Free Turbulent Mixing in Axial Pressure Gradients

1973 ◽  
Vol 40 (2) ◽  
pp. 375-380 ◽  
Author(s):  
G. J. Hokenson ◽  
J. A. Schetz
Keyword(s):  
Flow Field ◽  
Turbulent Mixing ◽  
Eddy Viscosity ◽  
Static Pressure ◽  
Initial Conditions ◽  
Near Field ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Axial Pressure ◽  
Flow Equations

The results of an experimental investigation of the free turbulent mixing of wakes and jets in axial pressure gradients are presented. The data include static pressure and velocity profiles and the turbulent intensity which is presented in terms of the parameter u′cL2¯(Δu)max2. It is hypothesized that the representation of the Reynolds stress by a generalized Clauser eddy viscosity model is scaled by this parameter. The experimentally observed dependence of this turbulence quantity on flow field dimensionality and the imposed pressure gradient places more stringent demands on the form of the eddy viscosity than has been shown before. However, the experimental data reveal some fortuitous behavior which aids in the specification of the spatial dependence of the turbulence parameter, leaving the scaling to be determined primarily by the initial conditions, i.e., the state of the turbulence in the near field. Substantial lateral static pressure gradients were observed in all two-dimensional cases studied. It is shown that the boundary-layer form of the viscous flow equations are inadequate in such cases, and a numerical solution of a system of equations that includes an approximate form of the lateral momentum equation provides predictions in good agreement with the data for the mean flow field.

scholarly journals Instability wave models for the near-field fluctuations of turbulent jets

2011 ◽  
Vol 689 ◽  
pp. 97-128 ◽  
Author(s):  
K. Gudmundsson ◽  
Tim Colonius
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Microphone Array ◽  
Near Field ◽  
Turbulent Jets ◽  
Instability Wave ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Scale Structures

AbstractPrevious work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described aslinearperturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

Mean-Flow Measurements in the Boundary Layer and Wake and Wave Field of a Series 60 CB = 0.6 Ship Model—Part 2: Scale Effects on Near-Field Wave Patterns and Comparisons with Inviscid Theory

1993 ◽  
Vol 37 (01) ◽  
pp. 16-24
Author(s):  
J. Longo ◽  
F. Stern ◽  
Y. Toda
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Scale Effects ◽  
Near Field ◽  
Wave Profile ◽  
Wave System ◽  
Mean Flow ◽  
Wave Elevation ◽  
Wave Patterns ◽  
Field Wave

Part 2 of this two-part paper presents additional results from a towing-tank experiment conducted in order to explicate the influence of wavemaking by a surface-piercing body on its boundary-layer and wake and provide detailed documentation of the complete flow field appropriate for validating computational methods. In Part 1 (Journal of Ship Research, Dec. 1992), wave profile, local and global wave-elevation, and mean-velocity and pressure field measurements for Froude numbers 0.16 and 0.316 for a 3.048 m Series 60 CB = 0.6 hull form are presented and discussed to point out the essential differences between the flows at low and high Froude number and to assess the nature of the interaction between wavemaking and the boundary layer and wake. In Part 2, scale effects on the near-field wave patterns are examined through wave profile and local and global wave-elevation measurements for 1.829 and 3.048 m models and Froude numbers 0.316, 0.3, and 0.25. The bow-wave amplitude and divergence angle are larger and the stern waves smaller for the smaller model. The latter scale effect is well known, but the former one is a new and unexpected result. Also, comparisons are made between the experimental results and those from a wavy inviscid-flow method, which provides an evaluation of the capabilities of the computational method. Although the computations predict the gross features of the wave system and velocity and pressure fields, they do not simulate the complex details of either the wave system or the flow field, especially close to the hull and wake centerplane.

scholarly journals Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number

2010 ◽  
Vol 643 ◽  
pp. 333-348 ◽  
Author(s):  
YONGYUN HWANG ◽  
CARLO COSSU
Keyword(s):  
Couette Flow ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Initial Conditions ◽  
Viscous Sublayer ◽  
Mean Flow ◽  
Stochastic Forcing ◽  
Output Analysis ◽  
Optimal Response ◽  
The Mean

