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Magnetization mechanism in amorphous ferromagnetic wires
Get PDFÇiftekararlılık için sınır uzunluğun üzerindeki bir amorf ferromanyetik telin üzerinde yaratılan eziğin ve küçük bobinler ile tele uygulanan yerel manyetik alanların telin DC manyetik histeresisine etkisi, deneysel olarak incelenmiş, sonuçlar bir model ile yorumlanmıştır. Bir grup amorf tel, ölçümden önce 0.75mm çaplı sert çelik iğneyle tele dik olarak ortadan değişik miktarlarda ezilmiştir. Diğer bir grup ölçüm de ortasından kesilip çeşitli aralıklar bırakılmış örneklerle yapılmıştır. Üçüncü bir grup deney de, tele 1.5mm uzunluğunda bobin(ler) sarılarak uygulanan manyetik alan(lar)ın telin manyetik histeresisi üzerindeki etkilerini incelemek üzere yapılmıştır. Birinci grup ölçümlerde kullanılan teller çiftekararlılık için sınır uzunluktan kısa olduğu halde ezik 20µm’yi aştıktan sonra histeresis döngülerinde iki aşamalı büyük Barkhausen sıçraması ile kademeli düşüş görülmüştür. İkinci grup deneylerden elde edilen histeresis döngüleri fark olarak birinci gruptakilerden sadece basamaklı gevşeyen kısımlarında daha büyük bir eğim göstermiştir. Aynı yerde tele sarılı küçük bir bobin ile tele artı yönlü manyetik alan uygulandığında ise, mıknatıslanma histeresis döngüsünde uzun, basamaklı bir gevşemeden sonra büyük bir Barkhausen sıçraması ile ters yönde doyuma gitmiştir. Döngünün çıkıcı kısmında ise ters mıknatıslanmanın, eksi bir dış alan değerinde büyük bir Barkhausen sıçraması ile başlayıp küçük basamaklarla doyuma gittiği görülmüştür. Bu çalışmada sunulan model, telin iç çekirdeğindeki manyetik bölge duvarı hareketi ve kapanma bölgelerindeki parçalanma sonucunda ortaya çıkan manyetik moment dağılımının bilgisayar yazılımları ile hesaplanması temeline dayanmaktadır. Hesap sonucu elde edilen histeresis döngüleri deneysel sonuçlarla uyum içindedir. Anahtar Kelimeler: Amorf tel, ezik, histeresis, ferromanyetik.Hysteresis loops in a ferromagnetic amorphous wire longer than the critical length are studied. Wires with a deformation in the middle are considered. Both theoretical and experimental studies using DC vibrating sample magnetometer were performed. Amorphous wires with compositions Fe-Si-B and with diameter 125µm of positive magnetostriction coefficient are used in the experiments. Samples have been deformed at the middle by pressing with a hard steel needle of 0.75mm diameter, perpendicular to the axis of the wire. Another group of measurements was carried out of the samples cut at the middle. A third group of experiments was intended to be a bridge to the hysteresis model proposed. 1.5mm coils were wound up at the middle of the wire under investigation to apply a local magnetic bias. An oppositely directed pair of local fields is applied with a pair of identical coils reversely connected is employed to investigate its effect on the hysteresis loop. The DC hysteresis loops were measured with a home made vibrating sample magnetometer. The sample vibrates sinusoidally along the axis of a long solenoid at the frequency of 23 Hz. The pick-up coils have been particularly designed to measure long samples. Magnetic field has been changed with a step of 0.3 A/m, and measured with a sensitivity of 0.01 A/m. In the first group of experiments, although the length of the wire is greater than the critical length for bistable behavior, after a threshold value of increasing, the hysteresis loop starts to narrow keeping its rectangular shape. Furthermore deformations more than 20 µm lead to two large Barkhausen jumps separated by a staircase relaxation. The only difference of the hysteresis loops yielded by the second group of experiments from the first is that the slope of the inclined parts is bigger than those in the first group. The unidirectional magnetic bias gave rise to a staircase relaxation, followed by a long Barkhausen jump in the descending branch of the loop. In the ascending branch, the domain wall completes its almost entire motion in a negative external field and the magnetization approaches saturation with staircase movements. As the current through the reversely connected pair of coils is increased, the hysteresis loop starts developing nearly horizontal tails first at the up right, and then at the bottom left corners. The model proposed in this work is based on the calculation of the magnetic moment distribution in the core of the wire by means of computer simulations. To simulate the magnetization process of the deformed wire, the total energy is taken as a function of five variables. Three of these correspond to the nucleation at two ends and at the middle of the wire while the remaining two represent the domain wall locations in the two regions. The simulation traces the gradient in the six dimensional energy landscape to find the set of coordinates, which, for a given value of external field, minimizes the total energy. Magnetization makes a jump to another stable position when the total energy loses its local minimum in the landscape. Since in general there are more than one energy minima along the entire process, a magnetic hysteresis occures. The total energy of the system is taken as the summation of mutual magnetostatic interactions along all the domains, Zeeman energy, and the anisotropy energies. Exchange interactions are taken into accound by assuming the domain wall motions along the wire. When the deformation created in the middle of the wire is represented by just an anisotropy field, but no nucleation allowed, the upper and lower halves of the calculated loop is shifted symmetrically to the right and to the left respectively, with horizontal stretch lines in the two directions. The horizontal lines result from the energy barrier created by the local anisotropy field in the middle. Although the great simplicity of this structure, it reveals the response mechanism of the wire beyond a certain threshold of deformation; no change in the hysteresis occurs before the threshold is reached. When the wall motion starts at a point around the deformation, and nucleation mechanism occurring at the deformed part and at the ends is taken into account, the same staircase character in the hysteresis loops is obtained as the experimental ones. The ends and the deformed part of the wire act as pinning sites. Keywords: Amorphous wire, deformation, hysteresis, ferromagnetic
The Kropina change of the projectively flat Randers metrics
Get PDFboyutlu bir manifoldu üzerinde bir Riemann metriği ve bir diferansiyel form olsun. aralığında sınıfından koşulunu sağlayan pozitif bir fonksiyon olmak üzere, fonksiyonunu göz önüne alalım. Herhangi bir için ise, fonksiyonu bir Finsler metriği oluşturur. Bu şekilde tanımlanan Finsler metriklerine metriği adı verilir. alınırsa metriklerinin özel bir sınıfını oluşturan Randers metriği elde edilir. ve , sırasıyla, ve metriklerine sahip iki Finsler uzayı olsun. ile tanımlanan metrik dönüşümüne bir Kropina dönüşümü denir (Singh, Prasad ve Kumari, 2003). Özel olarak, bir Riemann uzayının metriği olarak alınırsa, , bir Kropina uzayının metriğine indirgenmiş olur (Shen, 2001). Bu çalışmada, öncelikle aralarında bir Kropina dönüşümü tanımlı olan iki Finsler uzayının sprey katsayıları arasındaki ilişki elde edilmiştir. Daha sonra, bir Randers metriğinin projektif düz olması için gerek ve yeter olan koşulların, bu ilişkide kullanılması ile “projektif-düz bir Randers uzayını, projektif-düz bir Finsler uzayına dönüştüren Kropina dönüşümü” için gerek ve yeter koşul elde edilmiş ve bu koşul altında Finsler dönüşüm uzayının skaler flag eğriliği elde edilmiştir. Anahtar Kelimeler: Kropina dönüşümü, Randers metrikleri, -eğrilik, flag eğrilik, skaler flag eğrilik.Let M be a manifold. A function satisfying the following properties is called a Finsler metric: a) F is on b) for any , is a Minkowski norm on . The pair (M,F) is called a Finsler space. Let be a Riemannian metric and be a differential form on an dimensional manifold . Consider the function where is a positive function on and satisfying. Then, is a Finsler metric if for any (Shen Z., 2001). If then F becomes Randers metric. Every Finsler metric and the spray coefficients of induce a spray which determines the geodesics of M (Shen Z., 2001, Abate and Patrizio, 1994). And the spray coefficients of are . A geodesic on a Finsler space is given by the differential equation A Finsler metric on an open subset is projectively flat if and only if it satisfies the following system of equations (Rapcsák, 1961). In this case, the spray coefficients of are , where is given by. The scalar function is called the projective factor of . The Riemann curvature of a manifold with a Berwald connection is defined by For a tangent plane containing the flag curvature is defined by , where such that . If (a scalar function), is said to be of scalar flag curvature. If , is said to have a constant flag curvature (Bao and Robles, 2004, Shen Z., 2004). The transformation of the Finsler metric given by is called a Kropina change. If is a metric function of a Riemannian space, then reduces to the metric function of the Kropina space. In this work, a Kropina change of the metric function given by between projectively flat Randers space with metric and the Finsler space with metric is studied and it is proved that the Finsler space is projectively flat under a Kropina change if and only if the differential equation is satisfied. Next, it is shown that for a Kropina change between a projectively flat Randers space and a projectively flat Finsler space, the scalar flag curvature of is. Keywords: Kropina change, Randers metrics, -curvature, flag curvature, scalar flag curvature.
