Pülzasyonlu akışın enjektör verimine etkisi

Abstract

Kinetik enerjisi yüksek bir huzmeyi diğer bir akım ile karıştırarak ikinci akıma enerji verme olayı enjektör (veya ejektör)lerin ana prensibini oluşturur. Böyle bir hidrolik veya aerolik transformatörün geniş uygulama alanları mevcuttur. Jet uçaklarında itme arttırıcı olarak kullanılan türden, kazan besleme enjektörüne, nehirlerde tarama ve kum çıkartma işinde kullanılan enjektörlerden, dişçilikte kullanılan salya emici özel enjektöre kadar yayılan uygulama alanlarında, sistemin verimi kullanma yerinde varılmak istenen amaca göre tanımlanır. Bu yüzden değişik enjektör tanımlan mevcuttur. Enjektör ve ejektörler üzerine yapılmış teorik ve pratik bir çok çalışma mevcuttur. Bu çalışmada esas itibariyle üzerinde şimdiye kadar hiç durulmamış bir konunun ilk adımım atmak amaçlanmıştır. Ancak önce boyutsuz enjektör karakteristiklerine açıklık getirilmiş, boyut analizi kullanılarak enjektör karakteristiklerinin tipik şekli anlatılmıştır. Daha sonra 1991 yılında Elger, McLam ve Taylor tarafindan ortaya atılan karakteristikler analiz edilmiş ve bu araştırmacıların iddiaları incelenmiştir. Teorik olarak klasik N=f(M) debi katsayısı karakteristiğine ek olarak, Z=<|)(M) püskürtme katsayısı karakteristiğinin tüm benzer geometrili enjektörleri temsil edebileceği gösterilmiştir. Ayrıca bazı varsayımlarla teorik olarak hesaplanan Z püskürtme katsayısının, ne dereceye kadar gerçeğe yakın olduğunu incelemek için yapılan deneylerin sonuçlan kullanılarak ve yeni ortaya atılan karakteristiklerden deneysel değerler alınarak, püskürtme katsayısı hesaplanmıştır. Pülzatif akışın, enjektör karakteristiği özellikle verimi üzerindeki etkisini görebilmek için, enjektör primer akımı üzerinde kontrollü bir pülzasyon yaratılması amacıyla özel bir tesisat geliştirilmiş ve elde edilen akım, alan oram 0.35 olan bir enjektörde çeşitli şartlarda denenmiştir. Deneyler 3 farklı pülzasyon frekansında tekrar edilmiş ve elde edilen boyutsuz karakteristikler, pülzasyonsuz daimi rejimde çalışan enjektör karakteristiği ile karşılaştınlmıştır. Pülzasyonlu akışta çalkantıların şiddetini karakterize etmek için x çalkantı faktörü tanımlanmıştır. Basmç ölçmelerinde transdüser çıkışlarının amplifiye edilerek bilgisayara verilmesi ile veriler analize edilerek çalkantıların formu, periyodikliği ve şiddetleri belirlenmiştir. Elde edilen periyodik çalkantıların harmonik titreşime çok yaklaştığı standart sapma değerleri ölçülerek tespit edilmiştir. Kullanılan sistemde çalkantı faktörü pülzasyon frekansı ile azalmaktadır. Debi titreşimleri ile basınç titreşimlerinin faz farkından doğan faz faktörü doğrudan bilgisayar girdilerinden hesaplanmış ve birincil akımın sanal enerji girişlerinde düzeltmeler yapılmıştır. Elde edilen sonuçlar pülzasyonlu akışta, verimin hissedilir ölçüde arttığını göstermiştir. Artış miktan düzeltilmiş değerlerle de net bir şekilde gözlenmiştir. Pülzasyon frekansı 1 Hz olduğu zaman, olumlu etki en büyük değerine ulaşmıştır.

