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Computational Study on Supersonic Mixing Using Clover Nozzle

Z. A. Samitha1 College of Engineering Trivandrum, Kerala, 695016, India

Dani Davis2 Hindustan Aeronautics Limited, Bangalore, Karnataka, 560093, India

and

P. Balachandran3 Propulsion Research Division, LPSC, ISRO, Trivandrum, Kerala, 695547, India

[Abstract] A vital technical problem to be tackled in the development of advanced air breathing propulsion systems like air augmented rockets and dual mode combustion ramjets is the enhancement of mixing between two high speed gaseous streams. A radially lobbed nozzle is a potential candidate to enhance the mixing of two supersonic streams. In this study a computational work is carried out on supersonic mixing using a new radially lobbed nozzle called clover nozzle. Three-dimensional, compressible Navier-Stokes equations discretized using a coupled implicit finite volume method are used. Mixing characteristics of two types of clover nozzles are studied. The mixing is characterized by a parameter called momentum flux. The result has been compared with a conventional conical nozzle of same throat diameter and experimental results. The stagnation pressure loss is also analyzed. The result shows a complete mixing of the streams with marginal stagnation pressure loss within a short mixing length.

Nomenclature

T0 = Stagnation temperature (K) P0 = Stagnation pressure (Pascal) Ps = Static pressure (Pascal) Φ = Uniformity factor σµ (x) = standard deviation µav (x) = Average momentum flux DOM = Degree of mixing UM = Unmixed condition

I. Introduction IXING of two high speed streams in a short mixing chamber is a basic requirement for the efficient and reliable operation of scramjets, air augmented rockets and supersonic ejectors. Papamoschou and Roshko1

conducted experimental and theoretical studies and they have shown that the growth rate of shear layers that controls the mixing of two co-axial jets decreases substantially with increase in compressibility of the streams. This reduction in the growth of shear layers renders the mixing of co axial supersonic stream extremely slow. Hence methods of achieving enhanced mixing of supersonic jets play an important role in the development of advanced aerospace propulsion systems.

1 Professor, Department of Mechanical Engineering, College of Engineering Trivandrum. 2 Design Engineer, Engine and Test Bed Research & Design Center, Hindustan Aeronautics Limited, Bangalore. 3 Head, Propulsion Research Division, LPSC, ISRO, Trivandrum.

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47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-30

Copyright © 2009 by zasamitha. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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The multilobed forced mixer nozzle has been identified as an efficient tool in promoting enhanced mixing of compressible jets. Tillman2 had conducted a comparative study of mixing enhancement of supersonic streams using forced mixer nozzles. In this study they found that the mixing mechanism of a lobed nozzle is characteristically different from that of a conventional conical nozzle. In the case of jets from circular nozzles mixing is dominated by momentum transfer through the action of viscous shear stresses and small scale turbulence in the mixing layer. Hence the slow growth rate of supersonic shear layers renders the conical nozzle highly inefficient for applications involving supersonic mixing. A rectangular nozzle provides better mixing than a circular nozzle of the same exit area owing to the distribution of viscous shear stresses over a larger surface area. The jet mixing was characterized by measured distributions of total temperature, total pressure, static pressure and velocity. The study revealed that the generation of large scale vortex structures was effective in the mixing of supersonic jets.

A. K. Narayanan3 has experimentally established the efficiency of a six lobed petal nozzle in providing an appreciable enhancement of momentum mixing in supersonic flow. Anil and Damodaran4 used the petal nozzle as the primary nozzle in an experimental arrangement to simulate the air augmented rocket and obtained a fairly uniform temperature profile at the exit of a relatively short length of mixing chamber of L/D= 4.25. The suitability of the petal nozzle for various applications like supersonic ejector was also established. However, quantitative information available on various aspects of mixing enhancement in supersonic flow through the radially lobed nozzle is limited. Also the increase in stagnation pressure loss has not been studied at all.

An experimental study on mixing enhancement by petal nozzle in supersonic flow has been conducted by Srikrishnan, Kurian and Sriramulu5. The radial distribution of momentum flux was characterized by a mixing parameter called the degree of mixing. The loss in stagnation pressure associated with the mixing was also determined. The results were compared with the conventional conical nozzle and found that the six lobed petal nozzle is more suitable than the conical nozzle.

Jeyakumar and Balachandran6 conducted an experimental study on mixing enhancement in supersonic stream with axisymmetric cavities. It was observed that wall mounted cavities enhance momentum mixing of two supersonic streams within a mixing duct. However the stagnation pressure loss was marginally increased for cavities compared with no cavity configuration.

