Incompressible variable-density turbulence in an external acceleration field

Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of $1.05\leqslant R\equiv \unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{2}\leqslant 10$ are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate ${\sim}t^{1/2}$ followed by a turbulence-dominated regime with a growth rate ${\sim}t^{3}$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.

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Mixing and reaction in curved liquid shear layers

Journal of Fluid Mechanics ◽

10.1017/s0022112096004430 ◽

1997 ◽

Vol 334 ◽

pp. 381-409 ◽

Cited By ~ 3

Author(s):

P. S. KARASSO ◽

M. G. MUNGAL

Keyword(s):

Growth Rate ◽

Shear Layers ◽

Mixing Efficiency ◽

Concentration Profiles ◽

Scalar Mixing ◽

Product Concentration ◽

Chemical Product ◽

Unstable Layer ◽

Mixed Fluid ◽

Liquid Shear

The concentration field of mixing layers subject to stabilizing and destabilizing streamwise curvature was investigated at post-mixing-transition conditions. A set of operating conditions was implemented, identical to those at which straight layers were previously investigated in the same facility, in order to compare the effects of hydrodynamic instabilities upon scalar mixing. Quantitative imaging of planar laser-induced fluorescence was used for (i) passive scalar measurements, and (ii) chemical product measurements. Similar to the straight mixing layer, the results for the curved layers show that beyond the mixing transition the layer continues to evolve, and undergoes a small change in its scalar structure. At conditions just past the mixing transition both stable and unstable layers have average mixed-fluid compositions which are uniform across the layer, and average chemical product concentration profiles which are symmetric. At more fully developed conditions, the scalar field evolved: the average mixed-fluid concentration developed a small lateral variation, while the chemical product concentration profiles became asymmetric. Similar to the straight layer, the mixture-fraction PDF is believed to be of the tilted type for the most fully developed layer examined, with the marching PDF being a poor representation. Consistent with previous investigations, the growth rate of the unstable layer was found to be higher than that of straight or stable layers. The most important result is that the measured mixing efficiency of all the layers (curved and straight) was found to be the same: both the total mixed-fluid composition, and the volume fraction of mixed fluid were the same for all unstable, stable, and straight layers. The amount of mixed fluid (and of chemical product formed) was larger for the unstable layer, but always in a fixed proportion to the layer's thickness. The lack of increase in the mixing efficiency for the unstable layer is surprising, given that previous hydrodynamic measurements had shown enhanced turbulent transport for the unstable case. Thus, for all liquid shear layers studied, the rate of scalar mixing appears to be directly proportional to the entrainment rate (which essentially determines the layer's growth rate), and not to any hydrodynamic measures.

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RECIRCULATION OF CONFINED VARIABLE DENSITY TURBULENT JETS

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-2003-0015 ◽

2004 ◽

Vol 27 (4) ◽

pp. 279-294

Author(s):

A. Benaissa ◽

M.F. Bardon ◽

J.E.D. Gauthier ◽

F. Anselmet ◽

E. Ruffïn

Keyword(s):

Experimental Data ◽

Turbulent Flow ◽

Flow Pattern ◽

Initial Conditions ◽

Numerical Study ◽

Turbulent Jets ◽

Variable Density ◽

Confined Jets ◽

Recirculating Flow ◽

Density Ratios

An investigation of recirculating characteristics of circular turbulent confined jets with large density variations is presented. This numerical study aims at testing analytical predictions associated with the Craya-Curtet number. It investigates also its effect on the dynamic field and recirculation. It appears that for different density (He-air, CO2-air) and geometry ratios, the non-isothermal Craya-Curtet number [1] is not sufficient to describe the flow pattern or predict its recirculation. Depending on the momentum, aspect and density ratios of the flow, the centre of the recirculating flow (the eye) tends to reach the initial (non-self-preserving) region of the jet and influences the development of the jet. As a consequence, predictions are not in agreement with theory. The reason is that initial conditions do not satisfy the hypothesis used in the prediction of recirculation theory. Calculations are performed in three configurations: CO2, air and He. These configurations are fully developed pipe jets evolving in an air secondary turbulent flow. Validations are performed using experimental data [2] obtained in similar configurations for the three gases.

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Anatomy and physiology of Cattail as related to different population densities

Planta Daninha ◽

10.1590/s0100-83582015000100001 ◽

2015 ◽

Vol 33 (1) ◽

pp. 01-12 ◽

Cited By ~ 7

Author(s):

F.F. CORRÊA ◽

R.H. MADAIL ◽

S. BARBOSA ◽

M.P. PEREIRA ◽

E.M. CASTRO ◽

...

