6 th Indo-German Winter Academy 2007 IIT Guwahati, India, December 13-19, 2007 Flow Through Axial and Centrifugal Compressors by Kartik Sharma Mentors Prof. Gautam Biswas Prof. Subrata Sarkar
Outline of the Presentation Introduction to Dynamic Compressors Axial Compressors- Basic Working Principle Centrifugal Compressors- Basic Working Principle Flow through Axial Compressors Flow through Centrifugal Compressors Comparison of Axial and Centrifugal Compressors Summary
Introduction-Dynamic Compressors Density of the fluids change with temperature and pressure as they pass through the compressible flow or Turbo machines. Dynamic Machines (a type of turbo machines) use rotating vanes or impellers to impart velocity and pressure to the gas. These machines operate by developing a high gas velocity and converting this velocity into pressure in the diffusing flow passage. They do operate at relatively higher speeds to provide higher flow rate in relation to their physical size. There are mainly two types of Dynamic Compressors - 1. Centrifugal Compressors 2. Axial Compressors
Axial Compressors They are rotating, aerofoil based compressors in which the working fluid principally flows parallel to the axis of rotation. They produce a continuous flow of compressed air, have the benefits of high efficiencies and large mass flow capacity, particularly in relation to their cross-section.
Basic Principles of Axial Compressors The basic components of an axial flow compressor are a rotor and stator, the former carrying the moving blades and the latter the stationary rows of blades. The stationary blades convert the kinetic energy of the fluid into pressure energy, and also redirect the flow into an angle suitable for entry to the next row of moving blades. Each stage will consist of one rotor row followed by a stator row, but it is usual to provide a row of so called Inlet guide vanes at the beginning. For a compressor, a row of rotor blades followed by a row of stator blades is called a Stage
Working of Axial Compressors
Centrifugal Compressors A centrifugal compressor is a radial flow rotodynamic fluid machine that uses mostly air as the working fluid and utilizes the mechanical energy imparted to the machine from outside to increase the total internal energy of the fluid mainly in the form of increased static pressure head.
Components of a Centrifugal Compressor A centrifugal compressor consists of three main parts; A Stationary Casing A Rotating Impeller which imparts high velocity to the fluid. It may be single or double sided. A Diffuser having a number of fixed diverging passages in which the air is decelerated with consequent rise in pressure.
Schematic Views of a centrifugal compressor
The figure shows the sectional diagram of a single entry and single outlet centrifugal compressor.
Principle of Operation Air is sucked into the impeller eye and whirled outwards at high speed by the impeller disk. At any point in the flow of air through the impeller the centripetal acceleration is obtained by a pressure head so that the static pressure of the air increases from the eye to the tip of the impeller. The remainder of the static pressure rise is obtained in the diffuser, where the very high velocity of air leaving the impeller tip is reduced to almost the velocity with which the air enters the impeller eye.
Usually, about half of the total pressure rise occurs in the impeller and the other half in the diffuser. Owing to the action of the vanes in carrying the air around with the impeller, there is a slightly higher static pressure on the forward side of the vane than on the trailing face. The air will thus tend to flow around the edge of the vanes in the clearing space between the impeller and the casing. This results in a loss of efficiency and the clearance must be kept as small as possible. Sometimes, a shroud attached to the blades to eliminate such a loss, but it is avoided because of increased disc friction loss and of manufacturing difficulties.
Parameters of Compressor Operation Normal Operating Point- It is the head-capacity point at which the usual operation is expected and at which optimum efficiency is desired Compressor Rated Point- It is determined as follows; 1. The highest speed necessary to meet any specified operating conditions. 2. The rated capacity required by compressor designs to meet all operating points. This capacity point is selected to best encompass the specified operating conditions within the scope of the expected performance curve.
Normal Speed- It is the speed corresponding to the requirements of the normal operating point. One hundred percent speed- It is the speed corresponding to the requirements of the compressor rated point. It may be greater than or equal to the normal speed. Maximum continuous speed- It is the upper limit of the operating speed of the compressor. For variable speed compressors, it should be 105% of the speed of the compressor rated point.
Operating Characteristics of a Compressor The operating range is the region between the surge point and the choke point. Surge point is the point when the flow is reversed in the compressor.
Choke point is the point when the flow has reached a Mach=1.0,the point where no more flow can get through the unit, a Stone Wall. When Surge occurs, the flow is reversed and all the forces acting on the compressor (specially thrust forces) can lead to the destruction of the compressor. Choke conditions cause a large drop in efficiency but don t lead to any destruction of the unit.