The basic principle of the jet pump is the transfer of momentum from one stream of fluid to another. The jet pump depends on the driving force of a high velocity jet for its pumping action. High velocity stream is provided by a high pressure source and discharges into a mixing chamber where motion is imparted to the entrained fluid by means of exchange of momentum. The purpose of the difiuser which follows the mixing chamber is to convert the kinetic energy to pressure head. In addition to the advantage of having no moving parts, one can mention among the merits of a jet pump, its simple construction, relatively low cost and selfpriming feature. Jet pumps and ejectors have been used in industry for a long time. They are used in combination with centrifugal pumps where suction lifts are high; in the chemical industry and laboratory; in the water treatment field for effective chemical mixing and in the dentist's surgery to keep the saliva level down. SIMPLE ENJECTOR THEORY Fig.[l] shows a jet pump in the simplest sense- a jet pump is any device which mixes high and low speed fluid streams to produce a combined fluid stream leaving the device. Fig. [1] A simple jet pump Suppose that a stream with high energy entering at section (1), mixes with a low energy streamn entering at section (2) and the mixture leaves the device at section (3). vu Energy flow rates at section (1), (2) and (3) are written respectively as pgQA,pgQ2H2,pgQ3H3. The energy taken from the injected flow can be written as pgQ^H^ - H3 ) while the energy imported to the second stream i.e. suction flow can be expressed as pgQ2(H3 -H2). If the efficiency is defined as the ratio of the power actually delivered to suction stream to that supplied by the jet stream, then Q2(Hi-H2) = where M is the flow ratio and N is the head ratio. This is the efficiency expression Gosline and O'Brien had stated in 1934, which had been used widely since then. Depending upon the method of using, design and place of the enjector, this expression may differ. Assume, (i) interior walls of the jet pump are smooth, (ii) a single fluid flows through the jet pump, (iii) elevations are known, (iv) cavitation does not occur, (v) inlet fluid streams are fully developed. Dimensional analysis gives insight about the number of variables needed to qualify jet pump performance. If the variables u,p,D and the shape are taken as independent variables and the flow rates Qj and Q2 are added to them, all other parameters are considered to be dependent variables as for example Hx, 1^, and H3 in Fig. [1] can be found. But for an incompressible flow if all the pressures are increased or decreased at the same amount, no difference would occur in the flow patterns and rates. Then the dependent variables will be; (H, -H%) and (fi, -H2) (2) and two equations are required and will be enough to characterize the flow, Hx -H3 =f(p,M,Q],Q2,D,form) (3) H% -H2 = y,(p,»,QvQ2,D,form) (4) Putting shape in the two functions, for all similar geometry's, Hx-H%=fx{p,M,QvQ2,D) (5) H3-H2=^(p,M,QvQ2,D) (6) V1U will be found. When % teorem is applied for 6 variables for each relations, there must be 3 non-dimensional independent numbers to characterize any condition in the phenomenon. They are related to each other by a characteristic equation. ç>(xl,z2,x3) = 0 (7) These non-dimensional parameters can be grouped as, 1 *=^-=Re (9) 2 u ^3=-^ (io) Only two of them can be arbitrarly chosen. If n2 and nz are independent variables two characteristic equations may be written in terms of - and Re as follows, Vx2/2g JKQX Hl~Hl = K-,Re) (12) vx2iig ^a ; v J For higher values, since Reynolds number would lose its effect, the same equations can be written as, 2,._=/(^Re) (H) V'llg JKQ, = f&) (13) Hl H> = «<% (14) vl2/2g ^e, When the performance characteristics of an enjector is taken into consideration, following parameters can be chosen as independent variables, p: density u,: viscosity d: nozzle diameter D: mixing chamber diameter Hx~Hy The energy spent in the system H% -H2 : The energy gained from the enjector IX Now that the working condition is absolutely fixed all other variables ı considered as dependent variables. Let us chose Qj as the dependent variable. Qx: The fluid volume flow rate entering the system The dimensional analysis would give four non-dimensional number. n, =- ^ = N : Head Ratio nd2 n2 = - J ! =Z : Injection Ratio n=(-f=R : Area Ratio j2g(H -H.)D k, = ! = Re : Reynolds Number v If the Re similarity is negligible, then and one characteristic equation can be written as N=f(Z,R) (16) In virtue of the % theorem, we can state that any couple of independent dimensional power can be chosen arbitrarly. Then if M, R are taken as indepen variables and N dependent variable, a second characteristic equation arises, N=f(M,R) (17) Most of the time this only characteristic is considered to represent an inje of given geometry while for conventional enjectors, equation (16) can be determ therotically. In 1991, Elger, McLam and Taylor in a research article, claimed that enjector characteristic by Gosline and O'Brien is not enough to design an enjector incapable of characterizing a jet pump. The two equations they recommend to use are defined by equations (13) (14) in the following form. K'=$m=f4*e-R) (18) ^-i^^4'Ke-R) (19) Kj and K2 are the jet flow loss coefficient and the suction flow loss coefficie They also recommend using the flow fraction Q2/Q3 as the independent variable instead of the flow ratio Q2/Ql. Because the flow ratio, which ranges from 0 to co, can compress results near low values of the flow ratio. The flow fraction, which ranges from 0 to 1, doesn't have this problem. Flow ratio can be calculated from flow fraction using conservation of mass. This forma has a more general character. Since the new curves are based on the assumption that the variables are measured at the bolt-in points of the jet pump, a designer doesn't need to estimate head losses inside a jet pump. PULSATING FLOW Pulsating flow is defined as the flow field in which the flow variables at the points lying on a given pipe cross-section with the exception of those in the boundary sub-layer exhibit periodic oscillations may be of a sinusoidal or other form and their amplitudes may have any value. In general term the energy flow rate at a section can be expressed as, Hl\ 'p^ V.n.dS (20) where dS is the elemantary surface. For a circular cross section are have, E = 2n][p+^-\Vj-dr (21) and for the potential flow the total head, (JP+/|i)=Pt (22) being constant we obtain simply, E=PtQ (23) For pulsating flows this value changes from one instant to another and we have to consider the average flow of energy. The energy of the volume flow rate given to the system by the fluid is measured by transducers and calculated with computers during the tests. To evaluate the mean of energy flow rate to following expression is to be used. E = Up.Q.dt (24) XI If the real volume flow rate, passing through a section in the pulsating flow is to be found, the multiplications of the mean values of P.Q should be taken in a wide spread time interval. On the other hand with mean pressure and flow rates we have, apparent energy flow rates as E0 =Q.P (25) Since, in general the appaent energy is measured during a test, a pulsating factor should be used to take into account the phase difference between Q and P. This factor, which is non-dimensional, is given as the proportion of the real energy flow rate to the apparent flow rate. E [P QT The fluctuation factor defined as the proportion of the standard deviation to mean value, is also an important factor in tests. *=-? (27) y For pressures for flows of purely sinusoidal character this factor can theoritically be calculated from ~İ& (28) where the standart deviation is a factor of the as,,= İ (29) RESULTS There have been done numerious investigations on enjectors. In the present work, an unknown topic had been tried to be chosen. First, the general characteristics, dimensional analysis, and efficiency methods were discussed. Recently jet pump characteristics had been taken into consideration and shown that the characteristics we had been using are enough to present the jet pump curves and to design one. To characterize the intensity of the fluctuation in the pulsating flow, the fluctuating factor x is defined and used. With the amplification of the pressure measurement signals taken from transducers to computers, the form of the fluctuation, the periodicity, and the intensities had been shown. Xll It's been found that the periodic fluctuation is very close to harmonic oscillations according to standard deviation results. In the system, the fluctuation factor decreases proportional to the pulsation frequency. In the next step, the effect of pulsating flow on the jet pump efficiency is examined. A special system which produces a controlled pulsating flow is used and an enjector of area ratio 0.35 had been tested. When the enjector efficiency characteristics working in an uniform and steady flow is compared with the characteristics working in a pulsating flow, positive results were seen. The experiments carried out in three different frequencies revealed that pulsating primary flows promotes the nergy exchange and that the efficiency of the jet pump is substantially increased. Another point is, although 1 Hz doesn't produce the maximum fluctuation, it causes the maximum improvement in efficiency.