BARRIER. Journal of Hydrodynamics, Ser. B,1 (2001),28-33 China Ocean Press, Beijing - Printed in China
|
|
- Helena Dalton
- 7 years ago
- Views:
Transcription
1 28 Journal of Hydrodynamics, Ser. B,1 (2001),28-33 China Ocean Press, Beijing - Printed in China WAVE TRANSMISSION AND BARRIER REFIECTION D UE TO A THIN VERTICAL Ξ Gao Xue2ping Hydraulics Instit ute, School of Civil Engineering, Tianjin U niversity, Tianjin300072, China Nakamura Takayuki, Inouchi Kunimitsu Ehime University, Matsuyama , Japan Kakinuma Tadao Nagasaki Comprehensive U niversity, Nagasaki , J apan (Received Oct ) ABSTRACT: A numerical method, the boundary fitted coordinate method ( BFC ), was used to investigate the transmission and reflection of water waves due to a rigid thin vertical barrier descending from the water surface to a depth, i. e., a curtain2wall type breakwater. A comparison between the present computed results and previous experimental and analytical results was carried out which verifies the prediction of the BFC method. Wave transmission and reflection due to the barrier were computed, and the transmission and refiection coefficients were given in a figure. KEY WORDS : wave transmission, wave reflection, vertical barrier, boundary fitted coordinate method thin 1. INTROD UCTION A t rain of surface water waves incident f rom infinity on an obstacle present in water, experiences t ransmission and reflection by and over or below t he obstacle. The obstacle may be in t he form of a rigid t hin vertical barrier. The rigid t hin barrier descending from the water surface to a depth, which is also called curtain2wall type breakwater, is one type of t hin vertical barriers. Numerous st udies for t his type barrier have been conducted experimentally, t heoretically and numerically. Wiegel (1960) devised a semi2empirical solution for t he t ransmission coefficient s in intermediate and shallow water conditions based on energy flux. Ursell ( 1974 ) developed an analytical solution for the transmission coefficients in deep water condition. Morigira et al., ( 1960 ) examined t he characterstics of wave t ransmission and wave force acting on t he st ruct ure experimentally. Liu et al., ( 1982 ) st udied t he t ransmission and reflection coefficient s of bot h t he vertical and inclined t hin breakwater by t he boundary integral equation met hod ( B IEM ). Theoretical solution was obtained by eigenf unction expansion met hod for t he t ransmission and reflection coefficient s by Losada et al., ( 1992). Mandal et al., ( 1994 ) st udied t he reflection and t ransmission coefficient s by an appropriate one2term Galerkin approximation. In t he present st udy, a numerical met hod, t he boundary fitted coordinate method (BFC), is used to study the transmission and reflection due to the rigid thin vertical barrier descending from the water surface to a depth (curtain2wall type breakwater). With the BFC method, which is suitable for free surface flow problems, one t ransforms a p hysical domain into a rectangular domain using a suitable t ransform and solves the governing equations (the N2S equation and continuity equation ) by finite difference approximation. Moreover, satisfying accurately t he complex p hysical boundaries is t he greatest advantage of t he numerical met hod. The FF T met hod toget her wit h t he resolution technique presented by Goda and Suzuki ( 1976 ) are used to calculate t he incident, reflected and t ransmitted wave height s. Some computed result s are compared wit h previous analytical solutions and experimental data to verify t he prediction of the BFC method. Wave transmission and reflection due to the barrier are computed, and the transmission and reflection coefficient s for various cases are given in a figure. 2. BOUNDARY FITTED COORDINATE METHOD The p hysical domain is t ransformed into t he rectangular domain representing accurately t he complex p hysical boundary ( Fig. 1 ). Governing equations and boundary conditions are also t ransformed. In t he rectangular domain, t he t ransformed governing equations are solved by t he finite difference met hod. Ξ This is supported by the Returned Student Foundation of State Education Ministry of China
2 29 where w 1 = w - s u, w 2 = w 1-5s 5 (7) = s 5 2 s s s 5 s 5 (8) Fig. 1 Coordinate transformation ( a) Physical domain and (b) rectangular domain 2. 1 Governing equations Wave motion is governed by t he continuity equation and Navier2Stokes equations. In two2 dimensional Cartesian coordinates, t hese equations are expressed as 5 x + 5 z 5 t 5 t = 0 (1) + u 5 x + w 5 z = - 5 P 5 x + 52 u 5 x u 5 z 2 + g x + u 5 x + w 5 z (2) = - 5 P 5 z + 52 w 5 x w 5 z 2 + g z (3) and s = s ( x, t) is the surface elevation ( Fig. 1), s = 5s/ 5, s = 5 2 s/ Boundary conditions Free surface conditions. The f ree surface conditions include kinematic and dynamic boundary conditions. In t he p hysical domain, t he kinematic condition is expressed as 5s 5 t + u 5s 5 x = w (9) By considering the normal stress and tangential stress at t he f ree surface, t he dynamic boundary conditions are expressed as ( Kawamura and Hijikata, 1995) : P = s x x (1 + s 2 x ) 3/ v s x 5 z + s 2 x 5 x - s x 5 z + 5 x (10) where ( x, z) is the physical domain coordinate ; t is time ; u and w are t he corresponding component s of 5 z + 5 x - 2 s x s x the velocity in the x and z directions ; P = p/ ( pis the pressure, is the density of water) ; g x and g z are t he component s of unit body force in t he x and z directions respectively ; is the kinematic viscosity coefficient. By a suitable t ransformation ( see Kawamura and Hijikata 1995 ; Gao et al., 1998), t he governing equations in t he p hysical domain of t he coordinate system ( x, z, t) as above are transformed into the rectangular domain of the coordinate system (,, ) t he dynamic conditions as follows : P = - s s 5 5 ( su) ( w 1) = 0 (4) 5 + u 5 + w 1 2 s 5 = - 5 P 5 - s 5 P s 5 + u + g x (5) 5 + u 5 + w 1 2 s 5 = P s 5 + w + g z (6) 5 x - 5 z = 0 (11) where is the surface tension, and s x = 5s/ 5 x, s x x = 5 2 s/ 5 x 2. In the rectangular domain, the surface conditions are reduced to t he kinematic condition : 5s 5 = w 1 ; at = 1 (12) 5 - s 1 s (13) 1 s 5 = s s 5 at = 1 (14) Rigid boundary conditions. A rigid boundary may be either of two types ; non2slip or free slip. Here the non2slip condition is utilized, that is, in the physical domain, t he normal and tangential velocities at t he
