Investigation of scalar measurement error in diffusion and mixing processes

In variable density, multi-fluid and reacting flows, the degree of molecular mixing is a critical component of turbulent transfer and mixing models. Also, in many microflows and low Reynolds number flows, scalar diffusion length- and time-scales play a significant role in the mixing dynamics. Characterization of such molecular mixing processes requires scalar measurement devices with a small probe volume size. Spatial averaging, which occurs due to finite probe volume size, can lead to errors in resolving the density or scalar gradients between pockets of unmixed fluids. Given a probe volume size and a priori knowledge of the functional profile of the diffusion layer being measured, we obtain an estimate for the measurement error due to spatial averaging and make the corrections accordingly. An analytical model for the measure of scalar mixing is developed as a predictor for the growth of scalar gradients in a variable scalar flow. The model is applied to a buoyancy-driven mixing layer with a Prandtl number of 7. Measurements within the mixing layer have shown that initial entrainment of unmixed fluid causes a decrease in the measured amount of molecular mixing at the centerplane. Following this period of initial entrainment, the fluids within the mixing layer exhibit an increase in the degree of molecular mixing.     

Shock wave calibration of under-expanded natural gas fuel jets

Natural gas, a fuel abundant in nature, cannot be used by itself in conventional diesel engines because of its low cetane number. However, it can be used as the primary fuel with ignition by a pilot diesel spray. This is called dual-fuelling. The gas may be introduced either into the inlet manifold or, preferably, directly into the cylinder where it is injected as a short duration, intermittent, sonic jet. For accurate delivery in the latter case, a constant flow-rate from the injector is required into the constantly varying pressure in the cylinder. Thus, a sonic (choked) jet is required which is generally highly under-expanded. Immediately at the nozzle exit, a shock structure develops which can provide essential information about the downstream flow. This shock structure, generally referred to as a “barrel” shock, provides a key to understanding the full injection process. It is examined both experimentally and numerically in this paper.

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On the mixing of axi-symmetric ducted jets

Because of practical application to jet pumps, ejectors, furnaces and similar devices, the turbulent discharge of a round jet into a coaxial duct and the mixing patterns in the various regions into which the flow may be divided, are of considerable interest. In this paper the mixing of an incompressible jet with a similar fluid in a cylindrical tube is considered up to the plane which marks the disappearance of potential flow. Under the assumption of similarity of velocity profile and with neglect of the wall boundary layer and nozzle wake, the continuity and momentum equations, in integral form, are solved for the velocities and mixing region radii at any given section. Prandtl's momentum transfer hypothesis may be used to determine the dependence of these on distance downstream. By examining the various flow regimes in detail this analysis is formally able to cover ratios of primary to secondary flow velocities of from one to infinity and, similarly, all ratios of duct to nozzle diameters, thereby extending earlier investigations. It also corrects work on similar basis in which inappropriate linearisations were made. The ‘exact’ results constitute a basis from which extension to include additional effects may be made.     

Passive mixing control of plane parallel jets

An experimental study on the mixing of two plane, unventilated, parallel jets reveals an instability characterized by sinuous flapping of the jets and enhanced mixing of the jets with the ambient fluid. The frequency and amplitude of the instability is shown to be a function of the jets spacing and momentum flux ratios, with the maximum mixing occurring for cases with matched momentum flux. When the momentum flux of the two jets is mismatched by as much as a factor of three, the flow becomes steady. Schlieren flow visualization and hot-wire anemometry demonstrate and quantify the large-scale mixing. The instability has a strong frequency and amplitude dependence on the momentum ratio of the jets. The Strouhal number is also found to decrease with the spacing between the jets. The instability described provides a means to passively control the jet mixing with the ambient.     

Nonstationary processes in starting strongly underexpanded jets

Results of the investigation of nonstationary efflux of argon by the electron-beam-sounding method are presented in [1]. Comparing the regularities obtained in that paper for the front motion of material during efflux from a nozzle with computations [2] for nonstationary expansion from a spherical source and the experimental results in [3] permitted clarification of the singularities of the influence of counter pressure and the temperature factor in jet expansion. The density distribution in nonstationary nitrogen and argon jets is obtained in this paper and study of the regularities of the front motion of the escaping gas is continued.Translated from Zhurnal Prikladnoi Mekhiniki i Tekhnicheskoi Fiziki, No. 1, pp. 34–40, January–February, 1978.     

