"Otto Cycle.  Constant sp. heat ratio. See Problem 5.5"


"Engine Data"

r_c = 7											"Compression Ratio"

"Working Fluid Data"

gamma = 1.3										"Specific Heat Ratio"
c_v = 0.946										"[kJ/kg-K]  Constant Volume Specific Heat"

"Fueling Data"

Q_LHV = 44000									"[kJ/kg]"
AF = 15.0
m_r = (1-x_r)/(1+AF)							"ratio of mass of fuel to mass of charge"

"Starting Point Data -- Point 1"


{T_i = 270}										"[K]"
T_1 = 360										"[K]"
P_1 = 50											"[kPa]"

"End of Compression -- Point 2"

P_2/P_1 = r_c^gamma
T_2/T_1 = r_c^(gamma-1)

"Combustion at constant volume -- Point 3"

c_v*(T_3-T_2) = m_r * Q_LHV
P_3/P_2 = T_3/T_2

"End of Expansion -- Point 4"

P_3/P_4 = r_c^gamma
T_3/T_4 = r_c^(gamma-1)

"Point - 5 describes the gas remaining in the cylinder at the end of blowdown.
It has just experienced an isentropic expansion from 4 to 5.  Remember, most of the gas has exited."

P_5 = 100

(P_5^(1/gamma-1))/(P_4^(1/gamma-1)) = T_4/T_5

"Calculation of Efficiency - Method Involving First Law.  Calculate Heat Added minus
heat rejected.  Set it equal to net work.  Divide by heat added."

q_add = m_r*Q_LHV
q_rej = c_v*(T_4-T_1)
w_c = q_add - q_rej
eta_1 = w_c/q_add

"Calculation of Efficiency - Temperatures"

eta_2 = 1 - (T_4-T_1)/(T_3-T_2)

"Calculation of Efficiency - Formula with Compression Ratio and Gamma"

eta_3 = 1 - r_c^(1-gamma)

"Calculation of Imep"

c_p = gamma*c_v
R = c_p - c_v
imep_1 = w_c / ( (R*T_1/P_1)*(1-1/r_c))

"Formula -- 5.32"

imep_2 = P_1 * (q_add/(c_v*T_1)) * (1/(gamma-1)) * (r_c/(r_c-1)) * eta_3

"Formula -- 5.33"

imep_3 = P_3 * (1/((gamma-1)*r_c^gamma))*(r_c/(r_c-1))*(eta_3/((c_v*T_1/q_add)+1/r_c^(gamma-1)))

"Calculate imep ratios"

imep|p1 = imep_1/P_1
imep|p3 = imep_3/P_3


"Calculation of residual fraction - equation 5.35"

P_e = P_5
P_i = P_1

x_r = 1/r_c * (P_e/P_i)^(1/gamma) / ( 1 + q_add/(c_v*T_1*r_c^(gamma-1)))^1/gamma

"Calculation of  inlet temperature T_i based on this"

T_1 / T_i = (1-x_r)/( 1 - 1/(gamma*r_c)*(P_e/P_i + gamma-1))

"Alternative work calculations based on integrating PV relations"

w_12 = c_v*T_1*(1-r_c^(gamma-1))
w_34 = c_v*T_3*(1-1/r_c^(gamma-1))
w_calt = w_34-w_12

"Power calculation"

N =2400/60										"[1/s]"
n_R = 2
mass = 0.00045									"[kg]"
W_ind = mass*w_c
P_ig = 4*W_ind * N / n_R
P_hp = P_ig*convert(kw,hp)
eta_4 = W_ind/(mass*q_add)

"Engine Volume Calculations"

P_1*V_1 = mass*R*T_1
V_2 = V_1/r_c
V_d = V_1-V_2
V_liters = 4*V_d*convert(m^3,liter)					"[liter]"

"Friction Work and Power"

W_p = (P_e-P_i)*(V_1-V_2)							"[kJ]"
imep_test = W_ind / V_d
P_p = 4*W_p * N / n_R
P_in = P_ig - P_p
eta_5 = (W_ind-W_p)/(mass*q_add)

"Fuel Consumption"

mass_fuel = mass*m_r
mfdot = 4*mass*m_r*N/n_R							"[kg/s]"
isfc = mfdot/P_ig * convert(kg,mg)/convert(kJ,J)
fuel|hr = mfdot*convert(kg/s,kg/hr)
density = 0.75									"[kg/liter]"
vol|hr = fuel|hr/density								"[liter/hr]"
speed = 100									"[km/hr]"
mileage = speed/vol|hr							"[km/liter]"
mpg = mileage*convert(km/liter,mile/gal)