Kanal içinde yoğuşmanın sayısal modellenmesi
Numerical modelling of condensation in channel flow
Yazar: MUTLU İPEK
Danışman: YRD. DOÇ. DR. LEVENT ALİ KAVURMACIOĞLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı
Derece: Yüksek Lisans, 2015
Konu: Mühendislik Bilimleri = Engineering Sciences

Özet:
Yoğuşma olayına birçok mühendislik probleminde rastlanabilir. Özellikle tekstil, gıda ve kağıt sektörlerinde kurutma prosesi içerisinde karşılaşmak mümkündür. Bunun dışında; iklimlendirme sistemlerinde, endüstriyel kurutucularda ve ev tipi çamaşır kurutma makinelerinde yoğuşma olayı kapalı çevrimin önemli bir parçasıdır. Kapalı çevrim kurutma sistemlerinde, kurutulacak nesneden çekilen nemli havanın öncelikle yoğuşturulması gerekir. Bu yüzden yoğuşma olayı sistem performansı üzerinde doğrudan etkilir. 
Kanal içinde nemli havanın yoğuşmasının sayısal olarak çözümlenmesinde sonlu hacimler yöntemiyle çözümleme yapan FLUENT 14.5 adlı HAD kodu kullanılmıştır. Karalı rejimde çözüm yapılmıştır. Yoğuşmalı akışın modellenmesinde FLUENT 14.5 kodu içerinde yer alan buharlaşma- yoğuşma modeli seçilmiştir. 
Çok fazlı akışın modellenmesinde, FLUENT 14.5 kodu içerisinde bulunan Eulerian çok fazlı akış modeli tercih edilmiştir. Eulerian çok fazlı akış modelinde momentum korunum denklemleri her bir faz için ayrı ayrı çözümlenmektedir. Kanal içerisindeki akışa ait türbülans etkileri k-ε türbülans modelleri ile incelenmiştir. Sayısal çözümlemenin uzunluğu göz önüne alınarak, türbülans transport denklemleri fazlar için ayrı ayrı çözdürülmek yerine, fazlar için ortak olarak çözdürülmüştür. Ayrıca, her bir çözüm ağı elemanında fazların hacimsel oranlarının hesaplanmasına yönelik hacimsel oran denklemi çözümlenmiştir. Böylece bir adet süreklilik denklemi, altı adet momentum denklemi, bir adet enerji denklemi, iki adet türbülans transport denklemi ve bir adet hacimsel oran denklemi olmak üzere her bir iterasyon için toplam on bir adet denklem sistemi çözümlenmiştir.
Kanal içinde yoğuşmanın sayısal modellenmesinde kapsamında gerçekleştirilen HAD analizlerinde, fazlar arası momentum transferi etkilerinden sürüklenme kuvveti incelenmiştir.  Sürüklenme kuvveti modeli olarak Schiller ve Naumann (1937) tarafından önerilen sürüklenme kuvveti modeli kullanılmıştır. Yüzey gerilme kuvvetinin hesaplanmasında, havanın yoğuşturucu kanalına giriş ve çıkış sıcaklıklarının ortalaması olan 70°C'deki değeri; 0,064 N/m yüzey gerilme katsayısı olarak kullanılmıştır. Fazlar arası ısı transferinin modellenmesinde ise Ranz ve Marshall (1952) tarafından geliştirilen model kullanılmıştır.
Tez çalışmasında tek paslı hava yoğuşturmalı yoğuşturucuya sahip kurutucu ile deneysel çalışmalar yapılmıştır. Deneylerde kararlı rejimde yoğuşma hızı ve kanal çıkışında proses havasının ortalama sıcaklığı elde edilmiştir. Deneysel sonuçlar HAD analizleri ile karşılaştırılmıştır.
HAD analizlerinde nemli hava yoğuşturucu kanalına 72 °C (345,15 K) ve % 85 bağıl nemde girmektedir. Bu değerler havanın ve su buharının kanala giriş kütlelerinin hesaplanmasında kullanılmıştır. Yoğuşturucu kanalı dışında yalnızca taşınımla ısı geçişi olduğu kabul edilmiştir. Kanal çevresindeki havanın sıcaklığı ve ısı taşınım katsayısı deney sonuçları kullanılarak hesaplanmıştır. Modelde kullanılan ısı taşınım katsayısı U= 150 W/m2K ve hava sıcaklığı 34 °C (307,15)'dir. 
