Cyrus K. Madnia

Numerical simulation of non-circular jets

Abstract Results are presented of numerical simulations of spatially developing, three-dimensional jets issued from circular and non-circular nozzles of identical equivalent diameters. Elliptic, rectangular and triangular jets are considered with aspect-ratios of 1:1 and 2:1. Flow visualization results show that large scale coherent structures are formed in both cornered and non-cornered jets. The axis-switching phenomenon is captured in all non-unity aspect-ratio jets and also in the equilateral triangular jet. The square jet does not show axis-switching; however, the rotation of its axes by 45 ° is shown to play a significant role in its entrainment characteristics. All the non-circular configurations are shown to provide more efficient mixers than does the circular jet; the isosceles triangular jet is the most efficient one. It is demonstrated that the near field entrainment and mixing is characterized by the mean secondary flow induced by the stream-wise vortices. The transport of a passive Shvab-Zeldovich scalar variable is used to determine the limiting rate of mean reactant conversion in a chemical reaction of the type Fuel + Air → Products. The results show that the largest product formation occurs in the isosceles triangular jet and the lowest occurs in the circular jet. It is also shown that the 2:1 triangular jet has the shortest scalar core whereas the rectangular jet has the longest core.

Interaction of a Turbulent Round Jet with the Free Surface

Abstract : An experimental study of the interaction of an underwater turbulent round jet with the free surface was conducted. Flow visualization, 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 approach the free surface. These waves propagate at an angle with respect to the flow direction. The propagation angle increases as the strength of the interaction is increased by increasing the momentum flux of the jet or reducing the distance of the jet to the free surface or both. Propagation of these waves in the flow direction is suppressed by the surface current produced by the jet. Far downstream the surface motions are caused by the large scale vortical structures interacting directly with the surface. The fundamental scaling parameters of the free-surface jet have been determined. The velocity scale is the velocity obtained from the combination of jet momentum, density and depth of the jet and the length scale is the distance of the et to the free surface. It is shown that the centerline velocity decay when scaled with these parameters collapses to a universal curve for different depths of the jet.

Direct numerical simulation of a laminar vortex ring

Results are presented of direct numerical simulations (DNS) of a viscous, laminar ring. The effects of different generator configurations and velocity programs on the formation and post‐formation characteristics of the ring are studied. It is shown that during the formation phase of the ring, total circulation and impulse in the flowfield are approximately the same for the ‘‘nozzle’’ and ‘‘orifice’’ generators. It is also found that throughout this period the slug flow model under‐predicts the total circulation in the flow. During the formation phase, the simulation results for the time evolution of total circulation and location of the vortex spiral center are in agreement with the experimental findings of Didden [J. Appl. Mech. Phys. (ZAMP) 30, 101 (1979)]. The results of the flow visualization studies show that during the post‐formation phase a vortex bubble is formed. As the bubble propels itself forward a wake is formed in the rear of the bubble. The impulse and vorticity from the bubble are continuo...

Structure of a Turbulent Reacting Mixing Layer

Abstract Results are presented of direct numerical simulations (DNS) of an unsteady, three-dimensional, temporally developing, compressible mixing layer under both non-reacting and reacting non-premixed conditions. In the reacting case, a simple chemistry model of the type A + rB -»(1 + r)Products is considered. Based on simulated results, it is shown that at sufficiently large Reynolds numbers the global and statistical features of mixing transitions are similar to those observed experimentally. At sufficiently large Mach numbers, it is shown that eddy shockletsdo indeed exist in three-dimensional (3D) flow. However, the strength of these shocks is less than that in two-dimensional (2D) layers of the same compressibility level. Aided by the analysis of the DNS data, the extent of validity of the “Steady Laminar, Diffusion Flamelet Model” (SLDFM) and the “Conditional Moment Method“ (CMM) are assessed. In the evaluation of the SLDFM, DNS results for different stoichiometric coefficients and reaction types ...

