ArticlePDF Available

Abstract and Figures

We investigate the flow in planar microscale nozzles and find that design and analysis paradigms based on the assumption of a dominant isentropic core with moderate viscosity corrections are not valid. Instead, the flow downstream of the throat is dominated by boundary layers that may choke the flow to subsonic velocities. The geometrical expansion ratio is found to be essentially irrelevant, instead, the length from throat to exit plane is found to be a much more important design parameter. Full 3D simulations are required to predict the flow topology; thermophysical modeling of the expanding gas has a noticeable impact on predicted performance. An analytical estimation of the Knudsen number in the expanding flow is given, allowing to determine its values from the expansion pressure ratio. An axial thrust analysis suggest truncation of the nozzle, resulting in a predicted 20% increase in thrust and 30% increase in specific impulse compared to the baseline configuration. The work has been carried out within the European Commission co-funded PRECISE project which was focused on designing and testing a micro chemical propulsion system thruster prototype using catalytically decomposed hydrazine as propellant.
Content may be subject to copyright.
Flow characteristics of monopropellant
micro-scale planar nozzles
Daniel T. Banutia,
, Martin Grabea, Klaus Hannemanna
aGerman Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology,
Spacecraft Department, G¨ottingen, Bunsenstr. 10, Germany
We investigate the flow in planar microscale nozzles and find that design and
analysis paradigms based on the assumption of a dominant isentropic core with
moderate viscosity corrections are not valid. Instead, the flow downstream of
the throat is dominated by boundary layers that may choke the flow to subsonic
velocities. The geometrical expansion ratio is found to be essentially irrelevant,
instead, the length from throat to exit plane is found to be a much more im-
portant design parameter. Full 3D simulations are required to predict the flow
topology; thermophysical modeling of the expanding gas has a noticeable impact
on predicted performance. An analytical estimation of the Knudsen number in
the expanding flow is given, allowing to determine its values from the expansion
pressure ratio. An axial thrust analysis suggest truncation of the nozzle, result-
ing in a predicted 20% increase in thrust and 30% increase in specific impulse
compared to the baseline configuration. The work has been carried out within
the European Commission co-funded PRECISE project which was focused on
designing and testing a micro chemical propulsion system thruster prototype
using catalytically decomposed hydrazine as propellant.
Keywords: MEMS, rocket engine, hydrazine, cube sat, satellite, propulsion
Corresponding author, email:; Currently at Caltech, Pasadena, CA
91125, USA
Preprint submitted to Elsevier October 20, 2018
1 Introduction 2
2 Methods 4
3 Preliminary analysis 7
3.1 Thruster configuration . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Rocket performance fundamentals . . . . . . . . . . . . . . . . . 8
3.3 Thermochemical analysis . . . . . . . . . . . . . . . . . . . . . . 9
3.3.1 Hydrazine decomposition . . . . . . . . . . . . . . . . . . 10
3.3.2 Heat loss and composition . . . . . . . . . . . . . . . . . . 10
3.4 Analytical assessment of nozzle flow properties . . . . . . . . . . 12
3.4.1 Nozzle Knudsen number . . . . . . . . . . . . . . . . . . . 13
4 Simulations 15
4.1 Conditions............................... 15
4.2 Effects of geometry and composition . . . . . . . . . . . . . . . . 16
4.3 Analysis of the baseline nozzle . . . . . . . . . . . . . . . . . . . 20
4.4 Truncatednozzle ........................... 22
5 Conclusion 24
6 Acknowledgments 24
1. Introduction
Interest in micro chemical propulsion systems (µCPS) is growing with the
beginning commoditization of small scale satellites (Marcu [28]). This is fur-
ther facilitated by the the recent surge in cheap launch systems that allow for
more launch opportunities, e.g. SpaceX, and by companies that develop launch-
ers particularly for the small satellite market, e.g. Vector, RocketLab, Virgin
The European Commission co-funded project PRECISE (Gauer et al. [9,
10]) focused on designing and testing a µCPS thruster for application in a for-
mation flying mission. The thruster was developed to use MEMS technology
to etch µCPS nozzles and combustion chambers into silicon wafers like com-
puter chips, allowing for cheap and scalable mass production. The prototype
was designed to use catalytically decomposed monopropellant (hydrazine1) to
achieve high performance using a simple propulsion system. Owing to the man-
ufacturing method, such engines exhibit characteristics which set them apart
from macro scale nozzles. The two-dimensional geometry of high aspect ratio
etched geometries differs radically from classical rotationally symmetric nozzles,
impacting design procedures and performance evaluation.
A number of small scale engines and nozzles have been investigated experi-
mentally and numerically [16, 21, 1, 26], in 2D [35, 30, 13] and 3D [16, 35, 1, 26].
Rarefaction is of prime importance outside of the nozzle, for example for plume-
structure interaction [26]. Its effect is found to be negligible for integral perfor-
mance measures, such as thrust [13, 7, 26, 25]. Exit pressures exceeding 1 kPa
are used to ensure the validity of continuum models using Navier-Stokes equa-
tions with no-slip boundary conditions [13, 7]; these models are even used at
exit pressures of 50 Pa [19] and 0 Pa [6].
However, analyses are typically based on evaluation of constant property
pure ideal gases, thus the impact of variable properties has not been assessed.
Furthermore, a Knudsen number analysis can typically only be performed a
posteriori [13].
In the present paper, we extend these studies to the case of a monopropellant.
In a preliminary study, we demonstrate the impact of the composition and the
thermo-chemical modeling of the exhaust gas. We show how gas temperature
affects the monopropellant decomposition, and derive a closed form estimation
of the nozzle core flow Knudsen number. Finally, we evaluate 3D nozzle flow and
introduce an improved nozzle that outperforms the baseline contoured nozzle
by 30%.
1While hydrazine is considered hazardous, this choice was a boundary condition in the
PRECISE project due to its performance and the prior experience of the project partners
with this propellant.
2. Methods
A combination of methods is used for the present study. The preliminary
analysis in Sec. 3 is carried out using a combination of numerical and analytical
approaches. Specifically, equilibrium chemistry is evaluated using CEA [29, 12].
The simulation results discussed in Sec. 4 were obtained using the DLR TAU
code, a hybrid grid, finite volume, compressible CFD solver developed by the
German Aerospace Center (DLR). For the flow conditions investigated herein
(chamber pressure 10 bar, exit pressure ratio of p0/pe= 30) we assume that
continuum flow governed by the Navier-Stokes equations with no-slip boundary
conditions is applicable, consistent with [7, 13, 6, 19].
