Video summary

12. Kompresor sentrifugal

Main summary

Key takeaways

Educational

Main ideas & concepts covered (Centrifugal compressor)

Centrifugal compressor fundamentals

A centrifugal compressor (shown as the white-arrow part) is compared to a centrifugal pump. In general, it:

  • Produces a higher pressure increase than an axial compressor “at one level.”
  • Has a lower mass flow rate than axial compressors.
  • Therefore, centrifugal compressors are commonly used in systems that are compact/smaller in size.

With appropriate design/materials and higher power impellers, pressure ratio capability can be increased (stated up to several times the inlet pressure).

Applications mentioned

  • Gas turbines (compact machines)
  • Process/chemical industry, where processed gases must be pressurized (e.g., “chemical factories working with high…”)

Typical construction / components

The video lists three main components:

  1. Volute casing / casing
  2. Rotor / impeller
  3. Diffuser / diffuser passages (including directing/silent blades)

Impeller characteristics

  • Impeller blades are described as mainly radial (perpendicular to a reference circle).
  • The impeller includes:
    • Rotor
    • Outer circle / impeller rim
    • Airfoil profiles

Diffuser role

  • Directs gas flow and converts kinetic energy → potential pressure energy.
  • In simplified treatment, the diffuser is treated as having negligible work, and diffuser losses are sometimes ignored.

Flow path description (fluid through the compressor)

The fluid enters near the inlet (near the arrow direction), then flows:

  • into the impeller
  • into the diffuser
  • into the casing/volute
  • and finally exits as the fluid outlet

Within the casing, the flow is described as moving azimuthally before exiting.

Geometry variables (diameters)

Key diameter notations mentioned include:

  • Inlet diameter at impeller inlet: D₁
  • Tip diameter at inlet: D₁t (tip diameter mentioned)
  • Outlet diameter at impeller exit: D₂

The transcript also discusses relationships for average diameters and inlet/outlet velocity-triangle elements (some formula text is partially garbled).

Velocity triangle & similarity to axial-compressor relations

Centrifugal compressor analysis uses speed triangles and similar relationships to axial-compressor theory, involving:

  • absolute velocity C
  • relative velocity W
  • blade speed U
  • flow angles at inlet/outlet (α, β)

The transcript states that corresponding speed-triangle cosine/sine relations apply at inlet and outlet.

Work and energy relations (Euler turbine/pump-type equation)

Compressor work per unit mass is tied to an Euler equation-type relationship, based on blade speeds and velocity components (often involving terms like U₂, U₁, Cθ2, Cθ1, depending on the form).

A thermodynamics-based relation connects work with stagnation enthalpy rise. Under simplifying diffuser assumptions, stagnation enthalpy leaving/entering certain sections can be related directly.

Mass flow vs pump analogy

The video contrasts:

  • compressible flow (compressor)
  • incompressible fluid (pump)

and emphasizes using mass flow rate for compressible analysis.

Special case: “without prewhirl/free swirl” (α₁ = 90°)

A special inlet condition is considered:

  • With α₁ = 90°, terms like Cw1 = C1 cos(90°) become zero (as stated).

The work expression simplifies and becomes mainly dependent on U₂ and the exit tangential component.

Static enthalpy increase interpretation

The video derives an expression for increase in static enthalpy from work and kinetic-energy terms.

Interpretation:

  • The rise in static enthalpy corresponds to increases in pressure and internal energy (with compressibility effects).
  • Compressible effects cannot be treated the same as incompressible friction heating only.

Pressure ratio and isentropic efficiency

The total isentropic efficiency relationship is used to connect:

  • stagnation states (inlet/outlet)
  • isentropic work
  • actual work

It then derives a pressure ratio equation using:

  • inlet total temperature T₀₁
  • inlet/outlet blade speeds and velocity-triangle parameters
  • gas properties k (gamma) and gas constant R

It also mentions simplification again for the no prewhirl case (α₁ = 90°).

Slip factor corrections

Like pump theory, centrifugal compressors use slip factor corrections:

  • Stodola slip factor (ε / “zeta”/σ style naming in transcript)
  • Smith factor / Smith formula (empirical correction)

For a radial impeller (β₂ = 90°), the slip factor formulas simplify.

Slip reduces effective work:

  • work/unit mass = (slip factor) × theoretical work terms

H–s (enthalpy–entropy) diagram explanation

The video explains:

  • the isentropic line (ideal compression)
  • the actual/polytropic process path

Energy conversion is described as:

  • Rotor: kinetic energy increases substantially
  • Diffuser: kinetic energy is converted back into pressure/enthalpy (potential energy increase)

Differences between ideal and actual paths correspond to losses, and stagnation enthalpy behavior is tied to diffuser assumptions.

Compressor characteristic curve & operating lines

Compressor performance is plotted similarly to pumps:

  • Y-axis: pressure ratio
  • X-axis: mass flow rate
  • Curves depend on speed (multiple lines for different RPM)

Performance/efficiency map

  • Efficiency contours/elliptical shapes.

