Experimental studies of a plane buoyant surface jet

Results are presented from an experimental study of the conditions of formation of a plane buoyant jet with different initial values of the density Froude number.     

The flip-through of a plane inviscid jet with a free surface

The growth of a two-dimensional liquid jet is modelled, in which an inviscid incompressible fluid is in irrotational flow. On the moving free surface, the pressure is constant. The flow is symmetric with respect to the y-axis. The free-surface fluid particle that lies on the y-axis is Q and it has position y = Y(t). A velocity potential is presented that describes the local features of the flow near the centreline, and which contains essentially two unknowns: the velocity V(t) = d Y/d t of Q, and a length L(t). Near Q the free surface is a time-dependent parabola, whose curvature is directly proportional to a third unknown, F(t). The kinematic and dynamic free-surface boundary conditions constrain V, L and F to satisfy three ordinary differential equations. The solutions are a one-parameter family that separate into five types. For one type the free-surface curvature changes sign during the motion, so that the free surface changes from concave to convex—it executes flip-through. Soon after flip-through, there is a local maximum in the pressure, with respect to time and space. A short time later there is a maximum in the acceleration of Q. As t tends to infinity, V tends to a constant, V _∞. An estimate is made of the time scale for flip-through, based on pressure changes, and it is found to decrease as V _∞ increases. When V _∞ is chosen very large, the values of the large maxima in pressure and acceleration become sensitive to small changes in the initial conditions. The results focus on the highly transient pressure field. The findings may help to describe the flip-through of a steep fronted water wave meeting a plane impermeable wall.     

Two-dimensional buoyant jet in a current

Summary When an effluent is discharged into a current at or near the bed, it may be advantageous to have the effluent flowing along the bed for some distance, thickening en route, so that it will have become diluted sufficiently before it reaches the surface. This can be achieved provided the effluent is discharged from a narrow long slot into the ambient current; the effluent plume then flows near the bed due to the pressure drop on the lee side of the emerging effluent.To confirm that this type of effluent flow could exist, laboratory experiments were conducted in which warm water at about 76° C was discharged vertically upwards from a slot 1 cm wide into an ambient current at a temperature of about 12° C. It was observed that the discharged effluent rose a short distance above the slot, due to its initial momentum, and then re-attached itself to the rigid floor, continuing along the floor as it slowly thickened. The temperature and its fluctuation, the velocity and the thickness of the layer, were measured for various ratio of the ambient velocity to the jet velocity and densimetric Froude numbers at the slot. It was found that flow in the layer at a certain distance from the slot is dynamically similar, and that the measured data can be described by non-dimensional similarity functions in the density and velocity field. It was also shown, both theoretically and experimentally, that the depth and the dilution factor, based on the maximum temperature of the under-flowing layer, increases linearly with down-stream distance from the slot.It was further found that the coefficient of skin friction depends on Richardson number and that the coefficient remains constant for a given flow condition.Notation C ₁,C ₂ constant coefficients equation (2.12) - C _f coefficient of skin friction - F ₀ densimetric Froude number equation (4.9) - F _x,F _y components of the buoyancy force inx andy direction - f ₁(),f ₂(),g ₁()g ₂(),g ₁₂() universal functions equation (2.4) - g– acceleration due to gravity - I ₁,I ₂ integrals of functionf ₁() andf ₂() equation (2.15) - h– characteristic thickness of the underflowing layer - h ₀ depth of the warm layer at section A-A (Fig. 1) - H depth of the ambient current - n index associated with raw data - N total number of digitized data - p pressure - R ratio of the ambient velocity to the jet velocity - R _e Reynolds number based at the slot - R _i Richardson number equation (2.12) - T local arithmetic mean value of temperature - T ₀ temperature of the jet at slot exit - T _a temperature of the ambient current - T _m maximum temperature at each section - t _n instantaneous point temperature - t time - root-mean-square of temperature - U local mean velocity in the mean flow direction - U _a average mean velocity of the ambient current (see Fig. 1) - U ₀ jet velocity at the slot exit - U _* shear velocity - V local mean velocity in the vertical direction - velocity fluctuation ofU andV component respectively - w slot width - X ₀ non-dimensional distance from the virtual origin - x, y system of co-ordinates (Fig. 1) - relevant length scale at which the temperature excess is half of its maximum value - non-dimensional transverse distance - angle of inclination of the rigid boundary - ratio between the length scale and the characteristic thicknessh - kinematic viscosity - local mass density - ₀ mass density at slot exit - _a mass density of the ambient current - ₀ mass density excess at the slot exit - _m maximum of mass density excess at each section - ₀ shear stress at rigid boundary - ₁, ₂, ₁, ₂ universal functions equations (4.5, 4.6, 4.7, 4.8)     