The DLR TAU code has been validated for various space propulsion cases,
including high-pressure gaseous combustion [17], cryogenic transcritical combus-
tion [2], combustion instabilities [3], and scramjets [20, 22]. Detailed descriptions
of the solver can be found in Gerhold [11], Schwamborn et al. [31], Mack and
Hannemann [27], Hannemann [14], and Karl [20].
The system of governing equations is solved using a Godunov type finite
volume method. Second order spatial accuracy is obtained using MUSCL re-
construction at cell interfaces [34]. We use Liou’s AUSMDV Riemann solver
[24]. The Spalart-Allmaras [32] turbulence model is used in a RANS framework.
A mixture of chemically reacting ideal gases is governed by the Navier-Stokes
equations. Reynolds decomposition to total and partial densities and Favre de-
composition to the remaining flow variables yields the set of equations to solve
numerically. In integral form, they read
∂t ZZZ
SdV . (1)
Here, ~
Uis the vector of conservative variables
The inviscid Euler fluxes can be written as
Finv =
accompanied by the viscous terms
Fvisc =
(ρD)eff Tρs
keff TT+ (ρD)eff PshsTρs
ρ+ (P ~u)T
The viscous stress tensor Pis modeled according to the Stokes hypothesis,
P=µ~uT+ (~uT)T2
3µ(T~u)I. (5)
Using the Spalart-Allmaras turbulence model, an additional equation for eddy
viscosity µtis solved. The effective species diffusion (ρD)eff is modeled using
the laminar (without subscript) and turbulent (subscript t) Schmidt numbers
(ρD)eff =µ
Sc +µt
The effective thermal conductivity is similarly calculated using the Prandtl num-
keff =k+kt=k+Pr
µk. (7)
The Dufour effect (thermal diffusion due to concentration gradient) is taken into
account. The source terms ~
Sinclude the chemical contribution to the species
transport equations ωs,
Here, as we only regard frozen flow, ωs0 and no sub grid scale filters are
Chemical equilibrium calculations are carried out using CEA (Gordon and
McBride [29, 12]). Fluid models for N2H4, NH3, N2, H2have been identified and
integrated into the TAU solver. We chose the NASA 7-coefficient polynomial
expressions [5] as our caloric fluid models, as given by
P,i/R0=a1,i +a2,iT+a3,i T2+a4,iT3+a5,i T4,(9)
i/R0T=a1,i +a2,iT
5+a6,i/T . (10)
Blottner et al. curve fits [4] are used to calculate species laminar viscosity,
µs= 1 Ns
The individual values are then combined using Wilke’s mixing rule [36]
81 + Ms
Mm1/2"1 + µs
Thermal conductivity is computed using a modification of the Eucken correction
by Hirschfelder et al. [15]
s+ (cv)vib
s+ (cv)e
Sc .(14)
The mixture heat conductivity is then determined following Zipperer and Hern-
ing [37],
The diffusion fluxes are calculated from viscosity and a constant Schmidt num-
ber using Fick’s law. Then, the diffusion coefficient Dreads
Sc (16)
Caloric data were available for all concerned species. Transport coefficients
were not available for N2H4. Due to its apparent similarity to water, data of
the latter have been used for gaseous hydrazine. Validation has been carried
out by comparison with the NIST database [23]2. Again, no data were available
for hydrazine.
2Data are not available for the whole temperature range. Upper limits in the database for
hydrogen, nitrogen, and ammonia are 1000 K, 2000 K, and 700 K, respectively.
Figure 1: Ratio of specific heats temperature dependence for hydrazine decomposition prod-
ucts hydrogen, nitrogen, and ammonia. γ= 1.4 corresponds to calorically perfect hydrogen
and nitrogen; γ= 1.33 corresponds to calorically perfect ammonia.
Figure 1 compares the CEA based TAU model with NIST reference data.
Lowering of γfor increasing temperature is due to the successive excitation of
molecular degrees of freedom. In the case of ammonia, a larger discrepancy has
been found between data obtained from CEA and data from NIST (open green
triangles in Fig. 1). For lower pressures (1 bar) the agreement is found to be
much better (open circles in Fig. 1). Due to the ideal gas modeling within TAU,
high pressure effects might not be captured. However, the discrepancy arises at
conditions of simultaneous high pressures and low temperatures, which we do
not expect to encounter: the high pressure, high temperature gas in the com-
bustion chamber expands in the nozzle to a low pressure, low temperature state,
and will hence not affect actual performance analysis of the µCPS thruster.
3. Preliminary analysis
In this section, we will perform a brief initial investigation of the µCPS. First,
we introduce the geometry and operating conditions; second, we review briefly
rocket performance metrics; third, we study the possible variation of exhaust
gas properties and their impact on performance; fourth, we derive expressions
for nozzle Knudsen and Reynolds numbers.
3.1. Thruster configuration
Figure 2 is a schematic of the thruster. The geometry is etched into silicon,
resulting in a high aspect ratio, rectangular cross section. The exit width is
1.070 mm, the distance from throat to exit is 2.250 mm, the throat width is
0.09 mm, the depth of the nozzle is 0.07 mm. Liquid hydrazine is supplied
through the feedline and vaporized in the vaporization chamber (1). The vapor
is then distributed and injected into the chamber (2), where it passes through
a catalyst bed (3). We assume the flow is frozen afterwards. The present paper
focuses on the expansion of the flow from the plenum (4), through the throat
(5) and the parabolic nozzle (6), until the nozzle exit (7). Expansion of the
plume (8) is not considered here.
Figure 2: Schematic of µCPS thruster.
3.2. Rocket performance fundamentals
The standard measures of rocket performance [33] will be briefly introduced,
before we proceed to analyze the µCPS. The thrust Fis the force that the engine
exerts on the spacecraft. In integral form, it is a function of axial velocity u,
the pressure p, and a reference area A,
(ρuu +p)dA. (17)
The specific impulse, Isp , is a measure of global efficiency, relating fuel mass
flow ˙mto thrust F, using the standard acceleration g0,
Isp =F
As common in engineering, the global efficiency can be expressed as the product
of the inner efficiencies, i.e. quality of combustion measured as chamber pressure
p0acting on the nozzle throat area A,
and the thrust coefficient, measuring the quality of expansion through the noz-
Isp =cFc
The exit velocity uecan be calculated assuming 1D isentropic flow with constant
using the exit pressure pe, the ratio of specific heats γ, the molar mass M, and
the universal gas constant R. The maximum velocity that can be achieved for
pe0 is
umax =s2γ
Equations (22,23) show that fluid properties affect thruster performance via
the isentropic exponent γand the molar mass Mof the exhaust gas. We will
now proceed to investigate the range of γand Mwe expect in our thruster, and
the corresponding impact on performance.
