Fluidyne ısı makinasının analizi
Analysis of the fluidyne heat engine
Yazar: CİHAT ASLANTÜRK
Danışman: DOÇ.DR. A. FERİDUN ÖZGÜÇ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı
Derece: Doktora, 1997
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Fluidyne ısı makinesi = Fluidyne heat engine

Özet:
Isının mekanik enerjiye dönüştürülmesinde kullanılan Fluidyne Isı Makinası, hiçbir hareketli katı parça içermeyen, kolaylıkla imal edilebilen, atık ısıların değerlendirilmesinde son derece kullanışlı olan alternatif bir ısı makinasıdır. Literatürde 'Sıvı Pistonlu Motor' olarak da anılan makina, günümüze kadar daha çok pompalama uygulamalarında kullanılmıştır. Ancak, makinanın ısıl sistemlerde kontrol elemanı olarak da kullanılabileceği düşünülmektedir. Günümüze kadar bu konuda yapılan çalışmalar, genellikle deneysel ağırlıklıdır. Teorik çalışmaların yeterli olmadığı literatür araştırması sonucu görülmüştür. Bu güne kadar yapılan modellerde sıvı kolonlarına ait denklemler lineer hale getirilerek basitleştirme yapılmıştır. Ancak bu yaklaşım, titreşim hareketi yapan sıvı kolonlarına ait genliklerin, kolon yüksekliklerine göre çok küçük olması durumunda doğru sonuçlar vermektedir. Termodinamik inceleme ise, makinaya ait çevrimin kullanılan akışkanın hava olması durumunda Stirling çevrimi, hava-buhar karışımı olması durumunda ise Stirling ve Rankine çevrimlerinin bir bileşimi şeklinde olduğu kabul edilerek yapılmıştır. Bu çalışmaların, makinanın çalışması hakkında genel sonuçlar ortaya çıkarmadığı, yalnızca bazı parametrelerin etkilerini yaklaşık olarak verdiğini söylemek mümkündür. Bu çalışmada, Fluidyne Isı Makinası 'nın çalışmasını açıklayacak bir matematiksel modelin oluşturulması amaçlanmıştır. Model kontrol hacmi formülasyonu ile her bir sıvı kolonu için momentum denklemi, toplam sıvı kütlesinin korunumu denklemi, buhar bölgesi için kütle ve enerji korunumu denklemleri yazılarak oluştulmuştur. Oluşturulan model ile bir non-lineer adi diferansiyel denklem takımı elde edilmiş ve denklem takımı Runge-Kutta yöntemi ile çözülmüştür. Modelin doğruluğu yapılan deneylerin sonuçlan ve literatür ile karşılaştırılarak araştırılmıştır. Elde edilen deneysel veriler ve model sonuçlan değerlendirilerek farklı ısıtma gücü ve doluluk oranlarında, sıvı kolonlarına ait konum-zaman diyagramları, termodinamik çevrime ait P-V diyagramları ile makinanın çıkış güçleri ve verimleri hesaplanmıştır. Yapılan deneylerde iş yapan akışkanın su buharı olmasına karşın, model herhangi bir akışkanın kullanılmasını mümkün kılmaktadır. Karşılaştırmalar, modelin deney sonuçlarıyla uyumlu olduğunu göstermektedir. Elde edilen model, optimum tasarım verecek parametrelerin tespit edilmesine imkan sağlamaktadır.

Abstract:
For many years, the energy demand of the world has been provided by burning fossil fuels. During the last couple of decades, increasing awareness on environmental pollution has lead to stronger emission standards. This has compelled researchers to concentrate their works on the efficient use of energy obtained from the fossil fuels and effective and economical utilisation of many types of renewable energy sources. Fluidyne is a heat engine which utilises waste heat or solar energy. Therefore it suits very well the above mentioned purpose. The objective of the current study is to model Fluidyne mathematically and perform some experiments to test the applicability of the model and obtain guidance for the modelling. Fluidyne is a very simple heat engine without any moving parts using a liquid column as a piston to convert heat into mechanical energy. It is comprised of a displacer and an output column. The displacer is a loop made up of hot and cold columns and connected to the output column on the hot column side. The working fluid confined between the hot and cold columns is heated in the hot side and cooled in the cold side. This results in a change in the volume and pressure of the fluid within the upper part of the loop connecting the two columns. This pressure change works against the friction in the liquid columns in the hot and cold columns resulting in an oscillatory motion of the liquid in the output column. In order to use Fluidyne optimally to produce mechanical energy, its operation characteristics needs to be determined. This could be achieved by modelling the engine mathematically and performing experiments to test the model whether it reflects the physical mechanisms involved realistically. In this study a mathematical model has been developed and an experimental rig was set up to test the mathematical model. The mathematical model was developed writing the conservation equations for the liquid columns and the working fluid inside the upper part of the loop. Phase change of the working fluid was also considered and evaporation and condensation rates were included in the model. The set of non-linear differential equations forming the model were solved using Runge-Kutta method. An experimental rig closely resembling the mathematical model was fabricated. Experiments were performed to determine the oscillation characteristics of the columns and heat losses from the system. The results from the solutions and experiments were compared to examine the quality of the model. Efficiency of the engine as function of filling ratio and heat input was obtained. Experimental set-up and experimental work The experimental set-up used in this study is shown in Figure 1. The rig is made up of a combination of glass and plastic tubing. The sections numbered as 1, 2 and 3 areglass tubes of 35.5 mm internal diameter with 0.5 mm wall thickness. The rest of the portions of the rig are plastic tubes of 25 mm inner 40 mm outer diameter. Copper tubes of 13 mm diameter fitted with rubber caps were inserted into the hot and cold columns in order to provide heat input and cooling. Rubber caps were fixed to the ends of the hot and cold column tubing and were sealed using silicone adhesive. 