3 30 rigid boundary are zero. Therefore, in t he rectangular domain, t he rigid boundary conditions are expressed as at = 0, u = w = 0 (15) 2. 3 Finite dif f erence approxi m ation The governing equations (4) (6), together with boundary conditions (12) (15), are solved by t he finite difference approximation. A staggered mesh system is used, i. e., velocities are defined at cell boundaries while pressure is defined at cell center. Forward differencing in time and centered differencing in space are utilized in t he finite difference approximation. 3. METHOD OF COMPUTATION AND VERIFICATION 3. 1 Com putational method For t he p hysical domain ( Fig. 2 ), given t he incident boundary and open boundary conditions, t he wave motion is calculated by t he boundary fitted coordinate met hod described as above. A train of the second2order Stokes waves is given at t he incident boundary. The Sommerfeld radiation condition is utilized at t he open boundary. For the initial condition, the fluid is assumed to be entirely at rest, and the physical domain is divided into cells, the size of a cell in the x direction is about x = L / 50 ( L is incident wavelength), the size of a cell in the z direction is about z = h/ 25, where h is still water depth, and z will change as time continues. The time step t = s is taken in this paper simply. Fig. 2 A thin vertical barrier descending from the water surface to a depth and coordinate system 3. 2 Com putation of incident, ref lected and t ransmitted w ave heights It is well known that, in a wave flume, waves generated by a wave paddle propagate forward in the flume and are reflected by a test st ruct ure ; t he reflected waves propagate back to the wave paddle and are reflected ; t he reflected waves propagate forward again and t he process is repeated until t he multi2 reflected waves are fully attenuated ; then the value of the incident wave height may be changed. Like a wave flume, because of the reflection due to a barrier in t he p hysical domain, when waves a stable state, the value of incident wave height may be different from the one given initially. Therefore, it is necessary to determine t he incident wave height when waves reach a equilibrium state. In t his st udy, t he FF T met hod toget her wit h t he resolution technique presented by Goda and Suzuki ( 1976) are utilized to determine t he incident wave height and resolve t he reflected and t ransmitted wave height s. The specific procedures for t he calculation can be summarized as follows. The first step is to record t he time historys of wave surface elevations. A two wave system is utilized for recording wave surfaces at different locations along t he wave propagation direction. The spacing of t he two wave gages has to be determined based on t he fundamental frequency f 1 ( = 1/ T) and the frequency of the highest harmonic f n ( = 1/ n T), which might be t he t hird or fourt h harmonic f requency. It is suggested that the spacing of the wave gages should be greater than L 1 and less than L n, where L 1 and L n are the wavelengths corresponding to the fundamental frequency f 1 and the frequency of the highest harmonic f n, respectively. The second step is to calculate t he Fourier components, i. e., the amplitudes of sine and cosine terms, by the FFT method from the time history of wave surface elevations recorded. The t hird step is to calculate t he amplit udes corresponding to different order harmonic f requencies by the formula presented by Goda and Suzuki (1976). The fourt h step is to calculate t he incident and reflected wave heights by summing the energies of all frequency components from f 1 of f n. The energies of resolved incident and reflected waves, E in and E rf, are as follows : E in E rf = 1 2 g f n ( a in ) 2 i (16) i = f 1 = 1 2 g f n ( a rf ) 2 i (17) i = f 1 where a in and a rf, are the amplitudes of incident and reflected waves, respectively corrsponding to different order harmonic f requencies. Converting the energies, E in and E rf, to the so2 called representative wave height s ( incident and reflected wave heights), H i and H r, leads to
