public void ODEImplicitRungeKutta5Jacobian()
{
//VAN DER POL'S EQUATION
//In this example the OdeImplicitRungeKutta5 class is used to solve the van der Pol equation:
//y''-mu*(1-y^2)*y'+y=0
//If y0=y and y1=y' then:
//y'0 = y1, y0(0)= 2
//y'1 = ((1 - y0 ^2) * y1 - y0)/rpar, y1(0)=-0.66
//using DotNumerics.ODE
OdeFunction YDot = new OdeFunction(VPol);
OdeJacobian Jac = new OdeJacobian(JacVPol);
OdeImplicitRungeKutta5 rungeKutta = new OdeImplicitRungeKutta5(YDot, Jac, 2);
double[,] sol;
double[] y0 = new double[2];
y0[0] = 2.0E0;
y0[1] = -0.66E0;
double x0 = 0;
double xf = 2;
sol = rungeKutta.Solve(y0, x0, 0.2, xf);
for (int i = 0; i < sol.GetLength(0); i++)
{
ObjectDumper.Write("X = " + sol[i, 0].ToString() + " Y1 = " + sol[i, 1].ToString() + " Y2 = " + sol[i, 2].ToString());
}
//private double[] VPol(double T, double[] Y)
//{
// double[] ydot = new double[2];
// double rpar = 1.0E-6;
// ydot[0] = Y[1];
// ydot[1] = ((1 - Math.Pow(Y[0], 2)) * Y[1] - Y[0]) / rpar;
// return ydot;
//}
//public double[,] JacVPol(double T, double[] Y)
//{
// double[,] jacobian = new double[2, 2];
// double rpar = 1.0E-6;
// jacobian[0, 0] = 0.0E0;
// jacobian[0, 1] = 1.0E0;
// jacobian[1, 0] = (-2.0E0 * Y[0] * Y[1] - 1.0E0) / rpar;
// jacobian[1, 1] = (1.0E0 - Math.Pow(Y[0], 2)) / rpar;
// return jacobian;
//}
}
private void button_Run_Click(object sender, EventArgs e)
{
/***************** Defining initial conditions **************/
d_p_i = Convert.ToDouble(textBox_d_p_i.Text) * Math.Pow(10, -6); // Initial droplet diameter [m]:
T_d_i = Convert.ToDouble(textBox_T_d_i.Text); // Initial temperature of the droplet [K]:
T_inf_i = Convert.ToDouble(textBox_T_inf_i.Text); // Initial temperature of the surrounding air [K]:
phi_inf_i = Convert.ToDouble(textBox_phi_inf_i.Text); // Initial relative humidity of surrounding air [RH]:
double V_a = Convert.ToDouble(textBox_V_a.Text) * Math.Pow(10, -3); // Volume flow rate of air [m^3/s]:
double V_w = Convert.ToDouble(textBox_V_w.Text) * Math.Pow(10, -6); // Volume flow rate of water [m^3/s]:
double tf = Convert.ToDouble(textBox_tf.Text); // Evaluation time
double delta_t = Convert.ToDouble(textBox_delta_t.Text); // Time step
/***************** Calculation of initial water vapour pressure **************/
// Saturation pressure calculation (2007, P.T. Tsilingiris) [Pa]:
double p_s_i = (0.7073
- 2.7036E-2 * (T_inf_i - 273.15)
+ 4.3609E-3 * Math.Pow(T_inf_i - 273.15, 2)
- 4.6626E-5 * Math.Pow(T_inf_i - 273.15, 3)
+ 1.0347E-6 * Math.Pow(T_inf_i - 273.15, 4)
) * Math.Pow(10, 3);
p_inf_i = phi_inf_i * p_s_i / 100; // Initial water vapour pressure in the surrounding air [Pa]:
/***************ODE Solver*********************/
OdeFunction YDot = new OdeFunction(Equation);
OdeImplicitRungeKutta5 rungeKutta = new OdeImplicitRungeKutta5(YDot, 4);
double[] y0 = new double[4];
y0[0] = d_p_i;
y0[1] = T_d_i;
y0[2] = p_inf_i;
y0[3] = T_inf_i;
double x0 = 0;
double xf = tf;
/**************Solution out********************/
/*************Error handler*********************/
this.label_Error.Text = "Error: no error";
try
{
sol = rungeKutta.Solve(y0, x0, delta_t, xf);
//Solution identifier which is 0 if the droplets do not fully evaporate
droplet_evaporated = 0;
}
catch
{
//Error lable
this.label_Error.Text = "Error: Droplet evaporated";
//Solution identifier which is 1 if the droplets do fully evaporate
droplet_evaporated = 1;
}
if (droplet_evaporated == 0)
{
/***************Printing number of datapoints**********/
solLength = sol.GetLength(0);
string input1 = solLength.ToString();
this.textBox_number_of_data_points.Text = "";
this.textBox_number_of_data_points.Text = input1;
/*********************Converting data*******************/
//Creating arrays to store datapoints
tValues = new double[solLength];
d_pValues = new double[solLength];
t_dValues = new double[solLength];
p_infValues = new double[solLength];
T_infValues = new double[solLength];
//Storing datapoints in arrays
for (int i = 0; i < solLength; i++)
{
tValues[i] = sol[i, 0];
d_pValues[i] = sol[i, 1];
t_dValues[i] = sol[i, 2];
p_infValues[i] = sol[i, 3];
T_infValues[i] = sol[i, 4];
}
//Claculating evaporation percentage
