Aperiodic Aero-foil Kinematics

     This post is about a 2D NACA 0012 aero-foil undergoing forced aperiodic heaving. Heaving motion is achieved by the plot shown in Fig. 1. Plot within Fig. 1 represents position of airfoil at various time steps.

Fig. 1, The position of aero-foil

     The animation of the vorticity contours are shown in Fig. 2. The velocity, pressure and vorticity for aperiodic heaving is shown in Fig. 3. A comparison will be made with heaving later, if ever 😀. As far as aerodynamic forces are concerned, per-cycle C_{l, avg} is at 0.63 as compared to 0.0 for periodic heaving. C_{d, avg} aperiodic heaving is at 0.162 as compared to 0.085 for periodic heaving. Of course, this is done on a coarse mesh. If ever I write a paper about this... 😀

Fig. 2, Top Row, Aperiodic, periodic heaving airfoil 

     

Fig. 3, Top Row, L-R, Vorticity, pressure. Bottom Row, Velocity 

     If you want to collaborate on the research projects related to turbomachinery, aerodynamics, renewable energy, please reach out. Thank you very much for reading. 

Flapping Aerofoil For Propulsion

     This post is about a 2D NACA 0012 aerofoil undergoing forced flapping motion for propulsion purposes. Heaving motion is achieved by applying a vertical velocity on the aerofoil based on the Eqn. 1. Similarly the pitching motion is achieved by applying a rotational velocity, governed by Eqn. 2.

v_y = 2*π*f_h*H_o*sin(2*π*f_h*t)                                              Eqn. 1

ω = -2*π*f_h*ϑ*sin[(2*π*f_h*t) + 1.5708]                               Eqn. 2

     w.r.t. Eqn. 1-2 reduced frequency is defined as (2*π*f_h*H_o/U∞)), f_h is the frequency of oscillations, while ω, t and ϑ_o represent rotational velocity, instantaneous time and maximum pitching angle. H_o is the heaving amplitude and U∞ is the free stream velocity.

     The flapping motion is achieved by a combination of the heaving and pitching. In this particular simulation, the aerofoil is in the propulsion mode, meaning the feathering parameter χ is less in magnitude than 1.0. Feathering parameter is defined by Eqn. 3.

χ = ϑ/arctan(h0*2*π*f_h/U∞)                                  Eqn. 3

     The boundary conditions employed for the simulation are at Re 1,000, K = 1.41, H_o = aerofoil chord length, χ = 0.5489 and f_h = 0.003391 Hz. The animation of the pressure, vorticity and velocity contours is shown in Fig. 1.

Fig. 1, Flow animation, fluid flow direction is from left to right.

     The results of present simulation are compared with [1]. In terms of maximum lift, a maximum deviation of 5% is observed as compared to [1], as shown in Fig. 2. The maximum lift coefficient for available data is ~4.224 while the maximum lift coefficient from the present simulation is ~4.057. The average thrust produced is within 2% of [1]. Average thrust coefficient per cycle from [1] is 0.9957 while the result from present simulation reveals the thrust coefficient to be 1.0098.

Fig. 2, A comparison of coefficient of lift.

If you want to collaborate on the research projects related to turbo-machinery, aerodynamics, renewable energy, please reach out. Thank you very much for reading.

References

[1] https://doi.org/10.1017/jfm.2017.508

Formation Flight Computational Fluid Dynamics

     This is a post about computational fluid dynamics analysis of formation flight.

     The results from an analysis of three unmanned combat aerial vehicles (UCAVs) flying in a V-type formation are presented. The chosen UCAV configuration, shown in Figs. 1-2 and available for download here, is named SACCON (Stability And Control Configuration) UCAV. This configuration is used because of the availability of the geometric and aerodynamic data, used in the validation and verification of the numerical analysis. The SACCON UCAV is designed by NATO's (North Atlantic Treaty Organization) RTO (Research and Technology Group) under Applied Vehicle Task Group (AVT-161) to assess the performance of military aircrafts.