Effect of vortex generators to the flow around circular cylinder
Get PDFDairesel silindir etrafındaki akım, son derece karmaşık yapısı ve mühendislik uygulamalarında sıkça karşılaşılan bir akım tipi olması nedeniyle, yaklaşık bir asırdır hidro-aerodinamik alanda araştırmacıların temel konularından birisi olmuştur. Öte yandan, sınır tabaka ayrılması özellikle dolgun cisimler etrafındaki akışı değiştirerek büyük miktarda enerji kaybına yol açan bir olaydır. Buna bağlı olarak, hidro-aerodinamik pek çok aracın performansı akım ayrılmasının yeri tarafından kontrol edilmektedir. Akım ayrılmasının engellenmesi ya da geciktirilmesi için kullanılan en etkili yöntemlerden biri pasif girdap yaratıcılardır. Girdap yaratıcılar, neden oldukları sınır tabaka içine gömülen girdaplardan dolayı oluşan makro ölçekteki hareketler ile duvar yakınındaki akışın yeniden düzenlenmesini sağlamaktadır. Çalışmadaki amaç, girdap yaratıcıların dairesel silindir etrafındaki akışa ve girdap oluşma mekanizmasına olan etkilerinin deneysel olarak ortaya konmasıdır. Çalışmada, dairesel silindirin yakın iz bölgesi DPIV ile görüntülenmiştir. Deneyler, Newcastle Üniversitesi Emerson Kavitasyon Tüneli’nde gerçekleştirilmiştir. Çalışmada, 1.6 mm yüksekliğinde, akış yönüne ±10 derece açı yapacak şekilde kullanılan girdap yaratıcıların silindir çevresine dört farklı açıda yerleştirildikleri vakalar ve girdap yaratıcı içermeyen yalın silindir vakası yer almaktadır. Çalışmadaki Reynolds sayısı 41300 ve buna karşılık gelen silindir akış rejimi ise kritik-altı rejimdir. Ölçümlenen akış alanlarının analizi, Reynolds Ayrıştırması ve POD olmak üzere, iki ayrı türbülanslı akış alanı ayrıştırma tekniği ile gerçekleştirilmiştir. İz bölgesindeki girdaplılık, gerilme dağılımı, salınım frekansı gibi pek çok akış özelliği ortaya konmuştur. Yalın silindir vakası için yapılmış olan ölçümler literatür ile karşılaştırılmıştır. Girdap yaratıcıların etkisi, vakaların kendi aralarında ve yalın silindir ile karşılaştırmaları ile belirlenmiş, sonuçlar tartışılmıştır. Anahtar Kelimeler: Dairesel silindir etrafındaki akış, girdap yaratıcılar, DPIV. Flow around a circular cylinder has been one of the basic research subjects in hydro-aerodynamics area in almost a hundred years. Related to its complex flow characteristics there are many aspects that make this topic most interesting including surface curvature of the cylinder, severe adverse pressure gradient, massive flow separation, oscillation of the separation point, unstable wake and hence vortex shedding, high sensitivity to free stream properties, aspect ratio, blockage, vortex street formation and completely variable flow pattern between flow regimes. Besides, boundary layer separation causes large energy losses especially by changing the flow pattern around bluff bodies. Accordingly, the performance of many hydro-aerodynamic vehicles is controlled by the location of the separation point. Thus, besides the importance of the separation control as a basic research subject, it can be regarded as an important engineering problem. One of the most effective methods used for preventing and delaying flow separation is the use of passive vortex generators. The macro scale motions of the vortices embedded in the boundary layer caused by the vortex generators provide over tuning of the flow in the vicinity of the wall. Thus, two important subjects of the fluid mechanics are considered in this study. The aim of the study is to experimentally investigate the effect of the streamwise vortex generators on the flow around circular cylinder and vortex formation mechanism. Wake oscillations of the circular cylinder and vortex shedding is visualized with digital PIV system which is the most suitable measurement system for determination of the general flow topology such as vortex structures and stress distribution. The experiments are conducted at Emerson Cavitation Tunnel, School of Marine Science and Technology, Newcastle University. The study consists of five cases including bare cylinder and four cases with vortex generators in which the generators are located at 50, 60, 65, and 70 degrees angles from the first stagnation point. The bare cylinder and vortex generators cases are coded as VG0000, VG1650, VG1660, VG1665, and VG1670, respectively. Vane type vortex generators which are 1.6 mm in height are paced with ±10 degrees sweep angles on the cylinder. The Reynolds number investigated is 41300, which corresponds to the sub-critical flow state. All the measurements were conducted at the midspan of the cylinder and the measurement area according to the cylinder diameter was 2.6Dx0.9D, in X and Y directions, respectively. The free stream velocity was 0.588 m/s and the inlet turbulence intensity and turbulence length scale of the free stream at this velocity were 1.73% and 0.22D, respectively. The analysis of the flow fields extracted from the PIV images are processed with two different turbulent flow field decomposition techniques including Reynolds decomposition, and Proper Orthogonal Decomposition (POD). The flow properties such as vorticity, stress distribution and oscillation frequency are derived from the analysis. The results of the measurements conducted for the bare cylinder are compared with the data in the open literature. These indicate that the results are in good agreement with the results of the similar studies in literature. Experimental results show that the vortex generators highly affect the near wake and hence the boundary layer of the cylinder. First of all, Reynolds averaged flow fields indicate that the shear layers get closer to each other, bend towards the centerline, and the width of the near wake decreases. These events clearly indicate that the flow separation is delayed on the measurement plane. One can observe that the vortex formation length and the wake closure length are increased considerably with the downstream motion of the separation location as shown in the literature. The amount of the global mean circulation in the flow fields is also increased because of the vortex generators while the width of the shear layers is decreased. The more concentrated pattern of the shear layers provide the vortex formation process to occur at a longer distance from the cylinder. It is expected that the increase in the vortex formation length causes the low pressure area behind the cylinder to move with the vortices and hence decreases the suction at the rear side of the cylinder. With the displacement of the shear layers towards the wake centerline and the thinning of the shear layers, the Strouhal number is increased approximately 41% at VG1650, and then is decreased slowly probably due to the reduction of strength of the forming vortex. It is obvious that the strength of the stresses due to both turbulent and coherent motions decreases because of the vortex generators. Keywords: Flow around circular cylinder, vortex generators, DPIV.
