scholarly journals A complete analytical solution to the integro-differential model describing the nucleation and evolution of ellipsoidal particles

2021 ◽  
Author(s):  
Margarita Nikishina ◽  
Dmitri Alexandrov
Keyword(s):  
Analytical Solution ◽  
Asymptotic Series ◽  
Saddle Point Method ◽  
Supersaturated Solution ◽  
Physical Parameters ◽  
Differential Model ◽  
Ellipsoidal Particles ◽  
Model Equations ◽  
Theory And Experiments ◽  
Good Agreement

In this paper, a complete analytical solution to the integro-differential model describing the nucleation and growth of ellipsoidal crystals in a supersaturated solution is obtained. The asymptotic solution of the model equations is constructed using the saddle-point method to evaluate the Laplace-type integral. Numerical simulations carried out for physical parameters of real solutions show that the first four terms of the asymptotic series give a convergent solution. The developed theory was compared with the experimental data on desupersaturation kinetics in proteins. It is shown that the theory and experiments are in good agreement.

scholarly journals Approximate analytical solution of the integro-differential model of bulk crystallization in a metastable liquid with mass supply (heat dissipation) and crystal withdrawal mechanism

2021 ◽  
Author(s):  
Irina Nizovtseva ◽  
Alexandr Ivanov ◽  
Irina Alexandrova
Keyword(s):  
Distribution Function ◽  
Analytical Solution ◽  
Size Distribution ◽  
Mass Exchange ◽  
Heat Dissipation ◽  
Approximate Analytical Solution ◽  
Size Distribution Function ◽  
Saddle Point Method ◽  
Heat And Mass Exchange ◽  
Differential Model

This paper is devoted to an approximate analytical solution of an integro-differential model describing the process of nucleation and growth of particles in crystallizers, taking into account the thermal-mass exchange with the environment and the removal of product crystals from the metastable medium. The method developed in this work for solving model equations (kinetic equation for the particle size distribution function and balance equations for temperature/impurity concentration) is based on using the saddle point method for calculating the Laplace-type integral. It is shown that the degree of metastability of the liquid decreases with time at a fixed value of the mass inflow from the outside (heat flow to the outside). The crystal size distribution function has the form of an irregular bell-shaped curve, which increases with the intensification of heat and mass exchange with the environment.

The study of acoustic scattering from a single sound-permeable sphere

2018 ◽  
Vol 13 (4) ◽  
pp. 79-91 ◽  
Author(s):  
E.Sh. Nasibullaeva
Keyword(s):  
Speed Of Sound ◽  
Numerical Technique ◽  
Acoustic Scattering ◽  
Computer Time ◽  
Physical Parameters ◽  
Fast Method ◽  
Scattering Field ◽  
Permeable Sphere ◽  
Test Verification ◽  
Good Agreement

The paper presents a generalized mathematical model and numerical investigation of the problem of acoustic scattering from a single sound-permeable sphere during the passage of two types of waves - spherical from a monopole radiation source and a plane one. In solving the Helmholtz equation, a numerical technique based on the fast method of multipoles is used, which allows achieving high accuracy of the results obtained at the lowest cost of computer time. The calculations are compared with known experimental data and a good agreement is obtained. The formulas for calculating the main characteristic of the scattering field (the total scattering cross section) for a sound-permeable sphere are generalized. The effect on this characteristic of the physical parameters of media outside and inside the sphere, such as the density and speed of sound, is shown. A numerical parametric analysis of the pressure distribution around a single sound-permeable sphere for different values of the wave radius, density, and speed of sound of the outer and inner medium of the sphere is carried out. The obtained results will later be used for test verification calculations for the numerical solution of the generalized problem of acoustic scattering of a set of sound-permeable spheres (coaxial or arbitrarily located in space).

scholarly journals Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2452
Author(s):  
Tian Qiao ◽  
Hussein Hoteit ◽  
Marwan Fahs
Keyword(s):  
Analytical Solution ◽  
Storage Site ◽  
Co2 Leakage ◽  
Transient Pressure ◽  
Flow Paths ◽  
Abandoned Wells ◽  
Diffusivity Equation ◽  
Carbon Dioxide Co2 ◽  
Good Agreement