Porous flow at a vertical surface in free convection (Laminar boundary layer)

An approximate method is developed for calculating heat transfer at a vertical surface in free convection with uniform inward and outward porous flow and a laminar boundary layer. Design formulas are given, and the results obtained are analyzed.     

On the free convection boundary layer on a vertical plate with prescribed surface heat flux

The free convection boundary layer on a vertical plate with a prescribed surface heat flux proportional to (1 +x ²)^µ (µ a constant) is discussed. For µ > –12 the boundary-layer solution develops from a similarity solution valid forx small to the one valid forx large. However, with µ –12 the similarity equations forx large are not solvable and the behaviour for largex in this case is discussed. It is found that there are two cases to consider, namely µ < –12 and µ = –12. In both cases the leading-order problem is homogeneous involving an arbitrary constant which is determined from an integral property of the full boundary-layer problem. However, in the former case the asymptotic behaviour is algebraic, with the perturbation to the leading-order solution, arising from the heat flux boundary condition, being ofO[x ^1+2µ]. The latter case also involves logarithmic terms, with the perturbation to be leading-order solution now being ofO[(logx)^–1].     

Heat and mass transfer in a binary laminar boundary layer with free convection on a vertical porous surface

An approximate analytical solution of heat and mass transfer in a binary laminar boundary layer with free convection on a vertical surface is presented. The numerical solution is compared with an approximate analytical solution obtained by another method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 1, pp. 19–28, July, 1971.     

Computational-theoretical investigation of buoyant jet flows

The results of mathematical simulation of fully developed plane buoyant jet flows are presented. The solution is found within the framework of the model of a laminar boundary layer in the Boussinesq approximation using the method of matched asymptotic expansions. Analytical dependences of the basic characteristics of a jet flow on the Prandtl number and density parameter have been constructed.     

Oscillatory Marangoni convection in a conducting fluid layer with a deformable free surface in the presence of a vertical magnetic field

Summary. Linear stability theory is applied to the problem of the onset of oscillatory Marangoni convection in a horizontal layer of electrically conducting fluid heated from below in the presence of a vertical magnetic field. The fluid layer is bounded from below by a rigid boundary and from above by a deformable free surface. The critical Marangoni number M _c, the critical wavenumber a _c and the critical frequency _c are obtained for wide ranges of the Prandtl number #E5/E5#₁, the magnetic Prandtl number #E5/E5#₂, the crispation number C _r and the Chandrasekhar number Q. We present numerically a necessary and sufficient condition for oscillatory Marangoni convection to occur.     

Unsteady free convection flow over a continuous moving vertical surface

Summary The problem of heat transfer in the unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid has been investigated. Both constant surface temperature and constant surface heat flux conditions have been considered. The nonlinear coupled partial differential equations governing the flow have been solved numerically using the Keller box method and the Nakamura method which both give closely similar solutions. The results indicate that the cooling rate of the sheet can be enhanced by increasing the buoancy parameter or the velocity of the sheet. It is found that a better cooling performance could be achieved by using a liquid as a cooling medium rather than a gas. The overshoot in the velocity occurs near the surface when the buoyancy parameter exceeds a certain critical value.     

Steady flow of a buoyant plume into a constant-density layer

The upward flow of a buoyant plume emanating from a horizontal fissure into a two-layered fluid region is considered. Solutions are computed numerically for a range of fissure widths and water depths. It is shown that for a given fluid depth and fissure size there is a minimum flow rate beneath which no steady solutions exist. At this limiting flow, the fluid detaches from the wall of the fissure via a stagnation point. Solutions exist for all values of flow rate above this minimum. Exact solutions are presented for very large flow rates.     

