20th Annual CFD Symposium, August 09-10, 2018, Bangalore

Keywords: Micronozzle, Aspect Ratio, Convergent Divergent nozzle, Thrust efficiency, Boundary layer.

1 – Propulsion Division, CSIR-National Aerospace Laboratories, Bangalore

2 – Expert Consultant

3 – Professor, PARK College of Engg. & Technology, Coimbatore

4 – Corresponding author: Email – rajashekarc@nal.res.in

INFLUENCE OF NOZZLE GEOMETRY ON THE PERFORMANCE OF RECTANGULAR, LINEAR, SUPERSONIC MICRO-NOZZLES

K Mukesh1, K Vijaya Sankaran1, G Uthaya Sankara Athith1, G Sriram1, S Chenthil Kumar1, Shambhoo1, C Rajashekar1,4, A. P. Haran3 and JJ Isaac1,2,3

Abstract

Mini-satellite propulsion systems have been studied since 1960s and are still proving to be challenging both in scientific investigations and practical applications. It has shown a significant growth during the past three decades and the study on the development of microthrusters for altitude control and attitude correction of satellites in orbit using green propellants is one of the major areas of research now. Microthrusters which are capable of producing thrusts around 1N to 10N are used to orient mini-satellites and even nano-satellites, known as ‘CubeSats’. These thrusters operate in pulsed modes with each pulse lasting only a few milliseconds. This work presents the computational analyses carried out to investigate the influence of nozzle geometry on the performance of 5N thrust-class rectangular, linear, supersonic micro-nozzles. The dimensions of the nozzle reduce proportionally with the design thrust of the nozzle, and correspondingly the boundary layer effects become dominant and more significant at this scale. Nozzle throat aspect ratio and corner fillet radius effects were studied and optimum values were determined at this scale.

Nomenclature

Abbreviations:

AR - Aspect Ratio

CEA - Chemical Equilibrium with Applications

CFD - Computational Fluid Dynamics

HAN - Hydroxyl Ammonium Nitrate

MSL - Mean Sea Level

RoC - Radius of Curvature

Symbols:

𝐴∗ - Throat area (mm2)

𝐴𝑒 - Exit area (mm2)

𝐼𝑠𝑝 - Specific Impulse (s)

𝑘 - Specific heat ratio

𝑀 - Mach number

𝑃0 - Inlet stagnation pressure (kPa)

𝑝𝑒 - Exit static pressure (kPa)

𝑝𝑎 - Ambient pressure (kPa)

𝑅𝑒 - Reynolds number

𝑅𝑡 - Throat radius (mm)

𝑇𝑎 - Ambient Temperature (K)

𝑇𝑒 - Exit static temperature (K)

𝑇0 - Adiabatic Temperature or Stagnation Temperature (K)

𝑌+ - Non-dimensional wall distance

𝛼 - Divergence half-angle

𝜆 - Divergence loss factor

Introduction

Axisymmetric microthrusters are conventionally employed in NanoSats/CubeSats for attitude and altitude corrections. The micro-nozzles employed in these propulsion systems are of the order of a few millimetres in dimensions. The flow through such nozzles with small geometric dimensions pose many design as well as performance challenges due to the low Reynolds number flow regimes, particularly during the start-up and shut-down phases. From manufacturing and structural considerations of micronozzles, a nozzle with a rectangular cross-section would be preferable to the conventional axisymmetric nozzle. The Aspect Ratio of such a nozzle is defined at the throat, as the ratio of its width to the height; the width is constant throughout the length (See Fig. 1a). In this paper, the cold flow numerical investigations carried out to study the effects of nozzle geometry on the performance of supersonic rectangular linear micronozzles are discussed. The reduction in core flow at the nozzle throat results in adverse effects on the thrust produced. Other important factors which were noted at this scale were the effects of the side walls (changes with aspect ratio) on the core flow.

Another important parameter which was studied for its implication on the performance of these rectangular nozzles was the corner fillet (See Fig. 1b). A finite fillet is inevitable during manufacture and moreover it could have structural advantages. The sharp corners give rise to thicker boundary layers which could hinder the performance. Numerical investigations of the nozzles with filleted corners were done, with the fillet radius as a function of the hydraulic diameter at the throat of the nozzle. As a starting point of the investigation, the null hypothesis was that the performance of the nozzle was unaltered by corner filleting at this scale and if the performance was adversely affected by the displaced boundary layer, the alternative hypothesis may be concluded as valid.

