Oluklu sıvı sızdırmazlık sistemlerindeki kaçak akış miktarının sayısal olarak incelenmesi
Numerical investigation of leakage amount in grooved liquid seal
Yazar: ÖMER DEHAN ÖZBOZ
Danışman: DR. ÖĞR. ÜYESİ VEDAT TEMİZ
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Konstrüksiyon Bilim Dalı
Derece: Yüksek Lisans, 2022
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Hesaplamalı akışkanlar dinamiği (HAD) = Computational fluid dynamics (HAD) ; Kaçak akı = Leakage flux ; Sızdırmazlık sistemleri = Sealing systems

Özet:
Bu çalışmada, bir vidalı pompa tasarımı için oluklu sıvı sızdırmazlık sisteminin geometrik özelliklerine bağlı kaçak akış miktarının araştırılması, hesaplamalı akışkanlar dinamiği yöntemi ile yapılmıştır. Vidalı pompanın fiziksel özelliklerine bağlı olarak, analizlerde kullanılacak geometrik ve sınır sabitleri belirlenmiştir. Vidalı pompa dakikada 2950 devir ile çalıştığında 10 MPa basınçlı sıvı su üretme kapasitesine sahiptir, sızdırmazlık sistemi bu durum göz önüne alınarak incelenmiştir. Sızdırmazlık yüzeyi için kullanılabilir uzunluk 30 mm ile sınırlıdır ve rotorun yarıçapı 15 mm'dir.
Oluk geometrilerinde incelenecek değişkenlerden, rotor stator arasındaki boşluğu tanımlayan kleransın 20 ile 40 mikrometre arasında değişmesi beklenmektedir. Bu sebep ile 20, 30 ve 40 mikrometre değerleri, incelenecek geometrilerin çeşitlendirilmesinde kullanılmıştır. Oluk geometrilerinin boyutlarının çeşitlendirilmesi için genişlikte 1,0 mm ve 1,5 mm; derinlikte ise 0,5 mm ile 1,0 mm kullanılmıştır. Çeşitlendirilmiş bu parametrelere bağlı 4 farklı geometrinin incelenmesi gerçekleştirilmiştir. Bu geometrilerden bir tanesi dikdörtgen şekilli oluk (Model A) iken diğer üç tanesi üçgen şekilli oluk geometrisinde oluşturulmuştur. Üçgen şekillerinin iki tanesi dik kenarlı üçgen şeklinde olup, birinde rotor eksenine dik kenar, akışın oluğa giriş yaptığı bölgede iken (Model B), diğerinde tam tersi olarak rotor eksenine dik kenar oluğun çıkış yaptığı bölgede (Model C) olacak şekilde tanımlanmıştır. Üçüncü üçgen şekilli geometri ise ikiz kenar şeklindedir (Model D). Belirtilen boyutsal ve şekilsel çeşitlendirmeler, beş oluklu modeller üzerinden incelenmiştir. 
Sızdırmazlık sistemindeki kaçak akış miktarının belirlenmesi için Realizable k-ε Reynolds Averajlı Navier-Stokes modeli; 2 boyutlu modellerde düzlem dışı hız vektörünü hesaplayan Axisymmetric Swirl modeli ile beraber kullanılmıştır. Sonlu hacimler programında tanımlanan akış ortamına, programda tanımlı sıvı su materyali atanmıştır. Sıvı su programda 998,2 kg/m3 öz kütleye ve 0,001003 kg/m-s viskoziteye sahiptir. Akış ortamını doğru tanımlayabilmek için, boyutsuz y+ uzaklığının, duvar sınırındaki ilk hücreler için 3'ten daha küçük olması gerekmektedir. Bu çalışmada y+ değerinin maksimum 1,5 olması hedeflenerek, akış ortamı düzenli hücreler ile ayrıklaştırılmıştır.
Akış girişinin tanımlandığı sınır koşulunda 10 MPa toplam basınç tanımlanmış, akışın çıktığı sınır koşulunda ise 0 MPa statik basınç değeri tanımlanmıştır. Rotor ve stator sınırlarının yüzey pürüzlülüğü ihmal edilerek; stator durağan duvar olarak, rotor ise dönme hızı, 2950 rpm'e denk gelen, 309 rad/s olan hareketli duvar olarak tanımlanmıştır.
İncelemeler sonucunda en önemli parametrenin rotor stator arası klerans olduğu, bunu takip eden ikincil en önemli parametrenin oluk genişliği olduğu doğrulanmıştır. 
Kleransa bağlı olarak oluşturulan oluklu modeller, oluksuz modeller ile karşılaştırıldığında, görülmüştür ki, kleransın 20 mikrometre olduğu durumda (Re≈500) oluklar kaçak akış miktarını belirgin bir şekilde arttırmaktadır. 30 mikrometre kleranslı modellerde (Re≈1150) bu belirgin artış azalmakta. 40 mikrometre kleranslı modellerde ise (Re≈2100) oluklar, akış miktarını belirgin bir şekilde azaltmaktadır. Kleransın oluşumunun olasılıksal olması ve kleransın düşük olduğu durumda zaten kaçak akış miktarının azaldığı düşünülerek oluklu sızdırmazlık sisteminin kullanılması uygun görülmüştür.