Fig. 1, SACCON UCAV

Fig. 2, Technical drawing for the SACCON UCAV

     The simulation is performed using commercially available computational fluid dynamics code.  The details about the solver and the discretization schemes are presented next. The simulation is performed using SIMPLE-R solver for pressure-velocity coupling. The diffusive terms of the Navier-Stokes equations are discretized using central differentiating scheme while the convective terms are discretized using the upwind scheme of second order. The κ-ε turbulence model with damping functions is implemented to model turbulence. The simulation predicts three-dimensional steady–state flow over UCAVs.

     The Reynolds and Mach number of flow are set at 1e6 and 0.15, respectively. The two trailing UCAVs are placed 3 wingspans behind the leading UCAV. The trailing UCAVs are a wingspan apart. The V-type configuration is chosen because it is the most common observation in birds (author's observation). The V-type formation is shown in Fig. 3. All three UCAVs are at 5° angle-of-attack.

Fig. 3, The V-type formation (top view)

     The boundaries of the computational domain are located at a distance equivalent to 10 times the distance between the nose of the leading UCAV and the tail of the trailing UCAV. The mesh is made of 821,315 cells. Mesh controls are used to refine the mesh in the areas of interest i.e. on the surfaces of the UCAVs and in the wake of all three UCAVs. A cartesian mesh with immersed boundary method is used for the present study. The computational domain with mesh is shown in Fig. 4 while a closeup of the mesh is shown in Fig. 5.

Fig. 4, The computational domain and mesh

Fig. 5, Closeup of mesh, notice the refined wakes of the UCAVs

     For validation and verification, the lift and drag forces from the present study are compared with studies [1-2]. The results are in close agreement with [1,2] As a result of flying in a formation, an improvement in the lift-to-drag ratio of 10.05% is noted. The lift-to-drag ratio of the trailing UCAVs is at 11.825 in comparison with a lift-to-drag ratio of a single UCAV, i.e. 10.745. The lift coefficient is increased by 7.43% while the drag coefficient decreased by 2.174%. The reason(s) to why the efficiency increases will be looked upon later, if ever the author has the time and will power ☺.

     The results from post processing of the simulations are presented in Figs. 6-7. The pressure iso-surfaces colored by velocity magnitude are shown in Fig. 6. While the velocity iso-surfaces colored by pressure magnitude are shown in Fig. 7.

Fig. 6, Flight direction towards the reader

Fig. 7, Flight direction away from the reader

     Thank you very much for reading. If you would like to collaborate on research projects, please reach out.

[1] https://doi.org/10.2514/1.C031386

[2] https://doi.org/10.1155/2017/4217217

High Camber Wing CFD Simulation

     This post is about the numerical simulation of a high camber, large aspect ratio wing. The wing had an aspect ratio of 5:1. The Reynolds number of flow was 500,000. The wing was at an angle of attack of zero degree. The aero-foil employed had a cross section of NACA 9410.

     The software employed was Flow Simulation Premium. A Cartesian mesh was created using the immersed boundary method. The mesh had 581,005 cells. Among those 581,005 cells, 55,882 were at the solid-fluid boundary. A time step of ~0.00528167 s was employed*. The domain was large enough to accurately trace the flow around the wing without any numerical or reversed flow errors. The software employs κ-ε turbulence model with damping functions, SIMPLE-R (modified) as the numerical algorithm and second order upwind and central approximations as the spatial discretization schemes for the convective fluxes and diffusive terms. The time derivatives are approximated with an implicit first-order Euler scheme.

     The mesh is shown in Fig. 1. The four layers of different mesh density are also visible in Fig. 1, the mesh is refined near the wing surface using a mesh control. The velocity around the wing section is shown in Fig. 2, using a cut plot at  the center of the wing. In Fig. 2, the wing body is super imposed by pressure plot. The velocity vectors showing the direction of flow are superimposed on both the wing body and the velocity cut plot.

