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  1. Home/
  2. Amit Chilap/
  3. Air Standard Cycle

Air Standard Cycle

1.AIM: Write a program that can solve an OTTO-Cycle and to make a plot of Pressure VS Volume during the Otto-cycle and also to calculate the thermal efficiency of the OTTO-Cycle. 2.GOVERNING EQUATIONS IF ANY:    3.OBJECTIVES OF THE PROJECT: To solve the Otto-Cycle.  Plot the P-V graph of the cycle. Calculate…

    • Amit Chilap

      updated on 15 Feb 2021

    1.AIM:

    • Write a program that can solve an OTTO-Cycle and to make a plot of Pressure VS Volume during the Otto-cycle and also to calculate the thermal efficiency of the OTTO-Cycle.


    2.GOVERNING EQUATIONS IF ANY: 

     

    3.OBJECTIVES OF THE PROJECT:

    • To solve the Otto-Cycle. 
    • Plot the P-V graph of the cycle.
    • Calculate the efficiency of the Otto-Cycle.

     

    • The workflow of the project. 
      • Collect the given data.
      • Calculate the swept volume and clearance volume from the given data using formulas 1&2.
      • Using Vs & Vc calculate the volume conditions at each stage i.e. V1, V2, V3, V4 by using formulas 3&4.
      • Using formula 5 calculate the pressure at each stage i.e. P1, P2, P3, P4.
      • Using formula 6 calculate the pressure at each stage i.e. T1, T2, T3, T4.
      • Since from stage 2-3 & stage 4-1 volume remains constant, so it gets a straight line on the P-V graph
      • As stage 1-2 & stage 3-4 are adiabatic compression & adiabatic expansion its volume changes continuously. And its volume is calculated using form 7.
      • Now using formula 8, the pressure is calculated for stage 1-2 i.e. adiabatic compression, and also for stage 3-4 i.e. adiabatic expansion.
      • Now the process of stage 1-2 and stage 3-4 can plot on a P-V graph.
      • And finally using formula 9 the efficiency of the given Otto-Cycle is calculated.

     

    4.BODY OF THE CONTENT:

     

    • Matlab Programming language is used.
    • Main Program is attached below. 
    • %Write code that can solve an otto cycle and make plots for it.
      %Here are the requirements
          %Your code should create a PV diagram
          %You should output the thermal efficiency of the engine.
      
      %Given Data.
      % P1=0.1MPa, T1=35 Degree Celcius, T3= 1100 Degree Celcius
      % Bore=12cm, Stroke=10cm, Connecting Rod=15cm, Compression Ratio=9, Gamma=1.4
          
      close all
      clear all
      clc
      
      %Given Data/Conditions 
      p1=0.1; %in MegaPascals %Pressure at Stage 1.
      t1=308; %in kelvin %Temperature at Stage 1.
      t3=1373; %in kelvin %Temperature at Stage 3.
      bore = 0.12; %in m 
      stroke = 0.1; %in m
      con_rod = 0.15; %in m
      cr = 9;
      gamma=1.4;
      
      %calculatig v1,v2,v3,v4
      v_swept = (pi/4)*bore^2*stroke; %in m^3 %Swept Volume by piston.
      v_clearance = v_swept/(cr-1); %in m^3 %&Clearance Volume.
      
      v1 = v_swept + v_clearance; %in m^3 %Volume at Stage 1.
      v2 = v_clearance; %in m^3 %Volume at Stage 2.
      v3=v2; %in m^3 %Volume at Stage 3.
      v4=v1; %in m^3 %Volume at Stage 4.
      
      %Calculating State Variables at 2
      %p1v1^gamma=p2v2^gamma
      p2=p1*(v1/v2)^gamma; %in MPa %Pressure at Stage 2.
      
      %p1v1/t1=p2v2/t2
      t2=(p2*v2)/(p1*v1)*t1; %in kelvin %Temperature at Stage 2.
      
      %Supplementary programs: Function(engine_kinematics) is created in the MatLab to calculate the instantaneous Volume.
      %and by calling the function volume change is calculated from stage 1-2.
      V_com=engine_kinematics(bore,stroke,con_rod,cr,180,0); %in m^3 %Volume change from stage 1-2.
      P_com=p1*v1^gamma./V_com.^gamma; %in MPa %Pressure change from stage 1-2.
      
