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OdEngineNew.hpp
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OdEngineNew.hpp
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#pragma once
#include <iostream>
#include "Coef.hpp"
#include <cmath>
#include <Eigen/Dense>
#include <fstream>
#include <algorithm>
enum ExitCase{sub, sup}; //flow exit cases: subsonic, supersonic
class OdEngine{
public:
Eigen::RowVectorXd time_; // time array
Eigen::RowVectorXd p_c_; // chamber pressure array
Eigen::RowVectorXd R_; // grain inner radius array
Eigen::RowVectorXd m_; // mass flow rate array
Eigen::RowVectorXd p_e_; // exit pressure array
Eigen::RowVectorXd u_e_; // exit velocity array
Eigen::RowVectorXd Thrust_; // exit velocity array
double A_e_; // exit cross section area
double A_t_; // throat cross section area
double MinThickness_; // casing minimum thickness
double CharacteristicVelocity_; // characteristic velocity ( c* )
double p_max_; // maximum pressure
double TotalImpulse_; // total impulse
// constructor
OdEngine(double A_throat_, double A_exit_, double Dt_, std::string datfile_,double SafetyFactor_)
:A_e_(A_exit_), A_t_(A_throat_)
{
//function to solve the system of the 2 ode, to find the functions p_c = p_c(t), R = R(t)
CombustionPhase(Dt_);
DecompressionPhase(Dt_);
WrightChamberPressureToFile(datfile_);
//function to calculate the characteristic velocity (c*)
CharacteristicVelocity_ = CharacteristicVelocity(Dt_);
//maximum chamber pressure
p_max_ = p_c_.maxCoeff();
// function to calculate the minimum thickness of the casing taking as input the safety factor
MinThickness_ = MinThickness(SafetyFactor_);
}
OdEngine() = default;
OdEngine(const OdEngine &other) = default;
~OdEngine() = default;
// function to calculate the chamber temperature taking as input the time moment
// the temperature is assumed to increase exponentially reaching the theoretical combustion chamber at time moment, t = tc (tc is defined by the user in the Coef.hpp header file)
// for t >= tc, the temperature remains constant
double T(double time){
if (time<tc)
{
return (273.15+20)*exp(log(KNDX_PROPELLANT[CombustionTemperature]/(273.15+20))*time/tc);
}
if(time>=tc){
return KNDX_PROPELLANT[CombustionTemperature];
}
}
// function to calculate the total burning area taking as input the grain inner radius, r
double BurningArea(double r){
double l = GRAIN[Length] - BurningCaseCoef*(2*r - GRAIN[InnerDiametre]);
return GRAIN[NumberOfGrains]*(
2*pi*r*l
+ 2*(pi*pow(GRAIN[OutDiametre],2)/4 - pi*r*r));
}
// function to calculate the density of the gas inside the chamber, using the perfect gas law and taking as inputs the time moment, time and the pressure
double density_0(double p_0, double time){
return p_0/(KNDX_PROPELLANT[GasConstant] * T(time));
}
// function to calculate the empty volume inside the chamber taking as input the grain inner radius, r
double EmptyVolume(double r){
double l = GRAIN[Length] - BurningCaseCoef*(2*r - GRAIN[InnerDiametre]);
return 0.25*pi*pow(GRAIN[OutDiametre], 2)*LengthOfInsulator
-GRAIN[NumberOfGaps]*0.25*pi*pow(GRAIN[OutDiametre], 2)*GRAIN[Gap]
-GRAIN[NumberOfGrains]*pi*(0.25*pow(GRAIN[OutDiametre], 2) - r*r)*l;
}
// gamma constant of the exhaust gasses
