Showing papers on "Similarity solution published in 1981"

Structure and similarity of nitric oxide production in turbulent diffusion flames

Abstract: On the basis of Favre-averaged equations a similarity solution for the flow field and the mixture field is derived. Using the p.d.f. (probability density function) formulation and an asymptotic expansion for large activation energies of the NO reaction, an algebraic expression for the mean turbulent NO production rate is obtained. The result explains the “rich shift” of NO production by the influence of mixture fraction fluctuations. Integration over the flame yields a formula for the emission index. In the experimental part, the total NO production in vertical diffusion flames of H2, CH4, C3H8, natural gas and a CO/H2 mixture was measured. When the experimental emission index is compared with the theoretical index, a dependence on the diameter appears. This points to an influence of the turbulence length scale. Large coherent structures may be responsible for a reduction in NO production.

The long time asymptotics of solutions to the generalized Burgers equation

Abstract: The long time (i.e. range following a wavefront) behaviour of finite-amplitude sound waves in ducts ('horns') of variable cross section is considered, the wave evolution being governed by a generalized form of Burgers equation. The type of initial data far behind and far ahead of the wavefront is restricted to a transition from one constant state to another. It is proved that the form of the wave for large range is dependent on the limiting value of a certain function of the duct parameters. We have termed the various cases that arise 'supercylindrical', 'cylindrical' and 'subcylindrical', for reasons that should be clear from the details to follow. The analytic form of the limiting profile is determined in all but one case. In particular, it is shown that the similarity solution for cylindrical waves possesses very strong global stability properties.

Effects of inertia in forced corner flows

Abstract: When viscous fluid is contained in the corner between two planes intersecting at an 0 angle a, a flow may be ‘forced’ either by relative motion of the two planes keeping a constant (the ‘paint-scraper ’ problem- Taylor 1960) or by relative rotation of the planes about their line of intersection (the hinged-plate problem -Moffatt 1964). In either case, a similarity solution is available describing the flow sufficiently near the corner, where inertia forces are negligible. In this paper, we investigate the effects of inertia forces, by constructing regular perturbation series for the stream function, of which the leading term is the known similarity solution. The first-order inertial effect is obtained analytically, and, for the Taylor problem with a = Qn, 25 terms of the perturbation series for the wall stress are generated numerically. Analysis of the coefficients suggests that the radius of convergence of the series is given by r 1 U( /v z 9.1, where r is distance from the corner, U is the relative speed of the planes, and v is the kinematic viscosity of the fluid. For the hinged-plate problem, discussed in 5 5, the unsteadiness of the flow contributes to an inertial effect which is explicitly incorporated in the analysis. For both problems, streamline plots are presented which indicate the first influence of inertia forces at distances from the corner at which these become significant.

On the dynamics of the ice sheets 2

Abstract: The equation which describes the motion of an ice sheet under its own weight has a cylindrically symmetric similarity solution. The initial value problem of the equation of motion which has been linearized in the deviations from this similarity solution is solved by an expansion of the solution in terms of eigenfunctions of the linearized equation. The linearized equation determines, for all ice sheets of the same volume, an asymptotically stable motion. These results are compared with the corresponding results of the two-dimensional case (Halfar, 1981).

The fluid-filled cylindrical membrane container

Abstract: The static shape of a fluid-filled membrane cylinder can be described by a set of nonlinear differential equations. These equations depend on a nondimensional parameter β representing the relative importance between pressure and the gravity force. The solution is found by three methods: similarity solution for small β, asymptotic solution for large β, and numerical integration.

A Unified Analysis of Concurrent Modes of Flame Spread

Abstract: A theoretical study is conducted of the spread of flames in gas flows moving in the direction of flame propagation. The study draws on the fact that concurrent flame spread configurations have common general characteristics, thus allowing a unified treatment of the problem. The analysis, although approximate, provides an analytic expression for the rate of flame spread over the surface of thermally thick fuels in laminar gas flow configurations that accept a similarity solution. The predicted flame spread rates for these particular flows provide limits for the rates of spread in other non-similar gas flow configurations.

Mixed convection row on vertical surface

Abstract: Mixed convective heat transfer on a vertical surface has been investigated for uniform free stream velocity and for several values of Prandtl number. An exact similarity solution is obtained for the case of a wall temperature that is inversely proportional to the distance from the leading edge. The non-dimensional temperature distribution suggests that over large η the boundary layer temperature is less than the free stream temperature.

A method to obtain some similarity solutions to the generalized Newtonian fluid

Abstract: It is shown that a similarity solution to the Rayieigh flow problem for a generalized Newtonian fluid exists if the fluid boundary (y=0) is given a velocityU(t) α t1/2. Furthermore, if the fluid is of the power-law type then similarity solutions exist ifU(t) α tσ (orU(t) α eσt), whereσ is any real number.

Hydrodynamics and mass transfer characteristics of a liquid/liquid stirred cell

Abstract: The hydrodynamics and mass transfer characteristics of a stirred cell for contacting immiscible phases are examined. When each phase is stirred with a rotating disk in laminar flow, such that the interface is stationary, the rate of diffusion in the absence of any interfacial resistance is obtained using a similarity solution. The hydrodynamics, specifically the radial velocity derivative at the interface, which is the most important component of the mass transfer solution, is obtained by combining the solutions for a finite disk and for the relationship between disk velocity and fluid core velocity. Excellent experimental agreement, within 5% of the theory, is observed.

On the decay of laminar jets in ambient streams

Abstract: Earlier analysis, Middleton, of the laminar discharge of a ‘strong’ incompressible jet, due to a line or point source of momentum, into an unbounded co-flowing stream of the same density, is extended to the case of plane and round ‘weak’ jets the velocity in which only slightly exceeds the ambient velocity In addition to recovering Goldstein’s solutions for ‘wake-like’ flows, use of the momentum integral equation provides approximate relationships for the decay of the centre velocities from the strong to the weak situations Comparison is made with Wygnanski’s perturbation approach, suitably extended, and it is concluded that for the plane jet case, for which the agreement is better, the curve for the centre-plane velocity is correct to within about 12% throughout its range The present approach is applicable to any flow for which a similarity solution exists as a first order solution, and is especially suitable when two such solutions exist for large and small values of an appropriate parameter Its use also throws light on the form to be adopted for a perturbation expansion