Zorlama etkisi altındaki yalpa hareketinin çekirdek güvenli bölgeleri
Get PDFRolling motion of the ship has always been popular subject of the researchers. The reason for this can be IMO rules or the present IS (Intact Stability) code of the ships is based on the rules which are not based on rational reasoning and which was accepted 30 years ago or rolling motion of the ship could not be explained completely by researchers. Although the ships especially the small ships such as fishing vessels and research vessels ensure IMO stability criteria or the present IS code, they could still capsize due to combined environmental effects. The present stability criteria are insufficient because the rules are only based on the static stability at calm water and they do not include any effect of nature of the sea and dynamic response of the ships directly. Thus, IMO should renew its rules to include dynamic effects. Oscillatory sudden capsizing, oscillatory symmetric and anti-symmetric build-up capsizing can not be explained by present stability criteria. Only non-oscillatory capsizing can be explained by current rules. In this study, the kernel safe basin concept was presented to improve the present stability criteria. Kernel safe basin is the smallest safe basin in the roll angle and roll angular velocity phase space. If the ship is stable or not in a dangerous situation, there is no erosion at kernel safe basin of the ship. The condition which causes erosion at kernel safe basin more than an agreed amount can be named as dangerous situation. The boundary of kernel safe basin is determined by using the Lyapunov function of the non-excited roll motion and defines a reserve energy level. The maximum roll angle of the kernel safe basin is dependant on the working environment of the vessel. In this study, it was assumed to be 25ofor external excitation case and 20o for parametric excitation case. However, kernel safe basins that have different sizes, were also investigated in the PhD. Thesis. Although the rolling motion is strongly coupled with sway and yaw motion, in this study it was assumed to be uncoupled with other ship motions by defining roll center. The uncoupled roll motion was examined by using the integrity curves which show the amount of erosion occurred at kernel safe basin under the influence of external and parametric excitation. In this study, the importance of damping moment, excitation amplitude, excitation frequency and bias angle on the stability of the ships were shown from the investigation of the uncoupled rolling motion under external excitation. Increment of damping moment caused to decrease the risk of capsizes. Thus, the ship could survive or operate for rougher waves. Both increment of wave height (excitation amplitude) and bias angle caused to increase the erosion occurred at kernel safe basin. Thus it could be said that the ship should operate at smaller waves when the bias exists. When excitation frequency to natural frequency ratio is around 0.8, the maximum erosion occurred at kernel safe basin. Thus it can be concluded that main resonance case is the most critical case for safety of vessel in beam seas. While examining the protection of kernel safe basins under the influence of parametric and external excitation, the ratio of metacentre height variation of the ship was assumed to be function of the heading angle and the ratio of the component of wave length in the direction of ship heading to ship length. In addition, it was assumed that there was constant wind effect while modeling rolling motion. The results showed that the small increment of metacentre height (GM) over the value defined by IMO caused the increment of erosion occurred at kernel safe basin for stern quartering waves whereas the waves which come from the stern of the ship with an angle (0o-15o), caused less erosion at kernel safe basin. The small decrement of GM under the value defined by IMO caused to decrease the erosion occurred at kernel safe basin for stern quartering waves whereas the erosion increased for stern waves (0o-15o). If the value of GM is too small than the IMO defined value, both stern and stern quartering waves caused too much erosion at kernel safe basin. However, it should not be forgotten that the encounter frequency and angle are also operational variables (they can take different values by changing the velocity and heading of the ship) for following seas so in the evaluation of the transverse stability of the ships not only the design factors but also the operational factors should be considered. Keywords: Kernel safe basin, rolling motion, Lyapunov direct method. Gemilerin yalpa hareketi bilim adamları ve araştırmacıların her zaman popüler bir araştırma konusu olmuştur. Bunun sebebi IMO kurallarının ve şu anki mevcut IS kodunun rasyonel temellere dayanmayan ve en az 30 yıl önce kabul edilmiş kurallara dayanması, ya da yalpa hareketinin araştırmacılar tarafından tamamıyla açıklanamamış olmasına bağlanabilir. Bu konu üzerine çalışma yapmamızın sebebi de mevcut IS kodunu geliştirilmesine bir katkı sağlamaktır. Bu makalede, gemilerin enine stabilitesinin matematiksel yöntemlerle irdelenmesinde yeni bir yaklaşım olarak "çekirdek güvenli bölge kavramı" ortaya çıkarılmıştır. Çekirdek güvenli bölge, yalpa açısı ve yalpa açısal hızından oluşan faz uzayındaki sağlanması gereken en küçük güvenli bölgedir. Bu bölgenin dış sınırı zorlanmamış yalpa hareketinin Lyapunov fonksiyonu kullanılarak belirlenmektedir. İzin verilen en büyük yalpa açısı ise geminin çalışma koşullarına bağlı olarak çıkartılmaktadır. Çekirdek güvenli bölgenin belli bir miktardan fazla erozyona uğraması, geminin stabilitesinin büyük bir tehlike içerisinde olduğu anlamına gelmektedir. Dışarıdan ve parametrik zorlama etkisi altında, rüzgar ve sönüm kuvvetlerinin çekirdek güvenli bölgenin büyüklüğü üzerindeki etkileri gösterilmiş ve geminin çalışma koşullarına bağlı olarak stabil olup olmadığı ortaya konulmuştur. Karşılaşma frekansı doğal frekans civarında olduğu zaman en tehlikeli durumlar gözlemlenmiş, sönümün arttırılması geminin devrilme olayının daha büyük dalgalarda oluşmasını sağlamıştır. Ön meyil açısının arttırılması ise daha küçük yükseklikli dalgaların tehlikeli hale gelmesine yol açmıştır. Kıç omuzluktan gelen dalgalarda enine metasantr yüksekliğinin IMO tarafından belirlenen sınırın biraz üzerine çıkarılması, kıçtan gelen dalgalarda ise enine metasantr yüksekliğinin sınırın biraz altına indirilmesi geminin devrilme riskini arttırmıştır. Anahtar Kelimeler: Çekirdek güvenli bölge, yalpa hareketi, Lyapunov Direkt Yöntemi.  
