Initial Stage of Natural Convection Over a Hot Aerosol Sphere

2006 ◽  
Vol 129 (6) ◽  
pp. 695-701
Author(s):  
Elaad Mograbi ◽  
Ezra Bar-Ziv
Keyword(s):  
Prandtl Number ◽  
Linear Process ◽  
Navier Stokes ◽  
Transient Temperature ◽  
Square Root ◽  
Analytical Treatment ◽  
Initial Development ◽  
Initial Flow ◽  
Linear Solution ◽  
Initial Stage

Background: Analytical study is presented on the transient problem of buoyancy-induced motion due to the presence of a hot aerosol sphere in unbounded quiescent fluid. Method of Approach: Because the initial flow field is identically zero, the initial stage of the process is governed by viscous and buoyancy forces alone where the convective inertial terms in the momentum and energy balances are negligible, i.e., the initial development of the field is a linear process. The previous statement is examined by analyzing the scales of the various terms in the Navier-Stokes and energy equations. This scale analysis gives qualitative limitations on the validity of the linear approximation. A formal integral solution is obtained for arbitrary Prandtl number and for transient temperature field. Results: We consider, in detail, the idealized case of vanishing Prandtl number for which the thermal field is developed much faster than momentum. In this case, analytical treatment is feasible and explicit expressions for the field variables and the drag acting on the particle are derived. Detailed quantitative analysis of the spatial and temporal validity of the solution is also presented. Conclusions: The linear solution is valid throughout space for t<10 diffusion times. For t>10, an island in space appears in which inertial effects become dominant. The transient process is characterized by two different time scales: for short times, the development of the field is linear, while for small distances from the sphere and finite times, it is proportional to the square root of time. The resultant drag force acting on the sphere is proportional to the square root of time throughout the process.

scholarly journals Stochastic Analysis of Natural Convection in Vertical Channels with Random Wall Temperature

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Ryoichi Chiba
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Random Process ◽  
Wall Temperature ◽  
Correlation Time ◽  
Channel Wall ◽  
Velocity Fields ◽  
Transient Temperature ◽  
Horizontal Distance ◽  
Mean Square

This study attempts to derive the statistics of temperature and velocity fields of laminar natural convection in a heated vertical channel with random wall temperature. The wall temperature is expressed as a random function with respect to time, or a random process. First, analytical solutions of the transient temperature and flow velocity fields for an arbitrary temporal variation in the channel wall temperature are obtained by the integral transform and convolution theorem. Second, the autocorrelations of the temperature and velocity are formed from the solutions, assuming a stationarity in time. The mean square values of temperature and velocity are computed under the condition that the fluctuation in the channel wall temperature can be considered as white noise or a stationary Markov process. Numerical results demonstrate that a decrease in the Prandtl number or an increase in the correlation time of the random process increases the level of mean square velocity but does not change its spatial distribution tendency, which is a bell-shaped profile with a peak at a certain horizontal distance from the channel wall. The peak position is not substantially affected by the Prandtl number or the correlation time.

scholarly journals Choice and Limits of a Fluid Model for the Numerical Study in Dynamic Fluid Structure Interaction Problems

2003 ◽  
Author(s):  
Jean Franc¸ois Sigrist ◽  
Christian Laine ◽  
Dominique Lemoine ◽  
Bernard Peseux
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Model ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Linear Solution ◽  
Fluid Structure ◽  
Design Engineers ◽  
Inviscid Incompressible Fluid ◽  
Basic Fluid

This paper is related to the study of a nuclear propulsion reactor prototype for the French Navy. This prototype is built on ground and is to be dimensioned toward seismic loading. The dynamic analysis takes the coupled fluid structure analysis into account. The basic fluid models used by design engineers are inviscid incompressible or compressible. The fluid can be described in a bidimensional by slice or a three-dimensional approach. A numerical study is carried out on a generic problem for the linear FSI dynamic problem. The results of this study are presented and discussed. As a conclusion, the three-dimensional inviscid incompressible fluid appears to be the best compromise between the description of physical phenomena and the cost of modeling. The geometry of the reactor is such that large displacements of the structure in the fluid can occur. Therefore, the linearity hypothesis might not be longer valid. The case of large amplitude imposed oscillating motion of a cylinder in a confined fluid is numerically studied. A CFD code is used to investigate the fluid behavior solving the NAVIER-STOKES equations. The forces induced on the cylinder by the fluid are computed and compared to the linear solution. The limit of the linear model can then be exhibited.

