Design Diesel Cycle

IDEAL DIESEL CYCLE SIMULATOR 

AIM:

• Simulation of an ideal diesel cycle based on end-user driven data
• Obtain Efficiency, Torque and net work output from the simulated diesel cycle.
• Understand the influence of Compression Ratio, Cut-off Ratio and Stroke-Length on Efficiency. 

INTRODUCTION:

Diesel cycle is a Thermodynamic air-standard cycle  for Compression-Ignition Reciprocating Engines invented by Rudolph Diesel . The ideal air-standard diesel engine undergoes 4 distinct processes. Two of the four processes of the cycle are adiabatic reversible processes. In this cycle the heat is transferred to the working fluid at constant pressure. Fuel is ignited by heat generated during the compression of air in the combustion chamber, into which fuel is injected.

P-V Diagram

Looking Up the Procces flow:

Process 1-2 : Isentropic Compression (Reversible adiabatic Process)

• The air inside the cylinder is compressed isentropically from a volume V1 to V2.
• Work is done by the piston on air inside the cylinder, which means an external work has to be done by the engine to accomplish the compression.

Process 2-3 : Isobaric Heat Addition ( Constant Pressure Heat addition)

• With the pressure being constant, fuel is added externally until volume V3 is reached.
• In this process , heat is added into the system which helps in combustion of  the air-fuel mixture.

Process 3-4 : Isentropic Expansion (Reversible adiabatic Process)

• The air-fuel mixture inside the cylinder expands from V3 to V4 due to rapid combustion . This expansion is accounted by downward motion on the piston.
• Here work is done by the gases on the piston, thus powering the engine by pushing the piston down.
• In this process, a net work output is produced by the engine

Process 4-1 : Isochoric Heat Rejection ( Constant Volume Heat rejection)

• With the volume being constant, heat is removed until pressure decrease P1.
• Heat is removed from the system, by flushing out the combustion gases.

Programming Language Used : MATLAB

Desired Output:  i)   P-V Diagram - Ideal Diesel Cycle respect to end-user data .

                         ii)  Torque and Net Work output from the cycle.

                         iii) Thermal Efficiency of the designed cycle.

                         iv) Mean Effective Pressure of the designed cycle.

                         v)  Effect of Compression Ratio and Cut-Off Ratio on Efficiency of the cycle.

                        vi)  Efficiency variation of the cycle influenced by the Stroke-Length of cylinder.

Formulas And Assumptions:

Assumptions:       i) Length of connecting rod to Stroke length ratio - 1.75:1

                          ii) Specific heat of air at constant volume, C_v = 0.718 kJ/kg.K   

                         iii) Compression factor accepted for simulation: 14 to 23    

Constant Values:  i) Universal Gas constant ,      R = 0.287 kJ/kg.K

                          ii) Molecular weight of diesel , M = 180

                         iii) No. of crankshaft rotation in a cycle = 2 ( 4 stroke cycle)

Formula:             i) Compression Ratio,  CR = V₁/V₂

                         ii) Cut-off Ratio,             α = V₃/V₂

                         iii) Ratio of specific heat ,k = C_p/C_v

                         iv) Thermal Efficiency ,η _diesel: 

                       v) Net Work Done = η _diesel / Heat Added

                      vi) Heat Added (Q_a) = mass*C_p*∆T

                      vii) mass = P*V*M/ R*T ( P*V = n*R*T)

                     viii) Mean Effective Pressure (MEP) = Net Work done / Displacement Volume

                      ix) For adiabatic process, $\mathrm{PVk\; =}$ = constant

                      x)  Torque = (MEP* Displacement Volume)/(2*π*No. of crankshaft rotation in a cycle) 

MATLAB CODING:

% DESIGN YOUR IDEAL DIESEL CYCLE
clear all
close all
clc

disp('-------------------------------------------')
disp('        DESIGN YOUR DIESEL CYCLE           ')
disp('-------------------------------------------')
disp('   ENTER ENGINE PARAMETERS AND PRESS OK    ')
disp('-------------------------------------------')

%EXTRACTING THE ENGINE PARAMETERS
pause(2);
inputeng = inputdlg({'Cylinder Bore Diameter (mm)','Cylinder Stroke Length (mm)','No. of Cylinder(s)'},'ENGINE PARAMETERS',[1 50; 1 50; 1 50]);

