Dilution jet mixing program, supplementary report

The velocity and temperature distributions predicted by a 3-D numerical model and experimental measurements are compared. Empirical correlations for the jet velocity trajectory developed are presented. The measured velocity distributions for all test cases of phase through phase 3 are presented in the form of contour and oblique plots. quantification of the effects of the following on the jet mixing characteristics with a confined crossflow are: (1) orifice geometry momentum flux ratio and density ratio; (2) nonuniform mainstream temperature and velocity profiles upstream of dilution orifices; (3) cold versus hot jet injection; (4) cross-stream flow are a convergence as encountered in practical dilution zone geometries; (5) 2-D slot versus circular orifices; (6) discrete noncirculcer orifices; (7) single-sided versus opposed jets; (8) single row of jets

Transition mixing study empirical model report

The empirical model developed in the NASA Dilution Jet Mixing Program has been extended to include the curvature effects of transition liners. This extension is based on the results of a 3-D numerical model generated under this contract. The empirical model results agree well with the numerical model results for all tests cases evaluated. The empirical model shows faster mixing rates compared to the numerical model. Both models show drift of jets toward the inner wall of a turning duct. The structure of the jets from the inner wall does not exhibit the familiar kidney-shaped structures observed for the outer wall jets or for jets injected in rectangular ducts

Numerical computations of swirling recirculating flow

Swirling, recirculating, nonreacting flows were computed using a 2D elliptic program consisting of three tasks. The computations in Task 1 and 2 were made using an independent analysis for the two coaxial swirling flows. The Task 2 computations were made using the measured profiles of the mixing region. In Task 3, a modified 2D elliptic program was employed to include the effects of interaction between the inner and outer streams

Dilution jet mixing program, phase 3

The objectives of the program were: (1) to extend the data base on mixing of a single-sided row of jets with a confined crossflow, (2) to collect a data base on mixing of multiple rows of jets with confined crossflow, (3) to develop empirical jet mixing correlations, and (4) to perform limited three-dimensional calculations for some of these test configurations. The tests were performed with uniform mainstream conditions for several orifice plate configurations. Schematics of the test section and the orifice configurations are given. Temperature and pressure measurements were made in the test section at 4 axial and 11 transverse stations, using a 60-element rake probe. The measured temperature distributions for these tests are reported

Dilution Jet Mixing Program, phase 1

The effect of jet to mainstream density ratio, flow area convergence as encounted in transition sections, and nonuniform mainstream profile upstream of dilution orifices on the mixing of a row of jets with a confined cross flow was quantified. It is found that: (1) jet spreading rate in transverse direction is increased with increasing J, H/D and with decreasing S/D; (2) the density ratio has only a second order effect on the jet mixing characteristics for a constant momentum ratio; (3) the temperature distributions in the jet mixing region are strongly influenced by the undisturbed mainstream profile; (4) flow area convergence enhances mixing in radial and transverse directions. An asymmetric convergent duct with flat wall injection has the same jet mixing characteristics as a symmetric convergent duct. An asymmetric convergent duct with slant wall injection has a faster jet spreading rate in the transverse direction

Dilution jet mixing program, phase 3

The main objectives for the NASA Jet Mixing Phase 3 program were: extension of the data base on the mixing of single sided rows of jets in a confined cross flow to discrete slots, including streamlined, bluff, and angled injections; quantification of the effects of geometrical and flow parameters on penetration and mixing of multiple rows of jets into a confined flow; investigation of in-line, staggered, and dissimilar hole configurations; and development of empirical correlations for predicting temperature distributions for discrete slots and multiple rows of dilution holes

Schwinger's Propagator Is Only A Green's Function

Schwinger used an analytic continuation of the effective action to correctly compute the particle production rate per unit volume for QED in a uniform electric field. However, if one simply evaluates the one loop expectation value of the current operator using his propagator, the result is zero! We analyze this curious fact from the context of a canonical formalism of operators and states. The explanation turns out to be that Schwinger's propagator is not actually the expectation value of the time-ordered product of field operators in the presence of a time-independent state, although it is of course a Green's function. We compute the true propagator in the presence of a state which is empty at $x_+ = 0$ where $x_+ \equiv (x^0+x^3)/\sqrt{2}$ is the lightcone evolution parameter. Our result can be generalized to electric fields which depend arbitrarily on $x_+$.Comment: 18 pages, LaTeX 2 epsilo