Numerical and Experimental Methods in Fluid Dynamics

In  this  study,  a  microcontroller  based  data  logger  for  measuring wind  speed  and wind  direction  has  been designed.  The  designed  system  uses  the  Atmel microcontroller  family  which  consists  of  sensor  inputs,  a  microcontroller  and  a data storage device. The system was designed and developed to measure the wind speed  and direction  with  the  help  of  anemometer  and  wind  vane sensors respectively.  The  results  were  stored  in  an Electrically  Erasable  Programmable Read Only Memory (EEPROM) for  post process analysis. The collected data were transmitted to a PC  through an RS-232 serial interface, and were processed using the  208W  Data  logger  support software.  Wind  speed  and  direction measured  by the microcontroller-based  data  logging  system  were  analyzed using  line  graphs, scatter  correlation  charts  and  wind roses.  Wind  speeds  were  measured  at  9.00 a.m,  12.00 noon  and  5.00  p.m  using  fabricated  sensors  and  also  at  JKUAT meteorological  station.  The  correlation  indices  of microcontroller–based  data logger  instrumentation  system data  and  JKUAT  meteorological  data  were determined.  The correlation  indices  for  the  corresponding  three  times  were calculated as 0.997, 0,997 and 0.999 respectively. Thus the wind speed measured by  the  fabricated  sensor  was  found to  correlate  strongly  to  the  to  the  JKUAT Meteorological datasheet. Wind rose analysis revealed that the wind direction was fairly  consistent  from  between  180^0 and  170^0which  is  generally  from  South  to South-east for the months of August and September.

We present an algorithm that uses the Z-transform operator to face the problem of heat transmission in a single thermal zone composed by multilayered walls. The method is very flexible and could be adopted to calculate the transfer function coefficients able to simulate the thermal behaviour of a room in free floating. Knowing the transfer function coefficients, it is possible to simulate the dynamic profile of each inner surfaces temperature and furthermore of the inner air temperature.The proposed algorithm is fully described granting maximum clarity. The explicitness of all steps of the calculus make possible the definition of a method that is able to vary all of the calculus parameters such as sampling g period, number of roots, number of poles or number of coefficients.To assess the reliability of the algorithm, we carried out a comparison between simulation data obtained from our method, from Fourier steady-state algorithm and those obtained from TRNSYS.

The effect of free surface height on the submerged synthetic jet parallel to the surface in quiescent flow is studied experimentally. The purpose of the study is to understand the vortex ring structure of synthetic jet and their effects on the free surface. Flow visualization using Laser Induced Fluorescence (LIF) and measurement of time-averaged streamwise and crossstream velocities carried out using Laser Doppler Velocimetry (LDV) are reported. Due to change in free surface height (H), vortex ring drifts from centerline and surface perturbations are observed. Analysis of the velocity field reveals that the velocity normal to the surface reduces while the velocity parallel to the surface increases as the vortex ring approaches the free surface. Previous studies also suggest similar phenomenon for submerged continuous jets.

Atomic functions present an effective mathematical apparatus for interp olation of functions. Given
function is represente d as a sum of scaled shifts of
compactly supp orted atomic function. Fundamental prop erty of such interp olation is that derivatives of given function are simultaneously interp olated with corresp onding derivatives of interp olation. This prop erty allows application of atomic
function to numerical solution of differential equations.

In this paper, we have presented a 2D Lagrangian two-phase numerical model to study the deformation of a droplet suspended in a quiescent fluid subjected to the combined effects of viscous, surface tension and electric field forces. The electrostatics phenomena are coupled to hydrodynamics through the solution of a set of Maxwell equations. The relevant Maxwell equations and associated interface conditions are simplified relying on the assumptions of the so-called leaky dielectric model. All governing equations and the pertinent jump and boundary conditions are discretized in space using the incompressible Smoothed Particle Hydrodynamics method with improved interface and boundary treatments. Upon imposing constant electrical potentials to upper and lower horizontal boundaries, the droplet starts acquiring either prolate or oblate shape, and shows rather different flow patterns within itself and in its vicinity depending on the ratios of the electrical permittivities and conductivities of the constituent phases. The effects of the strength of the applied electric field, permittivity, surface tension, and the initial droplet radius on the droplet deformation parameter have been investigated in detail. Numerical results are validated by two highly credential analytical results which have been frequently cited in the literature. The numerically and analytically calculated droplet deformation parameters show good agreement for small oblate and prolate deformations. However, for some higher values of the droplet deformation parameter, numerical results overestimate the droplet deformation parameter. This situation was also reported in literature and is due to the assumption made in both theories, which is that the droplet deformation is rather small, and hence the droplet remains almost circular. Moreover, the flow circulations and their corresponding velocities in the inner and outer fluids are in agreement with theories.

Sports and cultural play a crucial part in giving us complete education. They're necessary for health and recreation. A sound body is as necessary as a sound mind. Sports are as important as book learning for all students, boys and girls. Sports and games keep us physically fit. In this study, "higher secondary school levels of participation in sports and cultural and its relationship were investigated. Sample study was made for the academic year 2018-2019 and 2019-2020 in the Government Higher Secondary School, Pudukkottai district, Killukottai. In this study 228 students (boys and girls) were actively involved in the sports and 176 students (boys and girls) participated in the cultural activities. Students from 5 th to 12 th standard boys and girls are selected for this sample study. In this study we are focusing, the student's involvement in sports and cultural activities by using statistical tools like descriptive statistics, correlation and chi-square test. To manipulate the calculation with comparison of actual results Minitab software was used.

Experiments and numerical simulations were carried out in order to contribute to a better understanding and prediction of high-pressure injection into a gaseous environment. Specifically, the focus was put on the phase separation processes of an initially supercritical fluid due to the interaction with its surrounding. N-hexane was injected into a chamber filled with pure nitrogen at 5 MPa and 293 K and three different test cases were selected such that they cover regimes in which the thermodynamic non-idealities, in particular the effects that stem from the potential phase separation, are significant. Simultaneous shadowgraphy and elastic light scattering experiments were conducted to capture both the flow structure as well as the phase separation. In addition, large-eddy simulations with a vapor-liquid equilibrium model were performed. Both experimental and numerical results show phase formation for the cases, where the a-priori calculation predicts two-phase flow. Moreover, qualitative characteristics of the formation process agree well between experiments and numerical simulations and the transition behaviour from a dense-gas to a spray-like jet was captured by both.

This study uses a large eddy simulation model to investigate the effect of a submerged rectangular cylinder on the hydro-dynamics of free surface flows. The simulation results are validated with the results of flume experiments. Then the numerical model is utilized to examine the influences of Reynolds number, Froude number, and blockage ratio on the flow field and the force coefficients of the deck. The simulation results reveal that the drag coefficient is dependent on the deck's Froude number and blockage ratio of the bridge deck, rather than the Reynolds number. For both subcritical and transcritical flows, the drag coefficient increases as the blockage ratio increases. However, due to the wave-induced drag, the drag coefficient of the cylinder in transcritical flows is greater than that in subcritical flows with the same blockage ratio. On the other hand, the lift coefficient is a function of the submergence ratio and the deck's Froude number. The separation shear flow on the upper side of the cylinder is constrained by the water surface when the submergence ratio < 2.0, and resulting in an asymmetric pressure distribution on the upper and lower sides of the deck, which subsequently generates a downward force on the bridge deck.

In parts 1 - 3 the method was described for solving cases of unidirectional flow. It was, obviously, an introduction to the concept of the method. In part 4 it is shown how this method can be used to solve an exemple of 2 dimensional flow. The square box problem with no convection is solved with this method in order to show its viability to be applied in cases of multidirectional fow

The motion of fluids which are incompressible could be described by the Navier-Stokes differential equations. However, the
three-dimensional Navier-Stokes equations for modelling turbulence misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would greatly affect the field of fluid mechanics. In this paper, which had been published in an international journal in 2010, a reasoned, practical approach towards resolving the issue is adopted and a practical, statistical kind of mathematical solution is proposed.

Highlights  New first and second order schemes to solve the heat or diffusion equation.  Unconditional stability for the heat equation, no stepsize requirements.  Explicit and one-step methods, easy to implement and parallelize.  Handy to apply regardless of space dimensions and grid irregularity. Abstract: We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do not approximate the time derivatives by finite differences, but use constant-neighbour and linear neighbour approximations to decouple the ordinary differential equations and solve them analytically. During this process, the timestep-size appears not in polynomial, but in exponential form with negative exponents, which guarantees stability. We compare the performance of the new methods with analytical and numerical solutions. According to our results, the methods are first and second order in time and can be much faster than the commonly used explicit or implicit methods, especially in the case of extremely large stiff systems.

This Process Engineering Guide is one of a series of guides on non-Newtonian flow prepared for GBH Enterprises.

Fluid flow in chemical plants is usually turbulent, and viscosities have to be high before laminar flow predominates. When viscosities are high, the fluids are often non-Newtonian in character. In this field of non-Newtonian flow, laminar flow predominates and this is covered by GBHE-PEG-FLO-303. There are still many instances when turbulent flow of non-Newtonian fluids is encountered.

This guide presents the basis for the prediction of flow rate - pressure drop relationships for the turbulent flow of non-Newtonian fluid through circular pipes under isothermal conditions. The Guide also deals with drag reduction by polymeric materials and fibre suspensions.

This Guide presents the basis for the prediction of flow rate - pressure drop relationships for the laminar flow of non-Newtonian fluid through circular pipes and selected fittings under isothermal conditions. In addition, the prediction of velocity profiles and hence residence time distributions are covered.

The Scope is subject to the following limitations:

(a) the fluid is homogeneous and remains so under all conditions, i.e. if the material is a suspension of solids, then the solids do not settle;

(b) the fluid is purely viscous in behavior, i.e. it does not exhibit time-dependency of a thixotropic or anti-thixotropic kind, nor is it viscoelastic. This restricts the predictions to fluids the rheological properties of which may be expressed in the form: shear rate is a function of shear stress;

(c) the flow is laminar;

(d) there is no slip at the wall. Advice on the procedure to be adopted if slip does occur is given in Clause 8;

(e) the flow occurs under isothermal conditions.

Two distinct cases will be considered:

(1) prediction based on idealized rheological models which aim to approximate the observed behavior, and

(2) predictions based directly on experimental measurements of the rheological properties.

This article demonstrates the usefulness of the computational platform formed by Excel, its Solver add-in, and the associated VBA programming language as an educational platform for design analyses of pump-pipe systems. The article focusses on the determination of the optimum standard-size pipe for a pump-pipe system to highlight the advantages of the Excel-based method in comparison with the traditional design method using charts and data tables.

Particle-laden o ws are of great interest since they occur in a variety of industrial applications, such as chemical reactors or internal combustion engines in which either solid or liquid particles are injected in a gas o w. These two-phase o ws are characterized by a high level of dynamic coupling, heat and mass transfer between the phases. Other complex

In turbulence models we create mathematical models that describe the flow properties of a flowing fluid. A turbulence model is a computational procedure to close the system of mean flow equations and so that a more or less wide variety of flow problems can be calculated. However, far less precision has been achieved in creating a mathematical model that approximates the physical behavior of turbulent flows. Reynolds stress model is used to get the flow behavior and compared with the theoretical solution and the inferences are drawn. I. INTRODUCTION Due to the development in the Computer Aided Design / Computer Aided Engineering technology, now it is possible to analysis the fluid flow problem, in general any engineering problems. The CFD approach has come in this way, when compared to the theoretical and wind tunnel approach. In the present work of flow analysis over cylinder is made for turbulence models and postprocessor velocity contour. Initially the geometry is created and then the fluid domain is discritized by mesh. In the solver and postprocessor its solutions and result are obtained. Basically a theory of CFD-turbulence models and new software tool are applied. This technique may be used for designing of any fluid equipment by using the advantage of CAE. Because of the chaotic-like and apparently random behavior of turbulence, we will need statistical techniques for most of our study of turbulence. CFD is a tool that helps solve a wide range of problems in Fluid Dynamics and Heat transfer. These phenomena are governed by sets of partial differential equations which in most cases have no analytical solution. In addition to the governing equations, we also need the boundary and initial conditions, material properties, and geometrical details in order to completely describe the problem.

ABSTRACT:
Numerical simulations were used to optimize the cooling performance of a hybrid cooling device; consisting of a micro-channel and an imbedded impinging jet through which fluid is injected into the module. Three-dimensional heat flow characteristics the hybrid scheme were analyzed using standard k-ε turbulent model. Results obtained in course of the simulations using water, PF-5052, and HFE-7100 as working fluids showed positive agreement with previous studies. Rectangular geometry and 1.3 x 1.248 mm2 cross-section yielded the highest Nusselt number. Increase in jet Reynolds number decreases thermal resistance and overall hybrid surface temperature. Also, increase channel height showed a corresponding decrease in micro-channel width hence hybrid surface temperature. Water and copper produced the highest thermal performance for the working fluid and substrate material respectively. Conclusions from this study are used to suggest an optimized hybrid model for effective thermal management.
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This experimental study investigates the effects of internal geometry modifications on the performance of a curved Sweeping Jet actuator. The modifications are applied to the geometry of the feedback channel and the mixing chamber Coanda surface, and the resulting actuator properties are evaluated using time-resolved static pressure measurements inside the actuator and hot-wire measurements of the external flow. The major result is that small, localized modifications of the curved sweeping jet actuator geometry can lead to a complete change in the external flow regime, making the jet velocity distribution homogeneous, similar to the angled variant of the actuator. The Coanda surface shape is identified as the primary cause of the external jet adopting the bifurcated or homogeneous flow regime. The relationships between the sweeping frequency, jet deflection angle, required supply pressure, and pressure fluctuations are analyzed and discussed in detail. External flow behavior and coh...

In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.

Numerical results are compared with experimental results for z/d=0 and x/d=0.125, 0.5, 1.25. Abstract The flow characteristics over a sphere are predicted numerically. Experimental studies have been done in a low speed wind tunnel. In order to verify numerical results velocity and turbulence intensity measurements were done in centerline of sphere. Drag forces were measured for high Reynolds numbers of Re≈30000-140000. The wake region was explored in detail and turbulence and velocity values have been performed numerically at 53000. Reynolds number, at three different locations (z/d=0, 0.125, 0.25, 0.625 and 0.875) downstream of the sphere. Especially, stations which were critical turbulence levels were determined. Numerical predictions are carried out by using the commercial CFD package Fluent. The results of the presented CFD predictions are shown to be in good agreement with the experimental data.

Modeling the flow of non-Newtonian fluids in porous media is a challenging subject. Several approaches have been proposed to tackle this problem. These include continuum models, numerical methods, and pore-scale network modeling. The latter proved to be more successful and realistic than the rest. The reason is that it captures the essential features of the flow and porous media using modest computational resources and viable modeling strategies. In this article we present pore-scale network modeling techniques for simulating non-Newtonian flow in porous media. These techniques are partially validated by theoretical analysis and comparison to experimental data.

This Guide is one of a series produced for GBH Enterprises.

The calculation of chemical equilibria for a single notional reaction is rarely difficult. A typical example is given in GBHE-PEG-RXT-813. The solution of such cases is well understood; the mass action equation generates a polynomial relationship between conversion and equilibrium constant (or free energy) which can be solved (at worst iteratively) and the relevant root selected by inspection.

Extension of this approach to more than one reaction rapidly becomes untenable for hand calculation due to the highly non-linear nature of the resulting simultaneous equations. The solution of these multi-reaction equilibrium problems has been investigated since the early days of the Second World War when interest in rocket motor design became strategically important. Indeed, work for the V2 at the "Hermann Göring Air Force Research Institute" provided some of the earliest papers on the subject.

To this day, combustion/explosion problems remain the mainspring of research effort in this area and a number of commercially available computer programs have appeared in the public domain.

This document provides guidance on the interpretation of viscometric data obtained from different measuring devices and their correlation into forms usable for design purposes. It does not cover the design of pipes or equipment handling non-Newtonian fluids.

This article is focused on the choice of a suitable turbulence model for simulations of an industrial pump's intake, from the perspective of accuracy and, partially, also the CPU time. Twelve steady-state and transient simulations were made on a fine computational mesh, using turbulence models such as: the shear stress transport (SST), the scale-adaptive simulation (SAS), the Reynolds stress model, the explicit algebraic Reynolds-stress model, the detached eddy simulation and the large eddy simulation (LES). The curvature-correction (CC) option was assessed for the SST and SAS turbulence models. The results were compared with the LES and with published experimental results. Although all the models could predict the main floor vortex, there were still some substantial differences. It can be able to conclude that it is better to use either the SST-CC turbulence model, due to its low-computational resources and far better results than the SST model, or the SAS-CC turbulence model, since its predictions are quite similar to the LES results. In the final step, good agreement with experimental results was shown for a longer simulation with the SAS-CC turbulence model.

Did any physics experts expect SUPERRELATIVITY paper, a physics revolution producing the EINSTEIN-RODGERS RELATIVITY EQUATION, producing the HAWKING-RODGERS BLACK HOLE RADIUS, and producing the STEFAN-BOLTZMANN-SCHWARZSCHILD-HAWKING-RODGERS BLACK HOLE RADIATION POWER LAW, as the author gave a solution to The Clay Mathematics Institute's very difficult problem about the Navier-Stokes Equations? The Clay Mathematics Institute in May 2000 offered that great $million prize to the first person providing a solution for a specific statement of the problem: " Prove or give a counterexample of the following statement: In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier-Stokes Equations. " Did I, the creator of this paper, expect SUPERRELATIVITY to become a sophisticated conversion of my unified field theory ideas and mathematics into a precious fluid dynamics paper to help mathematicians , engineers and astro-physicists? [1]. Yes, but I did not expect such superb equations that can be used in medicine or in outer space! In this paper, complicated equations for multi-massed systems become simpler equations for fluid dynamic systems. That simplicity is what is great about the Navier-Stokes Equations. Can I delve deeply into adding novel formulae into the famous Schwarz-schild's equation? Surprisingly, yes I do! Questioning the concept of reversibility of events with time, I suggest possible 3-dimensional and 4-dimensional coordinate systems that seem better than what Albert Einstein used, and I suggest possible modifications to Maxwell's Equations. In SUPERRELATIVITY, I propose that an error exists in Albert Einstein's Special Relativity equations, and that error is significant because it leads to turbulence in the universe's fluids including those in our human bodies. Further, in SUPERRELATIVITY, after I create Schwarzschild-based equations that enable easy derivation of the Navier-Stokes Equations, I suddenly create very interesting exponential energy equations that simplify physics equations, give a mathematical reason for turbulence in fluids, give a mathematical reason for irreversibility of events with time, and enable easy derivation of the Navier-Stokes Equations. Importantly, my new exponential Navier-Stokes Equations are actually wave equations as should be used in Fluid Dynamics. Thrilled by my success, I challenge famous equations by Albert Einstein and Stephen Hawking [2] [3]. Keywords * BA (Dble Maj Maths); Hon DSc (Taxila Institute for Research), http://institute.iqmind.org/institute/; World Genius Directory 2014 Genius of the Year—Asia, www.psiq.org/home.html.

The two-dimensional simulation described in part 4 is considerably more complex than the three first parts, that threated one-dimensional flow. However, it is limited to the presence of linear therms only, which is a very limited universe. The most important cases that need to be simulated with numerical methods ar the ones in which the non-linear therms are present, for in those cases no analytical solution is possible. In this part 5, it will be shown how to use this method when the convective therms ARE present.