Yatay Borular İçinde Akmakta Olan Soğutucu Alışkanın Buharlaşması Esnasında Isı Taşınım Katsayısının Değişiminin Çeşitli Parametrelere Göre İncelenmesi

Abstract

Dairesel kesitli yatay borular içinde buharlaşarak akmakta olan bir soğutucu akışkanın söz konusu olduğu hallerde ısı taşınım katsayısının çeşitli parametrelere göre nasıl değiştiğinin incelendiği bu çalışmada, önceden yapılmış deney sonuçları veri olarak kullanılmış ve nümerik yöntemler yardımıyla bir teori üretmede yararlı olabilecek ampirik ifadeler elde edilmeye çalışılmıştır. Deney sonuçları, ampirik ifadelerin elde edilmesinde faydalanılan bilgisayar rutinlerine uygun hale getirilmek için önce boyutsuzlaştırılmıştır. Elde edilen sonuçlar da boyutsuz olmakla birlikte kolayca fiziksel büyüklükler cinsjnden ifade edilebilmektedir. Verileri değerlendirerek bağıntıyı elde etmek için 50 farklı matematiksel metod ayrı ayrı incelenerek bunlardan en uygun ve olayın fiziksel yanını en iyi yansıtan bağıntı tercih edilmiştir. Deney ve hesap sonucu bulunan değerler birbirleri ile karşılaştırıldıktan sonra hem veriler ve hem de sonuçlar birer tablo halinde çalışmaya eklenmiştir. Elde edilen sonuçlar, matematiksel açıdan değil, fiziksel açıdan konuyu en iyi yansıtan tipte bağıntılar kullanılarak bulunduğu için, sapmalar açısından ancak belirli sınırlar içerisinde kalmıştır. Sonuçların irdelendiği bölümde, bu çalışma sırasında dikkate alınan diğer noktalar üzerinde durulmuş ve bunların etkisinin ne yönde olup nasıl hesaplanacağına dair önerilerde bulunulmuştur. Genel olarak elde edilen sonuç tatminkar bulunmuştur.