Anil and Damodaran7 experimentally investigated the performance of flow through a petal nozzle. The nozzle was fabricated and tested in a blow down tunnel. Total and static pressure distributions were measured radially along the major and minor planes at different axial locations. From this data momentum distributions were estimated. The results show that the momentum transfer in the radial direction is more rapid compared to an equivalent convergent divergent nozzle. Narayanan and Damodaran8 studied the performance of petal nozzle as an ejector. This study concluded that the ejector with a petal shaped nozzle for the primary flow has been shown to be very much superior to the one with a conventional conical nozzle. The large scale inviscid mixing process associated with the petal nozzle provides tremendous pumping benefits using very short shroud length.

The radially lobed nozzle9 is found to be effective in achieving mixing between two high speed streams. The free jet characteristics of the nozzle like radial pressure profile and estimated jet spreading and shear layer growth rate are indicative of good mixing performance. From experiments on dual isothermal streams the lobed nozzle is seem to be augmenting momentum mixing of supersonic streams. Pressure drop generated by the lobed nozzle can be attributed to the complex shock pattern in the jets evidenced by Schlieren pictures. The mixing mechanism in the radially lobed nozzle is found to be controlled by the axial vortices formed at the lobe tips.

Srikrishnan, Kurian and Sriramulu10 were experimentally investigated the thermal mixing and combustion in supersonic flow using petal nozzle. A hot gas jet issued supersonically from a lobed nozzle mixed with a cold supersonic jet in a circular mixing tube. The experiment results show that the petal nozzle achieves rapid mixing when the primary jet issues from it. A mixing duct of L/D = 3.73 is found to be sufficient to achieve nearly uniform temperature and momentum fields when a petal nozzle is used. A detailed survey of temperature and momentum fields inside the mixing tube, downstream of the lobed nozzle indicates the presence of large scale vortices in the flow field, which give rise to vigorous mixing. They also found that the petal nozzle results in better combustion, when it is used to inject the fuel rich gases into a supersonic combustor. The temperature rise across the supersonic combustor as well as the wall pressure distribution along the combustor revealed the superiority of the petal nozzle over the conventional one. The resulting temperature and pressure rises were measured and the supersonic combustion efficiency was found to be of the order of 60%. The performance of a conventional conical nozzle was found to be much inferior to that of the petal nozzle under identical conditions.

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Elangovan and Rathakrishnan11 carried out experiments on jets issuing from circular nozzles with grooved exits and the results compared with those of a plain nozzle. The nozzles were operated at fully expanded sonic and under expanded exit conditions. The shock cell structure of the under expanded jets from grooved nozzles appeared to be weaker than that of the plain nozzle, as indicated by lesser amplitudes of the cyclic variation of the pitot pressure. The iso-Mach contours indicate that the jet spread along the grooved plane is significantly higher than that along the ungrooved one. The mixing is also enhanced due to the stream wise vortices shed from the grooves.

Samitha Z. A., Swaraj Kumar B., Sheena S. S., and Balachandran P.12 were conducted an experimental study on performance of wavy shaped nozzle. They compared the results with a conventional conical nozzle of same area ratio. The results indicate that momentum distribution along the radial direction at all axial locations is more rapid as compared to an equivalent conical nozzle. The momentum flux is higher only at the central core of conical nozzle due to high velocity in the core region and then it diminishes till the flow reaches the wall of the nozzle. J. H. Kim, H.D. Kim, K. A. Park, S. Matsuo and T. Setoguchi13 were conducted an experimental and computational study to investigate the effectiveness of a variable critical nozzle. A rod with a small diameter was inserted into a conventional critical nozzle so that the effective cross-sectional area at the nozzle throat could be varied. Fluid flow through variable critical nozzle flow was analysed. Their computations predicted well the experimental discharge coefficient at high-Reynolds numbers, but the predictions became somewhat poor at low-Reynolds numbers. Samitha Z. A., Swaraj Kumar B. and Balachandran P.14 were conducted an experimental study on supersonic mixing using clover nozzle. They compared the results with a conventional conical nozzle of same area ratio. The result showed a complete mixing of the streams with marginal stagnation pressure loss within a short mixing length.

Samitha Z. A., Lajith V. and Balachandran P.15 were conducted an experimental study on effect of lobe angle of clover nozzle on coaxial supersonic streams. They found that increase in lobe angle produces more pressure loss and results emphasized that neither pure shear mixing nor vortex mixing alone is responsible for the mixing of coaxial supersonic streams. An optimum balance between both is required for a better mixing with minimum loss within in a short span.

