Khanh Tuoc Trinh
The Blasius empirical correlation for turbulent pipe friction factors is derived from first principles and extended to non-Newtonian power law fluids. Two alternative formulations are obtained that both correlate well with the experimental measurements of Dodge, Bogue and Yoo. Key words: Blasius, turbulent friction factor, power law fluids
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This paper presents a theoretical derivation of the empirical Blasius power law correlation for the friction factor. The coefficients in this correlation are shown to be dependent on the Reynolds number. Published experimental data is well correlated. Key words: Blasius, friction factor, turbulence, power law, log-law, wall layer
The classical experiments on turbulent friction in rough pipes were performed by J. Nikuradse in the 1930's. Seventy years later, they continue to defy theory. Here we model Nikuradse's experiments using the phenomenological theory of Kolmogórov, a theory that is widely thought to be applicable only to highly idealized flows. Our results include both the empirical scalings of Blasius and Strickler, and are otherwise in minute qualitative agreement with the experiments; they suggest that the phenomenological theory may be relevant to other flows of practical interest; and they unveil the existe…
We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ in the enstrophy-dominated case. We use …
A zonal similarity analysis of friction factors in pipe flow of power law fluids is presented. It uses the critical Reynolds number and friction factor at transition as estimates of the normalised velocity and distance between the wall and log-law layers and successfully collapses both Newtonian and non-Newtonian data for laminar, transition and turbulent flows. Key words: zonal similarity analysis, friction factor, Reynolds number, transition
Correlations of friction factors are presented for the general case of purely viscous non-Newtonian fluids without requiring a priori the adoption of a rheological model. They are based on an empirical estimate of the shift in the wall layer edge and the Kolmogorov point. The predictions of friction factors have the same level of accuracy as those of the Dodge-Metzner correlation but the visualisation is more compatible with measured velocity profiles. The general correlations obtained can be used to easily retrieve correlations for specific rheological models.
Turbulence intensity profiles are compared for smooth- and rough-wall pipe flow measurements made in the Princeton Superpipe. The profile development in the transition from hydraulically smooth to fully rough flow displays a propagating sequence from the pipe wall towards the pipe axis. The scaling of turbulence intensity with Reynolds number shows that the smooth- and rough wall level deviates with increasing Reynolds number. We quantify the correspondence between turbulence intensity and the friction factor.
In this work, the friction factor for steady periodically developed flow through micro-and mini-channels with periodic arrays of offset strip fins is analyzed. The friction factor is studied numerically on a unit cell of the array for Reynolds numbers ranging from 1 to 600, and fin height-to-length ratios below 1. It is shown that the friction factor correlations from the literature, which primarily focus on larger conventional offset strip fin geometries in the transitional flow regime, do not predict the correct trends for laminar flow in micro-and mini-channels. Therefore, a new friction fa…
A Favre-Averaging Shallow Water Framework for Aerated Flows with Friction Factor Decomposition
本文提出了一种基于浅水方程的 Favre 平均方法，用于预测高弗劳德数含气流的阻力，通过分解摩擦因子考虑混合密度变化，验证了该方法在实验数据中的有效性。
Drawing on an analogy to critical phenomena, it was shown that the Nikuradse turbulent friction factor ($f_t$) measurements in pipes of radius $R$ and wall roughness $r$ can be collapsed onto a one-dimensional curve expressed as a conveyance law $f_t Re^{1/4}=g_o(χ)$, where $Re$ is a bulk Reynolds number, $χ=Re^{3/4}\left({r}/{R}\right)$. The implicit function $g_o(.)$ was conjectured based on matching two asymptotic limits of $f_t$. However, the connection between $g_o(.)$ and the phenomenon it proclaims to represent - turbulent eddies - remains lacking. Using models for the wall-normal veloc…
The impact of wall roughness on fully developed laminar pipe flow is investigated numerically. The roughness is comprised of square bars of varying size and pitch. Results show that the inverse relation between the friction factor and the Reynolds number in smooth pipes still persists in rough pipes, regardless of the rib height and pitch. At a given Reynolds number, the friction factor varies quadratically with roughness height and linearly with roughness pitch. We propose a single correlation for the friction factor that successfully collapses the data.
This paper uses the estimates of phase-locked parameters at the onset of bursting presented in a companion paper to derive logarithmic correlations for turbulent friction factor losses in time-independent power law fluids. Two different techniques for analysis were used. They gave logarithmic correlations with different coefficients. But both correlations predicted 264 data points of friction factors published in the literature with a standard error of 1.3%. The derivations show how modern understanding of coherent structures embedded in turbulent flow fields can be used to derive engineering …
Completing Moody's friction diagram in the turbulent transitional regime
本文通过从湍流状态降速进入转捩区，研究穆迪图中层流与湍流之间摩擦系数的不确定性，发现不同驱动方式会显著影响转捩区的最终状态和路径。
In this paper we present electro-osmotic (EO) flow within a more traditional fluid mechanics framework. Specifically, the modified Bernoulli equation (viz. the energy equation, the mechanical energy equation, the pipe flow equation, etc.) is shown to be applicable to EO flows if an electrical potential energy term is also included. The form of the loss term in the modified Bernoulli equation is unaffected by the presence of an electric field; i.e., the loss term still represents the effect of wall shear stress, which can be represented via a friction factor. We show that that the friction fact…
We show that the main results of the analysis of the friction factor for turbulent pipe flow reported in G. Gioia and P. Chakraborty (GC), Phys. Rev. Lett. 96, 044502 (1996) can be recovered by assuming the Heisenberg closure hypothesis for the turbulent spectrum. This highlights the structural features of the turbulent spectrum underlying GC's analysis.
