JOURNAL OF PROPULSION AND POWER

Vol. 29, No. 5, September–October 2013

Numerical and Experimental Investigation of Unidirectional

Vortex Injection in Hybrid Rocket Engines

N. Bellomo,∗ F. Barato,† M. Faenza,‡ M. Lazzarin,§ A. Bettella,¶ and D. Pavarin**

University of Padua, 35131 Padova, Italy
DOI: 10.2514/1.B34506
A study on vortex injection in hybrid rocket engines with nitrous oxide and paraffin has been performed. The
investigation followed two paths: first, the flowfield was simulated with a commercial computational fluid dynamics
code; then, burn tests were performed on a laboratory-scale rocket. The computational fluid dynamics analysis had
the dual purpose to help the design of the laboratory motor and to understand the physics underlying the vortex flow
coupled with the combustion process compared with axial injection. Vortex injection produces a more diffuse flame in
the combustion chamber and improves the mixing process of the reactants, both aspects concurring to increase the c

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efficiency. A helical streamline develops downstream of the injection region, and the pitch is highly influenced by
combustion, which straightens the flow due to the acceleration in the axial direction imposed by the temperature rise.
Experimental tests with similar geometry have been performed. Measured performance shows an increase in
regression rate up to 51% and a c
efficiency that rises from less than 80% with axial injection up to more than 90%
with vortex injection. Moreover, a reduction of the instabilities in the chamber pressure has been measured.

Nomenclature some drawbacks, such as low-regression rate and efficiency. These

At = nozzle throat area drawbacks have limited the widespread use of hybrids. The low-
a = multiplication coefficient for regression rate regression rate is related to the blocking effect in the grain surface,
Gox = mass flux in combustion chamber which limits the heat transfer to the fuel wall. The low efficiency is
Lg = grain length due to the typical features of hybrid combustion. In fact, the oxidizer
Mf = mass of burned fuel and the fuel enter in the combustion chamber from different paths,
Mm = molar mass and they burn within a characteristic boundary-layer diffusion flame.
m_ tot = mean total mass flow In this way, the efficiency is limited by the amount of mixing in the
n = exponential coefficient for regression rate turbulent boundary layer.
O∕F = oxidizer to fuel mass ratio In the last decades, vortex injection has been proposed as a possible
p, pc = pressure, mean chamber pressure solution to both the main hybrid drawbacks. Vortex injection
Ru = universal gas constant increases the wall heat flux and the turbulent mixing. In this way, it is
r = radial coordinate possible to achieve high values of regression rate and efficiency.
T = temperature Several researchers tested various types of swirl injection, among
t = time which were Knuth et al. [1–3], Yuasa et al. [4], Masugi et al. [5], Myre
u r , uz , uθ = radial, tangential, and axial velocity et al. [6], and Gomes et al. [7].
z = axial coordinate A survey of swirl and vortex hybrid studies is given in [8]. A con-
μ = dynamic viscosity current numerical and analytical activity has been carried out [9–12].
ρf = density of fuel Considering single circular port hybrid engines, two main types of
ρ = density vortex injection can be defined in relation to the injector location.
ϕi , ϕe , ϕm = initial, final, and mean diameter of the grain One is the head-end vortex injection (also called unidirectional),
ω = vortex angular velocity and the other is the aft-end vortex injection (or bidirectional). In the
head-end injection, the oxidizer enters the chamber at the same
position of a classical hybrid rocket, but with a strong tangential
I. Introduction component. The fluid particles flow through the port from the head
end to the nozzle following a helical path.
H YBRID rockets present several advantages compared with
solid and liquid ones, mainly simplicity, safety, low cost,
reliability, and throttling capabilities. However, hybrids have also
In contrast, in the aft-end injection tested by Knuth et al. [1–3] the
swirling oxidizer enters the chamber just upstream of the converging
part of the nozzle. This configuration generates a pair of coaxial
bidirectional vortices in the combustion port. The outer vortex spirals
Presented as Paper 2011-5675 at the 47th AIAA/ASME/SAE/ASEE Joint toward the head end of the motor across the fuel surface, mixing and
Propulsion Conference & Exhibit, San Diego, CA, 31 July–3 August 2011; burning with the pyrolyzed fuels. At the head end, the vortex flows
received 11 November 2011; revision received 30 March 2013; accepted for inward toward the motor axis and forms an inner vortex, which spirals
publication 14 April 2013; published online 18 June 2013. Copyright © 2013
by the American Institute of Aeronautics and Astronautics, Inc. All rights
downward and out of the nozzle.
reserved. Copies of this paper may be made for personal or internal use, on Most of the previous works is about gaseous injection. However, in
condition that the copier pay the $10.00 per-copy fee to the Copyright almost all applications the oxidizer has to be stored in liquid phase in
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include order to achieve a good density impulse. Few experiments have been
the code 1533-3876/13 and $10.00 in correspondence with the CCC. performed with liquid vortex injection. Some of them have been
*Research Fellow, CISAS G. Colombo; nicolas.bellomo@unipd.it. discussed by Kitagawa et al. [13] using liquid oxygen (LOX) and by
†
Research Fellow, CISAS G. Colombo; francesco.barato@studenti.unipd. Pucci [14] and Wilkinson et al. [15] using nitrous oxide. The results
it. of these works seem to indicate that nitrous oxide gives better results,
‡
Ph.D. Student, CISAS G. Colombo; martina.faenza@studenti.unipd.it.
§
Research Fellow, CISAS G. Colombo; marta.lazzarin@unipd.it.
probably because it decomposes exothermically whereas LOX is
¶
Researcher, Department of Mechanical Engineering, CISAS G. Colombo; much more difficult to vaporize.
alberto.bettella@unipd.it. In the present paper, a vortex injector is used to enhance the
**Researcher, Department of Mechanical Engineering, CISAS G. performance of a hybrid rocket engine with paraffin as fuel and
Colombo; daniele.pavarin@unipd.it. nitrous oxide as oxidizer. As far as the authors know, this is the first
1097
 1098 BELLOMO ET AL.

time that liquid vortex injection has been used with a liquefying applied in the throat and injection regions. The number of elements is
propellant. Paraffin wax permits very high regression rates due to 1.9 × 106 .
entrainment of liquid droplets. In this work, a further increase in Details of the mesh are presented in Fig. 2. This setup is the result
the regression rate has been achieved with the combination of of a convergence analysis that indicated a need of a finer mesh
entrainment and vortex flow. An increase of more than 10% in (0.1 mm element dimension) in the nozzle throat and injection
combustion efficiency has been demonstrated. zone with respect to the remaining fluid volume (1 mm element
Meanwhile, the fluid flow inside the vortex hybrid has been dimension). The axial and tangential velocity components in the
studied analytically and numerically, particularly by means of middle of the combustion chamber at 3 mm from the grain surface
computational fluid dynamics (CFD) simulations. These simulations and the average values of temperature and pressure have been used
revealed some interesting features like the presence of a forced vortex for the analysis. Convergence has been considered as achieved when
flowfield and highlighted the mechanism of swirl decay, the main all increments between two different meshes in the previously
cause being the axial acceleration of the fluid due to combustion. mentioned variables were below 3%.
First, the numerical analysis will be presented, followed by the The oxidizer is N2 O injected at 25°C, whereas the fuel is paraffin
descriptions of the experimental results. injected at 725 K already decomposed using the following reaction:
Cn H2n
2 → H2
n∕2 C2 H4 . The fuel temperature has been
II. Numerical Investigation selected for simplicity as the paraffin normal boiling temperature.
The real surface temperature of the regressing fuel was unknown, but
The fluid field has been investigated with a commercial CFD code. a sensitivity analysis in the expected range has been performed
The purpose was to study the main differences in the flow using two
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showing a negligible influence on the results.

