Laminar Stagnation-point Flow Research Articles

Three dimensional MHD stagnation flow due to a stretchable rotating disk

The three dimensional steady MHD laminar stagnation point flow of an electrically conducting fluid on a radially stretchable rotating disk in the presence of a uniform vertical magnetic field is the main concern of the present study. The problem is an extension of the well-known von Karman stagnation problem to the configuration with a stretchable disk with or without rotation. An exact similarity reduction of the Navier–Stokes equations leads to a system of ordinary differential equations describing the stagnation flow. The system is governed by a stretching and a rotation parameters, based on the wall stretching and angular velocity. Employing a highly accurate spectral numerical integration scheme, the effects of these parameters on the flow are examined. The quantities of particular physical interest, such as the torque and the wall shear stresses are calculated and discussed. Contrary to the classical von Karman flow, for small rotational speeds of the disk, magnetic field is found to thicken the boundary layer when small wall stretching is taken into account.

Fluid Flow and Heat Transfer of Combined Convection over Upward-Facing, Horizontal Circular Disks Placed in Vertical Downward Flow

Experimental investigations have been carried out on combined convective flows over upward-facing, circular heated disks placed in a vertical downward flow of forced convection. The experiments were performed with air in the ranges of the Reynolds and Grashof numbers as: 100 < ReD < 2×104, 104 < GrD < 107. The flow fields over disks are first visualized with smoke. The results showed that a twin-vortex appears over the disk intermittently when the buoyancy force is beyond a criterion, and that the onset of the above twin-vortex can be predicted with the Richardson number as GrD/ReD2 = 3.1. The overall heat transfer coefficients from the disks were subsequently measured. The results showed that the coefficients are increased significantly from those of the laminar stagnation point flows with the occurrence of the twin-vortex, and that the relative increase in the average Nusselt numbers of the combined convective flows against those of the stagnation point flows can be predicted with the above Richardson number.

Theoretical analysis of the direct decomposition of methane gas in a laminar stagnation-point flow: CO 2-free production of hydrogen

In this work, a theoretical analysis is developed to predict the decomposition temperature of methane gas, CH 4, in a planar stagnation-point flow over a catalytic carbon surface. Hydrogen is produced (without CO 2 as a byproduct) by means of a heterogeneous reaction mechanism, which is modeled with five heterogeneous reactions, including adsorption and desorption reactions. The mass species, momentum, and energy conservation equations for the gas phase are solved, taking into account that the temperature of decomposition is characterized by the Damköhler number. Therefore, the critical temperature conditions for the catalytic thermal decomposition are found by using a high activation energy analysis for the desorption kinetics of the adsorbed hydrogen component, H ( s ) . Specifically, the numerical estimations show that, for increasing values of the velocity gradient associated with the stagnation flow, the temperature of decomposition grows, depending on the surface coverages of the product species.

Theoretical analysis for the heterogeneous decomposition of hydrogen sulfide to hydrogen on an iron-metallic plate in a laminar stagnation-point flow

In this work, we have theoretically analyzed the conversion process of hydrogen sulfide, H2S, to atomic hydrogen, H0, in a planar stagnation-point flow over an iron-metallic surface. We assume that a binary mixture of hydrogen sulfide and methane composes the laminar stagnation flow. In order to characterize this complex phenomenon with very specific chemical activities on the surface of the metallic plate, we propose a heterogeneous reaction scheme based on four reactions: two electrochemical, one adsorption and an additional exothermic reaction needed to complete the direct conversion of hydrogen sulfide to hydrogen on the surface of the iron. The nondimensional governing equations, which include the mass species and momentum conservation of the mixture and the molecular diffusion of hydrogen into the iron plate, are numerically solved by conventional finite-difference methods. The numerical results show the critical conditions of the H2S decomposition as functions of the involved nondimensional parameters of the present model. In particular, we show parametrically the influence that has the initial concentration of H2S on the surface coverage of the chemical products HS− H+ and H0 derived from the chemical and electrochemical reactions.

