User:Sunilchaudhary21/sandbox
Compressor characteristic is the curve to show the behaviour of fluid like change in pressure, temperature, entropy, flow rate etc as it passes through the compressor at different compressor speeds. The function of Compressors is to increase the fluid pressure that is the exit pressure is much higher than the inlet pressure and due to this property it is widely used like in refrigerator, cars, jet engine etc. These curves are plotted between various parameters and some are as follows
Performance of a compressor is usually specified by curves of delivery pressure against mass flow rate for various fixed values of rotational speed at given values of inlet pressure and temperature. These performance characteristic curves are usually plotted with dimensionless variables for this we start with implicit functional relationship of all the variables as [3]
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Where
= characteristic linear dimension of the compressor
= rotational speed
= mass flow rate
and = stagnation pressure at compressor inlet and outlet
and = stagnation temperature at compressor inlet and outlet
= characteristics gas constant
By making use of π-theorem, we obtain the non-dimensional groups (π terms) as [3]
, , ,
When we are concerned with the performance of a machine of fixed size compressing a specified gas and D may be omitted from the groups and we can write
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/08/Fig_2._pressure_ratio_vs._flow_coefficient.jpg/300px-Fig_2._pressure_ratio_vs._flow_coefficient.jpg)
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 ratio is plotted against in the form of family of curves, each curve of a family being drawn for fixed values of as shown in Figure 1.
The plot between pressure rise and flow rate is same as pressure ratio vs. mass flow rate with a small difference as in here we take pressure difference between inlet and outlet of the compressor instead of their ratio.
First we have to know about the loading, pressure and flow coefficient which are as follow-
Loading coefficient
Pressure coefficient =
So we can see that
Where
= impeller tip speed
= head
and also
Flow coefficient
So assuming a function to relate Loading coefficient and the Flow coefficient
A compressor gives its best performance while operating at its design point but it is also expected to operate away from the design point.
Therefore, knowledge about its behavior at off-design operation is also necessary. The quantity can be assumed constant in a wide range of incidence. This is justified in view of small variations in the air angles at the rotor and stator exits. Therefore, writing
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Fig_9_velocity_compressor_triangle.jpg/400px-Fig_9_velocity_compressor_triangle.jpg)
Where
= blade peripheral velocity
and are absolute air velocity at the rotor inlet and outlet
and are relative velocity at rotor inlet and outlet
= absolute air velocity at the stator outlet
and are the angles shown in the following Figure 2.
If the design values are identified by the superscript
At off-design conditions [3]
This equation also gives the off-design characteristic of an axial-flow compressor. The figure shown below depicts theoretical characteristic curves for some values of the constant . For positive values of , the curves are falling, while for negative values rising characteristics are obtained.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/6/61/Fig_1.Off_design_characteristic_curve_of_a_compressor_stage.jpg/200px-Fig_1.Off_design_characteristic_curve_of_a_compressor_stage.jpg)
Theoretical characteristic curve
[edit]Theoretical characteristic curve of the compressor is the plot to show behavior
of the fluid without considering losses due to shock and friction[4] Cite error: The <ref>
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the compressor at different constant speeds. The curve as shown in Figure 4. is plotted between
pressure coefficient and flow coefficient
for different values of as shown in fig. From fig. Its clear that as
the flow coefficient increases the pressure gained
per unit mass flow rate of the fluid decreases and due to this
pressure coefficient at higher mass flow rate will be low.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/5/54/Fig_4._actual_characteristic_curve_of_compressor.jpg/200px-Fig_4._actual_characteristic_curve_of_compressor.jpg)
Actual characteristic curveCite error: The <ref>
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[edit]Actual characteristic curve of the compressor is the modified version of the theoretical characteristic curve. In this we take care of both shock and friction losses as shown in the Figure 5. As seen in the figure the steepness of the curve increases at higher mass flow rates because since there will be higher frictional losses at high flow coefficient (Darcy’s friction law).
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Fig._5._surging.jpg/300px-Fig._5._surging.jpg)
Surging is the complete breakdown of steady flow in the compressor which occurs at low flow rate. Surging takes place when compressor is operated off the design point and it affects the whole machine and this is aerodynamically and mechanically undesirable. It can damage the rotor bearings, rotor seals, compressor driver and affect the whole cycle operation. It results in high temperature, high vibration and leads to flow reversal.[3]
Surge process
[edit]Assuming the compressor operates at point A () on the characteristic curve (let at constant speed ) as shown in Figure 5. Now if the flow rate is reduced to by closing a control valve on the delivery pipe, the static pressure upstream of the valve is increased. This increased pressure () is then matched by the increased delivery pressure (at B) which is developed by the compressor. Now further reducing the flow (to and ), the increased pressures in the delivery pipe are again matched by the compressor delivery pressures at C and S on the characteristic curve.