%Checking for missing input
for i = 1:3
    if (isempty(inputeng{i}))
    err = msgbox('AN EMPTY PARAMETER INPUT FOUND. Please Retry','ERROR','error');    
    clc
    return
    end
end

D = str2num(inputeng{1});
L_s = str2num(inputeng{2});
n = str2num(inputeng{3});
nr = 2; % 4-Stroke cycle

%calculating CC of engine
cc1 = ((pi/4)*(D^2)*(L_s)*n)/(1000);
cc2 = ceil(cc1);
cc = 100*(ceil(cc2/100));
clc
if(cc == 0)
   b = msgbox('Engine Parameters Not Acceptable. Kindly Retry','ERROR','error');
   return
end
clc

disp('-------------------------------------------')
disp('          NOTE: 1 bar = 100000 Pa          ')
disp('          NOTE: 1 atm = 101325 Pa          ')
disp('          NOTE: 1 Deg. Celsius = 273K      ')
disp('-------------------------------------------')
disp(' Compression ratio - Ratio between the start and end volume for the compression phase(Process 1-2)[V1 / V2]') 
disp(' Cut off ratio     - Ratio between the end and start volume for the combustion phase(Process 2-3) [V3 / V2]')
disp('-------------------------------------------')
disp('       ENTER PARAMETERS AND PRESS OK       ')
pause(2)

%Accepting Initial Parameters of the cycle
inputcnd = inputdlg({'Atmospheric  Pressure (bar)  :','Initial temperature (Celsius) :','Compression ratio :','Cut Off Ratio :'},'INITIAL PARAMETERS',[1 50; 1 50; 1 50; 1 50]);

%checking for missing input conditions
for j = 1:4
    if (isempty(inputcnd{j}))
    Err = msgbox('AN EMPTY INPUT FIELD FOUND. Please Retry','ERROR','error');    
    return
    end
end

p1 = str2num(inputcnd{1});
if(p1 == 0)
   perr = msgbox('Initial Pressure Not Acceptable. Kindly Retry','ERROR','error');
   return
end
pD1 = p1*100000;
    
t1 = str2num(inputcnd{2});
if(t1 == 0)
   terr = msgbox('Initial Temperature Not Acceptable. Kindly Retry','ERROR','error');
   return
end
tD1 = t1 + 273; %conversion to kelvin
cr = str2num(inputcnd{3});
a = str2num(inputcnd{4});
r = 0.287;
cv = 0.718;
cp = cv + r;
gamma = cp/cv;
clc

%checking for Compression ratio values.
if(cr < 14)
   e = msgbox('Very Low Compression Ratio.Try with values >= 14','ERROR','error');
   return
else if(cr > 23)
      f = msgbox('High Compression Ratio. Try for values <= 23','ERROR','error');
      return
    end
end

%checking for cut-off ratio value
if(a == 0)
   j = msgbox('Minimum value for Cut off Ratio cannot be 0','ERROR','error');
   return
end
clc

%swept volume
v_s = (pi/4)*(D^2/(1000*1000))*(L_s/1000);
%clearance volume
v_c = v_s/(cr-1);

%Finding the variable at different states
% STATE 1
vD1 = v_s+v_c;

%STATE 2
vD2 = (v_c);
%Since pv^gamma = Constant (adiabatic reversible process)
pD2 = pD1*(cr^gamma);
%Since p1v1/t1 = p2v2/t2
tD2 = tD1*(cr^(gamma-1));

%For compression curve from state 1 to state 2
CMP_volD =linspace(vD1,vD2,100);
CMP_presD = (((vD1./CMP_volD).^gamma)*pD1);

%STATE 3
vD3 = a*vD2;
%since p3v3/t3 = p2v2/t2
pD3 = pD2;
tD3 = a*tD2;

%STATE 4
vD4 = vD1;
%Since pv^gamma = Constant (adiabatic reversible process)
pD4 = pD3*((vD3/vD4)^gamma);
%p3v3/t3 = p4v4/t4
tD4 = (pD4*vD4*tD3)/(pD3*vD3);

txty = (pD4+pD2)/2;
txtx = (vD1+vD3)/3;

