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TwoDimensional Width Average Model Of Estuarine Circulation Y. Arafat
Prediksi Salinitas ui Estuari Menggunakan Jaringan Syara£ Tiruan (Artificial Neural etwork) I. Suprayogi, N. Anwar, Edijatno, M.I. Irawan
Pola Bayangan pada Tatanan Bangunan Permukiman Tradisional Kudus Kulon J. Wardoyo
Karakter Visual Area Kelenteng Kawasan Pecinan Semarang E. Darmawan dan M. M. Sudarwani
..
Pengukuran AFR (Air Fuel Ratio) pada Spark Ignition Engine (SIE) Menggunakan Estimator Neural Network A. ·santoso, Kasmawi, M.S. Rokim, A. Nugroho, dan M. Anis
. Sistem Utra (Universal Mobile Telecommunication System Terrestrial Radio Access) FDD (Frequency Division Duplex) pada UMTS (Universal Mobile Telecommunication System Terres trial) W.A Prijono
Disain Tiga Buah Transformator Satu Fasa Asimetri untuk Pencatu Motor Induksi Tiga Fasa dengim Sumber Satu Fasa H. Santoso
A .Novel Rugby-Ball Antenna For Ultra Wide Band (Uwb) Communications R. Yuwono
Analisis Faktor Intensitas Tegano-an Berdasarkan Teknik J-Integral dan Ekstrapola i Perpindahan
· ,...
:>
M. A. Choiron dan M . R. W. Hariadi
Pen aruh Frak i olume Serat Kena£ Terhadap Sifat Mekanik Komposit dengan Matriks Poliester D.B. Darmadi
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.
FAKULTAS TEKNIK VE §ITA§ RAWilA "
:.. ::·
JURNAL
T E K
FAKULTAS TEKNIK UNIVERSITAS BRAW IJAYA PENANGGUNG JAWAB PEMIMPIN UMUM PEMIMPIN REDAKSI DEWAN REDAKSI
REVIEWER UNTUK EDISI INI
REDAKTUR PELAKSANA
KESE~ETARIATAN
Dekan Fakul as Te"-' ,_. :._-:ubraw. Pembantu De ·an I F~i.c ul :a Teknik Unibraw. Ir. Antariksa, _ l.Eng. P. .D. Prof. Ir. Budiono _ lts:nad, \1.S.E.E., Ph.D. Prof. Dr. Ir. Suhard·ono, D1pl. HE., \f.Pd. Dr. Ir. Galih Widjil Pan 0 arsa, DEA. , Prof. Ir. IS.G. \\'ardana, \I.Eng., PhD. Ir. Aclunad \\'icaksono, \1.Eng. Ph.D. Ir. Agus Suharyanto, \1.Eng., Ph.D. DR. Ir. Ludfi Djakfar, \15CE Prof. Ir. Sudjito. Ph.D . DR. Ir. Arief RachmansYah Dr. Ir. Rachm.ad Jayadi, \l.Eng CG. f) Dr. Ir. Djoko Legowo CCG\1) Dr. Ir. Budi Prayitno, \1.Eng Ir. Antariksa, M.Eng., Ph.D. (L -IBR.-\ \ .) Prof. Ir. Budiono Mismail, \.1SEE., Ph. D (G~IBRAW) Ir. Didik NotoSudjono, \.1Sc., Ph.D (BPPT JAKARTA) Ir. Syari Martinius, MSc (ITB) Dr. Ir. Soekrisno Suparman (GG\1) Hendi Bowoputro, ST., MT. Mach. Agus Choiron, ST., MT. Dian Sisinggih, ST., MT. Suprapto. ST., MT. Herry Santosa, ST., MT. Adi Jani, SE. Desi Kurniasari, SPd.