Fig. 1, The computational domain.

Fig. 2, The velocity and pressure plots.

     The results of the simulation was validated against the results from XFLR5 software. XFLR5 predicted slightly higher lift and slightly less drag on the wing for same boundary conditions because the XFLR5 simulations were inviscid.

     Thank you for reading. If you would like to contribute to the research, both financially and scientifically, please feel free to reach out.

     *Time step is averaged because of the fact that a smaller time step was employed at the start of the numerical simulation.

Computational Fluid Dynamics Analysis of a Symmetrical Wing, Update 01

     This post is about the computational fluid dynamics analysis of a wing. The wing analyzed employed the NACA 0021 section throughout. The wing had a span of 4 m and a chord length of 1 m. The Reynolds number was kept at 3,000,000. The software employed was SolidWorks Flow Simulation Premium.

     The mesh had a total of 385,064 cells of which 84,826 cells were in contact with the wing surface, as shown in Fig. 1. The results are, indeed, mesh independent. Mesh controls were employed to refine the mesh near the wing surface. The computational domain employed was of cylindrical shape.

 

Fig. 1, The computational mesh around the wing.

 

     The velocity variation at various angles of attack around the wing cross-section is shown in Fig. 3 while the pressure variation on the wing surface is shown in Fig. 4. The results were validated against experiments conducted by [1].

 

Fig. 2, Velocity variation around the wing at 0-25 degree AOA, 5 degree increments.

 

Fig. 3, Pressure variation at the wing surface at 0-25 degree AOA, 5 degree increments.

     The purpose of this blog is maintain my online portfolio. I did this analysis because I realized I haven't written anything of this nature before. All of my previous simulations and/or blog entries were from the propulsion, renewable energy and turbo-machinery areas.
 

     Update 01

     CAD files are available here.

 

    
     Thank you for reading. If you would like to collaborate on research projects, please feel free to contact.

     [1] Fernando A. Rocha, Adson A. de Paula, Marcos d. Sousa, André V. Cavalieri, and Vitor G. Kleine, "Lift enhancement by wavy leading edges at Reynolds numbers between 700,000 and 3,000,000," Proceedings of the 2018 Applied Aerodynamics Conference, AIAA AVIATION Forum, Atlanta, GA, 2018.

     https://doi.org/10.2514/6.2018-3816

11x7 Aeronautic Propeller Characteristics (Using CFD) (Verified and Validated) (Update 02)

     This post presents the results from an aeronautic propeller CFD analysis.

    
     An 11x7 propeller was modelled using SolidWorks CAD package using the geometry from [1]. The simulations were run at two different rotational velocities and each rotational velocity was simulated at three advance ratios. The mesh for the 3,000 RPM rotational velocity had 213,205 total cells among which 24,048 cells were at the solid fluid boundary. While, the mesh for the 5,000 RPM rotational velocity had 369,963 total cells among which 68,594 cells were at the solid fluid boundary. A mesh control was employed to refine the mesh near the propeller geometry and at the boundary of the rotating region and the stationery domain for all of the cases simulated. This was done to ensure accuracy of the results was within an acceptable range. The results of the numerical simulations are plotted along with the experimental results [1] in Fig. 1.

Fig. 1 J= Advance Ratio, η_prop = propeller efficiency

     It can be seen from Fig. 1 that the trends for the propeller efficiency are in agreement with the experimental results. To increase the mesh density for the mesh independence test, the number of cells in  each of the respective co-ordinate directions was increased by a factor of 1.1. The mesh is shown in the Fig. 2.

Fig. 2 The computational mesh around the propeller.

     The computational domain size was at 2D x 2D x 2.4D, D being the propeller diameter, as shown in Fig. 3. In Fig. 3, the curved teal arrow represents the direction of rotation of the sliding mesh. The blue arrow represents the direction of free stream velocity while the brown arrow represents the force of gravity.

