The current work presents a tensor formulation of the Lumley Decomposition (LD), introduced in its original form by Lumley (1967b), allowing decompositions of turbulent flow fields in curvilinear coordinates. The LD in his form is shown to enable semi-analytical decompositions of self-similar turbulent flows in general coordinate systems. The decomposition is applied to the far-field region of the fully developed turbulent axi-symmetric jet, which is expressed in stretched spherical coordinates in order to exploit the self-similar nature of the flow while ensuring the self-adjointness of the LD integral. From the LD integral it is deduced that the optimal eigenfunctions in the streamwise direction are stretched amplitude-decaying Fourier modes (SADFM). The SADFM are obtained from the LD integral upon the introduction of a streamwise-decaying weight function in the vector space definition. The wavelength of the Fourier modes is linearly increasing in the streamwise direction with an amplitude which decays with the -3/2 power of distance from the virtual origin. The streamwise evolution of the SADFM re-sembles reversed wave shoaling known from surface waves. The energy- and cross-spectra obtained from these SADFM exhibit a -5/3- and a -7/3-slope region, respectively, as would be expected for regular Fourier modes in homogeneous and constant shear flows. The approach introduced in this work can be extended to other flows which admit to equilibrium similarity, such that a Fourier-based decomposition along inhomogeneous flow directions can be performed.
In the current work the reconstruction of the far-field region of the turbulent axi-symmetric jet is performed in order to investigate the modal turbulence kinetic energy production contributions. The reconstruction of the field statistics is based on a semi-analytical Lumley Decomposition (LD) of the PIV sampled field using stretched amplitude decaying Fourier modes (SADFM), derived in Hodžić et al. 2019, along the streamwise coordinate. It is shown that, a wide range of modes obtain a significant amount of energy directly from the mean flow, and are therefore not exclusively dependent on a R…
Lumley [Lumley J.L.: Adv. Appl. Mech. 18 (1978) 123--176] provided a geometrical proof that any Reynolds-stress tensor $\overline{u_i'u_j'}$ (indeed any tensor whose eigenvalues are invariably nonnegative) should remain inside the so-called Lumley's realizability triangle. An alternative formal algebraic proof is given that the anisotropy invariants of any positive-definite symmetric Cartesian rank-2 tensor in the 3-D Euclidian space $\mathbb{E}^3$ define a point which lies within the realizability triangle. This general result applies therefore not only to $\overline{u_i'u_j'}$ but also to ma…
Numerical simulations of turbulent round jets, using explicit-filtered LES technique, are performed, for three different Reynolds numbers(Re = 3600, 88000, 400000), to understand the Reynolds number effect on subsonic jets with Mach number 0.9. Eigth-order compact schemes are used for spatial derivative estimation. Second order Runge-Kutta method is used for Time evolution of flow. One-parameter fourth-order compact filter is used for low-pass explicit filtering of transported variables. Decreased centreline axial velocity decay rate and reduced turbulence intensities are observed as jet Reyno…
We propose a family of two-phase-fluid models for a full-cone turbulent round jet that describe its dynamics in a simple but comprehensive manner with the apex angle of the cone being the main disposable parameter. The basic assumptions are that (i) the jet is statistically stationary and that (ii) it can be approximated by a mixture of two fluids with their phases in dynamic equilibrium (so-called Locally Homogeneous Flow). To derive the model, we impose either full or partial conservation of the initial mass and total power fluxes, introducing mass and power loss factors as disposable parame…
We propose a two-phase-fluid model for a full-cone turbulent round jet that describes its dynamics in a simple but comprehensive manner with only the apex angle of the cone being a disposable parameter. The basic assumptions are that (i) the jet is statistically stationary and that (ii) it can be approximated by a mixture of two fluids with their phases in dynamic equilibrium. To derive the model, we impose conservation of the initial volume and total momentum fluxes. Our model equations admit analytical solutions for the composite density and velocity of the two-phase fluid, both as functions…
In this paper, the novel experimental data reported by Qin et al. [1] are used to assess the predictive capability of the Realizable k-epsilon (RKE) model and Reynolds stress transport (RST) model for buoyant jets and understand the reasons for discrepancies. In particular, we present the comparison between simulation results of a turbulent buoyant jet flow in the self-similar region with high-resolution experimental data obtained for a jet injected from a 2 mm nozzle into a 300x300x300 $mm^3$ tank, with nominal Reynolds number equal to 10,000. Results show that streamwise velocity profiles pr…
