3-Mech - IJMPERD - NUMERICAL - Sundarraj - Paid

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD ) ISSN 2249-6890 Vol.2, Issue 3 Sep 2012 19-27 © TJPRC Pvt. Ltd.,

NUMERICAL INVESTIGATION ON EFFECT OF EXPANSION RAMP ON STAGED TRANSVERSE INJECTION OF FUEL IN A SUPERSONIC COMBUSTOR K.SUNDARARAJ1 & S.DHANDAPANI 2 1 2

Dean, Mahendra Engineering College, Namakkal, Tamilnadu, India

Principal Dr. N.G.P. Institute of Technology, Coimbatore, Tamilnadu, India

ABSTRACT This work involves an application of the computational fluid dynamics to a problem associated with the flow inside the supersonic combustor of a scramjet engine. A method for augmenting the mixing of air and the fuel in the existing canonical model by introducing the expansion ramps on both the sides of the injectors suggested and the effectiveness of expansion ramps was numerically analysed. The combustor models were simulated using the finite volume based code FLUENT and the governing equations were solved by means of a coupled explicit method using shear-stress transport (SST)

K-ω turbulence model.

The numerical simulations of the flow through the combustor model with the expansion ramp are reported in comparison with the canonical model. The investigation shows that the use of the expansion ramp contributes to the formation of the streamwise vortices and promotes mixing between air and fuel.

KEYWORDS: Scramjet Engine, Supersonic Combustor, Loss Of Stagnation Pressure, Staged Transverse Injection, Sst K-ω Turbulence Model, Expansion Ramps, Vorticity

INTRODUCTION The desire for hypersonic flight necessitated the supersonic combustion ramjet (Scramjet) engine potentially expanding the flight speed envelope to the Mach 15 range. The term hypersonic refers to speeds in excess of Mach 5, five times the speed of the sound i.e. 1520 m/s at a typical operational altitude of 32.5 km (Anderson 2007). The overall performance of the scramjet engine depends on the efficiency of the mixing and combustion processes in the combustor. Several fuel injection schemes have been employed during the last four decades to enhance the penetration and mixing of the fuel injected into the supersonic airstream (Deepu 2007). In this study the focus is upon the modification of the geometry of the staged transverse injection scheme which is employed in scramjet engines (Deepu 2006, Abbitt et al. 1992 and Abbitt et al. 1993). Numerical experiments were conducted to find a more efficient method to augment the mixing characteristics of staged transverse injection behind the rearward facing step. It is predominantly a numerical investigation executed utilizing the commercial CFD code FLUENT (FLUENT 2001).

K.Sundararaj & S.Dhandapani

20

Figure 1 Staged transverse injection behind a rearward facing step (Source: Abbitt et al. 1991)

A typical combustion chamber involving staged transverse injection of the fuel behind a rearward facing step is shown in Figure 1. The staged transverse injection behind a rearward facing step is a highly three dimensional flow which involves the complex flow features such as boundary layer separation, reattachment, curved bow shocks, shock shear layer and shock-boundary layer interactions, jet induced counter-rotating vortices and Mach disks (Abbitt et al. 1991). The rearward facing step helps to sustain combustion by providing a recirculation for the fuel-air mixture. The staging of injectors provides improved penetration and the mixing of injectant along with a recirculation region between the injectors for additional flame holding.

This study is intended to introduce a method to enhance the mixing characteristics, by suitably modifying the geometry of the combustor. A well designed supersonic combustor will improve the overall performance of the scramjet engine.