 Fig. 3 The computational domain.

Fig. 4 The pressure distribution and the velocity vectors around the propeller.

     The CAD model files and the simulation setup files for the numerical analysis are available here.

     Thank you for reading. If you'd like to collaborate on research projects, please reach out.

[1] Brandt, J. B., & Selig, M. S., “Propeller Performance Data at Low Reynolds Numbers,” 49th AIAA Aerospace Sciences Meeting, AIAA Paper 2011-1255, Orlando, FL, 2011.

doi.org/10.2514/6.2011-1255

 

Update 01

     Results from the mesh independent study are now available.

Update 02

     CAD model files are now uploaded. The CFD simulation setup files are also included.

11x4.7 Aeronautic Propeller Characteristics (Using CFD) (Verified and Validated) (Update 02)

     This post presents the results from an aeronautic propeller CFD analysis.

     An 11x4.7 propeller was modelled using SolidWorks CAD package using the geometry from [1]. The simulations were run at two different rotational velocities and each rotational velocity was simulated at three advance ratios. The mesh for the 3,000 RPM rotational velocity had 206,184 total cells among which 22,103 cells were at the solid fluid boundary. While, the mesh for the 6,000 RPM rotational velocity had 357,300 total cells among which 64,012 cells were at the solid fluid boundary. A mesh control was employed to refine the mesh near the propeller geometry and at the boundary of the rotating region and the stationery domain for all of the cases simulated. This was done to ensure accuracy of the results was within an acceptable range. The results of the numerical simulations are plotted along with the experimental results [1] in Fig. 1.

Fig. 1 J= Advance Ratio, η_prop = propeller efficiency

 

     It can be seen from Fig. 1 that the trends for the propeller efficiency are in agreement with the experimental results. The fine mesh had the number of cells in each of the respective co-ordinate directions increased by a factor of 1.1. The mesh is shown in the Fig. 2.

 

Fig. 2 The computational mesh around the propeller.

 

     The computational domain size was at 2D x 2D x 2.4D, D being the propeller diameter, as shown in Fig. 3. In Fig. 3, the curved teal arrow represents the direction of rotation of the sliding mesh. The blue arrow represents the direction of free stream velocity while the brown arrow represents the force of gravity.

Fig. 3 The computational domain.

Fig. 4 The pressure distribution and the velocity vectors around the propeller.

     The CAD model and numerical simulation setup files are available here.

 

     Thank you for reading. If you'd like to collaborate on research projects, please reach out.

     [1] Brandt, J. B., & Selig, M. S., “Propeller Performance Data at Low Reynolds Numbers,” 49th AIAA Aerospace Sciences Meeting, AIAA Paper 2011-1255, Orlando, FL, 2011.

doi.org/10.2514/6.2011-1255

 

Update 01

     Mesh independent test results are now available.

 

Update 02

     CAD files for the propeller including the CFD analysis setup are now available.

Marine Propeller Characteristics (Using CFD) (Verified and Validated)

     This post presents the results from a marine propeller CFD analysis. The key thing about this CFD analysis was that the propeller efficiency obtained was within 7% of the experimental results, by using only 112,081 total cells in the computational mesh, of these cells, 21,915 cells were at the solid fluid boundary. The results are, indeed, mesh independent. The software employed was Flow Simulation Premium. The results of the numerical simulations are plotted along with the experimental results in Fig. 1.

Fig. 1 K_T = coefficient of thrust, 10K_Q = coefficient of torque multiplied by a factor of 10, η_prop = propeller efficiency

 

     It can be seen from Fig. 1 that the trends for the thrust and the torque coefficients and the propeller efficiency are in agreement with the experimental results. The experimental data was taken from here. The flow conditions were following. The propeller diameter was at 0.254 m. Propeller rotational velocity was at 15 rev/s. The propeller inclination angle was at 12°. Fluid considered was water. To change the advance ratio, fluid flow velocity was altered. The computational domain size was at 2D x 2D x 3.2D, D being the propeller diameter, as shown in Fig. 3. The mesh is shown in the Fig. 2.

