Air and Gas Compressors MCQ Quiz - Objective Question with Answer for Air and Gas Compressors - Download Free PDF

Explanation:

Work Input in a Reciprocating Air Compressor

• The work input in a reciprocating air compressor refers to the amount of energy required to compress a given mass of air from an initial pressure and temperature to a higher pressure. This energy depends on the process path the compression follows (e.g., isothermal, isentropic, or polytropic).

Compression follows PV = Constant (isothermal process).

Thermodynamic Analysis:

• In a reciprocating air compressor, the compression process can follow different thermodynamic paths, such as isothermal, adiabatic (isentropic), or polytropic processes.
• The work input in a compression process is given by the area under the pressure-volume (P-V) curve. Hence, the work done depends on the process path.
• For an isothermal process (PV = Constant), the temperature of the air remains constant during compression. Achieving this requires perfect heat transfer with the surroundings, ensuring that the heat generated during compression is removed continuously.

Work Done in an Isothermal Process:

The work done during isothermal compression is given by:

W_isothermal = mRT ln (P₂/P₁)

• m: Mass of air being compressed
• R: Specific gas constant
• T: Absolute temperature of the air (constant in an isothermal process)
• P₁: Initial pressure of the air
• P₂: Final pressure of the air

In an isothermal process, the work input is proportional to the natural logarithm of the pressure ratio (P₂/P₁), and the temperature remains constant. This results in the least amount of work compared to other processes because the heat generated during compression is removed, preventing a rise in temperature and pressure beyond what is necessary for the given pressure ratio.

Why Isothermal Compression Requires Minimum Work:

• During isothermal compression, the temperature of the air remains constant, which helps reduce the pressure rise for a given volume reduction.
• The reduction in pressure rise results in a lower area under the P-V curve, minimizing the work input.
• In contrast, in adiabatic or polytropic processes, the temperature increases during compression, leading to a higher pressure rise and, consequently, more work input.

Practical Challenges:

• While isothermal compression is theoretically the most efficient, achieving perfect isothermal conditions in practice is challenging due to the difficulty in maintaining continuous heat transfer during rapid compression.
• To approximate isothermal compression, intercoolers are often used in multi-stage compressors to cool the air between stages, reducing the overall work input.

Concept:

We use the polytropic process equations and mechanical efficiency to determine the power input required for compressing air in a reciprocating compressor.

Given:

• Mass flow rate of air, \( \dot{m} = 20 \, \text{kg/min} = 0.333 \, \text{kg/s} \)
• Inlet pressure, \( P_1 = 110 \, \text{kPa} \)
• Inlet temperature, \( T_1 = 300 \, \text{K} \)
• Outlet pressure, \( P_2 = 660 \, \text{kPa} \)
• Polytropic index, \( n = 1.25 \)
• Gas constant, \( R = 0.287 \, \text{kJ/kg·K} \)
• Mechanical efficiency, \( \eta_{\text{mech}} = 80\% = 0.8 \)
• Given: \( (6)^{0.2} = 1.43 \)

Step 1: Calculate the Polytropic Work Done

The work done per kg of air for a polytropic process is:

\( W_{\text{polytropic}} = \frac{n}{n-1} \times R \times T_1 \times \left[ \left( \frac{P_2}{P_1} \right)^{\frac{n-1}{n}} - 1 \right] \)

Substitute the values:

\( W_{\text{polytropic}} = \frac{1.25}{0.25} \times 0.287 \times 300 \times \left[ (6)^{0.2} - 1 \right] \)

\( W_{\text{polytropic}} = 5 \times 0.287 \times 300 \times (1.43 - 1) \)

\( W_{\text{polytropic}} = 184.515 \, \text{kJ/kg} \)

Step 2: Calculate the Indicated Power

The indicated power is the work done multiplied by the mass flow rate:

\( P_{\text{indicated}} = \dot{m} \times W_{\text{polytropic}} \)