Natural convection flow far from a horizontal plate

1999 ◽  
Vol 387 ◽  
pp. 227-254 ◽  
Author(s):  
VALOD NOSHADI ◽  
WILHELM SCHNEIDER
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
The Self ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Self Similar ◽  
Similar Solutions

Plane and axisymmetric (radial), horizontal laminar jet flows, produced by natural convection on a horizontal finite plate acting as a heat dipole, are considered at large distances from the plate. It is shown that physically acceptable self-similar solutions of the boundary-layer equations, which include buoyancy effects, exist in certain Prandtl-number regimes, i.e. 0.5<Pr[les ]1.470588 for plane, and Pr>1 for axisymmetric flow. In the plane flow case, the eigenvalues of the self-similar solutions are independent of the Prandtl number and can be determined from a momentum balance, whereas in the axisymmetric case the eigenvalues depend on the Prandtl number and are to be determined as part of the solution of the eigenvalue problem. For Prandtl numbers equal to, or smaller than, the lower limiting values of 0.5 and 1 for plane and axisymmetric flow, respectively, the far flow field is a non-buoyant jet, for which self-similar solutions of the boundary-layer equations are also provided. Furthermore it is shown that self-similar solutions of the full Navier–Stokes equations for axisymmetric flow, with the velocity varying as 1/r, exist for arbitrary values of the Prandtl number.Comparisons with finite-element solutions of the full Navier–Stokes equations show that the self-similar boundary-layer solutions are asymptotically approached as the plate Grashof number tends to infinity, whereas the self-similar solution to the full Navier–Stokes equations is applicable, for a given value of the Prandtl number, only to one particular, finite value of the Grashof number.In the Appendices second-order boundary-layer solutions are given, and uniformly valid composite expansions are constructed; asymptotic expansions for large values of the lateral coordinate are performed to study the decay of the self-similar boundary-layer flows; and the stability of the jets is investigated using transient numerical solutions of the Navier–Stokes equations.

scholarly journals Conjugate Solutions of Navier-Stokes Equation with Deformed Pore Structure

2014 ◽  
Vol 8 ◽  
pp. 30-48
Author(s):  
V.I. Popkov ◽  
V.I. Astafiev ◽  
V.P. Shakshin ◽  
S.V. Zatsepina
Keyword(s):  
Stokes Equation ◽  
Deformation Theory ◽  
Cluster Structure ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Porous Space ◽  
Navier Stokes Equation ◽  
Linear Solution ◽  
Regional Problems ◽  
Final Speed

Within the framework of block self-organizing of geological bodies with use of deformation theory the mathematical solution of a problem for effective final speed is proposed. The analytical and numerical integrated solutions of Navier-Stokes equation for deformable porous space were obtained. The decisions of multi-scaled regional problems «on a flow basis» were also presented: from lithology of rock space - to a well and from a well - to petro-physics. The evolutionary transformation of the linear solution of the equation on mass conservation up to the energetically stable non-linear solution of the equation on preserving the number of movements is also offered. Basing upon the analytical solution of Navier-Stokes equation and model of A.N. Kolmogorov we have obtained the energy model of turbulence pulsing controlled chaos, conjugated with risk stability of average well inflow and cluster structure of Earth defluidization.

pRTA (Probe Recovery Temperature Anemometry)

Volume 1 ◽  
2004 ◽  
Author(s):  
Masahiro Ishibashi
Keyword(s):  
Prandtl Number ◽  
Flow Velocity ◽  
Contact Point ◽  
Recovery Factor ◽  
Angle Of Incidence ◽  
Square Root ◽  
Critical Nozzle ◽  
Axis Of Symmetry ◽  
Thermocouple Wire ◽  
Recovery Temperature

