Jet Mixing Layer Research Articles

Investigation of turbulent flows via pseudo flow visualization part I: Axisymmetric jet mixing layer

Hot-wire anemometer measurements obtained in the near-field axisymmetric jet mixing layer by Glauser and George [1] are examined using a pseudo flow visualization (PFV) technique. Pseudo flow visualization is a visualization procedure used to manipulate data obtained from an array of probes to create a graphical representation of the instantaneous and fluctuating velocity components of a flow field. An indicator function was employed to identify the frequency content of each velocity-time trace, giving insight into the analysis of the visualizations. From this application, the natural shedding frequency, or preferred mode, of the large-scale structures was determined and compared with the conventional streamwise and radial spectral measurements acquired by Glauser and George [1]. Furthermore, the wavelength of the preferred mode, nondimensionalized by the jet exit diameter, was determined to be approximately 2.4, a result consistent with the work of Crowe and Champagne [2]. In Part 1 the technique is developed and discussed for the fundamental and fairly well-researched mixing layer of the axisymmetric jet. Our aim is to verify the effectiveness of PFV in the context of a well-documented flow. In Part 2, this technique is then applied to an industrial flow field, namely, the mixing region of a lobed mixer

Turbulent mixing noise from supersonic jets

There is now a substantial body of theoretical and experimental evidence that the dominant part of the turbulent noise of supersonic jets is generated directly by the large turbulence structures/instability waves of the jet flow. Earlier, Tam and Burton provided a description of the physical mechanism by which supersonically traveling instability waves can generate sound efficiently. They used the method of matched asymptotic expansions to construct an instability wave solution which is valid in the far field. The present work is an extension of the theory of Tam and Burton. It is argued that the instability wave spectrum of the jet may be regarded as generated by stochastic white noise excitation at the nozzle lip region. The reason why the excitation has white noise characteristics is that near the nozzle lip region the flow in the jet mixing layer has no intrinsic length and time scales. The present stochastic wave model theory of supersonic jet noise contains a single unknown multiplicative constant. Comparisons between the calculated noise directivities at selected Strouhal numbers and experimental measurements of a Mach 2 jet at different jet temperatures have been carried out. Favorable agreements are found.

DEVELOPMENT OF A REYNOLDS STRESS MODEL WITH A CROSS DIFFUSION OFκIN THEϵEQUATION

SUMMARY This study intends to improve the predictability of the existing second-order closure turbulence models without tuning the model constants. For this purpose, a Reynolds stress model with a cross diffusion of κ in the ϵ equation is derived based on the physically more realistic assumption that small turbulent eddies can be anisotropic. The proposed Reynolds stress model differs from the existing Reynolds stress model in two aspects; an anisotropic dissipation model, , is adopted, and an additional cross diffusion term, Cϵ 3 ϵ/ κ ∂(κ 2/ ϵ ∂κ/∂ Xt)/∂ Xt is included in the ϵ equation. The proposed Reynolds stress turbulence model (RSMX), the existing Reynolds stress model (RSM) and a two-equation eddy viscosity model, the κ - ϵ model, are then tested in three turbulent free shear flows, namely plane jet, round jet, and plane mixing layer flows. It is shown that the proposed RSMX of turbulence model performs better than the existing turbulence models in all the three free shear flows concerned.

An application of the stochastic estimation to the jet mixing layer

The linear stochastic estimation is a powerful technique that provides a means of estimating conditional eddies given unconditional two-point correlation data. This procedure was used to reconstruct estimates of multipoint conditional averages of the dominant structures in the jet mixing layer of Glauser and George (Proceedings of the Sixth Symposium on Turbulent Shear Flows, Toulouse, France, 1987). The pseudodynamic evolution of these conditional eddies was systematically compared to the instantaneous velocity fields and the results were quantified in terms of the percentage of the energy captured by the multipoint stochastic estimates. It was found that the single-point estimates do not yield adequate representations of the instantaneous velocity field, but that two reference points located on opposite sides of the shear layer yield realistic estimates, with little gained by adding more reference points.

The Nonlinear Instability Characteristics of Waves in Free Shear Layers

A more general mean flow first harmonic theory is derived and some consequences are discussed. The theory is applied to the Bickley jet and tanh mixing layer profiles.

