Day 7 - Diesel Power Plant

Heat Generated by Fuel

Qg = mf HV

Heating Value of Fuel

HV = 41130 + 139.6 (API)

Air-Fuel Ratio

Mass of Air

Mass Balance

ma + mf = mg

Volume Displacement

Vd = π/4 D² L N c x acting

Volume Displacement: x when 2 stroke

x = 1

Volume Displacement: x when 4 stroke

x = 1/2

Volume Displacement: Piston Rod Neglected

Vd = π/4 D² L N c x acting

Volume Displacement: Piston Rod Considered

Vd = π/4 D² L N c x + π/4 (D²-d²) L N c x

Piston Speed

PS = 2 L N

Indicated Power

IP = MEPi Vd

MEPi using indicator diagram

MEPi = AK / L

Indicator Diagram: Average Area of Diagram

A = (A1+A2) / 2

Brake Power

BP = MEPb Vd = 2 π N T

Torque

T = W x arm = F x distance

Friction Power

FP = IP - BP

Mechanical Efficiency

e_mech = BP / IP

Generator Efficiency

e_gen = GO / BP

Indicated Thermal Efficiency

Brake Thermal Efficiency

Combined Thermal Efficiency

Volumetric Efficiency

Va

Pa Va = ma Ra Ta

Indicated Specific Fuel Consumption

Brake Specific Fuel Consumption

Combined Specific Fuel Consumption

Indicated Heat Rate

Engine Heat Rate

Engine-Generator Heat Rate

Generator Speed

Frequency if not given

f = 60 hz

Percent Share of Input: BP

BP = 0.34 Qg

Percent Share of Input: Cooling Loss

Cooling Loss = 0.3 Qg

Percent Share of Input: Friction/Radiation/etc

Friction = 0.1 Qg

Percent Share of Input: Exhaust Loss

Exhaust Loss = 0.26 Qg

Mass balance in engine

ma + mf = mg

Heat balance in engine

Qg = cooling loss + friction loss + exhaust loss + BP

Cooling Loss in the Engine

Cooling Loss = mw cp (t2 - t1)

Engine Operating at Higher Elevation: Engine Constants

Friction Power

Mass of Fuel Consumption

Volume of Air Required

Indicated Power directly proportional to density of air

Engine Operating at Higher Elevation: Friction Power

FP1 = FP2 → IP1-BP1 = IP2-BP2

Engine Operating at Higher Elevation: Mass of Fuel Consumption

mf1 = mf2 → ma1 / A/F1 = ma2 / A/F2

Engine Operating at Higher Elevation: Volume of Air

Va1 = Va2 → mRT/P1 = mRT/P2

Engine Operating at Higher Elevation: Indicated Power is directly proportional to density

IP1 / IP2 = p1 / p2

Temperature and Pressure Relations at higher elevation: Temperature Only find T2

Temperature and Pressure Relations at higher elevation: Temperature Only Find BP2

Temperature and Pressure Relations at higher elevation: Pressure Only Find P2

Temperature and Pressure Relations at higher elevation: Pressure Only Find BP2

Temperature and Pressure Relations at higher elevation: Temperature and Pressure

Waste Heat Recovery Boiler

mg cp (t1 - t2) = ms (hs - hf)

Problem 2: Find engine efficiency given stroke number, bore, stroke, rpm, and clearance volume

e = 1 - 1/rk^k-1

Problem 2: Find rk given stroke number, bore, stroke, rpm, and clearance volume

rk = (1 + c) / c

Problem 2: Find c given stroke number, bore, stroke, rpm, and clearance volume

c = V2 / Vd

Problem 2: Find V2 given stroke number, bore, stroke, rpm, and clearance volume

V2 = clearance volume

Problem 2: Find Vd given stroke number, bore, stroke, rpm, and clearance volume

Vd = 2 pi/4 D² L N c x

Problem 8: Find BP given acting, stroke number, cylinder number, diameter, stroke, piston rod diameter, rpm, mep1, mep2

e_mech = BP / IP

Problem 8: Find IP given acting, stroke number, cylinder number, diameter, stroke, piston rod diameter, rpm, mep1, mep2

IP = MEPi + Vd = IP1 + IP2

Problem 8: Find Vd1 given acting, stroke number, cylinder number, diameter, stroke, piston rod diameter, rpm, mep1, mep2

Vd1 = pi/4 D² L N c x

Problem 8: Find Vd2 given acting, stroke number, cylinder number, diameter, stroke, piston rod diameter, rpm, mep1, mep2

Vd1 = pi/4 (D²-d²) L N c x

Problem 16: Find BP2 given BP1, P1, T1, P2, T2, e_mech

BP2 = BP1 x P2/P1 x sqrt(T2/T1)

Problem 22: Find mass of cooling water required given BP, T1, T2, cp

Qcw = m_cw x cp x (t2-t1)

Problem 22: Find Qcw required given BP, T1, T2, cp

Qcw = 0.3 Qg

Problem 22: Find Qg required given BP, T1, T2, cp

BP = 0.34 Qg

Problem 24: Find IP given cylinders, stroke number, bore, stroke, rpm, torque w/ all cylinders, torque w/ 1 cylinder out, mf, HV, ma, Ta

IP = 2 pi N (Tall - Tout) #cyl

Problem 26: Find Power given V, compression ratio, heat addition, rpm

Power = ms (h1 - h2)

Problem 26: Find ms given V, compression ratio, heat addition, rpm

m = p V

Problem 26: Find h1-h2 given V, compression ratio, heat addition, rpm

e = (h1 - h2) / heat addition

Problem 26: Find e given V, compression ratio, heat addition, rpm

e = 1 - 1/rk^k-1

Problem 35: Find power developed given height, Q, rpm, friction torque, velocity

WP = γ Q H - Losses

Problem 35: Find Losses given height, Q, rpm, friction torque, velocity

Losses = BP_friction + KE = 2 pi N T + ½ mV²