Improving TNFGN velocities via utilizing time series analysis of continuous GPS stations
Get PDFKampanya tipi GPS gözlemleri kullanıcıya elindeki alıcı sayısından daha fazla sayıda noktada gözlem yapma imkânı vererek ölçü bölgesinin daha yüksek konumsal çözünürlükle izlenmesine olanak sağlamaktadır. Diğer taraftan, kampanya tipi veriler zamansal olarak seyrektirler ve küçük sıçramaları tespit edemeyecek kadar yetersizdirler. Sabit GPS noktasında toplanan sürekli GPS verileri ile yer kabuğu hareketlerine yönelik kinematik modelleme çalışmalarını gerçekleştirmek mümkün olabilmektedir. Bu çalışmada; sabit GPS istasyonları zaman serileri analizi ile hesaplanan periyodik etkilerin TUTGA hızlarına düzeltme olarak getirilerek daha gerçekçi hıza ulaşılması için bir yaklaşım önerilmiştir. Verileri herkese açık 6 sabit GPS istasyonundan elde edilen veriler GAMIT-GLOBK yazılımı ile değerlendirilerek zaman serileri analizine hazır hale getirilmiştir. EBOK analizi ile seçilen istasyonlara ait en uygun modelin Beyaz Gürültü ve Kırpışma Gürültüsünün birleşimi olduğu görülmüştür. Zaman serileri içindeki anlamlı sinyallerin frekanslarını ve genliklerini istasyon bazında hesaplamak amacıyla GPS zaman serilerine, boşluklu veriler için oldukça uygun bir yöntem olan Lomb-Scargle algoritması uygulanmıştır. Tüm istasyonlarda ortak olarak senelik ve altı aylık etkilerin baskın olduğu tespit edilmiştir. Böylece, TUTGA hızlarına düzeltme olarak getirilecek periyodik etkilerin hangilerinin modelleneceğine karar verilmiştir. Senelik ve altı aylık etkilerin, TUTGA hızlarına nasıl ilave edilebileceğine dair bir algoritma geliştirilerek, hız alanının iyileştirilmesi için bir yöntem önerilmiştir. Çalışmadan elde edilen sonuçlara ilişkin bir değerlendirme yapılarak, Türkiye genelinde ve bölgesel olarak nasıl uygulanabileceğine ilişkin yatay ve düşey hızlar için bir değerlendirme yapılmıştır. Anahtar Kelimeler: Sabit GPS, zaman serileri analizi, spektral analiz, TUTGA.Campaign type GPS measurements provide higher resolution spatial monitoring of region by supplying to the observer more station than of his receiver number. On the other hand, campaign type measurements return baseline measurements with very coarse temporal sampling. This may not be a major problem for studying only slow, steady interseismic deformations, but changes in this behavior which occur over timescales less than the separation in observations will be missed by field campaigns. It is possible to make geodetic and geodynamic calculations, carry out kinematic modeling of crustal movements via using continuous GPS measurements obtained from CGPS stations. In this study, an algorithm is investigated to receive more accurate velocity field and improve velocity obtained from campaign type GPS measurements by adding corrections to the velocities via utilizing time series analysis of continuous GPS stations. Another important usage of velocities is the densification of geodetic networks. According to the Big Scale Mapping Guide, velocities of C1 and C2 points are produced using TNFGN velocities via interpolating at related sites. Thus, obtaining accurate and reliable velocities at networks like TNFGN becomes essential. In the event that TNFGN velocities are evaluated from campaign type measurements, it is more than normal to encounter errors at densification networks due to error propagation rule. Public data of Ankara, İstanbul, Trabzon, Mersin, Gebze and Antalya stations is used as test measurements.13 ITRF stations are included to the processes for realization of datum in ITRF2000. GPS processes were done by GAMIT-GLOBK software and time series are created in ITRF2000. Also, outliers were removed at this stage. Pope test was applied to the time series and they became ready to time series analysis. Time series of related stations are prepared by completing the GPS process until the beginning of the year 2006 that constitutes the scope of this study. As with many other geophysical phenomena, noise in GPS position time series can be described as a power law process. Maximum Likelihood Estimation (MLE) was applied to investigate stochastic noise properties of GPS time series. Time series were tested by different noise models and a combination of white noise+flicker noise was found best describing model. In case only white noise model used, in other words using solely Least Squares Adjustment, uncertainties would be underestimated 7 times at north and east component and 8 times at up component. Missing values cause gaps in what otherwise would be evenly sampled data, and an even sampling may sometimes be impossible in the first place, for technical reasons. When Fourier analysis is used, and some data points are missing, they have to be provided in a more or less arbitrary way. The Lomb-Scargle algorithm has several computational advantages over more common approaches, such as Fourier analysis, including direct treatment of missing values and an estimate of a false discovery rate. Lomb-Scargle algorithm which is suitable for unequally spaced time series was applied to investigate the amplitudes and frequencies of dominant signals on a station by station basis. Seasonal signals are a potentially important part of the error budget for continuous GPS sites. Annual and semi-annual signals were determined dominant common to all sites. Thus, these periodical signals were chosen to be brought as corrections to TNFGN velocity field. An algorithm is suggested on how to apply annual and semi-annual effects in order to improve both deformation measurements and TNFGN velocities. Firstly, annual and semi-annual quantities derived from spectral analysis of all three components of continuous GPS stations, are interpolated at selected grid points. Periodic effects related to north and east component found inadequate for modeling throughout Turkey. Instead, it is proposed to use the horizontal periodic effects in an area of 10-20 km around the CGPS station. Annual and semi-annual periodics of vertical component are found convenient for interpolating at grid points. After obtaining the measurement epochs of TNFGN sites, corrections are computed at those related epochs. Finally, after adding corrections to coordinates, new velocities are obtained. New velocities are found consistent with the velocities that are derived from a complete time series analysis. An assessment is given to evaluate the results obtained from this study on how to apply both locally and in the vicinity of Turkey for horizontal and vertical velocity fields. Keywords: Continuous GPS, time series analysis, spectral anaysis, TNFGN
DEM (Digital Elevation Model) production from 1:16.000 scale aerial photographs and accuracy modeling