% for expansion curve fromstate 3 to state 4
EXP_volD =linspace(vD3,vD4,100);
EXP_presD = (((vD3./EXP_volD).^gamma)*pD3);

%Thermal Efficiency
T_EFD = 1-((1/(cr^(gamma-1)))*(((a^gamma)-1)/(gamma*(a-1))));
Tpercent = T_EFD*100;

%Finding the NET WORK OUTPUT
R = 287.1;
mass = pD1*vD1*180/(R*tD1);
Qa = mass*cp*(tD3-tD2)*1000;
Qr = mass*cv*(tD4 - tD1)*1000;
Wnet = Qa*T_EFD/1000; % kJ

%Finding Mean Effective Pressure and Torque
MEP = Wnet/(vD1 - vD2)/100000; %bar
Torque = (MEP*100000*v_s)/2*pi*nr; %Nm
x = cc; 
y = Tpercent; 
z = cr;
work = Wnet;

%Displaying the output
OUTPUT = msgbox({['MEAN EFFECTIVE PRESSURE (bar) = ',num2str(MEP)],['THERMAL EFFICIENCY (%) = ',num2str(y)],['Net WORK DONE (kJ) = ',num2str(work)],['TORQUE (Nm) =', num2str(Torque)],['COMPRESSION RATIO = ',num2str(z)],['DESIGN CC  = ',num2str(x)],['Click OK to Continue']},'RESULT','help');
disp(' To View P-V Diagram , Press OK  ');
uiwait(OUTPUT);
clc
cd('E:\')
%Saving output as table(.xlsx)
fnameip1 = inputdlg({'Enter filename for Output Report(Spreadsheet)'},'SAVE AS',[1 50]);
str1 = string(fnameip1);
str2 = '.xlsx';
file = append(str1,str2);

restable = table({'Design CC';'Thermal Efficiency (%)';'Net Work Done (kJ)';'Mean Effective Pressure (bar)';'Torque (Nm)'},[cc;Tpercent;Wnet;MEP;Torque],'Variablenames',{'PARAMETERS','VALUE'});
writetable(restable,file,'Sheet',1,'Range','A1:B6')
clc

%Plotting the Cycle Pressure - Volume Curve
m = 1;
figure(m)
hold on
grid on
title('DIESEL CYCLE (ideal)')
hold on
plot(CMP_volD,CMP_presD,'--','color','r','linewidth',3)
hold on
plot([vD2 vD3],[pD2 pD3],'color','k','linewidth',2)
hold on
plot(EXP_volD,EXP_presD,'--','color','b','linewidth',3)
hold on
plot([vD4 vD1],[pD4 pD1],'color','k','linewidth',2)
xlabel('VOLUME (m^3)    >>>>','color','b')
ylabel('PRESSURE (Pa)    >>>>','color','b')
text(txtx,txty,'Enclosed Area gives Net work output')
fill([CMP_volD EXP_volD],[CMP_presD EXP_presD],[0.7 0.7 0.7])
legend('Adiabatic Compression','Constant Pressure Heat Addition','Adiabatic Expansion','Constant Volume Heat Rejection')

%Creating push button to save the plot.
Control1 = uicontrol('String','Save Plot','Callback','uiresume(figure(m))');
uiwait(figure(m))

%Saving the PV Plot
fnameip2 = inputdlg({'Enter filename for PV Plot'},'SAVE AS',[1 50]);
str3 = string(fnameip2);
saveas(figure(m),str3,'jpg')

%Plotting variation of efficiency wrt Compression and Cut-off Ratios
%Case 1 - Keeping Cut-Off Ratio Constant
gamma1 = 1.4;
a1 = a;
cr1 = linspace(14,23,10);
M = 1;
figure(M)
for i1 = 1:10
    T_EFDa(i1) = 1-((1/(cr1(i1)^(gamma1-1)))*(((a1^gamma1)-1)/(gamma1*(a1-1))));
    Tpercenta = T_EFDa*100;
    i1 = i1+1;
end
subplot(2,1,1)
plot(cr1,Tpercenta,'-*','color','g','linewidth',2.5)
grid on
axis([13 24 55 70])
xlabel('Compression ratio')
ylabel('Thermal Efficiency (%)')
title('Thermal Efficiency Vs Compression Ratio');


