Radyal pompalarda eksenel yükün belirlenmesi ve dengelenmesi
Determination and balancing of axial thrust in radial pumps
Yazar: ABDURRAHMAN TÜRKMEN
Danışman: PROF. DR. ERKAN AYDER
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Isı-Akışkan Bilim Dalı
Derece: Yüksek Lisans, 2020
Konu: Makine Mühendisliği = Mechanical Engineering

Özet:
Turbopompa  veya pompa gibi sistemlerde tasarım aşamasında en çok dikkat edilmesi gereken konulardan biri eksenel kuvvet dengeleme işlemidir. Yeterince dengelenmemiş bir eksenel kuvvet, sistemde istenmeyen gürültülere, yıkıcı titreşimlere sebebiyet verebilir ve/veya rulman ömrünü önemli ölçüde azaltabilir.
Bu gibi sorunların çözümü için birçok  pompa elemanı geliştirilmiştir ve çoğu ayrıntılı bir şekilde incelenmiştir. Bu elemanlar, tez kapsamında bahsi geçen, dengeleme deliği, dengeleme tamburu, dengeleme pistonu, aşınma halkası, labirent sızdırmazlık elemanı, dengeleme kanatçığı ve girdap kırıcıdır. Dengeleme deliği çarkın arka yüzeyinden çarkın emme kısmına doğru açılan bir deliktir. Bu delik sayesinde çarkın arka haznesinin basıncıyla beraber kuvvetin etkidiği yüzey azalır ve eksenel kuvvetin azaltılması sağlanır. Dengeleme tamburu yaklaşımında  ise tamburun ön tarafında tasarlanan dar aralıktan geçen akışkanın basıncı düşer ve tamburun arka yüzeyine etkiyen düşük basınç sayesinde eksenel kuvvet azaltılmış olur. Aşınma halkası çarkın ön ve arka kısmında, çark ile arasında çok küçük bir açıklık kalacak şekilde yerleştirilir. Burada da amaç yine basıncın düşmesi ve kuvvet dengesinin sağlanmasıdır.  Diğer yapılar da farklı mekanizmalar ile olsa da, nihayetinde üzerlerinden geçen akışkanın  basıncını değiştirirler ve eksenel yük kontrolünü mümkün hale getirirler.
Tez kapsamında, tasarlanmış bir pompa çarkı geometrisi kullanılmış ve bu geometriye salyangoz akış hacmi ve ön-arka kaçak akış bölgeleri eklenmiştir. Daha sonra ilk olarak çarkı ve salyangozu içeren tüm pompa için HAD analizleri yapılmıştır. Buradan elde edilen çark çıkışı statik basıncı, kaçak akış bölgelerindeki akış analizleri için giriş koşulu olarak alınmıştır. Ön kaçak akış analizi, iki boyutlu eksenel simetrik akış kabulü yapılarak, farklı aşınma halkası açıklığına göre yapılmış ve en uygun açıklık değeri ve buna karşılık gelen eksenel kuvvet belirlenmiştir. Daha sonra arka kaçak akış analizi gerçekleştirilmiş ve çark yüzeyine temas eden  aşınma halkasının eksene olan uzaklığının tasarlamış olan pompa için  ideal değeri bulunmuştur. 
HAD analizleri ile elde edilen değerler literatürde mevcut olan yaklaşımlar kullanılarak belirlenen değerlerle karşılaştırılarak uyumlulukları ve farkları değerlendirilmiştir.

Abstract:
In systems such as turbopumps or pumps, one of the most important issues in the design phase is axial force balancing. An insufficiently balanced axial force can cause unwanted noises, destructive vibrations in the system, and/or bearing life may be reduced. For the solution of such problems, numerous pump structures are developed and inspected in detail. Among these structures, there are balancing hole, balancing drum, balancing piston, wear ring, labyrinth sealing element, radial rib and swirl breaker. 
Balancing hole is a hole opened from the back surface of the pump impeller towards the suction part of it. Thanks to this hole, the pressure of the rear chamber of the impeller drops and force balancing takes place. Diameter, radial position and drilling angle can be changed so that different flow needs can be met. However, there is disatvantage of this structure; there is a remarkable amount of fluid passing through the hole and it causes a power loss for the pump.
The balancing drum is located between the two impeller in a multistage pump and a flow occurs from its narrow gap from one impeller to another. The pressure of the fluid passing through the narrow space decreases and consequently the axial force changes. In this way, the force can be balanced. 
The balancing piston is actually the back side of the impeller with one orifice at the outer end and one orifice at the inner end of the impeller, and a gap between these two structures. The orifices are basically narrow gaps and the flow passing through them loses its pressure. Thus, the force acting on the back side of the impeller is reduced and the overall thrust is controlled.
The wear ring is placed so that the front and back of the impeller faces to a very small gap between the impeller and the wear ring. Here the fluid is forced through this gap and gains speed. While passing through such small gap with high speed, it loses its energy and consequently its pressure and the pressure that is downstream of the wear ring has lower pressure, which allows the designer to balance the axial force. The length and clearance values of the wear ring can be modified to obtain proper flow properties and axial loads. 