double gamma = KNDX_PROPELLANT[SpecificHeatRatio];
// function to calculate the value of the mathematical function F(M,ratio) = MachNumberFromAreaMachNumberRelation(M,ratio) - ratio, as it is defined in the relation 4.9
double F(double M, double RATIO){
return (1/M)*pow((2/(gamma+1))*(1+((gamma-1)/2)*M*M),(gamma+1)/(2*(gamma-1)))-RATIO;
}
// derivative of function F with respect of the Mach number, M
double dF(double M){
double a1 = pow(2,1+(gamma+1)/(2*(gamma-1)));
double a2 = pow((0.5*(gamma-1)*M*M+1)/(gamma+1),(gamma+1)/(2*(gamma-1)));
double a3 = M*M*((gamma-1)*M*M+2);
return a1*(M*M-1)*a2/a3;
}
// area mach number relation, solved for the mach number using newton-raphson method, NozzleMassFlowRateew = M_old - F(M_old)/[dF/dM(M_old)]
// CASE = sup or sub
double MachNumberFromAreaMachNumberRelation(int CASE){
double ratio = A_e_/A_t_;
double gamma = KNDX_PROPELLANT[SpecificHeatRatio];
double err = 1;
double M_0;
switch (CASE)
{
case sub:
M_0 = 0.1; // initialize M for the subsonic case
while(fabs(err)>1e-3){
err = -F(M_0,ratio)/dF(M_0);
M_0 -= F(M_0,ratio)/dF(M_0);;
}
return M_0;
break;
case sup:
M_0 = 2; // initialize M for the supersonic case
while(fabs(err)>1e-3){
err = -F(M_0,ratio)/dF(M_0);
M_0 -= F(M_0,ratio)/dF(M_0);;
}
return M_0;
break;
default:
break;
}
}
//
// the system of the 2 odes is written in the form dp/dt = f1(r, p, t), dr/dt = f2(r, p, t)
double NozzleMassFlowRate(double p_0, double time){
double p_a = 1e5;
double M_e = sqrt((2/(gamma-1))*(pow(p_0/p_a, (gamma-1)/gamma) - 1));
if (M_e < MachNumberFromAreaMachNumberRelation(sub))
{
return p_0 * A_e_ * sqrt(2*gamma/(gamma-1) * (1/KNDX_PROPELLANT[GasConstant]*T(time)) * pow(p_a/p_0, 2/gamma) * (1 - pow(p_a/p_0, (gamma-1)/gamma)));
}
else{
return p_0 * A_t_ * sqrt(gamma/(KNDX_PROPELLANT[GasConstant] * T(time))) * pow(2/(gamma+1) , (gamma+1)/(2*(gamma-1)));
}
}
// function to calculate the value of f1
double f1(double r, double p_0, double time){
return (KNDX_PROPELLANT[GasConstant]*T(time)/EmptyVolume(r))
*(BurningArea(r)*KNDX_PROPELLANT[BurnRateCoef]*pow(p_0, KNDX_PROPELLANT[BurnRateExponent])
*(KNDX_PROPELLANT[Density] - density_0(p_0,time))
-NozzleMassFlowRate(p_0,time));
}
// function to calculate the value of f2
double f2(double r, double p_0, double time){
return KNDX_PROPELLANT[BurnRateCoef] * pow(p_0 , KNDX_PROPELLANT[BurnRateExponent]);
}
// RUNGE KUTTA 4 ORDER K FUNCTIONS
double k1_f1(double r, double p_0, double dt, double time){
return dt*f1(r,p_0,time);
}
double k1_f2(double r, double p_0, double dt, double time){
return dt*f2(r,p_0,time);
}
double k2_f1(double r, double p_0, double dt, double time){
return dt*f1(r + k1_f2(r,p_0,dt,time)/2, p_0 + k1_f1(r,p_0,dt,time)/2, time + dt/2);
}
double k2_f2(double r, double p_0, double dt, double time){
return dt*f2(r + k1_f2(r,p_0,dt,time)/2, p_0 + k1_f1(r,p_0,dt,time)/2, time + dt/2);
}
double k3_f1(double r, double p_0, double dt, double time){
return dt*f1(r + k2_f2(r,p_0,dt,time)/2, p_0 + k2_f1(r,p_0,dt,time)/2, time + dt/2);
}
double k3_f2(double r, double p_0, double dt, double time){
return dt*f2(r + k2_f2(r,p_0,dt,time)/2, p_0 + k2_f1(r,p_0,dt,time)/2, time + dt/2);
}