      %Calculating State Variables at 3
      %p3v3/t3=p2v2/t2
      p3 =p2*v2/t2*t3/v3; %in MPa %Pressure at Stage 3.
      
      
      %Calculating State Variables at 4
      %p1v1^gamma=p2v2^gamma
      p4=p3*(v3/v4)^gamma; %in MPa %Pressure at Stage 4.
      
      %p3v3/t3=p4v4/t4
      t4=(p4*v4)/(p3*v3)*t3; %in kelvin %Temperature at Stage 4.
      
      %Supplementary programs: Function(engine_kinematics) is created in the MatLab to calculate the instantaneous Volume.
      %and by calling the function volume change is calculated from stage 3-4.
      V_exp=engine_kinematics(bore,stroke,con_rod,cr,0,180); %in m^3 %Volume change from stage 3-4.
      P_exp=p3*v3^gamma./V_exp.^gamma; %in MPa %Pressure change from stage 3-4.
      
      %efficiency=1-1/(cr)^(gamma-1)
      efficiency=1-1/(cr)^(gamma-1); %Efficiency Of the Air-Standard_Cycle.
      
      %Displaying the Conditions of Pressure, Volume and Temperature at each stage.
      disp('Conditions at State 1')
      disp(['P1=' num2str(p1) ' MPa ; V1=' num2str(v1) ' m^3 ; T1=' num2str(t1) ' k'])
      disp(' ')
      disp('Conditions at State 2')
      disp(['P2=' num2str(p2) ' MPa ; V2=' num2str(v2) ' m^3 ; T2=' num2str(t2) ' k'])
      disp(' ')
      disp('Conditions at State 3')
      disp(['P3=' num2str(p3) ' MPa ; V3=' num2str(v3) ' m^3 ; T3=' num2str(t3) ' k'])
      disp(' ')
      disp('Conditions at State 4')
      disp(['P4=' num2str(p4) ' MPa ; V4=' num2str(v4) ' m^3 ; T4=' num2str(t4) ' k'])
      disp(' ')
      disp(['Efficiency=' num2str(efficiency*100) '%'])
      
      %Ploting the Otto-Cycle.
      figure(1)
      hold on 
      plot(v1,p1,'*','color','r')%Ploting the Conditions of Pressure and Volume stage 1.
      plot(v2,p2,'*','color','r')%Ploting the Conditions of Pressure and Volume stage 2.
      plot(v3,p3,'*','color','r')%Ploting the Conditions of Pressure and Volume stage 3.
      plot(v4,p4,'*','color','r')%Ploting the Conditions of Pressure and Volume stage 4.
      plot(V_com,P_com,'linewidth',3,'color','r') %Ploting the Process change of Pressure and Volume from stage 1-2.
      plot([v2,v3],[p2,p3],'linewidth',3,'color','g') %Ploting the Process change of Pressure and Volume from stage 2-3.
      plot(V_exp,P_exp,'linewidth',3,'color','r') %Ploting the Process change of Pressure and Volume from stage 3-4.
      plot([v4,v1],[p4,p1],'linewidth',3,'color','g') %Ploting the Process change of Pressure and Volume from stage 4-1.
      xlabel('Volume in m^3') %Labeling the X-Axis.
      ylabel('Pressure in MPa') %Labeling the Y-Axis.
    • Supplementary Program to calculate Instantaneous Volume
    • %Supplementary programs:Function(engine_kinematics) is to calculate the instantaneous Volume.
      
      function [V] = engine_kinematics(bore,stroke,con_rod,cr,crank_start,crank_end)
      
      a=stroke/2; %Crank-Pin Radius.
      R=con_rod/a; 
      
      v_s=(pi/4)*bore^2*stroke; %Swept Volume.
      v_c= v_s/(cr-1); %Clearance Volume.
      
      theta=linspace(crank_start,crank_end,100); %Range and no. of outputs to be calculated.
      
      %Formula to calculate instantaneous Volume during movement of the piston.
      % V/v_c=1+(cr-1)./2.*(1+R-cosd(theta)-(R^2-sind(theta).^2).^0.5)
      V=v_c.*(1+(cr-1)./2.*(1+R-cosd(theta)-(R^2-sind(theta).^2).^0.5));
      
      end 
    • Results

     

    5.CONCLUSION:

    • Output Results of the Air-Standard-Cycle Program

     

    • Graph Of Otto-Cycle.

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