Biyolojik sistemlerden esinlenilmiş, atımlı jet itme sistemine sahip bir su altı aracının kavramsal dizaynı ve itme veriminin sayısal değerlendirmesi
Conceptual design of a biologically inspired pulsed-jet underwater vehicle and numerical evaluation of propulsive efficiency
Yazar: MUSTAFA KEMAL ÖZALP
Danışman: PROF. DR. ABDİ KÜKNER
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Gemi ve Deniz Teknoloji Mühendisliği Ana Bilim Dalı
Derece: Yüksek Lisans, 2014
Konu: Gemi Mühendisliği = Marine Engineering
Dizin: Sayısal akışkanlar dinamiği = Computational fluids dynamic

Özet:
Bu çalışmada kalamarın ve deniz anası gibi atımlı jetlerle hareket eden deniz canlılarının itme sistemlerinden esinlenerek, kavramsal bir araç tasarlanmıştır. Atımlı jetleri oluşturmak için piston-silindir mekanizması kullanılmıştır.Birinci bölümde kalamarın yüzmesi ve girdap halkaları üzerine olan geçmiş çalışmalar incelenmiş; atımlı jet sistemiyle hareket eden sualtı araçları incelenmiştir.
İkinci bölüme, direnç hesaplamaları sırasında kullanılan akış denklemleri ve türbülans modeli açıklanarak başlanmıştır. Aracın tasarımı için başlangıç formu olarak, direnç deneyi verileri bilinen DREA parametrik denizaltı modeli seçilmiştir. DREA modelinden yeni modeller türetmeden önce sayısal olarak aracın direnci tekrar hesaplanmış ve teyit edilmiştir. Bu çalışmadaki tüm sayısal hesaplamalarda araç iki boyutlu eksenel simetrik olarak incelenmiştir. Ardından, ana modelden yola çıkarak, kıç kısmında belirli oranlarda açıklık bulunan yeni formlar türetilmiştir. Amaç, aracın kıç kısmında atımlı jetlerin tahliye edilebileceği bir çıkış açmaktır. Ana modelin kıç eğrisinin karakteristiği en az değiştirilerek belirli piston-çıkış çap oranlarına sahip 5 adet model türetilmiştir. Bu modeller arasından, direnç değeri ve yerleştirilecek itme sisteminin performans değişkenleri göz önüne alınarak, De=0.4Dp modeli seçilmiştir.
Üçüncü bölümde, atımlı jet sisteminin performans parametreleri açıklanmış ve bunların hangi aralıklarda olacağı belirlenmiştir. Ardından, atımlı jetler tarafından oluşturulacak itmenin nasıl hesaplanacağı açıklanmıştır. Atımlı jetlerin oluşturduğu itme sayısal olarak hesaplanmıştır. Direnç hesaplamalarında olduğu gibi burada da ANSYS ICEM CFD ve ANSYS Fluent yazılımları kullanılmıştır. Analizlere geçmeden önce, piston hareketinin nasıl modellendiği açıklanmış ve oluşturulan ağ örgüsünün özelliklerinden bahsedilmiştir. 
Dördüncü bölümde "senaryo -1" adında bir senaryo oluşturulmuş ve bu senaryo için belirlenen performans parametreleri için hesaplamalar yapılmıştır. Bu senaryoda piston 0.5 m/s'lik hız ile, 0.15 s'lik püskürtmeler yaparak ve püskürtmeler arasında 0.1 s dinlenerek toplamda 1 s boyunca çalışmaktadır. Bu durumda, sistemin araca verdiği ortalama itme kuvveti hesaplanmıştır. Daha önceden oluşturulmuş olan hız-direnç kuvveti tablolarından yararlanarak, aracın bu itme kuvveti ile hangi hızda sürekli olarak sevk edebileceği saptanmıştır. Saptanan araç hızı, kontrol hacminin "giriş" sınırında akış hızı olarak tanımlanmış ve böylece, gerçek bir hareket sırasında aracın üzerine gelecek ters yönde akışın etkisi modellenmiştir. Ters yönde akışın etkisiyle yeni itme değeri ve o ortalama itme kuvvetine karşılık gelen hız güncellenerek analizler tekrarlanmıştır. Ta ki, ardışık analizlerden elde edilen ortalama itme kuvvetleri arasındaki fark, belli bir hata yüzdesnin altına inene kadar. Ardından, yine iteratif olarak, aracı aynı sürekli hızda sevk edecek bir sürekli jet için piston hızı belirlenmiştir. Her iki jet modunda da piston hızı ve ortalama itme değerleri belirlendikten sonra, atımlı ve sürekli jet modu için itme verimleri hesaplanmıştır. Bu koşullar altında sürekli jet itme verimi atımlı jet itme veriminden % 6.6 daha yüksektir. Ancak senaryo -1 sonunda sistemin girdap halkası üretmediği görülmüştür. Bunun sebebi araç hızı değerinin jet hızından daha yüksek olmasıdır. Girdap halkası üretiminin olması ve halkalardan azami miktarda yararlanabilmek için, araç hızı-jet hızı oranı 0.5'ten küçük olacak şekilde, araç hızı ve çalışma oranı (〖St〗_L ) arasında bir matematiksel ilişki kurulmuştur. Bu matematiksel bağıntı sonucu 〖St〗_L≤0.08 olması gerektiği hesaplanmıştır.
