148 research outputs found
Axisymmetric form of Kármán-Howarth equation and its limiting forms
No full textInternational audienceKinematics and dynamics of homogeneous axisymmetric turbulence have been derived with the assumption that the properties of the turbulence are invariant with respect to rotation about a preferred direction λ. In particular, the "axisymmetric" equivalent of Karman-Howarth "isotropic" equation is derived using Lindborg's representation of the two-point correlation tensors of homogeneous axisymmetric turbulence. When the more constraining assumption of isotropy is made, this equation reduces to the well-known Karman-Howarth equation. There are two interesting limiting forms of the axisymmetric Karman-Howarth equation: the axisymmetric form of the energy balance equation and the axisymmetric form of the vorticity balance equation
The axisymmetric equivalent of Kolmogorov's equation
No full textInternational audienceA type of turbulence which is next to local isotropy in order of simplicity, but which corresponds more closely to turbulent flows encountered in practice, is locally axisymmetric turbulence. A representation of the second and third order structure function tensors of homogeneous axisymmetric turbulence is given. The dynamic equation relating the second and third order scalar structure functions is derived. When axisymmetry turns into isotropy, this equation is reduced to the well-known isotropic result: Kolmogorov's equation. The corresponding limiting form is also reduced to the well-known isotropic limiting form of Kolmogorov's equation. The new axisymmetric and theoretical results may have important consequences on several current ideas on the fine structure of turbulence, such as ideas developed by analysis based on the isotropic dissipation rate ∈iso or such as extended self similarity (ESS) and the scaling laws for the n-order structure functions
Axisymmetric form of Kármán-Howarth equation and its limiting forms
No full textInternational audienceKinematics and dynamics of homogeneous axisymmetric turbulence have been derived with the assumption that the properties of the turbulence are invariant with respect to rotation about a preferred direction λ. In particular, the "axisymmetric" equivalent of Karman-Howarth "isotropic" equation is derived using Lindborg's representation of the two-point correlation tensors of homogeneous axisymmetric turbulence. When the more constraining assumption of isotropy is made, this equation reduces to the well-known Karman-Howarth equation. There are two interesting limiting forms of the axisymmetric Karman-Howarth equation: the axisymmetric form of the energy balance equation and the axisymmetric form of the vorticity balance equation
Numerical simulation of turbulent pipe flow
No full textMany experimental and numerical studies have been devoted to turbulent pipe flows due to the number of applications in which theses flows govern heat or mass transfer processes: heat exchangers, agricultural spraying machines, gasoline engines, and gas turbines for examples. The simplest case of non-rotating pipe has been extensively studied experimentally and numerically. Most of pipe flow numerical simulations have studied stability and transition. Some Direct Numerical Simulations (DNS) have been performed, with a 3-D spectral code, or using mixed finite difference and spectral methods. There is few DNS of the turbulent rotating pipe flow in the literature. Investigations devoted to Large Eddy Simulations (LES) of turbulence pipe flow are very limited. With DNS and LES, one can derive more turbulence statistics and determine a well-resolved flow field which is a prerequisite for correct predictions of heat transfer. However, the turbulent pipe flows have not been so deeply studied through DNS and LES as the plane-channel flows, due to the peculiar numerical difficulties associated with the cylindrical coordinate system used for the numerical simulation of the pipe flows. This chapter presents Direct Numerical Simulations and Large Eddy Simulations of fully developed turbulent pipe flow in non-rotating and rotating cases. The governing equations are discretized on a staggered mesh in cylindrical coordinates. The numerical integration is performed by a finite difference scheme, second-order accurate in space and time. The time advancement employs a fractional step method. The aim of this study is to investigate the effects of the Reynolds number and of the rotation number on the turbulent flow characteristics. The mean velocity profiles and many turbulence statistics are compared to numerical and experimental data available in the literature, and reasonably good agreement is obtained. In particular, the results show that the axial velocity profile gradually approaches a laminar shape when increasing the rotation rate, due to the stability effect caused by the centrifugal force. Consequently, the friction factor decreases. The rotation of the wall has large effects on the root mean square (rms), these effects being more pronounced for the streamwise rms velocity. The influence of rotation is to reduce the Reynolds stress component and to increase the two other stresses and . The effect of the Reynolds number on the rms of the axial velocity
