Düz ve genişletilmiş yüzeylerde karlanma esnasındaki ısı ve kütle geçişinin deneysel incelenmesi ve düz levha için yeni bir kütle geçişi korelasyonu geliştirilmesi
Experimental investigation of heat and mass transfer during frosting on flat and extended surfaces and development of mass transfer correlation on flat plate
Yazar: ADEM AKSOY
Danışman: PROF. DR. MUSTAFA ÖZDEMİR
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Makine Mühendisliği Teknolojileri Bilim Dalı
Derece: Doktora, 2024
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Isı akısı = Heat flux ; Isı geçişi katsayısı = Heat transfer coefficient ; Kar çözme yöntemi = Defrost method ; Kütle aktarımı katsayısı = Mass transfer coefficient ; Nem geçişi = Humidity transfer

Özet:
Bu çalışmada düz levhada ve kanatlı levhada karlanma esnasındaki; kar kalınlığı, biriken kar kütlesi ve ısı akısı ölçülmüştür. 
Kurulan deney tesisatında ilk olarak yatay düz levha ön ucunda homojen kabul edilebilecek bir hava hızı dağılımı sağlanmıştır. Hava sıcaklığı 21,9°C, bağıl nem %80 ve hava hızı 0.7 m/s iken; hava çıkış tarafındaki levha yüzey sıcaklıkları her testte farklı olarak; -15,1, -11,2, -7,1°C olduğu durumda yatay düz levhada kar oluşturulmuş ve bu koşullarda anlık kar kalınlığı, test sonunda ise biriken kar kütlesi ölçülmüştür. Literatürde çok nadir rastlanan, karlanma esnasındaki sürekli ısı akısı ölçümü de yapılmıştır. Biriken kar kütlesi bilindiğinden gizli ısı akısının hesaplanması mümkün olmuştur. Gizli ısı akısının hesaplanması toplam ısı akısı bilindiğinden duyulur ısı akısının da hesaplanmasını sağlamıştır. Duyulur ısı akısından anlık ortalama taşınımla ısı geçiş katsayıları hesaplanmıştır. Biriken kar kütlesi değerlerinden ortalama taşınımla kütle geçiş katsayıları hesaplanmıştır. Ortalama kütle geçiş katsayılarından ortalama Sherwood sayıları hesaplanmıştır.
Yüksek düz levha sıcaklığında karlanmanın ilk aşamalarında beklenmedik bir ısı akısı artışı gözlemlenmiştir. Kar yüzey sıcaklığını bilmeyi gerektirmeyen, boyutsuz levha uzunluğu parametresini de içeren yeni bir boyutsuz kütle geçişi korelasyonu geliştirilmiştir. Kütle geçiş korelasyonu; hava sıcaklığından, hava hızından, bağıl nemden, levha sıcaklığından, levha uzunluğundan, levha genişliğinden ve zamandan türetilen; Reynolds sayısı, Fourier sayısı, özgül nem, boyutsuz sıcaklık, boyutsuz levha uzunluğu parametrelerinden oluşmaktadır. Korelasyon oluşturulurken önceki araştırmacıların kar kütlesi ölçümleri sunulan ölçümlere dahil edilerek oldukça geniş bir aralıkta geçerli olan bir korelasyon geliştirilmiştir. Korelasyonun geçerli olduğu aralık; hava hızı için 0,7 – 2,5 m/s, hava sıcaklığı için 5 – 22°C, levha sıcaklığı için      -5 – -25 °C, bağıl nem için %50 – %83,73 ve levha uzunluğu için 85,6 – 300 mm'dir. Levha uzunluğunun boyutsuzlaştırılması korelasyonun geçerliliğini artırmıştır. 