Senaryo -1'den edilen bilgilerle "senaryo -2" adında yeni bir senaryo oluşturulmuştur. Bu senaryoda piston 0.5 m/s'lik hız ile, 0.08 s'lik tek bir püskürtme yapmıştır. 〖St〗_L=0.08 değeriyle oluşturulan bu senaryo için araç hızı-jet hızı oranı 0.373 olarak hesaplanmıştır ve belirli bir hassasiyetle, olması gereken araç hızı-jet hızı oranı hesaplanabilmiştir. Senaryo -2 sonunda sürekli jet itme veriminin atımlı jet itme veriminden %22.7 daha verimli olduğu görülmüştür.
Beşinci bölümde, beklenenin aksine, atımlı jet itme veriminin sürekli jet veriminden daha düşük olmasının sebepleri araştırılmış ve açıklanmıştır. Atımlı jet modunda verimi düşüren en büyük etken, piston dinlenme süresinde iken nozul eksenin iki yönlü akışın olmasıdır. Yatay doğrultuda salınımlar yapan silindir içindeki akışkan kütlesi, piston üzerine önce vakum etkisi oluşturarak direnci artırır. Ardından nozulun iç kısmında ters yönlü girdap halkası oluşur ve silindir içerisine dış ortamdan akışkan dolmaya başlar. Bu sebeple araç çevresindeki akış da bozulur.
Altıncı bölümde, atımlı jet itme verimini düşüren etkiler yorumlanmış ve bu etkilerin tasarımsal sebeplerden olduğuna karar verilmiştir. Aracı atımlı modda daha verimli hale getirebilmek için piston dinlenme safhasında iken, nozul eksenin iki yönlü akışı kesecek bir mekanizma olması önerilmiştir. Buna ek olarak, istenen araç hızı- jet hızı oranında seyrederken yüksek 〖St〗_L değerinde çalışabilmesi için, fazlaca büyük olan silindir hacmi ve piston çapının küçültülmesi önerilmiştir.
Özetlenecek olursa, yapılan kavramsal tasarım bu haliyle atımlı jet modunda istenen verimi elde edememiştir. Bunun için atımlı jet sistemi tasarımı üzerinde çeşitli düzenlemeler yapılması gerekmektedir. Piston-silindir mekanizması yerine daha verimli ve daha kompakt bir itme sistemi kullanılması da araştırılmalıdır.

Abstract:
In this study, a biologically inspired pulsed-jet underwater vehicle is designed conceptually and its propulsive efficiency against a steady jet system is numerically evaluated.
In the first chapter, a background about biological pulsed-jet systems and vortex rings is given. Vortex rings and pulsed-jets are coupled concepts. At the initiation of each pulse, a vortex ring is formed due to the thin shear layer roll-up. Some elemental concepts are explained along with the vortex rings; such as formation number, effect of co-flow and nozzle-exit over pressure. Then, information about lately studied pulsed-jet vehicles is given. It is stated that pulsed-jet efficiency is up to 50% higher than steady jet efficiency.
Second chapter is about choosing the model which is going to be equipped with pulsed jet system. DREA model submarine is chosen as a main model. The main reason of choosing DREA model is that experimental results of drag test are available. The form of pulsed jet vehicle is reproduced from DREA model. In this study, a numerical approach is adopted. Thus, before reproduction of new models, experimental drag results are needed to be validated numerically.