injector types, one axial injector (classical shower head) and a vortex The boundary conditions are an inlet with fixed mass flow on the
one. surfaces where fuel and oxidizer are injected, an outlet with fixed
Another aim was also to understand vortex behavior in the pressure at 1 bar at the nozzle exit, and a wall with no slip condition on
combustion chamber and the main parameters of influence. These the other surfaces. In the simulations without the nozzle, an opening
simulations, also, helped in the design of the injector and burn tests, condition was defined where the flow exits. A reference chamber
defining important features like orifice diameter and position. pressure of 25 bar was imposed.
The turbulence model used is k-ε with scalable wall functions. All
A. Simulation Setup spatial numerical schemes are at least second order.
The geometry consists in a cylindrical combustion chamber, a In the vortex case, the injection channels are oversized with respect
conical nozzle, and a swirl injector plate. Injectors are modeled as six to the true ones, because the simplification of gaseous oxidizer
channels oriented in order to introduce the oxidizer with both an axial would have led to a too-high injection velocity (near unitary Mach
and a tangential component (see Fig. 1). The oxidizer is injected with number). A similitude with liquid injection has been calculated with
an angle of 45 deg with respect to the main axis of the motor. The fuel the following scheme: the mass flow has been extrapolated from
is injected from the lateral surface of the cylinder (dark area in Fig. 1), experiments; given temperature and pressure in the tank, density can
with a specified mass flow rate identified experimentally. Two kinds be calculated; then, actual hole dimension and mass flow permit us to
of simulations have been performed, with and without nozzle, to evaluate the velocity in the injection holes. The hole diameter used in
evaluate the effect of this component in straightening the flow lines the simulations is estimated using the same mass flow and velocity of
due to the acceleration of the fluid. It will be shown later that the pitch the liquid case, but with density given from the ideal gas law.
of the helical fluid flow is not constant but can vary depending on From real holes of 1.2 mm in diameter, the “gaseous” holes have a
geometry, the effect of combustion heating, and the presence of the diameter of 4.95 mm. In the axial injection simulation, the area from
nozzle after the combustion chamber. which the oxidizer enters the combustion chamber is the whole
The mesh is unstructured and elements are tetrahedral, with a circumference that generates the cylinder. This has been observed to
maximum size of 1 mm; smaller elements up to 0.3 mm have been be a better choice than injection from single channels, comparing the

Fig. 1 Fluid flow geometry: a) details on injection and b) whole geometry with fuel injection.

Fig. 2 CFD mesh: a) detail of the injection area and b) side section view of the entire mesh.
 BELLOMO ET AL. 1099
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Fig. 3 Comparison between CFD chemistry formula and thermochemical calculations from CEA: a) molar fractions, b) mass fractions, and c) percent
difference.

solutions with a simulation with liquid injection and vaporization an impingement zone near the injection location, a swirl zone along
[16]. In fact, in the axial case the gas flow resulting from droplets the grain, and finally the exit zone.
evaporation has already a more uniform advancing front at a much Near the injection, the flow is not fully stabilized, the oxidizer is
lower velocity than the injection one. ejected from the holes and strikes the chamber surfaces, and it is then
The chemistry of the flame is treated with the eddy dissipation bent and follows the curvature of the grain; backflow is present.
model. The reaction formula is the following: 151N2 O
25C2 H4 → In the grain zone, the motion is stabilized, the fluid follows a helical
148N2
23CO2
27CO
40H2 O
10O2
6NO
10OH
path, and the swirl angle tends to be straightened by various forces
2O
5H2
2H. Products are in decreasing order of mass (discussed later). Near the exit, the swirl angle sharply decreases.
concentration. The selection of the products comes from an analysis The main difference, except the trivial streamlines (shown in
of the combustion with a thermochemical software (CEA), choosing Fig. 5) with a helical shape, is the flame contour shown in Fig. 6.
only those chemical species that have a molar fraction higher than The vortex injection enables a more diffuse flame, enhancing
10−3 . A comparison between the formula applied in these simulations the mixing of the reactants in the combustion chamber. As a
and CEA calculation is shown in Fig. 3. consequence, the burn process is more effective, increasing the
Kinetic effects have not been included in the simulation because efficiency of the rocket. It is important to remark that in this paper the
the combustion regime is driven by diffusion. This solution has term flame refers to the region where hot combustion products are
already been validated in previous works [17] about hybrid rockets present. The zone where the combustion takes place is in contrast
CFD simulations and is justified by the high-Damköhler number. very thin and located near the walls.
The main simplifications are the ideal gas equation (especially not Another feature is a pressure gradient in radial position, but this
proper for N2 O) used for all materials, the fact that the oxidizer is detail will be discussed in the next section.
injected in gaseous state. The fuel is also injected in the gaseous phase The faster the fluid entering the chamber (higher speed means
and already decomposed. The effect of droplet entrainment on the gas lower orifice diameter), the more this effect is enhanced. It has to be
flow is neglected. The chemical reaction is simplified: only one noticed, however, that this simulation has the simplification of
reaction, no backward reactions, no homogeneous decomposition of gaseous injection and does not take into account phenomena like
N2 O due to temperature effect, and no kinetic effect in reaction have cavitation and evaporation, typical of nitrous oxide.
been taken into account. Another important characteristic of the vortex flow is a backflow
current (from now on called rip tide) near the oxidizer injection, in the
B. Numerical Simulations Analysis center of the diameter of the chamber, shown in Fig. 7.
It can be seen that there is a recirculation zone just downstream of
Simulation of vortex injection has been conducted studying the the injector plate due to a low-pressure region, demonstrated
flowfield of the oxidizer in the combustion chamber in many aspects. by Fig. 7d, in which a radial profile of this variable is shown. In
A summary of the simulated cases is reported in Table 1. Fig. 7c, the streamlines in the center are going backward with respect
In all cases, a backflow is present after injection. This is due to low to the external component. This recirculation zone has a volume
pressure between the holes of the injection plate. The fluid field can that decreases going from cold simulation to blowing, hot, and nozzle
be divided in three sections (see Fig. 4), considering velocity profiles: cases.
In Fig. 8, axial and tangential velocity are plotted over an axial line
placed 1 mm away from the grain (12.4 mm from center). Velocity in
Table 1 Simulated cases the nozzle case is scaled according to chamber pressure. It can be
Sim. Description Short name
noticed from the steps that the grain starts after 25 mm from the
no. injection, and it is 190 mm long. In the same line, in Fig. 9 the swirl
A Vortex injection, no nozzle, only oxidizer injected Cold
angle is plotted over all the CFD configurations. This has been
B Vortex injection, no nozzle, fuel injected from grain Blowing defined as
surface but no chemical reactions enabled
C Complete combustion without nozzle Hot

D Complete combustion with nozzle Hot
nozzle uz
E Comparison of case D with axial injection Axial δ  atan (1)
uθ
 1100 BELLOMO ET AL.

