4 results
Interaction of a turbulent round jet with the free surface
- C. K. Madnia, L. P. Bernal
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- Journal:
- Journal of Fluid Mechanics / Volume 261 / 25 February 1994
- Published online by Cambridge University Press:
- 26 April 2006, pp. 305-332
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The interaction of a turbulent round jet with the free surface was investigated experimentally. Flow visualization, free-surface curvature measurements and hot-film velocity measurements were used to study this flow. It is shown that surface waves are generated by the large-scale vortical structures in the jet flow as they interact with the free surface. These waves propagate at an angle with respect to the flow direction which increases as the Froude number is increased. Propagation of the waves in the flow direction is suppressed by the surface current produced by the jet. Farther downstream the surface motions are caused by the large-scale vortical structures. Characteristic dark circular features are observed in shadowgraph images associated with concentrated vorticity normal to the free surface. The normal vorticity is believed to be the result of vortex line reconnection processes in the turbulent flow. Measurements of the mean velocity and turbulence intensity are reported. Owing to the confinement by the free surface, the decay rate of the maximum mean velocity is reduced by a factor of √2 compared to an unconfined jet.
Non-Gaussian scalar statistics in homogeneous turbulence
- F. A. Jaberi, R. S. Miller, C. K. Madnia, P. Givi
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- Journal:
- Journal of Fluid Mechanics / Volume 313 / 25 April 1996
- Published online by Cambridge University Press:
- 26 April 2006, pp. 241-282
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Results are presented of numerical simulations of passive scalar mixing in homogeneous, incompressible turbulent flows. These results are generated via the Linear Eddy Model (LEM) and Direct Numerical Simulation (DNS) of turbulent flows under a variety of different conditions. The nature of mixing and its response to the turbulence field is examined and the single-point probability density function (p.d.f.) of the scalar amplitude and the p.d.f.s of the scalar spatial-derivatives are constructed. It is shown that both Gaussian and exponential scalar p.d.f.s emerge depending on the parameters of the simulations and the initial conditions of the scalar field. Aided by the analyses of data, several reasons are identified for the non-Gaussian behaviour of the scalar amplitude. In particular, two mechanisms are identified for causing exponential p.d.f.s: (i) a non-uniform action of advection on the large and the small scalar scales, (ii) the nonlinear interaction of the scalar and the velocity fluctuations at small scales. In the absence of a constant non-zero mean scalar gradient, the behaviour of the scalar p.d.f. is very sensitive to the initial conditions. In the presence of this gradient, an exponential p.d.f. is not sustained regardless of initial conditions. The numerical results pertaining to the small-scale intermittency (non-Gaussian scalar derivatives) are in accord with laboratory experimental results. The statistics of the scalar derivatives and those of the velocity-scalar fluctuations are also in accord with laboratory measured results.
The effects of heat release on the energy exchange in reacting turbulent shear flow
- D. LIVESCU, F. A. JABERI, C. K. MADNIA
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- Journal:
- Journal of Fluid Mechanics / Volume 450 / 10 January 2002
- Published online by Cambridge University Press:
- 09 January 2002, pp. 35-66
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The energy exchange between the kinetic and internal energies in non-premixed reacting compressible homogeneous turbulent shear flow is studied via data generated by direct numerical simulations (DNS). The chemical reaction is modelled by a one- step exothermic irreversible reaction with Arrhenius-type reaction rate. The results show that the heat release has a damping effect on the turbulent kinetic energy for the cases with variable transport properties. The growth rate of the turbulent kinetic energy is primarily in uenced by the reaction through temperature-induced changes in the solenoidal dissipation and modifications in the explicit dilatational terms (pressure–dilatation and dilatational dissipation). The production term in the scaled kinetic energy equation, which is proportional to the Reynolds shear stress anisotropy, is less affected by the heat release. However, the dilatational part of the production term increases during the time when the reaction is important. Additionally, the pressure–dilatation correlation, unlike the non-reacting case, transfers energy in the reacting cases, on the average, from the internal to the kinetic energy. Consequently, the dilatational part of the kinetic energy is enhanced by the reaction. On the contrary, the solenoidal part of the kinetic energy decreases in the reacting cases mainly due to an enhanced viscous dissipation. Similarly to the non-reacting case, it is found that the direct coupling between the solenoidal and dilatational parts of the kinetic energy is small. The structure of the flow with regard to the normal Reynolds stresses is affected by the heat of reaction. Compared to the non-reacting case, the kinetic energy in the direction of the mean velocity decreases during the time when the reaction is important, while it increases in the direction of the shear. This increase is due to the amplification of the dilatational kinetic energy in the x2-direction by the reaction. Moreover, the dilatational effects occur primarily in the direction of the shear. These effects are amplified if the heat release is increased or the reaction occurs at later times. The non-reacting models tested for the explicit dilatational terms are not supported by the DNS data for the reacting cases, although it appears that some of the assumptions employed in these models hold also in the presence of heat of reaction.
Passive-scalar wake behind a line source in grid turbulence
- D. LIVESCU, F. A. JABERI, C. K. MADNIA
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- Journal:
- Journal of Fluid Mechanics / Volume 416 / 10 August 2000
- Published online by Cambridge University Press:
- 10 August 2000, pp. 117-149
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The structure and development of the scalar wake produced by a single line source are studied in decaying isotropic turbulence. The incompressible Navier–Stokes and the passive-scalar transport equations are solved via direct numerical simulations (DNS). The velocity and the scalar fields are generated by simulating Warhaft's (1984) experiment. The results for mean and r.m.s. scalar statistics are in good agreement with those obtained from the experiment. The structure of the scalar wake is examined first. At initial times, most of the contribution to the scalar variance is due to the flapping of the wake around the centreline. Near the end of the turbulent convective regime, the wake develops internal structure and the contribution of the flapping component to the scalar variance becomes negligible. The influence of the source size on the development of the scalar wake has been examined for source sizes ranging from the Kolmogorov microscale to the integral scale. After an initial development time, the half-widths of mean and scalar r.m.s. wakes grow at rates independent of the source size. The mixing in the scalar wake is studied by analysing the evolution of the terms in the transport equations for mean, scalar flux, variance, and scalar dissipation. The DNS results are used to test two types of closures for the mean and the scalar variance equations. For the time range simulated, the gradient diffusion model for the scalar flux and the commonly used scalar dissipation model are not supported by the DNS data. On the other hand, the model based on the unconditional probability density function (PDF) method predicts the scalar flux reasonably well near the end of the turbulent convective regime for the highest Reynolds number examined. The scalar source size does not significantly influence the models' predictions, although it appears that the time-scale ratio of mechanical dissipation to scalar dissipation approaches an asymptotic value earlier for larger source sizes.