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Supersonic Axisymmetric Jet Flow

Figure 1 is described in the surrounding text
Figure 1. Mach number contours for supersonic axisymmetric nozzle jet flow.

Flow Description

This case involves a "submerged" turbulent supersonic jet emanating from an axisymmetric convergent-divergent Mach 2.2 nozzle. This nozzle was studied by J.M. Eggers in 1962. Velocity profiles and eddy viscosity distributions were obtained within the jet. The working fluid is air and the nozzle is operated at the pressure ratio corresponding to perfect expansion.

Table 1 lists the ambient conditions for the flow field, which is quiescent.

Table 1. Ambient conditions.
Mach Pressure (psia) Temperature (R) Angle-of-Attack (deg) Angle-of-Sideslip (deg)
0.0 14.7 525.0 0.0 0.0

Table 2 lists the inflow conditions for the nozzle or plenum conditions. The nozzle pressure ratio (NPR, ambient static pressure to nozzle total pressure) is 0.09063, which corresponds to a perfect expansion with an exit Mach number of 2.22.

Table 2. Nozzle inflow conditions.
Total Pressure (psia) Total Temperature (R)
162.2 525.0

The reference Reynolds number is

Reref = aref Xref / (nu)ref = 78.8E+06
where aref is the speed-of-sound and (nu)ref is the kinematic viscosity using conditions at the nozzle inflow total pressure and temperature. The reference length is Xref = 1.0 ft

The Reunolds number based on the nozzle exit velocity and radius, ue = 1770 ft/sec and re = 0.5035 in is

Reref = ue re / (nu)ref = 3.35E+06

Geometry

The geometry is the axisymmetric, converging-diverging nozzle profiles as defined by Eggers.

The geometry can also be obtained from the grid file axinoz.x.fmt, which is in the Plot3d format (3D, formatted, whole, multi-block). The internal contour of the nozzle is defined by the JMAX grid line of zone 1. The external contour of the nozzle is defined by the J1 grid line of zone 2. There is a small base area at the exit of the nozzle connecting the internal and exterior contours. This is part of the I1 grid line of zone 3. The axis-of-symmetry is defined by the J1 grid lines of zones 1 and 3 and these should be r = 0. The units of the grid dimensions are feet.

Computational Domain and Boundary Conditions

This case primarily examines the jet flow field downstream of the nozzle exit; however, the internal converging-diverging nozzle is included in the computational domain. Because the jet is supersonic, the upstream and farfield boundaries were placed fairly close to the nozzle exit. The downstream boundary is placed approximately 145 nozzle exit radii downstream to capture the length of the jet. The domain widens downstream to capture the expansion of the jet. The nozzle inflow is from a plenum in which the total pressure and total temperature are known. The fairfield boundaries can be assumed at ambient conditions.

Comparison Data

Experimental data obtained by Eggers (1966) is used for comparison of computational results. This data was obtained from Appendix B ('Tabulation of Velocity Profiles') of Eggers report. This data is available in the following two ASCII files:

axial.dat

This file contains the jet centerline velocity and a measure of the jet width as a function of axial distance.
profile.dat
This file contains the measured velocity profiles and related parameters at each of the axial measurement locations

Each file contains data in nondimensional form. Per the reference, axial and radial distances were nondimensionalised by the nozzle exit radius (0.5035 in.), velocities by the nozzle exit velocity (1765 ft/sec) and density by the nozzle exit density (0.1501 lbm/ft3). The following nomenclature describes the variables used in the data files.

Table 3. Nomenclature for experimental data files.
x Axial distance downstream of the nozzle exit.
r5 at a given axial station, the radial distance at which the velocity is equal to 1/2 of the centerline velocity at the same axial location.
u Local axial velocity.
U Centerline velocity at a given axial location.
rho Local density.

Computational Studies

Table 4. Computational studies peformed for the supersonic axisymmetric jet flow case.
Study Category Person Comments
Study #1 Example J.W. Slater Axisymmetric flow.

References

Eggers, J.M. "Velocity Profiles and Eddy Viscosity Distributions Downstream of a Mach 2.22 Nozzle Exhausting to Quiescent Air," NASA TN D-3601, September 1966. [PDF] (Download Accessible PDF Plug-in)

Contact Information

Questions or comments about this case can be sent be emailed to John.W.Slater@nasa.gov at the NASA Glenn Research Center.

Last Updated: Wednesday, 10-Feb-2021 09:39:00 EST