Identification of vortex motions in turbulent mixing of choked jets

A specially adapted schlieren system is used to generate fluctuating signals which respond strongly to large scale coherent components of a turbulent mixing jet flow and which have a relatively reduced response to random disturbances. The schlieren signals also provide a direct indication of the presence of vortex-like structures in the turbulent mixing layers by virtue of the phase relationship of the schlieren signals to the pressure field. This system gives a clear resolution of the fluctuating periodic effects associated with vortex structures in the flow from a choked convergent nozzle. It has thus been possible to determine that vortex-like eddies are associated with the feedback screech mechanism, and also generate periodic disturbances due to their passage through the diamond shaped wave structure in the flow. The regular disturbances in the flow move at 0.77 of the fully expanded flow velocity. Phase spectral observations demonstrate clearly the vortex like structure of coherent disturbances in the flow by virtue of the quadrature phase relation between the schlieren and microphone signals. Movement of the sensing microphone in the pressure field external to the flow shows disturbance propagation at the acoustic velocity, and also shows that disturbances at Strouhal numbers above 0.7 emanating from the inner mixing zone can be identified by an additional time delay to reach the microphone and only influence the microphone when it is located downstream of the flow sensing schlieren system due to confinement of pressure disturbances within Mach cones of the flow.     

Numerical simulations of vortices in mixing layers and plane jets

Direct numerical simulations of two-dimensional mixing layers and jets are presented first within the temporal approximation, and then with spatial calculations. The evolution of a temperature field as a passive scalar is investigated simultaneously. Besides usual statistical quantities, the results are presented through visualisations of coloured vorticity- and temperature-contours in order to describe the evolutions of the fields with time. Concentrated vortices develop and the evolution of the layer is dominated by the interactions between these eddies which can be viewed as the coherent structures observed in laboratory experiments.     

Time-averaged flow characteristics and mixing properties of double-concentric jets

We examined the flow behaviors and mixing characteristics of double-concentric jets using laser-assisted smoke flow visualization method to analyze typical flow patterns and binary boundary detection technique to investigate jet spread width. Time-averaged velocity vectors, streamline patterns, velocity distributions, turbulence properties, and vorticity contours were analyzed using Particle Image Velocimetry (PIV). Topological flow patterns were analyzed to interpret the vortical flow structures. Mixing properties were investigated using a tracer-gas concentration detection method. Four characteristic modes were observed: annular flow dominated mode, transition mode, central jet dominated mode-low shear, and central jet dominated mode-high shear. The jets’ mixing properties were enhanced by two major phenomena: the merging of annular flow and central jet at the centerline and the large turbulence fluctuations produced in the flow field. The merging of the jets induced stagnation points on the central axis in the annular flow dominated mode, which caused reverse flow on the central axis and drastic turbulence fluctuations of the near field region. When the central jet penetrated the recirculation region in the other three modes, the stagnation points on the central axis and the reverse flow vanished. Therefore, the mixing behaviors were prominently enhanced in the annular flow dominated mode.     

LES and RANS modelling of under-expanded jets with application to gaseous fuel direct injection for advanced propulsion systems

