INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, VOL. 37, 1915-1930 (1994) SELF-SIMILAR SOLUTIONS FOR AXISYMMETRIC JETS USING TWO TURBULENCE MODELS N. A. GHAZZAWI AND N. J. RABADI zyxwvu Unioersity of Jordan, Faculty of Engineering and Technology, Deportment of Mechanical Engineering. Amman, Jordan SUMMARY Similarity solutions for incompressible axisymmetric jets using a k--E and a constant eddy diffusivity turbulence models are considered. For the k--E model, the governing equations are very complex. Therefore, a transformation that simplifies these equations and makes them amenable to efficient numerical solution is used. Results for the velocity, turbulent kinetic energy and dissipation rate are obtained. Also, velocity decay rate, growth rate, entrainment and kinetic energy decay rate are determined. zyxw A comparison with experi- mental data and other zyxwvuts works utilizing a parabolic marching asymptotic solution to the full partial differential equations is made. This comparison shows that similarity zyxwv solutions are more accurate than solutions using numerical marching procedures. INTRODUCTION A considerable amount of work has been done on jets because of their importance in a wide variety of engineering applications. Some of these applications are: jet flow inside combustion chambers, jets in aerospace devices,jet pumps and ejectors, discharge of effluents and discharges from draft tubes and certain other outlets into rivers. Self-similar solutions of turbulent incompressible jets issuing into stagnant surroundings belong to an established class of fluid dynamics problems. Schlichting’ similarity solution assumed a constant value for the eddy viscosity, while Tollmien’s used simple Prandtl mixing length hypothesis for shear stress where the eddy viscosity is dependent upon the lateral co-ordinate.2 More recent applications3 zyxwvu ’ of two-equation turbulence models to the jet problem produced more realistic solutions. Rodi4 solved the governing parabolic partial differential equations of jets using numerical marching procedure. His technique introduced a degree of inaccuracy that is distinguished separately from the inaccuracy resulted from turbulence mo&lling.6 Vollmers and Rotta’ developed similarity solutions to the turbulent jet problem. They indicated that the resulting set of governing ordinary differential equations are highly non-linear and singular at the jet edge. Shooting methods are used to integrate the equations. Paullay et al.’ used the k--E model to formulate plane and radial jet problems in similarity variables. A mean stream function approach is used whereby a co-ordinate transformation is applied that accounts for the lateral distribution of the similarity variable. The transformation used overcomes the singularity of the equations at the jet edge. Moreover, it decouples the governing equations rendering them amenable to efficient numerical solution using finite differ- ence technique. Hijazen and Rabadi’ used the k--E model and the constant eddy viscosity model to solve for the development of an axisymmetric jet issuing into stagnant surroundings. A numerical marching CCC 0029-5981/94/111915-16$9.00 zyxwvu 0 1994 by John Wiley & Sons, Ltd. Received I6 November 1992 Revised 21 September 1993