Effects of Compressibility and Heat Release In a High Speed Reacting Mixing Layer

Abstract Results are presented of direct numerical simulations of a two-dimensional temporally developing high speed mixing layer under the influence of a second-order non-equilibrium chemical reaction of the type A + B→ Products + Heat. Simulations arc performed with different magnitudes of the convective Mach number and with different chemical kinetics parameters for the purpose of examining the isolated effects of the compressibility and the heat released by the chemical reaction on the structure or the layer, A full compressible code is developed and utilized, so that the coupling between mixing and chemical reaction is captured in a realistic manner. The results of numerical experiments indicate that at the initial stages of the layers growth, the heat release results in a slight enhanced mixing, whereas at the intermediate and the final stages, it has a reverse influence. The effect of compressibility is the same in all stages of the development: increased compressibility results in a suppressed mix...

Characteristics of chemically reacting compressible homogeneous turbulence

Direct numerical simulations (DNS) are conducted to study the turbulence-chemical reaction interactions in homogeneous decaying compressible fluid flows. The reaction is of a single-step irreversible Arrhenius type. The results indicate that the heat of reaction has a noticeable influence on the solenoidal and the dilatational turbulent motions. The effect of reaction on the solenoidal velocity field is primarily due to variation of the molecular diffusivity coefficients with temperature and appears at small scales. However, the dilatational motions are affected more than the solenoidal motions and are intensified at all length scales. The decay rate of the turbulent kinetic energy is dependent on the molecular dissipation and the pressure-dilation correlation. In isothermal reacting cases, the net contribution of the pressure-dilatation is small and the turbulent energy decays continuously due to viscous dissipation. In the exothermic reacting cases, the pressure-dilatation tends to increase the turbulen...

The effects of heat release on the energy exchange in reacting turbulent shear flow

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 x 2 -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.

Flame–vortex interaction in a reacting vortex ring

Direct numerical simulations are used to study the flame–vortex interaction in a laminar reacting vortex ring. The chemical reaction occurs by a one-step, Arrhenius-type reaction that mimics the combustion of typical hydrocarbon and air. The ring is generated by an axisymmetric jet that is impulsed to emit a cold fuel through a nozzle. The fuel enters a quiescent ambient at a much higher temperature. By adjusting the ratio of the ambient and fuel temperatures, the ignition either occurs during the formation or post-formation phase of the ring. When ignition occurs during the formation phase of the ring, the bulk of combustion is by a flame at the front of the vortex bubble. When ignition is delayed until after the formation phase, most of the reaction occurs inside the vortex ring. It is found that premixing the fuel and the oxidizer enhances the amount of product formation. The heat released from the reaction significantly affects production, redistribution, and diffusion of the vorticity throughout the ...

Johnson-Edgeworth Translation for Probability Modeling of Binary Scalar Mixing in Turbulent Flows

Abstract A family of Probability Density Functions (PDFs) generated by Johnson-Edgeworth Translation (JET) is used for statistical modeling of the mixing of an initially binary scalar in isotropic turbulence. The frequencies obtained by this translation are shown to satisfy some of the characteristics of the PDFs generated by the Amplitude Mapping Closure (AMC) (Kraichnan, 1989; Chen et al., 1989). In fact, the solution obtained by one of the members of this family is shown to be identical to that developed by the AMC (Pope, 1991). Due to this similarity and due to the demonstrated capabilities of the AMC, a justification is provided for the use of other members of JET frequencies for the modeling of the binary mixing problem. This similarity also furnishes the reasoning for the applicability of the Pearson Family (PF) of frequencies for modeling of the same phenomena. The mathematical requirements associated with the applications of JET in the modeling of the binary mixing problem are provided, and all...

Small scale structure of homogeneous turbulent shear flow

The structure of homogeneous turbulent shear flow is studied using data generated by direct numerical simulations (DNS) and a linear analysis for both compressible and incompressible cases. At large values of the mean shear rate, the rapid distortion theory (RDT) limit is approached. Analytical solutions are found for the inviscid compressible RDT equations at long times. The RDT equations are also solved numerically for both inviscid and viscous cases. The RDT solutions, confirmed by the DNS results, show that the even order transverse derivative moments of the dilatational and solenoidal velocity fields are anisotropic, with the dilatational motions more anisotropic than their solenoidal counterparts. The results obtained for the incompressible case are similar to those obtained for the solenoidal motions in the compressible case. The DNS results also indicate an increase in the anisotropy of the even order transverse derivative moments with the order of the moment, in agreement with the RDT predictions...