MECA-H-40: Turbomachinery course Axial compressors Pr. Patrick Hendrick Aero-Thermo-Mecanics Year 013-014
Contents List of figures iii 1 Axial compressors 1 1.1 Introduction............................... 1 1. Two-dimensional flow through a stage................. 1..1 Notations............................ 1.. Assumptions........................... 3 1..3 Velocity triangles........................ 3 1..4 How can I build an axial compressor?............. 5 1..5 Why is it so difficult?...................... 5 1..6 Influence/limitation of the axial velocity........... 6 1..7 Performance curves....................... 6 1..8 Surge and rotating stall.................... 7 i
ii Contents
List of Figures 1.1 Schematic representation of a stage of an axial turbocompressor.. 1. Schematic representation of an axial compressor........... 3 1.3 Velocity triangle............................. 4 1.4 C L vs. AOA............................... 6 1.5 Performance curves........................... 7 1.6 Wöhler diagram............................. 8 1.7 Rotating stall.............................. 10 iii
Axial compressors 1 This chapter discusses the principle of axial compressors. Axial compressors are excellent for high mass flow rates (up to at least 1000 kg/s), for very high pressure ratio s (up to 45 or higher) while a maintaining high isentropic efficiency. 1.1 Introduction Unlike radial or centrifugal compressors, a fluid particle in an axial compressor stays at a constant distance from the shaft of the machine. The Euler-Rateau formula shows that energy may be transmitted to the fluid by acting on the tangial velocity component or the relative velocity in the rotor. P R = ṁ R u V u (1.1) P R ṁ R = (v v 1) (w w 1) (1.) Operating principle: the compression is carried out in a number of stages, placed in series. Each stage consists of a ring of rotor blades (the rotor) and a ring of stator blades (the stator). The rotor blades are fixed on the drum; the stator blades are fixed at the casing. In the rotor, the mechanical energy available on the shaft is converted into pressure energy and kinetic energy that is communicated to the fluid. In the stator, part of this kinetic energy is transformed into pressure energy. The relative velocity at the entrance of the rotor and absolute speed at the entrance of the stator must have an incidence angle as the fluid does not detache. Given that the pressure must be increased in the rotor and stator channels, the shape of the vanes should be such that the flow channels are divergent. The curvature of a compressor blade is always lower than that of turbine blades to avoid this detachment. Behind the 1
Axial compressors last stage, the flow must be re-oriented axially before entering into the combustion chamber. Hypothesis: the actual flow through the machine is relatively complex. The actual three-dimensional flow is studied using a two-dimensional model. A model is obtained by a cut of the compressor following a surface of revolution, which is then developed in a plane. By this approach the flow is studied in a row. 1. Two-dimensional flow through a stage 1..1 Notations Consider a section of the compressor according to a cylindrical surface of radius r m. A stage is made out of a rotor and a stator. The first stage is sometimes preceeded by a distributor whose vanes may have an adjustable angle. The last stage must restore an axial flow (Fig. 1.1). Figure 1.1: Schematic representation of a stage of an axial turbocompressor The following notation is applied: 0 : inlet of the distributor 1 : inlet of the rotor : outlet of the rotor/inlet of the stator 3 : outlet of the stator v a : axial velocity v : absolute velocity
1. Two-dimensional flow through a stage 3 w : relative velocity u : tangential velocity α : angle between the absolute and the axial velocity β : angle between the relative and the axial velocity 1.. Assumptions Constant specific weight ρ: to prevent a detachment of the boundary layer, the pressure increase in a stage must be limited, it can then be assumed that the specific weight ρ is constant in a stage. In reality, the speccific weight ρ increases between stages (Fig 1. - ṁ = ρv ax A : A ==> ρ ). Constant axial velocity v a : the axial velocity through the compressor is assumed to be constant. Velocity between two stages (v 3 = v 1 - in reality v 3 is larger than v 1 ) : in the space between two stages, we consider that the fluid presents the same mechanical and thermodynamic characteristics. Figure 1.: Schematic representation of an axial compressor 1..3 Velocity triangles At the inlet of a stage, the fluid has an absolute velocity v 1 which is identical to the absolute velocity v 3 of the preceding stage. By vectorially subtracting the peripheric velocity u, the speed relative w 1 to the rotor inlet is obtained. The angle between this relative speed and the blade tip must be sufficiently limited so that
4 Axial compressors Figure 1.3: Velocity triangle the fluid does not detache (Fig. 1.3). The increased of the pressure of the fluid through the rotor requires that the relative velocity is deflected toward the axial direction so that, given the constant axial velocity component direction: w < w 1. By applying the equation of the kinetic energy in a relative space: P R = ( v v1 ṁ R ) + ( u u 1 P R = ( v v1 ṁ R ) ( w w1 ) ) ( w w1 ) (1.3) (1.4) to maximize the fraction P R ṁr, w 1 must be higher than w. Physical interpretation of p: By applying the energy equation in the wheel: W W 1 and the formula of Euler-Rateau: u u 1 + g(z z 1 ) = h h 1 (1.5) P R = ( v v1 ṁ R ) + ( u u 1 ) ( w w1 ) (1.6)
1. Two-dimensional flow through a stage 5 It follows that: P R = ṁ ( v v ) 1 R + h h 1 = ht h t1 = h t3 h t1 (1.7) Given that the enthalpy does not vary in a fixed pipe (the stator) and v 1 = v 3, the power on the wheel becomes: and taking into account: P R = ṁ R (h 3 h 1 ) = ṁ R c p (T 3 T 1 ) (1.8) P R = ṁ R p ρ (1.9) p is the increase of pressure that would be achieved in a stage if the compression is done without any friction. 1..4 How can I build an axial compressor? The value of the degree of reaction R: R = (P R) a (P R ) t = h h 1 h t3 h t1 (1.10) R = R = ( v v 1 ( ) w w 1 ) ( w w 1 (w w 1) (v v 1) (w w 1) ) (1.11) (1.1) will impact the contribution of the static pressure and of the kinetic energy into the compressor pressure ratio. 1..5 Why is it so difficult? The difficulty in the construction of an axial compressor is the pressure gradient p. Indeed, the smaller w, the higher the pressure gradient. If this gradient is too high, the fluid will detach from the blade. A solution is to change the angle of attack (AOA), but keep in mind that the angle of attack is connected to the lift coefficient of the blade C L. If the angle of attack becomes too high, the lift coefficient decreases sharply (Fig. 1.4).