Get PDFHava fotoğrafı ve uydu görüntülerindeki veriler, çok uzun zamandır klasik yollarla ve operatörler tarafından elle çizilmekteydi. Bilgisayar teknolojisi ve dijital görüntü işleme alanlarındaki gelişmeler, günümüzde bu işlemlerin otomatikleşmesine olanak sağlamaktadır. Otomatikleşmenin hedefi hızı arttırmak ve değerlendirme masraflarını azaltmaktır. Bu kapsamda fotogrametri alanında otomatikleşmenin büyük oranda sağlandığı işlemlerden birisi de Sayısal Yükseklik Modeli (SYM) üretimi olmuştur. Bununla birlikte otomatik yöntemlerin doğruluklarını artırmak amacıyla birçok çalışma yapılmasına rağmen, birçok alanda klasik yöntemlerin doğruluklarına ulaşılamamıştır. SYM üretiminde klasik yöntem olan fotogrametrik değerlendirme ile eş yükseklik eğrilerinin çizimi ve otomatik yöntem olan görüntü eşleme ile SYM üretimi ve doğruluklarının araştırılması konusunda çeşitli çalışmalar yapılmıştır. Ancak bu çalışmalarda elde edilen sonuçlar kullanılan kaynak veriye, üretim yöntemine, topoğrafik özelliklere, üretilen SYM’nin çözünürlüğüne ve karşılaştırmada kullanılan referans veriye göre farklılık göstermektedir. Bu çalışmada iki farklı bölgede (Bursa ve Ankara) 1:16.000 ölçekli hava fotoğrafları kullanılarak fotogrametrik değerlendirme ile üretilen eş yükselti eğrilerinden ve otomatik görüntü eşleme ile SYM üretimi yapılmış ve her iki yöntem doğrulukları bakımından karşılaştırılmıştır. Çalışmanın ikinci aşamasında Bursa bölgesinde üretilen SYM kullanılarak SYM doğruluğu eğim ve çözünürlüğe göre modellenmiştir. Model olarak birinci ve ikinci dereceden bir polinom seçilerek, polinom katsayıları dengeleme ile hesaplanmıştır. Elde edilen sonuçlar, SYM doğruluğu ve çözünürlüğün büyük oranda korelasyonlu olduğunu, SYM çözünürlüğündeki düşüşle beraber SYM doğruluğunda da düşüş gerçekleştiğini göstermiştir. Anahtar Kelimeler: Sayısal yükseklik modeli, otomatik görüntü eşleme, hava fotoğrafları.Aerial photographs and satellite imagery have been evaluated manually by the operators for a long time for the extraction of the vector data. Computer technology and digital image processing technologies have been developed and this development provides to perform these extraction processes automatically or semi-automatically. The aim of making the processes automatic is to increase the speed of collecting the data and to reduce the cost. Digital elevation model production has been one of the most automated process of photogrammetry. Although, formats and accuracy for some formats of digital elevation models are standardized, data sources, quality of data sources and production methods of digital elevation models to provide or improve the standards are not determined clearly. Nonexistence of standards and production criteria causes loss of time and money and production of digital elevation models without known standards and accuracies. Also these nonstandard productions cause data loss of digital elevation models which are needed dense work and source. Many researches are made about the production of digital elevation models from different data sources and with different methods. In all of the studies, digital elevation models having different resolutions and data sources are produced and the accuracies of digital elevation models are investigated. The results of these studies vary according to the source data, resolution, ground control point distribution, production method, topography and reference data for the accuracy assessment. On the other hand, the accuracies are investigated in these studies, but the duration of digital elevation model productions are neglected generally. This situation prevents the optimization of production. Photogrammetry provides the most frequently used data sources and techniques for generating digital elevation models (Stocks & Heywood, 1994), either by direct generation of digital elevation models or indirectly via its use in topographic mapping for production of contour lines. Photogrammetry either involves stereoscopic techniques for interpretation of aerial photography or digital image correlation applied to aerial photographs. In this study, digital elevation models are produced by automatic image matching from 1:16.000 scale aerial photographs and the accuracies of digital elevation models are assessed. Also digital elevation models are produced from contour lines compiled from the same sources. Optimum data collection interval and accuracy of digital elevation models are investigated. Automatic image matching and photogrammetric compilation methods for digital elevation model production are compared. Accuracies are also investigated according to the resolution of digital elevation model and slope of topography. Some solutions are suggested for the areas having high errors. Two different test regions are used for the study. First region is Gölbaşı near Ankara. Gölbaşı is a test region used for different purposes for aerial photography. 40 1:16.000 scale aerial photographs of the region were taken in 2002. Second region is an area at the proximity of Bursa. 1:16.000 scale aerial photographs of the region were taken right after the 1999 Gölcük Earthquake. Five meter interval contour lines were compiled from stereo models for Gölbaşı region. First digital elevation model was produced from these contour lines. At the second stage, a digital elevation model was produced from the same area by automatic image matching. These digital elevation models are compared with 27 check points which are measured at the field by GPS. Root Mean Square Error (RMSE) of the digital elevation model produced from contour lines is found to be 0.61 meter. RMSE of digital elevation model produced by automatic image matching is found to be 2.98 meters. Five meter interval contour lines were compiled from stereo models for Bursa region also. Nine digital elevation models with the resolutions changing from 1 meter to 256 meters were produced from the contour lines. Digital elevation models are compared with 25 meter interval main contour lines which were compiled more precisely. RMSE of the digital elevation model is found to be 0.61 meter. Also the accuracies of digital elevation models changing with the resolution of digital elevation model and slope of topography are tried to be modeled with a polynomial equation. The results showed that the accuracy is correlated highly with digital elevation model resolution. Keywords: Digital elevation model, automatic image matching, aerial photographs
The moderating effects of technology-based interactions on the service provider-customer relationships
Get PDFİlişki Odaklı Pazarlama (İOP), işletmelerin birbirleri, tedarikçileri ve müşterileri ile işbirliği yaparak, karşılıklı ekonomik değeri artırmak, maliyetleri düşürmek için geliştirilen programları uyguladıkları bir süreçtir. İOP günümüzde perakende, servis tüketicileri için de araştırılmakta olup, özellikle servis yoğun sektörlerde işletmeler İOP stratejilerini uygulayarak, uzun dönemde daha çok getiri sağlayacak müşterilerini tanıyıp onları korumayı, onlarla ilişkilerini daha güçlü ve karlı hale getirmeyi amaçlamaktadırlar. Bu amaçla, bilişim ve iletişim teknolojilerindeki gelişmelerden yararlanılarak müşterilere teknoloji tabanlı telefon, cep telefonu ve İnternet gibi farklı hizmet kanalları ile ulaşılmaktadır. İOP programlarının nasıl algılandıklarını araştıran, bu amaçla yakınlık kalitesi, yakınlık memnuniyeti gibi değişken yapılarını test eden çalışmalar bulunmaktadır. Ancak bu çalışmalar daha çok ilişkilerin yüz yüze geliştiği ortamlarda gerçekleş-tirilmektedir. Bankacılık sektöründe teknoloji kanalları sıklıkla ve başarılı uygulamalar ile kullanılmakta, düşük maliyetleri nedeniyle müşteriler bu kanalları kullanmaya özendirilmektedirler. Araştırmanın amacı, tüketicilerin, bankacılık işlemlerini gerçekleştirmek için kullandıkları teknoloji hizmet kanallarının, bankalarına duydukları yakınlığı nasıl etkilediğini irdelemektir. Bir anket çalışması sıklıkla belli bir teknoloji hizmet kanalını kullanan bireysel bankacılık müşterilerinden veri toplanmıştır. Kullanılan model İOP kuramına, tüketicilerin teknoloji kanallarında gerçekleştirdikleri bankacılık işlemlerinin performansını nasıl algıladıklarını ölçen yeni bir yapının eklenmesi ile geliştirilmiştir. Çalışma sonuçları modeli büyük oranda desteklemekte, teknoloji hizmet kanallarının ilişki kalitesi algılamasını olumlu yönde etkilediği sonucu ortaya çıkmaktadır. Anahtar Kelimeler: İlişki odaklı pazarlama, teknoloji tabanlı hizmet kanalları, ilişki kalitesi, tüketici davranışı.Relationship Marketing (RM) is defined as engaging in cooperative and collaborative activities with business partners and end-user customers to create or enhance mutual economic value at reduced cost. RM, initially applied between companies, is currently being applied to consumer markets and is studied both