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Effect of variable shape ramp in ramjet engine diffuser.


The working principle of the ramjet is to decelerate high speed air flow to create high pressure and low speed, then mix and combust fuel, and finally expel hot air with burnt fuel out through the De Laval nozzle. The ramjet engine in this study has a nominal operation point of 3.5 Mach for the inlet, a maximum static temperature of 1800 K, and a maximum static pressure of 2.5 bar. The length is split into three equal sections for the compressor, the combustor, and the nozzle. This study also includes the detailed design of the inlet, its component layout, and its assembly. The purpose of the inlet is to decelerate and compress the incoming supersonic airflow to provide high pressure for the combustor. The combustor also requires the flow to be subsonic so that the fuel can be ignited by a spark and controlled explosion created. The inlet ramp angle is varied in order to maintain a consistent performance and the control of the ramp angle is done manually possible and therefore the total operating speed of the Ram jet engine can be controlled. The air flow is single sided and the airflow is assumed to be two dimensional. The variation of the shape, thickness of ramp manually and the 2D flow is to improve the range of input speeds for the inlet and account for any inconsistencies in the airflow.

Due to the complexity of shock waves and boundary layers interaction, the use of the traditional techniques, like the method of characteristic or streamline tracing, becomes inadequate for preliminary design stage. Computational Fluid dynamics (CFD) has allowed engineers to test new designs quickly before carrying out experiments. Integrating CFD and other computer-aided simulation programs, a system has been developed for the preliminary design of high speed inlets and four bodies. [1] At high supersonic/low hypersonic speeds, several challenges face the inlet designer. The problems of multiple modes of operation and dual flow must be solved. High temperatures must be considered; shock stability is no easily achieved and the effects of three-dimensional flow, including corner flow and sidewall shock boundary layer interaction require complex bleed control systems. Inlet bleed and leakage cause serious performance penalties at the high speed conditions. Drag at off-design conditions is a problem, and weight reduction is a constant concern. [2]

2. Oblique Shock Waves:

As a supersonic engine airplane moves through a free stream with supersonic speed, the air molecules are deflected around the object. When consider compressibility effect on the free stream. The density of the stream varies locally as the free stream is compressed by the supersonic airplane. When supersonic engine airplane moves faster than the speed of sound, and there is an abrupt decrease in the flow area, shock waves are generated in the flow. Oblique Shock waves and normal shocks are very small regions in the gas where the gas properties change by a large amount.



Across a shock wave, the static pressure, temperature, and gas density increases enormously. Here we can see the basic difference between the Mach and shock wave. The oblique shock wave formed over the concave corner of the ramp is shown in fig. 1.

If the envelope of the disturbance created by the supersonic flight. The strong disturbances cleave into an oblique shock wave to the free stream and oblique shock is stronger than the Mach wave (i.e.) fig. 2. Using the continuity equation and the fact that the tangential velocity component does not change across the shock, trigonometric relations eventually lead to the [theta]-[beta]-M equation which shows 9 as a function of M1, [beta], and [gamma], where [gamma] is the Heat capacity ratio.

The following equations are used to calculate the downstream properties of the ram air.

[p.sub.2]/[p.sub.1] = 1 + 2[gamma]/[gamma] + 1 ([M.sup.2.sub.1] [sin.sup.2] [beta] - 1 (1)

[p.sub.2]/[p.sub.1] = ([gamma] + 1 ([M.sup.2.sub.1] [sin.sup.2] [beta]/ ([gamma] - 1 ([M.sup.2.sub.1] [sin.sup.2] [beta] + 2

[T.sub.2]/[T.sub.1] = [p.sub.2]/[p.sub.1] [[rho].sub.1]/[[rho].sub.2] (3)


tan [theta] = 2 cot [beta] [M.sup.2.sub.1] [sin.sub.2] [beta] - 1/ [M.sup.2.sub.1] ([gamma]+ cos2[beta]) + 2 (5)

The above equation is called the [theta]-[beta]-M relation. This relation is vital to an analysis of oblique shocks strength related to the Mach no and Deflection angle of the object.

3. Effect of Ramp Angle Variation on Mach Number:

There are two shock solution for the every Mach no. and deflection angle. Why can't we use both solutions for ramjet application? The changes across the oblique shock wave are severe as p increases, the larger value of P will have the strong shock solution and the smaller value of p will have the weak shock solution. We can clearly say that the strength of the shock depends on both deflection angle and the Mach number of the object. The weak and strong solution of the wedge is shown in fig.3. Weak oblique shock waves produces smaller entropy change. The weak shock produces a small disturbance in the flow behind the shock wave, the next important solution of oblique shock waves are strong oblique shock waves, if normal shock waves created over the wedge, the tremendous changes in the physical quantities in the ahead and behind the shock wave and within the ramjet subsonic diffuser and also heat transfer occur in a non-equilibrium state. The strong solution of oblique shock creates moreover similar to a normal shock wave but physical properties changes slightly less in the strong solution of the oblique shock wave.


