The swirling radial free jet

Summary A general similarity solution suggested by Watson for the problem of the laminar, radial, free-jet with swirl has been previously discussed by Riley who also calculated the order to which the solution was valid. That problem is considered in more detail here and higher order terms are given. It is shown that a perturbation scheme for the stream function consisting of a series of inverse powers of and which uses the asymptotic similarity solution as the basic solution is inadequate, and a modification to the series so as to include terms like ⁿ (ln ) ^m must be adopted in order to satisfy the boundary conditions. It is also shown that the general similarity solution may be obtained from the asymptotic series representing the general case with swirl for certain special values of the free constants and also for the no-swirl or free-jet problem. The asymptotic series is given to order ^–13 for the case of swirl and to order ^–29 when there is no swirl.     

Hydromagnetic laminar and turbulent free jet

The flow of a laminar and turbulent plane free jet of a viscous, incompressible, electrically conducting fluid in the presence of a transverse magnetic field is studied. Using the Prandtlvon Mises transformation, in both the cases, closed form solutions are obtained. A remarkable similarity with the nonmagnetic solutions is noticed. Critical values of the magnetic interaction parameter are determined when the dragging action of the initial momentum is exactly balanced by the retarding effect of the magnetic field resulting in the zero axial velocity field.On leave from V.V. (P.G.) College, Shamli-247776, INDIA.     

Raman Measurements of Cryogenic Injection at Supercritical Pressure

Understanding the complex environment of rocket chambers involves a good knowledge of injection phenomena and gives the designer the ability to employ time and cost saving modeling tools to design a higher performance engine. This project looked at injection processes in the supercritical regime using cryogenic nitrogen. Experimental data taken by 2-D Raman imaging allowed the comparison of density and divergence angels with computational models. These parameters provide much information about the jet development and mixing with the surrounding gas. The process used to derive divergence angles from Raman images proves difficult to compare directly with other techniques.     

The entrainment of air by water jet impinging on a free surface

High-speed cine and video photographs were used to capture the flow patterns of a column of water jet impinging into a pool of water. The impact results in air entrainment into water in the form of a void with no mixing between the water in the jet and the surrounding water. Conservation of fluid momentum shows that the rate of increase of the height of the air void depends on the drag coefficient of the jet front. By neglecting the frictional losses, the application of energy conservation yields an expression that relates the maximum height of the air void with the properties of the water jet.     

Three-dimensional viscous jet flow with plane free boundaries

The problem of steady three-dimensional viscous flow with plane free boundaries, induced by a linear source or sink, is solved. The nonuniqueness of the solution in the case of a source and its vanishing in the case of a sink, as the Reynolds number reaches a certain critical value, is proved. The problem is investigated within the framework of the known class of the exact solutions of Navier–Stokes equations generalized in this study.     

Finite element analysis of axisymmetric free jet impingement

A numerical algorithm to determine the impingement of an axisymmetric free jet upon a curved deflector is presented. The problem is considered within the potential flow theory with the allowance of gravity and surface tension effects. The primary dependent variable is the Stokes streamfunction, which is approximated through finite elements using the isoparametric Hermite Zienkiewicz element. To find the correct position of the free boundaries, a trial-and-error method is employed which amounts to solving a boundary value problem (BVP) for the Stokes streamfunction at each iteration step. An efficient method is proposed to solve this BVP. The algorithm to find the correct position of the free boundaries is tested by computing the impingement upon an infinite disc and a hemispherical deflector. To confirm the correctness of the solution, each problem has been solved using several different mesh gradings. A comparison between the Zienkiewicz and the other standard C⁰ finite elements is also given.     

A numerical study of a rectangular jet along a shear free boundary: Surface jet

A numerical simulation of a rectangular surface jet is performed at a Reynolds number of ${\mathit{Re}}_j=4400$. The global parameters of the jet e.g. maximum velocity decay, jet surface normal and lateral spread rates, entrainment, jet momentum flux and turbulent momentum flux are in agreement with several other studies reported in the literature. It is shown that the mean velocity and Reynolds stress profiles scale with the maximum local streamwise velocity and jet half width in the surface normal and lateral directions. The current simulation provides balance, explicitly calculated budgets for the turbulence kinetic energy, Reynolds normal and shear stresses. The surface jet develops a thin layer of fast moving fluid in the lateral direction near the surface. This layer is called the ‘surface current’. It has been suggested that the surface current arises due to the Reynolds stress anisotropy in the near surface region. The current study shows that this explanation is incomplete. The turbulence production for the Reynolds stress in the lateral direction is negative, which can drive the mean flow in the lateral direction. The higher level of negative production in the near surface region is responsible for the development of the surface current.     

Phase-averaged measurements in an isosceles triangular turbulent free jet

Digital time series hot-wire data, acquired in the near field of a turbulent free jet of air issuing from a sharp-edged isosceles triangular orifice, have been post-processed using a phase-averaging procedure to determine the coherent and random contributions to turbulence statistics. The Reynolds number, based on the equivalent diameter of the orifice, was 1.84×10⁵. It was found that momentum transfer by the Reynolds primary shear stress occurs mainly via the coherent primary shear stress.     

Calculation of the trajectory of a plane free jet

A method is proposed for calculating the trajectory of a plane jet of an incompressible liquid, subjected to the action of two flows, directed at different angles to the original direction of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 178–182, May–June.     

Effective control of propagation of a free turbulent jet

Experimental data are presented on the propagation of a free (submerged) turbulent air jet with artificially regulated-by exciting pulsations of a given frequency in the pipe-decay rate. The experimental results are easily generalized using the Strouhal number.     

Design and operation of the free jet elongational rheometer

The controlled free jet instability is used for elongational rheometry of polymer solutions. The instantaneous elongational viscosity represents a convenient comparative parameter. Its dependence on the operating parameters and the conditions of operation will be discussed.