double evaporation = 100
- ((4 / 3 * Math.PI
* Math.Pow((d_pValues[solLength - 1] * Math.Pow(10, 6)) / 2, 3))
/ (4 / 3 * Math.PI
* Math.Pow((d_p_i * Math.Pow(10, 6)) / 2, 3)) * 100);
//Calculating relative humidity
double relativeHumidity = (p_infValues[solLength - 1]
/ (
(0.7073
- 2.7036E-2 * (T_infValues[solLength - 1] - 273.15)
+ 4.3609E-3 * Math.Pow(T_infValues[solLength - 1] - 273.15, 2)
- 4.6626E-5 * Math.Pow(T_infValues[solLength - 1] - 273.15, 3)
+ 1.0347E-6 * Math.Pow(T_infValues[solLength - 1] - 273.15, 4)
) * Math.Pow(10, 3)
)) * 100;
//phi_inf = (Y[2] / p_s) * 100;
// Data with two decimal points
double d_p_end = Math.Truncate(d_pValues[solLength - 1] * Math.Pow(10, 8)) / 100;
double t_d_end = Math.Truncate(t_dValues[solLength - 1] * 100) / 100;
double T_inf_end = Math.Truncate(T_infValues[solLength - 1] * 100) / 100;
double T_inf_diff = Math.Truncate((T_infValues[0] - T_infValues[solLength - 1]) * 100) / 100;
double p_inf_end = Math.Truncate(p_infValues[solLength - 1] * 100) / 100;
double evap_end = Math.Truncate(evaporation * 100) / 100;
double phi_inf_end = Math.Truncate(relativeHumidity * 100) / 100;
// Printing end result
string d_p_end_str = d_p_end.ToString();
string t_d_end_str = t_d_end.ToString();
string T_inf_end_str = T_inf_end.ToString();
string T_inf_diff_str = T_inf_diff.ToString();
string p_inf_end_str = p_inf_end.ToString();
string evap_end_str = evap_end.ToString();
string phi_inf_end_str = phi_inf_end.ToString();
this.textBox_d_p_end.Text = "";
this.textBox_d_p_end.Text = d_p_end_str;
this.textBox_T_d_end.Text = "";
this.textBox_T_d_end.Text = t_d_end_str;
this.textBox_T_inf_end.Text = "";
this.textBox_T_inf_end.Text = T_inf_end_str;
this.textBox_T_inf_diff.Text = "";
this.textBox_T_inf_diff.Text = T_inf_diff_str;
this.textBox_p_inf_end.Text = "";
this.textBox_p_inf_end.Text = p_inf_end_str;
this.textBox_evap_end.Text = "";
this.textBox_evap_end.Text = evap_end_str;
this.textBox_phi_inf_end.Text = "";
this.textBox_phi_inf_end.Text = phi_inf_end_str;
//Converting datapoints to input units
d_pValues_mum = new double[solLength];
multi = 1000000;
for (int i = 0; i < solLength; i++)
{
d_pValues_mum[i] = d_pValues[i] * multi;
}
// Clearing charts
foreach (var series in chart_all.Series)
{
series.Points.Clear();
}
// Populating chart with datapoints
for (int i = 0; i < solLength; i++)
{
chart_all.Series["Droplet diameter"].Points.AddXY(tValues[i], d_pValues_mum[i]);
chart_all.Series["Droplet temperature"].Points.AddXY(tValues[i], t_dValues[i]);
}
// Setting Y-axis values on upper chart
chart_all.ChartAreas[0].AxisY.Maximum = d_pValues_mum[0] + (d_pValues_mum[0] / 10);
chart_all.ChartAreas[0].AxisY.Minimum = d_pValues_mum[solLength - 1] - (d_pValues_mum[solLength - 1] / 10);
// Setting Y-axis values on lower chart
chart_all.ChartAreas[1].AxisY.Maximum = T_inf_i + (T_inf_i / 100);
chart_all.ChartAreas[1].AxisY.Minimum = t_dValues[solLength - 1] - (t_dValues[solLength - 1] / 100);
// Setting axis decimals and lable on upper chart
chart_all.ChartAreas[0].AxisX.LabelStyle.Format = "#.#";
chart_all.ChartAreas[0].AxisY.LabelStyle.Format = "#";
chart_all.ChartAreas[0].AxisX.Title = "Time [s]";
chart_all.ChartAreas[0].AxisY.Title = "Droplet diameter [μm]";
// Setting axis decimals and lable on lower chart
chart_all.ChartAreas[1].AxisX.LabelStyle.Format = "#.#";
chart_all.ChartAreas[1].AxisY.LabelStyle.Format = "#";
chart_all.ChartAreas[1].AxisX.Title = "Time [s]";
chart_all.ChartAreas[1].AxisY.Title = "Droplet temperature [K]";
}
else
{
//Printing N/A in the result boxes
this.textBox_d_p_end.Text = "";
this.textBox_d_p_end.Text = "N/A";
this.textBox_T_d_end.Text = "";
this.textBox_T_d_end.Text = "N/A";
this.textBox_T_inf_end.Text = "";
this.textBox_T_inf_end.Text = "N/A";
this.textBox_p_inf_end.Text = "";
this.textBox_p_inf_end.Text = "N/A";
this.textBox_evap_end.Text = "";
this.textBox_evap_end.Text = "N/A";
this.textBox_phi_inf_end.Text = "";
this.textBox_phi_inf_end.Text = "N/A";
this.textBox_number_of_data_points.Text = "";
this.textBox_number_of_data_points.Text = "N/A";
// Clearing charts
foreach (var series in chart_all.Series)
{
series.Points.Clear();
}
}
}