We study properties of dilute polymer solutions which are known to depend strongly on polymer elongation. The probability density function (PDF) of polymer end-to-end extensions $R$ in turbulent flows is examined. We demonstrate that if the value of the Lyapunov exponent $λ$ is smaller than the inverse molecular relaxation time $1/τ$ then the PDF has a strong peak at the equilibrium size $R_0$ and a power tail at $R\gg R_0$. This confirms and extends the results of \cite{Lumley72}. There is no essential influence of polymers on the flow in the regime $λτ<1$. At $λ>1/τ$ the majority of molecule…
The present paper investigates high performance computing abilities of OpenFOAM for a low Reynolds number ($Re_D=2000$) axisymmetric jet subject to multiple zero net mass flux (ZNMF) actuators. First, parallel performance of OpenFOAM is tested by performing a scaling study up to $2048$ processors on a supercomputer of Flemish Supercomputer Center(VSC). Then, a method to improve the parallel efficiency is proposed. The method is based on developing a hybrid concept to calculate the statistical moments. This new concept combines ensemble and time averaging in order to allow data sampling in para…
Experiments and numerical simulations were conducted to investigate the dispersion of turbulent jets issuing from realistic pipe geometries. The effect of jet densities and Reynolds numbers on vertical buoyant jets were investigated, as they emerged from the side wall of a circular pipe, through a round orifice. Particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) techniques were employed simultaneously to provide time-averaged flow velocity and concentrations fields. Large eddy simulation (LES) was applied to provide further detail with regards to the three-dimensiona…
A population balance model coupled with large eddy simulations (LES) is adapted and applied to study the evolution of oil droplets in a turbulent jet including the effects of droplet breakup. A key unknown in simulating secondary breakup in turbulent multiphase jets is the inflow size distribution generated within the primary breakup zone near the nozzle exit. A mono-disperse injection inflow condition is commonly used for simplicity, but this choice is often unrealistic. In order to provide more realistic inlet conditions for LES, we develop a one dimensional (1D) parcel model to predict the …
We consider the frequency domain form of proper orthogonal decomposition (POD) called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space-time POD problem for statistically stationary flows and leads to modes that each oscillate at a single frequency. This form of POD goes back to the original work of Lumley (Stochastic tools in turbulence, Academic Press, 1970), but has been overshadowed by a space-only form of POD since the 1990s. We clarify the relationship between these two forms of POD and show that SPOD modes represent structures that evolve coherently i…
Buoyancy effects and nozzle geometry can have a significant impact on turbulent jet dispersion. This work was motivated by applications involving hydrogen. Using helium as an experimental proxy, buoyant horizontal jets issuing from a round orifice on the side wall of a circular tube were analysed experimentally using particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) techniques simultaneously to provide instantaneous and time-averaged flow fields of velocity and concentration. Effects of buoyancy and asymmetry on the resulting flow structure were studied over a range…
Wave Particle Turbulent Simulation of Spatially Developing Round Jets Using a Non Equilibrium Transport Model with a Mixing Length Characteristic Time Closure
Seedless velocimetry is gaining interest in many industrial and research applications. We report on a comparative study of time-resolved optical velocimetry using traditional, mirror-type knife-edge schlieren optics versus Background-Oriented Schlieren (BOS) of subsonic round turbulent helium jets in air at Red = 5,890 and 11,300. Digital images with 1024 pixels streamwise resolution (0 < x/d < 200) were captured at 6000 frames/s in large ensembles. Velocimetry was performed on these results by digital image correlation (DIC) using OpenPIV software, and by streak-schlieren analysis of x-t diag…
In light of recent renewed interest in streaks in turbulent jets, the current work explores their coexistence with vortex rings in the near field of turbulent round jets. A Reynolds number, $Re=1.5 \times 10^5$ jet is studied at two diameters downstream of the nozzle, using high-speed stereo particle image velocimetry. The spectra of individual velocity components reveal radially localized signatures of the large scale structures. The radial shapes of the spectral proper orthogonal decomposition modes corresponding to the signatures, confirm the presence of high speed streaks in the outer edge…
The paper is devoted to the investigation of the turbulent water boundary layer in the jet mixing flows using high-speed infrared (IR) thermography. Two turbulent mixing processes were studied: a submerged water jet impinging on a flat surface and two intersecting jets in a round disc-shaped vessel. An infrared camera (FLIR Systems SC7700) was focused on the window transparent for IR radiation; it provided high-speed recordings of heat fluxes from a thin water layer close to the window. Temperature versus time curves at different points of water boundary layer near the wall surface were acquir…
