Ses hızlı eksenel sıkıştırıcıların hızlı ve parametrik ön-tasarım bilgisayar modellemesi
A Computer model for the parametric and quick preliminary design of transonic axial compressors
- Tez No: 39148
- Danışmanlar: PROF.DR. KAAN EDİS
- Tez Türü: Doktora
- Konular: Enerji, Makine Mühendisliği, Energy, Mechanical Engineering
- Anahtar Kelimeler: Algoritmalar, Bilgisayar modellemesi, Eksenel basınç, Parametrik teknikler, Algorithms, Computer modelling, Axial pressure, Parametric techniques
- Yıl: 1993
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
Özet Bu çalışmada serbest dönme kuralına uyan, çevresel hız dağılımlı ses hızlı eksenel sıkıştırıcıların tasarımında hızla sonuca ulaşabilmek için Radyal denge denklemi üzerinde olabilecek basitleştirmeler yapılmış ve sonuçlar NASA'nın deney sıkıştırıcısı ile karşılaştırılmıştır. Bu karşılaştırma sonucunda modelin uygun sonuçlar verdiği belirlendikten sonra bazı parametreler değiştirilerek optimum değerlere etkileri incelenmiştir. Geliştirilen modelin önemli özelliklerinden biri de verileri değiştirerek çok çeşitli tasarım sonuçlarının elde edilmesine olanak sağlamasıdır. Aynı zamanda program kanat üzerindeki her noktanın koordinatını bulmaya imkan sağladığından kanat geometrisi üç boyutlu olarak hesaplanabilmektedir. Kullanılan sayısal teknikler ve yapılan basitleştirmeler sonucunda modelin hesaplama süresi birkaç saniye mertebesine indirilmiş ve tasarım simülasyonuna imkan sağlanmıştır. Bu tür bir algoritmadan bilgisayar yardımıyla tasarım amaçlı yararlanılabileceği gibi aynı zamanda bilgisayar yardımıyla eğitim için de yararlanılabilir. Modelle yapılan parametrik inceleme sırasında aynı kütlesel debi ve basınç oranını sağlayacak değişik dönme sayılan için optimum nokta tasarımları yapılmış ve verimi yüksek dönme hızlan için maksimum kütle debisinin azaldığı görülmüştür. Ayrıca gene yüksek dönme hızlarında şok kayıplarının verimi azaltıcı yönde etkili olduğu gözlenmiştir. Diğer yandan eksenel giriş hız profilinin kanat açılan üzerindeki etkileri incelenmiş ve aşın bir etkinin söz konusu olmadığı görülmüştür. Kullanılan algoritmanın bir analiz algoritması olmamasına karşın hesaplanan büyüklüklerin deneysel sonuçlarla kabul edilebilir yakınlıkta olduklar saptanmıştır. V1U
Özet (Çeviri)
Summary A Computer Model for the Parametric and Quick Preliminary Design of Transonic Axial Compressors In this study the radial equilibrium equation is simplified for a speedy preliminary design of free vortex blades of transonic compressors. The high speed of the design enables one to apply the techniques for CAD ( Computer Aided Design), CAE ( Computer Aided Education ) and with the engineering analysis programs for CAE (Computer Aided Engineering). A crucial difficulty of the analysis is the fact that the flow in a turbomachine is three dimensional. Wu [1] overcame this difficulty by introducing two dimensional surfaces namely S-l (blade to blade) and S-2 (meridional hub to shroud) as mean surfaces. (Fig. 1.1). We consider an axial turbomachine in which the flow in the blade row is supposed to be axisymmetric. For this analysis it is sufficient to concentrate en the meridional plane, at a particular axial station, along a given radius. We suppose there is no interaction between blade rows and vaneless space other then fulfilling of the equations for conservation of mass, energy and momentum and in particular we suppose that there is equilibrium between velocity and pressure forces between the blades and no curvature of streamline introduced by the blading along a given radius. The blades are considered as discontinuities in pressure, temperature and velocity vector. The radial component of the velocity is supposed to be negligible. For a zero radial component of velocity, the assumed equilibrium between pressure gradient and centrifugal force imposes, l±=Yl m pdR R K } along the radius at a given axial station The second principle of thermodynamics, written in differential form along the radius states that, Tds = dh 1 dp dR dR pdR K ' IXThe definition of total enthalpy gives a further relation, V2 V2 H = h+^- + ^- (3) 2 2 or, T = M d^ şk (4) dR dR e dR z dR v Eliminating h and p, leads to the classical simple radial equilibrium equation *L = T±+Va^+YL+Vz*K, (5) dR dR 6 dR R 2 dR v which is called Non Isentropic Simple Radial Equilibrium Equation (NISRE) Equation (5) provides a relation between the velocity components in function of radius for a given axial position, providing that the terms - and T - are known. The first one can be evaluated if the initial enthalpy distribution is known ahead of the rotor blade row (enthalpy is