Geological carbon storage is an effective method capable of reducing carbon dioxide (CO2) emissions at significant scales. Subsurface reservoirs with sealing caprocks can provide long-term containment for the injected fluid. Nevertheless, CO2 leakage is a major concern. The presence of abandoned wells penetrating the reservoir caprock may cause leakage flow-paths for CO2 to the overburden. Assessment of time-varying leaky wells is a need. In this paper, we propose a new semi-analytical approach based on pressure-transient analysis to model the behavior of CO2 leakage and corresponding pressure distribution within the storage site and the overburden. Current methods assume instantaneous leakage of CO2 occurring with injection, which is not realistic. In this work, we employ the superposition in time and space to solve the diffusivity equation in 2D radial flow to approximate the transient pressure in the reservoirs. Fluid and rock compressibilities are taken into consideration, which allow calculating the breakthrough time and the leakage rate of CO2 to the overburden accurately. We use numerical simulations to verify the proposed time-dependent semi-analytical solution. The results show good agreement in both pressure and leakage rates. Sensitivity analysis is then conducted to assess different CO2 leakage scenarios to the overburden. The developed semi-analytical solution provides a new simple and practical approach to assess the potential of CO2 leakage outside the storage site. This approach is an alternative to numerical methods when detailed simulations are not feasible. Furthermore, the proposed solution can also be used to verify numerical codes, which often exhibit numerical artifacts.

scholarly journals Thermal ignition of a combustible over an inclined hot plate

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Mixed Convection ◽  
Convection Flow ◽  
Physical Parameters ◽  
Thermal Ignition ◽  
Mixed Convection Flow ◽  
Flow Properties ◽  
Continuous Transformation ◽  
Hot Plate ◽  
Ignition Characteristics ◽  
Good Agreement

AbstractIn this study, the ignition characteristics and the flow properties of the mixed convection flow are presented. Detailed formulations of the forced, natural and mixed convection problems have been discussed. In order to avoid inconvenient switch between the forced and natural convection we introduce a continuous transformation in the mixed convection. We make a comparison between these situations which reveal a good agreement. For mixed convection flow, the ignition distance is explicitly expressed as a function of the Prandtl number, reaction parameter and wall temperature. It has been observed that owing to the increase of the aforesaid parameters, the thermal ignition distance is reduced. Numerical results are illustrated for velocity, temperature, and concentration for different physical parameters. Furthermore, the development of combustion is presented by using streamlines, isotherms and isolines of fuel and oxidizer.

EQUATION OF STATE FOR HOT GLUON PLASMA WITH EFFECTIVE TWO LOOPS

2001 ◽  
Vol 16 (27) ◽  
pp. 1751-1759 ◽  
Author(s):  
XIN WANG ◽  
JIARONG LI ◽  
JUEPING LIU
Keyword(s):  
Equation Of State ◽  
Gluon Plasma ◽  
Physical Parameters ◽  
Finite Width ◽  
Debye Screening ◽  
Debye Mass ◽  
Analytical Results ◽  
Good Agreement ◽  
Hard Thermal Loops

We present analytical results for the equation of state for hot gluon plasma obtained with an effective perturbation based on hard thermal loops resummation theory. The effective two-loop results depend on Debye screening and finite width of gluons as physical parameters. Considering next-to-leading Debye mass and finite width effects, we find the equation of state to be in good agreement with recent lattice results for T≳2T c .

Analytical and Experimental Simulation of Loose Pedestal Dynamic Effects on a Rotating Machine Vibrational Response

1991 ◽  
Author(s):  
Pavel Goldman ◽  
Agnes Muszynska
Keyword(s):  
Excitation Frequency ◽  
Experimental Studies ◽  
Experimental Simulation ◽  
Physical Parameters ◽  
Vibrational Response ◽  
Rotating Machine ◽  
Qualitative Pattern ◽  
The Impact ◽  
Good Agreement ◽  
Periodic Changes

Abstract This report presents experimental, analytical, and numerical results describing vibrational phenomena in a rotating machine with one loose pedestal. The loose-pedestal machine rotor vibrations represent unbalance-related excited vibrations of synchronous and fractional subsynchronous regimes. In this study the loose-pedestal machine is first simulated by a simple vibrating beam excited by a shaker mounted on it. The shaker simulates an unbalanced machine rotor. The beam occasionally enters in contact with the foundation. The excited vibrations are modified by impacting occurrences, and by periodic changes in system stiffness. A new model of the impact has been developed. The results of analytical and experimental studies stand in a good agreement. They illustrate the existence of the synchronous regime and several subsynchronous fractional regimes in various excitation frequency ranges. The analysis adequately predicts the occurrence of these regimes and determines the physical parameters affecting them. The analytical and experimental results are then compared with the responses of experimental rotor rig with one bearing pedestal looseness. They show the same qualitative pattern.