The laminar stagnation-point flow against a solidifying moving shell

This paper considers the two-dimensional laminar stagnation-point flow due to a jet impinging onto a solidifying moving boundary. The flow is of interest in connection with the horizontal belt strip casting process. An exact solution to the Navier-Stokes equations is found that is shown to depend on a single ordinary differential equation. The solution is useful in the study of morphological and hydrodynamic instabilities within the impingement region. Solutions for the steady-state shape of the initial stages as well as the asymptotic behavior of the solidifying interface are also discussed in a perturbative manner.

OH Gas Phase Chemistry outside a Pt Catalyst

Using planar laser induced fluorescence we have measured the OH concentration profiles outside a Pt catalyst at 1, 5, and 10 torr. The catalyst was heated to 1300 K in a stagnation point flow consisting of 10% hydrogen and 90% oxygen directed onto the surface. The measurements were compared to a model describing a laminar stagnation point flow including a detailed mechanism with elementary reactions in order to describe both the gas phase and surface reactions. The simulation shows that the detected OH was not produced by gas phase reactions. Instead it is formed on the surface by H+O recombination, and a small percentage of it desorbs and diffuses out from the catalyst. At 1 torr the form of the OH gradient outside the catalyst was found to be determined solely by diffusion and convection. At 5 and 10 torr gas phase reactions also had to be included to correctly describe the shape of the OH concentration gradient. The dominant gas phase reaction is removal of OH molecules through reaction with hydrogen.

Extinction Mechanism of Lean Premixed Flames in a Laminar Stagnation Point Flow.

Effects of heat loss and flame stretch on the lean-limit extinction of laminar premixed flames in a stagnation point flow have been studied experimentally. The bulk stretch rate was varied from 40s-1 to 420s-1, while the Lewis number (Le) was varied from 0.85 to 1.8. The extinction of the lean propane/air flame (Le>1) is mainly caused by the flame stretch. On the other hand, the extinction of lean methane/air and lean methane/CO2-O2 flames (Le<1) is caused not only by flame stretch but also by heat loss, since the flame is intensified by the Lewis number effect. Therefore, heat loss is predominant in the case of the lean methane/CO2-O2 flame whose Lewis number is smaller than that of the lean methane/air flame.

Condensation in a mixing layer

A numerical study has been carried out on the formation of a water aerosol in a laminar stagnation point flow. The two impinging streams were at different temperatures and initial supersaturations. As the streams of vapor mixed, homogeneous nucleation occurred along with condensational particle growth. Attention has been focused on the impact of the mixing rate of the two streams on the aerosol dynamics. The mixing rate is determined by the velocity gradient of the flow. High mixing rates were found to reduce the aerosol mass at the stagnation point of the flow. However, particle number densities were not affected by the velocity gradient of the flow as the aerosol dynamics adjusted themselves to the different conditions.

Aerosol formation in an isothermal stagnation flow

An experiment has been performed in a laminar stagnation point flow in which two non-premixed reactants produced an aerosol of sub-micron particles. The reactants were NH3 and HCl. The rate of mixing of the reactants was determined by the velocity gradient or strain rate of the flow; the response of the aerosol dynamics to the flow field was measured with a laser light scattering technique. Laser Doppler Spectroscopy was used to measure the particle size. It was found that the particle size was independent of the strain rate of the flow. On the other hand, the particle number density decreased as the strain rate increased. It is argued that the intensity of light scattered from the aerosol is, therefore, a measure of the amount of product of the relatively slow NH3-HCl reaction.

Experimental and numerical investigation of soot deposition in laminar stagnation point boundary layers

Soot deposition from a hot gas flow to a cooled solid wall is investigated numerically and experimentally for laminar stagnation point flows. Numerical predictions of soot deposition are made by solving the coupled momentum, energy, and soot transport equations, which include the effects of variable transport properties and thermophoretic transport (i.e. mass transport down a temperature gradient) of soot particles. The results of the numerical computations indicate that the deposition rate, expressed in terms of the deposition velocity, increase with an increasing potential flow velocity gradient and decrease as the wall temperature approaches the freestream temperature. In addition, an insitu laser diagnostic technique is developed which provides simultaneous measurement of the soot deposit thickness and freestream soot concentration. The technique uses two laser beams (488 and 632 nm wavelength) coincident at a point adjacent to the deposition surface to measure the thickness of the deposit and the light extinction by airborne soot particles. Comparison of the experimental results to the numerical model indicates a critical velocity gradient beyond which the “sticking” fraction for the soot significantly decreases. This velocity gradient, which corresponds to maximum deposition, has been found to be approximately 2000 sec −1 for soot produced from fuel rich air/ethylene mixtures.