The current work presents an experimental investigation of the dynamic interactions between flow scales caused by repeated actions of the nonlinear term of the Navier-Stokes equation. Injecting a narrow band oscillation, representing a single Fourier mode, into a round jet flow allows the measurement of the downstream generation and development of higher harmonic spectral components and to measure when these components are eventually absorbed into fully developed turbulence. Furthermore, the dynamic evolution of the measured power spectra observed corresponds well to the measured cascaded dela…
The similarity of the two-point correlation tensor along the streamwise direction in the axi-symmetric jet far-field is analyzed, herein its utility in spectral theory. A separable two-point correlation coefficient has been the basis for the argument that the energy-optimized basis functions along the streamwise direction are Fourier modes (from the approach of equilibrium similarity theory). This would naturally be highly desirable both from a computational and an analytical perspective. The present work, however, shows that the two-point correlation tensor multiplied by the Jacobian is not d…
In this paper, we report the first evidence of an enhancement of the heat transfer from a heated wire by an external turbulent flow of superfluid helium. We used a standard Pt-Rh hot-wire anemometer and overheat it up to 21 K in a pressurized liquid helium turbulent round jet at temperatures between 1.9 K and 2.12 K. The null-velocity response of the sensor can be satisfactorily modeled by the counter flow mechanism while the extra cooling produced by the forced convection is found to scale similarly as the corresponding extra cooling in classical fluids. We propose a preliminary analysis of t…
An experimental Lagrangian study based on particle tracking velocimetry has been completed in an incompressible turbulent round water jet freely spreading into water. The jet is seeded with tracers only through the nozzle: inhomogeneous seeding called nozzle seeding. The Lagrangian flow tagged by these tracers therefore does not contain any contribution from particles entrained into the jet from the quiescent surrounding fluid. The mean velocity field of the nozzle seeded flow, $\langle \boldsymbol{U_φ} \rangle$, is found to be essentially indistinguishable from the global mean velocity field …
Direct numerical simulations of free round jets at a Reynolds number ($Re_{D}$) of $5000$, based on jet diameter ($D$) and jet-exit bulk velocity ($U_{e}$), are performed to study jet turbulence characteristics at supercritical pressures. The jet consists of $\mathrm{N_{2}}$ that is injected into $\mathrm{N_{2}}$ at same temperature. To understand turbulent mixing, a passive scalar is transported with the flow at unity Schmidt number. Two sets of inflow conditions that model jets issuing from either a smooth contraction nozzle (laminar inflow) or a long pipe nozzle (turbulent inflow) are consi…
We present a method for converting a time record of turbulent velocity measured at a point in a flow to a spatial velocity record consisting of consecutive convection elements. The spatial record allows computation of dynamic statistical moments such as turbulent kinetic wavenumber spectra and spatial structure functions in a way that bypasses the need for Taylor's Hypothesis. The spatial statistics agree with the classical counterparts, such as the total kinetic energy spectrum, at least for spatial extents up to the Taylor microscale. The requirements for applying the method is access to the…
This investigation is based on a DNS of a steady self-preserving incompressible axisymmetric turbulent jet at a Reynolds number of 2400. The DNS data enable accurate maps of the outer irrotational flow field, and also the vorticity field in the turbulent core of the jet. It is found necessary to define two separate boundaries of the jet. The first is an inner boundary (turbulent/nonturbulent, T/NT), from where vorticity rises steeply towards to the core. The second is an outer rotational/irrotational boundary, beyond which the flow may be considered irrotational. The velocity field beyond the …
Fundamental insight into the physics of buoyant gas dispersion from realistic flow geometries is necessary to accurately predict flow structures associated with hydrogen outflow from accidental leaks and the associated flammability envelope. Using helium as an experimental proxy, turbulent buoyant jets issuing from high-aspect-ratio slots on the side wall of a circular tube were studied experimentally applying simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) techniques. Two slots with an aspect ratio of 10 were considered in this study. The effects of …
Response modes computed via linear resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In th…
