Unit 4: Centrifugal Compressors - Subjective Questions

A centrifugal compressor increases the pressure of a gas by transferring mechanical energy from a rotating impeller to the fluid.

• Inlet: Gas enters the impeller eye approximately in the axial direction.
• Impeller: Rotating blades accelerate the gas and impart tangential momentum to it. Centrifugal action also moves the gas radially outward.
• Energy addition: The impeller increases both the static pressure and the absolute velocity of the gas.
• Diffuser: The high-velocity gas leaving the impeller passes through expanding flow passages. Its velocity decreases, and kinetic energy is converted into static pressure.
• Collector or volute: The compressed gas is collected and delivered to the outlet.

Thus, pressure rise occurs partly in the impeller and partly in the diffuser. The fundamental energy transfer is described by Euler's compressor equation.

The energy transformation takes place in two main stages:

1. Impeller:

• Shaft work is supplied to the rotating impeller.
• The impeller transfers energy to the gas by increasing its stagnation enthalpy.
• Both the static pressure and kinetic energy of the gas generally increase.
• The energy transfer per unit mass is
  

2. Diffuser:

• Ideally, no shaft work is exchanged in the diffuser.
• The flow area increases, causing the absolute velocity to decrease.
• A large portion of the kinetic energy is converted into static pressure.
• The stagnation enthalpy remains approximately constant for adiabatic flow without work, although losses reduce stagnation pressure.

Therefore, the impeller supplies energy, while the diffuser converts velocity head into useful static-pressure rise.

Apply the angular-momentum equation to a steady-flow control volume surrounding the impeller. The torque exerted on the fluid is

The power transferred to the fluid is

Using ,

Hence, the specific work done on the gas is

For an adiabatic impeller, this equals the stagnation-enthalpy rise:

If the gas enters axially without prewhirl, . Therefore,

For a perfect gas with constant specific heat,

The equation shows that compressor work depends on impeller speed and the change in the whirl component of absolute velocity.

For an adiabatic centrifugal compressor, the steady-flow energy equation gives

From Euler's equation,

The compressor isentropic efficiency is

Therefore,

For the corresponding isentropic compression of a perfect gas,

Thus, the total-pressure ratio is

Substituting Euler work,

This idealized relation neglects mechanical losses and assumes constant and .

The inlet velocity triangle relates three velocities:

• : absolute velocity of the gas entering the impeller.
• : blade peripheral velocity at the inlet radius.
• : velocity of the gas relative to the rotating blade.

They are related by

The absolute velocity may be resolved into:

• Meridional or axial component .
• Whirl component .

For axial entry without prewhirl,

and the relative inlet velocity has components and . If is the relative blade angle measured from the tangential direction,

The blade inlet angle should match the direction of at the design condition. A mismatch produces incidence, separation, and additional losses.

At impeller exit, the velocity relation is

Let be the meridional component and the whirl component of absolute velocity. For a backward-curved blade with relative exit angle measured from the tangential direction, the outlet triangle gives

Therefore,

Euler's compressor equation is

For axial entry without prewhirl, , so

Substituting for ,

or

In an actual impeller, slip reduces the exit whirl velocity. Consequently, the actual work and pressure rise are lower than the ideal values predicted by an infinite-blade analysis.

Because an impeller has a finite number of blades, the fluid does not exactly follow the blade direction at exit. The relative flow lags behind the blade, reducing the actual whirl component. This phenomenon is called slip.

A commonly used slip factor is

where is normally less than unity. For no inlet prewhirl, the actual Euler work becomes

If the ideal whirl velocity is multiplied by the slip factor,

Effects of slip include:

• Reduced energy transfer to the gas.
• Lower stagnation-temperature rise.
• Lower achievable pressure ratio.
• A change in diffuser inlet flow angle.

Slip depends on blade number, blade exit angle, impeller geometry, flow coefficient, and operating condition.

Forward-curved blades:

• The blade tips curve in the direction of rotation.
• They produce a relatively high exit whirl velocity and theoretical work.
• Their power requirement can rise rapidly with flow rate.
• They generally have poorer stability and are less common in high-performance compressors.

Radial blades:

• The blade exit is radial, ideally giving .
• For no prewhirl and ideal guidance, .
• The theoretical work is approximately .
• They are mechanically strong and suitable for high rotational speeds.

Backward-curved blades:

• The blade tips curve opposite to the direction of rotation.
• They produce less whirl and work than radial or forward-curved blades at the same speed.
• They usually offer better efficiency, a wider stable operating range, and favorable power characteristics.

Consequently, radial and backward-curved blades are widely used in centrifugal compressors.

The total static-pressure rise does not occur entirely within the impeller.

Pressure rise in the impeller:

• The impeller performs work on the gas and raises its stagnation enthalpy.
• Static pressure rises because of centrifugal effects and diffusion within the rotating blade passages.
• The gas also leaves the impeller with substantial kinetic energy.

Pressure rise in the diffuser:

• The diffuser performs no shaft work on the gas.
• Its increasing flow area reduces the absolute velocity.
• The reduction in kinetic energy produces an additional static-pressure rise.

For an ideal adiabatic diffuser,

Therefore, as decreases, and static pressure increase. In a real diffuser, friction, separation, and mixing cause stagnation-pressure loss, so not all the available kinetic energy is recovered as static pressure.

For no inlet prewhirl, . Euler work is

Therefore,

The actual stagnation-temperature rise is

The isentropic temperature rise is

Thus,

The total-pressure ratio is

Hence:

• Specific work:
• Actual stagnation-temperature rise:
• Total-pressure ratio: approximately

A vaneless diffuser is an annular space of increasing radius located immediately after the impeller. It contains no guide vanes.

Operation:

• High-velocity gas enters the annular passage from the impeller.
• As the gas moves outward, the available flow area increases.
• The absolute velocity falls, and kinetic energy is converted into static pressure.
• In an ideal vaneless region, angular momentum is approximately conserved, so
  

Advantages:

• Simple and robust construction.
• Relatively low cost.
• Wide operating range.
• Less sensitive to incidence changes at off-design conditions.

Limitations:

• Requires a relatively large radial dimension.
• Pressure recovery may be lower than that of a well-designed vaned diffuser.
• Long flow paths increase wall-friction losses.

Vaneless diffusers are preferred where broad operating range and stable performance are more important than compactness.

A vaned diffuser contains stationary guide vanes arranged around the impeller outlet. The passages between adjacent vanes increase in area in the direction of flow.

Working:

• Gas enters the diffuser vanes at a high absolute velocity.
• The vanes guide the gas while the passage area increases.
• Velocity decreases, converting kinetic energy into static pressure.
• The vanes can also remove whirl and direct the gas toward the collector.

Comparison:

• Pressure recovery: A vaned diffuser generally provides higher pressure recovery near its design condition.
• Size: It can achieve the required diffusion in a smaller radial space.
• Operating range: A vaneless diffuser usually has a wider stable operating range.
• Incidence sensitivity: A vaned diffuser is more sensitive to changes in inlet flow angle.
• Complexity: Vaned diffusers are more complex and costly.
• Stall risk: Excessive incidence or diffusion can cause vane-passage separation and rotating stall.

Thus, vaned diffusers favor compactness and high design-point performance, while vaneless diffusers favor simplicity and range.

Important diffuser vane design considerations include:

• Inlet vane angle: It should match the absolute flow angle leaving the impeller at the design point. Incorrect matching causes incidence and leading-edge separation.
• Leading-edge location: Adequate radial clearance from the impeller is required to reduce blade-wake interaction, noise, and unsteady loading.
• Passage-area variation: The area must increase gradually. Excessive divergence produces adverse pressure gradients and flow separation.
• Throat area: It must pass the required mass flow without undesirable choking while maintaining suitable velocity and diffusion.
• Vane number and solidity: More vanes improve flow guidance but increase blockage, wetted area, friction, and impeller-diffuser interaction.
• Vane profile: Rounded leading edges tolerate incidence variations, while smooth curvature reduces boundary-layer losses.
• Diffusion level: The velocity reduction per passage must be limited to avoid separation.
• Exit angle: It should provide suitable flow direction for the volute or return channel with minimum residual swirl.
• Surface finish and boundary layers: Roughness and end-wall boundary layers reduce pressure recovery.
• Operating range: The design must balance peak efficiency against stall margin and off-design performance.

A successful vane design therefore combines high pressure recovery with acceptable loss, choking margin, and stall resistance.

The diffuser throat is the minimum flow area between adjacent diffuser vanes. It strongly influences the maximum mass-flow capacity.

The continuity relation is

As mass flow increases, velocity at the throat rises. If the throat Mach number reaches unity, the passage becomes choked. Further reduction of downstream pressure then produces little or no increase in corrected mass flow.

Effects of an undersized throat:

• Premature choking.
• Limited compressor maximum flow.
• High losses due to excessive acceleration and shock formation in transonic operation.

Effects of an oversized throat:

• Lower flow guidance and weaker diffusion at the design point.
• Possible deterioration in pressure recovery.

The effective throat area is less than the geometric area because of vane thickness and boundary-layer blockage. Designers must therefore account for compressibility, blockage, incidence, and manufacturing tolerances.

Diffuser incidence is the angular mismatch between the approaching absolute flow direction and the diffuser vane inlet metal angle.

If is the impeller-exit absolute flow angle and is the diffuser vane inlet angle, incidence may be represented as

The sign convention may vary, but a nonzero magnitude indicates mismatch.

Causes:

• Operation away from design mass flow.
• Changes in impeller-exit whirl or meridional velocity.
• Slip-factor variation.
• Impeller wakes and nonuniform flow.
• Incorrect vane setting or geometry.

Effects:

• Leading-edge separation.
• Increased stagnation-pressure loss.
• Reduced pressure recovery and efficiency.
• Unsteady loading and noise.
• Diffuser stall at severe incidence.

Rounded leading edges, suitable impeller-diffuser spacing, variable vanes, and conservative diffusion can improve incidence tolerance.

Prewhirl is a tangential component of absolute velocity deliberately or unintentionally present in the gas before it enters the impeller. Thus, .

Prewhirl may be produced by:

• Fixed inlet guide vanes.
• Variable inlet guide vanes.
• Curved inlet ducts or upstream flow distortion.
• Residual swirl from an upstream compressor stage.

If prewhirl is in the same direction as impeller rotation, it is called positive prewhirl. If it is opposite to impeller rotation, it is called negative prewhirl.

Prewhirl changes:

• The inlet relative velocity .
• The relative inlet flow angle.
• Blade incidence.
• Euler work through the term .
• Compressor mass-flow, pressure-ratio, and power characteristics.

Variable inlet guide vanes commonly use controlled prewhirl to regulate compressor capacity and improve part-load operation.

At impeller inlet, the velocity relation is

Resolving the absolute velocity into meridional and whirl components, the tangential component of relative velocity is

If is measured from the tangential direction, the inlet triangle gives

Therefore, changing changes the relative flow angle and blade incidence.

Euler's equation is

For positive prewhirl, when the direction of rotation is taken as positive. Hence,

for unchanged exit conditions. Positive prewhirl therefore generally reduces work input and pressure rise. For negative prewhirl, , giving

so the theoretical work increases. In practice, prewhirl also changes mass flow, incidence, slip, losses, and exit conditions, so its total effect cannot always be predicted from the inlet term alone.

Positive prewhirl:

• Swirl is in the same direction as impeller rotation.
• It reduces the relative tangential speed at inlet.
• From , it generally reduces specific work.
• It usually lowers pressure ratio, power consumption, and compressor capacity.
• It can improve inlet incidence during part-load operation when properly controlled.

Negative prewhirl:

• Swirl is opposite to impeller rotation.
• It increases the relative inlet speed.
• The term becomes positive, increasing theoretical work.
• It may increase pressure rise but also raises relative Mach number, power requirement, and inlet losses.
• Excessive negative prewhirl can produce severe incidence and choking-related limitations.

Positive prewhirl is widely used for capacity control through variable inlet guide vanes. Negative prewhirl is less common because of its higher aerodynamic and mechanical demands.

Rotating stall is a flow instability in which one or more localized regions of separated or low-momentum flow, called stall cells, travel circumferentially around the compressor annulus. Their propagation speed is usually a fraction of rotor speed.

Causes:

• Operation at a mass flow below the design value.
• Excessive positive incidence at impeller or diffuser leading edges.
• Strong adverse pressure gradients.
• Excessive diffusion in blade or vane passages.
• Inlet distortion and nonuniform impeller-exit flow.

Development:

• Separation blocks part of a passage.
• Flow is diverted into neighboring passages.
• The altered incidence causes one neighboring passage to recover while another stalls.
• This process makes the stalled region propagate circumferentially.

Effects:

• Pressure and velocity fluctuations.
• Reduced pressure rise and efficiency.
• Noise and vibration.
• Cyclic blade or vane loading and possible fatigue.
• Reduced stable operating range.

Rotating stall may occur in the impeller, vaneless space, or vaned diffuser and can precede surge.

Rotating stall:

• A localized instability involving one or more circumferential stall cells.
• Flow continues through much of the compressor while some passages are stalled.
• Disturbances propagate around the annulus at a fraction of rotor speed.
• It causes periodic pressure fluctuations and blade loading.

Surge:

• A system-wide, low-frequency instability involving the compressor and connected ducts or plenums.
• It produces large oscillations of mass flow and pressure.
• Severe surge may cause periodic flow reversal through the entire compressor.
• It can generate violent vibration, noise, overheating, and mechanical damage.

Relationship:
Rotating stall can reduce compressor pressure capability and may trigger surge, but the two phenomena are physically distinct. Surge depends strongly on the complete compression-system dynamics.

Prevention and control:

• Operate with adequate margin from the surge line.
• Use anti-surge control to open a recycle or blow-off valve at low flow.
• Employ variable inlet guide vanes to control incidence and capacity.
• Use variable diffuser vanes where appropriate.
• Design conservative impeller and diffuser diffusion levels.
• Select suitable vane angles, throat areas, and impeller-diffuser spacing.
• Minimize inlet distortion and flow nonuniformity.
• Monitor corrected flow, pressure ratio, vibration, and dynamic pressure.

Anti-surge systems are designed to respond before operation crosses the surge-control line, thereby protecting the compressor while maintaining the widest practical operating range.