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[email protected] ISSN 0854-2139
DAFT AR I Volume XII No. 2 Agustus :
Teknik Sipil dan Perencanaan: Two-Dimensional Width Average Model Of Estuarine Circulation Y. Arafat
77
Prediksi Salinitas di Estuari Menggunakan Jaringan Syal"ai Tiruan (Artificial Neural Network)
87
I. Suprayogi, N. Anwar, Edijatno, dan M.I. lrawan
Pola Bayangan pada Tatanan Bangunan Permukiman Tradisional Kudus Kulon 95 J. Wardoyo
Karakter Visual Area Kelenteng Kawasan Pecinan Semarang
103
E. Darmawan dan M. dan M. Sudarwani
Teknologi Industri: Pengukuran AFR (Air Fuel Ratio) pada Spark Menggunakan Estimator Neural Network
Ignition Engine (SIE) 115
A. Santoso, Kasmawi, M.S. Rokim, A. Nugroho, dan M. Anis
Sistem Utra (Universal Mobile Telecommunication System Terrestrial Radio Access) FDD (Frequency Division Duplex) pada UMTS (Universal Mobile Telecommunication System Terrestrial)
126
W.A Prijono
Disain Tiga Buah Transformator Satu Fasa Asimetri untuk Pencatu Motor Induksi Tiga Fasa dengan Sumber Satu Fasa
138
H. Santoso
A Novel Rugby-Ball Antenna For Ultra Wide Band (UWB) Communications
144
R. Yuwono
Analisis Faktor Intensitas Tegangan Berdasarkan Teknik }-Integral dan Ekstrapolasi Perpindahan
149
M. A. Choiron dan M. R. W. Hariadi
Pengaruh Fraksi Volume Serat Kenaf Terhadap Sifat Mekanik Komposit Dengan Matriks Poliester D.B. Darmadi
154
TWO-DIMENSIONAL WIDTH AVERAGE MODEL OF ESITAR~L CIRCULATION Y. Arafat•
ABSTRACT A numerical model for the ca!!:ulation of estuarine flow and transport processes has been developed. The model is based on 2-D width average equations of hydrodynamic and solute transport, which are obtained by lateral integration of three-dimensional hydrodynamic and transport equations. The turbulence closure is formulated on the basis of mixing length and damping function. In the 2-D hydrodynamic model the continuity and momentum equations are solved using an implicit finite difference method. The implicit treatment of the vertical diffusion term results in a tridiagonal matrix in the vertical direction. The 2-D transport equation is solved using a splitting technique. In this technique the 2-D advection-diffusion problems is split into successive I -D pure horizontal convection, I -D pure horizontal diffusion and 1-D advection-diffusion problems. The 1-D pure horizontal advection equation is solved using the third-order Ultimate Quickest scheme, the I -D vertical advection-diffusion equation is solved using Tzanos method, and the 1-D pure horizontal diffusion equation is solved using Central- Scheme. Application of the model in a case study of Delta Upang in South Sumatra shows its predictive capability. The model showed good agreement with the field data. Key word: 2-d wide average model, splitting, estuarine, mixing length
INTRODUCTION Estuarine is region of transition from river to ocean, which at one of end fed by sources of fresh water. In this regions saline seawater and fresh riverwater meet each other. Because of mixing of salt and fresh water the distribution of salinity in an estuary is a gradually varying function of space and time. They are characterized by the possibility of tidal motions communicated from the sea, and by gradients of salinity and density associated with the progressive admixture of river water and seawater. The action of gravity upon the density difference between seawater and fresh water tends to cause vertical salinity stratification and a convection flow that has come to be known as estuarine circulation. Fresh water flows are dominant variables determining flow, distributions of salinity and circulation within the estuary. Estuaries traditionally have been classified according to their geomorphology and their salinity stratification. The terms a,re commonly applied are: coastal plain and fjord to express the geomorphology; and salt wedge or highly stratified (where freshwater flow dominates tidal currents), partially mixed or moderately stratified (where freshwater flow and tidal currents are relatively
balanced), and well mixed or vertically homogeneous (where tidal currents dominate freshwater flow) to express the relative salinity stratification. Many mathematical models used for salinity intrusion problems in estuaries are one dimensional, in that they use cross-sectional integrated forms of the equations of mass, momentum and salt content. These models require as input data information on the dispersion, i.e. the integrated effect of variation of velocity and concentration over the cross section. This in itself, limits their predictive capability. Depth integrated models applicable for mixed estuary, in which the density differences between bottom and surface are. small. This model does not appear to be very useful for circulation and salt intrusion for partially mixed or stratified estuaries, in which there are two fluids of different densities separated by a distinct interface. One of the more interesting problems in hydraulics is the study of de:gsity-induced flows in a stratified medium. A laterally two-dimensional width averaged model can be used to study this problem. A number of 2D-width averaged models have been used to handle stratified flow phenomena in estuary. For example, Hamilton (1975) developed a vertical two-dimensional numerical model of a