It is shown that the recovery temperature measured by a thin thermocouple wire inserted in airflow does not depend on the angle of incidence of the flow onto the wire and agrees very well with the theoretical value assuming the recovery factor of the square root of the Prandtl number. This fact allows RTA (Recovery Temperature Anemometry) employing a sensor of various structures; pRTA (probe RTA) is one of the examples where the thermocouple wire is bent at its contact point forming the probe apex. The paper demonstrates that pRTA measures the same flow velocity distributions in a critical nozzle as those by sRTA (streamwise RTA) where a thermocouple wire is settled parallel to the axis of symmetry of the nozzle.

scholarly journals NUMERICAL AND EXPERIMENTAL STUDY OF DAM-BREAK FLOOD PROPAGATION AND ITS IMPLICATION TO SEDIMENT EROSION

2012 ◽  
Vol 1 (33) ◽  
pp. 7
Author(s):  
Hung-Chu Hsu ◽  
A. Torres-Freyermuth ◽  
Tian-Jian Hsu ◽  
Hwung-Hweng Hwung
Keyword(s):  
Free Surface ◽  
Sediment Transport ◽  
Numerical Model ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Transport Processes ◽  
Dam Break ◽  
Navier Stokes ◽  
Suspended Sediment Transport ◽  
Initial Stage

Regarding the hydrodynamics, within the past two decades it has become popular in numerical modeling of free-surface flow to adopt a Reynolds-averaged Navier-Stokes approach, where the volume of fluid (VOF) method is utilized to track the evolution of free-surface. However, this robust numerical model has not been widely applied to the study of sediment transport processes. In this study, we shall extend the numerical model to simulate suspended sediment transport and study the erosion pattern during the initial stage of the dam break flow. We also conducted a series of experiments in a horizontal channel of rectangular section and recorded the snap shots of surface profiles of a dam- break wave during the initial stage of dam-break. Measured data is utilized here to study the hydrodynamics and to validate the numerical model.

scholarly journals A semi-implicit multiple-nested grid model for simulation of flow in a tropical storm

MAUSAM ◽  
2021 ◽  
Vol 47 (1) ◽  
pp. 1-20
Author(s):  
J.C. MANDAL
Keyword(s):  
Surface Friction ◽  
Tropical Storm ◽  
Implicit Scheme ◽  
Time Step ◽  
Fine Grid ◽  
Initial Development ◽  
Stage Of Development ◽  
Initial Stage ◽  
Grid Length ◽  
Grid Mesh

ABSTRACT .A three-layer three-dimensional, triply-nested primitive equation model. suitable to simulate tropical storm, has been designed. A grid telescopic technique has been used with a fine grid mesh of 18 km grid length in the centre which is surrounded by a medium mesh of 54 km grid length; this is again surrounded by a course grid mesh of 162 km grid length. Each mesh consists of 32 X 32 array of momentum points enclosing 31 X 31 array of mass points. The variables are staggered in space which reduces the amount of averaging to a minimum and hence improves accuracy. To suppress non-linear instability an improved finite difference scheme has been applied. A two-way interaction method has been adopt to match the solutions between grids of different lengths. To increase the time step for integration, a semi-implicit scheme has been used. The speed of the solution of the system of Helmholtz equations arising out of semi-implicit scheme has been appreciably increased by devising an iterative method. To examine the role of surface friction as postulated by Yamasaki (1977) and forced subsidence as hypothesized by Arnold (1977), Gray (1977) and Yanai (1961) at the initial stage of development of a tropical storm. numerical experiments have been accomplished with this model varying coefficient of surface drag. and specifying heat around the centre of the to disturbance which is considered as the effect of forced subsidence through an analytical function similar to one used by Harrison (1973). The integration was started from a weak barotropic vortex in &r8dient balance en and continued for 48 hours in two cases and 60 hours in one case. It is observed that surface friction may not be an essential factor at the initial stage of development of tropical storm when the vortex is weak. On the  other  hand, initial development could be initiated by forced subsidence. But in the subsequent stage, surface friction plays an important role to induce mass convergence in the boundary layer and to reduce horizontal of the disturbance. This preliminary experiment has yielded smooth and encouraging results.    