LIST OF SYMBOLS USED d

diameter of the injector (m)

f

mole fraction of H2

fmax maximum mole fraction of H2 H

height of the backward facing step

M

Mach number of the fluid flow

Mi

freestream Mach number of the air

Po

stagnation pressure (N/m2)

Poi

stagnation pressure at the inlet (N/m2)

21

y+

Numerical Investigation on Effect of Expansion Ramp on Staged Transverse Injection of Fuel in a Supersonic Combustor

wall y plus value

penetration distance of fuel along z-direction (m) ηm

mixing efficiency

ζ

streamwise vorticity (s-1)

GEOMETRY OF THE COMBUSTOR MODELS AND FLOW CONDITIONS Figure 2 shows the two combustor models of canonical model (Abbitt et al. 1992 and Abbitt et al. 1993) and the modified model on which numerical experiments are conducted respectively. The test section of the existing canonical model are designed such that its overall height, overall width and the height of the backward facing step are 11.03d, 15.79d and 1.65d respectively, where d is the diameter of the injector. The two Injectors are located at x = 0 and at x = 6.58d. The inlet section of the combustion chamber and the backward facing step are located at x = -10.65d and at x = -4.94d respectively.

In the modified model expansion ramps of angle of inclination 300 with respect to the main flow direction are provided. The diameters and the locations of the injectors remain the same as that of original model. The expansion ramps are expected to reduce the back pressure around the fuel injectors thereby improving the overall performance of the combustion chamber. The nominal operating conditions of freestream of air and the fuel are as detailed below.

Parameter

H2 Fuel

Air

Stagnation Pressure

274 KPa

263 KPa

Stagnation Temperature 300 K

300 K

Mach Number

2.0

2.0

Static Pressure

35 KPa

Static Temperature Fluid Velocity

139 KPa 167 K

518 m/s

250 K 317 m/s

COMPUTATIONAL METHODOLOGY APPLIED The conservation equations: three dimensional continuity equations for air and for hydrogen fuel, the three momentum equations and the energy equation are used for predicting the flow parameters. The turbulence model used in this study is the shear-stress transport (SST) K-ω model that combines the best aspects of both the k-ε and k-ω turbulence models (Menter 1994).

22

K.Sundararaj & S.Dhandapani

Canonical model

Combustor model with expansion ramps

Figure 2 Schematic diagram of the combustor models

After detailed numerical investigation for grid independence, the grid structure consisting 1080000 grid points was used for obtaining numerical results since it yielded grid independent solution and tallied with experimental data obtained by Eklund et al (1994). The complete experimental verification are detailed in the studies conducted by the same authors (Sundararaj and Dhandapani 2006 and 2007) which are not repeated herewith due to space constraint. The dimension of the grids used in the selected grid structure is 180 x 100 x 60 along x, y and z directions respectively. The maximum wall y+ obtained is 100 which occurs only in the far field regions whereas in most of the sensitive regions within the model the wall y+ is below 100. For turbulent flows, wall y+ values less than 100 are generally acceptable so that the cell closest to the wall can be safely said to be inside the log-law region (Rodriquez and Cutler, 2003)

RESULTS AND DISCUSSIONS It was intended to promote mixing characteristics by introducing expansion ramps to augment the mixing characteristics. In order to assess the performance of the combustor operating under various flow conditions the following six parameters are taken into consideration at any cross-flow plane of the combustor as suggested by various investigators Lee et al (1997) and Lee et al (1998). (i)

Maximum mole fraction of injectant fmax

(ii)

Penetration distance of the fuel in the transverse direction

(iii)Streamwisevorticity

(1)

(2)

23

Numerical Investigation on Effect of Expansion Ramp on Staged Transverse Injection of Fuel in a Supersonic Combustor

(iii)

Average Peclet number

(3)

(iv)

Average stagnation pressure

(4)

(v)

Mixing efficiency Ρm =

(5)

Figure 3 shows the comparison of the pressure contours in the plane z/d = 0 between the canonical model and the modified model with expansion ramps. Comparison shows that the canonical model develops high back pressure around the injectors. In the modified model the back pressure around the fuel injectors is reduced as a result of the flow expansion. The low back pressure around the injectors is more favorable to the generation of streamwise vorticity which greatly influences the mixing process. The study shows that the vorticity of the flow increases rapidly due to transverse injection of the fuel across the supersonic airstream (Waitz 1993). The use of expansion ramp near the injector causes further increase in streamwise vorticity which produces a large convection flow in the transverse direction and promotes the mixing between air and fuel. An increase in the mixing rate improves the performance of the supersonic combustion chamber.