Some fluid dynamic considerations in the modeling of flames

When in the analysis of combustion of premixed gases the diffusion of heat and species is ignored, the behavior of the flame and the surrounding gases can be described using only the conservation of mass and momentum equations, and by specifying the appropriate flame speed. Application of the general velocity decomposition principle, according to which a flow field is comprised of distinct volumetric, rotation, and potential components, naturally leads to a model in which the flame is regarded as a surface source of volume. For low Mach number flows, the flow-field is treated as being “slightly compressible,” where all the compressibility effects take place at the flame interface, and are manifested as a jump in the normal velocity component. Inspection of the dynamic effects of such a model, for the case of a 2-D finite open flame sheet, indicates that in addition the flame has to be regarded as a source of vorticity in order to satisfy the momentum equation, and to counteract the singularities in the flow field set up by the volumetric effects. The magnitude of the produced vorticity depends on the magnitude of the baroclinic term (▽ϱ × ▽ p) ϱ 2 induced by the flame. The effect of vorticity production on the velocity field is illustrated for the case of a steady laminar stagnation point flow. Even though the latter geometry is axisymmetric and our model applies to 2-D flows only, nevertheless important observations may be made. The theory and the results both indicate that the production of vorticity forms a integral part of the overall velocity field. This in contradistinction to other models of this type, in which the production of vorticity is ignored.

Stagnation-point combustion with radiation

The relatively simple character of diffusion flames in laminar stagnation-point flows has led to numerous theoretical and experimental studies of that system. Here, as a first step toward incorporating radiation in analyses eventually related to fire safety, a grey radiating diffusion flame, above a grey pyrolyzing solid fuel is considered. Shvab-Zeldovich variables are used in the analyses of steady, laminar, radiative, axisymmetric and Cartesian two-dimensional stagnation-point boundary layers. The velocity, temperature, and species fields are similar to analogous free convection flames. Two radiation approximations are compared for the case of a uniform absorption coefficient: (1) the exponential kernel and (2) the optically thin limit. The difference between these approximations proved insignificant; the simpler optically thin limit may be the method of choice. The results depend on eight parameters—five from non-radiating combustion; r , the mass consumption number; B, the mass transfer number; D c , a dimensionless heat of combustion; w , the fuel surface temperature; and Pr, the Prandtl number; and three radiation parameters: N 1 —a conduction/gaseous-radiation parameter; N 2 —a conduction/ambient-radiation parameter and e, the surface emissivity. For conditions typical of synthetic polymer fuels, surface emission dominates gaseous radiation to the fuel and the pyrolysis rate is slightly lower than a non-radiative analysis would predict. Excess pyrolyzate calculations for radiating systems are included.

Thermodynamic method to two dimensional stagnation flow and heat transfer

The purpose of this paper is to develop a variational technique, using the variational principle of non-equilibrium thermodynamics for the solution of laminar stagnation point flow and heat transfer in two dimensions. The governing principle of dissipative processes is formulated for the problem and then using the boundary conditions of the system the elementary trial functions of third degree are assumed for the flow and temperature fields in the vicinity of the wall. The viscous and thermal boundary layer thicknesses, the skin friction and the rate of heat transfer from the wall to the fluid are obtained. It is found that these new approximate results are quite close to the exact known ones. These results are better than those of the Karman-Pohlhausen technique.

Temperature Distribution in Laminar Stagnation-Point Flow with Axisymmetry

Temperature Distribution in Laminar Stagnation-Point Flow with Axisymmetry