Fig. 2 The computational mesh around the propeller.

 

Fig. 3 The computational domain.

 

     In Fig. 3, the curved teal arrow represents the direction of rotation of the sliding mesh. The blue arrow represents the direction of free stream velocity while the brown arrow represents the force of gravity. The Pressure distribution on the propeller blades and the velocity streamlines are shown in Fig. 4. The streamlines were drawn using line integral convolution, relative to the rotating frame of reference.

 

Fig. 4 The pressure distribution and the velocity profile around the propeller.

 

     If you'd like to collaborate on research projects, please reach out. Thank you for reading.

Parametric Cycle Analysis of an Ideal Ramjet Engine

Extract from my rejected thesis from my university days. Optimization of Thrust Per Unit Mass Flow of a Jet Engines by Optimizing the Overall Compression Ratio, to design Multi-diameter Inlets, because an inlet works best for a set specific of conditions. Hope it helps you in your scholarly work.

Ramjet engine

A ramjet engine is the simplest of all aircraft engines. It consists of an inlet or a diffuser, a combustor and a nozzle. Air is fed into the diffuser, it increases the static pressure and temperature of air by slowing it down. Then the air is fed into the combustor, where it is mixed with fuel and is ignited, resulting in increased energy. This corresponds to an increased temperature. The combustion occurs at a constant pressure for sub sonic flows. The nozzle then expand the gas to ambient pressure, with a decrease in temperature. This process results in increased in KE for gas.

Formulations

The formulations for the cycle analysis are as follows.

General Gas Constant, R=((g-1)/ g)*C_p

Velocity of Sound, a_o=(1000*g*R*T_o).^(1/2)
Total to Static Temperature Ratio, t_r=1+(((g-1)/2)*(M_o.^2))
Burner Exit Enthalpy to Ambient Enthalpy Ratio, t_l=T_t4/T_o
Velocity Ratio, v₉/a_o=M_o*((t_l/t_r).^(1/2))
Thrust per Air Flow, F/m_o=a_o*((v₉/a_o)-M_o)
Fuel Air Ratio, f=((C_p*T_o)/h_PR)*( t_l-t_r)
Thrust Specific Fuel Consumption, S=f/(F/m_o)
Thermal Efficiency, h_T=1-(1/t_r)
Propulsive Efficiency, h_P=2/(((t_l/t_r).^(1/2))+1)
Overall Efficiency h_O=h_T*h_P
Total to Static Temperature Ratio for Maximum Thrust per Air Flow, t_{r (maxFmo)}=t _l.^(1/3)
Mach Number of Flight for Maximum Thrust per Air Flow , M_{o (maxFmo)}=((2/(g-1))*( t_{r (maxFmo)}-1)).^(1/2)
Temperature at Station T_to (after Compression), T_to=t_r*T_o
Nozzle Exhaust Temperature, T₉=T_o*(t_l/t_r)

Calculations

By using these equations, and by entering the following inputs:

For Mach Number of Flight= 1

T_o= 216.7 K, g= 1.4, C_p= 1.004 KJ/(Kg.K), T_t4= 1,600 K, M_o= 1, h_PR= 42,800 KJ/Kg

We get the Following Results:

Station Temperatures for T-S Diagram

Ambient Temperature, Station T₀, 216.7 K
Temperature after Compression, Station T_to and T_t2, 260.04 K
Temperature at Nozzle Entry, Station T_t4, 1,600 K
Temperature at Nozzle Exit, Station T₉, 1,333.33 K

T-S Diagram generated from MATLAB

Results Based on the Data Entered

General Gas Constant= 0.286857 KJ/(Kg.K)