4 31 H i = 2 H r = 2 2 E in g 2 E rf g (18) (19) Transmitted wave height is also calculated by t he same energy consideration. According to t he procedure described above, incident, reflected and transmitted wave heights due to t he barrier ( curtain2wall type breakwater ) are calculated by the present BFC method ( Fig. 3). It is shown that the wave heights (incident, reflected and t ransmitted wave height s) along t he wave propagation are almost t he same, which means t hat t he present numerical met hod is valid for t he steady state calculations. After knowing these wave heights, the reflection and t ransmission coefficient s can be calculated as follows : behind a barrier were conducted in a 26m long, 1m wide and 1. 2m deep wave flume. Fig. 4 shows a comparison between computed and experimental wave surface elevations. It is shown t hat t he present met hod is good for t he predictions of wave deformations around a barrier. C r = H r H i (20) C t = H t H i (21) where H i is the incident wave height ; H r is the reflected wave height ; and H t is the transmitted wave height. Fig. 4 Comparison of wave surface elevations by a curtain2 wall breakwater. a,b,c : at 5. 82m, 3. 88m, 1. 94m in front of the curtain2wall breakwater. d : at 1. 94m behind the curtain2wall breakwater. Case : h = 0. 75m, H = m, T = s, d = 0. 21m Fig. 3 Wave heights near a curtain2wall breakwater. Case : h = 0. 75m, H = m, T = s, d = 0. 21m 3. 3 Com parisons of w ave surf ace elevations A numerical computation flume of 13. 2L ( L is the wavelength), where a barrier is located at 10. 2L from the incident boundary, is set up for the study by the present method. Calculations show that the waves are stable (see Fig. 3). For the case that there is a barrier in the physical domain, laboratory experiment s for measuring wave surface elevations at selected locations in f ront of and 3. 4 Com parisons of t ransmission coef f icients Transmission coefficient s computed by t he present met hod are compared wit h experimental data, numerical result s and analytical solutions published by researchers, including Wiegel ( 1960), Liu et al., (1982), Ursell ( 1974) and Losada et al., ( 1992). Figs. 5 ( a), 5 ( b) and 5 ( c) show the transmission coefficient s plotted versus d/ h for different relative water dept hs, kh = , and , respectively. The present computations are in good agreement wit h t he experimental data. 4. COMPUTED RESULTS AND DISCUSSION The barrier descending from the water surface to a dept h (curtain2wall type breakwater) is considered in
5 32 Fig. 5 (a) Comparison of transmission coefficients ( kh = ) Fig. 5 (c) Comparison of transmission coefficients ( kh = ) ts, C r, increase while transmission coefficients, C t, decrease. Moreover, as t he relative water dept h kh increases, the variations of reflection coefficients C r and transmission coefficients C t become smaller. This is because wave disturbance is confined within a layer near t he wave surface as t he relative water dept h kh increases. For t he fixed values of kh, as d/ h increases, C r increase and C t decrease. Table 1 Computational conditions relative water depth kh wave period T (s) incident wave height H (m) d/ h (refer Fig. 2) Fig. 5 (b) Comparison of transmission coefficients ( kh = ) t he present paper, Computational conditions are shown in Table W ave t ransmission and ref lection For different wave conditions and barrier sizes, extensive numerical computations have been carried out by t he present B FC met hod to investigate t he wave t ransmission and reflection due to t he t hin vertical barrier. Fig. 6 shows t he wave refection and transmission coefficients due to the thin vertical barrier descending f rom t he water surface to a dept h. It is observed that for fixed values of d/ h, as the relative water dept h kh increases, reflection coefficien 5. CONCL USIONS The main conclusions f rom t his st udy are summarized as follows. Comparisons between t he computed result s and previous analytical and experimental result s have been made. The t ransmission coefficient s due to a barrier descending from the water surface to a depth computed by t he boundary fitted coordinate met hod ( B FC ) shows good agreement wit h previous experimental data. A thin barrier descending from the water surface to a depth is investigated. For the fixed values of d/ h, as t he relative water dept h kh increases, reflection coefficients C r increase while transmission coefficients
6 33 REFERENCES Fig. 6 Wave reflection and transmission coefficients due to a curtain2wall breakwater C t decrease. Moreover, as the relative water depth kh increases, the variations of reflection coefficients C r and transmission coefficients C t become smaller. Wave t ransmission and reflection coefficient s due to t he barrier for various cases are given in a figure. 1. Gao Xueping, Inouchi K. and Kakinuma T., 1998 : Wave Motions Around Different Submerged Structures, Acta Oceanologica Sinica, 17(3), Goda Y. and Suzuki Y., 1976 : Estimation of Incident and Reflected Waves in Random Wave Experiments, Proc. 15th Coastal Engineering Conf, ASCE, 1, Honolulu, Kawamura H. and Hijikata K., 1995 : Simulation of Heat and Flow Maruzen Co. Ltd., Tokyo, (in Japanese) 4. Losada I. J., Losada M. A. and Roldan A. J., 1992 : Propagation of Oblique Incident Waves Past Rigid Vertical Thin Barriers. Appl. Ocean Res., 14, Liu P. L2F. and Abbaspour M., 1982 : Wave Scattering by a Rigid Thin barrier. J. Waterways, Port, Coastal and Ocean Div., ASCE, 108(WW4), Mandal B. N. and Dolai D. P., 1994 : Oblique Water Waves Diffraction by Thin Vertical Barriers in Water of Uniform Finite Depth. Appl. Ocean Res., 16, Morihira M., Kakizaki S. and Goda Y., 1960 : Experimental Investigation of a Curtain2Wall Breakwater, Report of Port and Harbour Research Institute, Japan, 3 (1). 8. Ursell F., 1974 : The Effect of a Fixed Vertical Barrier on Surface Waves in Deep Water, Proceedings of the Cambridge Philosophical Society, 43, Part 3, Wiegel R. L., 1960 : Transmission of Waves Past a Rigid Vertical Thin Barrier, J. Waterways and Harbors Div., ASCE, 86 (WW1), 112.
MODULE VII LARGE BODY WAVE DIFFRACTION
MODULE VII LARGE BODY WAVE DIFFRACTION 1.0 INTRODUCTION In the wave-structure interaction problems, it is classical to divide into two major classification: slender body interaction and large body interaction.