%Case 2 - Keeping Compression Ratio Constant
cr2 = cr; 
cutratio = a+5;
a2 = linspace(1,cutratio,10);
for j1 = 1:10
    T_EFDb(j1) = 1-((1/(cr2^(gamma1-1)))*(((a2(j1).^gamma1)-1)/(gamma1*(a2(j1)-1))));
    Tpercentb = T_EFDb*100;
    j1 = j1+1;
end
subplot(2,1,2)
plot(a2,Tpercentb,'-*','color','r','linewidth',2)
axis([1 11 20 70])
grid on
xlabel('Cut-off ratio')
ylabel('Thermal Efficiency (%)')
title('Thermal Efficiency Vs Cut-off Ratio');

hold off

%Creating push button to save the graph
Control2 = uicontrol('String','Save Plot','Callback','uiresume(figure(M))');
uiwait(figure(M))
%Saving the PV Plot
fnameip3 = inputdlg({'Enter filename for Efficiency Variation'},'SAVE AS',[1 50]);
str4 = string(fnameip3);
saveas(figure(M),str4,'jpg')

close all 
%Stroke Vs Efficiency
diameter = D;
length = L_s+50;
strokelength = linspace(1,length,100);
cutoffratio = a;

sv = (pi/4)*(diameter^2/(1000*1000))*(strokelength./1000);
cv = (pi/4)*(diameter^2/(1000*1000))*(((0.005.*strokelength)+0.5)./1000);

volume1 = sv+cv;
volume2 = cv;
compr = volume1./volume2;

eta = 1-((1./(compr.^(gamma-1)))*(((cutoffratio^gamma)-1)/(gamma*(cutoffratio-1))));
eff = eta.*100;

q = 1;
figure(q)

plot(strokelength,eff,'color','r','linewidth',2)
grid on
xlabel('StrokeLength (mm)');
ylabel('Efficiency (%)');
title('Efficiency Vs Stroke Length')
stra = num2str(D);
strb = '@ fixed bore diameter(mm) =  ';
strout = append(strb,stra);
text(20,50,strout)
%Creating push button to save the comparison
Control9 = uicontrol('String','Save Plot','Callback','uiresume(figure(q))');
uiwait(figure(q))
%Saving the PV Plot
fnameip9 = inputdlg({'Enter filename for Efficiency Variation'},'SAVE AS',[1 50]);
str9 = string(fnameip9);
saveas(figure(q),str9,'jpg')

cd('E:\')
close all
clc

disp('Files are Saved in New Volume (E:)')
pause(2)
final = msgbox('Simulation Finished Successfully, THANKYOU','SUCCESS');

close all 
clc

Brief Of Code:

1. Initially, the Engine parameters are obtained from the user defined values and the engine Cubic Capacity is calculated.
2. Then the Initial Parameters of the cycle (Atmospheric Pressure, Initial Temperature, Compression and Cut-off Ratio) is obtained again from the user defined values.
3. From the  values, all the Process variable [Pressure(P) , Volume(V), Temperature(T)]from state 1 - 4 is calculated.
4. Finally, the desired output parameters are calculated from respective formulas and is displayed through a Result Dialog box.
5. The P-V plot for the cycle, Efficiency variation plots and output result table reference to the input values are displayed and saved automatically with user defined filenames.

Understanding the Code:

• Line   6-10: Introduction and instruction to the user are displayed.
• Line      14: Accepting engine parameters from the user through input dialog box (inputdlg)
• Line 17-22: Empty field input in the parameters are checked and an error message is displayed (msgbox).
• Line 24-26: Input strings from inputdlg are converted into numbers (str2num) and Engine CC is calculated
• Line 36-40: If calculated CC is 0, error message is displayed(msgbox).
• Line 42-50: Displaying information for further simulation and instruction to user.
• Line      54: Accepting initial diesel cycle conditions from the user (inputdlg).
• Line  56-67:Field input in the parameters are checked and an error message is displayed if pressure or temperature value is zero (msgbox).
• Line 77-82: Empty field input in the initial conditions are checked and an error message is displayed (msgbox)
• Line 87-94: Value of compression ratio is checked to be within 14 to 23. If value is not within the limits, error is displayed.
• Line 97-100: Value of cut-off ratio entered is checked and if found zero, an error message is displayed.
• Line 103-106: Clearance volume and Swept volume is calculated from the engine parameters.
• Line 110-163: Diesel cycle state variables from state 1 to 4, thermal efficiency, Net work done , Mean effective pressure is calculated.
• Line 164-168: Desired output values from the calculations are displayed through dialog box (msgbox) and program waits for user action for further execution (uiwait)
• Line 170-178: The results obtained are made to save as an excel file (writetable) and filename is accepted from user (inputdlg)
• Line 180-198: The P-V diagram for the diesel cycle is plotted (plot) with the area inside plot depicting work done is shaded (fill())
• Line 200-207: A click button is introduced to the figure inorder to save the figure to the defined directory with user defined filename(uicontrol()).
• Line 210-243: Calculation and Plot for variation of efficiency with cut-off ratio and compression ratio is obtained.
• Line 245-251: A click button is introduced to the figure inorder to save the figure to the defined directory with user defined filename(uicontrol()).
• Line 257-270: Calculation of variation of efficiency with varrying stroke length.
• Line 272-282: Plotting the variation of efficiency vs Stroke length graph.
• Line 284-289: Creating a push button in the plot inorder to save the plot with user defined filename(uicontrol()).
• Line 295-297: Creating a dialog box to display end of simulation (msgbox())

Code Highlights:

• All the input value from the end-user is obtained through input dialog boxes (inputdlg()).
• All the obtained input values are once checked before calculations are started and any insufficiency or disproportions in data values are detected and an error message is displayed(msgbox()).
• Calculated output values are stored and saved to a file in defined directory(writetable()).
• Area in the plot representing the output from the simulation is highlighted (fill()).
• Appropriate pauses and wait time is provided for further executions of the program (pause() & uiwait()).
• Push buttons provided to save plots to the defined directory (uicontrol()).

SIMULATION PROCESS FLOW:

• Input Stage 1 : ENGINE PARAMETERS:

Input For Illustration:

• Cylinder Bore Diameter - 78mm
• Cylinder Stroke Length - 80mm
• No. of cylinders - 4 nos.

• Input Stage 2: INITIAL CONDITIONS

 Inputs for illustration:

• Atmospheric Pressure - 1.25 bar
• Initial Temperature - 30 Deg. Celsius
• Compression Ratio - 14
• Cut-Off Ratio - 1.5

RESULT:

• RESULT WINDOW

• OUTPUT PLOT - P-V DIAGRAM

• OUTPUT PLOT - Efficiency Variation wrt Compression & Cut-off Ratio

• OUTPUT PLOT - Efficiency Variation wrt Stroke-Length

• OUTPUT DATA FILE:

CONCLUSION:

An ideal diesel cycle simulation is performed through the input from the end-user with the help of MATLAB . The Pressure - Volume plot and the calculations of the desired output values are obtained.

From the simulation:

• For illustration, the ideal diesel cycle of  a 1600cc engine is simulated capable of doing 28.8kJ of work producing 90Nm Torque at around 62% of thermal efficiency.

From the efficiency variation study: 

• Efficiency Vs Compression Ratio: Efficiency is directly proportional to the compression ratio as efficiency increases with an increasing Compression ratio.
• Efficiency Vs Cut-off Ratio : Efficiency is having an inverse proportional relation with Cut-off ratio as Efficiency tends to decrease with an increased Cut-off Ratio.
• Efficiency Vs Stroke-Length : Efficiency increases gradually with stroke-Length. A longer Stroke - Bore ratio is found to produce higher efficiencies.

Hence  Low Cut-off ratio (α) and High compression ratio (k) along with a Longer Bore-Stroke ratio is desired for increased thermal efficiency.

FUTURE SCOPE:

• Modification to obtain T-S Diagram.
• Comparative analysis with a real world system.

Simulation Glances & Report:

Follow the link (ppt) to have a glance through simulation and input error tracing process:

https://drive.google.com/open?id=1Nvnqxuhq0Raxo0kDcJW2prXXHAgDcfdR

REFERENCE:

• https://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter3c.html
• https://en.wikipedia.org/wiki/Diesel_cycle
• https://in.mathworks.com/help
• http://www.qrg.northwestern.edu/thermo/design-library/diesel/diesel.html
• https://www.nuclear-power.net/nuclear-engineering/thermodynamics/thermodynamic-cycles