Fractal Plates Research Articles

Mixing Analysis of Laminar Flow in Static Mixers with Circle Grid Fractal Perforated Plate Elements

The static mixers are widely used in many industries to obtain the desired type of mixing. In the context of mixing process, two different fluids and have a different properties will mix in a single equipment to produce an another fluid with a new property. In this research, a new approach of static mixers was proposed for pipeline mixing. The flow pattern, pressure drop and mixing characteristics (coefficient of variation) were carried out by means of computer simulations. The static mixers introduced here consists of a series of perforated plate with circle grids fractal pattern elements. The simulations work were carried out by using a commercial package of Computational Fluid Dynamic (CFD), ANSYS CFX 14.0 software. Three levels of laminar flow with Reynolds numbers (Re) of 100, 200 and 400 respectively had been used to investigate the performance of the static mixers introduced here. The effectiveness of circle grid perforated plate static mixer had been evaluated by comparing the homogeneity level of mixing fluids for each flow simulated. The simulations gave a new insights in the flow pattern in circle grids fractal perforated plate elements. The pressure drop predictions compare favorably with literature data and the coefficient of variation (COV) value for circle grid perforated plate with 50% porosity at Reynolds number 100 was 0.0744 which is out of the range meanwhile at Reynolds number 200 and 400 was 0.0483 and 0.0247 respectively which are in the range of reasonable target for many applications. Mixing in the elements occurs through a combination of flow splitting and shearing at the junctions of successive elements. Besides that, simple installation and manufacturing of this type of static mixers makes the fractal perforated plate’s element an excellent static mixing device.

CFD Analysis of Circle Grid Fractal Plate Thickness on Turbulent Swirling Flow

In this paper, steady state, incompressible, swirling turbulent flow through circle grid fractal plate has been simulated. The aim of the simulation is to investigate an effect of the circle grid fractal plate thickness in order to reduce swirling due to swirl disturbance in pipe flow. The simulation and analysis were carried out using finite volume CFD solver ANSYS CFX. Three different thickness of fractal plate were used in the simulation work with the thickness of 1 mm, 3 mm and 6 mm. The simulation results were compared with the pressure drop correlation of BS EN ISO 5167-2:2003 and turbulent model used, standard k-ε model gave the best agreement with the ISO pressure drop correlation. The effects of circle grid fractal plate thickness on the flow characteristics which are swirl angle and tangential velocity have been investigated as well.

Circle grid fractal plate as a turbulent generator for premixed flame: an overview

This review paper focuses to ascertain a new approach in turbulence generation on the structure of premixed flames and external combustion using a fractal grid pattern. This review paper discusses the relationship between fractal pattern and turbulence flow. Many researchers have explored the fractal pattern as a new concept of turbulence generators, but researchers rarely study fractal turbulence generators on the structure premixed flame. The turbulent flow field characteristics have been studied tand investigated in a premixed combustion application. In terms of turbulence intensity, most researchers used fractal grid that can be tailored so that they can design the characteristic needed in premixed flame. This approach makes it extremely difficult to determine the exact turbulent burning velocity on the velocity fluctuation of the flow. The decision to carry out additional research on the effect circle grid fractal plate as a turbulent generator for premixed flame should depends on the blockage ratio and fractal pattern of the grid.

New Insights on Acid Etched Fracturing Conductivity

Successful acid fracturing stimulation in carbonate reservoirs largely depends on the acid etched fracture conductivity. However, accurate prediction of this parameter is difficult due to the lack of knowledge for delicately charactering rough fracture surface. To push the limitation of the current situation, an advanced mathematical model is proposed based on the fractal theory and previous models.Matlabsoftware is employed for generating rough surfaces with two variables, standard difference and fractal dimension. A partial differential equation is built to describe the fluid flow between two random fractal surfaces and finite element method is chosen to do simulation job. Comparative analysis of the flow ability between fractal surfaces and parallel plates is clarified at the final. The results show that fracture widths have the most influence on the conductivity, followed by fracture surface asperities. Moreover, fractal dimension and standard deviation, can also affect the fluid flow ability.

Drag and near wake characteristics of flat plates normal to the flow with fractal edge geometries

Past results have suggested that the drag coefficient and the shedding frequencies of regular polygon plates all fall within a very narrow band of values. In this study, we introduce a variety of length scales into the perimeter of a square plate and study the effects this has on the wake characteristics and overall drag. The perimeter of the plate can be made as long as allowed by practical constraints with as many length scales as desired under these constraints without changing the area of the plate. A total of eight fractal-perimeter plates were developed, split into two families of different fractal dimensions all of which had the same frontal area. It is found that by increasing the number of fractal iterations and thus the perimeter, the drag coefficient increases by up to 7%. For the family of fractal plates with the higher dimension, it is also found that when the perimeter increases above a certain threshold the drag coefficient drops back again. Furthermore, the shedding frequency remains the same but the intensity of the shedding decreases with increasing fractal dimension. The size of the wake also decreases with increasing fractal dimension and has some dependence on iteration without changing the area of the plate.

