Compressors Cheatsheet

Cheatsheet Content

### Centrifugal Compressor Working #### Principle of Operation Centrifugal compressors increase the pressure of a gas by converting kinetic energy into pressure energy. Gas enters the impeller axially, is accelerated radially outwards by the rotating impeller blades, and then diffuses in the volute casing, converting high-velocity, low-pressure gas into low-velocity, high-pressure gas. #### Construction A centrifugal compressor consists of: - **Impeller:** A rotating component with radial blades that accelerates the incoming gas. - **Diffuser:** A stationary component surrounding the impeller, consisting of diverging passages that slow down the high-velocity gas. - **Volute Casing:** A spiral-shaped casing that collects the gas from the diffuser and converts remaining kinetic energy into pressure, directing the gas to the outlet. - **Inlet Casing:** Guides the gas smoothly into the impeller. #### Working 1. **Inlet:** Air enters the compressor axially through the inlet casing. 2. **Impeller:** The rotating impeller blades impart kinetic energy to the air, accelerating it radially outwards to a high velocity. 3. **Diffuser:** The high-velocity air then enters the stationary diffuser. The diverging passages of the diffuser slow down the air, converting its kinetic energy into static pressure. 4. **Volute Casing:** Finally, the air enters the volute, where a further reduction in velocity and increase in pressure occur before it is discharged. *Figure: Schematic of a Centrifugal Compressor* ### Axial Flow Compressor Working Axial flow compressors increase gas pressure by passing it through a series of rotating (rotor) and stationary (stator) blade rows. The flow remains primarily axial. #### Working 1. **Rotor Blades:** The rotating blades accelerate the air and turn it in the direction of rotation. This increases the kinetic energy and slightly increases the pressure. 2. **Stator Blades:** The stationary blades immediately downstream of the rotor blades decelerate the air, converting the kinetic energy gained in the rotor into a rise in static pressure. They also redirect the flow for optimal entry into the next rotor stage. 3. **Multi-staging:** Multiple stages (rotor and stator pairs) are used in series to achieve the desired pressure ratio. Each stage contributes to a pressure rise. #### Velocity Triangles Velocity triangles are used to analyze the flow relative to the blades. - **Absolute Velocity (C):** Velocity of the fluid relative to a stationary observer. - **Relative Velocity (W):** Velocity of the fluid relative to the moving blade. - **Blade Velocity (U):** Tangential velocity of the blade. **Inlet Velocity Triangle (Rotor):** $C_1$: Absolute inlet velocity $U_1$: Blade speed at inlet $W_1$: Relative inlet velocity $\alpha_1$: Absolute flow angle $\beta_1$: Relative flow angle **Outlet Velocity Triangle (Rotor):** $C_2$: Absolute outlet velocity $U_2$: Blade speed at outlet $W_2$: Relative outlet velocity $\alpha_2$: Absolute flow angle $\beta_2$: Relative flow angle $$\begin{array}{c} \text{C}_1 \\ \text{U}_1 \\ \text{W}_1 \\ \alpha_1 \\ \beta_1 \end{array} \quad \text{vs} \quad \begin{array}{c} \text{C}_2 \\ \text{U}_2 \\ \text{W}_2 \\ \alpha_2 \\ \beta_2 \end{array}$$ *Figure: Inlet and Outlet Velocity Triangles for an Axial Compressor Rotor* ### Surging and Choking in Centrifugal Compressors These are unstable operating conditions that limit the compressor's performance range. #### Surging - **Definition:** Surging is an unstable operating condition characterized by flow reversal, severe vibrations, noise, and potential damage to the compressor. It occurs when the flow rate through the compressor is too low for a given pressure ratio. - **Mechanism:** At low flow rates, the pressure rise across the compressor becomes insufficient to overcome the system back pressure. This causes the flow to reverse, leading to a momentary drop in compressor discharge pressure. The system then rapidly re-establishes forward flow, and the cycle repeats, creating oscillations. - **Performance Curve:** On a compressor performance map (pressure ratio vs. flow rate), the surge line connects the points of maximum pressure ratio for various speeds. Operating to the left of this line leads to surging. #### Choking - **Definition:** Choking (or stonewalling) occurs when the flow rate through the compressor reaches a maximum limit, usually due to the flow velocity at some point (e.g., impeller eye or diffuser throat) reaching the speed of sound (Mach 1). Further reduction in downstream resistance will not increase the flow rate. - **Mechanism:** As the flow rate increases, the velocity of the gas through the compressor passages increases. When the velocity at a critical cross-section reaches sonic speed, no more mass flow can pass through that section, regardless of how much the pressure ratio is reduced. - **Performance Curve:** On a compressor performance map, the choke phenomenon is seen as a steep, almost vertical drop in the pressure ratio at high flow rates for a constant speed line. Operating to the right of this limit leads to choking. *Figure: Compressor Performance Map showing Surge and Choke Lines* ### Roots Blower #### Working Principle A Roots blower is a positive displacement rotary compressor that traps a fixed volume of air between two counter-rotating lobed rotors and moves it from the inlet to the outlet. #### Construction and Working 1. **Rotors:** Typically two identical, intermeshing, figure-eight or cycloidal-shaped lobes (rotors) are mounted on parallel shafts. These shafts are geared together externally to ensure synchronized counter-rotation without touching each other. 