Impingement
Exit zone Swirl zone zone

Fig. 4 Vortex fluid flow: zones description.

The variation in axial velocity is low going through the cold test to gradients in the swirl zone are low. Taking into account the relative
the blowing test, with a slight acceleration in this last case due to the gradient, this is still valid when the combustion is considered.
insertion of fluids (the fuel) in the combustion chamber; this Similar considerations can be done for the tangential velocity:
difference is higher when combustion takes place due to the the gradients in the swirl zone are low. However, in this case,
increasing temperature. The effect of the nozzle is negligible the addiction of the chemical reactions does not have a sensible
compared with that of the flow heating. In the first two cases, effect.
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Fig. 5 Streamline comparison in CFD analyses: a) axial injection, b) vortex cold, c) vortex blowing, d) vortex hot, and e) vortex hot plus nozzle; in cold and
blowing simulations, temperature is fixed at 300 K.
 BELLOMO ET AL. 1101
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Fig. 6 Flame temperature profile in axial (left) and vortex (right) injection: temperature profile (upper) in combustion chamber and N2 O mass fraction
(lower).

Considering the swirl angle in Fig. 9, the swirl zone gradients are In Fig. 5, the streamlines for all simulations are shown. In
low, and combustion effect can be seen once again. In this case, taking Fig. 5a, the trivial solution for axial injection is presented, where
into account what is happening to the velocity components, it can be all the lines are straight with a slight bend in the grain zone due to the
concluded that the combustion straightens the streamlines because it fuel injection. In Figs. 5b–5e, the vortex injector effects are
accelerates the axial component of velocity, whereas the tangential presented: as previously expressed (Fig. 9), the effect of combustion
one remains almost the same. It can also be seen that in any case swirl (Figs. 5d and 5e) is to accelerate the axial velocity, and the swirl
angle denotes a rapid decay of about 30% in the precombustion angle is lower compared with cold (Fig. 5b) and blowing (Fig. 5c)
chamber. cases.

Fig. 7 Rip tide effect in vortex injection: a) isosurface of axial velocity equal to 0 m∕s; b) plane after 2 cm from injection axial velocity plotted; c) forward
streamlines from that surface, with color ranged with maximum value at 0 m∕s based on axial velocity; and d) pressure plot after 4 mm from injection.
 1102 BELLOMO ET AL.

Fig. 8 Axial and tangential velocity over an axial line near the grain (distance 1 mm): cold, blowing, hot, and hot plus nozzle cases are compared; the
nozzle case is scaled according to chamber pressure.
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Fig. 9 Swirl angle over an axial line near the grain (distance 1 mm): cold, blowing, hot, and hot plus nozzle cases are compared.

C. Analytical Considerations according to chamber pressure), proving the theory, that there is no
Some important considerations can be done in the vortex fluid flow sliding (same angular velocity) between different radial positions.
using compressible Navier–Stokes equations, neglecting the gravity This is mathematically true when only the oxidizer is injected but is
and normal viscous terms. empirically valid also for the other cases, taking into account the
In cylindrical coordinates, balance in the tangential direction is the effect of the borders of the grain. In particular, it can be seen that the
following: change in tangential velocity is due to 1) friction with chamber walls

 in the cold case, 2) friction with fuel flow in the blowing case (this is
∂uθ ∂u u ∂u ∂u uu less effective, as suggested by the example of the no-friction table
ρ
ur θ
θ θ
uz θ
r θ  with air films), and 3) flame in the hot and hot
nozzle cases. The
∂t ∂r r ∂θ ∂z r

  CFD simulations confirm the forced-vortex behavior of the head-end
1 ∂p 1 ∂ ∂uθ 1 ∂2 uθ ∂2 uθ uθ 2 ∂u injected vortex flow. This fact represents a strong difference with
−
μ r
2 2
2 − 2
2 r (2)
r ∂θ r ∂r ∂r r ∂θ ∂z r r ∂θ respect to the Majdalani solution [12], in which a free vortex prevails.
The reason for this discrepancy is the following. In the aft-injected
Some simplifications can be introduced based on the following vortex (or double vortex) configuration, the fluid begins to go along
assumptions: steady-state flow, axis-symmetry − null derivative over the “wrong direction” so that it has to turn and pass from the outer
the tangential direction, neglected variation of tangential velocity in vortex to the inner vortex to get out of the nozzle. For this reason, a
the z direction, and low radial velocity compared with axial and significant radial velocity is present even when there is no blowing
tangential velocities. These last two assumptions have been validated from the sidewalls. This is in contrast with the case of the head-end
through CFD simulations. swirl flow, in which the fluid proceeds always in the “right” direction
In particular, in Fig. 10 (radial, axial, and tangential velocities over so that no significant radial velocity is present.††
a radial line in the middle of the grain) it is proven that the radial When the radial velocity is nonzero, Eq. (2) could be simplified to
component is negligible. Similar consideration for the gradient in the give an inviscid (free-vortex-type) solution.
axial position can be done using Fig. 8. In contrast, when the radial velocity is negligible it is necessary to
Equation (2) becomes retain the viscous terms in Eq. (2); otherwise, the equation would

 vanish completely. This fact explains why the two vortex injection
1 ∂ ∂u u
r θ − 2θ  0 (3) configurations have different leading-order solutions (free and forced
r ∂r ∂r r vortex, respectively).
Using this definition [Eq. (4)], we can then calculate angular
The only possible solution is the forced vortex: velocity for all cases (Tables 1 and 2).

ωr  uθ (4) ††
This is not exactly true, because, as shown in the following, a suction
effect exists near the head end that entrains part of the flow, forcing it to turn
where ω refers to the angular velocity of the vortex. It can be seen and move backward. However, this effect does not change the basic forced-
from CFD (Fig. 11, in which for the nozzle case the velocity is scaled vortex motion, as is confirmed by the CFD simulations.
 BELLOMO ET AL. 1103

100 1,003

1,0025
10
Velocity (log scale) [m/s]

1,002

1 1,0015

p/pi ratio
1,001
0,1
1,0005

0,01
1

0,9995
0,001 -15 -10 -5 0 5 10 15
-15 -10 -5 0 5 10 15
Radial position [mm]
Radial position [mm]
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Cold Blowing
tangential radial axial
Fig. 10 Velocity comparison in radial position: line taken at 10 cm from Hot Hot + Nozzle
injection (middle of the grain); velocity in log scale. Fig. 12 Pressure ratio comparison on a diametric line (middle grain):
hot plus nozzle case scaled according to chamber pressure.