In the following, we consider the thrust and the specific impulse as our
measures of performance. Due to the essentially constant mass flow rates, both
are proportional and can be considered synonymous in this study.
3.3. Thermochemical analysis
We can determine the exhaust gas composition and properties assuming
chemical equilibrium from the CEA [29, 12] package.
µ0.4462e-4 Pa s
ρ0.9590 kg/m3
T1340.15 K
M10.685 g/mol
p10.0 bar
Table 1: Conditions for decomposed hydrazine in chemical equilibrium at 10 bar.
3.3.1. Hydrazine decomposition
The micro liquid propellant rocket engine is designed to use hydrazine as
a monopropellant; the reaction is initiated in a catalyst bed. In a first step,
hydrazine decomposes exothermally into NH3and N2[8],
3N2H44NH3+ N2336,280 J.(24)
Subsequently, NH3decomposes endothermally into N2and H2:
4NH32N2+ 6H2+ 184,400 J.(25)
The global reaction can be characterized by the reaction scheme
3N2H44(1 ξ)NH3+ (1 + 2ξ)N2+ 6ξH2(26)
where ξdenotes the degree of ammonia decomposition. As ammonia dissocia-
tion is an endothermic reaction, ξeffectively controls the attained temperature.
The exhaust gas composition is determined by the degree of hydrazine decom-
At the nominal chamber pressure of 10 bar, chemical equilibrium yields the
fluid properties compiled in Table 1.
3.3.2. Heat loss and composition
Given the extreme volume-to-surface ratios encountered in planar micro-
scale configurations, heat transfer to the structure can have a large impact
on the flow conditions [26]. In the case of the µCPS, the walls will heat up
during operation. Initially, this will lead to a substantially reduced temperature
in the combustion chamber, until a sufficiently heated structure reduces heat
flux. Removing heat from the chamber will influence the reaction and thus the
mixture composition.
Figure 3: CEA chemical equilibrium calculation of hydrazine decomposition; products de-
pending on temperature (10 bar chamber pressure).
Figure 3 shows how the equilibrium composition changes at a nominal cham-
ber pressure of 10 bar over a temperature range from 200 K to 1500 K. Depletion
of hydrazine is complete for all equilibrium states. If the chamber walls are adi-
abatic, a temperature of 1340.15 K is reached. As can be seen, this operation
point corresponds to completely dissociated ammonia. All other states shown
in Fig. 3 can be arrived at by subsequent removal or addition of heat. The equi-
librium composition remains unchanged for temperatures exceeding 1000 K,
recombination of NH3occurs for lower temperatures until hydrogen is depleted.
Note that N2H4will not be formed again in equilibrium once it is decomposed.
Exit velocity and thus efficiency depend on molar mass and reservoir temper-
ature, as shown in Fig. 4. The mean molar mass decreases monotonically with
decreasing NH3fraction, as more and more H2molecules are formed with rising
temperature. The isentropic exponent behaves in a more complex manner. The
small isentropic exponent of NH3is reduced with rising temperature. At the
same time, the mass fraction of NH3reduces as it is consumed and H2and N2,
with their relatively high isentropic exponents, are formed. Once no NH3is left,
Figure 4: Molar mass M, isentropic exponent γ, and resulting Isp for equilibrium composition.
γreduces monotonous with rising temperature. Finally, these effects combine
to a specific impulse that grows monotonously with rising temperature.
It can be seen that heat loss in the combustion chamber which leads to lower
temperatures will give rise to a change in gas composition and a reduction in
efficiency. Vice versa, if the gas is heated beyond the adiabatic flame temper-
ature, the specific impulse can be increased (e.g. electrothermally enhanced
hydrazine thruster).
Figure 5 shows the sensitivity of the maximum exhaust velocity on γ. The
molar mass is chosen exemplarily to cover the extremes and the mid-range value
achieved for hydrazine decomposition (see Fig. 4), the chamber temperature
corresponds to equilibrium hydrazine decomposition at 10 bar T0= 1340.15 K,
determined using CEA.
3.4. Analytical assessment of nozzle flow properties
The goal of this section is to derive simple expressions that allow us to esti-
mate the core flow Knudsen and Reynolds numbers from the chamber, through
the nozzle throat, to the nozzle exit. This can be useful in determining the
numerical models to be used for CFD simulations.
Figure 5: Influence of ratio of specific heats γon theoretical maximum exhaust velocity for
hydrazine decomposition at 1340.15 K.
3.4.1. Nozzle Knudsen number
The Knudsen number is a nondimensional measure of the deviation from
continuum behavior in a flow. It is defined as the ratio of the molecular mean
free path λand a characteristic length scale Lin the flow,
Kn = λ
The mean free path can be calculated as a function of the viscosity µ, the density
ρ, the temperature T, the molar mass M, and the gas constant R,
2RT .(28)
Then, the ratio of two Knudsen numbers in frozen flow can be expressed as
In order to interpret this Knudsen number ratio in a nozzle flow, we express each
of the terms in Eq. (29) as a function of the pressure ratio assuming isentropic
expansion. Kinetic theory suggests that the viscosity ratio can be expressed in
terms of the temperature ratio [18] and thus a pressure ratio,
γ1.2 1.35 1.4 1.67
p0/p1.77 1.86 1.89 2.05
λ01.58 1.54 1.53 1.47
Table 2: Ratios of pressure and mean free path at nozzle throat.
The density ratio yields
and the temperature ratio becomes
Then, the ratio of the mean free paths can be written as
and the Knudsen number ratio is
At the nozzle throat, denoted by , (T0/T ) = 1
2(γ+ 1), so that
Lγ+ 1
For a γof 1.35 this can readily be evaluated to
Kn0= 1.54 L0
Figure 6 shows the evolution of the ration of mean free paths from the
pressure ratio. With knowledge of the geometry, a local Knudsen number can
be determined. Throat conditions are compiled in Table 2.
This method allows to estimate the Knudsen number a priori using Table 1
with Eqs. (27), (28), (34), and (35). Here, we calculate the chamber Knudsen
number as Kn0= 0.0258, the throat Knudsen number as Kn= 0.0399, and
the exit Knudsen number as Kne= 0.2806. These results are consistent with
values from the literature obtained from simulations [7, 30].
Pressure ratio p0/p1
Ratio of mean free paths 1/ 0
= 1.2
= 1.35
= 1.4
= 1.67
Figure 6: Ratio of mean free paths in expanding nozzle flow from Eq. (33) (solid lines); throat
conditions from Eq. (35) (symbols); exit condition for µCPS (vertical dashed line).
