Non-dimensional Length Scale Research Articles

Velocity Profile Representation for Fully Developed Turbulent Flows in Pipes: A Modified Power Law

In the design practices of many engineering applications, gross information about the flow field may suffice to provide magnitudes of the parameters that are essential to complete the design with reasonable accuracy. If such design parameters can be estimated following simpler steps, it may be possible to abandon the need to conduct expensive numerical and/or experimental works to produce them. In this work, we are interested in providing a generalized power law that depicts the velocity profile for fully developed turbulent flows. This law incorporates two fitting parameters m and n that represent the exponents of (1) a nondimensional length scale and (2) an overall exponent, respectively. These two parameters may be determined by fitting the experimental and/or computational data. In this work, fitting benchmark experimental and computational fluid dynamics (CFD) data found in the literature reveals that the parameter m changes over a relatively smaller range (between 1 and 2), while the parameter n changes over a wider range (between 1 and 12 for the range of Reynolds number considered). These two parameters (m and n) are, generally, not universal, and they depend on the Reynolds number (Re). A correlation was also developed to correlate n and Re in the turbulent flow region. In order to preserve the continuity of the derivative of the velocity profile at the centerline, a value of m equals 2 over the whole range of Re is recommended. Apart from the near wall area, the new law fits the velocity profile reasonably well. This generalized law abides to a number of favorable stipulations for the velocity profile, namely the continuity of derivatives and reduction to the laminar flow velocity profile for lower values of Re.

EFFECT OF INLET TURBULENCE INTENSITY ON TRANSPORT PHENOMENA OVER BLUFF BODIES

The effect of turbulence intensity on the transport phenomena over two-dimensional bluff bodies is studied in this work. Simulation is performed for an infinite circular cylinder and a square cylinder with the same hydraulic diameter D, which is also the nondimensional length scale. The computation is performed to cover the cross flow enclosing the laminar and turbulent regime for Reynolds numbers ranging up to 200,000 and inlet turbulence intensities from 5% to 40%. The Reynolds-averaged Navier-Stokes and energy equations are solved along with the transition shear stress transport (SST) model for the closure of turbulence. The results are initially validated with prior works for drag and thermal performance and experimental correlations. The analysis quantifies the influence of inlet turbulence intensity on enhancing heat transfer from the bluff bodies. However, the drag and pressure coefficients are not affected by the variation of inlet turbulence intensity.

Influence of Inlet Turbulence Intensity on Transport Phenomenon of Modified Diamond Cylinder: A Numerical Study

Flows around bluff cylinder have received the attention of many researchers over the years. Therefore, the purpose of this paper was to study the effect of turbulence intensity on the transport phenomena over modified diamond cylinders which is investigated in this work. The bluff cylinders considered are of diamond shape and extruded diamond shape. The hydraulic diameter of bluff bodies is taken as the non-dimensional length scale. The simulation is done to cover cross-flow covering the laminar and turbulent regime with the Reynolds number reaching up to 10,000, while the inlet turbulent intensity is varied between 5 and 20%. The influence of turbulent intensity on enhancing heat transfer from the body has been emphasized in this work. The transition SST models along with governing equations (continuity, momentum, and energy equations) are solved numerically with ANSYS Fluent 19.2. The simulation results are validated with established correlations, and excellent agreement is found. This work demonstrates that the transition SST model can effortlessly bridge all flow regimes for predicting the heat transfer. The study computes the influence of inlet turbulence intensity on augmenting heat transfer from the bluff cylinders. The pressure and drag coefficients are found to be unaffected by the inlet turbulent intensity.

Adaptive high-order discretization of the Reynolds-averaged Navier-Stokes equations

In this article, a dual-consistent high-order flux reconstruction (FR) or correction procedure via reconstruction (CPR) method is developed to solve the Reynolds-averaged Navier-Stokes (RANS) equations with the modified Spalart and Allmaras (SA) model. In this model, the non-dimensional length scale r depends on the distance to the nearest wall. To compute this distance to the nearest curved polynomial wall boundaries for each solution point, the FR/CPR high-order discretization is extended to solve the Eikonal equation. One internal and three external flow problems including a three-element high-lift configuration are considered to demonstrate the accuracy and efficiency of the present Eikonal solver. Additionally, an adjoint-based adaptive mesh refinement method is utilized to minimize the output error. The present method is demonstrated for several benchmark turbulent flow problems. The adaptive results are compared to other simulations or experimental data.