Consider a free stream at Mach no. 2 towards the ramp wedge at an angle of 10 deg and 20 deg as shown in fig. 4. The wave angle for the two wedges is 39.2 deg and 53 deg respectively. It shows that the pressure ratio of the flow changes enormously for the maximum wedge angle (i.e) 20 deg for the equal Mach no. in addition to this if we increase the wedge angle, we can attain maximum pressure ratio behind the ramp. It will help to increase the efficiency of the engine as well as increases the velocity of the ramjet.


4. Shock propagation and reflection:

An incident shock created at ramp is impinged on the upper wall of the diffuser inlet and reflected to the ramp. This wave is called reflected shock wave. The strength of the reflected shock wave is weaker than the incident shock. The four types of pseudo-stationary oblique shock-wave reflection patterns. It consists of

(a) Regular reflection (r.r.)

(b) Single Mach reflection (s.M.r),

(e) Complex Mach reflection (c.M.r.) and

(d) Double Mach reflection (d.M.r.).

The type of reflection pattern is a function of the incident shock-wave Mach number M, the wedge angle and the gas equation of state. The transition boundaries in the plane for oblique shock-wave reflection are reproduced from Lee & Glass (1982) for real air and a polytrophic equation of state with [gamma] = 1.40.


There are multiple set of shock waves can formed from the surface of the ramp wedge. It can intersect inside the supersonic diffuser and separated into the left running and right running shock waves. It causes a change in flow physical properties. Interaction of shock wave should be consider to further design of the subsonic diffuser of the ramjet engine.

5. Flow Analysis Using CFD:

The computational fluid dynamics analysis is made with fluent 6. Sonic inlet condition is assumed to achieve the results in the transonic conditions. Energy conservation and K-Epsilon model turbulence are defined for predict the flow conditions. The standard k- epsilon model in the fluent falls within this class of models and has become the workhorse of practical engineering flow calculations in the time since it was proposed by Launder and Spalding [4]. Velocity inlet boundary conditions are used to define the flow velocity along with all relevant scalar properties of the flow, at flow inlets. The magnitude of the velocity is defined as sonic inlet. A fluid zone is a group of cells for which all active equations are solved. There are four types of model which specifications are same solved by the same boundary conditions but the deflection angle of the ramp is different.

i) When the deflection angle is parallel to the ramp wedge surface (i.e.) 15 deg. The pressure and velocity contour inside the ramjet diffuser is shown in fig 6 and 7. The minimum angle of ramp deflection is considered. The pressure is increasing throughout the diffuser with drop in velocity. It shows that the ram effect in diffuser

creates the pressure rise.

ii) When the deflection angle of the ramp is considered as 25 deg. The pressure and velocity contour inside the ramjet diffuser is shown in fig 8 and 9. The slight change in angle of ramp deflection is considered positively. Ramp is structured like an aerofoil to reduce the pressure loss.





iii) When the deflection angle of the ramp is considered as 30 deg with conical shape. The pressure and velocity contour inside the ramjet diffuser is shown in fig 10 and 11. The flow properties immediately behind conical ramp design create the conical shock. However, because of the flow over a conical section of ramp is naturally three-dimensional, the flow field between the wave and conical surface of the ramp couldn't uniform for longer time. Moreover, the addition of a third dimension provides the flow with extra space to move through, hence relieving some of the obstructions set up by the presence of the body. This is called the "three-dimensional relieving effect." which is characteristic of all three-dimensional flows 1. Because of the three-dimensional relieving effect, the pressure rise behind the conical surface of ramp is affected.



The pressure and velocity of the flow changes but pressure rise is smaller than the wedge shape ramp at 25 deg smooth aerofoil shape ramp model.

iv) When the deflection angle of the ramp is considered as 45 deg with wedge shape. The pressure and velocity contour inside the ramjet diffuser is shown in fig 12 and 13.



Comparatively the pressure between the ahead and behind the ramp increases tremendously due to strong shock wave. The three dimensional relieving effect results in a weaker than shock wave for a wedge. The wedge shape ramp creates maximum pressure rise behind the ramp model. It proves that the maximum deflection angle with wedge shape creates the maximum pressure rise to develop high adiabatic flame temperature in the combustion chamber.


Every deflection angle of the ramp has two possible operating conditions and shock solution as discussed earlier. Consider air is passing with an inlet Mach no 3 over a ramp which is placed at an angle 15 deg. According to [theta]-[beta]-M relation, the ramp angle has two solution of oblique shock wave (i.e) 32 deg as weak and 84 deg as strong solution. Variation of the mach no is shown in table 1.

The temperature ratio (t) and pressure ratio increases when the wave angle increases. As shown in table 2, the pressure rise of the strong solution of deflection angle is 52% more than the pressure rise of the weak solution of deflection angle for deflection angle 30 deg.