4. Simulations
4.1. Conditions
The nominal engine discussed in [9, 10] has a mass flow of ˙m= 5 g/s and
a thrust of 10 mN. We calculate a number of test cases to study the impact
of the geometrical and thermo-chemical models, and to see whether the initial
design goals were met. Figure 7 shows the computational mesh; a quarter of the
physical domain is calculated, taking advantage of symmetries. The chamber
pressure is 10 bar with an exit pressure ratio of p0/pe= 30, ensuring continuum
flow, consistent with [7, 13, 6, 19].
Figure 7: Mesh
We consider two compositions, one in chemical equilibrium, and one with
ξ= 0.5. Computations of chemical equilibrium composition and properties have
ξ= 0.5 Equilibrium
Chemistry Frozen Frozen
YN2 0.5833 0.8738
YH2 0.0625 0.1257
YNH3 0.3542 0.0005
Table 3: Composition of the two considered states.
Case Geometry Properties Composition
I 2D planar inviscid equilibrium
II 2D rotational inviscid equilibrium
III 2D planar viscous equilibrium
IV 2D rotational viscous equilibrium
V 3D quarter viscous equilibrium
VI 3D quarter viscous, perfect gas equilibrium
VII 3D quarter viscous ξ= 0.5
Table 4: Overview of computational cases.
been carried out using the CEA code by Gordon and McBride [29, 12]. Table 3
shows species mass fractions of both states.
Table 4 gives an overview of the test matrix. In all cases, the composition
does not change. In order to assess the impact of composition, the chamber
temperature is held constant to the equilibrium temperature. To account for
wall heating during operation, a constant wall temperature of 800 K is set.
Table 5 summarizes these conditions.
The differences between the 2D planar, 2D rotational, and 3D quarter config-
urations are illustrated in Fig. 8, along with the respective boundary conditions.
In all cases, the contoured wall is a no-slip wall. Symmetry boundary condi-
tions are used based on the expected symmetric averaged flow field in a RANS
4.2. Effects of geometry and composition
Figure 9 compares flowfields for rotational 2D, planar 2D, and 3D compu-
tations, comparing viscous and inviscid results. It is impressive how any of
the simplified approaches Figs. 9(b) to 9(c) grossly overestimates the achieved
pressure outlet
total pressure
no-slip wall
symmetry planesymmetry plane
no-slip wall
(symmetry plane)
(a) 3D quarter and 2D planar. The
bottom is a no-slip wall in 3D, and a
symmetry plane in the 2D planar case.
no-slip wall periodic
axisymmetry axis
total pressure
pressure outlet
(b) Rotational. Computed is a 1
slice of the whole domain using pe-
riodic boundary conditions in az-
imuthal direction.
Figure 8: Boundary conditions.
Propellant N2H4(g)
Chemistry Frozen
T01340.15 K
Twall 800 K
p010.0 bar
Table 5: Flow conditions.
velocity compared to the appropriate 3D computation, Figs. 9(e) and 9(f).
The difference is not merely quantitative: using a more realistic representa-
tion, the whole topology of the flow field is qualitatively changed, it no longer
expand continuously towards the exit. Instead, the axial velocity reaches a local
maximum after a quarter nozzle length downstream of the throat. Boundary
layers grow from all walls, a separation bubble with a recirculation zone forms
in the nozzle.
The effect of composition modeling shown in Fig. 10 is less pronounced but
noticeable. Figure 5 shows that the exit velocity will increase with decreasing γ
(a) I: 2D planar, inviscid.
(b) II:2D rotational, inviscid.
(c) III: 2D planar, viscous.
(d) IV: 2D rotational, viscous.
(e) V: 3D viscous, center plane.
(f) V: 3D isometric view of quarter nozzle.
(g) Axial velocity scale in m/s.
Figure 9: Comparison of geometrical model influence on velocity distributions.
and M. The ξ= 0.5 case exhibits poor performance, consistent with its higher
molar mass caused by hydrogen still being bound in the ammonia molecule. The
perfect gas case VI exhibits reduced performance compared to the base case V
because of the higher isentropic exponent, see Fig. 1.
(a) V: equilibrium (b) VI: perfect gas (c) VII: ξ= 0.5
(d) Axial velocity scale in m/s.
Figure 10: Influence of composition on velocity distribution.
Table 6 compares key parameters such as mass flow, thrust, specific impulse,
and axial exit velocity for cases I through VII. In addition, the overall maximum
axial velocity umax and the position x(umax) where it is reached are given. None
of the cases reaches the nominal mass flow of 5 g/s; only the 2D cases reach
thrusts exceeding 10 mN. This is likely caused by the unobstructed expansion,
allowing to reach the maximum velocity towards or at the end of the nozzle.
Notably, the viscous rotationally symmetric case develops substantial boundary
layers that interact when growing inwards, while they grow independently in
the planar case.
However, when the realistic 3D geometry with boundary layers growing from
all walls is taken into account, the predicted thrust decreases by 30%, reaching
a mere 7 mN in the equilibrium composition cases. Clearly, 2D simulations are
not suited for performance predictions of micro scale planar nozzles. We will
continue with a more in-depth analysis of case V, the highest fidelity model.
Case ˙m F Isp ueumax x(umax)
in mg/s in mN in s in m/s in m/s in mm
I 4.40 11.0 256.0 2457.3 2457.3 2.25
II 4.69 12.4 269.9 2665.5 2665.5 2.25
III 4.31 10.4 246.7 2423.6 2423.6 2.25
IV 4.61 10.5 233.3 2567.6 2568.4 2.08
V 4.39 7.09 164.8 1153.5 2013.7 0.49
VI 4.30 6.91 163.8 1115.2 1992.9 0.47
VII 4.73 4.20 148.2 1036.8 1854.0 0.55
Table 6: Results of test matrix computations.
4.3. Analysis of the baseline nozzle
Figure 11 shows the baseline 3D result of case V in more detail for further
analysis. The height of the nozzle is vertically stretched twentyfold to aid clarity.
Contours on the 5 vertical slices perpendicular to the nozzle axis are again axial
velocity. The arrows show the velocity vector. The red convoluted plane marks
the Mach 1 isosurface.
Following the flow from the reservoir (left) to the nozzle exit (right), we
see how the initial homogeneous velocity distribution is accelerated towards
the throat. Before passing through the throat, the flow is subsonic. At the
throat, the boundary layer acts to prevent the wall near part of the flow to
reach supersonic velocities. Downstream, the boundary layers grow, stronger
from the planar bottom plane than from the contoured side wall. Less than
half the nozzle height exhibits the undisturbed maximum velocity at the first
slice after the throat. Further downstream, this core is diminished until it has
disappeared in the last two slices. The velocity distribution does not change
after the core is gone, resembling fully developed pipe flow. At the mid of the
nozzle, the bottom boundary layer has expanded to take up more than half of
the nozzle height. Close to the nozzle exit, they grow together, almost choking
the whole cross section. Finally, the flow expands right at the exit towards the
boundary condition.