Blade Types of a Compressor There are three impeller vane types defined according to the exit blade angles; Impellers with exit blade angle equal to 90 degrees are radial vanes Impellers with exit blade angle less than 90 degrees are backwardcurved or backward swept. Vanes with exit blade angle greater than 90 degrees are known as forward swept vanes. The forward-curved blade has the highest theoretical head. Backward-curved blades are most common since they have the lowest velocity leaving the impeller so diffuser has a much smaller head to convert. They also have a larger operational margin.
Blade Geometry They do suffer from problems of low energy transfer and complex bending stresses.
Compressor Characteristics The performance of a compressor is usually specified by curves of delivery pressure and temperature against mass flow rate for various fixed values of rotational speed at given values of inlet pressure and temperature. It is better to plot such performance characteristic curves with dimensionless variables. where D = characteristic linear dimension of the machine, N = rotational, m = mass flow rate,p01 = stagnation pressure at compressor inlet, = p02 stagnation pressure at compressor outlet, = t01,stagnation temperature at compressor inlet, t02= stagnation temperature at compressor outlet, and R = characteristics gas constant
Contd.. By making use of Buckingham's π theorem, we obtain the nondimensional groups (π terms) as ; The third and fourth non-dimensional groups are defined as 'nondimensional mass flow' and 'non-dimensional rotational speed' respectively. The physical interpretation of these two non-dimensional groups can be ascertained as follows;
Contd.. Therefore, the 'non-dimensional mass flow' and 'non-dimensional rotational speed' can be regarded as flow Mach number, and rotational speed Mach number, When we are concerned with the performance of a machine of fixed size compressing a specified gas, R and D may be omitted from the groups and we can write
Contd.. Though the terms and are truly not dimensionless, they are referred as 'non-dimensional mass flow' and 'non-dimensional rotational speed' for practical purpose. The stagnation pressure and temperature ratios and are plotted against in the form of two families of curves, each curve of a family being drawn for fixed values of. The two families of curves represent the compressor characteristics. From these curves, it is possible to draw the curves of isentropic efficiency for fixed values of Isentropic Efficiency is defined as;
Performance Curve of Centrifugal Compressors Point A- Represents the centrifugal pressure head produced by the action of the impeller on the air trapped between the vanes
Point B- Efficiency approaches its maximum and the pressure ratio also reaches its maximum. Further increase of mass flow will result in a fall of pressure ratio For mass flows greatly in excess of that corresponding to the design mass flow, the air angles will be widely different from the vane angles and breakaway of the air will occur. The pressure ratio drops to unity at 'C', when the valve is fully open and all the power is absorbed in overcoming internal frictional resistances
The operating point 'A' could be obtained but a part of the curve between 'A' and 'B' could not be obtained due to Surging. For any operating point D on the part of characteristics curve having a positive slope, a decrease in mass flow will be accompanied by a fall in delivery pressure. If the pressure of the air downstream of the compressor does not fall quickly enough, the air will tend to reverse its direction and will flow back in the direction of the resulting pressure gradient. When this occurs, the pressure ratio drops rapidly causing a further drop in mass flow until the point 'A' is reached, where the mass flow is zero.
When the pressure downstream of the compressor has reduced sufficiently due to reduced mass flow rate, the positive flow becomes established again and the compressor picks up to repeat the cycle of events which occurs at high frequency For any operating point on the part of the characteristics having a negative slope, decrease in mass flow is accompanied by a rise in delivery pressure and the operation is stable There is an additional limitation to the operating range, between 'B' and 'C'. As the mass flow increases and the pressure decreases, the density is reduced and the radial component of velocity must increase.
At constant rotational speed this means an increase in resultant velocity and hence an angle of incidence at the diffuser vane leading edge. At some point say 'E', the position is reached where no further increase in mass flow can be obtained no matter how wide open the control valve is. This point represents the maximum delivery obtainable at the particular rotational speed for which the curve is drawn.
