Çukur yapıların yüzey sürtünme direncine olan etkilerinin hesaplamalı ve deneysel olarak incelenmesi
Experimental and computational investigation of the effect of dimpled surfaces on skin friction reduction
Yazar: YASİN KAAN İLTER
Danışman: DOÇ. DR. UĞUR ORAL ÜNAL
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Gemi İnşaatı ve Gemi Makineleri Mühendisliği Ana Bilim Dalı / Gemi İnşaatı ve Gemi Makineleri Mühendisliği Bilim Dalı
Derece: Doktora, 2023
Konu: Gemi Mühendisliği = Marine Engineering

Özet:
Çoğu sıvı akışında, sürtünme direnci genel sürüklenme kuvvetinin ana bileşenidir. Hem çevresel önlemler sonucu kısıtlayıcı yasalar hem de ekonomik sebepler sonucunda enerji verimliliği konusu çok önemli hale getirmiştir. Sürtünme direncini azaltmak, demiryolu, karayolu ve hava taşımacılığı araçları veya gemiler ve su altı araçları gibi deniz sistemlerinin verimliliğinde kilit bir rol oynar. Sürtünme direncini düşürmeye yönelik yöntemleri genel başlık olarak aktif ve pasif olmak üzere ikiye ayrılmaktadır. Aktif yöntemler, sisteme bir enerji girdisi sonucunda çalışabilen yöntemlerdir ve ancak sisteme verilen enerjinin tasarruf edilen enerjiden düşük olması durumlarında avantaj sağlamaktadırlar. Buna karşın pasif yöntemler, herhangi bir enerji girdisi olmadan, varlıkları sebebi ile direnç düşürme özelliğine sahip yöntemlerdir. Kolay uygulanabilir olması, bakım – tutum masraflarının alternatiflerine kıyasla oldukça düşük olması gibi sebeplerle çukur yapılar, son yıllarda üzerinde yüzey sürtünme direncini düşürmeye yönelik araştırmaların arttığı pasif bir yöntem olarak yüksek ilgi görmektedir. Bu tez çalışması kapsamında çukur yapıların yüzey sürtünme direncine olan etkilerinin incelenmesine yönelik hesaplamalı ve deneysel çalışmalar gerçekleştirilmiştir. Bunun yanında çukur yapıların denizcilik uygulamalarına uygunluğu ile ilgili tartışmalara yer verilmiştir. 
Tez çalışması kapsamında gerçekleştirilen hesaplamalı ve deneysel çalışmalar, tam gelişmiş türbülanslı kanal akışı ortamında gerçekleştirilmiştir. Hesaplamalı çalışmalar içerisinde tam gelişmişlik koşulu, akış doğrultusunda tanımlanan kütlesel debi ve tam gelişmiş akış elde edilmesini sağlayan periyodiklik sınır koşulları ile sağlanmıştır. Bu sayede hesaplama gücü gereksinimleri ve ihtiyaç duyulan çözüm süreleri minimize edilerek farklı parametrelerin etkisinin incelenmesine olanak sunulmuştur. Gerçekleştirilen ön çalışmalar neticesinde çukur yapıların etkilerinin anlaşılabilmesi için sınır tabaka içerisinde meydana gelen türbülans yapılarının zamana bağlı incelenmesi gerektiği ortaya çıkmıştır. Dolayısı ile nümerik çalışmalar LES türbülans modeli kullanılarak gerçekleştirilmiştir. Türbülans yapılarının yüksek doğrulukla çözülebilmesi için ortaya çıkan çözüm ağı gereksinimleri ve uzun çözüm süreleri sebebi ile sadece yüzey sürtünme hızına bağlı Reynolds sayısı, Re_τ=180, kanal yüksekliği ve kanal kesit ortalama hızına bağlı Reynolds sayısı, Re_H=2,800 için incelemeler gerçekleştirilebilmiştir. Elde edilen sonuçlar çukur yapıların etkisiyle, sürtünme direncinde yaklaşık %5'e varan bir azalma elde edilebildiğini göstermiştir.
Tez çalışması kapsamında düz ve çukur yapılı levhalar üzerinde gerçekleştirilen deneysel çalışmalar, tam gelişmiş türbülanslı akış kanalında gerçekleştirilmiştir. FTFC (Fully Turbulent Flow Channel) olarak isimlendirilmiş kanal sistemi Strathclyde Üniversitesi Kelvin Hidrodinamik Laboratuvarında yer almaktadır. Deneysel çalışmalar kapsamında basınç düşüşü ve akım görüntüleme ölçümleri gerçekleştirilmiştir. Deneysel çalışmalardan elde edilen sonuçlar, nümerik çalışmalardan faydalanılarak, düşük Re_H sayılarında elde edilen etkilerin yüksek Re_H sayılarında da benzer olacağı kabulü ile, düzeltme katsayıları hesaplanarak yeniden hesaplanmıştır. Gelinen noktada basınç düşüşü ölçümlerinden yola çıkılarak hesaplanan direnç değişimlerinin düşük Re_H sayılarında nümerik çalışmalar ile benzerlik gösterdiği görülmektedir. Nümerik çalışma sonucunda en iyi sonuç veren D45_4 ve D60_3 vakaları, Re_H sayısının artması ile birlikte düzeltilmiş deneysel sonuçlara göre %20 oranlarına varan iyileştirme sergilemişlerdir. Bu sonuçlar literatürde yer alan öncül çalışmalar ile benzerlik göstermektedir. Kanal akışı fiziği gereği bu iyileştirme doğrudan direnç iyileştirmesi olarak değerlendirilmemelidir. Ancak deneysel çalışmaların nümerik çalışmalar ile uyum göstermesi, PIV ölçümleri neticesinde gözlemlenen akış alanlarının literatür ile benzerlik sergilemesi elde edilen sonuçların çukur yapıların potansiyelini ortaya koymaktadır. Yüksek Reynolds sayılarında bu etkilerin görülüyor olması, çukur yapıların su ortamında daha yüksek potansiyele sahip olabileceğini ve dolayısı ile denizcilik uygulamaları için önemli olabileceğini göstermektedir.

Abstract:
For most fluid flows, skin friction is the main component of the overall drag force. Both restrictive legislation as a result of environmental measures and economic reasons have made the energy efficiency issue very important. Reducing skin friction has a key role in the efficiency of rail, highway and airways transport vehicles or naval systems such as ships and underwater vehicles. 
In different studies, aiming at drag reduction by means of polymer additives or application of wall oscillation methods, which overwhelmingly indicate drag reduction of more than 40%, it is mentioned that the drag-reducing mechanism is interpreted as shifts on velocity profiles, velocity fluctuations and Reynolds stress profiles, increase in spanwise vorticity generations. 
In recent years, there is a growing interest in investigating turbulent skin friction-reducing capabilities of dimpled surfaces, which is previously known for its positive effects on heat transfer problems. A dimpled surface is a powerful passive solution for marine applications considering its large potential for skin friction reduction capabilities and practical applicability. In 1998, researchers discovered that dimpled surfaces can be used for skin friction reduction, and they showed that the drag reduction rates can be up to 20% with shallow dimples in a fully turbulent flow although they increase the form drag component. However, in 2008 a group of researchers reported no drag reduction in their studies. 
Some researchers mentioned that the drag-reducing phenomenon only occurs when the flow is turbulent and indicated that there is no clear reason for conflicting results found in the literature. A patent holder for the dimpled technologies suggests that drag reduction only occurs when the flow is turbulent and mentioned that a drag reduction level of up to 34% can be achieved. In 2004 a magazine presented a drag-reducing technique that uses circular dimples called "Tornado Like Technology (TLT)". It is stated that the dents on a surface of an object will generate tornado-like vortices that reduce the drag. This article involves the unique industrial application of dimpled surfaces, which are applied on a high-speed train model, in the open literature. The paper, however, did not provide any scientific background about the resistance reduction mechanisms of the dimples. Consequently, several dimple investigations were performed by using solely flat walls with regular arrays of spherical dimples due to the complexity of the physical mechanism A group of researchers mentioned retained energy levels at larger scales which are implying greater streamwise coherence and stability of the flow. In addition to the freestream flow conditions, the flow over the dimples is influenced by a variety of dimple parameters. The most significant of these parameters is the dimple depth. Previous studies showed that the resistance increases as the dimple depth to diameter ratio increases. For the dimples with depth-to-diameter ratios greater than 10%, flow separation is observed. Separated flow creates pressure drag and it lacks the gain on the wall shear stress. To be able to see dynamic flow structural characteristics some studies are focused on the flow structures with depth-to-diameter ratios greater than 20%. Also, the literature indicates that the drag reduction only occurred with coverage ratios higher than 70%. In addition, there is a strong dependency on dimple pattern orientation. In the recent experimental investigations on the physical mechanism of the effect of the dimples on the boundary layer flow, some recent studies argue that the drag reduction effect is related to the strong dependency on pattern orientation and dimple geometry. It is also mentioned that dimples influence the streamwise vorticity and it acts to reduce skin friction drag. It is believed that the spanwise flow components disrupt the normal cascading of the turbulent energy to the smaller scales for dissipation. This results in reduced turbulent energy production and stabilized flow results in the skin friction drag reduction with the dimples. Most recently a study showed that diamond-like dimple patterns can reduce mean drag by 7.4% while circular dimples have an increase of around 6%.
On the other hand, most of the dimpled studies were conducted by a fully developed channel flow. Fully developed channel flows, which are widely known as wall-bounded flows, are relatively simple flows for the verification and evaluation of theoretical models. The simple geometry of the channel is preferably suitable for the computational boundary layer investigations in terms of relatively low computational costs. In the experimental world, it is rather difficult to measure flow quantities, especially in the viscous sublayer region at high flow speeds. To be able to understand the flow characteristics and investigate the effect of the dimples or similar surface treatment methods in the turbulent boundary layers, extensive computational flow simulations become necessary. Computational methods and high-performance computers allow researchers to evaluate detailed flow fields and increase their knowledge of the physics of flow behaviours over different surface structures.
The above review highlights that dimple patterns have great potential as a passive drag-reducing solution while there still exist highly conflicting views and drag reduction rates reported in the literature as well as a lack of information about the frictional drag reduction mechanism.  Besides, most of the studies indicate the weaknesses of the numerical simulations in their ability to demonstrate drag reduction by using dimple geometries. In order to shed light on the aforementioned ambiguity and to provide further discussions to the related literature, this study presents an extensive computational investigation by means of large eddy simulations on the characteristics and physical mechanism of the fluid flow over dimpled surfaces in a fully developed channel flow. Within the framework of the study, which is part of the postgraduate study of the first author, various dimple depth-to-diameter ratios as well as different dimple arrangements and geometries with coverage ratios higher than 85% were considered. In addition to the detailed mean and instantaneous flow properties, a spectral analysis was also performed by using the Empirical Mode Decomposition (EMD) technique. Since strong evidence of the drag-reducing effect of the dimples has only been provided by the experimental studies so far, this study focused on the skin friction reduction mechanism and provide extensive views and discussions of the near-wall flow fields and wall shear stress distribution which are not easy to measure in an experimental study.
In this study, large-eddy simulations of the turbulent channel flow with various dimpled surfaces were presented together with experimental studies in a fully turbulent channel flow. The drag characteristics along with the time-averaged and instantaneous flow fields were extensively examined and the effect of the dimples was investigated. The study also included a spectral analysis in terms of the Hilbert-Huang spectrum of the velocity fluctuations and revealed the effect of the dimples on the frequency domain. The critical findings of the investigations are briefly addressed as follows.
All of the dimpled surfaces with the exception of the case with a staggered arrangement and the one involving the dimple geometry with a d/D rate of 8% considerably reduced the frictional drag component. The cases involving larger dimples cases with a higher diameter-based Reynolds number displayed better performance in terms of skin friction. With the application of the dimples, a frictional drag reduction of up to approximately 5% was obtained. 
The Reynolds numbers based on the diameter, or the depth of the dimples are not the sole physical parameter affecting the skin friction. The combination of these Reynolds numbers along with the dimple geometry and arrangement is effective in friction reduction. Within the Reynolds number range investigated in this study, a higher
Re_D and a lower Re_d were found to be desirable depending on the dimple configuration. 
Re_d along with the dimple geometry is the primary parameter affecting the form drag component. A higher value of  Re_d substantially increased the form drag. The two shallower cases as well as the diamond-shaped dimpled case produced an encouraging outcome displaying almost no increase in overall drag, indicating that further studies with a slight optimisation in the dimple geometry will most possibly result in a considerable drag reduction.
The main effective influence on surface friction originated from the mean flow. The amount of gradient of the tangential velocities in the inner part of the boundary layer at the immediate vicinity of the bottom wall is particularly related to the sectional area variation rates of the bottom wall. Indeed, lower gradient values will decrease the overall amount of τ ̅_w.
The flow direction in high-speed regions close to the wall is also a relatively effective physical property on the frictional resistance. If a high-momentum flow portion can be orientated to the spanwise direction, even if high shear stress levels exist on the fluid adjacent to the wall, a part of them will be transferred to the spanwise flow component, which will help decrease the skin friction in the streamwise direction.
For the Reynolds number examined in the study, the dimples did not reduce the high-frequency content of the flow and did not provide a more stable flow topology, contrary to what is pointed out in the open literature. The instantaneous flow topologies as well as the spectral investigations exposed a substantial increase in the high-frequency small-scale structure production, and a large rise in the fluctuation almost throughout the spectral span was recorded. 
Investigation of the time-averaged and instantaneous spanwise vorticities revealed an inverse relationship between the skin friction reduction performance and the level of the spanwise vorticity as well as the quantity of the smaller-scale structures in the vicinity of the wall. The flow was least disturbed by the diamond-shaped dimples, which resulted in the best skin friction reduction obtained. 
With the introduction of the dimples, strong counter-rotating pairs of alternating streamwise vortex zones were generated. However, contrary to the information given in the associated literature, the increase in the level of streamwise vorticities did not enhance skin friction reduction.    
The results suggest that future optimisation studies should consider the sectional area variation of the dimpled surface as the primary parameter by taking also the freestream velocity into account. An asymmetrical surface geometry in the xz plane may also be desirable to avoid the excessive wall shear stress increment towards the trailing edge as far as possible, which was also investigated by Ng et al. (2020). The side edges should be optimised such that a sufficient spanwise flow component that affects the middle zone of the dimple is ensured.
Experimental pressure measurement and flow visualisation studies were conducted in a fully turbulent flow channel facility of the University of Strathclyde with the exact physical conditions considered in this study. The results obtained from experimental studies were recalculated by calculating correction factors, assuming that the effects obtained at low Re_H numbers will be similar at high Re_H numbers, using numerical studies. At this point, it is observed that the resistance changes calculated based on pressure drop measurements show similarity with numerical studies at low Re_H numbers. The D45_4 and D60_3 cases, which give the best results in the numerical study, have shown improvements up to 20% according to the corrected experimental results as the Re_H number increases. Due to the physics of channel flow, this improvement should not be considered a direct resistance improvement. However, the compatibility of experimental studies with numerical studies, and the observation of flow areas similar to the literature as a result of PIV measurements, reveal the potential of dimple structures. The fact that these effects are seen at high Reynolds numbers indicates that dimple structures may have a higher potential in the water environment and therefore maritime applications should be examined.