Abstract:

Convergent-divergent nozzles are used to produce supersonic flow in many applications such as, rockets, missiles, gas turbine engines, and wind tunnels. The nozzles come as either convergent or convergent-divergent, and are designed using compressible fluid dynamics theory and numerical techniques known as Method of Characteristics (MOC) and finite difference McCormack’s predictor corrector method. Students taking gas dynamics or compressible flow theory courses are generally required to learn about these methods to analyze the flow characteristics through nozzle. In this paper we present interactive online software that is developed to design one-, and two-dimensional, including axi-symmetric, convergent-divergent nozzle using the Method of Characteristics and analyze the flow features such as Mach number, flow turning, pressure, and temperature and density variations in the nozzle.

The application is written in Java to allow for portability. The process through which the characteristic equations are solved is from the Gas Dynamics book by Zucrow and Hoffman1. This approach allows for both the two-dimensional planar and axially symmetric cases. The process begins with the determinations of an initial value line located via Sauer’s method. This initial value line is determined by solving for a barely supersonic line where the radial velocity is zero. This initial value line gives rise to the initial value problem and its solution via the unit processes explained in Zucrow and Hoffman1.

After the initial value problem is solved, the expansion contour is developed by solving the characteristic and compatibility equations over a non-simple region of the flow network. If the user provides a desired exit Mach number, it is located on the axis and the expansion contour is truncated at the characteristic that produces the desired exit Mach number. In order to determine the flow straightening contour that is necessary for parallel, uniform exit flow, a straight characteristic is drawn at the Mach angle such that it is long enough to allow an equivalent mass flow rate as the initial value line. The characteristics in this section are straight because it is a simple section consisting of characteristics of the same family that do not cross.

After the determination of the final straight characteristic (with uniform properties), a back stepping approach is used to determine the flow properties in the rest of the nozzle and to determine the straightening contour that will give rise to the desired, uniform exit conditions.

This application is intended to be hosted online for educational purposes. Users will be able to go online and change several parameters to see how the flow field and nozzle contour changes. A list of parameters is given at the end of this abstract. After the calculations are completed, data displayed to the user includes the nozzle contour, flow field gradients, thrust and efficiency ratings. The flow field is determined from the discrete points solved by the method of characteristics and then interpolated to give the smooth property distributions including static temperature, static pressure, static density, velocity, and Mach number.

This application will give the users an easier way of understanding converging-diverging nozzles flows and also will be able to develop new nozzle design for any specific application from the comfort of their home.

Reference
(1) Gas Dynamics, Vol 2. 1982

Keywords:

nozzles, fluid dynamics, interactive educational software, supersonic.