How does this qualitative view translate into actual nozzle performance? As
Figure 11: 3D view of quarter nozzle. Bottom and back planes are viscous walls, top and front
planes are symmetry axes. Contours are axial velocity in m/s. The red plane is the Mach 1
isosurface. The plot is vertically stretched twentyfold to aid clarity.
shown above, the acceleration of the flow is our ultimately desired action, as it
determines thrust. Contrary to classical macro scale rotational nozzles, the flow
in the small scale high aspect ratio nozzle does not accelerate all the way towards
the exit but reaches its velocity maximum closer to the throat. This lends itself
to the idea that a local evaluation along the central axis of the nozzle might
show a local thrust maximum, too. To do this, we integrate thrust according to
Eq. (17) across various cross sections of the nozzle. Figure 12 shows the result,
along with axial velocity, pressure, and the nozzle contour. Note that the thrust
scale does not start at zero. We see that the flow accelerates after the throat as
the pressure drops, until about x= 0.5 mm. Further downstream, the pressure
reaches a plateau, the velocity drops again. In the last third of the nozzle, the
pressure drops again, causing an inflection point in the velocity distribution:
the deceleration slows down and turns into acceleration at x= 2.0 mm.
The resulting flow is very different from classical nozzles. For both, thrust
increases after the nozzle throat is passed. However, lacking a further expansion
and acceleration, the thrust roughly stagnates at 0.4 mm <x<1.5 mm in the
planar micro nozzle. Towards the exit, the thrust further reduces to values below
the thrust at the throat–expansion through a mere pinhole could outperform a
Figure 12: Development of velocity, pressure, and resulting internal thrust along the central
nozzle designed after classical paradigms.
4.4. Truncated nozzle
The results shown in Fig. 12 suggest that a truncated nozzle might be the op-
timal solution in this case. Due to the large subsonic flow domains, a significant
upstream influence can be expected, so this might not be case after all. How-
ever, this is sufficient motivation to investigate this question with an additional
CFD computation on a new, truncated mesh. While the global thrust maxi-
mum occurs at x= 1.2 mm, a more compact nozzle with only minor penalty in
performance can be designed when cut at X= 0.5 mm.
Figure 13 shows the resulting flowfield. We see that the boundary layers
have not yet developed to the extent that they threaten a choking of the flow.
However, comparing the slice after the throat with the corresponding slice in
the full nozzle, Fig. 11, we see that the reached axial velocity is reduced.
In order to allow for a quantitative assessment of the relative quality of
both nozzles, Eqs. (17) to (20) have been evaluated and compiled in Tab. 7.
Nominal chamber pressure and mass flow have been used, hence camounts
Figure 13: Quarter flowfield of truncated nozzle. Bottom and back planes are viscous walls,
top and front planes are symmetry axes. Contours are axial velocity in m/s. The red plane is
the Mach 1 isosurface. The plot is vertically stretched twentyfold to aid clarity.
F Isp cFc rot ARARe
Nozzle in mN in s - in m/s - - - -
Contoured 7.1 144.8 1.07 1330 11.3 127.0 1.4 15.3
Truncated 9.2 187.6 1.38 1330 5.0 25.1 1.4 6.8
Table 7: Comparison of contoured full length and truncated nozzle.
to the identical value for both cases. Truncation of the nozzle has significantly
improved the performance of the engine. The expansion ratio =Ae/Ais
shown for both nozzles and compared to the ratio rot if the contour had been
used for a rotational nozzle instead. For expansion into vacuum, rot of the
contoured nozzle is a value one would traditionally choose. Finally, the aspect
ratio AR at throat and exit plane is defined as the ratio of width and depth.
5. Conclusion
Nozzles in µCPS, i.e. high aspect ratio, planar, micro nozzles, behave fun-
damentally different than classical, macro scale axisymmetric nozzles. Basic
assumptions of mostly isentropic flow with moderate boundary layers are re-
versed. Instead, a boundary layer dominated flow is found, essentially choking
the nozzle.
An analytical derivation of the core flow Knudsen number has been given,
allowing for an a priori estimation based on the pressure ratio which yields plau-
sible results. However, it may be more suitable in cases with a more substantial
isentropic core.
The classical recipe of adapting a nozzle for expansion into vacuum - i.e.
high expansion ratio realized over the required nozzle length to ensure only
moderate deflection - loses its significance. Instead, avoiding the axial build-up
of the boundary layers has become the dominant design constraint, calling for
short nozzles. In a way this is fortunate: as the etched depth is fixed, the cross
section only grows linearly with nozzle width, not with the square as is the case
for rotational nozzles, preventing the realization of high nozzles. Thus, new
approaches are needed for design and optimization.
We demonstrate that accurate modeling of variable exhaust gas properties
has a noticeable impact on performance prediction, and how heat loss to the
walls changes engine performance due to changing equilibrium composition.
Finally, we have to note that the analytically estimated Knudsen numbers
appear contradictory to the assumption in the literature that an exit pressure
of 1 kPa ensures continuum flow.
6. Acknowledgments
The research leading to these results has received funding from the Eu-
ropean Community’s Seventh Framework Programme (FP7/2007-2013) under
grant agreement No. 282948. Further information on PRECISE can be found
[1] Alina A. Alexeenko, Dmitry A. Fedosov, Sergey F. Gimelshein, Deborah
A. Levin, and Robert J. Collins. Transient heat transfer and gas flow
in a MEMS-based thruster. Journal of Microelectromechanical Systems,
15(1):181–194, 2 2006.
[2] D. T. Banuti, V. Hannemann, K. Hannemann, and B. Weigand. An efficient
multi-fluid-mixing model for real gas reacting flows in liquid propellant
rocket engines. Combustion and Flame, 168:98–112, 2016.
[3] S. Beinke, D. T. Banuti, J. Hardi, M. Oschwald, and B. Dally. Modelling
of a coaxial LOx/GH2 injection element under high frequency acoustic
disturbances. Progress in Propulsion Physics, in press.
[4] F.G. Blottner, M. Johnson, and M. Ellis. Chemically reacting viscous flow
program for multi-component gas mixtures. Sandia Laboratories, Albu-
querque, SC-RR-70-754, 1971.
[5] A. Burcat and B. Ruscic. Third millenium ideal gas and condensed phase
thermochemical database for combustion with updates from active ther-
mochemical tables. Report, Argonne National Laboratory, Argonne, IL,
[6] G. Cai, W. Sun, J. Fang, M. Li, Y. Cong, and Z. Yang. Design and per-
formance characterization of a sub-newton N2O monopropellant thruster.