18

16 The hypotheses of ideal gas and forced vortex lead to

14 u2θ ∂p ω2 rMm p
ρ   (7)
Tangential velocity [m/s]

12
r ∂r Ru T

10 Introducing the further hypotheses of null chemical and temperature

gradients in the radial direction, the previous equation can be
8 integrated between the center (r  0 and p  pi ) and radial position
6
r, providing


4 ω2 r2 Mm p
 ln (8)
2Ru T pi
2

0

-15 -10 -5 0 5 10 15 ω2 r2 Mm ρ
Radial position [mm]  ln (9)
2Ru T ρi
Cold Blowing
These equations highlight a centrifugal effect due to the rotation of
Hot Hot & nozzle
the flow, pushing the fluid toward the external wall of the combustion
Fig. 11 Tangential velocity comparison over a diametric line taken at
chamber, giving a pressure gradient effect as shown in Figs. 12 and
10 cm from injection (middle of the grain).
13.
Once again, increasing the complexity of the system causes results
In the cylindrical reference frame, balance in radial coordinates to be far from mathematical correctness: adding mass (blowing case)
gives does not give any significant disturbance, but when the combustion
takes place these formulas are no longer valid to predict the pressure

 distribution. However, the shape (increased pressure from center to
∂ur ∂u u ∂u ∂u u2
ρ
u r r
θ r
uz r − θ  walls) is still valid, and so is its effect on the flowfield.
∂t ∂r r ∂θ ∂z r When gradients of temperature or chemical species are present,
 
∂p 1 ∂ur 1∂ u
2
∂ u
2
u 2 ∂u this force acts as a mixer, letting the heaviest components (reactants)
−
μ
2 2r
2r − 2r − 2 θ (5)
∂r r ∂r r ∂θ ∂z r r ∂θ go in the outer part, while pushing the lighter ones (products of
reaction) into the center of the combustion chamber. For this reason,
Applying the same simplification as in the previous equation, we get the flame is more diffuse than using the axial injector (Fig. 6).
An important parameter in the study of swirling flows is the swirl
number. The swirl number is calculated as the nondimensional ratio
u2θ ∂p
ρ  (6) between the axial flux of the swirl momentum and the axial flux of the
r ∂r axial momentum:
R
Table 2 Mean angular velocities ρvz vθ r dA
SN  R
Rmax ρv2z dA
Short name Mean angular velocity, Mean angular velocity,
rad∕s deg ∕s
This swirl number can give information about the relative intensity of
Cold 1371 24 the rotational flow and how it varies along the motor because of
Blowing 1534 27
Hot 2319 40
heating, friction, mass addiction, and section changes.
Hot
nozzle 1987 35 It is possible to define a geometrical swirl number (SNg ) at
injection by the following formula:
 1104 BELLOMO ET AL.

1,003
between port diameter and injection diameter, and the possibility of
burning for the grain frontal face (or its inhibition).
1,0025 It is worth noting that the previous discussions about the
straightening of the streamlines do not hold for the bidirectional
1,002
vortex hybrid. In fact, in this case the axial velocity has an inherently
two-dimensional variation (changing direction passing from the
inner to the outer vortex) and so it is not possible to apply the same
1,0015 one-dimensional approach as previously. Considering a cylindrical
control volume corresponding to a slice of the outer vortex (a three-
p/pi ratio

1,001 dimensional ring), it is possible to show that the axial velocity should
not necessarily increase because of heating and/or mass addition
because some mass continuously escapes from the internal face
1,0005 separating the outer vortex from the inner one (the mantel location).
The Majdalani solution [12] predicts indeed a decrease of the axial
1 velocity in the outer core (as is expected from the boundary condition
of the inert head end, which imposes that the longitudinal velocity
should vanish approaching the head end of the chamber).
0,9995
-15 -10 -5 0 5 10 15
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Radial position [mm] III. Experimental Setup

Cold Theoretical To evaluate the performance of the vortex injection, four kinds of
Fig. 13 Pressure ratio on a diametric line (middle grain): comparison tests have been performed, combining vortex and axial injection with
between cold case and theoretical. pressurized and self-pressurized oxidizers.
In every group, four tests have been conducted, one cold (no grain
in the combustion chamber) and three hot (full combustion) with the
rinj − rport  · rinj
SNg  same configuration, for redundancy. The first was used to evaluate the
N port · r2port injector discharge and mass flow rate and to check the measurement
system.
This parameter is useful to compare different situations without the
need for specific measurements of fluid unknowns. The previous A. Laboratory-Scale Motor Design
equation is valid for a full-tangential (90 deg) injector. In the case of a The motor has been designed in terms of grain port diameter and
mixed axial–tangential injector, the swirl number should be length, tank pressure, and nozzle geometry. The choice to avoid the
multiplied by the sine of the injection angle. The geometrical swirl use of a pre- or postcombustion chamber has been intentional, to
number for the configuration considered in this paper is 22. study the effect of the injection alone.
Liquid injection is affected by a decrease of the swirl number The design had some constraints due to the fact that the
caused by liquid evaporation. In fact, the phase change of a liquid combustion chamber has been refurbished from other previous
oxidizer produces a swirl decay in a similar way as combustion. The experiments in our laboratory. In this view, the injector plate and the
tangential velocity remains nearly constant, whereas the axial maximum diameter of the grain (70 mm) were fixed. Also, the
component should accelerate (as density decreases) to respect the graphite nozzle has been refurbished, with a throat diameter of
continuity equation. Ultimately, the axial velocity after complete 15.7 mm and an exit diameter of 34 mm.
evaporation should be the same as for gaseous-fed engines (for the The rocket consists of the following parts (numbers in parentheses
same general design condition), whereas the injection velocity is refer to Fig. 14): an external combustion chamber (1); an interface
lower. In fact, injection velocity for a gas is on the order of hundreds between injector and hydraulic connections to the oxidizer tank (2);
of meters per second, whereas it is hardly above 50 m∕s for liquids. the rocket head (3), which acts as an interface between 1 and 2; the
Velocities intermediate between the two can be obtained in the case of injector (4); two pressure sensor interfaces (5); the paraffin grain (6);
two phase flows as is expected with self-press oxidizers (like N2 O). the nozzle (7); and its closure system (8 and 9).
As a first approximation, the swirl reduction for liquid evaporation Between 2 and the oxidizer tank is placed an electropneumatic ball
(SNl ) can be estimated in this way: valve.
A preliminary design has been performed using an analytical
ρg transient code to simulate the burn. The process was iterative, using
SNl  SNg the CFD simulations to develop the best injector dimensions in terms
ρl
of number of holes, size, and position in the injection face of the
combustion chamber; initial diameter of the port area; and grain
With this correction, the swirl number drops to 1.7. length. The results lead to a grain with an initial diameter of 25 mm
However, this simplified treatment considers a uniform fluid and a length of 190 mm. The injector has six holes of 1.2 mm in
mixture changing its density along the axial direction without taking diameter and 5.5 mm in length, placed over a circumference of 17 mm
into account the complex effect of droplets evaporation (two-phase in diameter. Detailed CAD drawings can be found in Fig. 15.
flow), and so the results should be taken in a qualitative manner. The injectors are made of stainless steel (AISI 316L).
Ultimately, the swirl number and its distribution along the axis The 45 deg mixed axial–tangential injector design was selected
have a crucial influence on engine performances and regression because it could fit on the already existing setup (hydraulics) without
uniformity. Considering the latter point, experimental results are major changes (as would be necessary for a full tangential injector).
contrasting. Some researchers found a pretty uniform burn along the All of the burn process during the tests is driven by a real-time
grain, whereas some others noted a strong consumption near the controller. Paraffin grain is manufactured using Parasur wax, casted
injection end. in a cylindrical mold. After cooling in air, it is extracted and finished
This fact is dependent on the complex flowfield that establishes in in a turning machine to achieve the correct dimensions.
the region between the injector and the initial part of the grain, which The measurement system is shown in Fig. 16, and composed of
can vary considerably from case to case. In particular, a critical aspect three pressure sensors and one temperature sensor (thermocouple J
is the eventual direct impingement of the oxidizer flow on the grain type after the oxidizer injection valve). One extensimetric pressure
surface, which usually induces a strong local increase of the heat flux transducer from Gefran, model TPSA, full scale 100 bar, accuracy
in the corresponding region. Finally, the resulting behavior is related 0.15%, and response time less than 1 ms, has been placed after the
to the geometry of the prechamber, the injection angle, the ratio oxidizer injection valve. Two piezoresistive pressure transducers
 BELLOMO ET AL. 1105

