Direct numerical simulation of free and forced square jets

"This study takes a Jacobian-free approach based on the Arnoldi iteration to present a method to perform hydrodynamic instability analysis based on Direct Numerical Simulations. The method employs high order spatial and temporal discretizations for the flow simulation and has very low requirements of computational time and memory, compared to conventional matrix-forming methods. Details of the numerical treatment applied to guarantee consistency in the numerical solution are discussed, such as mesh and domain dependencies, and buffer zones for the open boundary conditions. The implementation presented here is applicable to any flow with Cartesian geometry, however, the method can be extended to complex geometries and three-dimensional flows."

The purpose of this study is to numerically investigate the bed shear stress and near-bed mixing due to coherent vortex structures in the vicinity of a vertically wall-mounted circular cylinder subject to an imposed finite-depth oscillatory sinusoidal flow. Previous studies reveal that the Keulegan–Carpenter (KC) number influences the formation of lee-side wake vortex structures as well as the horseshoe vortex in front of a cylinder. Therefore, parametric studies in a moderately wide range of KC from 5 to 20 are numerically performed. In the present study, Direct Numerical Simulation (DNS) is conducted using the open-source software, OpenFOAM, that solves the three-dimensional unsteady incompressible Navier-Stokes equations using finite volume method. Nondimensional parameters used in the simulations are carefully chosen to represent the real physics. The numerical solutions are first validated using an analytical solution for the oscillating Stokes flow and the results are then systematically and quantitatively compared with the experimental measurements. The results show that the lee-side wake is significantly influenced by KC, and distinctive types of the lee-side wake are generated and classified based on KC. It is also found that both KC and the ratio of the thickness of the Stokes boundary layer to the water depth are heavily associated with the stability of the lee-side wake. In addition, the simulated size and lifespan of the horseshoe vortex agree well with the experimental data.

Turbulence structure near a wavy-sheared air-water interface was numerically investigated using a direct numerical simulation (DNS). The unsteady three-dimensional Navier-Stokes equations were numerically solved on both air and water sides for a wind-driven turbulent flow with a Reynolds number Re=6700, based on the maximum wave height and uniform velocity on the air side. Two boundary conditions [1] were used to determine the instantaneous shape of air-water interface. One was the dynamical boundary condition determined from the balance of the normal and tangential stresses acting on the wavy air-water interface, and the other was the kinematic boundary condition that describes the Lagrangian behavior of the air-water interface. The results show that the organized motion intermittently appears on the front side of the wavy interface in the air flow. The organized motion in the air flow gives high shear and pressure on the interface. The high shear and pressure acting on the wavy air-water interface induce the organized surface-renewal motion in the water flow beneath the air-water interface, which controls heat and mass transfer across the interface. The predictions well explain the previous measurements in the wind wave tank [2].

*† ‡ § This experimental study explores the nature and control of shear layer instabilities associated with the single jet in crossflow or transverse jet, a flowfield widely used in propulsive devices. These studies take advantage of prior experimental findings which suggest that the character of the jet’s nearfield shear layer instabilities can be significantly different for the transverse jet as compared with the free jet, and that the instabilities transition further when the jet-to-crossflow velocity ratio R is reduced below approximately 3.5. The differences in the stability characteristics of the jet in crossflow suggest the necessity of a “two-pronged” approach to the control of transverse jet penetration and spread, depending on the values of R, which is explored in this paper. For the transverse jet where R > 3.5, the instabilities are initiated beyond one diameter of the jet orifice, with a type of spatial evolution that indicates a convectively unstable flow. Such instabilities are affected by even low level sinusoidal forcing of the jet, which can then be used to control jet penetration and spread. For the case where R lies below 3.5, however, there is a rapid initiation of strong, distinct modes and harmonics near the jet exit that do not evolve spatially and are not affected by even strong external sinusoidal forcing of the jet. In this instance, strong jet forcing with a prescribed time scale is required to impact jet behavior. It is demonstrated that when the applied jet forcing waveform is a square wave with a prescribed temporal pulsewidth, significant jet response can be obtained even under globally unstable conditions.

Fig. 1. The evolution of the large-scale coherent structures from symmetric mode to asymmetric mode in the jet flow-field. (a)t=64.82; (b)t=93.62; (c)t=237.62; (d) t=381.62; A turbulent co-flow jet with flow Reynolds number of 6000 is studied numerically by using DNS technique. The flow is two-dimensional, compressible and spatial developing. The evolution of the coherent vortex structures in the near nozzle filed is investigated. To solve the Navier-Stokes equations directly, a new fourth-order compact finite difference scheme is chosen to discretize the spatial derivatives in non-uniform meshes. The five-stage fourth-order Runge-Kutta integration scheme is adopted to march the Euler terms with sufficient numerical accuracy and lower memory requirement. In addition, the non-uniform forth-order compact filter is utilized to eliminate the high wave number errors. Figure 1 shows the evolution of the coherent structures from symmetric mode to asymmetric mode. At first, the development of the large-scale coherent structures is symmetric pattern, as shown in Fig. 1(a). Then from the non-dimensional time t=93.62, the symmetry of the vortex structures is destroyed and the asymmetric coherent structures are dominant in the flow field, as shown in Fig. 1(b), (c) and (d).