More informationNUMERICAL SIMULATION OF REGULAR WAVES RUN-UP OVER SLOPPING BEACH BY OPEN FOAM
NUMERICAL SIMULATION OF REGULAR WAVES RUN-UP OVER SLOPPING BEACH BY OPEN FOAM Parviz Ghadimi 1*, Mohammad Ghandali 2, Mohammad Reza Ahmadi Balootaki 3 1*, 2, 3 Department of Marine Technology, Amirkabir
More informationNumerical Modelling of Regular Waves Propagation and Breaking Using Waves2Foam
Journal of Clean Energy Technologies, Vol. 3, No. 4, July 05 Numerical Modelling of Regular Waves Propagation and Breaking Using WavesFoam B. Chenari, S. S. Saadatian, and Almerindo D. Ferreira numerical
More informationAdaptation of General Purpose CFD Code for Fusion MHD Applications*
Adaptation of General Purpose CFD Code for Fusion MHD Applications* Andrei Khodak Princeton Plasma Physics Laboratory P.O. Box 451 Princeton, NJ, 08540 USA akhodak@pppl.gov Abstract Analysis of many fusion
More informationFrequency-domain and stochastic model for an articulated wave power device
Frequency-domain stochastic model for an articulated wave power device J. Cândido P.A.P. Justino Department of Renewable Energies, Instituto Nacional de Engenharia, Tecnologia e Inovação Estrada do Paço
More informationFLUID MECHANICS IM0235 DIFFERENTIAL EQUATIONS - CB0235 2014_1
COURSE CODE INTENSITY PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE FLUID MECHANICS IM0235 3 LECTURE HOURS PER WEEK 48 HOURS CLASSROOM ON 16 WEEKS, 32 HOURS LABORATORY, 112 HOURS OF INDEPENDENT
More informationVISCOSITY OF A LIQUID. To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied.
VISCOSITY OF A LIQUID August 19, 004 OBJECTIVE: EQUIPMENT: To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied. Viscosity apparatus
More informationNUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES
Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics
More informationRF-thermal-structural-RF coupled analysis on the travelling wave disk-loaded accelerating structure
RF-thermal-structural-RF coupled analysis on the travelling wave disk-loaded accelerating structure PEI Shi-Lun( 裴 士 伦 ) 1) CHI Yun-Long( 池 云 龙 ) ZHANG Jing-Ru( 张 敬 如 ) HOU Mi( 侯 汨 ) LI Xiao-Ping( 李 小
More informationAbaqus/CFD Sample Problems. Abaqus 6.10
Abaqus/CFD Sample Problems Abaqus 6.10 Contents 1. Oscillatory Laminar Plane Poiseuille Flow 2. Flow in Shear Driven Cavities 3. Buoyancy Driven Flow in Cavities 4. Turbulent Flow in a Rectangular Channel
More informationAcceleration levels of dropped objects
Acceleration levels of dropped objects cmyk Acceleration levels of dropped objects Introduction his paper is intended to provide an overview of drop shock testing, which is defined as the acceleration
More informationENS 07 Paris, France, 3-4 December 2007
ENS 7 Paris, France, 3-4 December 7 FRICTION DRIVE SIMULATION OF A SURFACE ACOUSTIC WAVE MOTOR BY NANO VIBRATION Minoru Kuribayashi Kurosawa, Takashi Shigematsu Tokyou Institute of Technology, Yokohama
More informationMECH 450F/580 COURSE OUTLINE INTRODUCTION TO OCEAN ENGINEERING
Department of Mechanical Engineering MECH 450F/580 COURSE OUTLINE INTRODUCTION TO OCEAN ENGINEERING Spring 2014 Course Web Site See the MECH 450F Moodle site on the UVic Moodle system. Course Numbers:
More informationDimensional Analysis
Dimensional Analysis An Important Example from Fluid Mechanics: Viscous Shear Forces V d t / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Ƭ = F/A = μ V/d More generally, the viscous
More informationWaves. Wave Parameters. Krauss Chapter Nine
Waves Krauss Chapter Nine Wave Parameters Wavelength = λ = Length between wave crests (or troughs) Wave Number = κ = 2π/λ (units of 1/length) Wave Period = T = Time it takes a wave crest to travel one
More informationTWO-DIMENSIONAL FINITE ELEMENT ANALYSIS OF FORCED CONVECTION FLOW AND HEAT TRANSFER IN A LAMINAR CHANNEL FLOW
TWO-DIMENSIONAL FINITE ELEMENT ANALYSIS OF FORCED CONVECTION FLOW AND HEAT TRANSFER IN A LAMINAR CHANNEL FLOW Rajesh Khatri 1, 1 M.Tech Scholar, Department of Mechanical Engineering, S.A.T.I., vidisha
More informationFinite Element Analysis for Acoustic Behavior of a Refrigeration Compressor
Finite Element Analysis for Acoustic Behavior of a Refrigeration Compressor Swapan Kumar Nandi Tata Consultancy Services GEDC, 185 LR, Chennai 600086, India Abstract When structures in contact with a fluid
More informationWavePiston Project. Structural Concept Development Hydrodynamic Aspects. Preliminary Analytical Estimates. February 2010
WavePiston Project Structural Concept Development Hydrodynamic Aspects Preliminary Analytical Estimates February 2010 WavePiston Project Structural Concept Development Hydrodynamic Aspects Preliminary
More informationNumerical Wave Generation In OpenFOAM R
Numerical Wave Generation In OpenFOAM R Master of Science Thesis MOSTAFA AMINI AFSHAR Department of Shipping and Marine Technology CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden, 2010 Report No. X-10/252
More informationNUMERICAL STUDY OF FLOW AND TURBULENCE THROUGH SUBMERGED VEGETATION
NUMERICAL STUDY OF FLOW AND TURBULENCE THROUGH SUBMERGED VEGETATION HYUNG SUK KIM (1), MOONHYEONG PARK (2), MOHAMED NABI (3) & ICHIRO KIMURA (4) (1) Korea Institute of Civil Engineering and Building Technology,