Fig. 14 Laboratory-scale rocket CAD drawing (in mm).

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Fig. 15 Injectors CAD drawing: a) axial injector and b) vortex injector (in mm).

from Kistler, model 4260A, full scale 70 bar, accuracy 0.1%, and igniter that takes fire with an applied overvoltage. Then, the oxidizer
response time less than 1 ms, have been placed in the combustion valve is opened after 3.5 s from the igniter start. The chamber pressure
chamber, one near injection and one near the nozzle. achieves its nominal value nearly 0.1 s after the valve signal.
Between pressure sensors in the combustion chamber and their
respective interface, a tube filled with water has been placed, to B. Feed Line Apparatus
protect them against high-temperature flow. Postprocessing fast The feed line is composed of a tank (different in pressurized and
Fourier transform (FFT) of the signal proved, according to theory, self-pressurized tests) and an electropneumatic ball valve.
that in this way the signal is not filtered by the liquid medium in The pressurized tests have been performed using a steel tank with a
comparison with the tube filled with air.
sliding piston inside (see Fig. 17), dividing the internal volume in two
Avideo camera was placed behind the rocket, to record every burn.
parts: one with the N2 O and the other with N2 at fixed pressure using a
Another one, but with high-speed recoding capabilities (420 fps), was
pressure regulator connected to a 200 bar tank.
placed aside from the nozzle, to record the plume.
The chosen pressure in the tank is 80 bar. After the filling of the
The rocket test bed was supported by two linear guides and linked
N2 O in the tank, the temperature is raised with a thermal electric
to ground with a load cell from Laumas, model CTOL, 300 kg of full
blanket to 25°C. Three J-type thermocouple sensors, placed at ¼, ½,
scale, with an accuracy of 0.03% full scale (FS), used to measure the
and ¾ of the tank height, are used to measure the temperature in the
thrust.
oxidizer side, coupled with a Gefran TK pressure sensor, accuracy
The rocket is ignited with a solid charge inserted directly in the
0.3% FS.
combustion chamber from the nozzle and fixed to the grain surface.
During the discharge, data on temperature, pressure, and position
The ignition starts thanks to an electric resistance inserted in the
of the piston allow calculation of the mass flow rate in the transient
regime.
Injection pressure Chamber pressure
Injection In the self-pressurized configuration, a fiberglass tank with an
and temperature sensors
aluminum liner is directly connected to the injection valve. Also, in
this configuration a thermal electric blanket is used to raise the
temperature in the tank to 25°C, to achieve an internal pressure of

Oxidizer tank N2O side

Linear
potentiometer

N2O
outlet
N2
inlet

Feed line Motor case N2 side Piston

Fig. 16 Laboratory-scale rocket operative configuration. Fig. 17 Pressurized tank schematics.
 1106 BELLOMO ET AL.
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Fig. 18 Hydraulic circuit schematics: a) self-pressurized and b) pressurized; tank filling line and safety systems are intentionally excluded from
drawings.

56.33 bar and a density of 744 kg∕m3 . For repeatability reasons, in Efficiency is calculated using a thermochemical software (CEA),
every test the same amount of N2 O has been charged (6 kg). retrieving theoretical characteristic velocity. Experimental character-
In this case, the mass flow is not measured during the transient istic velocity is evaluated as
phase but as the difference between the mass of the tank before and
after the burn divided by the burn time. The mass is measured with a pc · At
c  (10)
load cell (Laumas SL, 15 kg FS, accuracy 0.02%); it is not possible to m_tot
measure the mass of the tank during the transient phase because of the
noise in the measurement induced by the vibrations generated by the where pc is the value measured by the sensor placed slightly before
rocket during the burn. In Fig. 18a schematics of the hydraulic circuit the nozzle. In the self-pressurized test, it was not possible to measure
is proposed. the transient oxidizer mass flow; for this reason, the average value
was used.
After this process, a FFT is used to analyze the frequency domain
IV. Data Analysis of pressure and thrust signal. Data from the power spectrum are used
After each burn, data about thrust and pressure in the combustion to evaluate characteristic hybrid frequencies.
chamber, upstream of the injector and in the tank, are saved with a
sampling frequency of 1 kHz. In the pressurized tests, also the linear B. Regression Rate Analysis
position of the piston inside the tank is acquired, whereas in the self- Regression rate is evaluated with the Gox based on port diameter
pressurized tests the tank weight is recorded. Temperature data are mean, following [18]:
sampled at 10 Hz. A balance is used to measure the grain weight
s
before and after the burn, whereas with a decimal caliper the grain 4Mf
length and initial diameter have been obtained. ϕe 
ϕ2i (11)
πρf Lg
A. Data Reduction ϕe − ϕi
r_  (12)
The burn time is calculated observing the rise and descent phase of tb
the pressure in the combustion chamber. It is not possible to use the
valve actuation time, because this does not take into account the time 16m_ ox
Gox  (13)
lag of the valve movement or the chamber discharge. Usually, 0.3 s is πϕe
ϕi 2
the difference between valve actuation time (3 s) and burn time.
The oxidizer mass discharged during test in the self-pressurized r_
a (14)
configuration is calculated taking the average weight of the tank Gnox
before and after the burn. The average mass flow rate is calculated
dividing it by the burning time. In pressurized tests, the piston The number of tests was not sufficient to determine both regression
position gives the volume occupied by N2 O in the tank, whereas rate coefficients, a and n. For this reason, the value of n used in the
temperature and pressure data are fitted using NIST data to retrieve calculations was supposed equal to 0.5. This number comes out from
density; these values give the mass of the oxidizer, and a derivative is the observation of the chamber pressure during the burn, which
used to calculate the mass flow in the transient. These data, together remains constant when the mass flow is constant (pressure-regulated
with the fuel burnt mass, are used to evaluate mean total mass flow case, see Fig. 19). Moreover, this is also a typical value for the
and O∕F ratio. combination of N2O/paraffin hybrid rockets [19].
Regression rate analysis is then carried out, which is explained in These values have also been calculated with a methodology that
detail in the next section. takes into account the thrust termination response [18], using an
Then, an instability analysis is performed: a convenient time iterative process. First, the time lag in the valve response has to be
interval in the signal pressure is chosen, eliminating the ignition calculated, using the valve signal from the PLC and the rise time in the
transient, the beginning of the burn, and the thrust termination effect. injection pressure (see Fig. 20). The same lag time is applied to the
A linear least-squares fitting is performed, and the difference between valve closing time, with the hypothesis of the same time to open and
the fitting line and the measured pressure valued is used to estimate close a ball valve. From this point (valve closing effect) up to the end
the error. The standard deviation of the fitting and its ratio with burning (null pressure in chamber), pressure data are fitted with an
average chamber pressure is representative of instability. exponential law:
 BELLOMO ET AL. 1107
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Fig. 19 Chamber pressure during pressurized test: the dot and cross represent the initial and final burning times, respectively.