Interaction Between Impeller and Volute of Pumps at Off-Design Conditions

1986 ◽  
Vol 108 (1) ◽  
pp. 12-18 ◽  
Author(s):  
J. A. Lorett ◽  
S. Gopalakrishnan
Keyword(s):  
Analytical Solution ◽  
Flow Behavior ◽  
Cyclic Variation ◽  
Test Results ◽  
Flow Parameters ◽  
Pump Output ◽  
Simplifying Assumptions ◽  
Radial Thrust ◽  
Relative Flow ◽  
Good Agreement

In a centrifugal pump of volute type, the respective characteristics of the impeller and the volute are such that at only one operating point can the flow parameters be constant along the length of the volute. At off-design conditions the mismatching of characteristics causes variations of velocity and pressure along the periphery of the impeller. This in turn forces cyclic variation of the flow in the impeller channels, introduces variations of the inlet incidence and contributes significantly to the direction and the magnitude of the radial thrust. Furthermore, below a certain pump output, a complete flow reversal occurs over a part of the impeller periphery, thus explaining the onset of recirculation. The paper describes the calculation approach used to derive this aspect of the flow behavior. Because of difficulties in obtaining a closed analytical solution, a step by step computation is employed. Beginning with arbitrarily chosen conditions at the volute tongue, the program computes the flow parameters for following segments, using the continuity and the momentum equations, until the exit from the last segment is reached. The inherent unsteadiness of the relative flow in the impeller is explicitly accounted for. Since the inflow and the velocity in the first segment depend upon the exit conditions of the last, the initial input must be modified, and the computation repeated, until the values are compatible with the exit conditions. In spite of several simplifying assumptions, the results of the calculations show very good agreement with published test results.

Numerical Prediction of Turbulent Wakes Behind a Square Cylinder

1998 ◽  
Vol 14 (1) ◽  
pp. 23-29
Author(s):  
Robert R. Hwang ◽  
Sheng-Yuh Jaw
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Cylinder ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Vortex Shedding ◽  
Model Equations ◽  
Good Agreement

ABSTRACTThis paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

scholarly journals Complex Variable Meshless Manifold Method for Elastic Dynamic Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfen Gao ◽  
Gaofeng Wei
Keyword(s):  
Analytical Solution ◽  
Complex Variable ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Least Square ◽  
Dynamic Problems ◽  
Finite Covering ◽  
Moving Least Square ◽  
Elastic Dynamics ◽  
Good Agreement

Combining the finite covering technical and complex variable moving least square, the complex variable meshless manifold method can handle the discontinuous problem effectively. In this paper, the complex variable meshless method is applied to solve the problem of elastic dynamics, the complex variable meshless manifold method for dynamics is established, and the corresponding formula is derived. The numerical example shows that the numerical solutions are in good agreement with the analytical solution. The CVMMM for elastic dynamics and the discrete forms are correct and feasible. Compared with the traditional meshless manifold method, the CVMMM has higher accuracy in the same distribution of nodes.

scholarly journals DYNAMIC BEHAVIOR OF REINFORCED CONCRETE COLUMN UNDER ACCIDENTAL IMPACT

2021 ◽  
Vol 17 (3) ◽  
pp. 120-131
Author(s):  
Sergey Savin ◽  
Vitaly Kolchunov
Keyword(s):  
Reinforced Concrete ◽  
Analytical Solution ◽  
High Speed ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Shock Load ◽  
Dynamic Factor ◽  
Physical Parameters ◽  
Concrete Column ◽  
Reinforced Concrete Column

The analysis of scientific literature shows that to date, the physical parameters of the deformation of reinforced concrete bar structures during their dynamic buckling and the influence of the dissipative properties of the structural system on this process remain insufficiently studied. In this regard, the paper proposes an analytical solution to the problem of dynamic buckling of a reinforced concrete column when it is loaded with an impact load, taking into account the presence of initial geometric and (or) physical imperfections and damping properties of the system, as well as an analysis and assessment of the column deformationparameters based on the obtained analytical solution. An expression for the dynamic deflection of a bar element under its axial loading with a high-speed shock load, taking into account damping, is obtained in an analytical form. For practical calculations in a quasi-static formulation, the paper proposes an expression for the dynamic factor kd of bar structures under axial shock load. A numerical example of calculating a reinforced concrete column using the obtained analytical expressions with and without damping is considered. It was found that the maximum deflection of the elastic axis of the column under high-speed loading was achieved at t = 0.04 s. In this case, the total dynamic deflection taking into account damping was 4.8% less than the deviation without taking into account damping and 1.18 times more than the corresponding static value.

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