Power Consuming Fluid Machines - II BY Dr. P M V Subbarao Mechanical Engineering Department I I T Delhi Another set of Small Things !!!

Classification of Pumps

Classification of Compressors Rotodynamic Compressors Positive Displacement of Compressors Centrifugal Compressors Mixed Compressors Axial Compressors Reciprocating Compressors Rotory Compressors

Thermodynamic Comparison of Pump & Compressor Work input for unit mass in a Pump: Work input for unit mass in a Compressor:

Centrifugal Pump                                            

Centrifugal Compressors The centrifugal compressor consists essentially of a stationary casing containing a rotating impeller which imparts a high velocity to the air, and A number of diverging passages (Diffuser) in which the air is decelerated with a consequent rise in static pressure. Air is sucked into the impeller eye and whirled round at high speed by the vanes on the impeller disc. Centripetal acceleration leads to increase in rise of some amount of static pressure. The remaining increase in rise of pressure occurs in diffuser.

Anatomy of A Centrifugal Compressors

Va2 Vr2 Vw2 Va2 Vf2 Vr2 Vw2 b1 Vf1=Va1 Vr1

Work Consumed & Pressure or Head Rise In general air enters the impeller eye in axial direction. The axial portion of impeller of the vanes are curved so that the air can pass smoothly into the eye. Due to inertia, the air trapped between the impeller vanes is reluctant to move round with the impeller and prevents air acquiring a whirl velocity equal to the impeller speed (Vw2 < U). This is called slip and quantified as slip factor, s. where, n is number of vanes Theoretical Torque : Theoretical Power Consumed:

Power input factor, y Typical values for the power input factor, y : 1.035 – 1.04.

3 2 1

Stagnation Pressure Va22/cp Stagnation Temperature Stagnation Enthalpy

Work consumed by A compressor = Increase in Stagnation Enthalpy of gas Work consumed by A Pump = Increase in Stagnation Enthalpy of liquid

isentropic pressure rise due to (T03-T01). For an irreversible compression or pumping, the actual pressure rise is less than isentropic pressure rise due to (T03-T01). For a compressor:

Slip Factor, Power Input Factor & Efficiency Power input factor and slip factor are neither independent of one another nor of efficiency. The power input factor represents an increase in the work input, the whole of which is absorbed in overcoming frictional loss and therefore degraded into thermal energy. Power input factor should be as low as possible. Low values of Power input factor imply that the values of efficiency are high. However, the value of efficiency also depends on friction losses in the diffuser which does not affect power input factor. The slip factor limits the capacity of the compressor and this should be as high as possible. A high value of slip factor require higher number of vanes. Higher number vanes will increase frictional losses and hence increase the value of power input factor and decrease the value of efficiency. A suitable compromise must be found, and present day practice is : 19 – 21 vanes to get a slip factor value of 0.9.

The inlet mach number is controlled by Using the angle of prewhirl. Inlet Mach Number for Impeller and Diffuser At intake the air is deflected a certain angle before it passes into the radial channels on the impeller. The inlet Mach number: Vw1 b1 Vr1 The inlet mach number is controlled by Using the angle of prewhirl. Va1

The role of A Pump in a Fluid Handling System Delivery Pressure or Head Static Pressure or Head Suction Pressure or Head

Similarity Analysis Differential head of pump:

Similarity Analysis Pressure Ratio of A Compressor:

Affinity Laws for Centrifugal Pumps

Pump Characteristics Q, Discharge

Compressor Characteristics

Axial Flow Compressors

Axial Flow Compressors

Compressor Stage Va32/cp Va22/cp Va12/cp

Vr1 Va1 Va1 Vf1 Vw1 Vr2 Va2 Va2 Vf2 Vw2 Va3

Power input to the compressor: Current Practice: Theoretical Power input to the compressor:

For an isentropic compressor:

A high pressure rise per stage will decrease the number of stages for a given overall pressure rise. A high pressure rise per stage is obtained using: High blade speed. High inlet flow velocity. High fluid deflection in rotor blades.

Blade Speed For a given rotor speed the velocity of the blade at the tip will be maximum. The centrifugal stress in the rotor blades depends on the rotational speed, the blade material and length of the blade. The maximum centrifugal stress is given by, b, hub-tip diameter ratio. K varies in the range 0.55 – 0.65.

INLET CONDITIONS Vr1 Va1 Vr1 Va1

Fluid Deflection Vr1 Vr2 Vrmax

Frictional Losses

Multi Stage Compression Vr1 Vf Vf Mean Vf Mean Vf Fourth Stage First Stage Work done factor, l, decrease with number of stages.

Radial Variation of Blade Angles