Sonuç olarak, HAD analiz sonuçları ile deneysel sonuçlar karşılaştırıldığında değerlerin önemli ölçüde benzerlik gösterdiği belirlenmiştir. HAD analizleri sonucunda yoğuşturucu kanalında kararlı rejimde yoğuşan su miktarının 0,455 g/s olduğu hesaplanmıştır. Deneysel çalışmalarda ise kararlı rejimde yoğuşan su miktarının 0,5 g/s olduğu tespit edimişti. HAD analizleri ile deneysel sonuçlar arasında % 9'luk bir sapma bulunmaktadır. Bu sapma yoğuşmanın sayısal modellenmesinde kabul edilebilir bir değerdir. HAD analizlerine göre kanal çıkışındaki alan ortalama sıcaklık değeri 338,3 K  (65,15 °C)'dir. Deneysel sonuçlarda ise kanal çıkışındaki ortalama sıcaklık değeri 339, 45 K (66,3°C) olarak ölçülmüştür. Sayısal modelde kanal çıkışındaki ortalama sıcaklık değeri % 1,74 sapma ile elde edilmiştir.
Parametrik çalışma kapsamında;  kanal girişindeki hava hızının, kanal et kalınlığının ve türbülans modelinin kararlı rejimde yoğuşan su miktarına etkileri ilk HAD analizi sonucu ile karşılaştırılmıştır. 
Parametrik çalışmaların sonucunda, hava debisinin artışının belli bir noktadan sonra yoğuşan su miktarına etkisi azalmıştır. Kanal et kalınlığının artmasıyla birlikte kararlı rejimde yoğuşturucu kanalında yoğuşan su miktarının az da olsa azaldığı görülmektedir. Farklı türbülans modellerinin kararlı rejimde yoğuşan su miktarına ve kanal çıkışında alan ortalama sıcaklık değerine net bir etkisi görülmemiştir.

Abstract:
Condensation phenomenon can be encountered in many engineering problems. Particularly, it is possible to experience the condensation in drying process of textile, food and paper industries. Moreover, condensation phenomenon plays an important role in closed cycle drying systems such as, industrial dryers and household type laundry dryers. Becasue, in closed cycle drying systems, humid air is condensed primarily. Since, condensation directly affects the system performance.
Numerical modelling of condensation in channel flow has been analyzed by FLUENT 14.5 which utilizes the finite volume method. Analyzes has been carried out in steady state conditions. The evaporation- condensation model which is available in multiphase models in FLUENT 14.5 code has been utilized in analyzes. 
Multiphase Eulerian model which takes place in FLUENT 14.5 code has been used for numerical modelling of condensation in channel flow. In multiphase Eulerian model, conservation equatios have been resolved for each phase individually. The Eulerian multiphase model in ANSYS Fluent allows for the modeling of multiple separate, yet interacting phases. The phases can be liquids, gases, or solids in nearly any combination. With the Eulerian multiphase model, the number of secondary phases is limited only by memory requirements and convergence behavior. Any number of secondary phases can be modeled, provided that sufficient memory is available. For complex multiphase flows, however, you may find that your solution is limited by convergence behavior. ANSYS Fluent's Eulerian multiphase model does not distinguish between fluid-fluid and fluid-solid (granular) multiphase flows. A granular flow is simply one that involves at least one phase that has been designated as a granular phase. The ANSYS Fluent solution is based on the following: A single pressure is shared by all phases. Momentum and continuity equations are solved for each phase. The following parameters are available for granular phases: Granular temperature (solids fluctuating energy) can be calculated for each solid phase. You can select either an algebraic formulation, a constant, a user-defined function, or a partial differential equation. Solid-phase shear and bulk viscosities are obtained by applying kinetic theory to granular flows. Frictional viscosity for modeling granular flow is also available. You can select appropriate models and userdefined functions for all properties. Several interphase drag coefficient functions are available, which are appropriate for various types of multiphase regimes.
ANSYS Fluent uses one of two models for interphase mass transfer through evaporation-condensation depending on the multiphase and interfacial heat transfer models being used. In most cases the Lee model is used. The single exception is in the case that the Eulerian multiphase model is used in conjunction with the two resistance model for interfacial heat transfer, in which case the Thermal Phase Change model is used.
Generally, the analysis of gas–liquid flows is complicated considerably by the two phases that co-exist simultaneously in the fluid flow which often exhibit significant relative motion and heat transfer across the interfaces separating them. At these phase boundaries, the exchanges of mass, momentum and energy occur in a dynamic fashion. One adopted approach to resolve such flows is the customary two-fluid formulation based on the inter-penetrating media framework; each phase is present at every point, with a given frequency or probability, which happens to be the local void fraction or volume fraction of the gas phase. In the inter-penetrating media approach, the inter-phase exchanges of mass, momentum and energy are modelled as an inter-phase interaction term acting on each phase. For the general case of a two-fluid model, the exchanges taking place at the interfaces between the three phases are explicitly taken into consideration. In this sense, we can write three sets of conservations (one conservation equation for mass, momentum and energy of the gas phase as well as liquid phase) in terms of phase-averaged properties. The dynamics of the interaction between the three phases are fully described by constitutive equations governing the inter-phase mass, momentum and energy exchanges. 