Kanatlı levha çalışmalarında ise düz levha çalışmalarında üniform hava hızı dağılımı sağlanmış olan deney hücresine çok az çalışmada rastlanabilen kanat aralığı olan 4 mm aralıkla levha yüzeyine 19 mm yüksekliğinde 1 mm kalınlığında kanatlar konumlanmıştır ve karlanma incelenmiştir. 10°C hava sıcaklığında %75 bağıl nemde, hava hızı 0,7 m/s iken; kanatlı yüzeyi soğutan su banyosu sıcaklığı her testte farklı olarak; -23°C, -30°C, -33°C değerlerine getirilerek kanatlı yüzey üzerinde kar oluşturulmuştur. Hava çıkış kenarına yakın konumdan levha yüzey sıcaklığı, akış doğrultusunda ve akış doğrultusuna dik sıcaklıklar ise kanat üzerinde ölçülmüştür. Bunun yanında deney sonunda biriken kar kütlesi, literatürde çok nadir rastlanan sürekli ısı akısı ve sık kanatlı bir yapıda karlanmanın ön ve üst profilini oluşturan kar kalınlığı dağılımı da ölçülmüştür. 
Kanatlar arasındaki kar profili incelendiğinde kanat üst ucundan itibaren uzunca bir kısımda kar profili düz devam ederken tabana yakın kısımda kar birikimi sebebiyle daha kalın bir kar tabakası oluşmuştur. Ayrıca tabanda kanatların tam ortasındaki bölgede literatürde ilk defa bir kar tepesi gözlemlenmiştir. Kanatların ön yüzünde dışarı doğru bir kar tabakası birikimi de gözlemlenmiştir. Kanatların ön bölümü tıkandıkça hava yukarıya yönlenmektedir. Kanatlı yüzeylerin duyulur ısı geçişini arttırıcı bir etki yaptığı anlaşılmaktadır. Sıcaklık ve ısı akısı grafiklerinin eğimleri incelendiğinde en sıcak levha test şartı olan -23°C su banyosu testinin ikinci yarısında grafik eğimlerinin farklı olduğu görülmüştür, bu durum karlanmanın yüksek levha sıcaklığında etkisinin daha uzun sürdüğünü göstermektedir.

Abstract:
In this study, frost thickness, accumulated frost mass, and heat flux during frosting on flat plate and finned plate were measured.
In the experimental setup, Uniform air velocity distribution in the upstream is established in horizontal flat plate study. It was explained in the section describing the experimental setup that, despite the short distances, the air velocity distribution could be made uniform by using air straighteners and flow settling devices. The sections of the setup utilizing the flow straightener and flow settling means, along with their geometric properties, have been detailed. While describing the structure of air conditioning unit of the experimental setup, it was stated that the humidifier hose for humidifying the air was mounted as high as possible to allow efficient mixing of the steam with the air. It has been noted in this section that if the humidification efficiency were not sufficient, the end of the humidifier hose would need to be placed as close as possible to the fan's air intake. it is also explained that the air temperature is maintained by a cooler, heater, and the relay controlling the heater. The use of the heat flux sensor, which measures the heat flux during frositng, has also been explained. In this section, some practical information has also been provided for less experienced individuals who will set up the experimental apparatus. The stages from the beginning to the end of the experiments are described. The air velocity distribution measured at the front end of the plate is also stated in this section. The methods of how and where the surface temperatures were measured, the characteristics of the heat flux sensor that measures the heat flux, and how the relative humidity and air temperature were measured have been described. The frost thickness on the flat plate was measured from the middle of the plate, from the front end of the ruler. On the finned plate, however, rulers are mounted at the beginning of the experiment and, after the image is captured, they are removed from the surface to not obstruct the airflow. Before the experiment, the weight of the dry napkins is measured. At the end of the experiment, the accumulated frost mass is collected on napkins, and the change in weight of the napkins is measured. The change in weight on the napkins at the end of the experiment represents the accumulated frost mass.
Frost is formed on the flat plate at surface temperatures of -15.1, -11.2, -7.1°C, while the air temperature was 21.9 °C, the relative humidity is %80 and the air velocity 0.7 m/s; then under these conditions frost thickness, frost mass were measured. Since the frost thickness and frost mass were measured, the frost density has been calculated and presented. Continuous heat flux measurements under frosting which is very rare in literature were also performed. Since the accumulated frost mass is known, it has been possible to calculate the latent heat flux. The calculation of the latent heat flux, knowing the total heat flux, has also made it possible to calculate the sensible heat flux. Time averaged heat transfer coefficients have been calculated from the sensible heat flux measurements. Time averaged mass transfer coefficient have been calculated from the value of the accumulated frost mass. Time averaged Sherwood number have been calculated from the value of time averaged mass transfer coefficient. 