Near-wall coherent structures in the turbulent channel flow of a dilute polymer solution

Direct numerical simulations (DNS) of flow over an NACA-0012 airfoil are performed at a low and a moderate Reynolds numbers of Re(sub c)=50 times10(exp 3) and 1times 10(exp 6). The angles of attack are 5 and 15 degrees at the low and the moderate Reynolds number cases respectively. The three-dimensional unsteady compressible Navier-Stokes equations are solved using higher order compact schemes. The flow field in the low Reynolds number case consists of a long separation bubble near the leading-edge region and an attached boundary layer on the aft part of the airfoil. The shear layer that formed in the separated region persisted up to the end of the airfoil. The roles of the turbulent diffusion, advection, and dissipation terms in the turbulent kinetic-energy balance equation change as the boundary layer evolves over the airfoil. In the higher Reynolds number case, the leading-edge separation bubble is very small in length and in height. A fully developed turbulent boundary layer is observed in a short distance downstream of the reattachment point. The boundary layer velocity near the wall gradually decreases along the airfoil. Eventually, the boundary layer separates near the trailing edge. The Reynolds stresses peak in the outer part of the boundary layer and the maximum amplitude also gradually increases along the chord.

The effects of nanoparticle volume fraction in hydrodynamic and thermal characteristics of an incompressible forced 2-D plane jet flow are investigated. Direct Numerical Simulation (DNS) of a two dimensional incompressible plane forced jet flow for two nanofluids has been performed. The base fluid is water and the nanoparticles are Al O ,CuO 2 3 . The numerical simulation is carried out for the solid volume fraction between 0 to 4%. The results for both nanofluids indicate that any increase in the solid volume fraction decreases the amplitude of temperature, velocity time histories, the turbulent intensities and that of the Reynolds stresses. The results for both two nanoparticles also indicate that with any increase in nanoparticle volume fraction, the velocity amplitude of velocity time history, the turbulent intensities and Reynolds stress in 2 3 Al O -water are greater than that ofCuO-water nanofluid.

Statistics of inertial particle deviation from fluid particle trajectories in horizontal rough wall turbulent channel flow

Forced-convection heat transfer in a heated working fluid at a thermodynamic state near its pseudocritical point is poorly predicted by correlations calibrated with data at subcritical temperatures and pressures. This is suggested to be primarily due to the influence of large wall-normal thermophysical property gradients that develop in proximity of the pseudocritical point on the concentration of coherent turbulence structures near the wall. The physical mechanisms dominating this influence remain poorly understood. In the present study, direct numerical simulation is used to study the development of coherent vortical structures within a turbulent spot under the influence of large wall-normal property gradients. A turbulent spot rather than a fully turbulent boundary layer is used for the study, for the coherent structures of turbulence in a spot tend to be in a more organized state which may allow for more effective identification of cause-and-effect relationships. Large wall-normal gradients in thermophysical properties are created by heating the working fluid which is near the pseudocritical thermodynamic state. It is found that during improved heat transfer, wall-normal gradients in density accelerate the growth of the Kelvin-Helmholtz instability mechanism in the shear layer enveloping low-speed streaks, causing it to roll up into hairpin vortices at a faster rate. It is suggested that this occurs by the baroclinic vorticity generation mechanism which accelerates the streamwise grouping of vorticity during shear layer roll-up. The increased roll-up frequency leads to reduced streamwise spacing between hairpin vortices in wave packets. The density gradients also promote the sinuous instability mode in low-speed streaks. The resulting oscillations in the streaks in the streamwise-spanwise plane lead to locally reduced spanwise spacing between hairpin vortices forming over adjacent low-speed streaks. The reduction in streamwise and spanwise spacing between hairpin vortices causes them to interact more frequently by merging together and by breaking apart into smaller turbulence structures.

We use Direct Numerical Simulation (DNS) data to study inter-scale and inter-space energy exchanges in the near-field of a turbulent wake of a square prism in terms of a Kármán-Howarth-Monin-Hill (KHMH) equation written for a triple decomposition of the velocity field which takes into account the presence of quasi-periodic vortex shedding coherent structures. Concentrating attention on the plane of the mean flow and on the geometric centreline, we calculate orientation-averages of every term in the KHMH equation. The near-field considered here ranges between 2 and 8 times the width d of the square prism and is very inhomogeneous and out of equilibrium so that non-stationarity and inhomogeneity contributions to the KHMH balance are dominant. The mean flow produces kinetic energy which feeds the vortex shedding coherent structures. In turn, these coherent structures transfer their energy to the stochastic turbulent fluctuations over all length-scales r from the Taylor length to d and dominate spatial turbulent transport of small-scale two-point stochastic turbulent fluctuations. The orientation averaged non-linear inter-scale transfer rate a which was found to be approximately independent of r by Alves Portela et al. (2017) in the range 6 r 6 0:3d at a distance x1 = 2d from the square prism requires an inter-scale transfer contribution of coherent structures for this approximate constancy. However, the near-constancy of a in the range 6 r 6 d at x1 = 8d which was also found by Alves Portela et al. (2017) is mostly attributable to stochastic fluctuations. Even so, the proximity of 􀀀 a to the turbulence dissipation rate " in the range 6 r 6 d at x1 = 8d does require inter-scale transfer contributions of the coherent structures. Spatial inhomogeneity also makes a direct and distinct contribution to a, and the constancy of 􀀀 a=" close to 1 would not have been possible without it either in this near-field flow. Finally, the pressure-velocity term is also an important contributor to the KHMH balance in this near-field, particularly at scales r larger than about 0:4d, and appears to correlate with the purely stochastic non-linear inter-scale transfer rate when the orientation average is lifted.