Keyword(s):

Growth Rate ◽

High Density ◽

Root Anatomy ◽

Low Density ◽

Typha Angustifolia ◽

Anatomy And Physiology ◽

Shoot Ratio ◽

Root Shoot Ratio ◽

Apoplastic Barriers ◽

Density Population

The objective of this work was to evaluate the effects of the population density of Typha angustifolia plants in the anatomical and physiological characteristics. Plants were collected from populations of high density (over 50% of colonization capacity) and low density (less than 50% of colonization capacity) and cultivated under controlled greenhouse conditions. Plants from both populations were grown in plastic trays containing 4 L of nutritive solution for 60 days. At the end of this period, the relative growth rate, leaf area ratio, net assimilatory rate, root/shoot ratio, leaf anatomy, root anatomy, and catalase and ascorbate peroxidase activities were evaluated. Plants from high density populations showed increased growth rate and root/shoot ratio. Low density populations showed higher values of stomatal index and density in leaves, as well as increased palisade parenchyma thickness. Root epidermis and exodermis thickness as well as the aerenchyma proportion of high density populations were reduced, these plants also showed increased vascular cylinder proportion. Only catalase activity was modified between the high and low density populations, showing increased values in low density populations. Therefore, different Typha angustifolia plants show differences in its anatomy and physiology related to its origins on high and low density conditions. High density population plants shows increased growth capacity related to lower apoplastic barriers in root and this may be related to increased nutrient uptake capacity.

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Numerical study of asymmetric and axisymmetric thermal jet with entropy generation concept

JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES ◽

10.15282/jmes.15.1.2021.01.0601 ◽

2021 ◽

Vol 15 (1) ◽

pp. 7628-7636

Author(s):

D. Belakhal ◽

Kouider Rahmani ◽

Amel Elkaroui Elkaroui ◽

Syrine Ben Haj Ayech ◽

Nejla Mahjoub Saïd ◽

...

Keyword(s):

Entropy Generation ◽

Numerical Study ◽

Experimental Studies ◽

Three Dimensional ◽

Variable Density ◽

Current Investigation ◽

Numerical Resolution ◽

Different Temperatures ◽

Density Ratios ◽

The Impact

In the current investigation, numerical study of a thermal jet of asymmetric (rectangular and elliptical) and axisymmetric (circular) geometry was investigated with variable density to verify the impact of the ratio of density and geometry on the generation of entropy. The central jet was brought to different temperatures (194, 293 and 2110 K) to obtain density ratios (0.66, 1 and 7.2) identical to a mixture jet ((Air-CO2), (Air-Air) and (Air-He)), respectively. Solving the three-dimensional numerical resolution of the Navier Stocks for turbulent flow permanent enclosed on the turbulence model K-εstandard was made. The results acquired are compared with that carried out in previous experimental studies, where it was concluded that, the axisymmetric (circular) geometry increases the entropy generation.

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Investigating the entropy generation around an airfoil in turbulent flow

Aircraft Engineering and Aerospace Technology ◽

10.1108/aeat-01-2019-0006 ◽

2020 ◽

Vol 92 (7) ◽

pp. 1001-1017

Author(s):

Mohammad Reza Saffarian ◽

Farzad Jamaati ◽

Amin Mohammadi ◽

Fatemeh Gholami Malekabad ◽

Kasra Ayoubi Ayoubloo

Keyword(s):

Mach Number ◽

Turbulent Flow ◽

Turbulence Model ◽

Entropy Generation ◽

Turbulent Regime ◽

Content Type ◽

Sst Turbulence Model ◽

Effects Of Temperature ◽

Energy Equations ◽

Naca 0012

Purpose This study aims to evaluate the amount of entropy generation around the NACA 0012 airfoil. This study takes place in four angles of attack of 0°, 5°, 10° and 16° and turbulent regime. Also, the variation in the amount of generated entropy by the changes in temperature and Mach number is investigated. Design/methodology/approach The governing equations are solved using computational fluid dynamics techniques. The continuity, momentum and energy equations and the equations of the SST k-ω turbulence model are solved. The entropy generation at different angles of attack is calculated and compared. The effect of various parameters in the generation of entropy is presented. Findings Results show that the major part of the entropy generation is at the tip of the airfoil. Also, increasing the angle of attack will increase the entropy generation. Also, results show that with increasing the temperature of air colliding with the airfoil, the production of entropy decreases. Originality/value Entropy generation is investigated in the NACA 0012 airfoil at various angles of attack and turbulent flow using the SST turbulence model. Also, the effects of temperature and Mach number on the entropy generation are investigated.

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Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 1. Linear stability analysis

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.63 ◽

2013 ◽

Vol 721 ◽

pp. 268-294 ◽

Cited By ~ 24

Author(s):

L. Talon ◽

N. Goyal ◽

E. Meiburg

Keyword(s):