II. Problem Description A schematic diagram of the mixing setup is shown in Figure 1. The test nozzles (four leaf clover, six leaf clover

and conical nozzle) are attached to the settling chamber. Clover nozzles are having wavy shape at the exit section with a throat diameter of 10mm. It has converging and diverging angles as 250 and 30 respectively. The flow parameters are measured in a cylindrical mixing tube attached to the exit of the nozzles.

The stagnation pressures at primary and secondary settling chambers are 400kPa and 200kPa respectively. The

static pressure at the outlet of mixing tube is kept constant at 101.325kPa. The Reynolds number is found to be above 2300. Thus, the flow is typically turbulent.

Figure 1. Mixing setup

Two clover nozzles (four leaf and six leaf) and a conical nozzle are used for the comparative study. Both of the nozzles have the same exit area and area ratio corresponding to an exit Mach number of 1.5. The exit sections of clover nozzles are shown in figure 2.

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Figure 2. Major and minor planes of clover nozzles

Two principal planes are identified in the flow field downstream of clover nozzle. The plane that bisects the

outward lobe region is referred to as the major plane and the plane bisects the inward lobe region is called minor plane.

Figure 3. Photographs of conical and clover nozzles

Figure 3. shows photographs of conical and clover nozzles. The four leaf clover nozzle as the name indicates has four lobes radially in both inward and outward direction. The angle between the major and minor plane of four leaf clover nozzle is 450 and that of six leaf clover nozzle is 300.Flow properties are calculated at radial locations along the major and minor planes. The flow profiles at the exit of cylindrical mixing tubes of length L/Dexit =0, 1, 2, 3, 4, 5, 6, 7 respectively are determined.

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III. Computational Analysis The supersonic mixing of air using clover nozzle is simulated in Fluent. The governing equations given by the

conservation forms of mass, momentum and energy are discretized spatially using a finite volume scheme, in which the physical domain is subdivided into numerical cells and the integral equations are applied to each cell. Also, for the time derivatives in the governing equations, an implicit multi-stage time stepping scheme is used.

Standard k-epsilon turbulence model with the standard wall function is used. The boundary conditions are inlet

stagnation pressure and outlet static pressure, at the upstream and downstream boundaries, respectively. The symmetric conditions reduce computational effort for full domain and the adiabatic, no-slip conditions are applied to the solid walls.

An unstructured grid system of about 70,000 grid points is employed in computations. The fineness of the computational grids is examined to assure that the obtained solutions are independent of the grid employed. The grids are densely clustered in boundary layers, so that those provide more reasonable predictions. A solution convergence is obtained when the residuals for each of the conserved variables are reduced below the order of a magnitude 6. Another convergence criterion is to directly check the conserved quantities through the computational boundaries. The net mass flux is investigated to find out if there is an applicable imbalance through the computational boundaries. In the present study, the stagnation pressures P01 and P02 are given at the primary and secondary inlets respectively, and the static pressure Ps at the outlet of the mixing tube. The static pressure Ps is kept constant at 101.325kPa. The working gas is air and its temperature is kept constant at T0=300 K.

IV. Results and Discussion Figure 4 shows the computed static pressure distributions along the wall and the axis of mixing setup. The static

pressure decreases monotonously with distance and it continues to decrease up to the section. This means that the flow becomes supersonic downstream of the nozzle throat. Stagnation pressure distributions in clover and conical nozzles are shown in figure 5 and 6 respectively. Stagnation pressure loss in clover nozzle is high compared to conical nozzle. Figure 7 shows velocity distribution along axis in the test nozzles.

Figure 4. Static pressure distributions in test nozzles

Figure 5. Stagnation pressure distributions in clover nozzles

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Figure 6. Stagnation pressure distributions in conical nozzle

Figure 7. Velocity distribution along axis in test nozzles

Figure 8. Contours of velocity and stagnation pressure at various L/D ratios of six leaf clover nozzle.

The contours of velocity and stagnation pressure at various L/D ratios of six leaf and four leaf clover nozzle are shown in fig. 8 and 9. Fig. 10 shows the velocity and pressure contours at various L/D ratios of conical nozzle. Fig. 11 shows the momentum flux along the major and minor planes of six leaf Clover nozzle at different L/D ratio of 5. At L/D = 1 a clear distinction exists between the momentum flux in the two planes. The primary stream that possesses higher momentum, issues along the major plane through the lobe region. At L/D =1 the two streams still retain their identity and there is no appreciable mixing between the two.

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Figure 9. Contours of velocity and stagnation pressure at various L/D ratios of four leaf clover nozzle.