The radial rib is a radially positioned rectangular structure at the front or the back side of the impeller and consequently, it rotates with the shaft. While it rotates, it changes the pressure distribution of the flow passing through it by generating centrifugal force. Different pressure distribution patterns can be obtained by changing length, number, width, and radial position of the rib.
The swirl breaker is a groove structure that is placed on the casing of the system. It is located so that it stands face to face with the impeller surface. The rotating fluid coming out of the outlet of the impleller is directed into the front/back side of the impeller due to pressure gradient and it continues its rotation. A swirl breaker resists this rotating velocity component and forces it to slow down. By doing so, the kinetic energy of the fluid is converted into pressure head and the pressure is increased. The pressure around the swirl breaker is changed by modifying the depth, width, length, and thr number of the swirl breaker.
In the scope of the thesis, a pump impeller geometry is obtained and a volute geometry and front-back leakage flow geometries are added. However, leakage flow geometries are analyzed seperately from main flow because it is possible to reduce front leakage flow to 2D axisymmetric flow, and the back leakage flow to 1/6 periodic flow, which gives the opportunity to use much smaller mesh structures. For example, fort he front leakage flow, there is only 65000 mesh elements are generated. 
After that, firstly, a  CFD analysis is done for main flow geometries (impeller-volute). The impeller and the volute sections are meshed seperately. The 1/6 of the impeller, in other words one blade subsection, is meshed in TurboGrid program and having a structured mesh, and it is multiplied in CFX to obtain full geometry. The volute is meshed in ANSYS Meshing and it has unstructured mesh. All the solid surfaces have wall boundary condition and the first layer thickness is 0.002 mm and y+ values between 0-5 are obtained for all surfaces. The impeller outlet pressure is obtained and used in other geometries as inlet boundary condition. The axial force for the main flow is obtained to calculate the net axial force later. Also, the pressure values of the hub surface of the impeller are obtained and placed on a graph according to their radial position values, and a second order curve is fit on the values almost perfectly. After that, a proper radial location for the balancing holes is determined and the pressure at this point is used as the balancing hole outlet pressure during the back side leakage flow analysis.
Next, another series of CFD analysis are done for the front leakage flow for several gap clearances of the front wear ring. The radial position of the wear ring is fixed and it is placed just around the suction wall of the pump wheel. The geometry is 2D and the mesh is structured having first layer thickness 0.0005 mm. CFD analysis is performed as a 2D axisymmetric flow and the inlet condition is obtained from main flow analysis. The rotor wall has a rotational velocity and the casing wall is stationary.  The leakage flow rate and the axial force data for each analysis are recorded to calculate the net axial force later.
Finally, the back leakage flow is analysed. This is the crucial part of the thesis because the adjustment of the axial force is done by changing the radial position of the back side wear ring. Back side wear ring is free to move along the impeller back face.  While changing its radial position, the chamber having lower pressure can be increased and the chamber having larger pressure can get smaller and vise versa. 
Also there are six balancing holes connecting inside and back side of the impeller. That is why a 2D axisymmetric flow assumption is not appropriate for this analysis. Rather, a 1/6 repeating section of the geometry is used as a rotational periodic geometry that contains one balancing hole. Also, the flow geometry is divided into two pieces. One contains the balancing hole section on it, that is why it is not suitable to use a structured mesh. However, the other one is a fully sweepable geometry and the mesh used on it is a fully structured mesh. Because two sections are meshed seperately, and one has structured and the other one has unstructured mesh, there is non-conformal mesh on the common face of the sections.
The inlet boundary condition is obtained from main flow CFD analysis, and the oulet boundary condition is taken as 1 atm static pressure. In this thesis, 6 different radial positions (52, 55, 60, 65, 70 and 75 mm) for the wear ring are inspected and the results are recorded. Using other axial force data from other geometries, a net axial force is calculated for different radial positions of the back side wear ring. Eventually, a proper radial position for moderate axial force and total leakage is obtained. 
The results derived from CFD  analysis are compared to the methods currently available in literature and similarities/differences are examined. A theoretical formulation for the small gap flow between two rotating cylinders  is obtained from literature and a graph is drawn accordingly. After, the results obtained from CFD analysis are added to the graph and compared to the theoretical ones. 
At low Reynolds numbers, there is a similarity between results; however, increasing Reynolds number causes the difference in the results to increase. The main reason for this behaviour is probably that the theoretical formula is obtained for comparatively long cylindrical gaps, however, the wear rings are much narrow structures, that is why, for wear ring case the entrance effects are quite prominent.
There are also two different experimental results obtained from literature. One of them contains the experimental results for again long cylindrical gap flows and the same mismatch among the results are present here. The other one has the results for spesifically wear ring structures, the same structure analysed in this thesis, and as expected, there is a strong similarity between the experimental results and CFD results.