With the microdroplets of water serving as light scattering particles, the mist flow patterns of round micro-jets can be visualized using the Aerosol Jet(R) direct-write system. The visualization images show that the laminar mist jet appears to extend to more than 20 times the diameter of nozzle orifice, D, for jet Reynolds number Re < 600, especially with D = 0.3 mm and less. For smaller jets (e.g., with D = 0.15 mm), laminar collimated mist flow might be retained to 40xD for Re < 600 and for Re ~ 1500 within 20xD from the nozzle. The laminar part of mist flow associated with larger jets (e.g…
Comparisons studies between simulated variable density turbulent flows often consist of direct graphical representations where the level of agreement is determined by eye. This work demonstrates a formal validation methodology using an existing validation framework to examine the agreement between a simulated variable density jet flow and corresponding experimental data. Implicit large eddy simulations (ILES's) of a round jet and a plane jet with density ratio $s = 4.2$ were simulated using the compressible hydrodynamic code xRAGE. The jet growth, characterized by the spreading rates, was comp…
In this paper, we discuss selected adjoint approaches for the turbulent flow control. In particular, we focus on the application of adjoint solvers for the scope of noise reduction, in which flow solutions are obtained by large eddy and direct numerical simulations. Optimization results obtained with round and plane jet configurations are presented. The results indicate that using large control horizons poses a serious problem for the control of turbulent flows due to existence of very large sensitivity values with respect to control parameters. Typically these sensitivities grow in time and l…
Combustion in automotive and aerospace applications employing diesel, gas turbine and liquid rocket engines is preceded by injection and mixing of fuel and oxidizer at high pressures, often exceeding mixture critical values. Experimental observations indicate that the jets injected at supercritical pressures exhibit significantly different dynamics than the jets at subcritical conditions, owing to the lack of distinct liquid and gas phases in supercritical state. As a result, the averaged flow quantities such as the potential core length, jet spatial growth rate and velocity decay profiles dif…
This short article describes flow parameters, numerical method, and animations of the fluid dynamics video "LES of an Inclined Jet into a Supersonic Turbulent Crossflow" (http://ecommons.library.cornell.edu/bitstream/1813/14073/3/GFM-2009.mpg [high-resolution] and http://ecommons.library.cornell.edu/bitstream/1813/14073/2/GFM-2009-web.m1v [low-resolution] video). We performed large-eddy simulation with the sub-grid scale (LES-SGS) stretched-vortex model of momentum and scalar transport to study the gas-dynamics interactions of a helium inclined round jet into a supersonic ($M=3.6$) turbulent (…
This short article describes flow parameters, numerical method, and animations of the fluid dynamics video LES of an Inclined Jet into a Supersonic Cross-Flow (http://hdl.handle.net/1813/11480). Helium is injected through an inclined round jet into a supersonic air flow at Mach 3.6. The video shows 2D contours of Mach number and magnitude of density gradient, and 3D iso-surfaces of Helium mass-fraction and vortical structures. Large eddy simulation with the sub-grid scale (LES-SGS) stretched vortex model of turbulent and scalar transport captures the main flow features: bow shock, Mach disk, s…
Noise prediction requires the resolution of relevant acoustic sources on all scales of a turbulent flow. High-resolution direct numerical and large-eddy simulation would be ideal but both are usually too costly despite developments in high performance computing. Lower-order modeling approaches are therefore of general interest. A crucial but standing problem for accurate predictive modeling is the estimation of missing noise from the modeled scales. In this paper we address this problem by presenting a novel lower-order framework that couples the one-dimensional turbulence model to the Ffowcs-…
To investigate the influence of the orifice geometry on near-field coherent structures in a jet, Fourier-POD is applied. Velocity and vorticity snapshots obtained from tomographic particle image velocimetry at the downstream distance of two equivalent orifice diameters are analysed. Jets issuing from a circular orifice and from a fractal orifice are examined, where the fractal geometry is obtained from a repeating fractal pattern applied to a base square shape. While in the round jet energy is mostly contained at wavenumber m=0, associated to the characteristic Kelvin-Helmholtz vortex rings, i…
A novel method performing 3D PTV from double frame multi-camera images is introduced. Particle velocities are estimated by following three steps. Firstly, separate particle reconstructions with a sparsity-based algorithm are performed on a fine grid. Secondly, they are expanded on a coarser grid on which 3D correlation is performed, yielding a predictor displacement field that allows to efficiently match particles at the two time instants. As these particles are still located on a voxel grid, the third, final step achieves particle position refinement to their actual subvoxel position by a glo…