On the characteristic curve at the flow rates below ṁS provides lower pressure as seen in the fig. at D and E. But now the pipe pressures due to further reduction of flow by valve (let at point D) will be higher than the pressure at D and E. This unbalance between the pipe pressure and the compressor delivery pressure only exist for a very short time. This is because there is higher pressure in the pipe than the air pressure produced by the compressor and due to this reversing of the flow takes place and it leads to a complete break-down of the normal steady flow from the compressor to the pipe.
Surge cycle
[edit]Due to flow reversal, pressure in the pipe falls and the compressor regains its normal stable operation (let at point B) delivering the air at higher flow rate (). But the control valve is still corresponds to the flow rate . Due to this compressor’s operating conditions will again return to D through points C and S. And due to lower compressor pressure, the pressure falls further to and the entire phenomenon from point E to D repeats again and again and this cycle EBCSDE known as the surge cycle.
Surge point
[edit]Surge points are the peak points on the characteristic curves (as in Figure 5.) left of which the pressure generated by the compressor is less than the pipe pressure and these points initiates the surge cycle. These points on the curves are shown in the fig. by point S.[3]
Surge line
[edit]Surge line is the line which connects the surge points (S) on each characteristic curve corresponding to different constant speeds. The stable range of operation for the compressor is on the right hand side of the surge line.
Surge control line
[edit]Surge control line is the line which works as the indicating line for the surge control mechanism so that surge can be prevented in the system and proper steps can be taken. The line can vary for different surge control systems as its up to the system to decide the margin between operating point and the surge point. [7]
Surge margin
[edit]Surge margin is the indicator to show that how close is the system to the surge. It is different for the different surge control system as they employ different surge control lines.[8] The basic surge margin can be defined as
Surge margin =
Where
= mass flow rate at surge control line at a particular constant speed
= mass flow rate at surge line at the same constant speed.
Stalling
[edit]![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/47/Fig._6_stalling.jpg/300px-Fig._6_stalling.jpg)
Stalling is the separation of flow from the compressor blade surface as shown in the Figure 6. At low flow rates the incidence angle or angle of attack increases and due to this there occurs the flow separation on the suction side of the blades which is known as positive stalling. If the flow separation occurs on the pressure side of the blade then it’s known as negative stalling and this occurs due to negative incidence angle. But generally positive stalling is taken into consideration.
In the compressor at high pressure stages if there occurs a deviation from design point (at which compressor is designed to operate) the angle of attack exceeds its stalling value and stall cells (which are the regions where fluid starts to whirl at a particular location and don’t moves forward) to form at hub and tip of the blade. The size of these cells increases with decreasing flow rate. If the flow rate is further reduced these cells grow larger and it affects the whole blade height and this causes significant drop in the delivery pressure and at very low flow rate, flow reversal takes place which is known as surge. It also results in drop in stage efficiency of the compressor and its delivery pressure.Cite error: The <ref>
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Other compressor phenomena
[edit]Following are some other characteristics of the compressor
Choke/Stone wall point
[edit]Choking is the condition which occurs in the compressor in which it operates at very high mass flow rate and flow through the compressor can’t be further increased as mach number at some part of the compressor reach to unity i.e to sonic velocity and the flow is said to be choked. In compressor maximum volume flow rate is limited by cross-section at the inlet. This condition can be seen in the right side of the Figure 5. in which constant speed lines descends steeply. The point on constant speed line at which choking occurs is known as choke point or stone wall point. [9]
Choke line
[edit]Choke line is the line joining the choke points on different constant speed lines in the Figure 5. The operation on right side of choke line is not possible.
Constant efficiency lines
[edit]Constant efficiency lines are the elliptical shaped curves in the compressor characteristic curve along which the efficiency of the compressor remains constant.
Maximum allowable speed
[edit]Minimum required speed
[edit]References
[edit]- ^ Klassen, H.A., `Performance of low pressure ratio centrifugal compressors with four diffuser designs`, NACA, TN 7237, March 1973.
- ^ Nahimo, T. Etal., `Effect of Reynolds number on performance characteristics of centrifugal compressors with special reference to configurations of impellers`, ASME paper No.74-GT-59, 1974.
- ^ a b c d e f g h i j Yahya ,S.M, ”Turbine, Compressors & Fans”,4TH ED.McGraw Hill,2011.
- ^ Ferguson, T.B., The Centrifugal Compressor Stage, Butterworth, London, 1963.
- ^ Greitzer, E.M., `Surge and rotating stall in axial flow compressors`, ASME J. Eng. Power, Vol. 98. No. 2, April 1967.
- ^ Tsui, Chih-Ya et al., ` An experiment to improve the surge margin by use of cascade with splitter blades`, J. Eng. Thermophys,, Vol. 1, no. 2, May 1980.
- ^ http://www.gmrc.org/documents/GMRCSurgeGuideline_000.pdf
- ^ Cumpsty, N. A. (1989). Compressor Aerodynamics. Longman.
- ^ http://www.turbodriven.com/en/turbofacts/designCompressor.aspx