double k4_f1(double r, double p_0, double dt, double time){
return dt*f1(r + k3_f2(r,p_0,dt,time), p_0 + k3_f1(r,p_0,dt,time), time + dt);
}
double k4_f2(double r, double p_0, double dt, double time){
return dt*f2(r + k3_f2(r,p_0,dt,time), p_0 + k3_f1(r,p_0,dt,time), time + dt);
}
void CombustionPhase(double Dt){
time_.conservativeResize(1);
time_(0) = 0;
R_.conservativeResize(1);
R_(0) = GRAIN[InnerDiametre]/2;
p_c_.conservativeResize(1);
p_c_(0) = AmbientPressure;
int SIZE;
while (R_(R_.size()-1) < GRAIN[OutDiametre]/2)
{
SIZE = time_.size();
double new_p = p_c_(SIZE-1) + (k1_f1(R_(SIZE-1),p_c_(SIZE-1),Dt,time_(SIZE-1)) + 2*k2_f1(R_(SIZE-1),p_c_(SIZE-1),Dt,time_(SIZE-1))+ 2*k3_f1(R_(SIZE-1),p_c_(SIZE-1),Dt,time_(SIZE-1)) + k4_f1(R_(SIZE-1),p_c_(SIZE-1),Dt,time_(SIZE-1)))/6;
double new_r = R_(SIZE-1) + (k1_f2(R_(SIZE-1),p_c_(SIZE-1),Dt,time_(SIZE-1)) + 2*k2_f2(R_(SIZE-1),p_c_(SIZE-1),Dt,time_(SIZE-1)) + 2*k3_f2(R_(SIZE-1),p_c_(SIZE-1),Dt,time_(SIZE-1)) + k4_f2(R_(SIZE-1),p_c_(SIZE-1),Dt,time_(SIZE-1)))/6;
//update the sizes of the arrays
time_.conservativeResize(SIZE + 1);
R_.conservativeResize(SIZE + 1);
p_c_.conservativeResize(SIZE + 1);
// add the latest values in the new memory slot
R_(SIZE) = (new_r);
p_c_(SIZE) = (new_p);
time_(SIZE) = (time_(SIZE-1) + Dt);
// if statement to exit the loop if the rate of burning is extremely low
if(time_(SIZE) > 10){
break;
}
}
}
double f(double t, double p){
return - NozzleMassFlowRate( p, t)*KNDX_PROPELLANT[GasConstant]*T(t)/EmptyVolume(GRAIN[OutDiametre]/2);
}
void DecompressionPhase(double Dt){
double p_a = 1e5;
double k1,k2,k3,k4;
int SIZE;
while (p_c_(p_c_.size() - 1) > AmbientPressure)
{
SIZE = time_.size();
k1 = Dt*f(time_(SIZE-1),p_c_(SIZE-1));
k2 = Dt*f(time_(SIZE-1) + Dt/2, p_c_(SIZE-1) + k1/2);
k3 = Dt*f(time_(SIZE-1) + Dt/2, p_c_(SIZE-1) + k2/2);
k4 = Dt*f(time_(SIZE-1) + Dt, p_c_(SIZE-1) + k3);
//update the sizes of the arrays
time_.conservativeResize(SIZE + 1);
p_c_.conservativeResize(SIZE + 1);
// add the latest values in the new memory slot
p_c_(SIZE) = (p_c_(SIZE-1) + (k1 + 2*k2 + 2*k3 + k4)/6);
time_(SIZE) = (time_(SIZE-1) + Dt);
// if statement to exit the loop if the rate of burning is extremely low
if(time_(SIZE) > 10){
break;
}
}
}
void WrightChamberPressureToFile(std::string datfile){
std::ofstream Results;
Results.open(datfile);
if (Results.is_open())
{
Results<<"# time pressure"<<"\n";
for(int i = 0; i < time_.size()-1; ++i){
Results<<time_(i)<<" "<<p_c_(i)/1e5<<"\n";
}
Results.close();
}
}
double MinThickness(double SafetyFactor){
return 1e3*SafetyFactor*p_max_*GRAIN[OutDiametre]/(2*Sy); //mm
}
double CharacteristicVelocity(double Dt){
double Mp = GRAIN[NumberOfGrains]*(pi*GRAIN[OutDiametre]*GRAIN[OutDiametre]/4 - pi*GRAIN[InnerDiametre]*GRAIN[InnerDiametre]/4)*GRAIN[Length]*KNDX_PROPELLANT[Density];
double I = 0;
for (int i = 0; i < time_.size()-2; i++)
{
I += Dt*(p_c_(i+1) + p_c_(i))/2;
}
return I*A_t_/Mp;
}
void ExitConditions(){
p_e_.resize(time_.size());
u_e_.resize(time_.size());
Thrust_.resize(time_.size());
m_.resize(time_.size());
int k = 0;
int g = 1;
//std::cout<<"time case p_e_NSE p_c p_e_sup\n";
for (int i = 0; i < time_.size(); i++, k++)
{
double M_e_sup = MachNumberFromAreaMachNumberRelation(sup);
