Statistical modeling of compressible turbulent channel flow

Several questions that are relevant to turbulence modeling are addressed on the basis of recently obtained direct numerical simulation results of turbulent supersonic channel flow. In particular, this concerns the turbulence frequency production mechanism, wall damping effects on turbulence model parameters, and the relevance of compressibility effects. Limited support is found for usually applied models for the turbulence frequency production and wall damping effects. In contrast to that it is shown that turbulence frequency production mechanisms and wall damping effects may be explained very well on the basis of a frequency scaling that characterizes mean flow changes. The influence of compressibility is found to be relevant. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

DNS and scaling law analysis of compressible turbulent channel flow

Fully developed compressible turbulent channel flow (Ma = 0.8, Re = 3300) is numerically simulated, and the data base of turbulence is established. The statistics such as density-weighted mean velocity and RMS velocity fluctuations in semi-local coordinates agree well with those from other DNS data. High order statistics (skewness and flatness factors) of velocity fluctuations of compressible turbulence are reported for the first time. Compressibility effects are also discussed. Pressure-dilatation absorbs part of the kinetic energy and makes the streaks of compressible channel flow more smooth. The scaling laws of compressible channel flow are also discussed. The conclusions are: (a) Scaling law is found in the center area of the channel, (b) In this area, ESS is also found, (c) When Mach number is not very high, compressibility has little effect on scaling exponents.     

The Fanno model for turbulent compressible flow

We discuss the existence of a solution of the boundary value problem

     

A study of effects of wall-normal rotation on the turbulent channel flow

The effects of the wall–normal rotation on the turbulence channel flow have been studied. A series of direct numerical simulations have been performed with various rotation rates for Reynolds number 180 based on the friction velocity in the non–rotating case. All remarkable changes are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of contraction on turbulent channel flow

Summary Measurements in an effectively two-dimensional channel indicate that flow acceleration at constant Reynolds Number can have appreciable effects on the turbulence structure. As in wakes, the structure approaches equilibrium exponentially after the acceleration. The effect of acceleration appears to be (at least qualitatively) of the same kind as is observed when turbulence is subjected to rapid distortion.

---

Zusammenfassung Messungen in einem effektiv zwei-dimensionalen Kanal zeigen, daß eine Strömungsbeschleunigung bei konstanter Reynolds-Zahl einen wesentlichen Einfluß auf die Turbulenz-Struktur haben kann. Nach der Beschleunigung findet man eine exponentielle Annäherung an das Gleichgewicht, wie bei Dellen. Der Beschleunigungs-Effekt auf die Turbulenz erscheint, wenigstens qualitativ, von der gleichen Art zu sein wie der Einfluß von raschen Verformungen.

---

Symbols c _f skin-friction coefficient = - D half-width of the channel - L length of contraction=12 inches - dp/dx pressure gradient - V mean velocity in thex-direction,U=U ₀ aty=D - U mean velocity - average of the mean velocity - U ^* friction velocity = (₀/)^± - root mean square value of the turbulent velocity fluctuations inx, y andz directions - X coordinate in the direction of the flow;X=0 at the end of contraction - Y coordinate perpendicular to the surface of the wall on which measurements are madey=0 at the wall andy=D at the centre of the channel - ₀ Wall shear stress - density of the fluid - viscosity of the fluid - kinematic viscosity of the fluid=/     

Micromorphic description of turbulent channel flow

The simple microfluid theory of Eringen is employed to determine the velocity profile and microgyrations in a steady flow of viscous fluids between two parallel walls. The shearing stress, microrotations, microinertia and Reynold stresses are determined. The results are compared with the experimental work of Laufer.     