More informationDifferential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation
Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of
More informationNumerical modelling of wave interaction with coastal structures
Terug naar overzicht Numerical modelling of wave interaction with coastal structures dr ir Peter Troch Afdeling Weg-& Waterbouwkunde, Vakgroep Civiele Techniek TW15 Universiteit Gent, Technologiepark 904,
More information- particle with kinetic energy E strikes a barrier with height U 0 > E and width L. - classically the particle cannot overcome the barrier
Tunnel Effect: - particle with kinetic energy E strikes a barrier with height U 0 > E and width L - classically the particle cannot overcome the barrier - quantum mechanically the particle can penetrated
More information1 The basic equations of fluid dynamics
1 The basic equations of fluid dynamics The main task in fluid dynamics is to find the velocity field describing the flow in a given domain. To do this, one uses the basic equations of fluid flow, which
More informationStress and deformation of offshore piles under structural and wave loading
Stress and deformation of offshore piles under structural and wave loading J. A. Eicher, H. Guan, and D. S. Jeng # School of Engineering, Griffith University, Gold Coast Campus, PMB 50 Gold Coast Mail
More informationGPR Polarization Simulation with 3D HO FDTD
Progress In Electromagnetics Research Symposium Proceedings, Xi an, China, March 6, 00 999 GPR Polarization Simulation with 3D HO FDTD Jing Li, Zhao-Fa Zeng,, Ling Huang, and Fengshan Liu College of Geoexploration
More informationINTRODUCTION TO FLUID MECHANICS
INTRODUCTION TO FLUID MECHANICS SIXTH EDITION ROBERT W. FOX Purdue University ALAN T. MCDONALD Purdue University PHILIP J. PRITCHARD Manhattan College JOHN WILEY & SONS, INC. CONTENTS CHAPTER 1 INTRODUCTION
More informationUsing CFD to improve the design of a circulating water channel
2-7 December 27 Using CFD to improve the design of a circulating water channel M.G. Pullinger and J.E. Sargison School of Engineering University of Tasmania, Hobart, TAS, 71 AUSTRALIA Abstract Computational
More informationPractice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22
BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =
More informationDetermination of source parameters from seismic spectra
Topic Determination of source parameters from seismic spectra Authors Michael Baumbach, and Peter Bormann (formerly GeoForschungsZentrum Potsdam, Telegrafenberg, D-14473 Potsdam, Germany); E-mail: pb65@gmx.net
More informationContents. Microfluidics - Jens Ducrée Physics: Fluid Dynamics 1
Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More informationANALYTICAL INVESTIGATION OF SLAB BRIDGE DAMAGES CAUSED BY TSUNAMI FLOW
ANALYTICAL INVESTIGATION OF SLAB BRIDGE DAMAGES CAUSED BY TSUNAMI FLOW Keisuke Murakami, Yoshiko Sakamoto and Tetsuya Nonaka 3 Tsunami caused by Tohoku earthquake in had brought fatal damages on many kinds
More informationTHE EFFECTS OF UNIFORM TRANSVERSE MAGNETIC FIELD ON LOCAL FLOW AND VELOCITY PROFILE
International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 2, March-April 2016, pp. 140 151, Article ID: IJCIET_07_02_011 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=7&itype=2
More informationNUMERICAL MODELLING OF PIEZOCONE PENETRATION IN CLAY
NUMERICAL MODELLING OF PIEZOCONE PENETRATION IN CLAY Ilaria Giusti University of Pisa ilaria.giusti@for.unipi.it Andrew J. Whittle Massachusetts Institute of Technology ajwhittl@mit.edu Abstract This paper
More informationA fundamental study of the flow past a circular cylinder using Abaqus/CFD
A fundamental study of the flow past a circular cylinder using Abaqus/CFD Masami Sato, and Takaya Kobayashi Mechanical Design & Analysis Corporation Abstract: The latest release of Abaqus version 6.10
More informationThe Viscosity of Fluids
Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et
More informationVibrations of a Free-Free Beam
Vibrations of a Free-Free Beam he bending vibrations of a beam are described by the following equation: y EI x y t 4 2 + ρ A 4 2 (1) y x L E, I, ρ, A are respectively the Young Modulus, second moment of
More informationNatural Convection. Buoyancy force
Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient
More informationA moving piston boundary condition including gap flow in OpenFOAM
A piston boundary condition including gap flow in OpenFOAM CLEMENS FRIES Johannes Kepler University IMH Altenbergerstrasse 69, 44 Linz AUSTRIA clemens.fries@jku.at BERNHARD MANHARTSGRUBER Johannes Kepler
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationSimulation of Offshore Structures in Virtual Ocean Basin (VOB)
Simulation of Offshore Structures in Virtual Ocean Basin (VOB) Dr. Wei Bai 29/06/2015 Department of Civil & Environmental Engineering National University of Singapore Outline Methodology Generation of
More informationLecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2)
Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) In this lecture How does turbulence affect the ensemble-mean equations of fluid motion/transport? Force balance in a quasi-steady turbulent boundary
More informationTransmission Line and Back Loaded Horn Physics
Introduction By Martin J. King, 3/29/3 Copyright 23 by Martin J. King. All Rights Reserved. In order to differentiate between a transmission line and a back loaded horn, it is really important to understand
More informationCOMBINED PHYSICAL AND NUMERICAL MODELLING OF AN ARTIFICIAL COASTAL REEF
COMBINED PHYSICAL AND NUMERICAL MODELLING OF AN ARTIFICIAL COASTAL REEF Valeri Penchev and Dorina Dragancheva, Bulgarian Ship Hydrodynamics Centre, 9003 Varna, Bulgaria Andreas Matheja, Stephan Mai and
More informationIntroduction to acoustic imaging
Introduction to acoustic imaging Contents 1 Propagation of acoustic waves 3 1.1 Wave types.......................................... 3 1.2 Mathematical formulation.................................. 4 1.3
More informationABS TECHNICAL PAPERS 2008 A STERN SLAMMING ANALYSIS USING THREE-DIMENSIONAL CFD SIMULATION. Suqin Wang Email: SWang@eagle.org
ABS TECHNICAL PAPERS 8 Proceedings of OMAE 8 7 th International Conference on Offshore Mechanics and Arctic Engineering 15- June, 8, Estoril, Portugal OMAE8-5785 A STERN SLAMMING ANALYSIS USING THREE-DIMENSIONAL
More information7.2.4 Seismic velocity, attenuation and rock properties
7.2.4 Seismic velocity, attenuation and rock properties Rock properties that affect seismic velocity Porosity Lithification Pressure Fluid saturation Velocity in unconsolidated near surface soils (the
More informationFluid structure interaction of a vibrating circular plate in a bounded fluid volume: simulation and experiment
Fluid Structure Interaction VI 3 Fluid structure interaction of a vibrating circular plate in a bounded fluid volume: simulation and experiment J. Hengstler & J. Dual Department of Mechanical and Process
More informationRavi Kumar Singh*, K. B. Sahu**, Thakur Debasis Mishra***
Ravi Kumar Singh, K. B. Sahu, Thakur Debasis Mishra / International Journal of Engineering Research and Applications (IJERA) ISSN: 48-96 www.ijera.com Vol. 3, Issue 3, May-Jun 3, pp.766-77 Analysis of
More informationKeywords: Heat transfer enhancement; staggered arrangement; Triangular Prism, Reynolds Number. 1. Introduction
Heat transfer augmentation in rectangular channel using four triangular prisms arrange in staggered manner Manoj Kumar 1, Sunil Dhingra 2, Gurjeet Singh 3 1 Student, 2,3 Assistant Professor 1.2 Department
More informationSTUDY OF DAM-RESERVOIR DYNAMIC INTERACTION USING VIBRATION TESTS ON A PHYSICAL MODEL
STUDY OF DAM-RESERVOIR DYNAMIC INTERACTION USING VIBRATION TESTS ON A PHYSICAL MODEL Paulo Mendes, Instituto Superior de Engenharia de Lisboa, Portugal Sérgio Oliveira, Laboratório Nacional de Engenharia
More informationFundamentals of Electromagnetic Fields and Waves: I
Fundamentals of Electromagnetic Fields and Waves: I Fall 2007, EE 30348, Electrical Engineering, University of Notre Dame Mid Term II: Solutions Please show your steps clearly and sketch figures wherever
More informationLaminar Flow and Heat Transfer of Herschel-Bulkley Fluids in a Rectangular Duct; Finite-Element Analysis
Tamkang Journal of Science and Engineering, Vol. 12, No. 1, pp. 99 107 (2009) 99 Laminar Flow and Heat Transfer of Herschel-Bulkley Fluids in a Rectangular Duct; Finite-Element Analysis M. E. Sayed-Ahmed
More informationTrigonometry Hard Problems
Solve the problem. This problem is very difficult to understand. Let s see if we can make sense of it. Note that there are multiple interpretations of the problem and that they are all unsatisfactory.
More informationStudy on Drag Coefficient for the Flow Past a Cylinder
International Journal of Civil Engineering Research. ISSN 2278-3652 Volume 5, Number 4 (2014), pp. 301-306 Research India Publications http://www.ripublication.com/ijcer.htm Study on Drag Coefficient for
More informationFLOODING AND DRYING IN DISCONTINUOUS GALERKIN DISCRETIZATIONS OF SHALLOW WATER EQUATIONS
European Conference on Computational Fluid Dynamics ECCOMAS CFD 26 P. Wesseling, E. Oñate and J. Périaux (Eds) c TU Delft, The Netherlands, 26 FLOODING AND DRING IN DISCONTINUOUS GALERKIN DISCRETIZATIONS
More informationNumerical Simulation of CPT Tip Resistance in Layered Soil
Numerical Simulation of CPT Tip Resistance in Layered Soil M.M. Ahmadi, Assistant Professor, mmahmadi@sharif.edu Dept. of Civil Engineering, Sharif University of Technology, Tehran, Iran Abstract The paper
More informationPlate waves in phononic crystals slabs
Acoustics 8 Paris Plate waves in phononic crystals slabs J.-J. Chen and B. Bonello CNRS and Paris VI University, INSP - 14 rue de Lourmel, 7515 Paris, France chen99nju@gmail.com 41 Acoustics 8 Paris We
More informationChapter 2. Derivation of the Equations of Open Channel Flow. 2.1 General Considerations
Chapter 2. Derivation of the Equations of Open Channel Flow 2.1 General Considerations Of interest is water flowing in a channel with a free surface, which is usually referred to as open channel flow.