In order to develop a new mixing procedure, we conduct DNS (direct numerical simulation) of vector control for free jet. A nozzle is rotating around the streamwise axis of jet. From view of instantaneous vortex structures, it is found that the structures are modulate, compared with the case of the free jet. In contours of ensemble averaged streamwise velocity, the jet diffuses largely in the radial direction. In addition, in order to estimate the mixing performance, the statistical entropy is calculated. It is found that the mixing efficiency are improved than that of uncontrolled case. Further for a candidate case of vector control, a structural mode analysis is conducted with both POD(proper orthogonal decomposition) and DMD(dynamic mode decomposition). It reveals that a dominant mode structure which is governed with the rotating frequency of vector control, seems to contribute to the mixing enhancement downstream.

Direct numerical simulations are performed of spatial, three-dimensional, laminar jets of different inlet geometric configurations for the purpose of quantifying the characteristics of the flows; both single-phase (SP) and two-phase (TP) free jets are considered. The TP jets consist of gas laden with liquid drops randomly injected at the inlet. Drop evaporation ensues both due to the gaseous flow being initially unvitiated by the vapor species corresponding to the liquid drops, and to drop heating as the initial drop temperature is lower than that of the carrier gas. The conservation equations for the TP flow include complete couplings of mass, momentum, and energy based on thermodynamically self-consistent specification of the vapor enthalpy, internal energy, and latent heat of vaporization. Inlet geometries investigated are circular, elliptic, rectangular, square, and triangular. The results focus both on the different spreading achieved according to the inlet geometry, as well as on the considerable change in the flow field due to the presence of the drops. The most important consequence of the drop interaction with the flow is the production of streamwise vorticity that alters entrainment and species mixing according to the inlet geometry. Similar to their SP equivalent, TP jets are shown to reach steady-state entrainment; examination of the flows at this time station shows that the potential cores of TP jets are shorter by an order of magnitude than their SP counterpart. Moreover, whereas the TP circular jet exhibits a symmetric entrainment pattern well past the streamwise location of the potential core, noncircular jets display at the same location strong departures from symmetry. Furthermore, the SP-jet phenomenon of axis switching is no longer present in TP jets. The distributions of drop-number density, liquid mass, and evaporated species are compared for different inlet cross sections and recommendations are made regarding the optimal choice for different applications.

In order to develop a new mixing procedure, we conduct DNS (direct numerical simulation) of vector control for free jet. The nozzle is periodically oscillated by vector control. From view of instaneous vortex structures, it is found that the structures are modulate, compared with the case of the free jet. In contours of ensemble averaged streamwise velocity and turbulence kinetic energy, the jet diffuses largely in the oscillating direction. While, the jet shrinks in the perpendicular to this direction. As a result, the vector control can be expected for the improvement of mixing efficiency.

A new statistical coherent structure (CS), the velocity–vorticity correlation structure (VVCS), using the two-point cross-correlation coefficient $R_{ij}$ of velocity and vorticity components, $u_i$ and $\omega _j~ (i, j = 1, 2, 3)$, is proposed as a useful descriptor of CS. For turbulent channel flow with the wall-normal direction $y$, a VVCS study consists of using $u_i$ at a fixed reference location $y_r$, and using $|R_{ij} (y_r; x, y, z)|\geqslant R_0$ to define a topologically invariant high-correlation region, called $\mathit{VVCS}_{ij}$. The method is applied to direct numerical simulation (DNS) data, and it is shown that the $\mathit{VVCS}_{ij}$ qualitatively and quantitatively captures all known geometrical features of near-wall CS, including spanwise spacing, streamwise length and inclination angle of the quasi-streamwise vortices and streaks. A distinct feature of the VVCS is that its geometry continuously varies with $y_r$. A topological change of $\mathit{VVCS}_{11}$ from quadrupole (for smaller $y_r$) to dipole (for larger $y_r$) occurs at $y^{+}_r=110$, giving a geometrical interpretation of the multilayer nature of wall-bounded turbulent shear flows. In conclusion, the VVCS provides a new robust method to quantify CS in wall-bounded flows, and is particularly suitable for extracting statistical geometrical measures using two-point simultaneous data from hotwire, particle image velocimetry/laser Doppler anemometry measurements or DNS/large eddy simulation data.