Skin friction and heat transfer in hypersonic transitional and turbulent boundary layers
本文基于二重积分分析了高超声速转捩和湍流边界层中表面摩擦与传热的产生机制，揭示了转捩区过冲行为的原因及壁温、马赫数对湍流区各物理量贡献的影响。
An asymptotic $-1/2$ power-law scaling and a semi-empirical finite-$Re$ model were recently presented by Dixit et al. (2020) for skin friction in zero-pressure-gradient (ZPG) turbulent boundary layers (TBLs). In this work, a new derivation is presented which shows that these relations (i) fundamentally represent a dynamically-consistent scaling of skin friction for nominally two-dimensional ZPG TBLs and fully-developed pipes and channels, and (ii) apply individually to each of these flows. The new theoretical arguments are based on transfer of kinetic energy from mean flow to large eddies of t…
It is shown that initiated by action of molecular viscosity impulse flow, directed usually from the moving fluid to limiting it solid surface, can, under certain conditions, turn to zero and get negative values in the case of non-stationary flow caused by alternating in time longitudinal (along the pipe axis) pressure gradient. It is noted that this non-equilibrium mechanism of negative friction resistance in the similar case of pulsating blood flow in the blood vessels, in addition to the stable to turbulent disturbances swirled blood flow structure providing, can also constitute hydro-mechan…
Modelling friction and heat transfer in turbulent forced convection over porous lattices
本研究通过直接数值模拟，提出用Forchheimer系数替代粗糙度高度，将粗糙壁理论扩展至多孔表面，推导出摩擦系数与斯坦顿数公式，验证多孔基底可有效增强湍流传热。
In this paper, we use the well-known background method to obtain a rigorous lower bound on the volume flow rate through a helical pipe driven by a pressure differential in the limit of large Reynolds number. As a consequence, we also obtain an equivalent upper bound on the friction factor. These bounds are also valid for toroidal and straight pipes as limiting cases. By considering a two-dimensional background flow with varying boundary layer thickness along the circumference of the pipe, we obtain these bounds as a function of the curvature and torsion of the pipe and therefore capture the ge…
Modelling of pressure drop in periodic square-bar packed beds
研究通过数值模拟分析方形棒堆叠填料在不同旋转角度下的压力降特性，发现几何结构影响摩擦因子，基于旋转角度区分通道状和晶格状结构，揭示了摩擦因子与模块等效直径的关系。
Flows in fluid layers are ubiquitous in industry, geophysics and astrophysics. Large-scale flows in thin layers can be considered two-dimensional (2d) with bottom friction added. Here we find that the properties of such flows depend dramatically on the way they are driven. We argue that wall-driven (Couette) flow cannot sustain turbulence at however small viscosity and friction. Direct numerical simulations (DNS) up to the Reynolds number $Re=10^6$ confirm that all perturbations die in a plane Couette flow. On the contrary, for sufficiently small viscosity and friction, we show that finite per…
Mapping-based exact-integral formulation of skin-friction transformations for zero-pressure-gradient compressible turbulent boundary layers
该研究针对零压力梯度可压缩湍流边界层，提出基于映射的精确积分壁面摩擦变换，改进了经典范·德里斯特理论，基于VIPL的变换在宽马赫数和热输入范围内预测误差低至3.07%。
Direct Numerical Simulations are used to solve turbulent flow and heat transfer over a variety of rough walls in a channel. The wall geometries are exactly resolved in the simulations. The aim is to understand the effect of roughness morphology and its scaling on the augmentation of heat transfer relative to that of skin friction. A number of realistic rough surface maps obtained from the scanning of gas turbine blades and internal combustion engines as well as several artificially generated rough surfaces are examined. In the first part of the paper, effects of statistical surface properties,…
We study the behavior of the pulse waves of water into a flexible tube for application to blood flow simulations. In pulse waves both fluid friction and wall viscosity are damping factors, and difficult to evaluate separately. In this paper, the coefficients of fluid friction and wall viscosity are estimated by fitting a nonlinear 1D flow model to experimental data. In the experimental setup, a distensible tube is connected to a piston pump at one end and closed at another end. The pressure and wall displacements are measured simultaneously. A good agreement between model predictions and exper…
Enhanced heat transfer in a 2D serpentine micro-channel using elastic polymers
本研究通过Rheotool模拟Oldroyd-B流体在二维蛇形微通道中的流动，揭示了弹性湍流条件下基于Weissenberg数的三个传热与摩擦系数变化区域，发现弹性不稳定性显著增强了传热效率。
A numerical study on the effect of rolling friction on clogging of pores in particle-laden flows
本研究通过直接数值模拟探讨了滚动阻力对颗粒流中孔隙堵塞行为的影响，开发了离散元方法与浸没边界方法耦合的求解器，验证了滚动阻力在孔隙尺度上的作用。
Order of Magnitude Analysis and Data-Based Physics-Informed Symbolic Regression for Turbulent Pipe Flow
本研究通过量级分析和数据驱动的物理信息符号回归，推导出适用于不同粗糙度和雷诺数的摩擦因子紧凑相关式。
Deep Neural Networks with 3D Point Clouds for Empirical Friction Measurements in Hydrodynamic Flood Models
本文提出用实验室训练的深度神经网络从三维点云中直接测量曼宁糙率系数，并在一维及一维/二维耦合洪水模型中验证其能改进洪水预测、降低不确定性。
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