Circulation of the solid phase through a vertical gas jet injected into a layer of granular material

A method is developed for determining the mass of particles circulating through a vertical gas jet. On the basis of experimental data dependences are obtained for determining the circulation of particles and the velocities of their motion in the jet.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 4, pp. 635–640, October, 1979.     

Light scattering by surface waves on a vertical layer of liquid toluene

It is demonstrated that light scattering from surface waves on a vertical liquid layer can be used for the determination of surface tension and kinematic viscosity of the liquid under investigation. In contrast to usual approaches of surface light scattering, a setup is described that enables measurements with the same setup as that with experiments for the determination of other thermophysical properties by light scattering from bulk fluids and without an imposed grating or seed particles. The experiments rely on a heterodyne detection scheme and a signal analysis by photon correlation spectroscopy. First results are presented for toluene over a temperature range from 323 to 483 K at saturation conditions.     

Benzophenone-1,3-dioxane as a free radial initiator for photopolymerization

Benzophenone-1,3-dioxane (BP-DO), a hydrogen abstraction type photoinitiator for free radical polymerization, is synthesized and characterized. Its capability for acting as an initiator for the polymerization of methyl methacrylate (MMA), styrene (St) and multifunctional monomers is examined. The relative photopolymerization efficiencies of BP-DO, benzophenone (BP), and BP/ethyl-4-dimethylaminobenzoate (EDAB) are compared. The amounts of leachable photoinitiator are determined through the extraction experiments. In contrast to BP-based photoinitiators, BP-DO does not require an additional hydrogen donor for the initiation; it could be a substitute for the conventional initiator systems of BP and BP/EDAB.     

The spreading of a microstructural fluid over a solid surface

The kinetics involved in the spreading of a drop of microstructural fluid over a horizontal solid surface is investigated theoretically. A method is proposed for the measurement of material constants of the fluid, characterizing its micropolarity.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 2, pp. 253–261, February, 1989.     

Mixed convection boundary layer flow on a vertical surface in a saturated porous medium

Summary The flow of a uniform stream past an impermeable vertical surface embedded in a saturated porous medium and which is supplying heat to the porous medium at a constant rate is considered. The cases when the flow and the buoyancy forces are in the same direction and when they are in opposite direction are discussed. In the former case, the flow develops from mainly forced convection near the leading edge to mainly free convection far downstream. Series solutions are derived in both cases and a numerical solution of the equations is used to describe the flow in the intermediate region. In the latter case, the numerical solution indicates that the flow separates downstream of the leading edge and the nature of the solution near this separation point is discussed.     

Influence of background vertical motions on free convection over a thermally inhomogeneous horizontal surface

In a linear approximation the problem of the influence of background vertical motions on free convection over a thermally inhomogeneous horizontal surface has been solved analytically. The dimensionless number that determines this influence and that represents the ratio of the product of the characteristic velocity of background vertical motions and of the horizontal scale of thermal inhomogeneities to the coefficient of thermal diffusivity of the medium has been found. Descending motions may effectively suppress convection (not only decrease the height of penetration of convective motions into the medium but also to decrease their amplitude substantially). Ascending motions increase the height of penetration of convective motions into the medium and, to a lesser extent, the vertical component of convective velocity. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 1, pp. 97–101, January–February, 2008.     

Experimental study of free convection with porous blowing and suction on a vertical surface

The paper presents the results of an experimental study of the heat transfer and the temperature field in a free-convection boundary layer on a vertical surface with uniform porous blowing and suction and T_w=const. The method of measurement is described and the experimental data are compared with the theoretical results obtained by the authors in an earlier work. The experiments were carried out on a Zender-Mach interferometer. The theoretical and experimental results are found to be in good agreement. Critical values of the parameters are found, which determine the beginning of the transient and developed turbulent regions as a function of the rate of blowing or suction.     

The spreading of a non-Newtonian liquid over a horizontal plane with intensive heat-transfer and mass-transfer processes on the surface of the layer

We investigate the flow of a layer of highly viscous non-Newtonian liquid over a horizontal plane, accompanied by intensive heat-transfer and mass-transfer processes.