The prediction of shock structure in noncircular jets using conformal mapping with a pseudospectral hybrid scheme

Broadband shock associated noise, in supersonic jets operating off-design, is generated by the interaction of large-scale structures in the jet mixing layer and the quasiperiodic shock cell structure of the jet. In this work, the shock cell structure of supersonic jets with noncircular exit geometry is modeled using a linear analysis. The analysis requires the solution of the equations of hydrodynamic stability for zero frequency. The model takes into account the finite thickness of the jet shear layer using realistic velocity and density profiles. The effects of the shear layer turbulence are included by incorporating eddy-viscosity terms. The numerical method involves the transformation of the cross section of a given jet to a rectangular computational domain using a series of conformal mappings. A pseudospectral hybrid scheme is used in the computational domain to set up the finite-differencing scheme. The variation of the pressure fluctuation with downstream distance is given for an elliptic jet of aspect ratio 2. Comparisons with experimental data are made, where possible. This work is an extension of earlier work [P. J. Morris, T. R. S. Bhat, and G. Chen, J. Sound Vib. 132(2), 199–211 (1989)], where the shear layer was approximated by a vortex sheet. [Work supported by NASA Langley Research Center under NASA Grant NAG-1-657.]

Simulation of particle dispersion in an axisymmetric jet

Particle dispersion in an axisymmetric jet is analysed numerically by following particle trajectories in a jet flow simulated by discrete vortex rings. Important global and local flow quantities reported in experimental measurements are successfully simulated by this method.The particle dispersion results demonstrate that the extent of particle dispersion depends strongly on γτ, the ratio of particle aerodynamic response time to the characteristic time of the jet flow. Particles with relatively small γτ values are dispersed at approximately the fluid dispersion rate. Particles with large γτ values are dispersed less than the fluid. Particles at intermediate values of γτ may be dispersed faster than the fluid and actually be flung outside the fluid mixing region of the jet. This result is in agreement with some previous experimental observations. As a consequence of this analysis, it is suggested that there exists a specific range of intermediate γτ at which optimal dispersion of particles in the turbulent mixing layer of a free jet may be achieved.

A Numerical Investigation of the Influence of Heating on the Excitation of High and Low Mach Number Jet Flows

The influence of heating and velocity on the unsteady nature of jet mixing layers is investigated by solving the time-dependent compressible Navier-Stokes equations using MacCormack’s explicit finite difference algorithm. The computations are performed for jet Mach numbers of 0.3 and 0.8 with flow total temperatures up to 800K. The Reynolds number ranges from 3 × 105 to 1.3 × 106. Excitation is accomplished by imposing an acoustic pressure signal inside the jet duct. The objective of this effort is to compare the response of heated and unheated jets with acoustic excitation at high and low subsonic Mach Numbers. The preliminary results indicate that without acoustic excitation the mixing in the heated jet is greater than in the unheated case. It has also been found that for the low speed heated jets (M= 0.3, Tt = 672K) acoustic excitation causes the production of large scale vortex structures to occur in a regular periodic manner with organized periodic pairing at some Strouhal numbers. These results are in agreement with experimental data.

The universal nature of zero-crossing time and velocity scales in turbulent shear flows

RECENT studies have shown that the turbulence production process in shear flows is not entirely random, but rather quasiperiodic in nature. Since the large eddies play a decisive role in these processes in all shear flows, it is instructive to see if they bear any common characteristics. The possible universal distributions1 of time and velocity scales (T,up) in the low-frequency component of the turbulent signals—defined, respectivley, as the interval between successive zero crossings and the intervening absolute peak value of the longitudinal velocity signal—have been explored in a number of flows. These include the self-preserving regions of a turbulent boundary layer, plane jet, circular jet, and plane mixing layer and the initial mixing regions of a plane jet and circular jet. Both T and up distributions show universal trends: T distributions agree well with the log normal distribution except in their extreme excursions, whereas up distributions are intermediate between log normal and Gaussian distributions. Contents The large structure variates studied here are the zerocrossing interval T and the absolute value up of the velocity peaks or troughs between two successive zero crossings. The a.c. component in a typical unfiltered u signal of a turbulent shear flow is shown in Fig. 1. Such signals have a slowly varying component on which the high-frequency component rides. This slowly varying part can be obtained by suitably low-pass filtering the signal as shown in the figure. The lowfrequency component contains most of the kinetic energy and is considered to be the signature of the large structures. Tand up are two simple variables describing the time and velocity scales of the signal. To obtain T and up, the hot-wire w-signals were digitally filtered and processed. When up/up. is plotted against log (T/T) following Badri Narayanan,1 no clear trend becomes apparent (the overbars indicate time mean values). Noting that (T/T)~ ! is analogous to frequency, plots of up/up vs (T/T) for the nearwall point in the boundary layer and those in the plane jet are shown in Fig. 2. Distributions for other flows are similar. The data have not been averaged here in order to retain the scatter in the temporal data. The distributions appear similar to the one-dimensional power spectra of these flowfields. For example, the figure exhibits a decade where the data follow a -5/3 trend. The drop is slower at lower values of the ordinate, whereas it is faster at higher values. For the lowest

On the organized motion of a turbulent plane jet

Measurements of space–time correlations of longitudinal and normal velocity fluctuations and of temperature fluctuations support the existence of counter-rotating spanwise structures appearing alternately on opposite sides of the jet centreline in the self-preserving region of the flow. The frequency of these structures closely satisfies self-preservation. The asymmetric arrangement of the structures is first observed downstream of the position where the jet mixing layers nominally merge but upstream of the onset of self-preservation. Closer to the jet exit, the space–time correlations indicate the existence of spanwise structures that are symmetrical about the centreline.