Velocity of Sound= 295.003 m/s

Total to Static Temperature Ratio= 1.2

Burner Exit Temperature to Ambient Temperature Ratio= 7.38348

Gas Exit Velocity to Velocity of Sound Ratio= 2.4805

Thrust per Unit Airflow= 436.753 N/(Kg/s)

Fuel to Air Ratio= 0.0314327

Thrust Specific Fuel Consumption= 71.9691 (mg/s)/N

Thermal Efficiency= 16.6667 %

Propulsive Efficiency= 57.4629 %

Overall Efficiency= 9.57716 %

For Optimum Mach Number of Flight

Total to Static Temperature Ratio for Maximum Thrust per Air Flow= 1.94724
Optimum Mach Number of Flight for Maximum Thrust per Air Flow= 2.17629

For all the same values as above, except T_t4= 1,900 K, we get these results:

Station Temperatures for T-S Diagram

Ambient Temperature, Station T_o, 216.7 K
Temperature after Compression, Station T_t0 and T_t2, 260.04 K
Temperature at Nozzle Entry, Station T_t4, 1,900 K
Temperature at Nozzle Exit, Station T₉, 1,583.33 K

T-S Diagram from MATLAB

Results Based on the Data Entered
General Gas Constant= 0.286857 KJ/(Kg.K)
Velocity of Sound= 295.003 m/s
Total to Static Temperature Ratio= 1.2
Burner Exit Temperature to Ambient Temperature Ratio= 8.76788
Gas Exit Velocity to Velocity of Sound Ratio= 2.70307
Thrust per Unit Airflow= 502.41 N/(Kg/s)
Fuel to Air Ratio= 0.0384701
Thrust Specific Fuel Consumption= 76.5712 (mg/s)/N
Thermal Efficiency= 16.6667 %
Propulsive Efficiency= 54.0093 %
Overall Efficiency= 9.00155 %

For Optimum Mach Number of Flight

Total to Static Temperature Ratio for Maximum Thrust per Air Flow= 2.06205
Optimum Mach Number of Flight for Maximum Thrust per Air Flow= 2.30439

For all the same values as above, except T_t4= 2,200 K, we get these results:

Station Temperatures for T-S Diagram

Ambient Temperature, Station T_o, 216.7 K
Temperature after Compression, Station T_t0 and T_t2, 260.04 K
Temperature at Nozzle Entry, Station T_t4, 2,200 K
Temperature at Nozzle Exit, Station T₉, 1,833.33 K

T-S Diagram from MATLAB

Results Based on the Data Entered


General Gas Constant= 0.286857 KJ/(Kg.K)
Velocity of Sound= 295.003 m/s
Total to Static Temperature Ratio= 1.2
Burner Exit Temperature to Ambient Temperature Ratio= 10.1523
Gas Exit Velocity to Velocity of Sound Ratio= 2.90865
Thrust per Unit Airflow= 563.057 N/(Kg/s)
Fuel to Air Ratio= 0.0455075
Thrust Specific Fuel Consumption= 80.8222 (mg/s)/N
Thermal Efficiency= 16.6667 %
Propulsive Efficiency= 51.1686 %
Overall Efficiency= 8.5281 %

For Optimum Mach Number of Flight

Total to Static Temperature Ratio for Maximum Thrust per Air Flow= 2.16532
Optimum Mach Number of Flight for Maximum Thrust per Air Flow= 2.41383

For Mach Number of Flight= 2

By using these equations, and by entering the following inputs:

T_o= 216.7 K, g= 1.4, C_p= 1.004 KJ/(Kg.K), T_t4= 1,600 K, M_o= 2, h_PR= 42,800 KJ/Kg

Station Temperatures for T-S Diagram

Ambient Temperature, Station T_o, 216.7 K
Temperature after Compression, Station T_t0 and T_t2, 390.06 K
Temperature at Nozzle Entry, Station T_t4, 1600 K
Temperature at Nozzle Exit, Station T₉, 888.889 K