An Effect of Fractal Flow Conditioner Thickness on Turbulent Swirling Flow

Fractal flow conditioner is a flow conditioner with a fractal pattern and used to eliminate turbulence originating from pipe fittings in experimental fluid flow applications. In this paper, steady state, incompressible, swirling turbulent flow through circle grid space filling fractal plate (Fractal flow conditioner) has been studied. The solution and the analysis were carried out using finite volume CFD solver FLUENT 6.2. The turbulence model used in this investigation is the standardk-εmodel and the results were compared with the pressure drop correlation of BS EN ISO 5167-2:2003. The results showed that the standardk-εmodel gave a good agreement with the ISO pressure drop correlation. Therefore, the model was used further to predict the effects of circle grids space filling plate thickness on the flow characteristics.

Effects of the condenser fractal zone plate in a transmission X-ray microscope

One of the main benefits of a fractal plate is the formation of a sequence of subsidiary foci when used as a condenser. In order to further demonstrate the reliable use of a fractal zone plate in transmission X-ray microscopy, we studied how a condenser fractal zone plate produces the focal spot in a transmission X-ray microscope layout. We present and discuss the comparison in the X-ray region with a normal condenser zone plate and a numerical simulation that points out that the efficiency of the condenser depends on the structure and the material of the zone plate, and on the energy. This analysis paves a way for foreseen optical applications of modified zone plates in real microscope layouts.

Fractal square zone plates

In this paper we present a novel family of zone plates with a fractal distribution of square zones. The focusing properties of these fractal diffractive lenses coined fractal square zone plates are analytically studied and the influence of the fractality is investigated. It is shown that under monochromatic illumination a fractal square zone plate gives rise a focal volume containing a delimited sequence of two-arms-cross pattern that are axially distributed according to the self-similarity of the lens.

Fractal plate reconstructions with spreading asymmetry

Information theory and fractal analysis are the basis of a novel fitting criterion for simultaneous plate tectonic reconstructions of magnetic isochrons and fracture zone crossings of a range of ages, rather than a single isochron age. Accretionary boundaries are modeled as two-dimensional fractal structures including both contemporary spreading boundaries and reconstructed magnetic isochron and fracture zone crossings. Each model incorporates reconstruction parameters which describe the full accretionary history, including asymmetry. The reconstruction parameters are derived by spline interpolation in time of trial rotation pseudovectors, including variable asymmetric spreading between ridge segments. Iterative algorithms, without partial derivative constraints, converge on a nominally optimal model by minimizing the sum of two-dimensional fractal bins, over the range of bin-spacings, and produce thereby progressively refined fractal spectra. The new method can incorporate all isochron identifications from the selected plates and age range in the iterative calculation set. The solution set also provides continuous instantaneous rotation parameters, including asymmetries. An example data set illustrates the methodology and model results.

Fractality in turbulence

Fractality, as we introduce it, is an attribute relating to any object or system where the existence of self-similar replication of the whole is present in any order and scale. This phenomenon can be realized in any turbulent flow due to the self-similar flow structures in its energy cascade. This intrinsic natural fractality is dominant in any turbulent flow. This paper reports the effect of a forced fractality externally superimposed on a turbulent flow in a circular wind tunnel on this natural fractality. The forced fractality was created by a set of fractal orifice plates. The time correlation and energy spectra showed that the forced fractality significantly excites the natural fractality and increases flow mixing. Simultaneously, we found that the fractal orifice plate is much more efficient than the classical orifice plate with equal flow area in terms of the flow mixing.

Synthesis of fractal light pulses by quasi-direct space-to-time pulse shaping

We demonstrated a simple diffractive method to map the self-similar structure shown in squared radial coordinate of any set of circularly symmetric fractal plates into self-similar light pulses in the corresponding temporal domain. The space-to-time mapping of the plates was carried out by means of a kinoform diffractive lens under femtosecond illumination. The spatio-temporal characteristics of the fractal pulses obtained in this way were measured by means of a spectral interferometry technique assisted by a fiber optics coupler (STARFISH). Our proposal allows synthesizing suited sequences of focused fractal femtosecond pulses potentially useful for several current applications, such as femtosecond material processing, atomic, and molecular control of chemical processes or generation of nonlinear effects.

A modified fractal zone plate with extended depth of focus in spectral domain opticalcoherence tomography

In optical coherence tomography (OCT) systems, there is a trade-off between the depth offocus (DOF) and lateral resolution when conventional lenses are used. We propose a newmethod that employs a modified fractal generalized zone plate (MFraGZP) combinedwith a conventional lens to improve the trade-off effect, with an extended DOFof about 2.5 mm (14 times larger) while the lateral resolution is maintained at ∼ 9.5 µm. As an example, images of the calibration microspheres are obtained and demonstratedwith the extended DOF in a spectral domain OCT system.

Experimental study of a turbulent pipe flow through a fractal plate

We study flows forced through plates in a circular wind-tunnel. The plates are based on different iterations of a pattern which would correspond to the generation of a fractal object. Two types of patterns are considered: one leading to an orifice with a fractal perimeter, the other to a fractal equivalent of a perforated plate. We propose this approach as a systematic way to introduce scales forcing and construct a scale by scale multiscale flow. For the sake of comparison we also consider simple orifice plates having a different number of sharp edges but which are based on a single scale geometry (monoscale orifices). In terms of analysis we focus on the pressure drop across the plate as in terms of engineering application this is the most salient effect of the plate multiscale generation. We measure the pressure recovery as a function of the distance from the plate. We also use hotwire anemometry to understand the action of the fractal-based plate on the flow and measure velocity statistics on the pipe's axis. We found that as far as pressure drop recovery is concerned, it is not always necessary to choose large numbers of iteration for the fractal pattern. However, the velicity statistics can remember the order of the fractal generation over a long distance. In certain cases it would require a very long pipe to quantify the full recovery from the fractal-generated turbulent flow.

Fractal-Generated Turbulence in Opposed Jet Flows

The opposed jet configuration presents a canonical geometry suitable for the evaluation of calculation methods seeking to reproduce the impact of strain and re-distribution on turbulent transport in reacting and non-reacting flows. The geometry has the advantage of good optical access and, in principle, an absence of complex boundary conditions. Disadvantages include low frequency flow motion at high nozzle separations and comparatively low turbulence levels causing bulk strain to exceed the turbulent contribution at small nozzle separations. In the current work, fractal generated turbulence has been used to increase the turbulent strain and velocity measurements for isothermal flows are reported with an emphasis on the axis, stagnation plane and the distribution of mean and instantaneous strain rates. Energy spectra were also determined. The instrumentation comprised hot-wire anemometry and particle image velocimetry with the flows to both nozzles seeded with 1 \(\upmu\)m silicon oil droplets providing a relaxation time of ≃ 3 \(\upmu\)s. It is shown that fractal grids increase the turbulent Reynolds number range from 48–125 to 109–220 for bulk velocities from 4 to 8 m/s as compared to conventional perforated plate turbulence generators. Low frequency motion of the order 10 Hz could not be completely eliminated and probability density functions were determined for the location of the stagnation plane. Results show that the fluctuation in the position of the stagnation plane is of the order of the integral length scale, which was determined to be 3.1±0.1 mm at the nozzle exits through the use of hot-wire anemometry. Flow statistics close to the fractal plate located upstream of the nozzle exit were also determined using a transparent glass nozzle.

Is plate tectonics a case of non-extensive thermodynamics?

Bird (2003) [5] proposed that the distribution of areas of the tectonic plates follows a power law and that this distribution fitted well with the concepts of a few major plates and a hierarchical self-similar organization of blocks at the boundary scale, a fractal plate distribution and a self-organized system. Here we apply the concepts of non-extensive statistical mechanics (NESM) to plate tectonics. The application of NESM is appropriate to systems such as tectonic plates where non-linearity, long-range interactions, memory effects and scaling are important. We calculate the probability density function for the areas of the tectonic plates. Our results show that three classes (small, intermediate and large) of tectonic plates can be distinguished, which is consistent with the observations of Bird. Furthermore, taking into account that for the intermediate class of tectonic plates the cumulative frequency distribution behaves as a power law with exponent 1/3, we estimate a thermodynamic q parameter of q = 1.75 , which supports the conclusion that the plate tectonics system is a sub-extensive one.

A low-pass filter of wide stopband with a novel dual-layer fractal photonic band gap structure

The concept of the photonic bandgap(PBG) is extended to a novel architecture wh ich consists of two fractal PBG plates stacked up in the direction perpendicular to the plane of the substrate. This novel, dual-layer fractal PBG is presented here as the substrate for a microstrip line, and the resulting configuration builds a low-pass filter of wide stop-band. In the specific design, the dual-layer PBG includes two kinds of fractal PBGs with different periodicities in which one fractal PBG consists of a first-order Sierpinski carpet, and the other consists of third-order Sierpinski gasket. Simulated and measured transmission parameters in comparison with the corresponding two filters with monolayer PBG show that the filter with the proposed fractal PBG drastically enhances the width of the stop-band.

Surface Fractal Parallel Plate Models for Micropore Structures of Active Carbon

In order to analyze the micropore structures of active carbon, two types of surface fractal parallel plate models are calculated. It is shown that the disordered model, in which fractal surfaces are less restrictively piled up in the horizontal direction compared with the ordered one, can simulate the micropore size distribution of active carbon. The average micropore widthLavcan be expressed byLav=f(−ΔW/W) =g(n,DS), where −ΔW/Wis the percentage burnoff based on the ideally layered graphite model with the surface fractal dimensionDS= 2, andnis the number of the contraction mapping.