Fig 3 Comparison of contours of static pressure ratio P/Pi at the plane z/d=0

24

K.Sundararaj & S.Dhandapani

Figure 4 shows variation of all the important performance parameters along the flow direction for the model with expansion ramp in comparison with the canonical model.

Equations 1 to 5 are used to

determine the performance parameters. With reference to the graphs plotted in this figure the advantages of using the modified model over the canonical model are described as follows.

The maximum mole fraction fmax of H2 decreases more rapidly, particularly in the region x/d > 10.

The combustor models with expansion ramp have shorter mixing length i.e. the downstream distance at which the maximum mole fraction has decayed to 0.7. Higher reduction in the maximum mole fraction of the fuel results in enhancement of combustion process.

(a)

(b)

(c)

(d)

25

Numerical Investigation on Effect of Expansion Ramp on Staged Transverse Injection of Fuel in a Supersonic Combustor

(e) Fig 4. Variation of performance parameters along the main flow direction. a. Maximum mole fraction of H2 fuel, b. Transverse penetration distance of fuel c. Dimensionless average stagnation pressure, d. Streamwise vorticity e. Mixing efficiency

The penetration distance of the fuel should be high to avoid wall heating in combustor. The distance of penetration of the fuel from the bottom wall zH2 is almost same for the combustor models.

Consistent growth in the penetration distance along the z direction would result in reduction in wall temperature of the combustor.

The histories of average stagnation pressure ratio along the streamwise direction in combustor models analyzed. The quantity Poavg at any section of the combustor model is estimated by using the equation 5 and is presented in the graph in the dimensionless form. Generally, the mixing process produces a loss of stagnation pressure that results in a loss of thrust (Schetz J.A. (1970) and Settles G.S. and Dodson L.J. (1994). Both the models with and without expansion ramp show very similar histories of stagnation pressure i.e beyond the injectors the stagnation pressure falls continuously along the flow direction due to the bow shock, streamwise vortex pair and dissipation. The combustor models with expansion ramp show more stagnation pressure losses than the canonical model, showing less than eight percent loss at the farthest section x/d=30.0. The configuration with the ramp are unfavorable from the point of view of stagnation pressure loss but the enhancement of combustion process due to better mixing process increases.

Further, streamwise vorticity produces a large convection flow in the plane normal to the flow direction and promotes mixing, in Figure 4, sustainment of the streamwise vortices in the farfield regions seems to be the main cause for the enhancement of mixing rate in the configurations with the expansion ramp. The fluid particles expand towards the expanded region of the ramp and turns towards the main flow which helps the injectant to mix with air.

26

K.Sundararaj & S.Dhandapani

The variation of the mixing efficiency ηm calculated by using the

equation 5 shows that it

increases for both the configurations along the flow direction as the combustible area increases along the flow direction. In the convection dominated region ηm, increases more rapidly upto the section x/d~ 15 beyond which the rate of increase of ηm falls slightly as the mixing occurs mainly due to diffusion process. It can be seen in Figure 4 that the higher values of ηm is obtained for the configuration with the expansion ramp when compared with the canonical model.

CONCLUSIONS A method to augment the mixing characteristics staged transverse injection of fuel is suggested by introducing the expansion ramp on both the sides of the injectors to promote Streamwise vorticity. The supersonic combustor models were simulated using the finite volume based code FLUENT. A detailed investigation on flow through the combustor model with the expansion ramp shows that the back pressure around the injectors are reduced due to flow expansion taking place at the ramps. The modified model has shorter mixing length, equal penetration distances in the transverse direction. The modified models with ramp show the loss of stagnation pressure a little more than that of the canonical model. These Models with ramp show less than eight percent stagnation pressure loss at the farthest section x/d=30.0.

REFERENCES 1.

Abbitt J.D., Hartfield R.J. and McDaniel J.C. (1991), ‘Mole-Fraction Imaging of Transverse Injection in a Ducted Supersonic Flow’, AIAA Journal, Vol. 29, No. 3, pp. 431-435.

