuclear test carried out at Nevada test site. It is found that the proposed model is in good agreement with field data, whereas the UFC manual significantly underestimates the peak ground displacements under higher overpressures.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

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