Aerospace Science and Technology, 23:439–451, 2012.
[7] K. H. Cheah and J. K. Chin. Performance improvement on MEMS mi-
cropropulsion system through a novel two-depth micronozzle design. Acta
Astronautica, 69:59–70, 2011.
[8] A. Dadieu, R. Damm, and E.W. Schmidt. Raketentreibstoffe. Springer,
[9] M. Gauer, D. Telitschkin, U. Gotzig, Y. Battoneau, H. Johansson,
M. Ivanov, P. Palmer, and R. Wiegerink. PRECISE - development of a
mems-based monopropellant micro chemical propulsion system. In Proceed-
ings of the 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference &
Exhibit, Atlanta, GA, 2012. AIAA.
[10] M. Gauer, D. Telitschkin, U. Gotzig, Y. Battoneau, P. Rangsten, M. Ivanov,
P. Palmer, and R. Wiegerink. PRECISE - preliminary results of the MEMS-
based µCPS. In Proceedings of the 48th AIAA/ASME/SAE/ASEE Joint
Propulsion Conference & Exhibit, San Jose, CA, 2013. AIAA.
[11] T. Gerhold. Overview of the hybrid RANS code TAU MEGAFLOW -
numerical flow simulation for aircraft design. In Notes on Numerical Fluid
Mechanics and Multidisciplinary Design (NNFM), volume 89, pages 81–92.
Springer, 2005.
[12] S. Gordon and B.J. McBride. Computer program for calculation of complex
chemical equilibrium compositions and applications I. analysis. Technical
Report NASA RP-1311, NASA, 1994.
[13] B. J. Greemfield, W. F. Louisos, and D. L. Hitt. Numerical simula-
tions of multiphase flow in supersonic micro-nozzles. In Proceedings of
the 48th Aerospace Sciences Meeting including the New Horizons Forum
and Aerospace Exposition, Orlando, FL, 2011. AIAA.
[14] V. Hannemann. Numerische Simulation von Stoß- Stoß- Wechselwirkun-
gen unter Ber¨ucksichtigung von chemischen und thermischen Nichtgle-
ichgewichtseffekten. Technical Report FB 97-07, DLR, 1997.
[15] J.O. Hirschfelder, C.F. Curtiss, and R.B. Bird. Molecular Theory of Gases
and Liquids. Wiley, 1954.
[16] Darren Hitt, Charles M Zakrzwski, and Michael A Thomas. Mems-based
satellite micropropulsion via catalyzed hydrogen peroxide decomposition1.
10:1163, 11 2001.
[17] B. Ivancic, H. Riedmann, M. Frey, O. Knab, S. Karl, and K. Hannemann.
Investigation of different modeling approaches for CFD simulation of high
pressure rocket combustors. In Proceedings of the 5th European Conference
for Aeronautics and Space Sciences (EUCASS), Munich, Germany, 2013.
[18] James H. Jeans. An Introduction to the Kinetic Theory of Gases. Cam-
bridge University Press, 1940.
[19] L. Jing, X. You, J. Huo, M. Zhu, and Z. Yao. Experimental and numerical
studies of ammonium dinitramide based liquid propellant combustion in
space thruster. Aerospace Science and Technology, 69:161–170, 2017.
[20] S. Karl. Numerical Investigation of a Generic Scramjet Configuration. PhD
thesis, University of Dresden,
qucosa-68695, 2011.
[21] A. D. Ketsdever, R. H. Lee, and T. C. Lilly. Performance testing of a
microfabricated propulsion system for nanosatellite applications. Journal
of Micromechanics and Microengineering, 15:2254, 2005.
[22] S. J. Laurence, S. Karl, J. Martinez Schramm, and K. Hannemann. Tran-
sient fluid-combustion phenomena in a model scramjet. Journal of Fluid
Mechanics, 722:85–120, 2013.
[23] P. J. Linstrom and W. G. Mallard, editors. NIST Chemistry
WebBook, NIST Standard Reference Database Number 69, chapter National Institute of Standards and Technology,
Gaithersburg MD, 20899, retrieved 2016.
[24] M.-S. Liou. Ten years in the making - AUSM-family. In Proceedings of
the 15th Computational Fluid Dynamics Conference, Anaheim, USA, 2001.
[25] W. F. Louisos and D. L. Hitt. Viscous effects on performance of three-
dimensional supersonic micronozzles. Journal of Spacecraft and Rockets,
49(1):51–58, 2012.
[26] W.F. Louisos, A.A. Alexeenko, D.L. Hitt, and A. Zilic. Design considera-
tions for supersonic micronozzles. Int. J. Manufacturing Research, 3(1):80–
113, 2008.
[27] A. Mack and V. Hannemann. Validation of the unstructured DLR-TAU-
code for hypersonic flows. In Proceedings of the 32nd AIAA Fluid Dynamics
Conference and Exhibit, number AIAA-2002-3111, 2002.
[28] B. Marcu, G. Prueger, A. Epstein, and S. Jacobson. The commoditization
of space propulsion: Modular propulsion based on MEMS technology. In
Proceedings of the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Con-
ference & Exhibit, Tucson, AZ, 2005. AIAA.
[29] B.J. McBride and S. Gordon. Computer program for calculation of complex
chemical equilibrium compositions and applications II. user’s manual and
program description. Technical Report NASA RP-1311-P2, NASA, 1996.
[30] O. San, I. Bayraktar, and T. Bayraktar. Size and expansion ratio analysis
of micro nozzle gas flow. International Communications in Heat and Mass
Transfer, 36:402–411, 2009.
[31] D. Schwamborn, T. Gerhold, and R. Heinrich. The DLR Tau-code: Recent
applications in research and industry. In Proceedings of the European Con-
ference on Computational Fluid Dynamics (ECCOMAS CFD), Egmond
aan zee, Netherlands, 2006.
[32] P.R. Spalart and S.R. Allmaras. A one-equation turbulence model for
aerodynamic flows. AIAA Paper, (92-0439), 1992.
[33] G. P. Sutton and O. Biblarz. Rocket Propulsion Elements (7th Edition).
Wiley, 2001.
[34] Bram van Leer. Towards the ultimate conservation difference scheme. V.
A second-order sequel to godunov’s method,. Journal of Computational
Physics, 32(1):101– 136, 1979.
[35] M. R. Wang and Z. X. Li. Numerical simulations on performance of MEMS-
based nozzles at moderate or low temperatures. Microfluid Nanofluid, 1:62–
70, 2004.
