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Tel örgü katmanlardan oluşan gözenekli ortamda zorlanmış ısı geçişi

Başlık çevirisi mevcut değil.

  1. Tez No: 55913
  2. Yazar: MUSTAFA ÖZDEMİR
  3. Danışmanlar: DOÇ. DR. A. FERİDUN ÖZGÜÇ
  4. Tez Türü: Doktora
  5. Konular: Makine Mühendisliği, Mechanical Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1996
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 144

Özet

Tel örgü katmanlarından oluşan gözenekli ortamın, hidrodinamik ve zorlanmış ısı geçişi karakteristiklerinin incelendiği bu çalışmada, ortamın gözenekliliği, viskoz ve atalet geçirgenlikleri, dispersiyon ve ısı taşınım katsayıları teorik ve deneysel olarak tesbit edilmektedir. Gözenekli ortamın süreklilik modeli ve bu modele göre süreklilik, momentum ve enerji denkliklerinin elde edilişi kısaca açıklandıktan sonra sırasıyla aşağıdaki çalışmalar yapılmaktadır. Tel örgünün gözenekliliği ve gözenekliliğin hacimle değişimi deneysel olarak bulunmuş ve hacmin artışıyla gözeneklilikteki salınımların azaldığı görülmüştür. Ortamın temsili birim hacmini tesbit etmek için, seçilen hacim elemanlarıyla ortam taranarak gözenekliliğin sabit kaldığı hacim elemanı bulunmuştur. TBH olarak seçilen bu hacim elemanıyla temsil edilemeyen dış duvara yakın bölgelerde, gözenekliliğin eksponansiyel değiştiği kabul edilerek bu fonksiyona ait katsayılar tesbit edilmiştir. Ayrıca, tel örgülerde gözenekliliğin yaklaşık hesabı için yeni bir metod önerilmiş ve bu metod, deneysel sonuçlarla karşılaştırmıştır. Hazırlanan deney tesisatında Forchheimer akış rejimi için hidrodinamik deneyler yapılarak, basınç düşüşü-debi arasındaki ilişki tesbit edilmiştir. Bu ilişki yardımıyla gözenekli ortamın viskoz ve atalet geçirgenlikleri hesaplanmıştır. Düzgün dağılımlı ısı akısı sınır şartında ölçülen yüzey sıcaklıkları ve akışkan giriş-çıkış sıcaklıkları yardımıyla Nusselt sayısının kanal boyunca değişimi bulunmuş tur. Nusselt sayısı için Peclet sayısı ile akış doğrultusuna bağlı bir korelasyon fonksiyonu elde edilmiştir. Yüksek hızlarda ısıl sınır tabaka kanal sonuna kadar devam ettiği için, ölçülen üst yüzey sıcaklığına eksponansiyel bir eğri uydurularak tam gelişmiş haldeki Nusselt sayıları hesaplanmıştır. Tam gelişmiş ısı geçişi hali için bulunan Nusselt sayısının ve ısıl giriş uzunluğunun Peclet sayısı ile değişimi için deneysel sonuçlara göre korelasyon fonksiyonları elde edilmiştir. Deney tesisatı ve sınır şartlarına uygun matematik bir model kurulmuş ve buna göre yapılan formülasyonun hem yaklaşık hem de sayısal olarak çözümlerinden ısıl dispersiyon katsayıları tesbit edilmiştir. Deneysel sonuçlarla uyumlu ısıl dispersiyon katsayıları ile yapılan sayısal çözümden elde edilen Nusselt sayısının ve üst yüzey sıcaklığının akış doğrultusuyla değişimleri ile akışkan sıcaklıklarının akışa dik kesit boyunca değişimleri deneysel sonuçlarla karşılaştırmıştır.

Özet (Çeviri)