theoretically and practically. In service sectors especially, companies use RM strategies to know their customers that would provide long-term profits, to retain them and to enhance relationships. Advances in information and communication technologies are used for that purpose to analyze and predict customers' needs and to develop strategies. From consumers' perspective, relationship quality and relationship satisfaction are the constructs that are developed and studied to understand how consumers perceive RM programs. Relationship quality has had the greatest influence on relationship outcomes, such as objective performance and has been used as a key relational mediator, comprising of the dimensions of trust, commitment and relationship satisfaction. The RM research studies have usually been realized within the context of customer-service provider relationships where face-to-face interactions take place. Today companies use technology to reach their customers via phone, mobile phone, and the Internet. Banks use these technologies most frequently and successfully. The purpose of this study is to understand how the relationships that customers feel towards their providers are affected when service is delivered via technology-based channels and how customers feel when they use technology-based channels. The research involves application of a questionnaire to bank customers in general. More specifically, bank customers that use a particular technology-based service channel to realize their banking operations are randomly selected to form a sample. The model is tested using Structural Equation Modelling with software AMOS V7. The dependencies between several concepts, the existence of a multi-order construct like relationship quality necessitated the use of multivariate analysis. The model uses a widely studied notion that the relational mediator, relationship quality, affects relationship commitment, or loyalty as a relationship outcome. The two constructs preceding relationship quality are technology-based service media characteristics and the perceived performance of interactions on these media, in marketing terms, service channels. The two constructs are mainly designed to measure the critical factors of technology-based service channel usage and the drivers of perceived performance of such interactions. The results of the study confirm the majority of the research hypotheses proposed and that technology-based service interactions do not deplete the relationship quality perceived by banks customers. The ATM users and internet users perceive medium characteristics of technology-based options at differing levels. ATM users perceived privacy, security and interactivity more important compared to internet users, who perceive personalization and efficiency as more important. ATM users also perceive interactivity characteristic as higher in importance which could be related to their need to be directed by a friendly and interactive screen while realizing their operations. Internet users, however, perceive personalization and efficiency as more important. Service firms must prepare personalized screens and messages in order to increase their customers' commitment to their relationships. Efficiency is an important characteristics that both ATM users and internet users perceive as effective in their sense of relationship. In order to do that banks can provide user friendly interfaces that include easy to understand commands, simple to follow menus and sequencing of operations. Perceived trust in technological competence of service provider is an important variable in consumer's perception of higher performance and relationship quality. Service providers can offer new technology-based channels after verifying that consumers can reliably perform their operations. Service failures are the most important and critical incidents that service firms should handle with care. Perceived cooperation to use technology-based mediums is also effective in assessing performance of technology-based interactions. Service firms can use alternative methods so that they can serve their customers to install the necessary equipment for using technology-based channels at an advantage. Keywords: Relationship marketing, technology-based service channels, relationship quality, consumer behaviour
Stochastic modeling of inventory control problem in a distribution network and verification of the model
Get PDFBu çalışmanın amacı, bir dağıtım ağı için çok dönemli sipariş büyüklüğü belirleme problemi için bir stok yönetim modeli oluşturulması ve oluşturulan bu modelin benzetim ile doğrulanmasıdır. Çalışmada, merkezi bir depo ve N adet bayi ile çalışan iki aşamalı bir dağıtım ağında tüm yönetimin tek bir merkezden gerçekleştirildiği bir stokastik stok yönetim sistemi ele alınmıştır. Bayiler malları doğrudan ve yalnızca bir dağıtıcıdan karşılarken, dağıtıcı stoklarını dış bir tedarikçiden yenilemektedir. Ulaştırma kaynakları kısıtlardan dolayı tüm üyelerin dönemsel stok takibi yaptığı ve planlama süresinin tüm üyeler için aynı olduğu kabul edilmiştir. Stok bulundurma maliyetleri zamana bağlı olarak hesaplanmaktadır. Karşılanamayan tüm talepler daha sonra karşılanmak üzere bir bekleme listesine alınmakta ve hem zamana, hem de karşılanamayan talep sayısına bağlı olarak maliyetlendirilmektedir. Bayilerde ve depoda bulundurulan stok miktarı bir üst sınır seviyesi ile kısıtlanmıştır. Bayiler aynı maliyet yapılarına ve stok yenilenme dönemlerine sahiptirler fakat farklı talep ve maliyet parametrelerine bağlı olarak benzer olmadıkları düşünülmüştür. Varsayılan bu sistemin modellenmesi, sistemin bayi, dağıtıcı ve ulaştırma olarak belirlenen üç ayrı bileşeninin önce ayrı olarak ele alınması ve ardından ortak kısıtlar ve değişkenler aracılığıyla merkezi sistem için bütünleştirilmesi yoluyla yapılmıştır. Daha sonra geliştirilen bu modelin doğruluğu deneylerle gösterilmiş ve sunulan modelin varsayımların önerdiği sistem için geçerliliği kesikli benzetim kullanılarak incelenmiştir. İstatistiki testler modelin varsayılan sistemi yansıtma başarımının yüksek olduğu ve varsayılan sistemin iyileştirilmesi için kullanılabileceğini göstermiştir. Anahtar Kelimeler: Stok yönetimi, dağıtım ağı, kesikli benzetim.We focus on a multi period stochastic lot sizing problem in a two-echelon distribution network which operates under a Push Control System (PCS). The PCS is an integrated inventory control system for the supply chain, in which the supplier decides on the appropriate inventory levels of each product and on the inventory policies to maintain these levels. The main assumption of the push control system is centralized control and availability of end-item demand information. Suppliers monitor retailers? inventory levels in order to decide order quantities, shipping and timing of replenishment orders. A push control system allows chain members directly benefit from minimization of distortion of demand information (known as the bullwhip effect) which is transferred from downstream supply network members to upstream members (Çetinkaya and Lee, 2000). As a result, it becomes possible to reduce the stock out situations and inventory carrying costs, while increasing the customer service levels. Moreover, centralization of inventory decisions provides a reduction in the variability of system parameters, so makes it possible to deal with time varying demand without much complexity. Existing methods for the evaluation of periodic review, two-echelon policies are usually developed for systems with lead times of integer multiples of periods. This study is concerned with a system where review periods are longer than the replenishment lead times, in other words lead times are multiples (not necessarily integer) of period lengths. In