A Comparison of Micro-PIV Experiments in a Mini-Channel to Numerical and Analytical Solutions

2003 ◽  
Author(s):  
D. Newport ◽  
D. Curtin ◽  
M. Davies
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Exact Analytical Solution ◽  
Measurement Tool ◽  
Channel System ◽  
Micro Piv ◽  
Software Packages ◽  
Micro Systems ◽  
Experimental Rig ◽  
Good Agreement

In this paper, measurements are presented of the velocity profile in a mini-channel at different locations. The channel is rectangular in cross-section, approximately 1.2mm wide, 1.4mm deep and 29mm long. A micro-PIV system was used to obtain the velocity profiles at the inlet, mid-length and exit of the channel. The raw image maps were processed using three different commercial PIV software packages, and compared to an exact analytical solution. The mini-channel system was also simulated using a commercial CFD code as a further check on the dataset, and the experimental rig itself. It was found that the different processing procedures had little influence on the micro-PIV data, and good agreement was found with theory, numerical prediction and experiment. This establishes confidence in micro-PIV as a measurement tool in micro-systems.

Vibration Characteristics of Straight Blades of Asymmetrical Aerofoil Cross-Section

1969 ◽  
Vol 20 (2) ◽  
pp. 178-190 ◽  
Author(s):  
W. Carnegie ◽  
B. Dawson
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Limited Range ◽  
First Order ◽  
Special Cases ◽  
Theoretical Results ◽  
Theoretical Procedure ◽  
Good Agreement

SummaryTheoretical and experimental natural frequencies and modal shapes up to the fifth mode of vibration are given for a straight blade of asymmetrical aerofoil cross-section. The theoretical procedure consists essentially of transforming the differential equations of motion into a set of simultaneous first-order equations and solving them by a step-by-step finite difference procedure. The natural frequency values are compared with results obtained by an analytical solution and with standard solutions for certain special cases. Good agreement is shown to exist between the theoretical results for the various methods presented. The equations of motion are dependent upon the coordinates of the axis of the centre of flexure of the beam relative to the centroidal axis. The effect of variations of the centre of flexure coordinates upon the frequencies and modal shapes is shown for a limited range of coordinate values. Comparison is made between the theoretical natural frequencies and modal shapes and corresponding results obtained by experiment.

The Exploitation of Variability and Noise in Micro Devices

2007 ◽  
Author(s):  
Kiyohisa Nishiyama ◽  
M. C. L. Ward
Keyword(s):  
Statistical Theory ◽  
Brownian Motion ◽  
Random Noise ◽  
Mean Value ◽  
Measurement Tool ◽  
Electronic Circuits ◽  
Johnson Noise ◽  
Micro Systems ◽  
Switch Group ◽  
Good Agreement

The strength of Micro Systems Technology (MST) is the ability to fabricate a large number of small devices economically. However such devices tend to have errors caused by the variations of fabrication and inherent noise signals such as Brownian motion or Johnson noise. This paper develops the understanding of Micro Switch Group Sensors (MSGS), which works by exploiting this random noise. In the experimental work reported here, an MSGS comprising of 20 switches has been built using electronic circuits and tested to verify the performance. The output of the device is simply the number of switches turned on, this is then transformed into the expected mean value of the input signal using standard statistical theory. The performance of the devices was shown to be in good agreement with the theoretical prediction. The linearity and the standard deviation of the output signal of MSGS are investigated and it is concluded that an MSGS may be successfully applied as a measurement tool.

An Integral Equation Method for Predicting Acoustic Emission within Enclosures

1985 ◽  
Vol 199 (2) ◽  
pp. 133-137 ◽  
Author(s):  
D T I Francis ◽  
M M Sadek
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Acoustic Emission ◽  
Analytical Solution ◽  
Numerical Solution ◽  
Finite Element Methods ◽  
Exact Analytical Solution ◽  
Integral Equation Method ◽  
Absorption Characteristics ◽  
Good Agreement

A method is presented for calculating the acoustic emission of a vibrating body within an enclosure whose surface has known absorption characteristics. It is based on a numerical solution of the Helmholtz integral equation. Solutions are given for the case of a pulsating sphere within a sphere, and good agreement with the exact analytical solution is reported. The method is of value for small and medium scale problems at lower frequencies, where traditional techniques are less reliable. It is also potentially less demanding computationally than finite element methods.

scholarly journals Analytical Solution of the Time-Dependent Microfluidic Poiseuille Flow in Rectangular Channel Cross-Sections and Its Numerical Implementation in Microsoft Excel