More informationOpen channel flow Basic principle
Open channel flow Basic principle INTRODUCTION Flow in rivers, irrigation canals, drainage ditches and aqueducts are some examples for open channel flow. These flows occur with a free surface and the pressure
More informationHEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi
HEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi 2 Rajesh Dudi 1 Scholar and 2 Assistant Professor,Department of Mechanical Engineering, OITM, Hisar (Haryana)
More informationNumerical Investigation of Heat Transfer Characteristics in A Square Duct with Internal RIBS
merical Investigation of Heat Transfer Characteristics in A Square Duct with Internal RIBS Abhilash Kumar 1, R. SaravanaSathiyaPrabhahar 2 Mepco Schlenk Engineering College, Sivakasi, Tamilnadu India 1,
More information- momentum conservation equation ρ = ρf. These are equivalent to four scalar equations with four unknowns: - pressure p - velocity components
J. Szantyr Lecture No. 14 The closed system of equations of the fluid mechanics The above presented equations form the closed system of the fluid mechanics equations, which may be employed for description
More informationME6130 An introduction to CFD 1-1
ME6130 An introduction to CFD 1-1 What is CFD? Computational fluid dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions, and related phenomena by solving numerically
More informationLecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics
Lecture 6 - Boundary Conditions Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Outline Overview. Inlet and outlet boundaries.
More informationSIESMIC SLOSHING IN CYLINDRICAL TANKS WITH FLEXIBLE BAFFLES
SIESMIC SLOSHING IN CYLINDRICAL TANKS WITH FLEXIBLE BAFFLES Kayahan AKGUL 1, Yasin M. FAHJAN 2, Zuhal OZDEMIR 3 and Mhamed SOULI 4 ABSTRACT Sloshing has been one of the major concerns for engineers in
More informationDetermination of Acceleration due to Gravity
Experiment 2 24 Kuwait University Physics 105 Physics Department Determination of Acceleration due to Gravity Introduction In this experiment the acceleration due to gravity (g) is determined using two
More informationFREE CONVECTION FROM OPTIMUM SINUSOIDAL SURFACE EXPOSED TO VERTICAL VIBRATIONS
International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, Jan-Feb 2016, pp. 214-224, Article ID: IJMET_07_01_022 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1
More informationA wave lab inside a coaxial cable
INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 25 (2004) 581 591 EUROPEAN JOURNAL OF PHYSICS PII: S0143-0807(04)76273-X A wave lab inside a coaxial cable JoãoMSerra,MiguelCBrito,JMaiaAlves and A M Vallera
More informationNavier-Stokes Equation Solved in Comsol 4.1. Copyright Bruce A. Finlayson, 2010 See also Introduction to Chemical Engineering Computing, Wiley (2006).
Introduction to Chemical Engineering Computing Copyright, Bruce A. Finlayson, 2004 1 Navier-Stokes Equation Solved in Comsol 4.1. Copyright Bruce A. Finlayson, 2010 See also Introduction to Chemical Engineering
More informationInternational Journal of Food Engineering
International Journal of Food Engineering Volume 6, Issue 1 2010 Article 13 Numerical Simulation of Oscillating Heat Pipe Heat Exchanger Benyin Chai, Shandong University Min Shao, Shandong Academy of Sciences
More informationDimensional analysis is a method for reducing the number and complexity of experimental variables that affect a given physical phenomena.
Dimensional Analysis and Similarity Dimensional analysis is very useful for planning, presentation, and interpretation of experimental data. As discussed previously, most practical fluid mechanics problems
More informationTurbulence Modeling in CFD Simulation of Intake Manifold for a 4 Cylinder Engine
HEFAT2012 9 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics 16 18 July 2012 Malta Turbulence Modeling in CFD Simulation of Intake Manifold for a 4 Cylinder Engine Dr MK
More informationStudy on Pressure Distribution and Load Capacity of a Journal Bearing Using Finite Element Method and Analytical Method
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:1 No:5 1 Study on Pressure Distribution and Load Capacity of a Journal Bearing Using Finite Element Method and Method D. M.
More informationWhen the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.
Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs
More informationHydraulics Laboratory Experiment Report
Hydraulics Laboratory Experiment Report Name: Ahmed Essam Mansour Section: "1", Monday 2-5 pm Title: Flow in open channel Date: 13 November-2006 Objectives: Calculate the Chezy and Manning coefficients
More informationGroundwater flow systems theory: an unexpected outcome of
Groundwater flow systems theory: an unexpected outcome of early cable tool drilling in the Turner Valley oil field K. Udo Weyer WDA Consultants Inc. weyer@wda-consultants.com Introduction The Theory of
More information1) The time for one cycle of a periodic process is called the A) wavelength. B) period. C) frequency. D) amplitude.
practice wave test.. Name Use the text to make use of any equations you might need (e.g., to determine the velocity of waves in a given material) MULTIPLE CHOICE. Choose the one alternative that best completes
More informationModeling and Simulations of Cavitating and Bubbly Flows
Muon Collider/Neutrino Factory Collaboration Meeting Riverside, California, January 27-31, 2004 Modeling and Simulations of Cavitating and Bubbly Flows Roman Samulyak Tianshi Lu, Yarema Prykarpatskyy Center
More informationModel of a flow in intersecting microchannels. Denis Semyonov
Model of a flow in intersecting microchannels Denis Semyonov LUT 2012 Content Objectives Motivation Model implementation Simulation Results Conclusion Objectives A flow and a reaction model is required
More informationPhysical Science Study Guide Unit 7 Wave properties and behaviors, electromagnetic spectrum, Doppler Effect
Objectives: PS-7.1 Physical Science Study Guide Unit 7 Wave properties and behaviors, electromagnetic spectrum, Doppler Effect Illustrate ways that the energy of waves is transferred by interaction with
More information1. Lid driven flow in a cavity [Time: 1 h 30 ]
Hands on computer session: 1. Lid driven flow in a cavity [Time: 1 h 30 ] Objects choice of computational domain, problem adimensionalization and definition of boundary conditions; influence of the mesh
More informationSection 5.0 : Horn Physics. By Martin J. King, 6/29/08 Copyright 2008 by Martin J. King. All Rights Reserved.
Section 5. : Horn Physics Section 5. : Horn Physics By Martin J. King, 6/29/8 Copyright 28 by Martin J. King. All Rights Reserved. Before discussing the design of a horn loaded loudspeaker system, it is
More informationAnalog and Digital Signals, Time and Frequency Representation of Signals
1 Analog and Digital Signals, Time and Frequency Representation of Signals Required reading: Garcia 3.1, 3.2 CSE 3213, Fall 2010 Instructor: N. Vlajic 2 Data vs. Signal Analog vs. Digital Analog Signals
More informationv = fλ PROGRESSIVE WAVES 1 Candidates should be able to :
PROGRESSIVE WAVES 1 Candidates should be able to : Describe and distinguish between progressive longitudinal and transverse waves. With the exception of electromagnetic waves, which do not need a material
More informationEffects of Cell Phone Radiation on the Head. BEE 4530 Computer-Aided Engineering: Applications to Biomedical Processes
Effects of Cell Phone Radiation on the Head BEE 4530 Computer-Aided Engineering: Applications to Biomedical Processes Group 3 Angela Cai Youjin Cho Mytien Nguyen Praveen Polamraju Table of Contents I.
More informationCalculating resistance to flow in open channels
Alternative Hydraulics Paper 2, 5 April 2010 Calculating resistance to flow in open channels http://johndfenton.com/alternative-hydraulics.html johndfenton@gmail.com Abstract The Darcy-Weisbach formulation
More informationDevelopment of Optical Wave Microphone Measuring Sound Waves with No Diaphragm
Progress In Electromagnetics Research Symposium Proceedings, Taipei, March 5 8, 3 359 Development of Optical Wave Microphone Measuring Sound Waves with No Diaphragm Yoshito Sonoda, Takashi Samatsu, and
More informationBoundary Conditions of the First Kind (Dirichlet Condition)
Groundwater Modeling Boundary Conditions Boundary Conditions of the First Kind (Dirichlet Condition) Known pressure (velocity potential or total heard) head, e.g. constant or varying in time or space.
More informationINTERNATIONAL ASSOCIATION OF CLASSIFICATION SOCIETIES. Interpretations of the FTP
INTERNATIONAL ASSOCIATION OF CLASSIFICATION SOCIETIES Interpretations of the FTP CONTENTS FTP1 Adhesives used in A or B class divisions (FTP Code 3.1, Res A.754 para. 3.2.3) June 2000 FTP2 Pipe and duct
More informationFlow characteristics of microchannel melts during injection molding of microstructure medical components
Available online www.jocpr.com Journal of Chemical and Pharmaceutical Research, 2014, 6(5):112-117 Research Article ISSN : 0975-7384 CODEN(USA) : JCPRC5 Flow characteristics of microchannel melts during
More information2. THE TEORRETICAL OF GROUND PENETRATING RADAR:
Sixteenth International Water Technology Conference, IWTC 16 2012, Istanbul, Turkey 1 THE USE OF GROUND PENETRATING RADAR WITH A FREQUENCY 1GHZ TO DETECT WATER LEAKS FROM PIPELINES Alaa Ezzat Hasan Ministry
More informationSolitary Waves and PIV measurements at IGAW Wave Flume
Solitary Waves and PIV measurements at IGAW Wave Flume.1 -.1 -.2 3 3.5 4 4.5 5 5.5 6 V.Sriram, Research Scholar, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai 6 36,India.
More informationStructural Axial, Shear and Bending Moments
Structural Axial, Shear and Bending Moments Positive Internal Forces Acting Recall from mechanics of materials that the internal forces P (generic axial), V (shear) and M (moment) represent resultants
More informationLecture 5 Hemodynamics. Description of fluid flow. The equation of continuity
1 Lecture 5 Hemodynamics Description of fluid flow Hydrodynamics is the part of physics, which studies the motion of fluids. It is based on the laws of mechanics. Hemodynamics studies the motion of blood
More informationIHCANTABRIA and Marine Renewables
IHCANTABRIA and Marine Renewables Assessment and forecast of energy resources in the marine environment (waves, wind, currents, tides) Design, development and testing of marine renewable energy technologies
More informationPrinciple of Thermal Imaging
Section 8 All materials, which are above 0 degrees Kelvin (-273 degrees C), emit infrared energy. The infrared energy emitted from the measured object is converted into an electrical signal by the imaging
More informationThe simulation of machine tools can be divided into two stages. In the first stage the mechanical behavior of a machine tool is simulated with FEM
1 The simulation of machine tools can be divided into two stages. In the first stage the mechanical behavior of a machine tool is simulated with FEM tools. The approach to this simulation is different
More informationTennessee State University
Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.
More information(1) 2 TEST SETUP. Table 1 Summary of models used for calculating roughness parameters Model Published z 0 / H d/h
Estimation of Surface Roughness using CFD Simulation Daniel Abdi a, Girma T. Bitsuamlak b a Research Assistant, Department of Civil and Environmental Engineering, FIU, Miami, FL, USA, dabdi001@fiu.edu
More information