2. **Casing:** The rotors are housed within a precisely machined casing. 3. **Inlet/Outlet:** Air enters through the inlet port. 4. **Trapping:** As the rotors turn, air is trapped in the pockets formed between the lobes and the casing. 5. **Conveyance:** The trapped air is then carried around the periphery of the casing from the inlet side to the discharge side. 6. **Discharge:** As the lobes rotate further, the trapped air is exposed to the discharge port. Backflow from the discharge line compresses the trapped air before it is pushed out. There is no internal compression; compression occurs due to backflow from the discharge line. *Figure: Schematic of a Roots Blower* ### Vane-type Rotary Compressor #### Construction A vane compressor consists of: - **Rotor:** A cylindrical rotor, eccentrically mounted within a larger cylindrical casing. - **Vanes:** Multiple rectangular vanes are fitted into radial slots in the rotor. These vanes are free to slide in and out of the slots. - **Casing:** A stationary cylindrical casing. - **Inlet/Outlet Ports:** Openings in the casing for air entry and exit. #### Working 1. **Rotation:** As the rotor rotates, centrifugal force pushes the vanes outwards against the inner surface of the casing, creating a series of sealed chambers of varying volume. 2. **Inlet:** As a chamber passes the inlet port, its volume increases, drawing in air. 3. **Compression:** As the rotor continues to turn, the volume of the trapped air chamber decreases due to the eccentric mounting of the rotor relative to the casing. This reduction in volume compresses the air. 4. **Discharge:** When the compressed air chamber aligns with the outlet port, the high-pressure air is discharged. *Figure: Schematic of a Vane-type Rotary Compressor* ### Screw Compressor #### Working Principle A screw compressor is a positive displacement rotary compressor that uses two intermeshing helical rotors (screws) to trap and compress air. #### Operation 1. **Rotors:** The compressor consists of a male rotor (typically with convex lobes) and a female rotor (with concave flutes), which are precisely machined to intermesh. They are housed within a casing. 2. **Inlet:** Air enters through an inlet port at one end of the rotors. 3. **Trapping:** As the rotors turn, air is drawn into the spaces between the lobes and trapped as the rotors intermesh and seal off the inlet. 4. **Compression:** The intermeshing action of the helical rotors progressively reduces the volume of the trapped air pockets as they move axially from the inlet to the discharge end. This continuous reduction in volume compresses the air. 5. **Discharge:** When the compressed air pockets reach the discharge port at the other end, the high-pressure air is expelled. Screw compressors can be oil-injected (for sealing and cooling) or oil-free. ### Reciprocating vs. Rotary Air Compressors | Feature | Reciprocating Compressors | Rotary Air Compressors | | :--------------------- | :------------------------------------------------------- | :--------------------------------------------------------- | | **Principle** | Positive displacement (piston in cylinder) | Positive displacement (lobes, vanes, screws) or dynamic (centrifugal, axial) | | **Operation** | Intermittent, pulsating flow | Continuous, smooth flow | | **Pressure Ratio** | Very high, especially multi-stage | Moderate to high | | **Flow Rate** | Lower flow rates, suitable for small to medium demands | Higher flow rates, suitable for medium to large demands | | **Noise & Vibration** | High due to reciprocating motion and unbalanced forces | Lower, smoother operation | | **Maintenance** | Higher due to more moving parts (valves, piston rings) | Lower, fewer wearing parts in contact | | **Efficiency** | High volumetric efficiency at design points | Generally good, especially screw type | | **Size & Weight** | Generally larger and heavier for a given output | More compact and lighter | | **Cooling** | Often air-cooled for small, water-cooled for large | Often oil-injected for cooling and sealing | | **Applications** | Tyre inflation, small workshops, industrial processes, high pressure needs | Industrial plants, air tools, refrigeration, gas turbines | | **Discharge Air** | Pulsating, may require receiver tank | Steady, less need for large receiver | | **Speed** | Lower operating speeds | Higher operating speeds | ### Free Air Delivered (F.A.D) #### Definition Free Air Delivered (F.A.D) is the actual quantity of air delivered by a compressor, measured and expressed as a volume at specified standard atmospheric conditions (e.g., 1 atm and 15°C). It represents the volume of air that the compressor would deliver if the outlet air were expanded back to the ambient conditions. #### Why F.A.D is Less Than Displacement The theoretical displacement of a compressor is the volume swept by its moving parts (e.g., piston in a reciprocating compressor) per unit time. However, the actual F.A.D is always less than the theoretical displacement due to several factors: 1. **Volumetric Efficiency:** - **Clearance Volume:** In reciprocating compressors, there's always a small space (clearance volume) at the end of the piston stroke where some compressed air remains. This air re-expands during the suction stroke, reducing the amount of fresh air drawn in. - **Leakage:** Air can leak past piston rings, valve seats, and seals, reducing the amount of air delivered. - **Valve Losses:** Pressure drop across inlet and outlet valves, and the time required for valves to open and close, reduce the effective intake volume. - **Heating of Inlet Air:** The incoming fresh air can be heated by contact with hot compressor parts, increasing its volume and reducing its mass, which means less mass of air is actually compressed and delivered for a given volumetric intake. 2. **Pressure and Temperature Differences:** - F.A.D is measured at ambient conditions, while the air inside the compressor cylinder is at different pressures and temperatures. - The mass of air delivered is constant, but its volume changes significantly with pressure and temperature. If the air is heated inside the compressor, its volume expands, meaning a smaller mass of air occupies the same volume. 3. **Altitude and Humidity:** - If the compressor is operating at a higher altitude, the atmospheric pressure is lower, and the air is less dense. Therefore, for the same volumetric displacement, a smaller mass of air is taken in and delivered. - Humidity also affects air density. In essence, F.A.D accounts for all these real-world inefficiencies and conditions, providing a practical measure of the compressor's output in terms of usable air at standard conditions. ### Velocity Triangles for Centrifugal Compressor Impeller Velocity triangles are graphical representations of absolute, relative, and blade velocities at the inlet and outlet of the impeller. They are crucial for analyzing the energy transfer and performance. #### Notation - **U:** Blade tangential velocity ($U = \omega r$, where $\omega$ is angular velocity and $r$ is radius) - **C:** Absolute velocity of air - **W:** Relative velocity of air (relative to the blade) - **$C_m$:** Meridional (radial) component of absolute velocity - **$C_w$:** Whirl (tangential) component of absolute velocity - **$\alpha$:** Absolute flow angle (angle of $C$ with tangential direction) - **$\beta$:** Relative flow angle (angle of $W$ with tangential direction) - Subscripts 1 for inlet, 2 for outlet #### Inlet Velocity Triangle (Impeller Eye) At the inlet, air typically enters axially, meaning the absolute velocity ($C_1$) is largely meridional, and the whirl component ($C_{w1}$) is often zero (no pre-whirl). *Figure: Inlet Velocity Triangle* - $U_1$: Blade speed at inlet radius $r_1$. - $C_1$: Absolute velocity of air entering. - $W_1$: Relative velocity of air entering the blade. - If $C_{w1} = 0$, then $C_1 = C_{m1}$. - $W_1^2 = C_{m1}^2 + U_1^2$ (Pythagorean theorem) - $\tan \beta_1 = C_{m1} / U_1$ #### Outlet Velocity Triangle (Impeller Tip) At the outlet, the impeller imparts significant tangential velocity to the air. *Figure: Outlet Velocity Triangle* - $U_2$: Blade speed at outlet radius $r_2$. - $C_2$: Absolute velocity of air leaving the blade. - $W_2$: Relative velocity of air leaving the blade. - $C_{w2}$: Whirl component of absolute velocity at outlet. - $C_{m2}$: Meridional component of absolute velocity at outlet. - From the triangle: $C_{w2} = U_2 - W_2 \cos \beta_2$ - $C_2^2 = C_{m2}^2 + C_{w2}^2$ - $\tan \alpha_2 = C_{m2} / C_{w2}$ These triangles help in determining the work input to the compressor, which is related to the change in tangential momentum of the fluid (Euler's Turbomachinery Equation). ### Classification of Air Compressors Air compressors can be broadly classified based on their principle of operation and the pressure delivered. #### I. Based on Principle of Operation **A. Positive Displacement Compressors:** These compressors trap a fixed volume of air and then reduce its volume to increase pressure. 1. **Reciprocating Compressors:** - **Piston Compressors:** Use a piston moving in a cylinder. - **Single-acting:** Compression on one side of the piston. - **Double-acting:** Compression on both sides of the piston. - **Single-stage:** All compression in one cylinder. - **Multi-stage:** Compression in multiple cylinders in series for higher pressure ratios. - **Diaphragm Compressors:** Use a flexible diaphragm to compress air, preventing contact with moving parts (oil-free). 