Nonlinear Behavior of Micro Bubbles Under Ultrasound Due to Heat Transfer

2007 ◽  
Author(s):  
Chansoo Im ◽  
Jeong Eun Kim ◽  
Jae Young Lee ◽  
Ho-Young Kwak
Keyword(s):  
Heat Transfer ◽  
Volume Change ◽  
Stokes Equations ◽  
Nonlinear Behavior ◽  
Navier Stokes ◽  
Bubble Wall ◽  
Analytical Treatment ◽  
Navier Stokes Equations ◽  
Ideal Gases ◽  
Lost Work

Nonlinear behavior of a microbubble under ultrasound was investigated with consideration of heat transfer inside bubble and through the bubble wall. The polytropic relation which has been used for the process of volume change of ideal gases cannot properly treat the heat transfer involving the oscillating bubble under ultrasound. In this study, the heat transfer related to the motion of the bubble under ultrasound, which is affected by heat transfer across the bubble wall crucially was investigated by a set of solutions of the Navier-Stokes equations for the gas inside the bubble and an analytical treatment of the Navier-Stokes equations for the liquid adjacent to the bubble wall. The entropy generation due to finite heat transfer, which induces the lost work during bubble evolution, reduces the collapsing process, and affects the nonlinear behavior of bubble considerably.

A BGK model for small Prandtl number in the Navier-Stokes approximation

1993 ◽  
Vol 71 (1-2) ◽  
pp. 191-207 ◽  
Author(s):  
Fran�ois Bouchut ◽  
Beno�t Perthame
Keyword(s):  
Prandtl Number ◽  
Navier Stokes ◽  
Bgk Model ◽  
Stokes Approximation

scholarly journals Effects of nickel on the fern Regnellidium diphyllum Lindm. (Marsileaceae)

2012 ◽  
Vol 72 (4) ◽  
pp. 807-811 ◽  
Author(s):  
MA. Kieling-Rubio ◽  
A. Droste ◽  
PG. Windisch
Keyword(s):  
Aquatic Macrophytes ◽  
Natural Habitat ◽  
Southern Brazil ◽  
Rio Grande Do Sul ◽  
Initial Development ◽  
Stage Of Development ◽  
Primary Roots ◽  
Initial Stage ◽  
Essential Nutrient ◽  
Agricultural Areas

The heterosporous fern Regnellidium diphyllum occurs in southern Brazil and some adjoining localities in Uruguay and Argentina. Currently it is on the list of threatened species in the state of Rio Grande do Sul. Anthropic alterations such as the conversion of wetlands into agricultural areas or water and soil contamination by pollutants may compromise the establishment and survival of this species. Nickel (Ni) is an essential nutrient for plants but increasing levels of this metal due to pollution can cause deleterious effects especially in aquatic macrophytes. Megaspore germination tests were performed using Meyer's solution, at concentrations of 0 (control), 0.05, 0.5, 1, 5, 10, 20, 30, 50 and 100 mg L-1 of Ni. The initial development of apomictic sporophytes was studied using solutions containing 0 (control) to 4.8 mg L-1 of Ni. A significant negative relation was observed between the different Ni concentrations and the megaspore germination/sporophyte formation rates. Primary roots, primary leaves and secondary leaves were significantly shorter at 3.2 and 4.8 mg L-1 of Ni, when compared with the treatment without this metal. At 4.8 mg L-1, leaves also presented chlorosis and necrosis. The introduction of pollutants with Ni in the natural habitat of Regnellidium diphyllum may inhibit the establishment of plants in the initial stage of development, a problem to be considered in relation to the conservation of this species.

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