In frost thickness measurements on the flat plate, it has been observed that the frost thickness continuously increased. It has been determined that the fastest increase in frost thickness occurred in the first 15 minutes. Since the frost thickness can be measured over time, the rates of increase in frost thickness have also been calculated and presented. Accordingly, the rate of increase in frost thickness does not change after 30 minutes. It has been calculated from the measurements that the rate of increase in frost thicnkess does not change with the surface temperature after 30 minutes. When the frost layer photographs were examined, it was observed that at the 15th minute on the trailing edge of the plate, where the air leaves from the surface, a porous layer of frost was present, while a dense layer of frost was observed at the front end of the plate. The accumulation of frost mass changes less at lower plate temperatures. This is due to the change in saturated water vapor density with temperature being the dominant parameter in mass transfer. In experiments, it has been understood that the measurement uncertainty of the frost mass is important in determining the behavior of the frost layer. It has also been determined that the first 15 minutes is the time period when mass transfer is most intense during frosting process.
An unexpected increase in heat flux has been observed in the initial stages of frosting at high flat plate temperatures. When the values of frost layer density calculated from the measurements were examined, it was determined that the mentioned increase in heat flux is observed in the densest frost layer. Therefore, it has been concluded that the high density of the frost layer leads to the mentioned increase in heat flux. Under other conditions, the heat flux starts at a maximum value, decreases over time, and reaches a steady state. Time averaged convective heat transfer coefficients calculated from the sensible heat flux increase as the plate temperature increases, while the time averaged convective mass transfer coefficients decrease as the plate temperature increases. 
A new dimensionless mass transfer correlation that does not require frost surface temperature and additionally includes the dimensionless plate length is presented. The mass transfer correlation is based on dimensionless numbers, Reynolds, Fourier, specific humidity, dimensionless temperature, dimensionless plate length which are derived from air temperature, air velocity, air relative humidity, plate temperature, plate length, plate width and time information. In obtaining the correlation, frost mass measurements from previous researchers were added to the presented experimental results to develop a correlation valid over a wide range. As a result of the broad data set, the correlation is valid for the ranges between; air velocity of 0.7 – 2.5 m/s, air temperature of 5 – 22°C, plate temperature of -5 – -25°C, air relative humidity of %50 – %83.73 and plate length of 85.6 – 300 mm. The calculation capability of correlations has been compared in cases where the dimensionless plate length parameter is among the correlation parameters and when it is not. It has been determined in the mentioned comparison that the inclusion of the dimensionless plate length among the correlation parameters increases the calculation capability of the correlation, as evidenced by the reduction of the calculation error from 27% to 17%. The magnitude of the exponent of the dimensionless plate length has revealed the importance of including the dimensionless plate length among the dimensionless parameters. It has been determined that the Sherwood number changes more intensely at high plate temperatures.
In extendended surface study, finned surface were used. Fins with a rarely encountered spacing of 4 mm have been positioned on the plate surface at a height of 19 mm and a thickness of 1 mm in the test cell, which was supplied with a uniform air velocity distribution as in the flat plate studies, and frost formation was investigated. Frost was formed on the finned plate at water bath temperatures of -23, -30, -33°C, while the air temperature was 10°C, the relative humidity %75 and the air velocity 0.7 m/s; then under these conditions, the plate surface temperature near the trailing edge, and the temperatures along and perpendicular to the flow direction, were measured on the fin. In addition, at the end of the experiment, the accumulated frost mass, the continuous heat flux, and the frost thickness distribution formed on the front and upper side of the frost in a structure with narrow fin spacing were also measured.