Biosensors ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 67
Author(s):  
Patrick Risch ◽  
Dorothea Helmer ◽  
Frederik Kotz ◽  
Bastian E. Rapp
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Poiseuille Flow ◽  
Exact Analytical Solution ◽  
Rectangular Channel ◽  
Channel Cross Section ◽  
Analysis Tool ◽  
Complex Flow ◽  
Microsoft Excel ◽  
Navier Stokes Equation

We recently demonstrated that the Navier–Stokes equation for pressure-driven laminar (Poiseuille) flow can be solved in any channel cross-section using a finite difference scheme implemented in a spreadsheet analysis tool such as Microsoft Excel. We also showed that implementing different boundary conditions (slip, no-slip) is straight-forward. The results obtained in such calculations only deviated by a few percent from the (exact) analytical solution. In this paper we demonstrate that these approaches extend to cases where time-dependency is of importance, e.g., during initiation or after removal of the driving pressure. As will be shown, the developed spread-sheet can be used conveniently for almost any cross-section for which analytical solutions are close-to-impossible to obtain. We believe that providing researchers with convenient tools to derive solutions to complex flow problems in a fast and intuitive way will significantly enhance the understanding of the flow conditions as well as mass and heat transfer kinetics in microfluidic systems.

A modified wave approach for calculation of natural frequencies and mode shapes in arbitrary non-uniform one-dimensional waveguides

2011 ◽  
Vol 225 (12) ◽  
pp. 2864-2880 ◽  
Author(s):  
M Khoshbayani-Arani ◽  
N Rasekh-Saleh ◽  
M Nikkhah-Bahrami
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Natural Frequencies ◽  
Exact Analytical Solution ◽  
Mode Shapes ◽  
Transmission Matrix ◽  
Approximate Methods ◽  
One Dimensional ◽  
Wave Propagation Method ◽  
Number Of Segments

In this article, using the wave propagation method, the natural frequencies and mode shapes of an arbitrary non-uniform one-dimensional waveguide are calculated. The non-uniform rods and beams are partitioned into several continuous segments with constant cross-sections, for which there exists an exact analytical solution. At the end of each segment, waves in positive and negative directions are obtained in terms of waves at initial segment and subsequently, the calculations of the mode shapes become simple. By satisfying the boundary conditions, the characteristic equation is obtained and natural frequencies are calculated for both the arbitrary non-uniform rod and beam. Also, by adding waves in positive and negative directions at the end point of each segment, the mode shapes are obtained. To verify the modified wave method presented here, the frequencies and mode shapes of the rod and the beam with a polynomial cross-section having an exact analytical solution are compared and have been proven to be of high accuracy. Besides, comparisons of finite element method are also included. Therefore, this method can also be used to calculate the natural frequencies and mode shapes of rods and beams with any arbitrary variable cross-section for which no analytical solution is available. For the ‘Modified Wave Approach’ developed here, dimensions of transmission matrix remain constant if the number of segments is increased, while in general wave propagation method, dimensions of transmission matrix increase upon increasing the number of segments. Besides this novelty, this method has the advantage that it gives all the natural frequencies and mode shapes, unlike other approximate methods such as weighted residual, Rayleigh–Ritz, and finite difference methods which have their own shortcomings such as limited number of natural frequencies. Also, since each segment has an exact analytical solution, in contrast to other approximate methods, much higher accuracy is obtained even with only a few number of partitions.

scholarly journals A Novel Exact Analytical Solution Based on Kloss Equation towards Accurate Speed-Time Characteristics Modeling of Induction Machines during No-Load Direct Startups

2021 ◽  
Vol 11 (11) ◽  
pp. 5102
Author(s):  
Martin Ćalasan ◽  
Mohammed Alqarni ◽  
Marko Rosić ◽  
Nikola Koljčević ◽  
Basem Alamri ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Computer Simulation ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Induction Machines ◽  
Voltage Sags ◽  
Local Power ◽  
Acceleration Time ◽  
Protection Relay ◽  
Good Agreement

The acceleration time of induction machines (IMs) is essential for proper protection-relay settings of the machine to prevent voltage sags in local power areas. In this paper, mathematical modeling of IMs’ speed-time characteristics during no-load direct startup has been presented. Unlike the approaches presented in the literature, the proposed approach includes the bearing losses, in which two expressions of the speed-time characteristics of IMs during no-load direct startup are derived. The first expression was derived based on the Kloss equation used for representing the torque, and the second expression was derived based on the torque expression determined from the Thevenin equivalent circuit of the machine. The derived expressions’ accuracy was validated using laboratory measurement and computer simulation approaches. The results obtained show a good agreement between the measured and simulated speed-time characteristics of two IMs. Finally, the proposed formulations can provide a simple analytical base to enable accurate IM modeling.