[36] C.R. Wilke. A viscosity equation for gas mixtures. Journal of Chemical
Physics, 18:517–519, 1950.
[37] L. Zipperer and F. Herning. Beitrag zur Berechnung der Z¨ahigkeit tech-
nischer Gasgemische aus den Z¨ahigkeitswerten der Einzelbestandteile. Das
Gas- und Wasserfach, 4:49ff, 1936.
... The research into gas-dynamic processes in micronozzles based on mathematical modeling was carried out in [1,5,13,[20][21][22]. The studies carried out in [1,21,22] analyze the effect of the boundary layer being formed in micronozzles on gas dynamics and operational characteristics of micronozzle flows. ...
... The research into gas-dynamic processes in micronozzles based on mathematical modeling was carried out in [1,5,13,[20][21][22]. The studies carried out in [1,21,22] analyze the effect of the boundary layer being formed in micronozzles on gas dynamics and operational characteristics of micronozzle flows. It was shown that boundary layers dominate in the flow behind the nozzle throat able to decelerate the flow up to subsonic speeds. ...
The paper expresses a mathematical model of homogeneous gas motion with respect to formation processes and the growth of condensation nuclei. Since the condensed particles are small, the research is carried out with a single velocity motion model. The results obtained have shown that the application of the cylindrical tube leads to nonlinear flow effects. The flow responds to: the geometrical exposure related to flow transition from the conical diverging nozzle
... However, it is difficult to extend this method to larger-scale catalyst beds because the catalyst bed in monopropellant engines has thousands of unregular channels, which are too complex to be meshed. Due to the difficulties for modeling the decomposition of monopropellant, in the study of Li et al. to calculate the decomposition of DT-3 in a monopropellant thruster [16], and that of Banuti et al. to investigate the gas flow in planar microscale nozzles [17], they both used gas instead of liquid at the inlet boundary. This method is not only unable to calculate the delay caused by the reaction of decomposition, but also cannot accurately give the temperature near the injector. ...
Liquid monopropellant rocket engines are widely used in space propulsion and are developing in the direction of non-toxic and pollution-free propellants. The use of non-toxic monopropellants with a low decomposition rate makes the start-up and shutdown processes of the engines longer, and the gas inlet assumptions that were applicable to the calculation of hydrazine monopropellant engines cannot be used. Based on the steady-state calculation model of hydroxyl ammonium nitrate (HAN)-based monopropellant engine, we propose a combined model that considers decomposition of liquid monopropellant and non-equilibrium heat transfer between fluid and solid catalyst bed, and uses this model and the gas inlet hypothesis to calculate the working process of an HAN-based monopropellant rocket engine of 60 N thrust. The calculated results are compared with the test curve, and the results show that the decomposition of liquid monopropellant plays a key role in the starting and stopping processes. When the gas inlet assumption is adopted without considering the decomposition of the liquid monopropellant, the calculated start-up time is much shorter than the hot-firing test, and there is no tail-off section when shutting down. The pressure-rise and pressure-decay curve calculated by the combined model agree well with the test curve, and the maximum deviation during the steady state is less than 10%. For HAN-based monopropellant engines, the pressure rises slowly at the first start because the temperature of catalyst bed is lower, which results in a lower rate of decomposition. When restarted shortly after a shutdown, the pressure rises rapidly due to the high temperature of the catalyst bed and the high rate of decomposition. The HAN-based monopropellant can penetrate a few millimeters downstream of the injector, and there is a significant tail when the engine is shut down, which is caused by the continued decomposition of the remaining propellant after the shutdown.
... 598 leading to research on the use of monopropellant hydrazine thrusters for satellite applications. 599,600 Hydrazine has the ability to burn with air similar to gasoline and to decompose in a controlled mode in the absence of air, making it a very versatile fuel. 585 This characteristic made hydrazine an adequate fuel for a remotely piloted airplane called Mini-SNIFFER which is used in upper atmosphere analyses. ...
Alternative fuels are essential to enable the transition to a sustainable and environmentally friendly energy supply. Synthetic fuels derived from renewable energies can act as energy storage media, thus mitigating the effects of fossil fuels on environment and health. Their economic viability, environmental impact, and compatibility with current infrastructure and technologies are fuel and power source specific. Nitrogen-based fuels pose one possible synthetic fuel pathway. In this review, we discuss the progress and current research on utilization of nitrogen-based fuels in power applications, covering the complete fuel cycle. We cover the production, distribution, and storage of nitrogen-based fuels. We assess much of the existing literature on the reactions involved in the ammonia to nitrogen atom pathway in nitrogen-based fuel combustion. Furthermore, we discuss nitrogen-based fuel applications ranging from combustion engines to gas turbines, as well as their exploitation by suggested end-uses. Thereby, we evaluate the potential opportunities and challenges of expanding the role of nitrogen-based molecules in the energy sector, outlining their use as energy carriers in relevant fields.
... Further works would continue 587 leading to research on the use of monopropellant hydrazine thrusters for satellite applications. 588,589 Hydrazine has the ability to burn with air just as gasoline does, and to decompose in a controlled mode in the absence of air, making it a very versatile fuel. 574 This characteristic made hydrazine an adequate fuel for a remotely piloted airplane called Mini-SNIFFER which is used in upper atmosphere analyses. ...
div> The Haber-Bosch synthesis produces ammonia from hydrogen and nitrogen gases in a globally important energy-intensive process that uses coal or natural gas as a fuel and as a hydrogen source. Direct electrochemical ammonia synthesis from nitrogen and water using renewable energy sources presents an alternative to the Haber-Bosch process that would be sustainable and environmentally benign. Additionally, the different production structure of direct electrochemical nitrogen reduction technology suggests a supply chain alternative to the ammonia industry, and a method for load-leveling of the electrical grid. This alternative route to ammonia from dinitrogen would not require the same large capital investments as does the Haber-Bosch process, nor would it require access to a fossil fuel supply. We show that under certain scenarios, at feasibly achievable levels of energy efficiency with a future electrocatalyst, direct nitrogen reduction would be economically competitive or advantageous compared with Haber-Bosch-based ammonia production. </div
... 598 leading to research on the use of monopropellant hydrazine thrusters for satellite applications. 599,600 Hydrazine has the ability to burn with air similar to gasoline and to decompose in a controlled mode in the absence of air, making it a very versatile fuel. 585 This characteristic made hydrazine an adequate fuel for a remotely piloted airplane called Mini-SNIFFER which is used in upper atmosphere analyses. ...