The porous media have been used widely in many engineering fields such as heat storage, solid matrix heat exchangers, thermal insulation of buildings, cooling of electronic equipment, chemical reactors, space researches. Therefore, momentum and heat transfer through porous media have been the interest of many researches. Depending upon the application, natural, forced and mixed convection through some porous media have been examined both theoriticaly and experimentally. The solid matrix of the porous medium affects heat transfer and causes resistance to flow. Therefore, an ideal porous medium is such that the dispersion caused by solid matrix is high resulting in increased heat transfer rates, but has low resistance on the walls. Due to the high porosity of the medium made of the wire screen meshes, the specific surface area is decreased, consequently the resistance against flow is also decreased. On this reason, the characteristics of forced convection through the porous medium of the wire screen meshes is examined in this thesis. Porosity, viscous and inertial permeabilities, dispersion and heat convection coefficients of this medium are examined both theoritically and experimentally. The definition and classification of porous media have been made firstly. Then, the continuum model of a porous medium, the need for a continuum approach, the representative elemantary volume (REV) and its selection have been described in general. The conservation equations of the porous medium have been found by integrating the conservation equations of the fluid and solid phases according to the REV. In the continuity, momentum and energy equations obtained by the notion of continuum, there are some terms which are defined by the microscopic quantities such as pore velocity and pore temperature. These terms which show the drag on the solid-fluid interfaces, thermal conductivity of the medium and thermal dispersion arising from the flow must be defined by the mean quantities of the REV. Therefore, some models developed by using constitutive theory and experimental studies have been explained here. After defining generally these theoritical background on porous medium, the geometrical properties of the medium of wire screen meshes have been determined experimentally. For this, the wire volume of the screen and the heights of the screen layers measured. Then, the cross-sectional porosity variation based on volume was calculated by these measurements. A volume that contained both solid phase and void space was selected as a REV.and then, it was placed at every point within the porousmedium and the porosity was calculated according to this volume. When the porosity became constant, this volume was confirmed as the REV of the medium. This constant porosity was taken as the core region porosity. In the boundary region that could not be swept by the REV, the porosity variation was defined as an exponential function and the dimensionless coefficients of this function were determined according to the porosity measurements. On the other hand, a theoretical method was developed to calculate the wire volume and porosity of a single screen mesh. This method was compared with another method and the porosity measurements of this study. Hydrodynamic experiments conducted in the experimental apparatus that was explained in the following section. The relationship between pressure drop and flow rate was obtained in the range of Reynolds number from 1.5 to 12. The Reynolds number was based on the wire diameter and mean velocity. Then, the viscous and inertial permeabilities of the medium were calculated by the help of this relationship. Local Nusselt number variation based on the flow direction and Peclet number was determined experimentally. Then, some correlation functions of Nusselt numbers and the length of thermal entrance region were derived from experimental data. On the other hand, the fluid temperatures were measured in the cross-section perpendicular to the flow direction. After this experimental study, the momentum and energy equations obtained by the notion of continuum model of porous media, were arranged to simulate the experimental setup. Then, they were solved analitically and numerically to determine the thermal dispersion coefficients of the medium. The solutions obtained by using these dispersion coefficients were compared with experimental data. Thus,, the study on hydrodynamic and forced thermal convection of the porous medium of wire screen meshes has been completed for the range of Reynolds number from 1.5 to 12. And porosity, viscous and inertial permeabilities, heat convection and thermal dispersion coefficients were obtained in this range. Experimental Apparatus The apparatus shown in Fig. 1 was prepared to perform momentum and heat transfer experiments. This apparatus was constructed of plexyglass which was 5 mm and 10 mm in thickness, except the upstream reservoir. This reservoir which had dimensions of 520x520x1200 mm and made of fiberglass had a series of adjustable overflow dividers to provide a constant pressure head. The downstream reservoir measured 180x180x300 mm. The test section was in the form of a channel which was 180x50x500 mm in dimensions. The water which is held at a constant level in the upstream reservoir flows through porous medium in the channel into the downstream reservoir. The water level in the downstream reservoir varies according to flow rate. When the water column comes to a certain level at a flow rate adjusted by the exit valf, the exit pressure comes to a fixed value, also. Thus, a fixed pressure difference is obtained for the respective flow rate. xviThere were two pressure taps at the inlet and outlet of the test section as shown in Fig. 1. These pressure taps were connected to a vertical manometer. Thus, the pressures that could be determined by the water levels in the upstream and downstream reservoirs, were measured precisely by the help of the manometer. The set flow rate was calculated by measuring the volume of water drained for a given period of time. The medium was heated from the top. This approach was taken in order to eliminate natural convection effects. Heating was supplied by five identical strip heaters put on the copper plate which was 15 mm thick Each heater provided 200 watts maximum. These electrical heaters were supplied by an adjustable DC source. The uniform heat flux boundary condition could be maintained by suppling each heater with same voltage and current. The test section was insulated with asbestos cloth, asbestos plate and fiberglass. 