We compute the optimal response of the turbulent Couette mean flow to initial conditions, harmonic and stochastic forcing at Re = 750. The equations for the coherent perturbations are linearized near the turbulent mean flow and include the associated eddy viscosity. The mean flow is found to be linearly stable but it has the potential to amplify steamwise streaks from streamwise vortices. The most amplified structures are streamwise uniform and the largest amplifications of the energy of initial conditions and of the variance of stochastic forcing are realized by large-scale streaks having spanwise wavelengths of 4.4h and 5.2h respectively. These spanwise scales compare well with the ones of the coherent large-scale streaks observed in experimental realizations and direct numerical simulations of the turbulent Couette flow. The optimal response to the harmonic forcing, related to the sensitivity to boundary conditions and artificial forcing, can be very large and is obtained with steady forcing of structures with larger spanwise wavelength (7.7h). The optimal large-scale streaks are furthermore found proportional to the mean turbulent profile in the viscous sublayer and up to the buffer layer.

scholarly journals Experimental Study of Mean Flow Characteristics in the Near Field of Wedge-Shaped Swirling Jets

2020 ◽  
Vol 5 (10) ◽  
pp. 1199-1203
Author(s):  
Md. Mosharrof Hossain ◽  
Muhammed Hasnain Kabir Nayeem ◽  
Dr. Md Abu Taher Ali
Keyword(s):  
Flow Field ◽  
Near Field ◽  
Flow Characteristics ◽  
Velocity Profiles ◽  
Mean Flow ◽  
Mean Velocity ◽  
Potential Core ◽  
Swirling Jets ◽  
The Mean ◽  
Sinusoidal Flow

In this investigation experiment was carried out in 80 mm diameter swirling pipe jet, where swirl was generated by attaching wedge-shaped helixes in the pipe. All measurements were taken at Re 5.3e4. In the plain pipe jet the potential core was found to exist up to x/D=5 but in the swirling jet there was no existence of potential core. The mean velocity profiles were found to be influenced by the presence of wedge-shaped helixes in the pipe. The velocity profiles indicated the presence of sinusoidal flow field in the radial direction existed only in the near field of the jet. This flow field died out after x/D=3 and the existence of jet flow diminished after x/D=5.

scholarly journals Numerical investigation of algebraic oceanic turbulent mixing-layer models

2013 ◽  
Vol 20 (6) ◽  
pp. 945-954 ◽  
Author(s):  
T. Chacón-Rebollo ◽  
M. Gómez-Mármol ◽  
S. Rubino
Keyword(s):  
Turbulent Mixing ◽  
Finite Time ◽  
Eddy Viscosity ◽  
Initial Conditions ◽  
Mixing Layer ◽  
Turbulence Models ◽  
Warm Pool ◽  
Oceanic Circulation ◽  
Turbulent Mixing Layer ◽  
Numerical Instabilities

Abstract. In this paper we investigate the finite-time and asymptotic behaviour of algebraic turbulent mixing-layer models by numerical simulation. We compare the performances given by three different settings of the eddy viscosity. We consider Richardson number-based vertical eddy viscosity models. Two of these are classical algebraic turbulence models usually used in numerical simulations of global oceanic circulation, i.e. the Pacanowski–Philander and the Gent models, while the other one is a more recent model (Bennis et al., 2010) proposed to prevent numerical instabilities generated by physically unstable configurations. The numerical schemes are based on the standard finite element method. We perform some numerical tests for relatively large deviations of realistic initial conditions provided by the Tropical Atmosphere Ocean (TAO) array. These initial conditions correspond to states close to mixing-layer profiles, measured on the Equatorial Pacific region called the West-Pacific Warm Pool. We conclude that mixing-layer profiles could be considered as kinds of "absorbing configurations" in finite time that asymptotically evolve to steady states under the application of negative surface energy fluxes.