2.

Abbitt J.D., Segal C., McDaniel J.C., Krauss R.H. and Whitehurst R.B. (1992), ‘Experimental Investigation of a Supersonic Combustion Flowfield Employing Staged Transverse Injection Behind a Rearward-Facing Step’, AIAA paper, 92-0090.

3.

Abbitt J.D., Segal C., McDaniel J.C., Krauss R.H. and Whitehurst R.B. (1993), ‘Experimental Supersonic Hydrogen Combustion Employing Staged Injection Behind a Rearward-Facing Step’, Journal of Propulsion and Power, Vol. 9, No. 3, pp. 472-478.

4.

Anderson J.D. (2007), ‘Fundamentals of Aerodynamics’, Fourth Edition, McGraw-Hill Higher Education.

5.

Deepu M., Gokhale S.S. and Jayaraj S. (2006), ‘Numerical Modeling of Supersonic Combustion of Hydrogen in the Wake Region of a Strut’, Journal of Aerospace Sciences and Technologies, Technical Note, Vol. 58, No. 4, pp. 338-346.

6.

Deepu M., Gokhale S.S. and Jayaraj S. (2007), ‘Recent Advances in Experimental and Numerical Analysis of Scramjet combustor Flow Fields’, IE(I) Journal-AS, Vol. 88, pp. 13-23.

27

7.

Numerical Investigation on Effect of Expansion Ramp on Staged Transverse Injection of Fuel in a Supersonic Combustor

Eklund D.R., Fletcher D.G., HartfieldJr, R.J., McDaniel J.C., Northam G.B., Dancey C.L and Wang J.A. (1994), ‘Computational/ Experimental Investigation of Staged Injection into a Mach 2 Flow’, AIAA Journal, Vol. 32, No. 5, pp. 907-916.

8.

Fluent version 6.0 User’s Guide, Fluent Inc., Lebanon, New Hampshire 2001.

9.

Lee S.H., Jeung I.S. and Yoon Y. (1997), ‘Computational Investigation of Shock-Enhanced Mixing and Combustion’, AIAA Journal, Vol. 35, No. 12, pp. 1813-1820.

10.

Lee S.H., Jeung I.S. and Yoon Y. (1998), ‘Computational Investigation of Shock-Enhanced Mixing: Application to Circular Cross Section Combustor’, AIAA Journal, Vol. 36, No. 11, pp. 2055-2062.

11.

Menter F.R. (1994), ‘Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications’, AIAA Journal, Vol. 32, No. 8, pp. 1598-1604.

12.

Rodriguez C.G. and Cutler A.D. (2003), ‘Numerical Analysis of the SCHOLAR Supersonic Combustor’, NASA Technical report 2003-212689.

13.

Schetz J.A. (1970), ‘Interaction Shock Shape for Transverse Injection in Supersonic Flow’, Journal of Spacecraft, Vol. 7, No. 2, pp. 143-149.

14.

Settles G.S. and Dodson L.J. (1994), ‘Supersonic and Hypersonic Shock/ Boundary Layer Interaction Database’, AIAA Journal, Vol. 32, No. 7, pp. 1377 -1383.

15.

Sundararaj, K. and Dhandapani, S.(2006),“Numerical Simulation of Staged Transverse Injection of H2 Fuel in a Ducted Supersonic Airstream with SST K-ω Turbulence Model”, International Journal of Dynamics of Fluid, Vol. 2, No. 2, pp 245-262.

16.

Sundararaj, K. and Dhandapani, S.(2007), “Numerical Investigation on Influence of Injection Angle on Mixing in a Staged Transverse Injection of Fuel into Supersonic Airstream”, International Journal of Applied Engineering Research, Vol 2, No. 3, pp 467-481.

17.

Waitz I.A., Marble F.E. and Zukoski E.E. (1993), ‘Investigation of a Contoured Wall Injector for Hypervelocity Mixing Augmentation’, AIAA Journal, Vol. 31, No. 6, pp. 1014-1021.