Fig. 20 Valve closure effect.

pfit  p0 · e−t∕τc (15) C. Uncertainty Analysis

Uncertainty analysis has been performed using the classical Kline–
McClintock rule [20]; in general, if z is a function of x and y
p0 is evaluated as the average of the last 0.2 s of the chamber parameters, it is possible to write (i means uncertainty)
pressure before the valve closing effect. A typical value of τc is 0.15 s, s
but in the author’s algorithm it has been evaluated at each burn. An
2
2
∂z ∂z
iterative method (in the following formulas, i is the iteration number) iz  i
i (20)
∂x x ∂y y
is used to obtain new values for oxidizer mass flux, end diameter,
regression rate, and its a coefficient:
It has to be noted that this is a first-order approximation and that the
16m _ ox hypothesis of no correlation between x and y is implicit in this
Gox;i  (16) formulation. Then, relative error E is computed:
πϕe;i−1
ϕi 2
  s



∂z ix 2 ∂z iy 2
1
2n
1 2n
1 _ 2n
1 iz
ϕe;i · n · τc ai−1 mnox e−n c − 1
ϕ2n
1
t∕τ
 (17) Ez   x
y
n π f;i−1 z ∂x x ∂y Y
s

2
2
ϕf;i − ϕs ∂z ∂z
r_i  (18)  xE
yE (21)
2tb;eff ∂x x ∂y y

Uncertainties retrieved from direct measurements are shown in

r_i
ai  (19) Table 3.
Gnox;i In self-pressurized tests, oxidizer mass before and after the burn is
obtained using mean values in a certain time period, and standard
A maximum of 10 iterations are sufficient for convergence, defined as deviation is used as uncertainty.
the maximum residual of the variable of interest, with a threshold of In regression rate analysis, relative errors can be found in [18,21].
10−5 . For uncertainties, after some simplifications, formulas are
 1108 BELLOMO ET AL.


2
2
2
ϕi 2 2Mf
iϕe  i
i
iϕ
ϕe ϕs πρLg ϕe ϕMf πρ2 Lg ϕe ρ

2 1∕2
2Mf

iϕ (22)
πρL2g ϕe Lg
 2
2 1∕2
ϕ
ϕ2 r_
iϕe  i 2 e
itb (23)
4tb tb

2
2 1∕2
2Gox Gox
iϕe  · ϕ2i
ϕ2e 2
im_ (24)
ϕe
ϕi m
_

V. Results and Discussion

A preliminary three-burn test campaign with 4 s of burning time
was conducted with a vortex injector, but the regression rate was
considerably higher than expected and the grain was almost
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completely consumed. Then, the burning time was reduced to 3 s. No

major problems have been found during tests, except in one case (test
18) with self-pressurized oxidizer and vortex injection, where the
mass of the tank has not been correctly measured due to a misleading
lecture in the load cell. In some cases, cold flow has been performed
instead of the hot test, due to a failure in the ignition. When this event
Fig. 21 Paraffin grain after burn test: a) vortex injection and b) axial
occurred, the grain after the oxidizer discharge has been checked, and injection; oxidizer comes from the right.
because it was always in perfect condition it was used for the
following tests. Test data are summarized in the Appendix
Tables A1–A4. It was not possible to give a value to both the discharge coefficients
Usually, test comparisons are performed with a similar O∕F ratio due to the nature of nitrous oxide that tends to cavitate inside the
and reducing the length of the grain in case of higher regression rates. orifices and does not follow a precise liquid or gaseous behavior.
In our case, instead, it has to be noticed that the rocket dimensions are
the same in all tests and only the injector is changed. This is due to the
B. Regression Rate
poor knowledge of regression rate coefficients with vortex flow.
Regression rate analysis has been performed both taking into
account or not the thrust termination effect. Results are summarized
A. Injector Discharge
in Table 5.
The most important thing to notice in Table 4 is the discharge An increment in regression rate can be seen when using vortex
coefficient of the two injectors. injection. The increase is on the order of 51% in the pressurized case
In all cases (pressurized and self-pressurized tank), axial injection and 36% in the self-pressurized case. It has to be noticed that
has a higher mass flow rate than the vortex case also if chamber and
regression rate is higher also if oxidizer mass flux is lower (−33 and
tank pressures are equivalent, meaning a higher injector discharge
−39%). This last decrement is related to two reasons: one is the lower
coefficient. The hypothesis is that in the axial case after the feed line
mean mass flow rate (−12 and −26%), and the other is the larger
the fluid is only forced to enter a small orifice, whereas in vortex it
mean diameter because of the increased regression rate.
also has to change direction.
It is important then to evaluate the coefficients of the regression
rate equations (14) and (19), with the hypothesis of n  0.5 justified
Table 3 Variable uncertainties
by observation of the pressurized tests where the pressure in
Variable Uncertainty combustion chamber remains constant when oxidizer mass flow is
Grain initial diameter 0.1 mm constant. Calculations give an increment of the a coefficient of 84%
Grain length 0.1 mm in the pressurized tests and 75% in the self-pressurized tests.
Burned fuel mass 2g Some considerations may also be done on the grain shape after the
Fuel density 0.1 kg∕m3 burn. In Fig. 21, the classical hollow cylinder grain with axial
Burning time 0.1 s injection is shown. Comparing this with the picture in Fig. 21a, it can
be noticed that there are traces of the flow in the combustion chamber