A density-based solver with the classical fourth-order accurate Runge-Kutta temporal discretization scheme was developed and applied to study under-expanded jets issued through millimetre-size nozzles for applications in high-pressure direct-injection (DI) gaseous-fuelled propulsion systems. Both large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) turbulence modelling techniques were used to evaluate the performance of the new code. The computational results were compared both quantitatively and qualitatively against available data from the literature. After initial evaluation of the code, the computational framework was used in conjunction with RANS modelling (k-ω SST) to investigate the effect of nozzle exit geometry on the characteristics of gaseous jets issued from millimetre-size nozzles. Cylindrical nozzles with various length to diameter ratios, namely 5, 10 and 20, in addition to a diverging conical nozzle, were studied. This study is believed to be the first to provide a direct comparison between RANS and LES within the context of nozzle exit profiling for advanced high-pressure injection systems with the formation of under-expanded jets. It was found that reducing the length of the straight section of the nozzle by 50% resulted in a slightly higher level of under-expansion (∼2.6% higher pressure at the nozzle exit) and ∼1% higher mass flow rate. It was also found that a nozzle with 50% shorter length resulted in ∼6% longer jet penetration length. At a constant nozzle pressure ratio (NPR), a lower nozzle length to diameter ratio resulted in a noticeably higher jet penetration. It was found that with a diverging conical nozzle, a fairly higher penetration length could be achieved if an under-expanded jet formed downstream of the nozzle exit compared to a jet issued from a straight nozzle with the same NPR. This was attributed to the radial restriction of the flow and consequently formation of a relatively smaller reflected shock angle. With the conical nozzle used in this study and a 30 bar injection pressure, an under-expanded hydrogen jet exhibited ∼60% higher penetration length compared to an under-expanded nitrogen jet at 100 μs after start of injection. Moreover, the former jet exhibited ∼22% higher penetration compared to a nitrogen jet issued through the conical profile with 150 bar injection pressure.     

Centreline mixing characteristics of jets from nine differently shaped nozzles

 The centreline mixing characteristics of jets from nozzles with nine different cross-sectional shapes are compared. It is shown that the breakdown of axisymmetry of the initial jet configuration generally results in increased mean-velocity decay and increased RMS fluctuations. Received: 23 February 1999/Accepted: 7 May 1999     

Numerical simulation of vibrational relaxation processes in unsteady gas jets

Minsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 55–60, September–October, 1994.     

Passive scalar measurements in a planar mixing layer by PLIF of acetone

 Quantitative passive scalar measurements were performed in an incompressible planar mixing layer at Re _δ up to 10⁴ using planar laser-induced fluorescence of acetone seeded into one side of the layer. Probability density functions compiled from sets of images showed a preferred mixture composition, favoring the high-speed fluid, which extended across the layer. This preferred composition produced non-marching PDFs and an inflection in the average mixture fraction profile. The spatial resolution of the experiment was found to be sufficient to accurately measure the fraction of mixed fluid within the layer. The mixed fluid fraction was found to increase to an asymptotic value of 0.5 by Re _δ  ≈ 5,000, the approximate location of turbulent transition, in contrast to high Schmidt number experiments which show minimal mixing before the transition point. Received: 5 October 1999 / Accepted: 9 February 2001     

Laminar mixing of planar supersonic chemically reacting jets of unequal pressure

A study is made of the influence of a transverse pressure gradient on the mixing of reacting jets of fluorine and hydrogen. The real picture is simulated by a system of simplified Navier-Stokes equations. A comparison is made with calculations based on the complete Navier-Stokes equations and also boundary layer equations. Features of the shock waves are analyzed under conditions of strong heat release in the mixing layer. The influence of these features on the gain in laser situations is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 18–23, May–June, 1982.We thank G. N. Volchkova, Yu. P. Golovachev, V. A. Pospelov, M. Kh. Strel'ts, and M. L. Shur for helpful discussions.     

Reynolds number effects on the mixing behavior of axisymmetric turbulent jets

Measurements of time-averaged jet fluid mass fraction and unmixedness are reported along the centerlines of axisymmetric jets having Reynolds numbers (Re) covering a range of 3,950–11,880. Jet gases investigated are propane, carbon tetrafluoride, and sulfur hexafluoride. The slopes for the fall off of inverse centerline mass fraction with distance are found to be independent of Re for moderate downstream distances, but virtual origins for the data are shown to move downstream with increasing Re. Unmixedness measurements show that flows with higher Re require longer flow distances to achieve asymptotic behavior. Results of other investigations reported in the literature are discussed which support the conclusions of this work. The relationship between the centerline mixing and entrainment behaviors of these flows is explored.