Growth Rate ◽

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Stokes Equations ◽

Variable Density ◽

Local Concentration ◽

Miscible Displacements ◽

Instability Modes ◽

Finger Tip

AbstractA computational investigation of variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells is presented. As a first step, two-dimensional base states are obtained by means of simulations of the Stokes equations, which are nonlinear due to the dependence of the viscosity on the local concentration. Here, the vertical position of the displacement front is seen to reach a quasisteady equilibrium value, reflecting a balance between viscous and gravitational forces. These base states allow for two instability modes: first, there is the familiar tip instability driven by the unfavourable viscosity contrast of the displacement, which is modulated by the presence of density variations in the gravitational field; second, a gravitational instability occurs at the unstably stratified horizontal interface along the side of the finger. Both of these instability modes are investigated by means of a linear stability analysis. The gravitational mode along the side of the finger is characterized by a wavelength of about one half to one full gap width. It becomes more unstable as the gravity parameter increases, even though the interface is shifted closer to the wall. The growth rate is largest far behind the finger tip, where the interface is both thicker, and located closer to the wall, than near the finger tip. The competing influences of interface thickness and wall proximity are clarified by means of a parametric stability analysis. The tip instability mode represents a gravity-modulated version of the neutrally buoyant mode. The analysis shows that in the presence of density stratification its growth rate increases, while the dominant wavelength decreases. This overall destabilizing effect of gravity is due to the additional terms appearing in the stability equations, which outweigh the stabilizing effects of gravity onto the base state.

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Pre-Programmed Failure Behavior Using Biology-Inspired Structures

Volume 6: 33rd Design Automation Conference, Parts A and B ◽

10.1115/detc2007-34685 ◽

2007 ◽

Author(s):

Brian Bay ◽

Mike Bailey

Keyword(s):

Failure Modes ◽

Variable Density ◽

Failure Behavior ◽

Filler Materials ◽

Low Density ◽

Low Velocity ◽

Working Stress ◽

Component Strength ◽

Box Beams ◽

Increasing Demand

Core (filler) materials are key components of the sandwich panel and box-beams that are used in the design of lightweight structures. They perform a variety of elastic-range functions such as transferring and supporting working stresses and energy and collapse management. There is an increasing demand, however, for post-yield performance characteristics such as buckling control, impact toughness, and maintenance of component strength after damage. Low density is also an important consideration, as overall component mass is critical in most applications. These cellular solids need to perform well under normal working stress conditions, yet still resist damage from simple and unavoidable low velocity impacts. A new design approach is suggested by biological systems that have evolved for toughness and damage tolerance (bones, trees, plants, corals, etc.). These systems share the relatively low density cellular arrangements of common synthetic core materials, but also exhibit variable density gradients within the core. (Figures 1 and 2) This paper describes engineering design methods that are inspired by such biology. The result is that a design’s failure modes can be more effectively “designed-in”, controlling locations and amounts of failure.

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Effects of Roughness on Turbulent Flow in Microchannels and Minichannels

ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels ◽

10.1115/icnmm2008-62224 ◽

2008 ◽

Cited By ~ 2

Author(s):

Timothy P. Brackbill ◽

Satish G. Kandlikar

Keyword(s):

Experimental Study ◽

Laminar Flow ◽

Turbulent Flow ◽

Roughness Parameter ◽

Reynolds Numbers ◽

Turbulent Regime ◽

Roughness Effects ◽

Relative Roughness ◽

Roughness Elements ◽

Moody Diagram

The effect of roughness ranging from smooth to 24% relative roughness on laminar flow has been examined in previous works by the authors. It was shown that using a constricted parameter, εFP, the laminar results were predicted well in the roughened channels ([1],[2],[3]). For the turbulent regime, Kandlikar et al. [1] proposed a modified Moody diagram by using the same set of constricted parameters, and using the modification of the Colebrook equation. A new roughness parameter εFP was shown to accurately portray the roughness effects encountered in laminar flow. In addition, a thorough look at defining surface roughness was given in Young et al. [4]. In this paper, the experimental study has been extended to cover the effects of different roughness features on pressure drop in turbulent flow and to verify the validity of the new parameter set in representing the resulting roughness effects. The range of relative roughness covered is from smooth to 10.38% relative roughness, with Reynolds numbers up to 15,000. It was found that using the same constricted parameters some unique characteristics were noted for turbulent flow over sawtooth roughness elements.

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A Functional Scaling Relationship for Laminar to Turbulent Flow Regimes

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-16012 ◽

2011 ◽

Author(s):

George Papadopoulos

Keyword(s):

Turbulent Flow ◽

Stokes Equations ◽

Initial Conditions ◽

Flow Characteristics ◽

Flow Region ◽

Flow Regimes ◽

Transitional Flow ◽

Turbulent Regime ◽

Flow Profile ◽

Scaling Relationship

A dimensional analysis that is based on the scaling of the two-dimensional Navier-Stokes equations is presented for correlating bulk flow characteristics arising from a variety of initial conditions. The analysis yields a functional relationship between the characteristic variable of the flow region and the Reynolds number for each of the two independent flow regimes. A linear relationship is realized for the laminar regime, while a nonlinear relationship is realized for the turbulent regime. Both relationships incorporate mass-flow profile characteristics to fully capture the effects of initial conditions on the variation of the characteristic variables. The union of these two independent relationships is formed utilizing the concept of flow intermittency to further expand into a generic scaling relationship that incorporates transitional flow effects to fully encompass solutions spanning the laminar to turbulent flow regimes. The results of the analysis are discussed within the context of several flow phenomena (e.g. pipe flow, jet flow & separated flow) resulting from various initial and boundary conditions.

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