Linearized k-ε Analysis of Free Turbulent Mixing in Streamwise Pressure Gradients With Experimental Verification

1979 ◽  
Vol 46 (3) ◽  
pp. 493-498 ◽  
Author(s):  
G. Hokenson
Keyword(s):  
Turbulent Mixing ◽  
Eddy Viscosity ◽  
Turbulence Modeling ◽  
Free Stream ◽  
Physical Space ◽  
Stream Velocity ◽  
Length Scale ◽  
Pressure Gradients ◽  
Preliminary Estimate ◽  
Closed Form Solutions

The equations of momentum, turbulent kinetic energy, and dissipation are subjected to a coordinate transformation and linearized to obtain approximate closed-form solutions of free mixing problems. The linearization involves not only an assumption regarding the relative transverse uniformity of free mixing flow fields, but also a turbulence modeling approach in which a preliminary estimate of the length scale is a necessary input. As a by-product of this linearization, the equations partially decouple from one another and may, therefore, be solved sequentially. In order to provide the length scale and free-stream velocity dependence upon the transformed streamwise coordinate, a temporary transformation from the physical to the mathematical plane is developed on the basis of a classical eddy viscosity formula. Due to the analytical nature of the process, the input velocity and length scale thus obtained may be adjusted to conform with the desired velocity distribution in physical space, and the appropriate length scale computed from the solution of the equations. The analysis is favorably compared to experimental data on the turbulent mixing of two-dimensional wakes in adverse pressure gradients.

Algebraic Anisotropic Eddy-Viscosity Modeling for Application to Turbulent Film Cooling Flows

2011 ◽  
Author(s):  
Xueying Li ◽  
Jing Ren ◽  
Hongde Jiang
Keyword(s):  
Flow Field ◽  
Film Cooling ◽  
Eddy Viscosity ◽  
Viscosity Ratio ◽  
Equation Model ◽  
Wall Region ◽  
Mean Flow ◽  
Film Cooling Effectiveness ◽  
Jet In Crossflow ◽  
Comparison Of The Results

Under-predicting the spanwise spreading of film cooling is a big problem in the film cooling computation. This is mainly due to the incorrect simulation of the spanwise transport of the jet in crossflow by conventional isotropic eddy viscosity turbulent models. An improved algebraic anisotropic eddy viscosity method including both the influence of the wall and the strain of the mean flow field to the anisotropic ratio has been raised by the authors in the paper, referred to as Algebraic Anisotropic Eddy Viscosity (AAEV) method. An equation derived from the algebraic Reynolds stress transport equations is applied to compute the anisotropic eddy-viscosity ratio. The variation of the anisotropic eddy-viscosity ratio is a function of both the dimensionless wall distance and the local mean flow field. This method is applied to the two layer k-ε model with a one-equation model in near-wall region to form a new turbulent model- AAEV k-ε model. The new model is tested for the computation of a flat plate film cooling flow with an inclined row of streamwise injected jets. Comparison of the results between the AAEV k-ε model and two-layer k-ε model with the measured adiabatic film-cooling effectiveness distributions indicates that the AAEV k-ε model can correctly predict the spanwise spreading of the film and reduce the strength of the secondary vortices.

Directional Noise Reduction via Asymmetric Downstream Fluidic Injection

2017 ◽  
Author(s):  
Pankaj Rajput ◽  
Sunil Kumar
Keyword(s):  
Noise Reduction ◽  
Turbulent Mixing ◽  
Near Field ◽  
Acoustic Energy ◽  
Far Field ◽  
High Momentum ◽  
Mean Flow ◽  
Flow Measurements ◽  
Mixing Noise ◽  
Field Noise

The main aim of this investigation is to analyze directional noise reduction resulting from asymmetric high momentum fluidic injection downstream of a Mach 0.9 nozzle. Jet noise has been identified as one of the primary obstacles to increasing commercial aviation capacity. Microjets in cross flow are known to enhance turbulent mixing in the shear layer due to the induced stream-wise vortices. This enhanced mixing can be used for reorganizing the spatial distribution of acoustic energy. Targeted reduction in the downward-emitted turbulent mixing noise can be achieved by strategically injecting high momentum fluid downstream of the jet exhaust. Detailed Large Eddy Simulations were performed on a hybrid block structured-unstructured mesh to generate the flow field which was then used for near field and far field noise computation. Aeroacoustic analogy based formulation was used for computing far-field noise estimation. Benchmark cases were validated with preexisting experimental data sets. Mean flow measurements suggest shorter jet core lengths due to the enhanced mixing resulting from fluidic injection. The induced asymmetry due to the fluidic injection gives rise to an asymmetric acoustic field leading to targeted directional noise reduction in the far field as measured by pressure probes.