In this study "The change of heat convection coefficient with certain parameters in evaporating flow of refrigerants in horizontal tubes", the general heat convection coefficient has been considered as the function of certain physical and thermodynamical parameters in case of a refrigerant- flow with evaporation. A simple computer program and various numerical methods were used in order to characterize the situation best. Both the program and methods were obtained from various books and papers. The numerical methods, 50 different and unique equations, were gathered from mathematical books which are designed especially for engineering and curve-fitting applications. The computer program was an ordinary Microsoft Windows based program which runs on a personal computer. All data used for input for the program were taken from the paper of Chawla [1]. The experiments resulting these data were done by Chawla and given as tables within that study. In order to be able to use the data best, the variables were non- dimensionalized and rearranged. The experiments assumed the variables to be the vapor quality (in this study as x), the mass flow rate of the refrigerant (in this study as G), the heat flux or average load of the heater area (in this study as q), the inner diameter of the tube (in this study as d) and the saturation temperature of the refrigerant (in this study as t). As far as known, the vapor quality does not have a unit. The mass flow rate was given in kg(refr.)/h. For convenience this unit was rearranged to kg(refr.)/m2h. Average load of the heater area or the heat flux was given in terms of kcal/m2h. The inner diameter of the tube was given in mm, which was not satisfactory to meet the non-dimensionalization process. Thus, this unit was converted to m. Finally, the saturation temperature of the refrigerant 1 1 was given in terms of °C. The results obtained using these variables all were the average heat convection coefficients (in this study as h), which was measured in kcal/m2h°C. Although some of the units mentioned above are replaced by their up- to-date versions, such as Watts and Kelvin, these are left as-is, since they are still allowed. As mentioned above, all data were non-dimensionalized and rearranged in order to simplify the calculations. For example, the heat flux IX data were used after having been multiplied by the diameter of the tube and divided by the average heat conduction coefficient of the liquid phase of the refrigerant and the saturation temperature. That is, Qd - (1) H kt Similarly, the mass flow rate data of the refrigerant were used after having been divided by a certain mass flow rate, i.e. G^-f- (2) Go There was no need to non-dimensionalize the vapor quality since this variable was already non-dimensional. Therefore, the data of vapor quality were used as-is. The use of data without any dimension resulted to non-dimensional heat convection coefficients. As far as known from heat transfer, the results are Nusselt numbers. Nusselt number can simply be described as Nu = M (3) Using the parameters defined above, the Nusselt number can be given as a function of the vapor quality, flow rate of the refrigerant, inner diameter of the tube, saturation temperature of the refrigerant and the applied heat flux. That is, Nu = f(x,G,d,ts,q) (4) Here, the diameter should be considered as the hydraulic diameter of the tube. Note that this equation is fairly general and applicable to any tube with any form of cross-sectional area. In spite of this, the diameter has to be the same value as the inner diameter of the tube. The heat conduction coefficient, which appears in the denominator has to be the heat conduction coefficient of the media filling the tube completely. Since the evaporating refrigerant did have two phases, namely a liquid phase and a vapor phase, the heat conduction coefficient of the media had to be calculated specially for this case. For the sake of simplification, a general assumption could be made and the heat conduction coefficient of the liquid phase alone was taken instead of the combination of the two phases. This was right, because the effect of the vapor phase to the average heat conduction coefficient was very low compared to that of liquid. This assumption is not unique to this study [3]. Because the stuff was written in Turkish, all the sub- and superscripts were chosen among the letters from the Turkish alphabet, which denote the first letter of the word describing the object or situation. That is, the subscript s denotes the liquid phase, translated into Turkish "sıvı". Just like this example, numerous other variables and parameters mentioned within this study were taken their names from the Turkish language. The methods, which were utilized to solve the problem and obtain an empiric expression were stated in the appendix and gathered from mathematical books. All the experimental data, done by Chawla, were given as tables in the appendix. Also, the non-dimensional terms were also stated within the section about application of the methods. Similarly, the results were given as tables too. The comprehensive explanation of the methods were given as tables in the appendix. Of course, the selected method was considered much more extensively. The method which described the situation best was in form of a power law equation, which has the general expression of y = axb (5) Note that a and b are denoting the coefficients, which are affected by the two parameters, y indicates the result, namely the heat convection coefficient and x is the independent variable. It is important to remind that this x here does not stand for the vapor quality. Utilization of the selected method was separated into three parts. In the first part, only the heat flux was considered to be the independent variable, where the mass-flow rate and vapor quality were fixed values or parameters. In other words, the independent variable of the equation above was q, the result h and the two parameters G and x were enclosed within the coefficients a and b. The second step was the calculation of the coefficients (a and b) which took place in the selected method. Then, as soon as the general expression for certain values of G and x were obtained, the independent variable was changed. Within the second evaluation, the independent variable was x, where the two parameters had to be G and q. However, at this point another expression yielded a better result for many of the data. Unless the higher values of x, the data showed a tendency to be changing fairly linear. But after a certain value of x (that was 0.8), the general type changed and turned to the power law expression again. Normally, a third evaluation, which should have implied the mass flow rate as the independent variable, was to be awaited, some problems occured. The experimental data seemed to be extremely irregular for certain XI values of vapor quality (ranging from 0.1 to 0.5) and therefore unsuitable for any curve fit. The effect of mass flow rate change without the vapor quality being considered as a parameter yielded logical results and taken into consideration as well. A comparison between the experimental data and calculated results were given both graphically and as tables in the appendix. The step-by-step application of the selected method and other important statements were given in the relevant section of the study. Other information, such as the physical properties of the refrigerant 1 1, the heat transfer concepts, the liquid-vapor phase change phenomena were stated as independent sections within this thesis. Also, a general consideration of parameters affecting the heat convection and a vast research of previous studies on similar cases were added. Finally, the evaluation of the results and some suggestions for improvement took place. In that part, the future research probabilities and some other aspects (which were not considered here) were stated and argumented. One can say that the obtained result is fair and can be applied to problems with similar or same conditions.