Suharjoko 1 *, Srie Subekti 1 and Edy Sumirman 1

Transcription

1 International Journal of Applie Engineering Research ISSN Volume 1, Number 4 (017) pp Numerical Computations on Seiment Transport Moels Base on Threshol Seiment Motions of Shiel s Graphic ue to Simulation of the Groyne Placement Analysis Suharjoko 1, Srie Subekti 1 an Ey Sumirman 1 1 Civil Engineering Department, Vocational Faculty of Institute Technology, Sepuluh Nopember, Surabaya, Inonesia. 1 Orci: Abstract The numerical moel of seiment transport moelling is the computer program was constructe compose of -D flow by Navier-Stoke equation, seiment transport equations an ba eformations equations. In solving of seiment transport an ba eformations equation, require threshol of seiment that is the critical stress of motion parameters of each subgrae graations, but the critical stress motion parameters was calculate from searche on the Shiel's iagram, that s always consieration of each process computations, while in the computer program, implementation of seiment transport one repeately so that the usage of Shiel s iagram in the computer program will be ifficulty because to applie of Shiel s iagram can be o manually. Therefore, to usage of graphs on the computer program mush be abanone an nees an effort to moify the Shiel's iagram into mathematical equations. This paper escribes of manually process of the Shiel's iagram become a mathematical equation that can be applie easily in computer programming. Keywors: moify the Shiel's Graph, Seiment Transport Moels INTRODUCTION Programming on Seiment Transport Moels buil from the numerical computations of flow equation an seiment transport equation incluing be eformations equations. The seiment transport equation neee the threshol of seiment motions. The threshol of seiment motion is critical stress motion at which seiment particle begin to move, the conition threshol of seiment motion is usually expresse in terms of a critical shear stress or threshol shear stress ( cr ). In the threshol of seiment computations was nee the critical stress of motion parameters ( cr ) was calculate an searche from the Shiel's graph. In the calculation of seiment transport parameters are usually represente by seiment grain 50, which is the mean iameter of the existing seiment graation, there is assume one grae class. To be get accurate of the calculation will be mae the parameter seiment grain became some classes graation, so that each of class graation will be calculate the critical stress of seiment s motion an be eformations. This calculation is repeate on the next item for the upper class graation to the last class an be repeate on any time. So the accumulation of seimentation can be calculate from the sum of the results calculation of all class graations. In any calculation of each class seiment transport, requires the threshol of seiment motions that s to be consieration of the Shiel s graph, however in the computer program to calculation of seiment transport was one repeately, so that the usage of the Shiel s graph in the computer programing will be ifficult, therefore to support the Numerical Moel programming seiment transport neee of moifie Shiel iagrams into mathematical equations. This paper escribes of moifie Shiel iagrams into mathematical equations that s be supporte the computer programing of seiment transport moelling. Masen et al. (1976) on Tuomo Karvonen, (00), giving converte the Shiels iagram in to the relationship between the critical Shiels parameter an the seiment flui parameter. THE RESEARCHES HAS BEEN DONE Researches on Transport Seiment Programming On the explaine above, seiment transport program, is a program to buil of numerical computation of the -D Horizontal flow equation, the transport seiment equations an the ba eformations equation be computations together an repeately. On issues concern on seiment transport program, has been stuie by Suharjoko (01) an Suharjoko (014), an Jungseok, 005 to get etermination of the goo istance between the groyne. Heerevel (006), conucte a stuy on the submersible groyne aime to reucing the spee of the water flow at the bottom an increase in the upper stream (fairway). Branimarte et al, (006) an Prohaska (006), stuy of groyne functions as erosion control, while 14998