1) Output Column Tube, 2) Hot Column Tube, 3) Cold Column Tube 4-5)Dispacer horizontal lubes, (6) Cooling Water Tube, 7) Healer Tube 8-9) Fittings, 10) Thermocouples (11) Heater Figure 1. Experimental rig A cylindrical electric resistance heater of 10 mm diameter and 106 mm long was inserted into the copper tube on the hot column side in order to obtain a uniform heat flux heating condition. The heater has a resistance of 15 ohms and was supplied by an AC voltage regulator so as to apply a variable heat input. A multimeter was used to measure supply voltage and current. Mains water was flown inside the copper tube on the cold column side to provide cooling. The flow rate of the cooling water was measured using a marked up glass container. The inlet and outlet temperatures of cooling water and surface temperatures of the tubes at different locations marked on Figure 1 were measured by Cu-Cons. thermocouples. A typical experimental procedure was as follows. For a given heating rate and a filling ratio, the mains water was opened an the heater was put on. After steam was formed in the upper part of the loop, it took about 30 seconds to reach the steady state. The overall settling time from the start was dependent on the heating rate and the highest settling time was about 20 minutes. After steady state conditions were reached recording of the motion by video camera was carried out for about 30 seconds covering several periods of the oscillations. At the same time temperatures were monitored and recorded manually completing the experiment set.A Panasonic 2000 video camera capable of 25 shots per second was used to record the motions of the liquid columns. Graphics papers were placed behind the columns so that the displacement rates of the columns could be determined from the video pictures. Preliminary tests have shown the oscillations of the fluid columns to be Sine waves. In order to calculate the amplitudes, frequencies and phase lags of the fluid columns, an equation of the form given below was adopted. h(t) = A + Bcos(Ct + D) The coefficients of this displacement equation were obtained by least square fit from the experimental data for every set of experiment. The coefficients A, B, C and D represents the shift of the oscillation line from the reference line, the amplitude of oscillation, the frequency of the oscillation and the phase lag respectively. Starting from the displacement equation and using the momentum equation the volume and pressure were calculated for every experimental set. Theoretical Model Mathematical model was obtained by the use of control volume formulation. In that conservation equations of mass and momentum for the liquid columns and that of mass and energy for the working fluid in the upper part of the loop were written. In the latter the terms resulting from the phase change were included in both equations. As shown in Figure 3 Fluidyne was split into four control volumes, three for liquid (marked as 1,2 and 3) and one for steam (marked as 4). The following is the general form of momentum equation for a control volume in flowing fluid. r-_ Ul. » If this equation is written for the three liquid column of the present study, for i =1,2,3 takes the following form. Figure 2. The fluidyne heat engine xuiajZiZj +bizi+ci|zi|zi+dizizi+eizi+fizi = PX-Pj where the coefficients are aı=Pı> bi=°. Ci = Pi, di="T^1' ei=0' fı = PiS Add 8m l 87C|Lll d a2=Pi> b2=p,ldy, c2=p,, d2=- -, e2=- ?, f2=p,g Add Add, 87l(.l 87tuIo a3=Pi» b3=Pi1o> c3=p,, d3=--, e3=- -, f3=p,g Conservation of mass for the liquid columns can be written as; PiVto =p,[(z1+z2)Add+ldyAdy+(z3+l0)A0] = constant where the lefthand side of equation represents the liquid column mass at the beginning and the righthand side that of instantaneuos value. It is assumed that the effects of evaporation and condensation on the mass of liquid columns are negligible. Conservation equations of mass and energy for the steam region can be written as follows. dmv - rL = me-mc dt -[mvu] = Q-W + mehe-mchc Where, mv represents the mass of steam at a given instance, m e represents evaporation rate and rhc that of condensation, u is the internal energy of steam, Q and W are the net heat transfer between the control volume and ambient and work done against the ambient respectively. he and hc represent the anthalpies of incoming and outgoing steam for the control volume. Condensation and evaporation rates are given by the following equations respectively. mc=7cDbl0hm(Tv-Tw)/hfg m. = (hfg + CpAT)Results and conclusions Fluidyne described previously was modelled mathematically. The non-linear differential equations of the model were solved using Runge-Kutta method. Experiments were performed to provide guidance to the modelling and check the model where possible. Efficiency of the engine with respect to power was calculated and given in Figure 3 graphically. It can be seen clearly that theoretical calculations and the experimental results qualitatively agree very well though not quantitatively. The difference between the experimental and model results are thought to result from air suction into the steam region. 0.12 0.1 r? 0.08. c 0.06 o "3 e UJ 0.04 0.02 Filling Ratio =0.70 ? math, model - experimental 20 40 60 80 Input Power [W] 100 120 Figure 3. Efficiency vs. power, results of model and experiments. The following figure presents a typical indicator diagram obtained from the model. Figure 4 Typical indicator diagram obtained from the model. xvRelative displacement rates for hot, cold and output columns were calculated from the model and experimental data. The results for a typical experiment and corresponding theoretical case are given below in Figures 5 a and 5 b. 9P4 rt 900 99 »3 Figure 5. Displacement rates of the liquid columns, (a) Theoretical, (b) Experimental (Input Power=80 W, Filling Ratio=0.67) It can bee seen from the figures that there is as much as % 20 difference between the measured and calculated amplitudes for the hot and cold columns. As for the output column the difference drops to about % 9. Theoretical and experimental phase lag between the cold and hot columns differ by % 4. Judging from the results it was concluded that the mathematical model reflects the physical mechanisms reasonably well. xvi