T-S Diagram from MATLAB

Results Based on the Data Entered

General Gas Constant= 0.286857 KJ/(Kg.K)
Velocity of Sound= 295.003 m/s
Total to Static Temperature Ratio= 1.8
Burner Exit Temperature to Ambient Temperature Ratio= 7.38348
Gas Exit Velocity to Velocity of Sound Ratio= 4.05065
Thrust per Unit Airflow= 604.947 N/(Kg/s)
Fuel to Air Ratio= 0.0283827
Thrust Specific Fuel Consumption= 46.9177 (mg/s)/N
Thermal Efficiency= 44.4444 %
Propulsive Efficiency= 66.1086 %
Overall Efficiency= 29.3816 %

For Optimum Mach Number of Flight

Total to Static Temperature Ratio for Maximum Thrust per Air Flow= 1.94724
Optimum Mach Number of Flight for Maximum Thrust per Air Flow= 2.17629


For all the same values as above, except T_t4= 1,900 K, we get these results:

Station Temperatures for T-S Diagram

Ambient Temperature, Station T_o, 216.7 K
Temperature after Compression, Station T_t0 and T_t2, 390.06 K
Temperature at Nozzle Entry, Station T_t4, 1900 K
Temperature at Nozzle Exit, Station T₉, 1055.56 K

T-S Diagram from MATLAB

Results Based on the Data Entered

General Gas Constant= 0.286857 KJ/(Kg.K)
Velocity of Sound= 295.003 m/s
Total to Static Temperature Ratio= 1.8
Burner Exit Temperature to Ambient Temperature Ratio= 8.76788
Gas Exit Velocity to Velocity of Sound Ratio= 4.41409
Thrust per Unit Airflow= 712.163 N/(Kg/s)
Fuel to Air Ratio= 0.0354201
Thrust Specific Fuel Consumption= 49.7359 (mg/s)/N
Thermal Efficiency= 44.4444 %
Propulsive Efficiency= 62.3627 %
Overall Efficiency= 27.7168 %

For Optimum Mach Number of Flight

Total to Static Temperature Ratio for Maximum Thrust per Air Flow= 2.06205
Optimum Mach Number of Flight for Maximum Thrust per Air Flow= 2.30439

For all the same values as above, except T_t4= 2,200 K, we get these results:

Station Temperatures for T-S Diagram

Ambient Temperature, Station T_o, 216.7 K
Temperature after Compression, Station T_t0 and T_t2, 390.06 K
Temperature at Nozzle Entry, Station T_t4, 2200 K
Temperature at Nozzle Exit, Station T₉, 1222.22 K

T-S Diagram from MATLAB

Results Based on the Data Entered

General Gas Constant= 0.286857 KJ/(Kg.K)
Velocity of Sound= 295.003 m/s
Total to Static Temperature Ratio= 1.8
Burner Exit Temperature to Ambient Temperature Ratio= 10.1523
Gas Exit Velocity to Velocity of Sound Ratio= 4.7498
Thrust per Unit Airflow= 811.2 N/(Kg/s)
Fuel to Air Ratio= 0.0424575
Thrust Specific Fuel Consumption= 52.3391 (mg/s)/N
Thermal Efficiency= 44.4444 %
Propulsive Efficiency= 59.261 %
Overall Efficiency= 26.3382 %

For Optimum Mach Number of Flight

Total to Static Temperature Ratio for Maximum Thrust per Air Flow= 2.16532
Optimum Mach Number of Flight for Maximum Thrust per Air Flow= 2.41383

Conclusions

By looking at the results, we find the following results.

1.       The performance of any ramjet engine relies heavily on the stagnation temperature increase across the burner.
2.       To have efficient compression of the air, the ramjet requires high flight speeds.
3.       For ramjets, the static thrust is zero, they must be moving to develop thrust.

T-s diagrams available here, some how not showing here.
http://3dimensionaldesigningandmanufacturing.blogspot.com/2014/09/t-s-diagrams-for-parametric-cycle.html