• Yassir Arafat, ST., MT, Oosen Jurusan Teknik Sipil Fakultas Teknik Universitas Tadulako Sulawesi Tengah
JURNAL TEKNIK I Volume XII No.2- AGUSTUS 2005 ISSN 0854-2139
77
rectangular geometry to study circulation in the Rotterdam Waterway and vertical mixing within a tidal cycle (see Bowden & Hamilton, 1975). Hsu et al (1998) developed a numerical model to simulate the circulation and salinity distribution in the Tanshui Estuary. Park & Kuo (1993) also developed similar model. However, all mode; developed were based on traditional finite difference schemes. The use of the schemes for solving transport of particulate substances such as sediment particles may appear numerical problems, particularly for long time simulation. They are as the result · of convection due to gravitation effect, which may be dominant over turbulent diffusion, particularly during slack waters. For this situation the traditional finite difference schemes generally fails to be applied for long time simulations. In this study. a laterally integrated twodimensional. real time model of hydrodynamics and salinity has been deYeloped and expanded to handle salt intrusion in estuary. The model was based on combined expli it-impli it fmite difference scheme for solving the continuity and momentum equations, and uses a time splittin~ to solve the 2-D convectivediffusi ve equation governing the transport of salt. In this technique the _-D advection-diffusion problems is split into succe sive 1-D pure horizontal convection. 1-D pure horizontal diffusion and 1-D advection-diffusion problems. Higher-order ULID1A TE Q CKEST scheme has been used to solve the pure convection equation, while Tzanos and TVD Filer are used to solve the convectiondiffusion equation in vertical directions. Application of these scheme can produce non-oscillation solution, particularly when the model may be extended to simulate sediment transport equation. The spliting model has been tested with flume data from Delft Hydraulics Laboratory (DHL) and applied in Upang River, South Sumatra.
Continuity equation:
a(Bu) + a(Bw) ax az
Jl~ ·.-\L
(1)
0
Momentum equation in horizontal direction:
a(Bu) + a(Buu) + a(Buw) -~(BNx au )-~(BNz du) at ax az ax ax az az B
ap
=BX--p ax (2) Hydrostatic equation representing pressure gradient: .
()p -=-pg
(3)
()z
Salt transport equation:
a(sB) + a(sBu) + a(sBw) =~(BKx as) +~(BKz as) at ax az ax ax az az (4) Equation of state (5)
p=p0 (1+ks)
where t = is time; x = longitudinal coordinate; u =longitudinal velocity; w = vertical velocity; B = river width; p = pressure; g = gravitational acceleration; Nz and Kz are turbulent viscosity and are diffusivity, in vertical direction; Nx and Kz dispersion coefficient for momentum and mass, in horizontal direction; p and Po = water density and fresh water density; k = constant relating density to salinity =0.75
-~
G OVERNI NG EQUATION The hydrodynamic model is based on the principles of conservation of volume, momentum and mass. Consider, a right-handed Cartesian coordinate system with the x-axis directed seaward and the z-axis directed upward as shown in Fig.l. Laterally integrated two dimensional hydrodynamic and transport equation are obtained by integration 3D hydrodynamic and transport equations over ·idth .. The laterally integrated governing equations ulem open channel flow are:
=
F"W water
v
x ~.
h(x)
Sea water
a
a
Fig. 1. Two-dimensional side view
TEKNIK I Volume XII No.2- AGUSTUS 2005 ISSN 0854-2139
....
TURBULENCE CLOSER MODEL
pAz au = c D p au w iu w I
The system of governing equations (1) to (4) require a turbulence model to solve the equations. The simplest approach is eddy viscosity/diffusivity concept, using a mixing length concept. Prandtl (1875-1953) introduced the mixing length concept which states that a fluid parcel travels over length its momentum is transferred. Using the mixing length approach, the turbulent exchange coefficients of mass and momentum, respectively, Dz, is given as:
=az2 (l-_:..)21aul
Dz
(6)
az
H
In estuarine stratified flow, buoyancy effects influence the turbulence and these are accounted for in an empirical way. by using a dumping function, F(Ri). Thus The decrease of eddy coefficient with increasing stratification can be described in damping factors:
. az 2(l- -z) 21aul F(Ri)
Nz=DzF(Rt)=
Kz=DzG(Ri)=
(8)
az
H
2 auiG(Ri) az 2 (l-_:..) H az
(9)
1
= _1_ (ap;az) P
(au;azY
G(R;)
= (1 + /3m Ri )m
= (1 + f3s R;)n
TB =Az
au =Cd .ullull
oz
(13)
Where 'tb-bed shear stress, u 1 is the velocity at the first grid point above bottom and cd is the friction coefficient on order of 10· 3 , where Cd=g n 2 L'1z. 113 ; n = manning's friction coefficient ; L'lz = bottom layer thickness.