This indicates that at some point within the compressor sonic conditions have been reached, causing the limiting maximum mass flow rate to be set for the compressible flow. Choking is said to have taken place. Variations of pressure ratio over the complete range of mass flow for different rotational speeds
Analysis of an Axial Compressor An axial compressor is typically made up of many alternating rows of rotating and stationary blades called rotors and stators, respectively. Bernoulli Equation The first stationary row (which comes in front of the rotor) is typically called the inlet guide vanes or IGV. Each successive rotor-stator pair is called a compressor stage. Hence compressors with many blade rows are termed multistage compressors. Where: P T is the stagnation pressure P is the static pressure u is radial velocity v is tangential velocity w is axial velocity
The rotor adds swirl to the flow increasing the total energy carried in the flow by increasing the angular momentum (adding to the kinetic energy associated with the tangential or swirl velocity, ). The stator removes swirl from the flow. The stator rather converts the kinetic energy associated with swirl to internal energy (raising the static pressure of the flow). IGV also adds no energy to the flow. It is designed to add swirl in the direction of rotor motion to lower the Mach number of the flow relative to the rotor blades, and thus improve the aerodynamic performance of the rotor
Velocity and Pressure Profiles
Characteristics of Axial Compressors A typical stage in a commercial compressor will produce a pressure increase of between 15% and 60% (pressure ratios of 1.15-1.6) at design conditions with a polytropic efficiency in the region of 90-95%. Higher pressure ratios possible if the relative velocity between fluid and rotors is supersonic (Mach >1), but efficiency and operability are adversely affected. Modern jet engines use a series of compressors, running at different speeds; to supply air at around 40:1 pressure ratio for combustion with sufficient flexibility for all flight conditions
All compressors have a sweet spot relating rotational speed and pressure, with higher compressions requiring higher speeds Early engines designed for simplicity and used a single large compressor spinning at a single speed. Later designs have a second turbine and divide the compressor into "low pressure" and "high pressure" sections, the latter spinning faster. This Two-Spool design resulted in increased efficiency. Even more can be squeezed out by adding a third spool, but in practice this has proven to be too complex to make it generally worthwhile The aerofoil profiles are optimized and matched for specific velocities and turning.
Analysis of Axial Compressors Flow Through Stages Velocity Triangles
Two basic equations follow immediately from the geometry of the velocity triangles. These are; In which is the axial velocity assumed to be constant throughout the stage. The work done per unit mass is; Velocity Triangles
Where; U - blade peripheral velocity w - whirl component - absolute velocity of the air at the rotor entrance - angle of air velocity with the axial direction - relative velocity of air w.r.t. rotor < This turning of air is necessary to provide an increase in the effective flow area It is brought about by the camber of blades.
Using velocity triangles we have; Or; This input energy is absorbed usefully in raising the pressure and velocity of the air. A part of it will be spent in overcoming various frictional losses. Regardless of the losses, the input will reveal itself as a rise in the stagnation temperature of the air. If the absolute velocity of the air leaving the stage is made equal to that at the entry,the stagnation temperature rise will also be the static temperature rise of the stage so that;
In fact, the stage temperature rise will be less than that given by the above equation owing to three-dimensional effects in the compressor annulus. A factor λ<1 is used which is the measure of the ratio of actual workabsorbing capacity of the stage to its ideal value.
and the pressure ratio is given by; Where is the inlet stagnation temperature and is the stage isentropic efficiency;
Variation of the work-done factor with number of stages
Axial Velocity Distributions The radial distribution of axial velocity is not constant across the annulus but becomes increasingly peaky as the flow proceeds Settles down to a fixed profile at about the fourth stage Axial velocity distributions
Degree of Reaction It is a measure of the extent to which the rotor contributes to the increase in the static head of the fluid. Defined as the ratio of the static enthalpy rise in the rotor to that in the whole stage. Variation of Cp over the relevant temperature range will be negligibly small,so, enthalpy ratio is effectively the corresponding temperature ratio. Assuming the simplest case; =>
Where - static temperature rise in the rotor - static temperature rise in the stator Since all work input to the stage is transferred to air by means of rotor; we have; => =>
But, we have; Therefore => Degree of Reaction;
Using earlier equations, we have; => Also, we have;
Adding these two equations, we have; Using earlier derived expression, we have; As 50% reaction blading is important in design, we analyze for degree of reaction=0.5
It follows from velocity triangles that; i.e. i.e. (Vf is constant) We assumed,it follows that so, a 50% reaction stage is also known as Symmetrical Blading Therefore and has been assumed to be unity for simple analysis.
Analysis of Centrifugal Compressors No work is assumed to be done in the diffuser Energy absorbed is determined by inlet and outlet conditions at the impeller Air enters the impeller in axial direction, so initial angular momentum is zero.