6 Axial compressors Figure 1.4: C L vs. AOA 1..6 Influence/limitation of the axial velocity A high axial velocity v a is interesting from two points of view. First, because this speed exerts a positive influence on the value of P R and then because at a given velocity, the height of the blades will be lower, resulting in a reduction in the weight and dimensions of the compressor and a potentially higher N. An increase of the axial velocity is limited by the appearance of transonic zones causing shock waves (and, therefore, losses). Accordingly this, it must ensure that: M 1 < 0,9 (1.13) 1..7 Performance curves The variables of interest can be: Π c, P m, η g or η is,c. All this variables are function of the following variables: r 1, N, ṁ R, T 1, p 1, γ and µ 1 (Re 1 ). r 1, N, ṁ R are the turbomachinery parameters and the rest of the variables are called fluid parameters. There are, therefore, 7 variables to characterize an axial compressor. If we consider a fixed r 1 (for a given compressor), there remains 6 variables to fully characterize the compressor. Introduction of the reduced variables:
1. Two-dimensional flow through a stage 7 N red = u 1 = r πn 1 60 = c 1 γrt1 ṁ red = ρ 1v 1 A 1 c 1 ρ 1 A 1 = ρ 1 v 1 A 1 γrt1 p 1 rt 1 πr 1 Very often, the considered reduced variables are: N red = N T1 (1.14) = ṁ T 1 p 1 (1.15) N Tt,in (1.16) ṁ red = ṁ T t,in p t,in (1.17) The performance curves are shown in Figure 1.5. Figure 1.5: Performance curves 1..8 Surge and rotating stall Two phenomena will affect the operation of a compressor: The surge phenomenon: a phenomenon of large amplitude and low frequency. The surge phenomenon can take place in axial compressors and centrifugal compressors. It influences not only the compressor, but also the system to which the compressor is connected.
8 Axial compressors The rotating stall: a phenomenon of low amplitude and high frequency (leading to high compressor frequency - Fig. 1.6). The rotating stall occurs only in axial machines and only affects the operation of the compressor. Figure 1.6: Wöhler diagram 1..8.1 Surge When the flowrate decreases or/and the rotation velocity increases, the angle of attack of the rotor blades will increase. If the angle of attack becomes too large, the fluid can detach over the complete length and the full height of all blades of the rotor. This phenomenon is called the surge phenomenon. The ring is no longer able to transfer energy to the fluid, so that there is no more pressure rise in the stage. The air is not sufficiently compressed, the channels downstream in the machine are saturated. The fluid, which is located downstream in the machine, tends to flow back through the machine: the machine pumps. The downstream pressure decreases and the flow tends to recover its state. If the operating conditions of the compressor do not change, the phenomenon will recur. The velocity triangle shows that the angle of attack on a rotor blade increases: If, at constant rotation velocity, the flow rate decreases.
1. Two-dimensional flow through a stage 9 If, at constant speed, the rotation velocity increases. Some solutions can delay this surge phenomenon: The installation of directional vanes at the entrance (VIGV - Variable Inlet Guide Vanes). An air bleed after the first stages (ABV - Air Bleed Valves). 1..8. Rotating stall Aside of the surge phenomenon where the fluid detaches of the ring of blades, the fluid may also, in the case of an axial machine, detach locally. These areas rotate in the opposite direction of the blades, but with a lower speed. The rotating stall has a local effect and does not cause meaningful changes on the flowrate and/or on the pressure. Suppose that after a damaged blade, a stall occurs on blade (Fig. 1.7). The flowrate between the upper surface of the blade and the underside of the blade 3 decreases. The flowrate will be deflected towards the passage between blades 1 and and blades 3 and 4. It results in a reduction of the angle of attack of the relative velocity to the blade, so that the flow is recovering. The angle of attack of the relative velocity to the blade 3 increases causing a detachment of the fluid. Compared to the ring, the separation zone moves in the opposite direction of rotation with a speed lower than the rotation speed of the ring. It follows that the separation zone runs in the same direction as the ring, but at a smaller absolute velocity of rotation.
10 Axial compressors Figure 1.7: Rotating stall