such a case, determination of the order-up-to levels is not only dependent on demand distribution over lead times but also expected inventory levels through the period. Also, inventory carrying costs are charged not on the ending inventory levels of periods but on the average inventory levels of the periods. We assume two types of backorder costs: (1) per unit short, and (2) per unit short per time. When considering the two-echelon situation, we include transportation costs in terms of unit variable transportation costs and fixed batch costs for flow of the products from warehouse to retailers. We study a two-echelon distribution inventory system with a single central warehouse and N retailers. Retailers directly order from the warehouse to replenish their stocks where warehouse replenishes its stock from an outside supplier. All facilities follow a periodic inventory order policy where the length of planning periods are the same for all retailers as well as at the warehouse. We analyzed the retailer, warehouse and transportation components and combined them in to a total system model by system constraints and use of common variables. We developed a simulation model to test the mathematical model. The statistics of interest are determined as: retailer(s)' average inventory level, warehouse's average inventory level, retailer(s)' average backorder level, average number of backorders, and total system cost. The simulation is run 80 times for 20 periods for each experiment and mean and standard variation values of the selected statistics are collected. These values are then compared to the values determined by the mathematical model. The results show that the representation of given periodic review system by mathematical model is acceptable, since mathematically obtained values of most of the given variables are in acceptance region with a 5% type I error, which corresponds to a 95% confidence interval. This model can be used for estimation of cost figures and effects of changes in system parameters by a "what-if analysis" in similar practical situations. Moreover, it can be used in an inventory control optimization problem to determine the optimal lot sizes under given assumptions. The contribution of the study is the novel mathematical model structure which is suitable for handling systems with both longer and shorter lead times than the period length. The model captures the complex cost structures like piecewise linear transportation costs, fixed costs, inventory holding costs, and two types of shortage costs. We present different formulations for obtaining expected values of the parameters depending on the parameter characteristics and assumptions. For example, the expected number of back-orders is evaluated by the distribution of the demand during lead times of retailers and distributor plus the period length. Also, developed model is comprehensive in means of cost parameters handled and it can be easily simplified according to the needs of the business environment. Keywords: Inventory control, distribution network, discrete simulation
Lipase-catalyzed production of Human Milk Fat Substitutes (HMFS) containing gamma-linolenic acid
Get PDFAnne sütü yağına benzer yapılandırılmış yağların (YY) bitkisel kaynaklı yağlardan spesifik lipaz enzimlerinin katalizlediği interesterifikasyon (asidoliz) tepkimeleri ile üretilmeleri mümkün olmaktadır. Bu çalışmada gamma-linolenik asit (GLA) ile zenginleştirilmiş anne sütü yağına benzer YY’ların tripalmitin, fındık yağı serbest yağ asitleri (SYA) ve hodan (boraj) yağından elde edilen GLA konsantresi arasında gerçekleştirilen enzimatik asidoliz tepkimeleri ile üretilmesi ve tepki-yüzey yöntemi (TYY) ile reaksiyon koşullarının optimizasyonu amaçlanmıştır. Enzimatik asidoliz tepkimelerinde Rhizomucor miehei’den elde edilen ve bir sn-1,3 spesifik lipaz enzimi olan Lipozyme® RM IM kullanılmıştır. Tepki-yüzey yönteminde seçilmiş farklı faktörlerin etkilerinin incelenmesi ve optimum koşulların belirlenmesi amacıyla, 5 seviyeli Merkezil Bileşik Deney Tasarımı (CCD) kullanılmış ve "substrat mol oranı (Toplam yağ asitleri/Triaçilgliserol, Sr)", "reaksiyon sıcaklığı (T, ºC)" ve "reaksiyon süresi (t, saat)" değişken faktörler olarak seçilmiştir. Reaksiyonlar sonucunda seçilen tepkiler [oleik asit miktarı (%) ve GLA miktarı (%)] için, “çoklu regresyon” ve “geriye dönük eleme” yöntemleri uygulanarak başarılı kuadratik modeller elde edilmiştir. Hedeflenen özellikte ürün (%10 oranında GLA, %45 oranında oleik asit içeren) elde etmek için gerekli optimum koşullar [Sr: 14.8 mol/mol, T: 55ºC ve t: 24 saat] olarak bulunmuştur. Bu koşullarda modelin doğruluğu deneysel olarak da kontrol edilmiş ve çalışma sonucunda bebek beslenmesi ve sağlığı açısından önemli etkileri olan GLA ile zenginleştirilmiş ve anne sütü yağı ile benzer absorpsiyon özelliklerine ve yağ asidi kompozisyonuna sahip bir YY’ın üretimi mümkün olmuştur. Anahtar Kelimeler: Yapılandırılmış yağ, anne sütü yağı, gamma-linolenik asit, enzimatik asidoliz, tepki yüzey yöntemi.Breast milk is the main and most preferred source of nutrients for infants and human milk fat (HMF) is its component which supplies the highest fraction of the infant's required dietary energy. Human milks are characterized by the dominance of triacylglycerols (TAG) (more than 98% of HMF) where the saturated 16-carbon palmitic acid (C16:0) (20-30%) is in the sn-2 position (60-70%) of the glycerol backbone, the sn-1 and sn-3 positions are being taken by unsaturated fatty acids (FA). This unique structure is different from most vegetable oils and animal fats. Previous reports provided convincing information that the higher fatty acid (FA) and calcium absorption and efficient use of dietary energy was the result of this specific position of these fatty acids in triacylglycerol (TAG) moiety. Structured lipids (SL) resembling TAGs of human milk fat can be produced by interesterification from vegetable oils, using sn-1,3 specific lipases as biocatalyst and such TAG can be used in infant food formulations. There has also been a great interest for the supplementation of infant formulas with FA such as gamma-linolenic acid (GLA). In infant formulae, GLA-containing oil, especially borage oil is used for its health benefits and for its antagonist action on arachidonic acid (AA) metabolism. Since GLA is rapidly elongated to di-homo gamma-linolenic acid (DGLA) and subsequently ?5-desaturated to AA and is also cheaper and easier to produce than AA, an alternative way for supplementation of infant formulas with AA is to use GLA instead of highly active AA. Human milk fat substitutes (HMFS) containing GLA can be produced by enzymatic interesterification reactions. These formulae are also helpful where ?6-desaturase enzyme is insufficient. The purpose of the present work was to synthesize SLs resembling HMF enriched with GLA by enzymatic acidolysis reactions between tripalmitin, hazelnut oil FA and GLA in n-hexane. Commercially immobilized 1,3 specific lipase, Lipozyme® RM IM, obtained from Rhizomucor miehei, was used as the biocatalyst for the acidolysis reactions. Moreover it was aimed to model and optimize the reaction conditions via response surface methodology (RSM). For this purpose central composite design (CCD) with five levels and three factors; substrate molar ratio (Total FA/TAG, Sr)", "reaction temperature (T, ºC)" and "reaction time (t, hour)" were used. The reactions were optimized considering target GLA and oleic acid incorporation. Good quadratic models were obtained for the incorporation of GLA (response 1) and oleic acid (response 2) by "multiple regression" and "backward elimination". The determination coefficient (R2) values for the models were found to be 0.92 and 0.94. Based on the experimental results, the