Vanes have a curved axial portion for smooth entry of air. In the earlier figure, we have; - angle made by the leading edge of the vane with the tangential direction. - relative velocity of air at the inlet - absolute velocity of air at the impeller tip - tangential/whirl component of - Impeller speed at the tip Under ideal conditions, we have; =
Since air enters in axial direction; therefore; The energy transfer per unit mass is; Due to inertia, air trapped between the impeller vanes doesn t move round with the impeller. This results in a higher static pressure at the leading face than the trailing face. This prevents air acquiring whirl speed equal to the impeller speed. Slip Factor,σ takes into account this effect;
Value of σ lies between 0.9-0.92 In case of slip factor, energy transfer per mass becomes; A widely used expression for σ suggested by Stanitz from the solution of potential flow through impeller passages; where n is the number of vanes.
Power Input Factor Power input factor takes into account the effect of disk friction, windage etc. Its value lies between 1.035-1.04 Power Input is therefore more than that required by theoretical expression. Actual Work done per unit mass(power Input) is; where is the power input factor. Adiabatic work done is given by; Using earlier equation, we have;
Stagnation Temperature represents the total energy held by the fluid. No energy is added in the diffuser, so, stagnation temperature rise across the impeller is that equal to the whole compressor. If stagnation temperature at the outlet of the diffuser is ;then; => =>
- stagnation temperature at the end of ideal (isentropic) compression - stagnation temperature after the actual compression process. - isentropic efficiency
Losses in Centrifugal Compressors Frictional losses: A major portion of the losses is due to fluid friction in stationary and rotating blade passages. The flow in impeller and diffuser is decelerating in nature. Therefore the frictional losses are due to both skin friction and boundary layer separation. The losses depend on the friction factor, length of the flow passage and square of the fluid velocity. Incidence losses: During the off-design conditions, the direction of relative velocity of fluid at inlet does not match with the inlet blade angle and therefore fluid cannot enter the blade passage smoothly by gliding along the blade surface. The loss in energy that takes place because of this is known as incidence loss. This is sometimes referred to as shock losses.
Clearance and leakage losses: Certain minimum clearances are necessary between the impeller shaft and the casing and between the outlet periphery of the impeller eye and the casing. The leakage of gas through the shaft clearance is minimized by employing glands. The clearance losses depend upon the impeller diameter and the static pressure at the impeller tip. A larger diameter of impeller is necessary for a higher peripheral speed and it is very difficult in the situation to provide sealing between the casing and the impeller eye tip
Graphical Depiction of Losses Dependence of various losses with mass flow in a centrifugal compressor;
Axial Compressors vs. Centrifugal Compressors Direct Competition in the range of 24 to 90 cubic meters/sec act. Below 33 m3/sec act. the centrifugal is more attractive and above 61 m3/sec act, axial is preferable from economic and design point of view In general, two axial compressor stages are required to produce the same compression as that given by one centrifugal stage. Each axial stage (rotor blade plus the subsequent stator blade row) can develop 1400m to 1700 m of head on air, and slightly less on gases heavier than air. two complete stages together require about 50% of the axial length required by one centrifugal stage.
Axial Compressors are used for very high flows and low pressure ratios. They (80%-91%) have higher efficiency than centrifugal compressors (75%-87%). Centrifugal compressors are employed for medium flow rates and high pressure ratios. They (around 25%) have a higher operating region than axial compressor.(3%-10%)
Reason for High Efficiency of Axial Compressors The gas experiences less drastic changes of direction as it progresses through the stages of an axial machine. The general flow path in an axial compressor is a gradual screw shape through the blading and around the rotor drum in a predominantly axial direction,with minor perturbations through each blade row. In the centrifugal compressor,there are two 180 degrees turns in each stage, in addition to a spiral shaped path in the radial plane of each impeller from the impeller vane inner diameter to the diffuser periphery. the shorter,straighter flow path of the axial results in lower turbulence and turning losses
Summary Compressors are devices used to pressurize fluids. Main types of dynamic type compressors are axial and centrifugal compressors. Axial Compressors are used for very high flows and low pressure ratios while centrifugal compressors are used for moderate flow rates and high pressure ratios. In axial compressors, pressure ratio is achieved by passing the fluid through stages while in Centrifugal Compressors,high pressure ratio is achieved by the action of a rotating impeller and subsequent conversion of kinetic energy in static pressure head in the diffuser and impeller. Both compressors have their own advantages and limitations.
Acknowledgements I am thankful to Prof. Gautam Biswas and Prof. Subrata Sarkar for their guidance and valuable inputs which were influential in preparing the lecture. I am also thankful to Prof. Ravi Kumar and Prof. Amit Dhiman for their kind support.