Electromagnetic flow rate measurement in turbulent liquid metal channel flow

Flow control in hot aggressive melts is a big challenge for metallurgical and glass technology applications. For instance, during the production of float glass, the glass melt solidifies on the top of a liquid tin bath. To achieve a spatially homogeneous glass thickness, both global and local control of the thermofluiddynamic transport phenomena in the tin bath are crucial. The concept a global flow control involves the coupling of the non-contact electromagnetic flow rate measurement technique of Lorentz force velocimetry and the non-contact flow driving technique of electromagnetic pumps based on rotating permanent magnets. The paper presents a model experiment using the low-melting test melt GaInSn as well as numerical simulations using the commercial code FLUENT/MHD. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of mass loading on particle-laden turbulent channel flow

Results are presented for the behavior of particle-laden gases in a moderate Reynolds number vertical channel down flow. The effects of mass loading on the gas-phase turbulence and particle concentration are studied. A direct numerical simulation including models of wall-particle interaction is conducted. It is confirmed that particle feedback causes the turbulence intensities to become more non-isotropic as the particle loading is increased. The particle concentration exhibits a maximum close to the wall and a slight increase in the middle of the channel. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of bubbly flow in a vertical turbulent channel

The paper presents results of Direct Numerical Simulation of bubbly flow to analyse the interaction between the turbulent fluid and the bubbles. The simulations aim to investigate the effect of the bubble Reynolds number, related to the bubble size, and the void fraction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A three-layer asymptotic analysis of turbulent channel flow

In the classical theory for large-Reynolds number fully developed channel flow, the solutions obtained by asymptotic-expansion techniques for the outer Karman defect layer and the inner Prandtl wall layer are demonstrated to match through the introduction of an intermediate layer, based on a general intermediate limit. From an examination of the results for this general intermediate layer, the distinguished intermediate limit and the corresponding intermediate layer for which the turbulent and laminar contributions to the difference of the Reynolds stress from the wall stress are of the same order of magnitude are identified. The thickness of this distinguished intermediate layer is found to be of the order of the geometric mean of the thicknesses of the outer and inner layers     

Simulation of bed load transport in turbulent open channel flow

The paper reports on direct numerical simulations of a particle-laden open channel flow carried out to investigate the interaction between the dispersed and the continuous phase. The dispersed phase is represented by an immersed boundary method. The particle-particle collisions are accounted for by a physically motivated collision model. Two cases, one with shear stress below the threshold of mobilization and the other with shear stress above the threshold are considered. The different density ratios lead to different types of modification of the flow field by the formation of density-specific patterns of the particles. Light particles do not attain resting states but saltate evenly distributed in span-wise direction. Heavy particles tend to form stream-wise clusters of inactive particles. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some studies on transition from laminar to turbulent flow in a two-dimensional channel

Zusammenfassung In einem Wasserkanal wurden Versuche über den laminar-turbulenten Umschlag einer zweidimensionalen Strömung durchgeführt. Geschwindigkeitsmessungen der vorderen und hinteren Randzonen von künstlich erzeugten Turbulenz-Kernen ergaben eine (auf die mittlere Strömungsgeschwindigkeit und die Kanaltiefe bezogene) kritische Reynolds-Zahl von 1025±25. Messungen der Intermittenz längs des Kanals bei den Reynolds-Zahlen 3460, 3570 und 3850 zeigten, dass die Umschlagstheorie nach Emmons auch für Kanalströmung sinnvoll ist.     

Hydrodynamic interaction in suspended sediment distribution of open channel turbulent flow

In the present study, a theoretical model is proposed to predict the vertical distribution of suspended sediment in open channel turbulent flow. We derive our mathematical model based on the six prominent hydrodynamic mechanisms, which are upward sediment flux due to the turbulent diffusion, downward gravitational settling of the sediment, hindered settling phenomenon, secondary current, fluid induced lift force on the suspended particles and the gradient of Reynolds normal stress of the suspended sediment. The importance of the hydrodynamics is described by the changes of suspended sediment concentration profile in terms of the particle-flow interaction caused by those mechanisms. We also address the significance of the co-existence of those mechanisms for estimating the suspended sediment concentration profile. The present model agrees satisfactorily with a wide spectrum of experimental data in available literature. Unlike the previous researchers, we select a broad range of previously published models of vertical sediment concentration distribution for comparison analysis, and the proposed model shows better prediction accuracy which is confirmed by error analysis.     