Free vibration and biaxial buckling analysis of magneto-electro-elastic microplate resting on visco-Pasternak substrate via modified strain gradient theory

This paper deals with the theoretical analysis of free vibration and biaxial buckling of magneto-electro-elastic (MEE) microplate resting on Kelvin–Voigt visco-Pasternak foundation and subjected to initial external electric and magnetic potentials, using modified strain gradient theory (MSGT). Kirchhoff plate model and Hamilton’s principle are employed to extract the governing equations of motion. Governing equations were analytically solved to obtain clear closed-form expression for complex natural frequencies and buckling loads using Navier’s approach. Numerical results are presented to reveal variations of natural frequency and buckling load ratio of MEE microplate against different amounts of the length scale parameter, initial external electric and magnetic potentials, aspect ratio, damping and transverse and shear stiffness parameters of the visco-Pasternak foundation, length to thickness ratio, microplate thickness and higher modes. Numerical results of this study illustrate that by increasing thickness-to-material length scale parameter ratio, both natural frequency and buckling load ratio predicted by MSGT and modified couple stress theory are reduced because the non-dimensional length scale parameter tends to decrease the stiffness of structures and make them more flexible. In addition, results show that initial external electric and initial external magnetic potentials have no considerable influence on the buckling load ratio and frequency of MEE microplate as the microplate thickness increases.

Biaxial buckling analysis of double-orthotropic microplate-systems including in-plane magnetic field based on strain gradient theory

Background/purposeThis paper deals with analysis of biaxial buckling behavior of double-orthotropic microplate system including in-plane magnetic field, using strain gradient theory. MethodsTwo Kirchhoff microplates are coupled by an internal elastic medium and also are limited to the external Pasternak elastic foundation. Utilizing the principle of total potential energy, the equilibrium equations of motion for three cases (out-of-phase buckling, in-phase buckling and buckling with a plate) are acquired. In this study, we assumed boundary conditions of all the edges are simply supported. In order to get exact solution for buckling load of system, Navier approach which satisfies the simply supported boundary conditions is applied. ResultsVariations of the buckling load of double-microplate system subjected to biaxial compression corresponding to various values of the thickness, length scale parameter, magnetic field, stiffness of internal and external elastic medium, aspect ratio, shear stiffness of the Pasternak foundation and biaxial compression ratio are investigated. Furthermore, influence of higher modes on buckling load is shown. By comparing the numerical results, it is found that dimensionless buckling load ratio for in-phase mode is more than those of out of phase and one microplate fixed. Also it is shown that the value of buckling load ratio reduces, when non-dimensional length scale parameter increases. ConclusionHowever, we found when properties of plate are orthotropic the buckling load ratio is more than isotropic state. Also, by considering the effect of magnetic field, non-dimensional buckling load ratio reduces.

The Effect of Scale on the Applicability of Taylor’s Frozen Turbulence Hypothesis in the Atmospheric Boundary Layer

Taylor’s frozen turbulence hypothesis is the central assumption invoked in most experiments designed to investigate turbulence physics with time resolving sensors. It is also frequently used in theoretical discussions when linking Lagrangian to Eulerian flow formalisms. In this work we seek to quantify the effectiveness of Taylor’s hypothesis on the field scale using water vapour as a passive tracer. A horizontally orientated Raman lidar is used to capture the humidity field in space and time above an agricultural region in Switzerland. High resolution wind speed and direction measurements are conducted simultaneously allowing for a direct test of Taylor’s hypothesis at the field scale. Through a wavelet decomposition of the lidar humidity measurements we show that the scale of turbulent motions has a strong influence on the applicability of Taylor’s hypothesis. This dependency on scale is explained through the use of dimensional analysis. We identify a ‘persistency scale’ that can be used to quantify the effectiveness of Taylor’s hypothesis, and present the accuracy of the hypothesis as a function of this non-dimensional length scale. These results are further investigated and verified through the use of large-eddy simulations.

A Variational Model for Dislocations in the Line Tension Limit

We study the interaction of a singularly-perturbed multiwell energy (with an anisotropic nonlocal regularizing term of H1/2 type) and a pinning condition. This functional arises in a phase field model for dislocations which was recently proposed by Koslowski, Cuitino and Ortiz, but it is also of broader mathematical interest. In the context of the dislocation model we identify the Γ-limit of the energy in all scaling regimes for the number Nɛ of obstacles. The most interesting regime is Nɛ≈|ln ɛ|/ɛ, where ɛ is a nondimensional length scale related to the size of the crystal lattice. In this case the limiting model is of line tension type. One important feature of our model is that the set of energy wells is periodic, and hence not compact. Thus a key ingredient in the proof is a compactness estimate (up to a single translation) for finite energy sequences, which generalizes earlier results from Alberti, Bouchitte and Seppecher for the two-well problem with a H1/2 regularization.