regression coefficients and significance (P) values were calculated. Among first order parameters substrate molar ratio had negative effect on the oleic acid incorporation. Time was the most significant first order parameter followed by temperature and substrate molar ratio for GLA incorporation. For both responses, second order parameters, temperature*temperature and time*time had negative effects and were found to be significant. The predicted values obtained from the models had a linear relationship with the observed values which indicates that the generated models adequately represent the relationship between the response and reaction parameters. The optimal conditions generated from the models for the targeted GLA (10%) and oleic acid (45%) incorporation were: 14.8 mol/mol, 55°C and 24 h for substrate molar ratio, reaction temperature and reaction time, respectively. Models were verified using the optimal conditions obtained with RSM. The SL resembling HMFS contained palmitic acid at 73.9 %, which is also close to that of HMF. In this study, a HMFS product containing GLA was successfully produced having both the associated health benefits of GLA and similar fatty acid composition as well as similar absorption characteristics with human milk fat. This SL may be an important ingredient for commercial use in infant formula and contribute to the infant's nutrition and development. Keywords: Structured lipids, human milk fat, gamma-linolenic acid, enzymatic acidolyis, response surface methodology
Comparative analysis of calculation methods in hydraulic design of micro-irrigation laterals
Get PDFMikro-sulama sisteminin temel unsuru olan lateral borular, sistemin tamamında öngörülen üniformluk seviyesi, basınç yükü değişimi ve toplam sürtünme kaybı kriterlerine bağlı olarak tasarlanabilen hidrolik yapılardır. Hidrolik bakımdan lateraldeki akım, mansap yönünde damlatıcı debisindeki azalmayla birlikte, yere bağlı değişken debi fonksiyonunun geçerli olduğu düzenli boru akımıdır. Mikro-sulama sistemi lateral borularının projelendirilmesinde genellikle takip edilen metot, öngörülen damlatıcı özelliği, lateral boru uzunluğu ve boru çapı için, damlatıcı debileri arasındaki değişimin belirli bir sınır değerini aşmamasını sağlamaktır. Bir başka anlatımla, damlatıcı debileri arasındaki değişimin kabul edilebilir bir üniformluk katsayısını sağlayacak biçimde düzenlenmesidir. Diğer taraftan, lateral boyunca menba ve mansap noktalarındaki başlangıç ve sınır şartları ile belirlenen bir projelendirme aralığı içerisinden, sistemde öngörülen toplam yük kaybı ve üniformluk seviyesi kriterlerini sağlayacak optimum giriş basınç yükü değerinin belirlenmesi lateral hidroliğinin temel problemidir. Zira lateral boyunca enerji çizgisinin değişimi ve çıkış akımı dağılımı, lateral girişindeki basınç yükü değerine bağlı olarak farklı profillerde oluşmaktadır. Çalışmanın ilk kısmında, üniform eğimli ve sabit çaplı bir lateral boru için lateral hidroliğinin temel prensipleri sunulmaktadır. Çalışmanın ikinci kısmında, sabit veya yere bağlı değişken debi yaklaşımlarından hareketle ortaya konan 7 adet hidrolik hesap metodunda, tasarım parametreleri için elde edilen başlıca denklemlere yer verilerek, optimum giriş basınç yükünün belirlenmesinde, sağlanması gereken hidrolik kriterler değerlendirilmektedir. Söz konusu metotların karşılaştırmalı analizi için, farklı eğim koşulları ve damlatıcı karakteristikleri için örnek bir uygulama seçilerek, her bir metottan elde edilen sonuçlar, boyutsuz eğriler halinde karşılaştırılmaktadır. Anahtar Kelimeler: Sulama sistemleri, mikro-sulama, lateral hidroliği, pürüzsüz boru akımı, hidrolik tasarım, analiz. An important objective of any micro-irrigation (drip, trickle) system is a uniform distribution of water delivered through the emitters along the lateral line. Adequate analysis of micro-irrigation laterals is very important for the design and evaluation of micro-irrigation systems. The increasing progress in computer technology has led to the development of numerical methods of hydraulic analysis as the finite-element method, the finite difference method, successive approximations method, and others. Lateral pipes are hydraulic structures whose design is limited by the desired level of uniformity, pressure head variation and total friction loss criteria. Design of this system depends upon a good understanding of lateral hydraulics and emitter characteristics. Hydraulically, flow in the lateral pipe is considered to be a steady, spatially varied flow with decreasing emitter outflow in the downstream direction. With decreasing discharge along the lateral, the energy gradient line decreases. Computation of flow distribution requires knowledge of the variables such as pressure, flow rate, length or internal diameter of the lateral, orifice characteristics, and frictional losses in the system. The hydraulic design of a lateral or a sub-main unit in a micro-irrigation system has been a problem tackled by many authors. In applications of previous analytical approaches for trickle lateral hydraulic computation, the primary solution is based on a discharge that is uniform, although ramifications of the manufacturer's variability have been modeled based on the derived hydraulic profile. However, significant deviations from accurate numerical solutions in hydraulic analysis could be caused by this basic assumption of constant emitter outflow. Recently, some alternative hydraulic calculation methods with more accurate results were developed based on the spatially variable outflow approach. The errors caused by the basic assumption of spatial invariance of the emitter outflow are minimized when the new alternative approaches are used. Design of a lateral pipe includes the determination of the required operating inlet pressure head, the pipe length or the inside diameter and total friction head losses along the lateral, assuming that the total flow rate at the inlet, characteristic of the emitter, and the acceptable level of uniformity are known previously. In the first stage of this study, basic principles of lateral hydraulics are clearly analyzed, and then basic equations of the seven hydraulic calculation methods are evaluated based on the governing equations for the steady flow in a smooth pipe. In the second stage, for determining optimum value of the inlet pressure head, hydraulic criteria depend on the initial and boundary conditions along the pipe, are also evaluated. In the third stage, the comparison test for the design example based on determination of inlet pressure head was applied for zero and uphill slope cases and various emitter characteristics, and showed graphically in dimensionless form. In these figures, residual flow rate ratios, variation of total friction head losses and uniformity coefficients depend on the operating inlet pressure head range are also evaluated. Comparison test shows that the Forward-Step-Method (FSM) that takes into account the velocity head change and variation of the Reynolds number, which affects the selection of the proper friction coefficient formula to be applied along the different reaches of the lateral pipes, has the highest accuracy because only the basic equations of the hydraulics of steady pipe flow were used. To apply the method, a computer program in Visual Basic 6.0 language named LATCAD was developed for analyzing and designing of micro-irrigation laterals. A comprehensive comparison test clearly shows that the FSM method using LATCAD yields highly accurate results in comparison with the other analytical and numerical procedures examined here. Keywords: Irrigation systems, micro-irrigation, lateral hydraulics, smooth pipe flow, hydraulic design, analysis.
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