Characterisation of bubble clusters in simulations of upward turbulent channel flow

The paper reports on Direct Numerical Simulations of bubble-laden flows performed to investigate the interaction of bubbles with turbulence in an upward flow between two parallel vertical plates. Two simulations are presented with uniform bubble diameter and a third one with bi-disperse bubbles. Three different approaches are used to characterize bubble clustering in the investigated configuration. Horizontal pairing and tendency to form cluster has been found for all reported cases, slightly less pronounced in the bi-disperse swarm. Among other results, a 60°-alignment has been found by means of the angular pair correlation function for the mixed pairs in the bi-disperse swarm. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of wall conductivity on turbulent channel flow under spanwise magnetic field

The effect of wall conductivity on turbulence in electrically conducting fluid in the presence of a constant magnetic field is considered. A channel flow with a spanwise magnetic field is analyzed using high-resolution direct numerical simulations performed for the case of low magnetic Reynolds number. It is found that the effect of suppression of wall-normal momentum transfer and reduction of wall friction identified earlier for the flow with perfectly insulating walls is enhanced if the walls are electrically conducting. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow

The modified Reynolds mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are firstly derived. A new successive iteration method is developed to calculate the mean orientation distribution of fiber, and the mean and fluctuation-correlated quantities of suspension in a turbulent channel flow. The derived equations and successive iteration method are verified by comparing the computational results with the experimental ones. The obtained results show that the flow rate of the fiber suspension is large under the same pressure drop in comparison with the rate of Newtonian fluid in the absence of fiber suspension. Fibers play a significant role in the drag reduction. The amount of drag reduction augments with increasing of the fiber mass concentration. The relative turbulent intensity and the Reynolds stress in the fiber suspension are smaller than those in the Newtonian flow, which illustrates that the fibers have an effect on suppressing the turbulence. The amount of suppression is also directly proportional to the fiber mass concentration.     

Flow rate measurements in turbulent liquid metal channel flow using Time-of-Flight Lorentz force velocimetry

Non-contact flow control and flow measurements in hot and aggressive metal melts are big challenges in metallurgical applications. Time-of-Flight Lorentz force velocimetry (ToF LFV) is an electromagnetic measurement technique to meet these challenges. Our experimental results demonstrate that this method is well suited to measure flow rate in turbulent liquid metal channel flow without knowledge of both melt and magnetic field properties. Moreover, the measured flow profiles are in very good agreement with predictions of numerical simulations using the commercial program Package FLUENT MHD. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mach configuration in pseudo-stationary compressible flow

This paper is devoted to studying the local structure of Mach reflection, which occurs in the problem of the shock front hitting a ramp. The compressible flow is described by the full unsteady Euler system of gas dynamics. Because of the special geometry, the motion of the fluid can be described by self-similar coordinates, so that the unsteady flow becomes a pseudo-stationary flow in this coordinate system. When the slope of the ramp is less than a critical value, the Mach reflection occurs. The wave configuration in Mach reflection is composed of three shock fronts and a slip line bearing contact discontinuity. The local existence of a flow field with such a configuration under some assumptions is proved in this paper. Our result confirms the reasonableness of the corresponding physical observations and numerical computations in Mach reflection.

In order to prove the result, we formulate the problem to a free boundary value problem of a pseudo-stationary Euler system. In this problem two unknown shock fronts are the free boundary, and the slip line is also an unknown curve inside the flow field. The proof contains some crucial ingredients. The slip line will be transformed to a fixed straight line by a generalized Lagrange transformation. The whole free boundary value problem will be decomposed to a fixed boundary value problem of the Euler system and a problem to updating the location of the shock front. The Euler system in the subsonic region is an elliptic-hyperbolic composite system, which will be decoupled to the elliptic part and the hyperbolic part at the level of principal parts. Then some sophisticated estimates and a suitable iterative scheme are established. The proof leads to the existence and stability of the local structure of Mach reflection.