Fig. 1: (a) Representation of the aspect ratio for a rectangular linear nozzle; (b) 5N Mach 2 rectangular

ground nozzle geometry of aspect ratio 1.25 with fillet radius = 10% of the hydraulic diameter at the throat

Nozzle Geometric Parameters

The Nozzle Shape:

In order to generate supersonic flow, convergent-divergent nozzles are used in which the hot gases from the thrust chamber converge down gradually to a minimum area called the throat of the nozzle. The throat size is chosen to choke the flow and set the mass flow rate through the thruster

system. The profile of the linear nozzle is defined by three sections, namely, a converging section, curved throat section with a radius of curvature, and a diverging section. The converging section should have a smooth and well-rounded contour. So, a convergent cone-angle of 45° and a convergent area ratio of 4 was chosen for the design. Other design parameters such as the radius of curvature at the throat and the divergent half-angle were optimized for the 5N nozzle taken form Ref [2] as RoC = 1.5 and 𝛼 = 15°. The design methodology adopted in Ref [1] was adopted in this nozzle also.

Surface area-to-Volume ratio:

The surface area-to-volume ratio of a nozzle is in inverse proportion with the square root of its design thrust. Even the geometric parameters of the nozzle have effects on the surface-to-volume ratio for a given thrust. Investigations were carried out to understand the effect of the aspect ratio of 2D rectangular nozzles on this ratio (Figs. 2 & 3). Increase in nozzle surface area leads to a dominating frictional flow resistance resulting in reduced thrust and a higher weight penalty to the satellite. Fig. 3 reveals that the surface-to-volume ratio was least for the nozzles with aspect ratios between 0.75 to 1.75.

Fig. 2: Flow volume inside various aspect ratio rectangular linear nozzles. Note that the geometries

include a run-up of 4mm length (Images not to scale)

Fig. 3: Effect of its surface-to-volume ratio of the 5N Mach 2 rectangular nozzle on throat aspect ratio

Numerical Analyses and Discussions

Computational Fluid Dynamics had been employed to analyse such flows in a rectangular, linear 5N thrust class Mach 2 micronozzle for space applications. The simulated nozzle is the one to be used for ground simulation of the actual space nozzle. Therefore, it is to be operated at a higher inlet stagnation pressure than that in space to avoid flow separation, with discharge into an ambient pressure of 7kPa. The ground simulation nozzle was tested in a special nozzle test facility which enabled discharge into a reduced ambient pressure of 7kPa. The flow conditions are represented in Fig. 4. The 3D nozzles were modelled and meshed in GAMBIT and CFD analyses were carried out using ANSYS FLUENT 14.0 on the platform CSIR-4PI: ALTIX ICE P400 EX supercomputer. FLUENT and Tecplot 360 were used for post processing. The turbulence model used was k-ω SST. The computations were successfully carried out for different aspect ratio geometries with sharp corners and filleted corner nozzles. The nozzle with aspect ratio 1.25 was chosen for the corner fillet study and it was named AR1.25 for convenience. The computational flow domain and the boundary conditions applied for the simulations are illustrated in Fig. 5.

Fig. 4: Geometry and operating conditions represented for the nozzle with Aspect Ratio 1.25

Fig. 5: Flow domain and applied boundary conditions for the 5N Mach 2 rectangular linear nozzle

Computations revealed that there were negligible differences between cold flow simulations (𝑇0

= 300K, medium air) and hot flow simulations (𝑇0 = 1700K, medium = decomposition products of a blended HAN monopropellant). Moreover, the thrust and Isp efficiencies show a similar trend for hot and

cold flows, as evidenced in Fig. 6. Hence, nearly all the computations were carried out for cold flow simulation. Fig. 7 shows the Mach contours in cut-plane side and top views of the nozzle. Here, the efficiency of any performance parameter was defined as a ratio of its CFD value to the ideal value from isentropic calculations.

Fig. 6: Comparison between hot and cold flow operations of variation in performance parameters with the aspect ratio between 1 to 1.5 of the 5N Mach 2 rectangular linear nozzle (a) thrust efficiency and

(b) Isp efficiency (𝑃0=312.5 kPa; 𝑝𝑎= 7 kPa; 𝑇0= 1700 K(Hot), 300K(Cold); Medium = Air)

Fig. 7: Cut-plane side and top views showing the Mach number contours of 5N Mach 2 rectangular

nozzle (AR = 1.25; 𝑃0= 312.5 kPa; 𝑝𝑎= 7 kPa; 𝑇0= 300 K; Medium = Air)

The AR1.25 nozzle was simulated at lower throat Reynolds numbers to ascertain the effects on the boundary layer during the start-up and shut-down phases. Figs. 8a and 8b show the comparison of the subsonic boundary layers at the throat and nozzle exit sections of the AR1.25 nozzle for operations at Re = 3,64,000 and Re = 52,000, respectively for a back pressure of 7 kPa. Figs. 8c shows the operation at Re = 5,900 for a back pressure of 0.1 kPa (near vacuum simulation).