Subgrid-scale backscatter in reacting and inert supersonic hydrogen–air turbulent mixing layers

2014 ◽  
Vol 743 ◽  
pp. 554-584 ◽  
Author(s):  
J. O’Brien ◽  
J. Urzay ◽  
M. Ihme ◽  
P. Moin ◽  
A. Saghafian
Keyword(s):  
Mach Number ◽  
Kinetic Energy ◽  
Flow Field ◽  
Turbulent Mixing ◽  
High Speed ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Mixing Layers ◽  
Subgrid Scale ◽  
Combustion Dynamics

AbstractThis study addresses the dynamics of backscatter of kinetic energy in the context of large-eddy simulations (LES) of high-speed turbulent reacting flows. A priori analyses of direct numerical simulations (DNS) of reacting and inert supersonic, time-developing, hydrogen–air turbulent mixing layers with complex chemistry and multicomponent diffusion are conducted here in order to examine the effects of compressibility and combustion on subgrid-scale (SGS) backscatter of kinetic energy. The main characteristics of the aerothermochemical field in the mixing layer are outlined. A selfsimilar period is identified in which some of the turbulent quantities grow in a quasi-linear manner. A differential filter is applied to the DNS flow field to extract filtered quantities of relevance for the large-scale kinetic-energy budget. Spatiotemporal analyses of the flow-field statistics in the selfsimilar regime are performed, which reveal the presence of considerable amounts of SGS backscatter. The dilatation field becomes spatially intermittent as a result of the high-speed compressibility effect. In addition, the large-scale pressure-dilatation work is observed to be an essential mechanism for the local conversion of thermal and kinetic energies. A joint probability density function (PDF) of SGS dissipation and large-scale pressure-dilatation work is provided, which shows that backscatter occurs primarily in regions undergoing volumetric expansion; this implies the existence of an underlying physical mechanism that enhances the reverse energy cascade. Furthermore, effects of SGS backscatter on the Boussinesq eddy viscosity are studied, and a regime diagram demonstrating the relationship between the different energy-conversion modes and the sign of the eddy viscosity is provided along with a detailed budget of the volume fraction in each mode. A joint PDF of SGS dissipation and SGS dynamic-pressure dilatation work is calculated, which shows that high-speed compressibility effects lead to a decorrelation between SGS backscatter and negative eddy viscosities, which increases for increasingly large values of the SGS Mach number and filter width. Finally, it is found that the combustion dynamics have a marginal impact on the backscatter and flow-dilatation distributions, which are mainly dominated by the high-Mach-number effects.

Influence of nozzle configuration on the flow field of multiple jets

2017 ◽  
Vol 232 (9) ◽  
pp. 1639-1654 ◽  
Author(s):  
BT Kannan ◽  
NR Panchapakesan
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Near Field ◽  
Nonlinear Behavior ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Jet Flows ◽  
Mean Flow ◽  
Multiple Jets ◽  
Nozzle Configuration

Turbulent jet flows with multiple nozzle inlets are investigated computationally using OpenFOAM. The configurations vary from single to five axisymmetric nozzles. First-order closure is used with Reynolds-averaged Navier–Stokes equations. Computed results are compared with the available experimental data. The effect of nozzle configuration on the jet flow field is discussed with predicted mean flow and turbulent flow data. Near-field of multiple jets shows the nonlinear behavior. Multiple jets show better performance in the near-field based on entrainment, secondary flows, and area-averaged turbulent kinetic energy. The downstream evolution of the multiple jets differs for configurations with and without central jet. The shape parameter confirms the evolution of the multiple jets towards an axisymmetric jet.

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