Numerical simulation of turbulent pipe flow
No full textMany experimental and numerical studies have been devoted to turbulent pipe flows due to the number of applications in which theses flows govern heat or mass transfer processes: heat exchangers, agricultural spraying machines, gasoline engines, and gas turbines for examples. The simplest case of non-rotating pipe has been extensively studied experimentally and numerically. Most of pipe flow numerical simulations have studied stability and transition. Some Direct Numerical Simulations (DNS) have been performed, with a 3-D spectral code, or using mixed finite difference and spectral methods. There is few DNS of the turbulent rotating pipe flow in the literature. Investigations devoted to Large Eddy Simulations (LES) of turbulence pipe flow are very limited. With DNS and LES, one can derive more turbulence statistics and determine a well-resolved flow field which is a prerequisite for correct predictions of heat transfer. However, the turbulent pipe flows have not been so deeply studied through DNS and LES as the plane-channel flows, due to the peculiar numerical difficulties associated with the cylindrical coordinate system used for the numerical simulation of the pipe flows. This chapter presents Direct Numerical Simulations and Large Eddy Simulations of fully developed turbulent pipe flow in non-rotating and rotating cases. The governing equations are discretized on a staggered mesh in cylindrical coordinates. The numerical integration is performed by a finite difference scheme, second-order accurate in space and time. The time advancement employs a fractional step method. The aim of this study is to investigate the effects of the Reynolds number and of the rotation number on the turbulent flow characteristics. The mean velocity profiles and many turbulence statistics are compared to numerical and experimental data available in the literature, and reasonably good agreement is obtained. In particular, the results show that the axial velocity profile gradually approaches a laminar shape when increasing the rotation rate, due to the stability effect caused by the centrifugal force. Consequently, the friction factor decreases. The rotation of the wall has large effects on the root mean square (rms), these effects being more pronounced for the streamwise rms velocity. The influence of rotation is to reduce the Reynolds stress component and to increase the two other stresses and . The effect of the Reynolds number on the rms of the axial velocity
Hydrodynamic and rheological characteristics of a pseudoplastic fluid through a rotating cylinder
No full textInternational audienceThe fully developed turbulent flow of pseudoplastic (n¼0:75) and Newtonian fluids in an isothermal axially rotating cylinder has been carried out using a large eddy simulation (LES) with an extended Smagorinsky model. The simulation Reynolds number of the present predictions has been assumed to be Res ¼4000 at various rotation rates ð0N3Þ: This investigation seeks to assess the influence of the centrifugal force induced by the swirl on the mean flow quantities, turbulent statistics, and instantaneous turbulence structure to describe the rheological behavior and the turbulence features. The predicted results indicate that with increasing rotation rate, the pseudoplastic fluid tends to behave like a liquid when approaching the pipe center due to the lower apparent fluid viscosity in the logarithmic region as the pipe wall rotates. Moreover, the reduction in the pseudoplastic apparent viscosity in the core region induces a pronounced increase in the axial velocity profile further away from the pipe wall toward the core region. It is interesting to note that the growth of the centrifugal force induced by the swirl driven by the rotating pipe wall results in an apparent attenuation in turbulence intensities of the axial velocity fluctuation and, consequently, in the kinetic energy of turbulent fluctuations and the turbulent Reynolds shear stress of the axial-radial velocity fluctuations, as the pipe wall rotates. Moreover, the increased rotation rate leads also to a noticeable increase in the Root mean square (RMS) of the radial and tangential fluctuations. It can be said that the transport mechanism of turbulence intensities from the axial components to the other ones exhibits a marked increase with increasing pipe wall rotation
THE EFFECT OF POWER-LAW INDEX ON THE TURBULENCE FEATURES OF TURBULENT PIPE FLOW