Table 4 Oxidizer mass flow comparison

Type Mean tank pressure, bar Mean chamber pressure, bar Mean Δp (tank–chamber), bar Mean N2O mass flow, g∕s
Vortex pres. 77 23 54 272
Axial pres. 76 22 54 307
Vortex self-pres. 55 11 44 125
Axial self-pres. 58 12 46 169

Table 5 Regression rate data

Type Mean O∕F Mean Gox , Mean Gox enhanced, Reg. rate, Reg. rate enhanced, a coeff., a coeff. enhanced,
kg∕m2 · s kg∕m2 · s mm∕s mm∕s mm∕s mm∕s
Vortex pres. 2.48 203 210 4.85 5.09 0.3405 0.3514
Axial pres. 4.93 305 314 3.21 3.37 0.1843 0.1907
Vortex self-pres. 1.47 108 111 4.03 4.17 0.3882 0.3951
Axial self-pres. 3.03 178 183 2.94 3.05 0.2209 0.2262
 BELLOMO ET AL. 1109

Table 6 Measured and theoretical (CEA) efficiency Two mechanisms have been identified: a more diffuse flame
compared with the axial injection and a rip tide effect downstream of
Type Measured c, m∕s Theoretical c, m∕s Efficiency, %
the injector plate. The first is due to the helical flow that causes
Vortex pres. 1184 1294 92 centrifugal forces pushing the flame toward the grain walls. The
Axial pres. 1164 1541 76
Vortex self-pres. 1048 1147 90 second effect is shown in Fig. 22. As explained in the CFD section,
Axial self-pres. 1058 1352 78 there is a helical flow in the first part of the combustion chamber that
comes back, due to the low pressure in the center of the grain near the
orifices of the injector.
that remain in the grain. The pitch of the helical flow is increasing, as Figure 22b shows the axial velocity right after (2 mm) the injection.
demonstrated by CFD analysis in previous sections. The upper limit of the scale is limited to 0 m∕s to evidence the
The fuel consumption is not constant, but it increases sharply in the backflow. This flow takes also some unburned paraffin wax, as shown
first part, where the flow comes out from the injector orifices and in Fig. 22a: this is a picture of the injector after a burn, and the black
strikes on the grain surface, leaving clear marks. substance that covers the metal is unburned paraffin wax, ripped off
from the grain surface in the impingement zone.
C. Efficiency An important concern with swirling flows through nozzles is the
blocking effect on the mass flow caused by the centrifugal forces
An increase of the efficiency has been measured using vortex opposing the fluid approaching the throat. Several authors have
injection, as shown in Table 6. investigated this subject and developed some analytical solutions
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Fig. 22 Comparison between a) vortex injector after the burn and b) CFD simulation of the same burn.

Fig. 23 Chamber pressure plot: comparison between axial (upper) and vortex (lower) and pressurized (left) and self-pressurized (right).
 1110 BELLOMO ET AL.

Table 7 Linear fitting and instability analysis could determine a roll reaction on the propulsion unit. However, this
effect has been estimated as negligible in the current case. The use of a
Type STD (3σ) from pressure STD (3σ) from pressure
linear fitting, bar linear fitting, % mixer that disrupts the swirling flow before the nozzle entrance could
prevent the previous issues.
Vortex pres. 0.53 2.2
Axial pres. 1.52 6.4
Vortex self-pres. 0.27 2.2 D. Instability
Axial autopres. 0.86 6.5 Instability analysis starts from Fig. 23. Pressure in the combustion
chamber is plotted in representative cases for all combinations of
oxidizer pressurization type and injector. On the right, there are the
[22–25]. Those models have been used in this work to estimate the self-pressurized tests: it is possible to recognize the typical longer
effect of the swirling flow on the nozzle discharge coefficient. ignition time.
The input values needed for the calculations have been taken from Comparing the vortex injection (lower images) with the axial
the CFD simulations at a location slightly before the nozzle entrance. injection (upper images), it is evident that the chamber pressure is
The analytical models based on the free-vortex hypothesis give a constant in the first group, whereas a small rise is present in the latter.
higher blocking effect than those based on a forced-vortex solution. A tool has been used to retrieve some measurements of the instability
However, in the current cases all the predictions fall well below behavior for the tests: linear least-squares fittings. With this aid, it has
(pressure amplification <1%) the uncertainties in the experimental been shown that the vortex injection helps the pressure to remain
measurements. stable (see Table 7).
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The simulations show also a straightening of the streamlines From the comparison between thrust and pressure in combustion
passing though the nozzle because of the strong longitudinal chamber, it appears that something outside the nozzle throat had
acceleration. The flow exits with a little swirl component, and this some interference with the measurements. Possible causes are the

Fig. 24 Vortex flow simulation: fluid line detail in the nozzle.

Fig. 25 Vortex burn test, fast camera frames: pictures taken with a time step of 0.03 s.
 BELLOMO ET AL. 1111
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Fig. 26 FFT analysis: comparison between thrust (left) and pressure (right) signals.

interaction of the swirling flow with the nozzle or the outer ambient: combustion is considered, due to an increase in the axial velocity
the rocket has been placed in a container for safety reasons, and the given by the higher chamber temperature.
flow exits in a tube that ends in a noise suppressor device. Experimental investigations have been performed, considering
In Fig. 24, a CFD simulation of a vortex hybrid rocket is shown. It both self-pressurized and pressurized oxidizers. In both cases, the
can be seen from the image on the left that outside the nozzle a expected increase in efficiency has been proven. It has been shown,
tangential component of the velocity is still present. also, that the instability in the combustion chamber was lower than in
In Fig. 25, pictures are taken with a fast camera (420 fps) and the axial injection case. An increase in regression rate up to 51% has
reported every 0.03 s. Shock diamonds downstream of the nozzle been measured.
have been observed. There is a flame that surrounds the main plume Some issues in thrust measurements have been found that need
and rotates around it. further investigation: high impulses have been shown in the thrust
In axial injection, this phenomenon is not present. It must be clear profile, not reported in the pressure data in the combustion chamber;
that this is not an instability in the combustion chamber, comparing the hypothesis is that this is due to an effect of the helical flow outside
the FFT signal of the pressure and thrust measurement (Fig. 26), but the nozzle or to the interaction of the plume with the noise suppressor
something that needs further investigation linked to the flow device placed downstream.
downstream of the nozzle throat. Future research will investigate a wider range of operating
It was a singular fact that the thrust impulses were fully audible and conditions (e.g., chamber pressures, mass fluxes, and injection
very clear, with a sound similar to a hammer beat. velocity) and different swirl injectors. In particular, it would be
interesting to compare the results obtained so far by the 45 deg mixed
axial–tangential injector with those of a full tangential injector.
Moreover, the use of a mixer will be considered to further enhance the
VI. Conclusions efficiency and disrupt the swirling flow before the nozzle entrance.
A numerical and experimental investigation about vortex injection This work has confirmed the potential of the combination of
in a hybrid rocket engine with nitrous oxide as oxidizer and paraffin paraffin wax and vortex injection to increase substantially the
as fuel has been performed. In both analyses, a comparison with performance of hybrid rocket engines. The simplicity of a single port
classical axial shower-head injection has been investigated. geometry and self-pressurization together with cheap and
The purpose of computational fluid dynamics has been to help in environmentally friendly propellants could pave the way for several
the design of the experiments and to understand the main potential applications, for example, the implementation of reusable
characteristics of a vortex flowfield in terms of its effects due to fuel and affordable sounding rockets. For such an application, the paraffin
injection and combustion, particularly in comparison with an axial fuel formulations tested at the Center for Studies and Activities for
injection. In particular, it has been noticed that the flame in the vortex Space, G. Colombo, University of Padua, have demonstrated
motor is more diffuse and the helical streamline enhances the mixing satisfactory mechanical properties and melting temperature
(>80°C).
of reactants, increasing the efficiency. It has been observed from cold
flow analyses that the typical streamline of a vortex injector has a
helical shape and that the pitch tends to get larger when the Appendix: Burn Test Data

Table A1 Burn test data: mean value, part 1

Type Measured N20 Wax Mean Mean Mean Mean Gox Reg. Reg. rate a a coeff
burning burned, burned, N20 O∕F Gox , enhanced, rate, enhanced, coeff, enhanced,
time, s g g mass kg∕m2 · s kg∕m2 · s mm∕s mm∕s mm∕s mm∕s
flow,
g∕s
Vortex 3,37 917 370 272 2,48 203 210 4,85 5,09 0,34 0,35
pres.
Axial pres. 3,38 1039 213 307 4,93 305 314 3,21 3,37 0,18 0,19
Vortex 3,32 414 281 125 1,47 108 111 4,03 4,17 0,39 0,40
self-pres.
Axial 3,35 568 188 169 3,03 178 183 2,94 3,05 0,22 0,23
self-pres.
 1112 BELLOMO ET AL.

Table A2 Burn test data: mean value, part 2

Type Mean tank Mean chamber STD (3σ) from STD (3σ) from Mean Δp (tank– Measured Theoretical Efficiency, Mean
pressure, bar pressure, bar pressure linear fitting, pressure linear Chamber), bar c, m∕s c, m∕s % thrust,
bar fitting, % N
Vortex 77 23 0,53 2,2 54 1184 1294 92 758
pres.
Axial 76 22 1,52 6,4 54 1164 1541 76 727
pres.
Vortex 55 11 0,27 2,2 44 1048 1147 90 395
self-
pres.
Axial 58 12 0,86 6,5 46 1058 1352 78 392
self-
pres.

Table A3 Burn test data: part 1

Test Type Measured N20 Wax Mean N20 Mean Mean Gox , Mean Gox Reg. Reg. rate a a coeff
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burning burned, burned, mass flow, O∕F kg∕m2 · s enhanced, rate, enhanced, coeff, enhanced,
time, s g g g∕s kg∕m2 · s mm∕s mm∕s mm∕s mm∕s
6 Vortex 3,35 906 345 271 2,626 209 217 4,64 4,84 0,321 0,329
pres.
7 Vortex 3,34 915 379 274 2,414 201 208 4,98 5,21 0,351 0,361
pres.
8 Vortex 3,43 931 387 272 2,407 198 206 4,92 5,23 0,350 0,364
pres.
11 Axial 3,37 1074 190 319 5,651 332 341 2,95 3,09 0,162 0,167
pres.
13 Axial 3,41 1032 214 303 4,821 299 308 3,20 3,38 0,185 0,192
pres.
14 Axial 3,36 1012 235 301 4,305 285 294 3,48 3,64 0,206 0,213
pres.
17 Vortex 3,32 414 281 125 1,474 108 111 4,03 4,17 0,388 0,395
self-
pres.
21 Axial 3,33 584 175 175 3,335 189 194 2,80 2,90 0,203 0,208
self-
pres.
23 Axial 3,35 554 198 165 2,797 169 174 3,06 3,18 0,235 0,241
self-
pres.
24 Axial 3,37 565 191 168 2,959 175 180 2,96 3,08 0,224 0,230
self-
pres.

Table A4 Burn test data, part 2

Test Type Mean tank Mean STD (3σ) from STD (3σ) from Mean Δp Measured Theoretical Efficiency, Mean
pressure, chamber pressure linear pressure linear (tank– c, m∕s c, m∕s % thrust,
bar pressure, bar fitting, bar fitting, % Chamber), bar N
6 Vortex 77,3 23,5 0,53 2,2 53,8 1221 1308 93,36 764
pres.
7 Vortex 76,9 23,4 0,64 2,6 53,5 1170 1286 90,99 762
pres.
8 Vortex 77,8 23,1 0,41 1,7 54,7 1161 1287 90,22 748
pres.
11 Axial 76,4 22,1 2,04 8,7 54,3 1143 1580 72,34 744
pres.
13 Axial 76,6 22,0 1,15 4,9 54,7 1167 1541 75,74 711
pres.
14 Axial 76,4 22,6 1,38 5,7 53,8 1183 1503 78,67 726
pres.
17 Vortex 55,3 11,3 0,27 2,2 44,0 1048 1147 89,57 395
self-
pres.
21 Axial 57,4 12,1 1,6 12,1 45,3 1029 1393 73,92 360
self-
pres.
23 Axial 58,3 12,4 0,41 3,1 45,9 1069 1323 80,81 366
self-
pres.
24 Axial 58,0 12,4 0,58 4,3 45,5 1076 1340 80,32 449
self-
pres.
 BELLOMO ET AL. 1113

Acknowledgments No. 2103, 2009, pp. 915–935.

doi:10.1098/rspa.2008.0342
The research leading to these results has received funding from the [12] Majdalani, J., “Vortex Injection Hybrid Rockets,” Fundamentals of
European Community’s Seventh Framework Programme (FP7- Hybrid Rocket Combustion and Propulsion, edited by Kuo, K., and
SPACE-2010-1) under grant no. 262837 of the Space Exploration Chiaverini, M. J., Progress in Astronautics and Aeronautics, AIAA,
Research for Throttable Advanced Engine project. The authors thank Washington, D.C., 2007, pp. 247–276.
Federico Moretto, Enrico Geremia, and Marco Frasson, from the [13] Kitagawa, K., Mitsutani, T., Ro, T., and Yuasa, S., “Effects of Swirling
Center for Studies and Activities for Space, G. Colombo, University Liquid Oxygen Flow on Combustion of a Hybrid Rocket Engine,” 40th
of Padua, for their precious contribution to the test campaign, grain AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit,
manufacturing, and data analysis. Finally, the authors thank Stefano AIAA, Reston, VA, 2004; also AIAA Paper 2004-3479.
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