2. **Rotary Positive Displacement Compressors:** - **Screw Compressors:** Use two intermeshing helical rotors (screws). - **Oil-injected:** Oil lubricates, seals, and cools. - **Oil-free:** No oil in the compression chamber. - **Vane Compressors:** Use radial vanes sliding in an eccentrically mounted rotor. - **Lobe (Roots) Blowers:** Use two counter-rotating lobes to trap and move air. Primarily for low-pressure applications. - **Scroll Compressors:** Use two intermeshing spiral-like scrolls, one fixed and one orbiting. **B. Dynamic Compressors (Turbo Compressors):** These compressors impart kinetic energy to the air using high-speed impellers, which is then converted into pressure energy in a diffuser. 1. **Centrifugal Compressors:** - Radial flow, suitable for medium to high flow rates and moderate pressure ratios. - Single-stage or multi-stage. 2. **Axial Flow Compressors:** - Axial flow, suitable for very high flow rates and moderate to high pressure ratios, often used in gas turbines. - Multi-stage. #### II. Based on Pressure Delivered 1. **Low-Pressure Compressors:** - Discharge pressure up to 10 bar (145 psi). - Examples: Roots blowers, some single-stage reciprocating or rotary screw compressors. 2. **Medium-Pressure Compressors:** - Discharge pressure from 10 bar to 80 bar (1160 psi). - Examples: Multi-stage reciprocating, centrifugal, and screw compressors. 3. **High-Pressure Compressors:** - Discharge pressure above 80 bar. - Examples: Multi-stage reciprocating compressors (e.g., for air bottles, industrial processes), hyper compressors. ### Intercooling in Multistage Compression #### Purpose and Necessity of an Intercooler In multistage compression, an intercooler is a heat exchanger placed between compression stages. Its primary purpose is to cool the compressed air before it enters the next stage of compression. **Necessity:** 1. **Reduce Work Input:** Compressing air isothermally (at constant temperature) requires the least amount of work. Polytropic compression, which occurs in real compressors, involves a temperature rise. By cooling the air between stages, the compression process moves closer to isothermal, significantly reducing the work required for subsequent stages. 2. **Increase Volumetric Efficiency:** Cooling the air reduces its specific volume. This means that a greater mass of air can be drawn into the subsequent compression stage for a given swept volume, thus increasing the overall volumetric efficiency of the compressor. 3. **Improve Safety:** High temperatures can damage compressor components (e.g., lubricants, seals) and increase the risk of explosions, especially with oil-lubricated compressors. Intercooling keeps the operating temperatures within safe limits. 4. **Reduce Power Consumption:** Direct consequence of reduced work input. Less power is needed to achieve the desired pressure ratio. 5. **Reduce Compressor Size:** For a given output, lower operating temperatures and higher efficiency can lead to a more compact design. #### Differentiating "Perfect" and "Imperfect" Intercooling **1. Perfect Intercooling:** - **Definition:** Perfect intercooling occurs when the air is cooled back to its initial inlet temperature (the temperature at which it entered the first compression stage) before entering the next stage. - **Characteristics:** - Achieves the maximum possible reduction in work input and maximum increase in volumetric efficiency for a given interstage pressure. - Idealized condition, often used for theoretical calculations. - Requires a highly efficient intercooler and sufficient cooling medium. - **Impact on P-V Diagram:** On a P-V (pressure-volume) diagram, the compression line for each subsequent stage starts from the initial intake temperature, making the overall compression process closer to the ideal isothermal curve. **2. Imperfect Intercooling:** - **Definition:** Imperfect intercooling occurs when the air is cooled between stages, but not entirely back to the initial inlet temperature. The temperature of the air entering the subsequent stage is still higher than the initial inlet temperature. - **Characteristics:** - More realistic in practical applications due to limitations in heat exchanger effectiveness, cooling water temperature, or design constraints. - Still provides significant benefits over single-stage compression or compression without intercooling, but not to the extent of perfect intercooling. - The amount of work saved and efficiency gained is less than with perfect intercooling. - **Impact on P-V Diagram:** The compression line for each subsequent stage starts from a temperature higher than the initial intake temperature, indicating that some potential work saving is not realized. In summary, intercooling is vital for optimizing the performance, efficiency, and safety of multistage compressors, with perfect intercooling representing the theoretical ideal and imperfect intercooling being the practical reality.