\( P_{\text{indicated}} = 0.333 \times 184.515 = 61.5 \, \text{kW} \)

Step 3: Calculate the Power Input

The power input accounts for mechanical efficiency:

\( P_{\text{input}} = \frac{P_{\text{indicated}}}{\eta_{\text{mech}}} \)

\( P_{\text{input}} = \frac{61.5}{0.8} = 76.875 \, \text{kW} \)

Explanation:

Loading Coefficient of an Axial Flow Compressor

• The loading coefficient of an axial flow compressor is a non-dimensional parameter that represents the amount of energy imparted to the airflow by the rotor blades in a given stage of the compressor. It is an essential factor in determining the performance and efficiency of the compressor stage. The loading coefficient is typically expressed in terms of the stage work done and the peripheral velocity of the rotor (u).

The loading coefficient, often denoted as ψ, can be expressed mathematically as:

ψ = Δh/u²

Where:

• Δh: Stage work or enthalpy rise (J/kg).
• u: Peripheral velocity of the rotor (m/s).

The loading coefficient (ψ) is inversely proportional to the square of the peripheral velocity (u). As evident from the formula:

Explanation:

Turbocharger Compressor Drive

• A turbocharger is a device used to increase the power output and efficiency of an internal combustion engine by forcing more air into the combustion chamber. It consists of two main components: a turbine and a compressor. The turbine is driven by the exhaust gases from the engine, and the compressor is coupled to the turbine to compress the incoming air and deliver it to the engine at higher pressure.
• In a turbocharger, exhaust gases from the engine pass through the turbine, causing it to spin. This rotational energy is transferred to the compressor via a shaft. The compressor then draws in ambient air, compresses it, and delivers it to the engine's intake manifold at increased pressure. This process allows more air (and therefore more oxygen) to enter the engine, enabling the combustion of more fuel and resulting in increased power output.

Advantages of Turbochargers:

• Increased engine power output by allowing more air and fuel to combust.
• Improved fuel efficiency due to better utilization of exhaust energy.
• Reduction in engine size for the same power output, leading to lighter and more compact designs.
• Lower emissions as a result of more efficient combustion.

Disadvantages of Turbochargers:

• Turbo lag, which is the delay in power delivery as the turbine spools up.
• Increased complexity and cost of the engine system.
• Higher maintenance requirements due to additional components.

Concept:

Volumetric efficiency of a reciprocating compressor is defined as the ratio of actual volume of refrigerant drawn during suction to the swept (stroke) volume:

\( \eta_v = \frac{V_{suction}}{V_s} \)

Given:

Clearance volume, \( V_c = 0.0005~\text{m}^3 \)

Stroke volume, \( V_s = 0.01~\text{m}^3 \)

Suction volume, \( V_{suction} = 0.0084~\text{m}^3 \)

Calculation:

\( \eta_v = \frac{0.0084}{0.01} = 0.84 = 84\% \)

Concept:

Centrifugal compressor

• Air is drawn into the centre of a rotating impeller with radial blades and is pushed toward the centre by centrifugal force.
• This radial movement of air results in a pressure rise.
• The airflow rate is more than a reciprocating compressor. but the maximum pressure value is less than the reciprocating compressor.
• Centrifugal compressors were used in jet engines and smaller gas turbine engines.
• For larger engines, axial compressors need a lesser frontal area and are more efficient.

Pressure ratio for centrifugal compressor = 4 : 1

Pressure ratio for axial flow compressor = 1.2 : 1

Explanation:

Compressors are classified in two categories based on working principle:

Positive displacement type: In positive displacement type compressors, compression is achieved by trapping a refrigerant vapour into an enclosed space and then reducing its volume. Since a fixed amount of refrigerant is trapped each time, its pressure rises as its volume is reduced. When the pressure rises to a level that is slightly higher than the condensing pressure, then it is expelled from the enclosed space and a fresh charge of low-pressure refrigerant is drawn in and the cycle continues. Example:

• Reciprocating type
• Rotary type with sliding vanes (rolling piston type or multiple vane type)
• Rotary screw type (single screw or twin-screw type)
• Orbital compressors
• Acoustic compressors

Roto-dynamic type (Non-positive displacement type): The elevation of the pressure of the refrigerant vapour is by centrifugal force. In roto-dynamic compressors, the pressure rise of refrigerant is achieved by imparting kinetic energy to a steadily flowing stream of refrigerant by a rotating mechanical element and then converting into pressure as the refrigerant flows through a diverging passage. Example:

• Radial flow type (Centrifugal Compressor)
• Axial flow type

Explanation:

• Plate type or Reed type valves are used in reciprocating compressors.
• These valves are either floating or clamped, usually, backstops are provided to limit the valve displacement.
• Spring may be provided for smooth return after opening or closing
• The piston speed is decided by valve type. Too high speed will give excessive vapor velocities that will decrease the volumetric efficiency and throttling loss will decrease the compression efficiency. 
•  Plate valves are designed to withstand high pressure and dirty gas applications. 
•  Solenoid valve is control units which, when electrically energized or de-energized,  either shut off or allow fluid flow.
• A Poppet valve is typically used to control the timing and quantity of gas or vapor flow into an engine.

Multistage compression:

An increase in pressure ratio in a single-stage reciprocating compressor causes an increase in temperature, a decrease in volumetric efficiency, and an increase in work input. So for the same higher pressure ratio, multistage compression is efficient.

In multistage compression with intercooling, where the gas is compressed in stages and cooled between each stage by passing it through a heat exchanger called an intercooler. Ideally, the cooling process takes place at constant pressure, and the gas is cooled to the initial temperature T₁ at each intercooler. Multistage compression with intercooling is especially attractive when gas is to be compressed to very high pressures.

If an intercooler is installed between cylinders, in which the compressed air is cooled between cylinders, then the final delivery temperature is reduced. This reduction in temperature means a reduction in the internal energy of the delivered air, and since this energy must have come from the input energy required to drive the machine, this results in a decrease in input work requirement for a given mass of delivered air.

By multi-staging, the pressure ratio of each stage is lowered. Thus, the air leakage past the piston in the cylinder is also reduced. The low-pressure ratio in a cylinder improves volumetric efficiency.

Explanation:

Centrifugal Compressor :

• In these compressors, the required pressure rise takes place due to the continuous conversion of angular momentum imparted to the gas by a high-speed impeller into static pressure.
• It can work reasonably well in a contaminated atmosphere.
• It is able to operate efficiently over a wide range of mass flow rate at any particular speed.
• A pressure ratio of 5:1 may be obtained in a single-stage centrifugal compressor. By employing multi-stage staging (up to 8 stages) the delivery up to 400 atm. may be obtained.
• A multistage centrifugal compressor is used for high compression ratio so the width of blades reduces progressively in the direction of flow so as to get constant mass flow rate.
• The isentropic efficiency of the centrifugal compressor is around 75%.
• Centrifugal compressors accelerate the velocity of the gases (increases kinetic energy) which is then converted into pressure as the airflow leaves the volute and enters the discharge pipe.​

Concept:

Centrifugal compressor

Operating Principle:

A centrifugal compressor works by converting kinetic energy into pressure energy. The gas enters the impeller, where it gains kinetic energy through the impeller's high-speed rotation. This kinetic energy is then converted into pressure energy in the diffuser.

Performance Parameters:

Pressure Ratio:

• Centrifugal compressors typically achieve a low to moderate pressure ratio (ranging from 1.1 to 4) per stage.
• This makes them suitable for applications where the required pressure increase is not very high.

High Mass Flow:

• Due to their radial flow design, centrifugal compressors can handle high volumetric flow rates effectively.
• They are often used in situations requiring high mass flow rates at moderate pressures.