Figure 10. Contours of velocity and stagnation pressure at various L/D ratios of conical nozzle.

Figure 11. Momentum flux distributions along major and minor plane of six leaf clover nozzle and conical

nozzle at L/D ratio of 5.

At L/D =5 it is seen that the momentum profile becomes more or less uniform in the axial plane. At L/D =1 it can be seen that the high primary momentum has started diffusing in the angular direction. The conclusion is that a fair amount of momentum mixing has taken place between L/D = 1 and 5. This rapid mixing can be attributed to the generation of large-scale vortices.

The six-leaf clover nozzle at L/D=7 achieves a complete momentum mixing. The mixing achieved by conventional nozzle at this location is less uniform than that of the Clover nozzle.

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Figure 12. Momentum flux distributions along major and minor plane of four leaf clover nozzle and conical

nozzle at L/D ratio of 4.

Fig. 12 shows the comparison of momentum flux along the major and minor planes of four leaf Clover nozzle and conical nozzle at L/D ratio of 4. In this case also the momentum mixing is more or less uniform at L/D = 4. The depth of the lobed region in four leaf Clover nozzle is more than that of the six leaf Clover, so the generation of large-scale vortices is also more. This is the reason for larger mixing length required in six leaf Clover nozzle.

A. Degree of Mixing

To make a comparison between the mixing performance of the Clover and conical nozzle based on a quantitative assessment of the level of mixing achieved, a dimensionless parameter called uniformity factor Φ is defined,

Φ = 1-[σµ (x)/µav (x)]

Where σµ (x) is the standard deviation of the radial distributions of momentum flux at a given axial location

along the mixing tube. µav (x) is the average of momentum flux along a radial line at the location considered. This factor is basically a measure of the uniformity of the momentum flux distribution in the radial direction, at a given axial location. For a perfectly mixed flow, the distribution has to be uniform across the section. As there exists a momentum gradient between the primary and the secondary streams an unmixed flow field will be severely non-uniform in the radial direction, showing a higher momentum across the primary region and a lower momentum across the secondary region. The standard deviation stream in the definition of Φ represents non-uniformity. This is normalized by the average value of momentum flux and subtracted from unity, so that the resulting parameter would represent the degree of the uniformity at the given section. For a perfectly flat momentum profile (σµ (x) = 0), Φ will be equal to unity. The uniformity factor is used to define a mixing parameter called the degree of mixing (DOM). The DOM is defined as,

DOM = [(Φ- ΦUM) / (1- ΦUM)]

Where ΦUM is the value of Φ when the two streams are totally unmixed. It can be seen that when the two streams are completely mixed DOM will be equal to unity. And when they are totally unmixed DOM will be equal to zero. This parameter is used for comparing the extend of mixing achieved by the two types of nozzle.

The figures 13 and 14 show the comparison of uniformity factor and degree of mixing of clover nozzles with the conventional conical nozzle. It also gives comparison between experimental and computational results. From the figures it is clear that computational results are very closer to experimental results and the degree of mixing in Clover nozzles (four leaf and six leaf) is more than that in the conical nozzle. Comparing the Clover nozzles four leaf Clover nozzle is superior to the six-leaf Clover nozzle. This is because of the depth of lobe. In four leaf clover nozzle the depth of the lobe is more. The previous studies on petal nozzle had showed that the enhancement of mixing in radially lobed nozzles is due to the generation of large-scale vortices caused by the lobed region. It can be seen that DOM for the clover nozzles comes closer to the ideal value of unity at an L/D ratio of 7.Another notable feature is that with a Clover nozzle a practically complete mixing in radial direction can be obtained within an L/D of 5. This proves that the Clover nozzle achieves nearly complete momentum mixing in a three dimensional flow

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field, within a short mixing chamber. In practical applications a reduction in the length of mixing chamber is expedient as it implies a reduction in the overall bulk and weight of the propulsion system.

Figure 13. Comparison of uniformity factor

Figure 14. Comparison of degree of mixing

The enhancement of momentum mixing is of particular importance in acoustic and in applications like supersonic ejectors. Results of the present study can also give guidelines for further research on the application of radially lobed nozzles in air augmented and dual combustion propulsion systems.

B. Pressure Drop Factor

To characterize the drop in stagnation pressure a pressure drop factor (PDF) is defined. The primary and the secondary streams enter the mixing tube with different stagnation pressures. Hence PDF is defined as the difference between the weighted average stagnation pressures at the inlet and the axial station considered, normalized by the weighted average of the inlet stagnation pressures.