3. Upstream Boundary
Q(t) and s =known A
.
(14)
(10)
(ll.a) (ll.b)
where ~m, ~s. m and n are empirical parameter.
BOUNDARY CONDITION
.
2. Bottom Boundary Condition The condition no mass flux through the bottom boundary is effected by specifying zero vertical and diffusion coefficient there. The bottom stress, which account for resistance by friction at the estuarine bottom, is calculated using a quadratic law, that is at z=-h
u=
Many sets of relations for F(Ri) and G(Ri) have been proposed. In the literature some suggestions can be found. Optimization of the choice of such a set is part of study by calibration with time series flume data. Blosset al (1988) proposed the following form:
F(R;)
Where Co is the dimensionless drag coefficient (ca. 1.3 x 10'\ Pais the air density (1.2 x 10' 3) and Uw is the wind speed at the height of 10 m above surface.
The land boundary (X=O.O), it is assumed that the freshwater discharge Q (t) and salinity(s) are known .
Whre Ri = the Richardson number defined by : Ri
az
1. Free Surface Boundary Condition No mass flux at through the free surface is effected by specifying zero vertical velocity and diffusion coefficient there. Wind stress term in used to account for momentum introduced into the estuary. That is, at z = 11
Velocity is assumed constant over depth at this boundary or using a velocity profile obtained from field measurement.
4. Seaward Boundary At the sea boundary, the surface elevation must be specified as a function of time either with harmonic function l')(L,t) = 11L(t) or based on measurements. The boundary condition for longitudinal velocity must be imposed. Because generally no velocity profiles are available during whole tidal cycle, a weak condition is imposed. i.e. d 2U 2
=0
(15)
dx
Boundary condition for salt concentration:
a ~ =0
if u(z) >0
(16)
ac c,nax at=
if u(z)
:»,a
I
·2
.....
\
.
l
lsto a , llrre=13.001 0 :00,00
opo
>S.OC
5,00
, ...oo
10 .00
\
20,\X
'\\ ~)
!
'
·10
· 12
\
... ·18
l Sta. 4, Tirre= 12.361 1MO
~·"~Y
lsta. 2,1irre=12.241 :00.00
,...
0
•I"
6,00
10,00
15,00
20,00
>5,0
·2
·•
t\
·8
·10
~
l"0
I
0
·•
l
\
· 12
\
0
·•
"\~
ia
\\
· 14
·• ·10
· 18
=data;
~unty
·8
Salinity
Salinity
o-o--o ;
12,
20.0C
16,00
·2
·•
'"'
\ C)
saunty
ISta 12, Titre = 13.24 1 0 ~00
1.00
~
\0
:salinity
~80
' .\
!"
h
·10
0,80
0,201 ....
·2
·2
.
II
ISla 1S,T.,_ 13.481
0115
The simulations were carried out for 48 hours with time step, tot = 10 s. The simulation results are shown in Fig. 5. There are good agreement between the predicted salinity profiles and corresponding data for all section considered. The recirculation can also be predicted by the model as can be seen in Fig.6
JURNAL TEKNIK I Volume XII No. 2- AGUSTUS 2005 ISSN 0854- 2139
:I
ll
.....
0
5~~-10
-
~
-
. .
-
~
-
,
.