Variable control of jet decay

The influence of blowing radially inward with a pair of control jets toward the centerline of and close to the exit from a circular main nozzle is investigated. Two regimes of control-jet influence exist, corresponding to conditions where the control jets are swept away in. the turbulent mixing layer of the main jet or where they penetrate the central smooth-core flow. In the first regime, local velocity reductions in the main jet of up to 30% can be achieved with control-jet mass flows of 0.5% of that in the main-jet nozzle without severely distorting the main jet from its circular cross section. The action of the control jets is to promote more rapid mixing of the main-jet shear layer, and the response increases with the square of control-jet relative velocity and with the cube of its relative diameter. In the second regime, the main jet is strongly distorted from a circular cross section and local velocities in the main jet are less sensitive to control-jet velocity. The main-nozzle mass flow is influenced significantly in the second regime only when the control jets are very close to the main-nozzle lip.

Properties of the large structure in a slightly heated turbulent mixing layer of a plane jet

The convection speed and average inclination of the large structure in the turbulent mixing layer of a plane jet have been obtained using different techniques. Ensemble-averaged shapes of the signatures of velocity and temperature associated with this structure are also presented. An array of cold wires is used to simultaneously observe the temperature fluctuation θ at several points in space. A cold-wire/X-wire combination is used to measure θ, the streamwise u and the normal v velocity fluctuations. The front of the structure moves faster than the back and the average inclination of this structure to the jet axis is approximately 40°. A detection scheme, based on positive peaks of the cubed values of the temperature derivative, is used to identify the large structure and obtain average signatures of θ, u, v, and of the products uv, θ and vθ. These signatures are consistent with a vortex-like description of the large structure. They also reflect the existence of a thin interconnecting region or ‘braid’ between two consecutive vortical structures. This region is identified by the sharp changes in temperature and is interpreted as part of the large structure. In the central part of the mixing layer, at least 80% of the Reynolds shear stress and 50% of the average normal heat flux appear to be contributed by the large structure.

Visualization of the acoustic excitation of a subsonic jet

The response of a subsonic round jet to internal excitation by an acoustic wave has been examined using flow visualization and noise measurements. The jet was subjected to pulse excitation and to harmonic excitation. In both cases large-scale vortex ring structures were observed in the jet mixing layer. With pulse excitation, interactions between the vortex rings were observed, but no associated noise emission could be detected.

Spectra of Turbulent Static Pressure Fluctuations in Jet Mixing Layers

Spectral similarity laws are derived for the power spectra of turbulent static pressure fluctuations by application of dimensional analysis in the limit of large turbulent Reynolds number. The theory predicts that pressure spectra are generated by three distinct types of interaction in the velocity fields: a fourth order interaction between fluctuating velocities, an interaction between the first order mean shear and the third order velocity fluctuations, and an interaction between the second order mean shear rate and the second order fluctuating velocity. Measurements of one-dimensional power spectra of the turbulent static pressure fluctuations in the driven mixing layer of a subsonic, circular jet are presented, and the spectra are examined for evidence of spectral similarity. Spectral similarity is found for the low wavenumber range when the large scale flow on the centerline of the mixing layer is self-preserving. The data are also consistent with the existence of universal inertial subranges for the spectra of each interaction mode.

Influence of wave dispersion on vortex pairing in a jet

The geometry of large-scale structures in the turbulent mixing layer of a moderate Reynolds number jet is deduced from measurements of the fluctuating pressure in the hydrodynamic near field. The structures are rings of concentrated vorticity that distort with downstream distance until statistical axisymmetry disappears. The rings are spaced quasi-periodically and coalesce with each other, producing larger spacings. Statistical and flow-visualization techniques are applied to free and forced jets over a range of Reynolds numbers from 5000 to 50000 to demonstrate that rings of a given spacing do not coalesce with each other until they are far enough downstream that the local mixing layer has attained some critical thickness which scales with the wavelength of the vortex pair. Wave dispersion is evaluated as a plausible mechanism for localizing the coalescences. The central feature of the model is the observation that a shear layer is dispersive to wavelengths much longer than its thickness and non-dispersive to shorter waves.