14 Q 15 l)Upsteam reservoir, 2)Dividers, 3)Test section, 4)Porous medium, 5)Downstream reservoir, 6) Valf, 7)Pressufe taps, 8)Manometer, 9)Direct current source, 10)Tempe- rature props, 1 1 )Milivoltmeter, 12)Scanner, 13)Icebath,14)Water filter, 15)Pump Figure 1. Experimental Apparatus The surface and fluid temperatures were measured by NiCr-Ni thermocouples. 1 2 thermocouples were embedded in the copper plate close to the upper surface of the medium in order to measure the surface temperatures. 15 thermocouples were installed on the bottom surface. There were 5 thermocouples on the upper surface of the heaters and 5 at inner and upper parts of the insulation, also. There were three taps of thermocouple probes in order to measure temperature profile in porous medium at the cross-section perpendicular to flow direction. Porous medium was drilled at the positions of these taps to move the probs. The sensitive point of the temperature prob that had same kind of thermocouple was surrounded with a small copper ring. This copper ring was placed on top of a ceramic tube which xvncontained the thermocouple leads. An ice bath was used as the cold junction of all thermocouples. A milivoltmeter was used to measure the voltage of thermocouples. Results of Hydrodynamic Experiments The objective of these experiments was to determine the relation between pressure drop and flow rate in the porous medium. The viscous and inertial permeabilities were calculated after finding Ergun's constants. Here, the measure ment range covered the begining and developing regions of Forchheimer regime. Darcy regime in which AP/L changes linearly with um could not be observed in this study because of high errors in measurement of pressure. Furthermore, the experiments for turbulent flow that occurs at high flow rates could not be carried out with the experimental apparatus used. In the experiments, Reynolds number based on mean velocity and wire diameter was changed between 1.5 and 12. The experimental data implied a second order parabolic relationship between pressure drop and flow rate. This is an expected chracteristic of Forchheimer flow regime. When arranging this relationship with dimensionless quantities, it became, V L J uur for first medium, and v L J uur for second medium. = 3.0972(±0.1432)Rem+ 10.8462(±0.9924) = 3.1493(±0.1859)Rem + 58.8837(±1.4754) The pressure drop equation of Carman-Kozeny model for Forchheimer flow regime is V LJ\xum e3 e3 where Ae and BE are Ergun's constants. When this is compared with the above two, Ergun's constants according to mean porosity of the medium were calculated as AE=1 10.86110.14 BE=6.86±0.32 for first medium, AK=321.56±8.06 BE=4.61±0.27 for second medium. Since the viscous and inertial permeabilities are defined as e3d2“ e3d ”B K =,, K“ = _ ”“ F = E Ae(1-e)2 ”BE(l-e) VAT»*/* then they were calculated from the experimental data as follows. Kw=2.3050 \U* m2, K“=1.6144 10”4 m F=0.9404 for first medium Kw=0.4246 İÜ“8 m2, K.,=1.5877 10-4 m F=0.4104 for second medium XVIllResults of Heat Transfer Experiments The heat transfer experiments were carried out for the heat flux range of 4-7 kW/m2. Four different flow rates were considered for first medium and no temperature profile measurements were made. For the second medium, however, experiments were conducted for ] 1 different flow rates, and measuring temperature profiles at three of the flow rates considered. Inlet and outlet temperatures were measured for all of the flow rates in order to calculate overall heat transfer. The local Nusselt number was calculated by using the heated surface temperature, bulk temperature and heat flux data as hH q”H Nu_ = - - = ka k.(T0-b) Local Nusselt number variation along the channel indicated that the thermally developing flow extends to the entire channel length for high flow rates. For that cases, since the fully-developed conditions could not be attained, a curve fit was applied to the heated surface temperatures. From the curve fit functions, the surface temperatures were extrapolated for the length of 2L. Using the extrapolated surface temperature data, the Nusselt number was calculated. The Nusselt number calculated with this approach indicated that the fully-developed conditions were reached at 2L. A correlation fiinction for Nusselt numbers of the fully-developed flow case was obtained as Nub= 0.221 l(PemVDa7)n5992 10 d uae Ppa 2 0= + u - - -^- - V-3- dx r a dy2 K c5 o Paca < u > ox dy The boundary conditions were taken as < u > (0) = 0 < u > (H) = 0 veya (ko+kd) g~ d(H/2) dy = 0 d(x,H) r, 1c?(x,0) ^ = 0 -[ko(0) + k-(0)] ^ q; (0,y) = T The thermal dispersion conductivity was confirmed as the following formula. kd =yPaca %/d) * = [l-Exp(-y/o>d)].. Analitical solutions of the model were carried out with the assumptions of constant porosity and uniform velocity distribution. From the solutions, the dispersion coefficients were obtained as 0.12 and 0.17 for the first and second media respectively. The difference between experimental Nusselt numbers and that of the analitical solution were found to be 11% maximum. The equations of the model were solved numerically without any assumption. From the results, the dispersion coefficients were obtained as y=0.08, co=1.5 and 7=0.27, co=1.5 for the first and second medium respectively. Nusselt number variation and temperature profiles calculated using these dispersion coefficients were in good agreement with those of the experimental measurements.

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