-
'
15 . 20 25 20000
.()25-r--·-------· 0 05
0.1
015
-o.zs
Distance from mouth - · -
2,---~--~---;
005
02
0 10
, -o os
r
oos
~~
~~5
0
.() 2
.()\
-125
·125
·2.25 -
-z_zs-
-3zs t
.g~
§ ~
a
-~-25 -
-4.25·1 ":
·5.25
-6.25·
-625 -
-ezs·
·8.25 -
10 25 -
_.-
• 025 · '---""""'-:;--..,...,-,----'
Yaklclty
u(nV•l
· 11 .25 Vfioc/lly u(IWI)
Fig. 6 Flow circulation and velocity profiles when switchover flow from ebb to flood at Upang Estuarine CONCLUSIONS The numerical model has been developed for simulating time dependent, tidally forced, stratified circulation in an estuary. The model is based on 2-D width average equations of hydrodynamic and solute transport, which are obtained by lateral integration of three-dimensional hydrodynamic and transport equations. The turbulence closure is formulated on the basis of mixing length and damping function. The hydrodynamic model was formulated using an implicit finite difference technique, with implicit treatment of the vertical diffusion term resulting in a tri-diagonal matrix in the vertical direction. The 2D transport equation is solved using a splitting
technique. In this technique the 2-D advectiondiffusion problems is split into successive 1-D pure horizontal convection, 1-D pure horizontal diffusion and 1-D advection-diffusion problems. This allow to applied the most appropoate scheme for each problems. The splitting technique is optimal in the sense that the Courant number constraint was reduced to be only dependent upon the constraint for the one-dimensional scheme The numerical model has been applied to simulate salt transport fluxes in Delta Upang Estuary, and has shown its predictive capability. The model prediction showed good agreement with the field data
JURNAL TEKNIK I Volume XII No. 2 - AGUSTUS 2005 ISSN 0854- 2139
REFERENCES Bloss, S. , Lehfeldt, R. and Paterson, J. C., 1988, " Modelling Turbulent Transport in Stratified Estuary", Journal of Hydraulic Engineering, Vol.114, No.9, September, pp.l'll15-1131 Bowden, K.F., and Hamilton, P., 1975, "Some Experiment with a Numerical Model of Circulation and Mixing ir. a Tidal Estuary, " Estuarine and Coastal Marine Science. Vol.3, pp 281-301 Cahyono, M., 2000, "TVD Filter Algorithm for Solving Advective Transport Eq11ations", Proc. ITB, VOL.32, No.1, Supplement, pp.457-468 Cahyono, M. and Falconer, R. A., 1977, " Optimal Time Splitting for Two- and ThreeDimensional Advection-Diffusion Simulations Using Higher Order Finite Difference Schemes", Proc. Regional Seminar on Computational Methods and simulation in CMSE'97, Bandung, Engineering pp.VVV.C.5.1-10 Dunbar, D. S. and Burling, R. W., 1987, "A Numerical Model of Startified Circulation in Indian Arm, British Columbia", Journal of Geophysical Research, Vol.92, No.Cl2, November, pp.l3075-13105 Falconer, R. A. and Cahyono, 1993, "Water Quality Modeling in Well Mixed Estuarine Using Higher Order Accurate Difference Schemes", Advance in Hydro-Science and -Engineering, Vol. I (ed. Sam S. Y. Wang), University of Mississippi, pp.81-92
Hamilton, P .. 1975, " A Numerical Model of the Vertical Circulation of Tidal Estuaries and its Application to the Rotterdam Waterway," Geophysical Journal of the Royal Astronomical Society, Vol. 40, pp 1-21 Hsu, Ming-His and Kuo, A. Y., 1998, "Numerical Simulation of Circulation and Salinity Distribution in the Tanshui Estuary".Poc . Nat!. Sci. Counc. ROC(A). Vol. 23, No. 2, pp. 259-273 Leonard, B. P, 1991, "The ULTIMATE Conservative Difference Scheme Applied to Unsteady OneDimensional Advection", Comput. Methods Appl. Mech. Engrg., 88, pp. 17-74 Park, H. and Kuo, Y., 1993, "A Vertical Twoof Estuarine Dimensional Model Hydrodynamics and water Quality", Special Report in Applied Marine Science and Ocean Engineering No.321, School of Marine Science Virginia Institute of Marine Science, VA 23062 Perrels, P. A. J. and Karelse, M., 1988, "A TwoDimensional Laterally Averaged Model for Salt Intrusion in Estuaries", in Transport Models for Inland and Coastal Waters (ed. Fischer et al), Academic Press .P'randtl, L., 1925, "Berich uber Unter Suchugen zur Ansgibideten Turbulenz," Z. angln Math, Mech., Vol.5,, pp.136-139 Tzanos P.Constantine, 1990, " Central DifferenceLike Approximation for The Solution of The Convection-Diffusion Equation", Numerical Heat Transfer, Part B, Vol.17, pp 91-112 (Artikel diterima tg/.1/6105; disetujui tg/.416105; revisi tgl. 2516105)
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JURNAL TEKNIK I Volume XII No.2- AGUSTUS 2005 ISSN 0854- 2139