Stability/limits

  • Surge line: limit where flow reversal can occur
  • Choke line / stone wall: high-flow limit where compressibility effects appear (as described)

Qualitatively:

  • Surge relates to flow reversal (stalling)
  • Choking relates to speed of sound/compressibility limitations

Methodology / formulas / steps presented (as instructions)

A) Component identification & flow modeling (conceptual steps)

  • Identify the compressor region and model it as:
    • Impeller (rotor): adds energy via rotational motion
    • Diffuser (and volute casing): converts kinetic energy to pressure rise
  • Model flow using:
    • velocity triangle at inlet and outlet
    • thermodynamic relations using stagnation properties

B) Speed triangle / velocity relations (general approach)

Use inlet/outlet relationships among:

  • absolute velocity C
  • relative velocity W
  • blade speed U
  • flow angles (α₁, β₁, α₂, β₂)

Then apply trigonometric projections (cosine/sine components) to build Euler-type compressor work/unit-mass expressions.

C) Diffuser/work simplification assumptions (used in derivations)

Assume:

  • no significant work in the diffuser
  • diffuser losses ignored (in the simplified derivation)

Use this so stagnation enthalpy leaving/entering certain sections can be set equal or directly related.

D) Pressure ratio from efficiency (thermodynamic workflow)

  • Start with total isentropic efficiency definition (actual vs ideal compression).
  • Express isentropic work using:
    • total temperatures and gas properties (e.g., k, R)
  • Replace actual work using velocity-triangle/Euler work relations.
  • Solve for a pressure ratio of the form p₀,3 / p₀,1 (notation varies in the transcript).

E) Slip factor correction workflow

  • Compute slip factor using:
    • Stodola or Smith factors
  • Correct effective work:
    • ( W = \sigma \times (\text{theoretical work per unit mass}) )
  • In the special radial/β₂ = 90° case, use simplified slip factor expressions.

F) H–s diagram interpretation checklist

  • Identify:
    • isentropic path (ideal)
    • actual compression path (real)
  • Interpret energy conversion:
    • rotor: kinetic energy increase
    • diffuser: kinetic energy → pressure/enthalpy
  • Recognize that separation between paths corresponds to losses.

Worked example in the video (problem-solving procedure)

The video provides an example compressor problem and computes multiple outputs. The intended steps are:

Given

  • Impeller type: radial
  • Outlet diameter: D₂ = 165 mm
  • Speed: N = 46,000 RPM
  • Mass flow rate: ṁ = 0.6 kg/s (air)
  • Inlet diameter: D₁ = 63.5 mm
  • Entry height step: 25 mm (used for blade/meridional area/flow relation)
  • Inlet static conditions:
    • p₁ ≈ 93 kPa
    • T₁ ≈ 293 K
  • Total isentropic efficiency: ηₜ,is = 0.9
  • Gas property assumptions:
    • k = 1.4
    • R = 287 J/(kg·K)
    • cₚ = 1005 J/(kg·K)

Step sequence (as described)

  • Compute slip factor σ
    • Use Smith/Stodola-type slip factor simplified for radial conditions.
  • Compute rotor work per unit mass
    • For the “without prewhirl” case:
      • inlet whirl-related terms may become zero
    • Use a simplified corrected work form suggested by the transcript, e.g.:
      • ( W = \sigma \, U_2^2 )
  • Convert work to power
    • ( \dot{W} = \dot{m} \times W )
  • Determine inlet blade angle (β₁)
    • Use velocity triangle relations:
      • ideal gas density: ( \rho_1 = \frac{p_1}{R T_1} )
      • inlet absolute velocity from flow rate and inlet area
      • then compute blade angles via trigonometry (tan/cot relations mentioned)
  • Compute stagnation enthalpy at inlet
    • ( h_{0,1} = c_p T_1 + \frac{C_1^2}{2} ) (stated in words)
  • Compute stagnation enthalpy at outlet
    • ( h_{0,2} = h_{0,1} + W )
  • Compute outlet stagnation temperature
    • With ideal gas and constant (c_p):
      • ( T_{0,2} = \frac{h_{0,2}}{c_p} )
  • Compute isentropic outlet stagnation pressure
    • From isentropic efficiency:
      • relate actual outlet total temperature rise/work to isentropic work
    • Then use isentropic temperature-pressure relation:
      • ( p_{0,2} ) from ( T_{0,2s} / T_{0,1} ) using the (k/(k-1))-type relation

Outputs listed as requested

  • Entry blade angle
  • Outlet stagnation temperature
  • Outlet stagnation pressure

Note: Several numeric steps are muddled by subtitle errors; the overall procedure and computed outputs are clear.

Speakers / sources featured

  • Speaker: Kurniadi (mentioned in the opening as “with me Kurniadi”).

Original video