double p_e_sup = PressureFromMachNumber_Isentropic(p_c_(i),M_e_sup);
double p_e_NSE = p_e_sup*(
1
+ (2*gamma/(gamma+1)
*(M_e_sup*M_e_sup - 1))
);
// if (k%g == 0)
// {
// std::cout<<time_(i)<<" ";
// }
// supersonic isentropic case
if (AmbientPressure < p_e_NSE)
{
p_e_(i) = p_e_sup;
u_e_(i) = VelocityFromExitPressure_Isentropic(p_c_(i), p_e_(i), T(time_(i)));
// if (k%g == 0){
// std::cout<<"supersonic isentropic "<<p_e_NSE/1e5<<" "<<p_c_(i)/1e5<<" "<<p_e_sup/1e5<<"\n";
// }
}
else{
double M_e_sub = MachNumberFromAreaMachNumberRelation(sub);
double p_e_sub = PressureFromMachNumber_Isentropic(p_c_(i),M_e_sub);
//subsonic isentropic case
if (AmbientPressure > p_e_sub)
{
p_e_(i) = AmbientPressure;
u_e_(i) = VelocityFromExitPressure_Isentropic(p_c_(i), p_e_(i),T(time_(i)));
// if (k%g == 0){
// std::cout<<"subsonic isentropic "<<p_e_NSE/1e5<<" "<<p_c_(i)/1e5<<" "<<p_e_sup/1e5<<" "<<p_e_sub/1e5<<"\n";
// }
}
// subsonic normal shock case
else{
double lamda = AmbientPressure*A_e/(p_c_(i)*A_t);
double M_e = sqrt(-1/(gamma-1) + sqrt(pow(gamma-1, -2) + (2/(gamma-1))*pow(2/(gamma+1), (gamma+1)/(gamma-1))*pow(lamda,-2)));
double p_0 = pow(1 + 0.5*(gamma-1)*M_e*M_e, gamma/(gamma-1))*AmbientPressure;
p_e_(i) = AmbientPressure;
u_e_(i) = VelocityFromExitPressure_Isentropic(p_0, p_e_(i),T(time_(i)));
// if (k%g == 0){
// std::cout<<"subsonic non-isentropic "<<p_e_NSE/1e5<<" "<<p_c_(i)/1e5<<" "<<p_e_sup/1e5<<" "<<p_e_sub/1e5<<"\n";
// }
}
}
m_(i) = NozzleMassFlowRate(p_c_(i),time_(i));
Thrust_(i) = m_(i)*u_e_(i) + (p_e_(i) - AmbientPressure)*A_e_;
}
TotalImpulse_ = TotalImpulse();
}
double TotalImpulse(){
double I_t = 0;
double dt = time_(1) - time_(0);
for (int i = 0; i < Thrust_.size() - 2; i++)
{
I_t += dt*(Thrust_(i) + Thrust_(i+1))/2;
}
return I_t;
}
void WriteExitPressureToFile(std::string datfile){
std::ofstream Results;
Results.open(datfile);
if (Results.is_open())
{
Results<<"# time pressure"<<"\n";
for(int i = 0; i < time_.size()-1; ++i){
Results<<time_(i)<<" "<<p_e_(i)/1e5<<"\n";
}
Results.close();
}
}
void WriteMassFlowRateToFile(std::string datfile){
std::ofstream Results;
Results.open(datfile);
if (Results.is_open())
{
Results<<"# time mass flow rate"<<"\n";
for(int i = 0; i < time_.size()-1; ++i){
Results<<time_(i)<<" "<<m_(i)<<"\n";
}
Results.close();
}
}
void WriteExitVelocityToFile(std::string datfile){
std::ofstream Results;
Results.open(datfile);
if (Results.is_open())
{
Results<<"# time velocity"<<"\n";
for(int i = 0; i < time_.size()-1; ++i){
Results<<time_(i)<<" "<<u_e_(i)<<"\n";
}
Results.close();
}
}
void WriteThrustToFile(std::string datfile){
std::ofstream Results;
Results.open(datfile);
if (Results.is_open())
{
Results<<"# time thrust"<<"\n";
for(int i = 0; i < time_.size()-1; ++i){
Results<<time_(i)<<" "<<Thrust_(i)<<"\n";
}
Results.close();
}
}
double PressureFromMachNumber_Isentropic(double pc, double M){
double returnPressure =
pc
*pow(
1 + 0.5*(gamma-1)*M*M,
gamma/(1-gamma)
);
return returnPressure;
}
double VelocityFromExitPressure_Isentropic(double pc, double pe, double Tc){
double returnVelocity =
sqrt((2*gamma/(gamma-1))*KNDX_PROPELLANT[GasConstant]*Tc*(1 - pow(pe/pc, (gamma-1)/gamma)));
return returnVelocity;
}
};