A Modified Wave Approach for the Calculation of Natural Frequencies and Mode Shapes of the Rods with Variable Cross Section

2011 ◽  
Vol 110-116 ◽  
pp. 2537-2547
Author(s):  
M. Khoshbayani Arani ◽  
N. Rasekh Saleh ◽  
M. Nikkhah Bahrami
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Natural Frequencies ◽  
Exact Analytical Solution ◽  
Finite Difference Methods ◽  
Variable Cross Section ◽  
Mode Shapes ◽  
Variable Cross ◽  
Approximate Methods ◽  
Modified Method

Analytical solutions for vibration analysis of the rods with variable cross section are in general complex and in many cases impossible. On the other hand, approximate methods such as the weighted residual, Rayleigh-Ritz and finite difference methods also have their own shortcomings such as a limited number of natural frequencies and accuracy. Using the wave propagation method, the structure is partitioned into several continuous segments with constant cross-section, for which there exists an exact analytical solution. Waves in positive and negative directions at the entrance of each segment are obtained in terms of waves at the initial segment. Then, by satisfying the boundary conditions, the characteristic equation is obtained and all natural frequencies are calculated. By adding waves in positive and negative directions at each point, the shape modes are obtained. To verify this modified method, the frequencies and mode shapes of a rod with polynomial cross section, which has an exact analytical solution, are compared and have proven to be of highly accuracy. Therefore, this method can also be used to calculate the natural frequencies and its mode shapes of the rods with variable cross section for which no analytical solution is available.

scholarly journals The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Hamdy M. Youssef ◽  
Najat A. Alghamdi
Keyword(s):  
Heat Flux ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Constant Heat Flux ◽  
Bioheat Transfer ◽  
Skin Tissue ◽  
Phase Lag ◽  
Dual Phase ◽  
Constant Heat ◽  
Two Temperature

Abstract This work is dealing with the temperature reaction and response of skin tissue due to constant surface heat flux. The exact analytical solution has been obtained for the two-temperature dual-phase-lag (TTDPL) of bioheat transfer. We assumed that the skin tissue is subjected to a constant heat flux on the bounding plane of the skin surface. The separation of variables for the governing equations as a finite domain is employed. The transition temperature responses have been obtained and discussed. The results represent that the dual-phase-lag time parameter, heat flux value, and two-temperature parameter have significant effects on the dynamical and conductive temperature increment of the skin tissue. The Two-temperature dual-phase-lag (TTDPL) bioheat transfer model is a successful model to describe the behavior of the thermal wave through the skin tissue.

scholarly journals Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2452
Author(s):  
Tian Qiao ◽  
Hussein Hoteit ◽  
Marwan Fahs
Keyword(s):  
Analytical Solution ◽  
Storage Site ◽  
Co2 Leakage ◽  
Transient Pressure ◽  
Flow Paths ◽  
Abandoned Wells ◽  
Diffusivity Equation ◽  
Carbon Dioxide Co2 ◽  
Good Agreement

Geological carbon storage is an effective method capable of reducing carbon dioxide (CO2) emissions at significant scales. Subsurface reservoirs with sealing caprocks can provide long-term containment for the injected fluid. Nevertheless, CO2 leakage is a major concern. The presence of abandoned wells penetrating the reservoir caprock may cause leakage flow-paths for CO2 to the overburden. Assessment of time-varying leaky wells is a need. In this paper, we propose a new semi-analytical approach based on pressure-transient analysis to model the behavior of CO2 leakage and corresponding pressure distribution within the storage site and the overburden. Current methods assume instantaneous leakage of CO2 occurring with injection, which is not realistic. In this work, we employ the superposition in time and space to solve the diffusivity equation in 2D radial flow to approximate the transient pressure in the reservoirs. Fluid and rock compressibilities are taken into consideration, which allow calculating the breakthrough time and the leakage rate of CO2 to the overburden accurately. We use numerical simulations to verify the proposed time-dependent semi-analytical solution. The results show good agreement in both pressure and leakage rates. Sensitivity analysis is then conducted to assess different CO2 leakage scenarios to the overburden. The developed semi-analytical solution provides a new simple and practical approach to assess the potential of CO2 leakage outside the storage site. This approach is an alternative to numerical methods when detailed simulations are not feasible. Furthermore, the proposed solution can also be used to verify numerical codes, which often exhibit numerical artifacts.

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