Figure 15. Comparison of pressure drop factor

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The pressure drop factors are plotted for the clover nozzles and conical nozzle in Figure 15. The increase in pressure drop in the case of Clover nozzles is clearly seen. This additional pressure loss is more predominant at larger L/D ratios.

V. Conclusion A computational study is conducted on supersonic mixing using clover nozzles. Three-dimensional, compressible Navier-Stokes equations are used. Mixing characteristics of two types of clover nozzles are studied. The results are compared with a conventional conical nozzle of same throat diameter and experimental results. The stagnation pressure loss is also analyzed. A four-leaf clover nozzle provides complete lateral mixing of supersonic streams in a comparatively short length of the mixing chamber. For the present case, when the two streams are of Mach number 1.5 and 1 respectively the mixing was fairly complete within an L/D of 4, L/D = 7 gives a nearly flat momentum profile. For a six-leaf clover nozzle the corresponding values are 5 and 7 respectively. Superiority of the mixing performance of the clover nozzle over that of the conventional conical nozzle has been quantitatively assessed based on a comparative study of the momentum flux distributions in radial direction at the end of the mixing tubes of various lengths. The values of momentum flux showed that the mixing achieved by clover nozzle is close to the ideal case of complete mixing, whereas the performance of the conical nozzle is poor. The stagnation pressure loss associated with clover nozzle is more than that for conical nozzle. Comparing the clover nozzles the stagnation pressure loss in six-leaf clover nozzle is slightly less than that of the four-leaf clover. Comparing the mixing extent required for complete mixing it is shown that the clover nozzles are much superior to the conventional conical nozzle.

References 1 Papamoschou D., and Roshko A.,” The Compressible Turbulent Shear Layer: An Experimental Study,” Journal of Fluid

Mechanics, Vol. 197, Dec. 1988, pp. 453-477. 2Tillman T. G., Patrick W. P. and Paterson R. W., “Enhanced Mixing of Supersonic Jets,” Journal of Propulsion and Power,

Vol. 7, no. 6, 1991, pp. 1006-1114. 3A. K. Narayanan, and K. A. Damodaran, “Experimental Studies on Mixing of Two Co-Axial High Speed Streams,” Journal

of Propulsion and Power, Vol. 10, no.1, 1994. 4Anil K. N., and Damodaran K. A., “Preliminary Investigations on Improving Air Augmented Rocket Performance,” Journal

of Propulsion and Power, Vol. 10, no. 3. 1994. 5A. R. Srikrishnan, J. Kurian, and V. Sriramulu, “Experimental Study on Mixing Enhancement by Petal Nozzle in Supersonic

Flow,” Journal of Propulsion and Power, Vol. 12, no. 1, 1996. 6Jeyakumar S., and Balachandran, P. “Experimental Study on Mixing Enhancement in Supersonic Stream with Axi

Symmetric Cavities,” AIAA paper, 2003. 7Anil, K. N. and Damodaran, K., A., “Experimental Investigation on Flow through a Petal Nozzle,” Journal of the Institution

of Engineers (India) Vol.70, 1990. 8A. K. Narayanan, Dr. K. A. Damodaran, ”Supersonic Ejector Characteristics Using a Petal Nozzle,” Journal of Propulsion

and Power, Vol. 10, no. 5, 1994, pp. 742-743. 9Job Kurian, “Some Aspects of Mixing of High Speed Streams Using Radially Lobed Nozzle,” Proceedings of NCABE,

1996. 10A., R., Srikrishnan, J., Kurian, and V., Sriramulu, “An Experimental Investigation of Thermal Mixing and Combustion in

Supersonic Flows,” Journal of Combustion and Flame, Vol. 107, 1996. 11S. Elangovan and E. Rathakrishnan,”Studies on High Speed Jets from Nozzles with Internal Grooves,” The Aeronautical

Journal, 2002. 12Samitha Z. A., Sheena S. S. and Balachandran P., “Design and Testing of Clover Nozzle,” AIAA paper, 2005. 13J. H. Kim, H.D. Kim, K. A. Park, S. Matsuo and T. Setoguchi, “A Fundamental Study of a Variable Critical Nozzle Flow”,

Journal of Experiments in Fluids, 2005. 14Samitha Z. A., Swaraj Kumar B. and Balachandran P., “Experimental Study on Supersonic Mixing Using Clover Nozzle,”

ALAA paper, 2006. 15Samitha Z. A., Lajith V. and Balachandran P., “Effect of Lobe Angle of Clover Nozzles on Coaxial Supersonic Streams,”

EUCASS paper, 2006.