It is observed when examining the finned plate surface temperature measurements that after the plate surface cover is opened, the plate temperature first increases and then decreases. Less frost accumulates at higher plate temperatures, therefore, due to the slower frost accumulation at high plate temperatures, the clogging of the front part of the fins slows down. This situation leads to an extension of the duration for which the surface temperature remains at the maximum value. The temperatures at the front, middle, and rear of the fins also increase when the plate surface cover is opened. At first, the temperature values at the front, middle, and rear of the fin are different, but as time progresses, it is observed that the temperature values of the front and middle fin approach each other. This indicates that over time, due to frost accumulation at the front of the fins, the air cannot reach these areas and thus cannot heat them. The rear area of the fin has been the coldest region throughout the test, as it is the area where the air can reach the least, and therefore, heat the least. Upon examining the temperature changes on the fin surface along the fin height, it has been measured that after the first half of the experiments, the temperature differences between consecutive points at a vertical distance on the fin have increased. This indicates that as the front part of the fins becomes clogged, the heat transfer on the fins increases. The pause in the decrease of the temperature value near the tip of the fin can be said to provide information about the timing of the clogging of the front region of the fins. At the temperature measurement point near the base, it is observed from the measurements that the temperature drop continues uninterrupted.
When examining the slopes of the surface temperature and heat flux graphs, it is observed that the slopes of the graphs are different during the second half of the -23°C water bath test, which indicates that as the plate temperature increases, the effect of frost accumulation on heat transfer is spread over a wider period of time. When the surface cover is opened, the surface temperature and heat flux increase. Due to the increase in frost accumulation, the effect of the difference in plate temperature is negated towards the end of the test, and the heat flux values become very close to each other. As the bath temperature decreases, the finned plate surface temperature also decreases, resulting in an increase in the mass of accumulated frost as the bath temperature falls. The mass of accumulated frost was measured to calculate the latent heat transfer, and this was subtracted from the total heat flux measurement to calculate the sensible heat flux. At -23°C and -33°C water bath temperatures, it is observed that the sensible heat flux is higher. Considering that the front part of the finned plate is clogged and after a while, heat transfer occurs from the fins instead of the base, it is possible to say that the fins being warmer has an enhancing effect on the sensible heat transfer in the case of frost accumulation. It has been determined from the measurements of the mass of accumulated frost over time that the fastest frost accumulation occurs in the first 15 minutes.
When examining the upper side of the frost layer at the 15th minute, the formation of a frost layer extending outward on the front face of the fins has been observed. As the air moves between the fins, it loses moisture, resulting in a greater frost thickness at the air inlet section of the fins, while the frost thickness decreases towards the middle of the fin in the direction of the airflow. Additionally, it has been observed that frost accumulation forms outward at the fin tip area. When examining the thickness values of the frost layer measured from the top at the 15th minute, it is observed that the frost layer starts thin in the coldest water bath, and when the bath temperature is increased, the frost layer thickness also starts thin. Upon examining the average frost thicknesses, it is seen that the thickest frost layer forms at the lowest bath temperature. The upper views of the frost layer have been recorded at 15-minute intervals. At the 15th minute, despite the accumulation of frost between the fins, there is still a gap between them. From the 30th minute onwards, the space between the fins is being closed by the accumulating frost. After the 30th minute, there is no significant difference in the thickness of the frost layer measured from the top. Frost accumulation is not observed in the middle section of the fins according to the direction of air flow, as it ceases after a certain distance.
By positioning the camera behind the fins relative to the air flow, the front view of the frost accumulation has also been monitored. It is understood from the image that the air flow, which is blocked by the frost accumulation at the front, redirects towards the upper part of the fins, then passes over the middle section of the fins, and heads to the rear section, creating frost accumulation on the fin surfaces at the back. At the 15th minute, when examining the frost structure between the fins, it is observed that while the frost thickness continues evenly over a long section from the top end of the fin, a thicker layer of frost has formed near the base due to frost accumulation. As frost accumulates in the lower section, the air is directed to the upper section, resulting in the leveling of the frost layer. Additionally, for the first time in the literature, a frost peak has been observed in the middle area between the fins on the base. Upon examining the frost thickness at the front, it has been determined that the thick layer of frost on the lower section of the fin surface is a result of condensation on the upper part of the fin. When examining the change in frost accumulation on the front over time, it is observed that the thickening of the frost layer slows down after the 15th minute.