İkincil en önemli parametrenin oluk genişliği olduğu belirlenerek, incelenen modeller arasında 1,0 mm genişlikteki olukların, 1,5 mm genişlikte oluklara göre daha iyi sonuç verdiği gözlemlenmiştir. Bu bağlamda kullanılacak oluk genişliğinin 1,0 mm olmasına karar verilmiştir. 
Oluk geometrilerinin karşılaştırılmasında dikdörtgen kesitli olukların bütün durumlarda daha iyi sonuç verdiği görülmüş, bunun sonucunda dikdörtgen kesitli ve 1,0 mm genişliğe sahip, oluk modelleri, derinlik bakımından incelenmiştir. Bu inceleme sonucunda, analizi yapılan modeller arasında en iyi sonucu veren modelin 1,0 mm genişliğe ve 0,5 mm derinliğe sahip olan dikdörtgen kesitli oluk olduğu bulunmuş ve daha sonra oluk sayısının etkisi incelenmiştir. İnceleme sonucunda 11 adet oluğun bulunduğu sızdırmazlık sisteminin, olasılıksal olarak, hiçbir oluğun kullanılmadığı modele göre ortalamada %3 daha az kaçak akış miktarına sebep olduğu belirtilmiştir.
Çalışmada ayrıca üçgen oluklu modellerin sonuçları incelenerek, ileriki çalışmalarda trapez oluklu sistemlerin incelenmesinin daha iyi sonuç verebileceği belirtilmiştir.

Abstract:
In this research, the leakage investigation of a grooved liquid seal for a screw pump design due to the geometric properties, has been done with computational fluid dynamics method. With respect to the specifications of the screw pump, constant variables have been decided. The sealing system that has been examined in this study has been made for a pump capable of producing 10 MPa of liquid water at an operating condition of 2950 revolutions per minute. The available length for the sealing surface is limited with 30 mm and the radius of the rotor is 15 mm. In order to be able to fully investigate the groove's effect on the leakage, groove geometries have been placed on the rotor as 2 mm apart from the inlet and outlet, with the result that fully developed flow can occur at the inlet of the groove geometry.
The investigated groove geometries are located on the rotor surface and have three distinct control variables, these are clearance between rotor and stator, groove height and groove depth. Clearance is expected to be between 20 and 40 micrometers, due to this reason, clearance of 20, 30 and 40 micrometers have been investigated, in order to fully understand the flow behavior. The groove width variable has been assumed to be 1,0 mm or 1,5 mm and groove depth variable has been assumed to be 0,5 mm or 1,0 mm. With addition to these control variables, 4 distinct geometry patterns than can be described with the control variables have been investigated. The main investigated pattern has a rectangular groove shape (Model A), in addition to this model 3 triangular shaped grooves have been investigated. Triangular shapes can be described as two right triangular shape and one isosceles triangular shape (Model D). One of the right triangular shape's perpendicular edge to the axis of the rotor is located at the inlet of the groove (Model B), and the other triangular shape's perpendicular edge to the axis of the rotor is located at the outlet part of the groove (Model C). The created models have 5 number of equally distributed grooves.
Computational fluid dynamics analyzes have been done with Ansys 2020 R2 Fluent fluid simulation software. In order to be able to investigate the rotational flow, Pressure-Based Steady Axisymmetric Swirl equations have been used with Realizable k-ε RANS model. To the extent of obtaining the wall shear stress correctly, maximum y+ values of the first layer near the wall in the domain has been kept below 1.5. Flow domain have been divided with structured grids and as a result, all Model A grids have 1,0 orthogonality; Model B, C and D grids have an average of 0,95 orthogonality. 
Fluid zone material is assigned with built in water-liquid material that has 998,2 kg/m3 density and 0,001003 kg/m-s viscosity. Domain boundary conditions consist of stationary wall for stator boundary, pressure-inlet for the inlet boundary conditions with 10 MPa as the gauge total pressure and pressure-outlet for the outlet boundary conditions with 0 MPa as the static pressure. Operating conditions have been kept as 1 atm. Turbulence terms of the inlet and outlet boundary conditions have been specified with "Intensity and Hydraulic Diameter" method where the turbulent intensity is %5 and hydraulic diameter is two times the clearance value. Grooved rotor boundary condition has been specified with rotational moving wall boundary condition and assigned with 309 rad/s which is approximately 2950 rpm. In order to investigate the rotational velocity vectors' effects on the leakage, rectangular grooved models have been also analyzed with stationary wall boundary condition assigned on both the stator and the rotor wall.
