scholarly journals Gravity-driven film flow down a uniformly heated smoothly corrugated rigid substrate

2021 ◽  
Vol 930 ◽  
Author(s):  
G.R. Daly ◽  
P.H. Gaskell ◽  
S. Veremieiev

Gravity induced film flow over a rigid smoothly corrugated substrate heated uniformly from below, is explored. This is achieved by reducing the governing equations of motion and energy conservation to a manageable form within the mathematical framework of the well-known long-wave approximation; leading to an asymptotic model of reduced dimensionality. A key feature of the approach and to solving the problem of interest, is proof that the leading approximation of the temperature field inside the film must be nonlinear to accurately resolve the thermodynamics beyond the trivial case of ‘a flat film flowing down a planar uniformly heated incline.’ Superior predictions are obtained compared with earlier work and reinforced via a series of corresponding solutions to the full governing equations using a purpose written finite element analogue, enabling comparisons to be made between free-surface disturbance and temperature predictions, as well as the streamline pattern and temperature contours inside the film. In particular, the free-surface temperature is captured extremely well at moderate Prandtl numbers. The stability characteristics of the problem are examined using Floquet theory, with the interaction between the substrate topography and thermo-capillary instability modes investigated as a set of neutral stability curves. Although there are no relevant experimental data currently available for the heated film problem, recent existing predictions and experimental data concerning the behaviour of corresponding isothermal flow cases are taken as a reference point from which to explore the effect of both heating and cooling.

1981 ◽  
Vol 21 (06) ◽  
pp. 747-762 ◽  
Author(s):  
Karl E. Bennett ◽  
Craig H.K. Phelps ◽  
H. Ted Davis ◽  
L.E. Scriven

Abstract The phase behavior of microemulsions of brine, hydrocarbon, alcohol, and a pure alkyl aryl sulfonate-sodium 4-(1-heptylnonyl) benzenesulfonate (SHBS or Texas 1) was investigated as a function of the concentration of salt (NaCl, MgCl2, or CaCl2), the hydrocarbon (n-alkanes, octane to hexadecane), the alcohol (butyl and amyl isomers), the concentration of surfactant, and temperature. The phase behavior mimics that of similar systems with the commercial surfactant Witco TRS 10–80. The phase volumes follow published trends, though with exceptions.A mathematical framework is presented for modeling phase behavior in a manner consistent with the thermodynamically required critical tie lines and plait point progressions from the critical endpoints. Hand's scheme for modeling binodals and Pope and Nelson's approach to modeling the evolution of the surfactant-rich third phase are extended to satisfy these requirements.An examination of model-generated progressions of ternary phase diagrams enhances understanding of the experimental data and reveals correlations of relative phase volumes (volume uptakes) with location of the mixing point (overall composition) relative to the height of the three-phase region and the locations of the critical tie lines (critical endpoints and conjugate phases). The correlations account, on thermodynamic grounds, for cases in which the surfactant is present in more than one phase or the phase volumes change discontinuously, both cases being observed in the experimental study. Introduction The phase behavior of a surfactant-based micellar formulation is one of the major factors governing the displacement efficiency of any chemical flooding process employing that formulation. Knowledge of phase behavior is, thus, important for the interpretation of laboratory core floods, the design of flooding processes, and the evaluation of field tests. Phase behavior is connected intimately with other determinants of the flooding process, such as interfacial tension and viscosity. Since the number of equilibrium phases and their volumes and appearances are easier to measure and observe than phase compositions, viscosities, and interfacial tensions, there is great interest in understanding the phase-volume/phase-property relationships. Commercial surfactants, such as Witco TRS 10-80, are sulfonates of crude or partially refined oil. While they seem to be the most economically practicable surfactants for micellar flooding, their behavior, particularly with crude oils and reservoir brines, can be difficult to interpret, the phases varying with time and from batch to batch. Phase behavior studies with a small number of components, in conjunction with a theoretical understanding of phase behavior progressions, can aid in understanding more complex behavior. In particular, one can begin to appreciate which seemingly abnormal experimental observations (e.g., surfactant present in more than one phase or a discontinuity in phase volume trends) are merely features of certain regions of any phase diagram and which are peculiar to the specific crude oil or commercial surfactant used in the study.We report here experimental studies of the phase behavior of microemulsions of a pure sulfonate surfactant (Texas 1), a single normal alkane hydrocarbon, a simple brine, and a small amount of a suitable alcohol as cosurfactant or cosolvent. The controlled variables are hydrocarbon chain length, alcohol, salinity, salt type (NaCl, MgCl2, or CaCl2), surfactant purity, surfactant concentration, and temperature. Many of these experimental data were presented earlier. SPEJ P. 747^


Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.


Author(s):  
B. Elie ◽  
G. Reliquet ◽  
P.-E. Guillerm ◽  
O. Thilleul ◽  
P. Ferrant ◽  
...  

This paper compares numerical and experimental results in the study of the resonance phenomenon which appears between two side-by-side fixed barges for different sea-states. Simulations were performed using SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach and results are compared with experimental data on two fixed barges with different headings and bilges. Numerical results, obtained using the SWENSE approach, are able to predict both the frequency and the magnitude of the RAO functions.