No full textInternational audienceThe present study set out to reveal the influence of the flow behaviour index of the power-law fluid on the main features of the turbulence in especially at the vicinity of the wall. Toward this end, a large eddy simulation (LES) with a standard dynamic model has been devoted to a fully developed turbulent flow of pseudoplastic and dilatant fluids through an isothermal stationary pipe, at a simulation's Reynolds number of 4000. The emerged of this study suggest that the decreased flow behaviour index induces a pronounced enhancement in the generation of the axial turbulence intensities and a reduction in the transfer of these axial intensities to the tangential and radial intensities, The decreased flow behaviour index leads also to decrease the turbulent kinetic energy and to ameliorate the transport of the axial radial and tangential turbulence intensities from the vicinity of the wall towards the core region. Moreover, the skewness and flatness of the axial velocity fluctuations are almost independent of the flow behaviour index along the radial direction
LES of Turbulent Forced Convection of a Non-Newtonian Fluid in a Stationary Pipe: The Mean Quantities
No full textInternational audienceA fully developed forced convection heat transfer of a thermally independent shear thinning (n=0.75) and Newtonian fluids flowing inside a uniform heated axially pipe has been carried out numerically by means of the large eddy simulation (LES) with an extended Smagorinsky model at a simulation's Reynolds and Prandtl numbers equal to Res=4000 and Prs=1 respectively. The present investigation aims to ascertain the accuracy and reliability of the LES laboratory code predicted results and evaluate the effectiveness of the extended Smagorinsky model to resolve and describe the evolution of the main mean flow quantities and thermal statistics in the present computational domain especially at the wall vicinity. The Computations are based on a finite difference scheme, second order accurate in space and in time, the numeric resolution is 65 3 grid points in r, θ and z direction respectively, with length of the domain of 20R. The predicted results show an excellent agreement with the DNS results, the main findings show that the present LES laboratory code can be considered as a powerful tool for predicting the mean thermal quantities of the Non-Newtonian fluid. The reduction in the fluid flow index (n) results in enhancement in the mean axial velocity and a pronounced attenuation in the mean temperature over the radial direction, where leads also to noticeable drop in the average Nusselt number
LES of Turbulent Flow of The Non-Newtonian Fluid: The Turbulence Statistics
No full textInternational audienceA large eddy simulation (LES) with an extended Smagorinsky model has been carried to investigate numerically the fully developed turbulent flow of a shear thinning fluid (n=0.75) in a stationary pipe at a simulation's Reynolds number equals to 4000 with a grid resolution of 65 3 gridpoints in axial, radial and circumferential directions and a domain length of 20R. The present study set out to critically evaluate the influence of the Non-Newtonian rheological and hydrodynamic behaviour on the turbulence main features, as well as to ascertain the accuracy and reliability of the laboratory code predicted results. The turbulent flow statistics obtained compared reasonably well with the experimental data and DNS results. A reasonably good agreement has been obtained between the predicted results and available results of literature. The main findings suggest that the mean axial velocity fluctuations were generated in the wall vicinity and transferred to the radial and spanwise components, which resulted in to an enhancement in the kinetic energy of turbulent fluctuations along the radial direction. The energy transport from the axial fluctuations to the other fluctuations components between the flow layers was suppressed compared to that of the Newtonian fluid
Direct numerical simulation and large eddy simulation of turbulent pipe flow
No full textInternational audienceDirect Numerical Simulations and Large Eddy Simulations are performed for a fully developed turbulent pipe flow in non-rotating and rotating cases. The aim of this study is to investigate the effects of the Reynolds number and of the rotation number on the turbulent flow characteristics. The mean velocity profiles and many turbulence statistics are compared to numerical and experimental data available in the literature, and reasonably good agreement is obtained. In particular, the results show that the axial velocity profile gradually approaches a laminar shape when increasing the rotation rate, due to the stability effect caused by the centrifugal force. Consequently, the friction factor decreases. The Reynolds number dependence of the mean velocity profile decreases when the rotation rate increases. The rotation of the wall has large effects on the root mean square (rms), these effects being more pronounced for the streamwise rms velocity. Visualizations of the instantaneous velocity and vorticity fields exhibit turbulence structures with strong vorticity developing up to the pipe centre. These vortical structures are inclined and better organized with increasing N
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