The graph shows that the mach no up to maximum deflection angle of the ramp 30 deg. downstream properties of the air varies highly in strong shock wave solution. The velocity of the air is decreased with increasing pressure.






From the results of the Project, it can concluded that:

* Control of ramjet engine by varying ramp shape can attained easily.

* Ramjet engine can be controlled by varying ramp angle for both weak and strong shock solution is possible.

* Ramjet engine can attain hypersonic speeds from low supersonic speed by creating enormous pressure rise due to the development of strong shock solution for same ramp deflection angle.


[1.] May-Fun Lioul Thomas J. Benson and Charles J. Trefny, NASA Glenn Research Center, Cleveland, OH 44135, U.S.A.i, "An Interactive Preliminary Design System of High Speed Fore body and Inlet Flows"

[2.] Robert, E., Coltrin "High-Speed Inlet Research Program and Supporting Analyses"

[3.] Glazl, H.M., P. Colella, Glass and R.L., Deschambault, 1985. "A numerical study of oblique shock-wave reflections with experimental comparisons" Proc. R . Soc. Lond. A 398: 117-140.

[4.] Launder, B.E. and D.B. Spalding, 1974. "The Numerical Computation of Turbulent Flow". Computer Methods in Applied Mechanics and Engineering, 3: 269-289.

[5.] John, D., Anderson Jr "Modern Compressible Flow with Historical Perspective"--McGraw-Hill Series in Aeronautical and Aerospace Engineering,

[6.] Ansys Fluent user guide, Version 6.3

[7.] Theodore, A. Talay, 1975. Langley Research Center" Introduction to the Aerodynamics of Flight" Prepared at Langley Research Center, NASA.

[8.] Imrie, B.W., "Compressible Fluid Flow" London, Butterworths

(1) Sudharson. M, (2) Dr. David Rathnaraj. J, (3) Yuvraj. S, (4) Sathiyalingam. K

(1, 2, 3, 4) Sri Ramakrishna Engineering College, Coimbatore-641022, Tamil Nadu, India.

Received 25 January 2016; Accepted 28 April 2016; Available 5 May 2016

Address For Correspondence:

Sudharson. M, Sri Ramakrishna Engineering College, Coimbatore-641022, Tamil Nadu, India.
Table 1: Downstream Mach no for various wave angle at [M.sub.1]=3

S.No   Deflection   Weak shock   Downstream   Strong      Downstream
       angle deg    solution     Mach No.     shock       Mach No.
                    angle Deg                 solution
                                              angle deg

1      5            23           2.7          88          0.47
2      10           27           2.5          86          0.48
3      15           32           2.25         84          0.50
4      20           37           1.9          82          0.53
5      25           44           1.7          79          0.58
6      30           52           1.4          75          0.67

Table 2: Pressure ratio and Temperature ratio for
various wave angle at [M.sub.1]=3.

S.No   Weak shock   Static     Static
       solution     Pressure   Temperature
       angle Deg    ratio      ratio

1      23           1.453      1.114
2      27           2.054      1.241
3      32           2.821      1.388
4      37           3.771      1.559
5      44           4.925      1.761
6      52           6.355      2.006

S.No   Strong shock   Total      Static
       solution       Pressure   Temperature
       angle deg      ratio      ratio

1      88             10.323     2.677
2      86             10.292     2.672
3      84             10.234     2.662
4      82             10.137     2.646
5      79             9.973      2.618
6      75             9.651      2.564

Table 3 Downstream Mach no for various wave angle AT M1=6

S.No   Deflection   Weak shock   Downstream   Strong      Downstream
       angle deg    solution     Mach No.     shock       Mach No.
                    angle deg                 solution
                                              angle deg

1      5            13           5.33         88          0.40
2      10           17           4.67         87.6        0.41
3      15           22           3.99         86          0.42
4      20           28           3.33         85          0.44
5      25           34           2.82         83          0.47
6      30           40           2.33         81          0.51
7      35           48           1.8          78          0.58
8      40           57           1.4          74          0.72

Table 4: pressure ratio and Temperature ratio
for various wave angle at M1=6

S.No   Weak shock   Static     Static
       solution     Pressure   Temperature
       angle Deg    ratio      ratio

1      13           2.010      1.232
2      17           3.667      1.541
3      22           6.073      1.958
4      28           9.245      2.495
5      34           13.154     3.152
6      40           17.760     3.923
7      48           23.077     4.811
8      57           29.500     5.883

S.No   Strong      Total      Static
       shock       Pressure   Temperature
       solution    ratio      ratio
       angle deg

1      88          41.815     7.937
2      87.6        41.760     7.928
3      86          41.661     7.911
4      85          41.503     7.885
5      83          41.262     7.845
6      81          40.881     7.781
7      78          40.226     7.672
8      74          38.765     7.428
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Author:Sudharson, M.; Rathnaraj, David J.; Yuvraj, S.; Sathiyalingam, K.
Publication:Advances in Natural and Applied Sciences
Date:May 15, 2016
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