Fig. 8: Subsonic Mach number contours compared at throat and exit at (a) 𝑃0= 312.5 kPa; (b) 𝑃0= 45

kPa for 5N Mach 2 rectangular nozzle (AR = 1.25; 𝑝𝑎= 7 kPa; 𝑇0= 300 K; Medium = Air);

(c) 𝑃0= 5 kPa (AR = 1.25; 𝑝𝑎= 0.1 kPa; 𝑇0= 300 K; Medium = Air)

Figs. 9a and 9b show the variation of thrust efficiency and Isp efficiency and Fig. 10 show the

total pressure loss with an increase in aspect ratio from 0.25 to 2.5. Nozzle total pressure loss was observed to be below 3% for the geometries with aspect ratios beyond 1. For all the computational simulations, the surface roughness was maintained constant using the standard sand-grain roughness model in ANSYS FLUENT in which the roughness height and roughness constant were specified as 0mm & 0.5 mm respectively to simulate a smooth surface for all cases.

Fig. 9: Variation of performance parameters with the aspect ratio of the 5N Mach 2 rectangular linear nozzle (a) thrust efficiency and (b) Isp efficiency. (𝑃0=312.5 kPa; 𝑝𝑎= 7 kPa; 𝑇0= 300 K; Medium = Air)

Fig. 10: Variation of % total pressure loss with aspect ratio of the 5N Mach 2 rectangular linear nozzle

(𝑃0=312.5 kPa; 𝑝𝑎= 7 kPa; 𝑇0= 300 K; Medium = Air)

The corner fillet radius was varied from 10% to 40% of the hydraulic diameter at the nozzle throat as illustrated in Fig. 11 and the results were analysed. The reduction in cross sectional area due to corner filleting obviously leads to a reduction in the thrust produced. The ideal thrust was recalculated for the reduced throat area for the thrust efficiency calculations. Fig. 12 shows the variation of the thrust efficiency and Isp efficiency with the filleting radii.

Fig. 11: Flow volume inside various AR1.25 nozzle with various corner fillet radii. Note that the fillet

radius is defined as a fraction of the throat hydraulic diameter (Images not to scale)

Fig. 12: Variation of performance parameters with the corner fillet radius of 5N Mach 2 rectangular

linear AR1.25 nozzle (a) thrust efficiency and (b) Isp efficiency. (𝑃0= 312.5 kPa; 𝑝𝑎= 7 kPa; 𝑇0= 300 K;

Medium = Air)

Concluding Remarks

Computational analyses of the flow in 5N thrust class Mach 2 rectangular linear nozzles of various aspect ratios were carried out to evaluate their performances. The variations in thrust efficiency and Isp efficiency were found to be negligible beyond an aspect ratio of 1.5. When the nozzle was

operated at a lower throat Reynolds number, the subsonic boundary layer at the nozzle exit grew bigger, i.e., at the start and shut-off phases of the nozzle operation it would have thicker boundary layers at the exit, although no significant differences in this thickness was evidenced at the nozzle throat. This effect was also evidenced for a near start-up/shut-off simulation for space operation and the subsonic boundary layer was found to be more thicker than that for the ground operation.

The corner fillet effects were quite counter-intuitive as they do have degrading effects on the nozzle performance. Approximately 3-4% reduction in thrust and Isp efficiencies were observed. So,

the null hypothesis could be eliminated as such and the alternative hypothesis stands valid for the study. It can be inferred from Fig. 12 that there is a critical point beyond which the fillet radius doesn’t have any effect on the nozzle performance, which for the present case was around 10% of the throat hydraulic diameter. Therefore, corner filleting could be ascertained as a design option for specific thruster applications where the reduced thrust can be compensated by design optimization while maintaining the throat aspect ratio; in addition, manufacturing considerations also need to be taken into account. A finite non-zero value of surface roughness is also inevitable from the manufacturing aspect.

Acknowledgements

This work has been carried out as part of the project “Developmental Studies on Hydroxyl Ammonium Nitrate (HAN)-based Monopropellant Microthrusters” sponsored by the Propulsion Panel, AR&DB, Ministry of Defence, Govt. of India. The authors thank the Director, CSIR-NAL for permitting the work to be carried out. The first author also thanks the Director CSIR-NAL and Head, Propulsion Division, CSIR-NAL for permitting him to help carry out this work as part of his ME dissertation.

References

[1] Vijaya Sankaran. K, et al., “Performance Characteristics of the Supersonic Nozzle of a 10N Class Pulsed Micro thruster employed for Satellite Orbital Corrections.” 18th CFD Annual Symposium, August 10-11, 2016, CSIR-NAL Bangalore.

[2] Mukesh K, et al., “Design of the Propelling Nozzle of a 5N Thrust Class HAN based Monopropellant Microthruster.” Project Document, PD-PR-2018-1001.February, 2018. Propulsion Division, CSIR-NAL Bangalore.