ANSYS ICEM CFD software is used for mesh generation throughout the study. ANSYS Fluent software is used to solve the Navier-Stokes and turbulence equations. Throughout the study, flow is 2d, steady, axisymmetric, incompressible, turbulent and Newtonian. Since the geometry is axially symmetric and 3d effects are negligible, swirl is ignored during calculations. Thus, only the upper half of the vehicle is modeled. A hybrid mesh technique is used to mesh the computational domain. Quad cells are used to mesh the boundary region and triangular cells are used to mesh the outer region of the domain. For the half of the model, computational domain is 30 m long and the radial extent is 6m.
Pressure-based, steady, axisymmetric solver is used. SST k-ω turbulence model is chosen in order to model the turbulence in the flow. SST k-ω is widely used for drag calculations. It is based on k-ε and k-ω turbulence models and acts as k-ω model near wall regions and k-ε model in the free stream. Fluid is 25℃ water and fluid properties are defined same as the experimental conditions. The flow speed is 3.422  m⁄s in the +x direction. Throughout the solutions, SIMPLE scheme is used for pressure-velocity coupling. Momentum, turbulent kinetic energy and specific dissipation rate is calculated using second order upwind scheme.
Results show that there is a significant difference between experimental and numerical drag results. Some flow and mesh parameters are checked; such as y+, aspect ratio, quality, etc… The same problem is detected in other studies on DREA submarine model. Therefore, experiment conditions and results are evaluated again. For a 6m long model, the experiments were conducted in a wind tunnel with 3×3×30 m dimensions; width, height and length respectively. The main suspicion is the height and the width of the wind tunnel. For a 6 m long model, 1.5 m height and width at each side are thougth to be insufficient, especially at 54  m⁄s inlet velocity.
In order to check the effects of experimental domain on the drag, the computational domain is revised and set as the wind tunnel with wall boundary conditions. In the ex-domain for computations, the farfield boundary was defined as symmetry in order to avoid flow reflections from the wall. With the revised domain, analysis are repeated and the results show that there is a significant raise in the drag. This result suggests that the tunnel dimensions are insufficient for a 6 m long model. These findings lead us to compare numerical results with the analytical results of the flat plate drag. It is calculated that the difference between model viscous drag and the flat plate drag is 3%. 
After the validation process, the parametric tail form is reproduced in order to create an opening at the tail end. While reproducing new forms, a speacial attention is paid to preserve the characteristic of the tail curve. The tail of DREA model is defined with a second order polynomial. The degree of the polynomial of reproduced forms are also in the second order. Five tail forms are reproduced with different piston-opening diameter ratios. Except the tail forms, the nose and the body curves are preserved.
The drags of new models are calculated with the same approach as the DREA model. The drag values of D_e=0.8D_p and D_e=1.0D_p models are found suspicious. Thus, they are ignored during the selection of vehicle form. Considering the requirements of the pulsed-jet system and the drag values of models, D_e=0.4D_p model is chosen as the model which is going to be equipped with pulsed-jet system.
In the third chapter, the pulsed-jet propulsion system is designed and placed in D_e=0.4D_p model. The pulsed-jet propulsion system consists of a piston-cylinder mechanism. Piston-cylinder mechanism is placed to the body of the model in order to have a maximum cylinder volume. No cylinder inlet is modeled in order to keep the numerical calculations simple. While connecting cylinder to the nozzle, a smooth transition is needed in order the create minimum turbulence in the flow. Thus, a concave curve is used to connect cylinder and nozzle. It is seen that the flow at the exit plane is enough to be assumed as uniform. Latter, the performance parameters of a pulsed-jet system is explained. To manipulate the generated impulse, piston stroke ratio and duty cycle are used. During calculations, L/D is set to 4 and StL is changed between 0.375-0.75. Lastly, the calculation of hydrodynamic jet impulse is explained in chapter three.
In chapter 4, an imaginary testcase is created and named as "testcase -1". In testcase -1, the piston speed is 0.5 m⁄s, pulse duration is 0.15 s, piston rest duration is 0.10 s and analysis duration is 1 s. During analysis, vehicle is stationary and there is no co-flow. The impulse generated by pulses on the vehicle are recorded at each time step. At the end of analysis, forces acted on vehicle was averaged for the duration of analysis. Using drag force-thrust equality, the velocity corresponds to the thrust is estimated. For this purpose, the drag force-velocity graph is used. Then, in order to account the co-flow, a co-flow velocity is defined at the inlet boundary condition same as the vehicle velocity. The analysis is repeated with co-flow and thrust generated is updated. The net force in the presence of co-flow is calculated and the velocity corresponded to the new average thrust is updated at the inlet. Analyses are repeated with the updated co-flow velocity until the net force generated on the vehicle in the presence of co-flow is smaller than the 5% of the averaged thrust.
In order to compare the pulsed-jet propulsive efficiency to steady jet propulsive efficiency, a steady jet with the same averaged thrust is needed to be generated. For this purpose, slug model is used to predict the steady jet piston velocity. Steady jet piston velocity is predicted as 0.391  m⁄s  . With the predicted piston velocity, net average force generated on the vehicle is calculated by an analysis of 6 s in the presence of co-flow. The net average force is subtracted from the average thrust force and new piston velocity is estimated as 0.358  m⁄s. Analysis repeated with the updated piston velocity and the new net force calculated is in the acceptable error margin. After estimating average thrust and piston velocity values for both pulse modes, the pulsed jet and steady jet propulsive efficiencies are calculated. Considering energy given to the piston in order to propel vehicle at the same constant speed in both pulse modes, steady jet propulsive efficiency is % 6.6 higher than the pulsed jet propulsive efficiency. On the other hand, system efficiency for pulsed jet propulsion, considering the work done by the vehicle with respect to the work done by the piston, is more efficient than the steady jet system efficiency, %22.39 and %19.87 respectively.
In testcase -1, it is seen that there is no vortex rings generated by pulses. It is due to the higher vehicle speed with respect to the jet speed. Thus, a mathematical relation between piston speed and 〖St〗_L  is created. This mathematical relation is set to ensure the desired maximum vehicle speed to jet speed ratio which is 0.5. Using this mathematical relation which is created for D_e=0.4D_P form, it is seen that the 〖St〗_L value should not exceed 0.08.
In chapter 5, a new testcase is created in order to observe vortex rings and their effect to the pulsed jet efficiency. The new testcase is named as "testcase -2". In testcase -2, the piston speed is 0.5 m⁄s, pulse duration is 0.08 s, 〖St〗_L=0.08 and only one pulse is generated. Analysis duration is 1 s. It is calculated, considering energy given to the piston in order to propel vehicle at the same constant speed in both pulse modes, the propulsive efficiency of steady jet mode is %22.7 higher than the pulsed jet mode. In addition, the system efficiency of steady jet mode is higher than the pulsed jet mode, %21.4858 and %19.78 respectively.
In chapter 6, the reason for the lower pulsed jet propulsive efficiency is explained and some suggestions are made for the future work in order to raise the pulsed jet propulsive efficiency. There are two reasons of the lower pulsed jet propulsive efficiency for the vehicle designed. First and the most significant one is the lack of a flow penetrating mechanism which penetrates the flow at the nozzle exit plane bidirectionally. In this design, the fluid mass inside the cylinder oscillates back and forth while the piston is at rest. This oscillation causes a vacuum effect on the piston and increasing the drag of the vehicle. In addition, oscillation results in a generation of an opposite sign vortex ring inside the nozzle. This deforms the flow around the vehicle. It is not proved numerically in this study; but it is known to increase the drag of the vehicle.
One other effect of the lack of flow penetrating mechanism is the lower vortex ring contribution to the thrust. To achieve highest propulsive pulsed-jet efficiency, the pulse mode should be the fully-pulsed. This means that there should be a period of no flow between consecutive pulses. Here, there is a significant amount of backflow during piston rest period and this reduces the effect of nozzle exit over-pressure on starting jets. Nozzle exit over-pressure has a significant contribution thrust, especially at small L/D; such as in this study.
Second reason of the lower pulsed jet propulsive efficiency is very low 〖St〗_L. It is suggested to set the 〖St〗_L above 0.5. Here, because of the design constraints, it is not possible to set 〖St〗_L higher than 0.08. The reason for low 〖St〗_L is the very high cylinder volume and piston dimension.
As a conclusion, the vehicle designed has lower pulsed-jet propulsive efficieny than the steady jet efficiency. Two main reasons are the lack of flow penetrating mechanism at the rest stage of the piston and very low 〖St〗_L. For the future work, it is very important to develop a flow penetrating mechanism between pulses in order to increase the pulsed jet propulsive efficiency. The pulsing mechanism should also be revised in order to achive higher 〖St〗_L or an entirely new pulsing mechanism should be developed; such as IPMC (Ionic polymer-metal composite) based contracting mechanism.