Interference in a three-dimensional array of jets

The theoretical investigation here of a three-dimensional array of jets of fluid (air guns) and their interference is motivated by applications to the food sorting industry especially. Three-dimensional motion without symmetry is addressed for arbitrary jet cross-sections and incident velocity profiles. Asymptotic analysis based on the comparatively long axial length scale of the configuration leads to a reduced longitudinal vortex system providing a slender flow model for the complete array response. Analytical and numerical studies, along with comparisons and asymptotic limits or checks, are presented for various cross-sectional shapes of nozzle and velocity inputs. The influences of swirl and of unsteady jets are examined. Substantial cross-flows are found to occur due to the interference. The flow solution is non-periodic in the cross-plane even if the nozzle array itself is periodic. The analysis shows that in general the bulk of the three-dimensional motion can be described simply in a cross-plane problem but the induced flow in the cross-plane is sensitively controlled by edge effects and incident conditions, a feature which applies to any of the array configurations examined. Interference readily alters the cross-flow direction and misdirects the jets. Design considerations centre on target positioning and jet swirling.

Energy dispersion in turbulent jets. Part 2. A robust model for unsteady jets

In this paper we develop an integral model for an unsteady turbulent jet that incorporates longitudinal dispersion of two distinct types. The model accounts for the difference in the rate at which momentum and energy are advected (type I dispersion) and for the local deformation of velocity profiles that occurs in the vicinity of a sudden change in the momentum flux (type II dispersion). We adapt the description of dispersion in pipe flow by Taylor (Proc. R. Soc. Lond. A, vol. 219, 1953, pp. 186–203) to develop a dispersion closure for the longitudinal transportation of energy in unsteady jets. We compare our model’s predictions to results from direct numerical simulation and find a good agreement. The model described in this paper is robust and can be solved numerically using a simple central differencing scheme. Using the assumption that the longitudinal velocity profile in a jet has an approximately Gaussian form, we show that unsteady jets remain approximately straight-sided when their source area is fixed. Straight-sidedness provides an algebraic means of reducing the order of the governing equations and leads to a simple advection–dispersion relation. The physical process responsible for straight-sidedness is type I dispersion, which, in addition to determining the local response of the area of the jet, determines the growth rate of source perturbations. In this regard the Gaussian profile has the special feature of ensuring straight-sidedness and being insensitive to source perturbations. Profiles that are more peaked than the Gaussian profile attenuate perturbations and, following an increase (decrease) in the source momentum flux, lead to a local decrease (increase) in the area of the jet. Conversely, profiles that are flatter than the Gaussian amplify perturbations and lead to a local increase (decrease) in the area of the jet.

Energy dispersion in turbulent jets. Part 1. Direct simulation of steady and unsteady jets

We study the physics of unsteady turbulent jets using direct numerical simulation (DNS) by introducing an instantaneous step change (both up and down) in the source momentum flux. Our focus is on the propagation speed and rate of spread of the resulting front. We show that accurate prediction of the propagation speed requires information about the energy flux in addition to the momentum flux in the jet. Our observations suggest that the evolution of a front in a jet is a self-similar process that accords with the classical dispersive scaling$z\sim \sqrt{t}$. In the analysis of the problem we demonstrate that the use of a momentum–energy framework of the kind used by Priestley & Ball (Q. J. R. Meteorol. Soc., vol. 81, 1955, pp. 144–157) has several advantages over the classical mass–momentum formulation. In this regard we generalise the approach of Kaminskiet al. (J. Fluid Mech., vol. 526, 2005, pp. 361–376) to unsteady problems, neglecting only viscous effects and relatively small boundary terms in the governing equations. Our results show that dispersion originating from the radial dependence of longitudinal velocity plays a fundamental role in longitudinal transport. Indeed, one is able to find dispersion in the steady state, although it has received little attention because its effects can then be absorbed into the entrainment coefficient. Specifically, we identify two types of dispersion. Type I dispersion exists in a steady state and determines the rate at which energy is transported relative to the rate at which momentum is transported. In unsteady jets type I dispersion is responsible for the separation of characteristic curves and thus the hyperbolic, rather than parabolic, nature of the governing equations, in the absence of longitudinal mixing. Type II dispersion is equivalent to Taylor dispersion and results in the longitudinal mixing of the front. This mixing is achieved by a deformation of the self-similar profiles that one finds in steady jets. Using a comparison with the local eddy viscosity, and by examining dimensionless fluxes in the vicinity of the front, we show that type II dispersion provides a dominant source of longitudinal mixing.

Unsteady Flow in Extraction Modules of Industrial Steam Turbines

Industrial steam turbines are designed for application in power-, process- and chemical engineering. Particular modules ensure the optimum integration into power plants and other engineering processes. Extraction modules allow the controlled extraction of large steam quantities on certain and constant enthalpy levels. Valves regulate the amount of steam extracted from the turbine expansion path. Depending on the valve lift, different flow separation phenomena can occur peripherally inside the valves, causing undesired large unsteady fluid forces on the valve head and seat. Due to the compact design of the industrial steam turbines, these unsteady jets can influence the rotor dynamics as well as the blade loading of the adjacent stages. These fluctuations should be understood and avoided in order to enhance the reliability of steam turbines. In the present study the unsteady flow phenomena due to separation occurring circumferentially inside the valve of extraction modules are investigated numerically. First, the commercial 3D RANS CFD-solver (ANSYS CFX 14) is validated in the application to experimental results. Subsequently, the various flow patterns of the examined valve design are analyzed on a standalone numerical valve model in an extensive study. In order to assess the impact of these unsteady flow separations on other components, the complete extraction module is simulated in combination with the adjacent stages. The transient simulation results show pressure fluctuations downstream of the valves resulting in an unsteady load of the control valves, the shaft and the blading.

Experimental and Numerical Study on Flow Field and Heat Transfer Characteristics for a Periodically Unsteady Impinging Jet

An experimental investigation has been carried out to study the effect of unsteady periodically impinging jets on the flow field and heat transfer characteristics. The experiments are performed for steady jets and for typical periodical jets (i.e., sinusoidal and rectangular jets) at frequencies from 1.25 to 40Hz. The periodical jets are produced by a special mass flow rate controller. The investigation shows that the stagnation point heat transfer does not show any enhancement for the periodically impinging jets when the frequency is lower. Various signals of unsteady jets show distinguishing frequency dependences and the rectangular jet, which has a step change in signal function itself, is the most effective one for heat transfer improvement and the degree of enhancement is in the range 30–40% at frequency of 40 Hz. This increase is believed to be caused by higher oscillations and strong entrainments to the ambient fluid. The hotwire anemometry is used to measure the velocity at centerline of the nozzle and PIV is used to measure the phase-locked flow field of the periodically impinging jet. The flow field is also obtained by numerical simulation with CFD.

LES Analysis of Gas Flow and Mixing Process in an Unsteady Jet

The flow and mixing process of unsteady jets are fundamentally analyzed by large eddy simulations. The effects of nozzle velocity and turbulence intensity on the turbulent eddy structure and mixing process between the nozzle fluid and ambient fluid were investigated. The results show that a toroidal-shaped vortex, which emerges around the jet tip, primarily accelerates the entraining flow. Furthermore, the difference of jet density affects the shape of toroidal vortex formed near jet tip and the air entrainment. Jet with lower density is less entrained and suppresses turbulent mixing.