2012 ◽  
Vol 134 (6) ◽  
Author(s):  
M. Bachiri ◽  
A. Bouabdallah

In this work, we attempt to establish a general analytical approximation of the convection heat transfer from an isothermal wedge surface to fluids for all Prandtl numbers. The flow has been assumed to be laminar and steady state. The governing equations have been written in dimensionless form using a similarity method. A simple ad hoc technique is used to solve analytically the governing equations by proposing a general formula of the velocity profile. This formula verifies the boundary conditions and the equilibrium of the governing equations in the whole spatial region and permits us to obtain analytically the temperature profiles for all Prandtl numbers and for various configurations of the wedge surface. A comparison with the numerical results is given for all spatial regions and in wide Prandtl number values. A new Nusselt number expression is obtained for various configurations of the wedge surface and compared with the numerical results in wide Prandtl number values.


2003 ◽  
Vol 125 (1) ◽  
pp. 12-17 ◽  
Author(s):  
I. Hagiwara ◽  
D. W. Wang ◽  
Q. Z. Shi ◽  
R. S. Rao

A new analytical model is developed for the reduction of noise inside a cavity using distributed piezoelectric actuators. A modal coupling method is used to establish the governing equations of motion of the fully coupled acoustics-structure-piezoelectric patch system. Two performance functions relating “global” and “local” optimal control of sound pressure levels (SPL) respectively are applied to obtain the control laws. The discussions on associated control mechanism show that both the mechanisms of modal amplitude suppression and modal rearrangement may sometimes coexist in the implementation of optimal noise control.


1991 ◽  
Vol 1 (2) ◽  
pp. 139-151
Author(s):  
J.W. Grant ◽  
J.R. Cotton

The otolith organs were modeled mathematically as a 3-element system consisting of a viscous endolymph fluid in contact with a rigid otoconial layer that is attached to the skull by a gel layer. The gel layer was considered to be a viscoelastic solid, and was modeled as a simple Kelvin material. The governing differential equations of motion were derived and nondimensionalized, yielding 3 nondimensional parameters: nondimensional density, nondimensional viscosity, and nondimensional elasticity. The equations were solved using finite difference techniques on a digital computer. By comparing the model’s response with previous experimental research, values for the nondimensional parameters were found. The results indicate that the inclusion of viscous and elastic effects in the gel layer are necessary for the model to produce otoconial layer deflections that are consistent with physiologic displacements. Future experimental data analysis and mathematical modeling effects should include viscoelastic gel layer effects, as this is a major contributor to system damping and response.


2021 ◽  
Vol 2 (2) ◽  
pp. 36-43
Author(s):  
Evgeniy P. FIGURNOV ◽  
◽  
Yury I. ZHARKOV ◽  
Valeriy I. KHARCHEVNIKOV ◽  
◽  
...  

Methodology provided summarizes published, original and foreign theoretic and experimental data on the subject of heating and cooling of standard and shaped conductors of overhead power transmission line and uses those of them which are most affected to fundamental heat-transfer laws. Computation surface area of standard and shaped wire formulas are given. The common formula of convection heat transfer coefficient is provided, based on wind speed and direction, concerning antiicing mode. Parameters of this formula do not coincide with those existing, as they are based on experimental data on standard and shaped conductors but not on round tubes. Formula of computation of heat transfer power under the influence of solar radiation is given. Summarized formula of admissible continuous current computation is given, all the components have detailed description in the article.


Author(s):  
Hamid R. Hamidzadeh ◽  
Ehsan Sarfaraz

The linear in-plane free vibration of a thin, homogeneous, viscoelastic, rotating annular disk is investigated. In the development of an analytical solution, two dimensional elastodynamic theory is employed and the viscoelastic material for the medium is allowed by assuming complex elastic moduli. The general governing equations of motion are derived by implementing plane stress theory. Natural frequencies are computed for several modes at specific radius ratios with fixed-free boundary conditions and modal loss factors for different damping ratios are determined. The computed results were compared to previously established results. It was observed that the effects of rotational speed and hysteretic damping ratio on natural frequency and elastic stability of the rotating disks were related to the mode of vibration and type of circumferential wave occurring.


Author(s):  
Valentina Laface ◽  
Giovanni Malara ◽  
Felice Arena ◽  
Ioannis A. Kougioumtzoglou ◽  
Alessandra Romolo

The paper addresses the problem of deriving the nonlinear, up to the second order, crest wave height probability distribution in front of a vertical wall under the assumption of finite spectral bandwidth, finite water depth and long-crested waves. The distribution is derived by relying on the Quasi-Deterministic representation of the free surface elevation in front of the vertical wall. The theoretical results are compared against experimental data obtained by utilizing a compressive sensing algorithm for reconstructing the free surface elevation in front of the wall. The reconstruction is pursued by starting from recorded wave pressure time histories obtained by utilizing a row of pressure transducers located at various levels. The comparison shows that there is an excellent agreement between the proposed distribution and the experimental data and confirm the deviation of the crest height distribution from the Rayleigh one.


2016 ◽  
Vol 5 (1) ◽  
pp. 29
Author(s):  
Madhura K R ◽  
Uma M S

<p><span lang="EN-IN">The flow of an unsteady incompressible electrically conducting fluid with uniform distribution of dust particles in a constricted channel has been studied. The medium is assumed to be porous in nature. The governing equations of motion are treated analytically and the expressions are obtained by using variable separable and Laplace transform techniques. The influence of the dust particles on the velocity distributions of the fluid are investigated for various cases and the results are illustrated by varying parameters like Hartmann number, deposition thickness on the walls of the cylinder and the permeability of the porous medium on the velocity of dust and fluid phase.</span></p>


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