Research Papers: Fundamental Issues and Canonical Flows

Numerical Modeling and Analysis of Entrainment in Turbulent Jets After the End of Injection

[+] Author and Article Information
Satbir Singh1

 General Motors Global Research and Development, Warren, MI 48090satbirs@andrew.cmu.edu

Mark P. B. Musculus

Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551


Corresponding author. Present address: Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213.

J. Fluids Eng 132(8), 081203 (Aug 26, 2010) (10 pages) doi:10.1115/1.4002184 History: Received November 06, 2009; Revised July 13, 2010; Published August 26, 2010; Online August 26, 2010

Previous velocity and scalar measurements in both single-phase jets and two-phase diesel fuel sprays indicate that after the flow at the nozzle decelerates, ambient-gas entrainment increases compared to a steady jet. Previous studies using simplified analytical models and computational fluid dynamics (CFD) simulations using a one-dimensional (1D) inviscid, incompressible momentum equation have predicted that an “entrainment wave” propagates downstream along the jet axis during and after the deceleration, increasing entrainment by up to a factor of 3. In this study, entrainment is analyzed using the full compressible, unsteady Navier–Stokes momentum equations in axisymmetric two-dimensional (2D) CFD simulations of single-pulsed transient round gas jets. The 2D simulations confirm the existence of the entrainment wave, although the region of increased entrainment is distributed over a wider axial region of the jet than predicted by the simplified 1D model, so that the peak entrainment rate increases by only 50% rather than by a factor of 3. In the long time limit, both models show that the rate of mixing relative to the local injected fluid concentration increases significantly, approaching a factor of 3 or more increase in the wake of the entrainment wave (relative to a steady jet). Analysis of the terms in the momentum equation shows that the entrainment wave in the full 2D CFD predictions occurs in two phases. The entrainment first increases slightly due to a radial pressure gradient induced by a relatively fast acoustic wave, which the simple 1D model does not account for. The acoustic wave is followed by a slower momentum wave of decreased axial velocity initiated at the nozzle, which is convected downstream at the local flow velocities. The largest increase in entrainment accompanies the momentum wave, which is captured by the 1D momentum-equation model.

Copyright © 2010 by American Society of Mechanical EngineersThe United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.
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Figure 1

2D CFD-predicted centerline axial velocity as a function of axial distance for the three different mesh densities (z is the distance from the nozzle exit and D is the diameter of the nozzle)

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Figure 2

2D CFD-predicted normalized (with value at the centerline) axial velocity at 25 mm (18 diameters) downstream of the nozzle for the three different mesh densities (r is the distance from the jet axis and R is the radius of the nozzle)

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Figure 3

Experimentally measured (symbols), 1D model (dashed line), and 2D model (solid line) predicted centerline axial velocity for the 4.3 ms duration of injection (DOI) case as a function of time at various axial positions downstream of the nozzle

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Figure 4

Images of total velocity vectors colored by radial velocity component predicted by the 2D model for the 20.3 ms DOI case. The scale of the images is indicated along the sides of the bottom image. The dotted line indicates the edge of the jet, and the vertical line indicates the sampling location (z=25 mm) in later figures.

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Figure 5

Radial velocities at various times as a function of radial distance from the jet centerline and at an axial location of 25 mm (18 diameters) from the nozzle exit predicted by the 2D model for the 20.3 ms DOI case

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Figure 6

2D and 1D predicted normalized mixture fraction and axial velocity as a function of radial distance at 25 mm (18 diameters) away from the nozzle exit for the 20.3 ms DOI case

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Figure 7

Relative entrainment rate of 20.3 ms DOI case compared to the quasisteady case for (a) the 2D model and (b) the 1D model

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Figure 8

Cross-sectional averaged mixture fraction predicted by the 2D model for the 20.3 ms DOI case

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Figure 9

Mixture-normalized relative entrainment rate of the 20.3–ms DOI case compared to the quasi-steady case for (a) the 2D CFD model and (b) the 1D model.

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Figure 10

Temporal evolution of axial momentum terms (Eq. 1): 25 mm (18 diameters) downstream on the jet centerline

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Figure 11

Temporal rates of change in axial velocity (top) and modified pressure (bottom) on the jet centerline scaled by the downstream distance for clarity. The times after the start of the deceleration transient for each curve in microseconds are indicated on the plot.

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Figure 12

Temporal evolution of radial momentum terms (Eq. 2): 25 mm (18 diameters) downstream and 6.5 mm (5 diameters) from the jet centerline (near the jet edge)




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