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  Centrifugal Compressor °ü·Ã¼ö½Ä Á¤¸®
  ±Û¾´ÀÌ : ¿î¿µÀÚ   °íÀ¯ID : ¿î¿µÀÚ     ³¯Â¥ : 00-00-00 00:00     Á¶È¸ : 16366    
Centrifugal Compressor °ü·Ã¼ö½Ä Á¤¸®

¡Ý Compression Process

  1. Adiabatic

      (P V)^k = C, k = Cp/Cv
      ¾î¶°ÇÑ ¿­µµ °¡½º¸¦ ¾ÐÃà¿îÀüÀ» ÇÏ´Â µ¿¾È¿¡ ´õÇØÁö°Å³ª »©ÁöÁö ¾Ê´Â »óÅÂ
      ¾ÐÃൿ¾È¿¡ °¡½ºÀÇ ¿Âµµ»ó½ÂÀÌ ÀÌ·ç¾î Áø´Ù.

  2. Isothermal

      (P V) = C
      ¾ÐÃà¿îÀü µ¿¾È¿¡ »ó½ÂµÈ ¿­ÀÌ Á¦°ÅµÇ¾îÁ® °¡½ºÀÇ ¿Âµµ´Â ÀÏÁ¤ÇÏ´Ù.
      ÀϹÝÀûÀÎ ¼³ºñ¿¡¼­´Â ÀÌ·¯ÇÑ ¾ÐÃàÀº ÀÌ·ç¾î ÁöÁö ¾Ê´Â´Ù.

  3. Polytropic

      (P V)^n = C, k = Cp/Cv
      Polytropic ¾ÐÃàÀº  Adiabatic ¶Ç´Â Isothermal µµ ¾Æ´Ñ ¾ÐÃàÀÌ´Ù.

      nÀº ¾ÐÃà½Ã Compression Performance¿¡ ÀÇÇØ °áÁ¤µÇ¾îÁö´Â Ư¼ºÄ¡ÀÌ´Ù.
      ¸¸ÀÏ n = 1 Àΰæ¿ì ¾ÐÃàÀº Isothermal À̸ç n = k Àΰæ¿ì´Â Adiabatic
      º¸Åë Centrifual Compressor¿¡¼­´Â ³»ºÎÀûÀ¸·Î ³Ã°¢ÀÌ ÀÌ·ç¾î ÁöÁö ¾ÊÀ¸¸é,
      n > k °¡ µÇ¸ç polytropic Ư¼ºÀ» °®´Â´Ù.
      ¸¸ÀÏ ³»ºÎÀûÀ¸·Î ³Ã°¢ÀÌ µÇ¸é, n > 1.0 ¸é¼­ n < k °¡ µÈ´Ù.

      polytropic exponent n ´Â ¾ÐÃà°úÁ¤¿¡¼­ ´ÙÀ½°ú °°Àº °ü°è¸¦ °®´Â´Ù.

      n = log10 (P2/P1) / log10 (v1/v2)
 
      P : Absolute Pressure
      v : Specific Volume

      º»½ÄÀº Multi Stage CompressorÀÇ °¢ Single Wheels¿¡ ¸ðµÎ Àû¿ëµÈ´Ù.


¡Ý Efficiency

  1. Adiabatic Efficiency

      Adiabatic Efficiency
      = ÀÌ·Ð adaibatic horsepower / ½ÇÁ¦ brake horsepower @ Compressor Shaft
      = Compression Efficiency * Mechanical Efficiency

      ea = adiabatic work / polytropic work
        = [(P2/P1)^((k-1)/k) -1] / [(P2/P1)^((n-1)/n) -1]

      ea = ÀÌ·Ð adaibatic temperature rise / actual temperature rise
        = T1 [(P2/P1)^((k-1)/k) -1] / (T2 - T1)

  2. Adiabatic Shaft Efficiency

      Adiabatic & polytropic Efficiency¿¡´Â packing gland, oil pump, jounal
      bearing, thrust beraings µî¿¡¼­ÀÇ loss´Â Æ÷ÇÔµÇÁö ¾Ê´Â´Ù.

      - 500 HP ÀÌÇÏ  : 3% ÀÌ»ó loss
      - 500~1500 HP  : 1~3% loss
      - 1500 HP ÀÌ»ó : 1~1.5% loss

  3. Polytropic Efficiency

      Polytropic Efficiency
      = ÀÌ·Ð polytropic horsepower / ½ÇÁ¦ brake horsepower (@ Compressor Shaft)
      = Compression Efficiency * Mechanical Efficiency

      ep = [(k-1)/k) -1] / [(n-1)/n) -1]
      ÀϹÝÀûÀ¸·Î 0.70 < ep < 0.80 À̸ç 0.72°¡ ÀÌ»óÀûÀÌ´Ù.

      ep = loge [(P2/P1)^((k-1)/k) -1] / loge [T2 / T1]

 
¡Ý Head

  1. Adiabatic Head

      Ha = 144 P1V1 k/(k-1) [(P2/P1)^((k-1)/k) -1] Z1 [feet]
      Ha = R T1 k/(k-1) [(P2/P1)^((k-1)/k) -1] Z1 [feet]
      Ha = 1545 (T1 / M.W) k/(k-1) [(P2/P1)^((k-1)/k) -1] Z1 [feet]
      Ha = 53.3/Sp.Gr T1 k/(k-1) [(P2/P1)^((k-1)/k) -1] Z1 [feet]

      Ha : Total hea [feet]
      V1 : Suction Vulume [cu.ft/min]
      R  : Gas constant = 1545 / MW
      T  : Temperature [R]
      k  : Cp/Cv
      Z1 : Compressibility factor
      P1 : Inlet Pressure [psia]
      P2 : Discharge Pressure [psia]
      Sp.Gr : Specific Gravity

  2. Polytropic Head

      Hp = 144 P1 V1 (n/(n-1)) [(P2/P1)^(n-1)/n - 1] Z1 [feet]
      Hp = Z1 R T1 (n/(n-1)) [(P2/P1)^(n-1)/n - 1] Z1 [feet]
      Hp = 1545 (Z1 T1 / M.W) (n/(n-1)) [(P2/P1)^(n-1)/n - 1] Z1 [feet]

      Hp : Polytropic Head, = adiabatic head/ ea
      V1 : Suction Vulume [cu.ft/min]
      R  : Gas constant = 1545 / MW
      T  : Temperature [R]
      k  : Cp/Cv
      Z1 : Compressibility factor
      P1 : Inlet Pressure [psia]
      P2 : Discharge Pressure [psia]


¡Ý Brake horsepower

  HPg = 778 W (h2-h1) / 33000 = W Hp / 33000 ep
  shaft HPg = HPg / (0.99 ~ 0.97)

  BHP = P1 V1 [(k/(k-1)] [(P2/P1)^(k-1)/k - 1] [(Z1+Z2)/2 / Z1] / (229 ea)

  W      : Gas flow [lbs/min]
  h2, h1 : Discharge, inlet Enthalpy [Btu/Lb]
  HPg    : Gas Horsepower
  Hp    : Polytropic head [feet]
  ep    : Hydraulic or polytropic efficiency (0.70~0.80)
  BHP    : Brake horsepower @ Compressor shaft
  Z1    : Compressibility factor


¡Ý Peripheral Velocity (= Tip Speed)
 
  u = ¥ðD (RPM) / 720 [ft/sec]

  u : Peripheral Velocity [ft/sec]
  D : Impeller Diameter [in]
 

¡Ý Temperature Rise

  1. Adiabatic

      T2 = T1 (P2/P1)^(k-1)/k

  2. Polytropic
 
      T2 = T1 (P2/P1)^(n-1)/n

      T : Temperature Inlet, Discharge [R]
      P : Pressure Inlet, Discharge [psia]
 

¡Ý Sonic or Acoustic Velocity

  Vs = [k 32.2 R T Z]^1/2 [feet/sec]

  k : Cp/Cv
  R : Gas Constant = 1545 / Mw
  T : average absolute temperature [R]
  Z : Compressibility factor for gas at T

  Åë»ó gas velocity´Â sonic velocity ÁÖº¯ ¶Ç´Â ±× ÀÌ»óÀÌ µÇÁö ¾Êµµ·Ï ÇÑ´Ù.


¡Ý Specific Speed

  Ns = RPM * SQRT(V1) / Ha^0.75

  V1  : Flow rate @ Suction condition [cu.ft/min]
  Ns  : Totqal head of wheel [feet]
  RPM : actual speed of wheel [rpm]

  Centrifugal Compressor´Â º¸ÆíÀûÀ¸·Î ³ôÀº È¿À²»óÅ¿¡¼­ 1500~3000 rpmÀÇ
  Specific Speed °ªÀ» °®´Â´Ù.


¡Ý Affinity Laws

  1. Speed

      V2 = V1 (RPM2 / RPM1)
      H2 = H1 (RPM2 / RPM1)^2
      BHP2 = BHP1 (RPM2 / RPM1)^3

  2. Impellar Diameter (Similar)

      H2 = H1 (D2 / D1)^2
      V2 = V1 (D2 / D1)^3
      BHP2 = BHP1 (D2/D1)^5

  3. Impellar Diameter (Changed)
 
      H2 = H1 (D2 / D1)^2
      CFM2 = CFM1 (D2 / D1)
      BHP2 = BHP1 (D2/D1)^3

  4. Effect of temperature

      BHP2 = BHP1 (T1/T2)
 

   

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