usually uniform at compressor inlet). Across a stator blade row for an adiabatic machine, the enthalpy increase is zero, and across a rotor blade row, along a streamline, 1 being upstream of the rotor, and 2 downstream: &Hrot=u2Ve2-u,VBX (7) Between the blade rows,(in the vaneless space) H is evidently constant on a streamline. The term T- - can also be evaluated in principle, when the initial entropy ds distribution ahead of the rotor blade row is known. The value of - can be evaluated dR behind any blade row either through the use of loss correlations section by section or the potential flow plus boundary layer calculation in the blade to blade plane model including secondary flow effects. More precisely the relation between entropy and the usual compressor loss coefficient,7j _ Po\R Pp2R PoiR -Pi can be expressed through the politropic efficiency as follows, For any stream tube and for a perfect gas with constant Cp, (8) rhz5.\ - y-ii. pJpsl R*.In T IT i02 ' i01 (9) As=fl*ln For a stator, T =T l02 10\ For a rotor, XrjTnT* '02 '.'01/ Poi1 Po\ (10) (11) ^02 A>1 - (-, ' W2 * 82 U\“e\ ) which is particular form of (7) for perfect gases with constant Cc (12) The absolute total pressure ratio is obtained by the following expression, in the case of a rotor: P P P P 1 02 - 02 ?* 02Ü.'Olft P P P P *0\ r02R r0\R r0\ with (13) Poi P0iR and 'if”\hiRj (12) T -T +-^-\v -%- °* » Cp{* 2, (13) by definition of the total temperature. If total temperatures are substituted into the Euler turbomachine equation in terms of relative total temperatures for the case of cylindrical streamline, (14) T =T XIor in general, T =T + («22-“,2) 2C”(15) If there were no losses, ;02ft <“oiK Jid with again,.y/r-i ?*02ft V 1C T (16) ^.j =1 for w2=w, V ”oiR Jid For this latter case, from (9) one obtains:“o2fi - -^OIR ”K*0\R P\)~“o 1-GJ Pi 1- V ”<0\R J J 'Olfi ( t Vr-ı 1 - cut 1- ' v ^oı« y (17) which is also valid for stators, with or without change of radius. For the rotors with change of radius: *02R ~\*Q2R>jd“o\R l-ra r t \ r/.Vl 1- K*0ir J 'y-\ (18) ds The function S = f{R) and thus - can be evaluated from the upstream thermodynamic conditions and the loss coefficient, presenting the diffusion factor as follows: D = 1-5. v ^J rı'«ı rvei 2F<JW (for rotor) (19) 2oK (for stator) (20) D is a so called diffusion factor, introduced to establish the necessary link between the experimental results and the loss calculation procedure as shown in Figs. 1.13 and XJl_cos(j3 ) 1.14 as a function of co - ^-^ ( Compressor loss coefficient, output flow angle 2o”and solidity ) NISRE equation is simplified by dropping the terms representing streamline curvature effect and contraction effect. Axial velocity distribution is obtained from the continuity and radial equilibrium principles. In order to account for the losses, in the calculation process first an overall efficiency is estimated. And accordingly the calculated rotor outlet total pressures are determined as much higher then those of the expected values to compensate for the losses. This way all the rotor outlet quantities necessary for the use of loss correlation are determined. Then through the available data, diffusion factor, profile loss parameter and finally actual overall efficiency for the design conditions at hand is calculated. This procedure is repeated until the efficiency calculated from the assumed design conditions converges to the estimated one. This is the first stage of the design procedure. The second stage is the determination of the blade angles. For this purpose first angle of incidences and deviation angles are calculated. And to maintain an almost uniform enthalpy distribution at the rotor outlet the blade angles obtained from these angles are corrected. For manufacturing purposes, a parabolic variation of the blade angles with respect to radius can be fitted. Then some solid modeling programs are used and from the profile geometry the blade surfaces and the three dimensional appearance of the blades are described. Assumption of either uniform or parabolic inlet flow condition do not cause any significant difference in the blade angles. For the same total pressure increase and mass flow, different optimum designs have been realized at different tip speeds of the rotor. The parametric trend of the efficiencies does not change significantly at the rotation speeds below the test case but decreases for the values higher than that. A significant result obtained from this analysis is the fact that the mass flow rate at the choking point reduces rapidly as the speed of rotation increases. Xlll
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