Reciprocating Compressors MCQ Quiz - Objective Question with Answer for Reciprocating 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:

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:

For minimum work input, pressure ratio in each stage should be same in multi-stage compression.

For N-stage compression,

\(\frac{{{P_2}}}{{{P_1}}} = \frac{{{P_3}}}{{{P_2}}} = \frac{{{P_4}}}{{{P_3}}} = \frac{{{P_{N + 1}}}}{{{P_N}}} = constant\left( k \right)\)

\(\frac{{{P_{N + 1}}}}{{{P_N}}} = {\left( k \right)^N}\)

For two stage compression \({\rm{\;}}Pressure{\rm{\;}}ratio = {\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{1/2}}\)

\({W_{per{\rm{\;}}stage}} = {\rm{\;}}\frac{n}{{n - 1}}{\rm{\;}}{m_a}R{\rm{\;}}{T_1}\left[ {{{\left( {\frac{{{P_2}}}{{{P_1}}}} \right)}^{\frac{{n - 1}}{n}}} - 1} \right]{\rm{\;}}\)

i.e. W per stage  is function of pressure ratio and the inlet temperature T₁ for perfect intercooling the temperature after intercooling in each stage is same,

i.e. for two stage compression

T₁ = T₃

As pressure ratio and temperature at inlet are same, work done will be same in each stage.

By perfect inter cooling we will achieve the isothermal compression which required the least work and the efficiency will improve.

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:

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: 

• It is a device used to increase the pressure of a gas.
• The volumetric efficiency of a compressor is defined as the ratio of actual volume sucked by the compressor at the inlet to the swept volume.
• volumetric efficiency is given by, 
• \({\eta _v} = 1 + c - c{\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{\frac{1}{n}}}\)
• ⇒ \({\eta _{vol}} = 1 - C\left[ {{{\left( {\frac{{{p_2}}}{{{p_1}}}} \right)}^{\frac{1}{n}}} - 1} \right]\)
• where C is clearance ratio it is the ratio of clearance volume to swept volume.
• P₂ is the delivery pressure and P₁  is the suction pressure.
• So from the formula, it is shown with an increase in clearance ratio and pressure ratio volumetric efficiency is decreased.  

Volumetric efficiency decreases when

1. Outlet pressure Increases
2. Clearance ratio Increases

Volumetric efficiency increases when

1. 'n' increases
2. Inlet temperature increases

As the clearance ratio increases, the volumetric efficiency of the reciprocating compressor decreases as the pressure ratio increases. Options 2 and 4 both are correct but here, we have to select the most appropriate answer among the given options. So, here option 4 is the correct one.

Concept:

A reciprocating compressor or piston compressor is a positive-displacement compressor that uses pistons driven by a crankshaft to deliver gases at high pressure.

Clearance Ratio: It is the ratio of clearance volume to the swept volume.

Clearance volume: It is that volume which remains in the cylinder after the piston has reached the end of its inward stroke.

Swept Volume: Swept volume is the displacement of one cylinder. It is the volume between the top dead centre (TDC) and bottom dead centre (BDC). As the piston travels from top to bottom, it "sweeps" its total volume.

\(Clearance~ratio=\frac{Clearance~volume}{Swept~volume}=\frac{V_c}{V_s}\)

Calculation:

Given:

Since. the maximum volume = Vs + Vc 

The swept volume is 8/9 times the maximum volume.

⇒ Vs  =  8/9(Vs + Vc)

\(=\frac{V_c}{V_s}=\frac{1}{8}\)

\(Clearance~ratio=\frac{V_c}{V_s} = 0.125\)

So, the correct option is (3).

Explanation:

For reciprocating air compressor, the law of compression desired is isothermal and that may be possible at very low speeds.

• Due to minimum work input required in isothermal compression, it is the ideal process for compression.
• Constant pressure line 4-1 represents the suction stroke.
• Area 1234 represents the adiabatic work.

Isothermal compression:

• If the compression is carried out isothermally, then it follows the curve 1-2 which has less slope than both isentropic and polytropic processes.
• This work done that is area 1234 in isothermal process is considerably less than that due to adiabatic compression.
• Thus, the compressor will have higher efficiency if compression follows the isothermal process.
• It is not possible in practice to achieve an isothermal process, as the compressor must run very slowly.
• In practice, compressors run at high speeds which results in a polytropic process.
• The cold-water spray and multi-stage compression are used for approximating to isothermal compression while still running the compressor at high speeds.

Concept:

Volumetric efficiency: 

• It is defined as the ratio of the actual volume of air intake by the compressor to the swept volume.
• It is given as;

\(\eta_{v}=1+C-C(\frac{P_2}{P_1})^\frac{1}{n}~ \)

or, \(\eta_{v}=1+C-C(\frac{V_1}{V_2})~ \)

Where, C = Clearance ratio, P₁ = suction pressure

P₂ = discharge pressure, V₁ = suction volume, V₂ = discharge volume

Calculation:

Given:

C = 0.03

\(\frac{V_1}{V_2}\) = 8

Then, \(\eta_{v}=1+C-C(\frac{V_1}{V_2})=1+0.03-(0.03\times8)~ \)

\(\eta_{v}=0.79\times100=79~\)%

Thus, option (3) is correct answer.

Explanation:

Compressor:

• It is a device used to increase the pressure of a gas.
• The Volumetric efficiency of the compressor is defined as the ratio of actual volume sucked by the compressor at the inlet to the swept volume.
• Volumetric efficiency is given by:

\(\eta_v~=~1~+~C~-~C(\frac{P_2}{P_1})^{\frac{1}{n}}\) = \(\eta_v~=~1~-C[(\frac{P_2}{P_1})^{\frac{1}{n}}~-~1]\)

where C is clearance volume and it is the ratio of Clearance volume to the swept volume, P₂ is the delivery pressure and P₁ is the suction pressure.

• From the formula, it is clear that with an increase in clearance ratio and pressure ratio, volumetric efficiency decreases.

Explanation:

Compressor: A compressor is a power-consuming device that is used to increase the pressure of gases

Clearance volume – It is the volume which is remained in the cylinder even after the piston reaches the top dead center. It is denoted by Vc

Swept volume – It is the volume swept by the piston in the cylinder or the volume through which the piston travels. It is denoted by Vs

Clearance ratio (C) – It is defined as the ratio of clearance volume and swept volume or \(C = \frac{{{V_c}}}{{{V_s}}}\)

The relation between the clearance and stroke length for a compressor in the practical case is given by 

C = (0.005L + 0.5) mm

where C = clearance provided between cylinder head and piston, L = stroke length

Concept:

For perfect intercooling in the two-stage compressor,

\({P_i} = \sqrt {{P_1}{P_2}} \)

where P_i = Intermediate Pressure, P₁ = Suction pressure, P₂ = Delivery pressure

Calculation:

Given:

P₁ = 1.5 bar, P₂ = 54 bar

So, \({P_i} = \sqrt {{1.5}\times{54}} \)

P_i = 9 bar

Hence the intermediate pressure will be 9 bar.