2 International Journal of Applie Engineering Research ISSN Volume 1, Number 4 (017) pp Zhang (007), stuy on flow problems an the changes process on the river ba aroun the groyne, Armani (010), to analyze the problem of scouring an epositions in aroun a groyne system. Kuhnle et al, 1999, conucte experiments on groyne immerse (submerge spur ikes), an Zhang, Mizutani an Nakagawa (011), investigating the influence of groyne size against of the seimentation on be topography aroun groyne. Duan, 005, to preict be-loa seiment transport aroun the channel The stuies mentione above have been applie to simulate the flow pattern an to get an iea of the istribution of seiment concentration an the concentration on aroun the groyne. Researches of the Shiel s Graph Applications on numerical moeling The seiment transport equation neee the threshol of seiment motions. The threshol of seiment motion is critical stress motion strength at which seiment movement begins, the conition for incipient movement is usually expresse in terms of a critical shear stress or threshol shear stress, which will enote by cr. In the threshol of seiment computations was nee the critical stress of motion parameters ( cr ) was calculate an searche from the Shiel's graph. In the calculation of seiment transport parameters are usually represente by seiment grain 50, which is the mean iameter of the existing seiment graation, there is assume one grae class. To be get accurate of the calculation will be mae the parameter seiment grain became some classes graation so that, each of class graation will be calculate the critical stress of seiment s motion an then can be calculate the be eformations. This calculation is repeate on the next item for the uper class graation to the last class, so the accumulation of seimentation can be calculate from the sum of the results calculation of all class graations. The seiment transport equation neee the threshol of seiment motions. The threshol of seiment motion is critical stress motion strength at which seiment movement begins, the conition for incipient movement is usually expresse in terms of a critical shear stress or threshol shear stress, which I will enote by cr. In the threshol of seiment computations was nee the critical stress of motion parameters ( cr ) was calculate an searche from the Shiel's graph. Guo 00, Shiels-Rouse equation, The introuction of critical iameter is exactly analogous to Rouse s auxiliary parameter or Rouse Reynols number, i.e. eliminating the critical shear stress from the abscissa. Guo (1990) on Guo 00, propose a mathematical expression to get wie applications of numerical moeling, Haschenburger an Wilcock, 003, the wiely aplications Shiels iagram of unisize seiments, be represente on mathematical expression. Masen et al. (1976) on Tuomo Karvonen 00, converte the Shiels iagram in to the matematical expression of relationship between the critical Shiels S. parameter c an the seiment flui parameter Moifications of tke Shiel's graph to mathematical equation has one Tuomo Karvonen, 00, is set in forth orther Equation as follows log( )=0.003x x x x x Where x= Log ( S ). However, this equation still shown error value of Critical Shiels parameter at Shiel Number ( S ) value more than 600. Show that Moifications of tke Shiel's graph to mathematical equation must be ubate. Figure1: Moifications of the Shiel's graph has one Tuomo Karvonen,

3 International Journal of Applie Engineering Research ISSN Volume 1, Number 4 (017) pp METHODOLOGY AND SEDIMENT TRANSPORT MODELS EQUATIONS Metho to Developing Mathematical Moel on Seiment Transport Programming on Seiment Transport Moels buil from the numerical computations of flow equation by the Navier- Stokes an seiment transport equation incluing be eformations equations. The flow equation by the Navier- Stokes that meets from the mass conservation equations an momentum equations of water motion. The mass conservation equations erive from conservation of mass water motion an momentum equations erive from Newton's secon law. The seiment transport equation neee the threshol of seiment motions. The threshol of seiment motion is critical stress motion strength at which seiment movement begins, the conition for incipient movement is usually expresse in terms of a critical shear stress or threshol shear stress, which I will enote by cr. In the threshol of seiment computations was nee the critical stress of motion parameters ( cr ) was calculate an searche from the Shiel's graph. In the calculation of seiment transport parameters are usually represente by seiment grain 50, which is the mean iameter of the existing seiment graation, there is assume one grae class. The Seiment Transport Moels Equations a) Suspene Seiment Diffusion Equations Wexier (199) on Signh 005 evelope an analytical solution for two-imensional iffusion equation. The Migniot (1989) on Signh 005, The settling velocity cohesive seiment equations: Where : w sc w s w sc 50 w s = settling velocitys of cohesive seiment flocs = settling velocitys of single cohesive seiment Stoke Law is use to calculate the single cohesive seiment particle s ( s ) 18 c) Settlement of Suspene seiments Dyer 1986 on wiao 1998, introuce the equation to calculate the rate of setle seiment as follow, m pw s 1 t Where m is the mass seiment settle to be eposite, p is the seiment, an c are the shear stress an critical shear stress for settlement respectively. RS, for wie channels hyraulic raius R can be taken as the epth of flow h. Inri,s formula on Signh 005, propose the following formula for critical shear stress for incipient motion for seiment particle are: c Where c = Critical shear stress in gm/m, = mean iameter of seiment in mm, M = uniformity coefficient b) Settling velocity Liu 001, The settling velocity of suspene seiment w s give w s ( p 1) n n n Where, n is Normal iameter, p is seiment concentration an g is seiment concentration. ) Threshol of Seiment Computations in solving the seiment transport an ba eformations require threshol of seiment particle on each subgrae graations, which is the critical stress of motion parameters cr. However, the critical stress of motion parameters was calculate by searche from the Shiel's iagram. Computations on computer program in being usage of graphs shoul will be abanone, therefore nees to be one moify of the graph into mathematical equations. Consier the flow on the cohesive particles, the forces acting on the ba particle are shown in Figure

4 International Journal of Applie Engineering Research ISSN Volume 1, Number 4 (017) pp Figure : Forces acting on the particles of seiment. (Liu 001) If the critical friction velocyties u C,, inicating the situation in which the grain particles begin to move, then the rag force is equal to the friction force, an with simplification become the following equation. u. c ( s 1) C D f f C Seiment particles begin to move if ; u u. C L 4 3 critical friction velocity u.c, or b b, C critical bottom shear stress u.c, or C critical Shiels parameter u. c ( s 1) (Masen 1976 on Liu 001), to know the critical conition of seiment particles treshol can be calculate by Shiels iagram as shown in the following figure, that is graph of relationship between critical Shiel parameter with seiment flui parameters is seiment flui parameters can be calculate S ( s 1) an Critical Shiel 4 parameters follow the equation u. C, whose value ( s 1) can be etermine from the Shiel's graph of Figure 3 below. 0.1 u ( s 1) S ( s 1) 4 Figure 3: Shiels graph, the relationship between Seiment Flui Parameter S with Critical Shiels Parameter 15001

5 International Journal of Applie Engineering Research ISSN Volume 1, Number 4 (017) pp e) Be Elevation Change Singh, 005, the ba elevation changes ue to seiment erosion an seiment eposition may be represente as the following equation: zb ( 1 p ' m ) s ( C C ) ( qb qb )/ Ls t C an q b is a conitions that must be known in avance an can be approache C p, q p q, p b is bc b b b the graation of be material, C is the potential transport capacity of suspene-loa, q b is the potential transport capacity of be-loa. DISCUSSION Get the Digital Data of Shiel s Graph To change the graph into a mathematical equation, early times be one to reaing of the Shiel s graph of the relationship between critical Shiel parameters with seiment flui parameters into igital ata, the reaing result is as following Table 1. Then the ata which is the relationship between S an c to be change into the relationship between Log( S ), with c then o regression analysis. Table 1: The relationship of parameters S, Log( S ) an c S Log S c u 1) s ( S 4 ( s 1) Figure 4: The regression analysis resulte of the relationship between c an S REGRESSION ANALYSIS To simplify of Regression Analysis, the Log ( S ) parameter is replace by parameter x, then from these two parameters the regression equation is searche. The regression analysis has resulte the moifications Shiel's graph into the mathematical equation in a relationship between c an x as follows; c= x x x , where x= Log ( S ). The Stanar eviations yiel R= Plotting Data Regression Curve So that the evelop of mathematical equation moifications Shiel's graph, can be seen the comparison of the Shiel's graph by Karvonen 00 with the Shiel's graph by Suharjoko 017, can be seen in Figure 5 below. Figure 5: The regression analysis resulte of the relationship between c an S of the Shiel's graph by Karvonen 00 with the Shiel's graph by Suharjoko 1500

6 International Journal of Applie Engineering Research ISSN Volume 1, Number 4 (017) pp The Computation Application of Seiment Transport Moel to Simulation of the Groyne Placement After obtaining the mathematical formulation of the shiel's graph, the analysis of the seiment threshol an the ba eformation analysis will be easy, even the analysis can be improve in accuracy by performing an analysis base on the graing class. The moifie mathematical equations of Shiel Graphs greatly assist the process of calculating seiment transport programs to simulate the suspene istribution an ba eformation. The following were showen a simulation result of the process computations seiment transport programs to simulate the suspene istribution an ba eformation that's were analysis be consiering of each class graation suspene seiment. The characteristics of graation suspene seiments as shown in Figure 6 below Prosentage Loss Suspene graations Seive Size (mm) Figure 6: Suspene Seiment Graation Characteristics to be Stuie. The existing suspene graations were analyze in 5 graation classes of granules. The class ivisions are as follows; Table : The size that represents on each class of soil graation No. % class (mm) In the implementation of the simulation, consiering the important parameters are river with, angle bench, raius bench, current velocity, water epth, groyne length, groyne position an suspene seiment were resulte of the seimentation volume were be occurre. The above simulation results can be explaine as follows; by taking the example of groyne layout case, that is on channel with 0 m with turn angle 60 º, turn raius 40 m, groyne position in center of arc an length of groyne equal to 1/5 with of channel. upstream flow velocity = 1.4 m / sec, prouce as can be seen in figure below, the perspective of water faces occurring, Figure 7; The vektor velocities of water flow velocity, Figure 8; istribution of suspension seiment concentration an Fig. 9; seiment eposition (ba eformations) aroun the groyne. Thus, the moifie mathematical formulation of the Shiel graph, makes it easy for the Numerical Computations On Seiment Transport moel. Figure 7: The perspective of water faces aroun the groyne fiel occurring simulation result to the case of groyne size L / B = 1/5 at the angle bench β = 60º, raius bench 40 m, upstream velocity u = 1.4 m /sec 15003

7 International Journal of Applie Engineering Research ISSN Volume 1, Number 4 (017) pp U = 1.4 m/s Figure 8: The vektor velocities of water flow aroun the groyne fiel occurring simulation result to the case of groyne size L / B = 1/5 at the angle bench β = 60º, raius bench 40 m, upstream velocity u = 1.4 m /sec Figure 8: Distribution of Suspension Seiment Concentration 15004

8 International Journal of Applie Engineering Research ISSN Volume 1, Number 4 (017) pp Figure 9: Seiment Deposition (Ba Deformations) aroun The Groyne. CONCLUSION Computations in solving the seiment transport an ba eformations require threshol of seiment particle on each subgrae graations, which is the critical stress of motion parameters cr. However, the critical stress of motion parameters was calculate by searche from the Shiel's iagram. Computations on computer program in being usage of graphs shoul will be abanone, therefore nees to be one moify of the graph into mathematical equations. To get better then mae effort moification with regression analysis than yiele the moification of Shiel's graph obtaine equation of Critical Shiels parameter c as the following Equation c= x x x , where x= Log( S ), The Stanar eviations yiel R= The moifie mathematical formulation of the Shiel graph, makes it easy for the Numerical Computations On Seiment Transport moel ACKNOWLEDGMENT This research is finance by Directorate of Research an Community Service Directorate General Strengthening Research an Development Ministry of Research, Technology an Higher Eucation In accorance with the Contract Research Number: 617 / PKS / ITS / 017. REFERENCE [1] Tuomo Karvonen, Seiment Transport, Department of Civil an Environmental Engineering, Original material by 00. Helsinki University of Technology. K Whipple, Last upate [] Zhou Liu, SEDIMENT TRANSPORT Laboratoriet for Hyraulic og Havnebygning Instituttet for Van, Jor og Miljøteknik, Aalborg Universitet, ugave. Januar 001 [3] ALBERT GYR, An KLAUS HOYER, Seiment Transport, A Geophysical Phenomenon, Institute of Environmental Engineering, Swiss Feeral Institute of Technology, Zürich, Switzerlan [4] Moreau R., maylam, flui mechanics an its applications, Volume 8, Series EitorEcole Nationale Supérieure 'Hyraulique e Grenoble, Boîte Postale 95, 3840 Saint Martin 'Hères Ceex, France [5] Suharjoko, Mohamma Bisri, Rispiningtati, Muhamma Ruslin Anwar, Moelling Of Groyne Placement On The River Ben Base On Seimentation Analysis Using Numerical Simulation Approach By Finite Difference Metho International Journal of 15005

9 International Journal of Applie Engineering Research ISSN Volume 1, Number 4 (017) pp Engineering Research an Applications (IJERA), ISSN: 48-96, Vol. 3, Issue 1, January - February 013, pp [6] Suharjoko, Mohamma Bisri, Rispiningtati, Muhamma Ruslin Anwar, An Analysis Of The Groyne Placement At The River Ben Base On Current Flow Be Occurre, International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol:1 No:06, December 01, pp [7] Suharjoko; Mohamma Bisri; Rispiningtati; Muhamma Ruslin Anwar, The Seimentation Patterns on Groyne Fiel Due to Different Placement on the River Ben, AENSI Journals, Australian Journal of Basic an Applie Sciences, ISSN: , Journal home page: 8(18) December 014, Pages: [8] Guo Junke,Hunter Rouse An Shiels Diagram, Avances In Hyraulics An Water Engineering, Proc. 13th IAHR-APD Congress, vol., Worl Scientific, Singapore, 6-8 August 00, Pages: [9] Tuomo Karvonen, Transport of harmful substances (Yh ), Department of Civil an Environmental Engineering Helsinki University of Technology Original material, 00, Last upate