For solution method, pressure-velocity coupling scheme is selected as coupled scheme, and spatial discretization has been done with second order or second order upwind. For convergence criteria, built in absolute criteria for continuity equation has been assigned with 10-4, and 10-6 for all other equations. In order to ensure convergence is reached, additional convergence criteria have been added for rotor friction force and stator friction force with stop criterion of 10-6 with respect to the 5 iterations before. 
Investigation of rotational velocity's effect on the leakage of the rectangular grooves, showed that rotational velocity related leakage reduction occurs in every model, however this reduction is insignificant. 2-D streamlines also do not change when rotational and stationary models are compared. Even with the lowest axial velocity of 12,0 m/s (Re≈414), Taylor vortices have not been formed on the models.
Investigation of clearance's effect on the leakage performance showed that, clearance is the most important control variable. As the clearance increases, flow area and axial velocity component both increases and as a result more leakage value is observed. Also grooved liquid seals have been compared with annular seals with no groove, and it has been observed that groove's effect on the leakage changes with clearance thereby velocity. All of the grooved seals with 20 micrometer clearance (Re≈430) resulted significantly more leakage than the annular seals with the same clearance. When grooved seals with 30 micrometer clearance (Re≈1150) investigated with annular seals with the same clearance, this effect almost vanished and showed similar results. The same comparison with the clearance of 40 micrometer (Re≈2120) showed that, grooved liquid seal results significantly less leakage than the annular seals. Therefore, it has been seen that as the Reynolds number increases to 2100, advantage of the grooves on the leakage reduction increases.
The effect of the width of the groove on the leakage performance is not as significant as the clearance, however, it came forward as the second most important control variable in all of the models. It has been observed that when every other control variable kept same, grooves with 1,0 mm width showed observable less leakage than the grooves with 1,5 mm width. The reason for this effect is assumed to be, as the width of the groove decreases, the length of the clearance part of the seal increases, and an additional friction component occurs. If the local losses in the groove, related to the vortices does not decrease as much as the additional frictional term increases, reducing the width of the grooves, decreases the overall leakage of the seal.
The reason clearance and the width of the groove are the most important variables for the leakage performance is considered as, these variables not only affect the flow in the grooved part, they also govern friction term occurring at the clearance length of the seal. In this respect depth and the effect of the general geometry has been investigated together, since they mainly affect the grooved part of the seal.
When the depth of the grooves investigated, it has been observed that for the rectangular grooves with 1,0 mm width and 0,5 mm depth (Width/Depth=2,0) has better sealing performance than the grooves with 1,0 mm width and 1,0 mm depth (W/D=1,0). However, when the grooves with 1,5 mm width and 0,5 mm depth (W/D=3,0), compared with the grooves which have 1,5 mm width and 1,0 mm depth (W/D=1,5), the same significant effect has not been observed. The reason is thought to be width over depth ratio is an important factor for formation of the vortices in the grooves, and W/D=2 is a better ratio than 1,5 and 3. However since W/D ratios of 1,5 and 3,0 gives similar results, the optimum W/D ratio may occur between these values. For this reason, width to depth ratio of 2,25 and 2,5 should be investigated for future researches.
Investigation of the depth on the triangular shaped models showed that as the depth increases, the models perform better for leakage reduction. The reason for this occurrence is thought to be different in every model. For the right triangular models, which's angled edge is located at the outlet of the groove (Model B), this reason is thought to be; due to the presence of the angled edge, vortex in the groove cannot cover all the width of the groove. As the depth increases this effect vanishes and vortex may cover the whole length and as a result better result may be obtained. For the right triangular models, which's angled edge is located at the inlet of the groove (Model C), this reason is thought to be; the angled edge is restricting the occurrence of the vortex and as the depth increases, angle steepens and, this restriction effect vanishes, as a result vortex generation can occur and leakage reduces. When two right triangular models compared, it has been seen that Model C's results, are more unreliable than Model B's results. This is due to the fact that Model C has a restricting edge. However, when the angled steepens, Model C may result as good as rectangular grooves. 
When isosceles triangular shaped groove investigated, it has been seen that, due to the presence of angled edge on both inlet and outlet part, this model possesses the same effects that occurred on Model B and Model C. With this in mind, modeling a groove with trapezoidal shape may give better understandings for the angle of the edges' effects on leakage, since on trapezoidal models, depth may be kept as constant. 
After investigating depth and geometry's effect on the leakage, number of grooves' effect on the leakage performance have been searched with the best groove shape achieved, which is rectangular geometry with the width of 1,0 mm and depth of 0,5 mm. As a result, it has been seen that leakage result is affected with respect to the number of grooves almost in a linear relationship. This proves that the grooves' effect may be treated as a local loss factor. Also, from the probabilistic point of view, it has been shown that the seal with 11 grooves performs %3 better and precise than the seal without grooves.