Applications:

They are commonly used in applications where moderate pressure ratios and lower mass flow rates are required. Examples include refrigeration systems, small gas turbines, turbochargers, and HVAC systems.
Advantages:

• Compact and robust design.
• Less sensitive to variations in flow.
• Capable of handling a wide range of gases and operating conditions.
• Simpler and more economical maintenance compared to axial compressors.

Pressure ratio for centrifugal compressor = 4 : 1

Pressure ratio for axial flow compressor = 1.2 : 1

Explanation:

The isentropic efficiency of a compressor is defined as the ratio of the isentropic compressor work to actual compressor work.

\({\eta _{isen}} = \frac{{isentropic\;compressor\;work}}{{actual\;compressor\;work}}\)

Important Points

The efficiency of Reciprocating Air Compressor

• Isothermal efficiency → It is the ratio of work (or power) required to compress the air isothermally to the actual work required to compress the air for the same pressure ratio.
• Mechanical efficiency → It is the ratio of the indicated power to the shaft power or brake power of the motor or engine required to drive the compressor.
• Overall isothermal efficiency → It is the ratio of isothermal power to the shaft power or brake power of the motor or engine required to drive the compressor.
• Volumetric efficiency → It is the ratio of the volume of free air delivery per stroke to the swept volume of the piston.

The volumetric efficiency of a reciprocating air compressor with clearance volume is given by

\({\eta _v} = 1 + C - C{\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{1/n}}\)

where C is the clearance factor

\(C = \frac{V_c}{V_s}\)

Concept:

Compressor:

• The air compressor used in gas turbines is of rotary type mainly axial flow turbines. 
• It draws air from the atmosphere and compressed to the required pressure.

Compressors can be of two types:

1. Positive displacement type Compressor:
   • Positive displacement type like reciprocating compressors, Root's blower, and vane - sealed machines.
2. Rotary type Compressor:
   • Rotary type like centrifugal and axial flow compressor.

• The principal type of compressor used nowadays, in the majority of the gas turbine power plants are especially in aircraft applications, is the axial flow compressor.

Axial flow compressors:

• Axial flow compressors are used in all larger gas turbine units because of their high efficiency and capacity (larger air handling ability) and it is an alternative of the centrifugal compressor due to heavyweight and large cross-sectional area.
• In the axial flow compressor, the inlet and outlet of air are parallel to the rotating shaft axis.

Centrifugal compressors:

• Centrifugal compressors are more stable than axial flow ones but of much low capacity and not as efficient. 

Other Main components for gas turbine:

Combustion chamber: 

• The compressed air from the air compressor is drawn to the combustion chamber. 
• The fuel is injected into the air and then ignited in the combustion chamber. 
• It increased the pressure and temperature of the air instantaneously.

Turbine: 

• The high pressure and temperature air are expanded in the turbine.
• The turbine is also of the rotary type. During the expansion, the heat energy in the gas is converted into mechanical energy. 
• This mechanical energy is again converted into electrical energy by using the generator

Concept:

Gas turbines operate on the Brayton cycle/Joule cycle. The Brayton cycle consists of four internally reversible processes:

• Isentropic compression (in a compressor)
• Constant-pressure heat addition
• Isentropic expansion (in a turbine)
• Constant-pressure heat rejection

Work ratio: Work ratio in the gas turbine is defined as the ratio of net-work to the turbine work.

The net-work in the turbine is given by Wturbine – Wcompressor, because the compressor is work consuming device therefore it consumes the work.

\(Work - ratio = \frac{{{{\rm{W}}_{{\rm{net}}}}}}{{{{\rm{W}}_{{\rm{turbine}}}}{\rm{\;}}}} = \;\frac{{{{\rm{W}}_{{\rm{turbine}}}}{\rm{\;}} - {\rm{\;}}{{\rm{W}}_{{\rm{compressor}}}}}}{{{{\rm{W}}_{{\rm{turbine}}}}}} = 1 - \;\frac{{{{\rm{W}}_{{\rm{compressor}}}}}}{{{{\rm{W}}_{{\rm{turbine}}}}}}\)

Calculation: