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> > > 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 »óÅ > 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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