Interfacial momentum transfer is rather crucial to the modelling of gas–liquid flows. Considered as sources or sinks in the momentum equations, this interfacial force density generally contains the force due to viscous drag as well as the effects of lateral lift, wall lubrication, virtual mass and turbulent dispersion, which are lumped together as non-drag forces. These interfacial force densities strongly govern the distribution of the gas and liquid phases within the flow volume. In the case of dispersed flows, the interfacial drag force is a result of the shear and form drag of the fluid flow. For gas–liquid flows, non-drag forces have a profound influence on the flow characteristics, especially in dispersed flows. Bubbles rising in a liquid are subjected to a lateral lift force due to horizontal velocity gradient. In contrast to the lateral lift force, wall lubrication force constitutes another lateral force due to surface tension which is formed to prevent bubbles from attaching on the solid wall. This results in a low void fraction at the vicinity of the wall area. The virtual mass or added mass force arises because acceleration of the gas bubble requires acceleration of the fluid. It is generally taken to be proportional to the relative phase acceleration. turbulent dispersion force is taken as a function of turbulent kinetic energy in the continuous phase and gradient of the volume fraction. Moreover, inter-phase energy transfer plays an important role for modelling boiling flows. There are different models related with inter-phase momentum and heat transfer suggested by several researchers.  
In computational fluid dynamic (CFD) analysis, interfacial momentum transfer is rather crucial to the modelling of condensation in channel flow. Interfacial drag force whic is an interfacial momentum transfer effect has been investigated. Schiller ve Naumann drag force model has been applied as interfacial drag model. Ranz Marshall heat transfer correlation has been used as heat transfer model.
In this thesis, experimental studies have been carried out with a one channeled condenser dryer. In experiments, the condensation rate of humid air and the area averaged temperature at the end of the channel in steady state conditions have been obtained. Subsequently, experimental results have been compared with CFD analysis results. 
In the experiments, laundry dryer which has one process and two cooling channels condenser has been used. Experimental works have been conducted in Arçelik A.Ş. laboratories. First of all, wind tunnel experiments have been carried out in order to determine the flow rate of laundry dryer. Process and cooling air flow rates have been obtained respectively. Moreover, the value of process air flow rate is 17 l/s and the value of cooling air flow rate is 11,5 l/s. These values are significant for obtaining the condensation rate in condenser channel. Besides wind tunnel experiments, drying experiments have been conducted so as to determine the temperature distribution and condensation rate in condenser channel. In drying experiments several thermocouples have been placed at inlet and outlet of condenser channel. Moreover, relative humidity sensors have been placed at inlet and outlet of the condenser channel. During experiments, temperature and relative humidity data of condenser channel have been obtained. Furthermore, experimental data have been used for calculating the condensation rate in condenser channel. According to experimental data, humid air (process air) enters the condenser channel at 72 °C and % 85 relative humidity. Meanwhile, humid process air leaves the condenser channel at 66 °C. And % 100 relative humidity. Under these circumstances, condensation rate in condenser channel have been calculated using the programme Psyhcrom which is an add-in programme in Microsoft excel. Condensation rate with respect to time of experiment has been plotted for 5000 second. Between 2000th and 4000th seconds condensation rate becomes steady state. Therefore, steady state condensation rate has been obtained as 0,5 g/s.
In CFD analysis, fluid domain has been created in ANSYS geometry. Fluid domain refers to condenser channel which has a shape of rectangular prism. The dimensions of fluid domain are; width: 180mm, length: 280mm, thickness: 8mm. Structured grid has been created in ANSYS meshing for fluid domain of condenser channel. There is approximately 600000 hexahedral elements in fluid domain. Inlet temperature of humid air is 345,15 K and pressure of the system is 1 atm. Humid air enters the condenser channel with a velocity of 26.6 m/s. The relative humidity of humid air is % 85. Under these conditions, the saturation temeperature of humid air is 341,35 K. Convection is applied around condenser channel. Heat transfer coefficient of convection is calculated by using experimental data as U= 150 W/m2K. Moreover, turbulence effect in channel flow has been modelled by k-ε turbulence models. Considering the solution time of analyzes, turbulence transport eaquations have been resolved commonly for all phases. Besides these equations, volume fraction equation has been resolved for each phase in all iterations. 
As a result, experimental results have a good agreement with CFD analysis results substantially.   There is a % 9 deviation between CFD analysis and experimental results in steady state condensation rate of condenser channel. Moreover, the average temperature at the end of the condenser channel has been obtained by CFD analysis with  % 1,74 deviation compared to experimental results.
Effects of different parameters on condensation rate in channel have been investigated. These parameters are air flow rate and channel thickness. Moreover, effect of turbulence models used in the modelling has been research by using different RANS turbulence models.
As consequences of parametric works, the increasing air flow rate diminishes the condensation rate in channel. Hovewer, the air flow effect on condensation rate weakens after a certain value. Moreover, the increasing channel thickness decreases the condensation rate slightly. Furthermore, different turbulence models do not affect the condensation rate and the avarage temperature at the end of the channel significantly.