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What do we Measure, and Why?
Published in Richard J. Goldstein, Fluid Mechanics Measurements, 2017
For turbulent flows the characteristic length l is proportional to δ or the width of a jet or wake, i.e., a transverse length scale. The smallest scales in a turbulent flow are controlled by viscosity. The small-scale motion has much smaller characteristic timescales than the large-scale motion and may be considered statistically independent. We may think of the small-scale motion as being controlled by the rate of supply of energy and the rate of dissipation. It is probably reasonable to assume that the two rates are equal. Thus we consider the dissipation rate per unit mass ε and the kinematic viscosity v. From purely dimensional reasoning, we can form length, time, and velocity scales: () η=(v3ε)1/4τ=(vε)1/2uv=(vε)1/4
Introduction to convection
Published in Tariq Muneer, Jorge Kubie, Thomas Grassie, Heat Transfer, 2012
Tariq Muneer, Jorge Kubie, Thomas Grassie
The characteristic length, L, is a representative measure of the length of the surface over which the fluid flows. For example, for a flat plat with external parallel flow, as will be discussed in Section 7.2, the characteristic length is simply the length of the plate. However, for other surface geometries, such as those presented by angular or spherical objects, the characteristic length is taken as the length of the subject cross-section presented perpendicular to the direction of fluid flow. For external forced convection, a summary of the characteristic length, employed in the analysis of heat transfer from cylinders and spheres is given in Table 7.2.2. In this context, the characteristic length is usually referred to as ‘D’.
K
Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[computational, fluid dynamics, mechanics, thermodynamics] Dimensionless number in gas mechanics used to determine the computational regime for staging the mathematical approach. Ratio of the free path for molecular motion (λmolecule) and a characteristic length of the system (L): Kn=λmolecule/Lchar=kT/2πσ2PL, where k is the Boltzmann constant (1.3806504(24) × 10−23 J/m, T the temperature of the system, σ the particle hard shell diameter, and P the pressure. Primarily originating from the computational needs in fluid dynamics for rheology and rarified gases, specifically related to momentum transport theory. For instance, a Knudsen number of Kn ≤0.1 sets the boundary conditions where the fluid can be treated as a continuous medium, with the macroscopic parameters such as pressure, temperature, volume, velocity, and density. More confined is the regime: 0<Kn≤0.1, describing slip flow. No slip flow is characterized by Kn = 0. Under the condition of Kn≥1, the theoretical approach for the fluid requires a microscopic or molecular approach. Specifically under the conditions of, the trajectories of individual molecules need to be mechanically analyzed as macroscopic variables. Additionally, for Kn≥10 there are no statistically significant molecular interactions and the fluid is considered to be free molecular or collisionless. The segment 0.1 < Kn < 1 is the transition slip flow regime, treating the fluid as a continuous medium allowing for discontinuities at the boundaries in characteristics such as temperature and velocity while the flow transitions from diffusive (continuum) to ballistic or free molecular flow. The Knudsen number expresses the ratio of the mean free path length of molecular motion (e.g., Brownian motion) with respect to a characteristic length. The mean free path is inversely proportional to the fluid density. The characteristic length will be a direct function of the situation that needs to be computed, such as the dimensions and shape of an object submerged in a liquid or the diameter of a fluid flow in a pipe. An archetypal example of a small characteristic length is the flow of an aerosol through small diameter apertures and small size tubing. The Knudsen conditions will require Monte Carlo simulations in order to solve the fluid dynamics issues under the complex boundary conditions. The Knudsen number indicates the validity of either line of sight (Kn>1) or continuum (Kn < 0.01) for gas models.
Experimental investigation of substrate board orientation effect on the optimal distribution of IC chips under forced convection
Published in Experimental Heat Transfer, 2021
V K Mathew, Tapano Kumar Hotta
7. The non-dimensional numbers for the IC chips affecting the laminar forced convection heat transfer are then evaluated using the Eqns. 7 and 8, respectively. The Reynolds number is the ratio of the inertia force to viscous force in fluid flow and is the product of density times velocity times characteristic length divided by the viscosity coefficient. The Nusselt number is the ratio of convective to conductive heat transfer across the fluid boundary. The characteristic length of the IC chips is a scaling parameter and is taken L = 4A/P, as reported in Bergman et al. [28]. This is defined in this manner to develop suitable correlations, as discussed under Section 3.5.3.
A review of microfluidic concepts and applications for atmospheric aerosol science
Published in Aerosol Science and Technology, 2018
Andrew R. Metcalf, Shweta Narayan, Cari S. Dutcher
is defined as the ratio of the material dimension, , which depends on the fluid, to the characteristic flow dimension, , through or around which the fluid is traveling. The material dimension is the mean free path (gases), molecular spacing (liquids), or grain size (solids). The characteristic length scale is particle diameter, when describing particle-laden flow, or channel dimension (usually hydraulic diameter), when describing microfluidic flow. Typically, defines continuum flow, defines free molecular or kinetic flow, and between these extremes defines the transition regime (Squires and Quake 2005; Kulkarni et al. 2011; Seinfeld and Pandis 2016). In both microfluidics and aerosol science, the characteristic length scales can be on the same order as the material dimension leading to a range of possible flow regimes. For gas flows especially, several flow regimes can occur within the same microchannel (Gad-el-Hak 1999). In the design of microfluidic experiments, can be tuned to define a flow field which mimics an aerosol flow of interest.
A study on the resistance force and the aerodynamic drag of Korean high-speed trains
Published in Vehicle System Dynamics, 2018
The Reynolds number is a flow parameter defined as ρul/μ, where ρ is the air density, u is the freestream velocity, l is the characteristic length and μ is the dynamic viscosity. The drag coefficient is known to be mostly sensitive in the critical region of the Reynolds number that is supposed to be in the range from 2 × 106 to 4 × 106 for slender bodies, and the Reynolds number of the full-scale train is normally in the supercritical range [11] where the drag coefficient remains almost constant.