Hydrogen plasma processing of GaAs and AlGaAs using an electron cyclotron resonance plasma reactor, which is vacuum‐linked to a molecular‐beam epitaxial (MBE) growth chamber is reported. Native oxide removal and surface cleaning of GaAs is characterized using hydrogen plasma processing, subsequent thermal Cl 2 etching, and vacuum annealing. It is shown that surface reconstruction and excellent GaAs/GaAs interfaces can be achieved using these dry vacuum procedures. It is also shown that Al x Ga 1-x As native oxides can be removed for 0≤x≤1 using hydrogen plasma processing before MBE overgrowth. The best AlGaAs/AlGaAs interfaces are obtained using low microwave power during hydrogen plasma processing. O and C impurities detected at these interfaces increase with higher Al composition; Si interface impurities tend to increase with higher microwave power. In general, hydrogen plasma processing is judged effective for surface preparation before MBE growth for the complete range of AlGaAs alloys.
A simplified model is proposed to simulate the working process of hydroxyl ammonium nitrate-based monopropellant rocket engines. The porous medium model and volume-of-fluid model are used to solve for the internal flow field of a monopropellant engine containing a catalyst bed to emphasize the establishment of a propellant decomposition model. The decomposition process is assumed to be separable into mass transfer and quick energy release processes. The mass transfer process is described by a two-stage decomposition model that combines catalytic and thermal decompositions according to temperature. This paper explains how to implement the two-stage decomposition model by using a titration experiment and thermal decomposition data. A detailed example is provided involving the calculation of the steady-state flow field of a 150-N monopropellant rocket engine in FLUENT. The results obtained using only the catalytic decomposition model and the two-stage decomposition model were compared with those of hot-fire tests, and show that the two-stage decomposition model is accurate. The combustion chamber pressure obtained from two- and three-dimensional simulations for the flow field of the engine agreed with the results of hot-fire tests. The calculated external wall temperature of the lower catalyst bed was slightly higher than the measured temperature, whereas the external wall temperature of the upper catalyst bed was close to the measured values.
Conference Paper
Full-text available
An experimental combustor, designated BKH, is operated at DLR Lampoldshausen to investigate high frequency combustion instability phenomena. The combustor operates with liquid oxygen and gaseous or liquid hydrogen propellants at supercritical conditions analogous to real rocket engines. An externally imposed acoustic disturbance interacts with a series of 5 coaxial injection elements in the center of the chamber. Numerical modelling is being used to provide further insight and understanding of the BKH experiments. A URANS model of a single BKH injection element subjected to transverse acoustic velocity excitation has been computed using a specialized release of the DLR TAU code. This release includes a finite rate chemistry combustion model and a real gas capability for modelling cryogenic propellant injection. The single BKH injection element models are subjected to high frequency acoustic forcing representative of the acoustic disturbances in the BKH experiments. The representative acoustic disturbance is determined by reconstructing the acoustic field from the dynamic pressure sensor data. Optical data from the BKH experiments is analysed to extract the response of the flame at the excitation frequency for comparison with the numerical results. The single element model successfully reproduces the retraction of the dense liquid oxygen core during transverse velocity excitation as observed experimentally. The model also provides further insight into flattening and flapping of the oxygen core.
Full-text available
A method of second-order accuracy is described for integrating the equations of ideal compressible flow. The method is based on the integral conservation laws and is dissipative, so that it can be used across shocks. The heart of the method is a one-dimensional Lagrangean scheme that may be regarded as a second-order sequel to Godunov's method. The second-order accuracy is achieved by taking the distributions of the state quantities inside a gas slab to be linear, rather than uniform as in Godunov's method. The Lagrangean results are remapped with least-squares accuracy onto the desired Euler grid in a separate step. Several monotonicity algorithms are applied to ensure positivity, monotonicity and nonlinear stability. Higher dimensions are covered through time splitting. Numerical results for one-dimensional and two-dimensional flows are presented, demonstrating the efficiency of the method. The paper concludes with a summary of the results of the whole series “Towards the Ultimate Conservative Difference Scheme.”
Conference Paper
Full-text available
This paper summarizes the main topics and first highlights of the cooperation between DLR and ASTRIUM within the work package “CFD Modelling of Combustion Chamber Processes” conducted in the frame of the Propulsion 2020 Project. Within the addressed work package, DLR Göttingen and ASTRIUM Ottobrunn have defined several test cases where adequate test data are available and which can be used for proper validation of the CFD tools. In this paper the first test case, the Penn State chamber (RCM-1), is discussed. The achieved simulation results reproduce important validation parameters like the measured wall heat flux very well but also reveal some inconsistencies in the test data.
Full-text available
An experimental and numerical investigation of the unsteady phenomena induced in a hydrogen-fuelled scramjet combustor under high-equivalence-ratio conditions is carried out, focusing on the processes leading up to unstart. The configuration for the study is the fuelled flow path of the HyShot II flight experiment. Experiments are performed in the HEG reflected-shock wind tunnel, and results are compared with those obtained from unsteady numerical simulations. High-speed schlieren and OH∗ chemiluminescence visualization, together with time-resolved surface pressure measurements, allow links to be drawn between the experimentally observed flow and combustion features. The transient flow structures signalling the onset of unstart are observed to take the form of an upstream-propagating shock train. Both the speed of propagation and the downstream location at which the shock train originates depend strongly on the equivalence ratio. The physical nature of the incipient shock system, however, appears to be similar for different equivalence ratios. Both experiments and computations indicate that the primary mechanism responsible for the transient behaviour is thermal choking, though localized boundary-layer separation is observed to accompany the shock system as it moves upstream. In the numerical simulations, the global choking behaviour is dictated by the limited region of maximum heat release around the shear layer between the injected hydrogen and the incoming air flow. This leads to the idea of ‘local’ thermal choking and results in a lower choking limit than is predicted by a simple integral analysis. Such localized choking makes it possible for new quasi-steady flow topologies to arise, and these are observed in both experiments and simulation. Finally, a quasi-unsteady one-dimensional analytical model is proposed to explain elements of the shock-propagation behaviour.
In this paper, the combustion process of liquid propellant ammonium dinitramide (ADN)-methanol aqueous solution in a small space thruster is investigated experimentally and numerically. The phase doppler anemometer measurement is used to investigate the injection process and the results are used as the liquid boundary condition in the simulation to minimize uncertainties. Hot fire tests have also been operated to estimate the performance of the thruster. To simulate the complicated processes in the thruster, a modified multi-component droplet model is employed to simulate the evaporation process considering the interaction between the liquid droplet and the porous media. A non-equilibrium model for the porous media is used to describe the heat transfer in the catalyst bed. A reduced chemical mechanism containing 18 species and 40 reactions is used to simulate the reactions of gas-phase ADN and methanol. The results show that the decomposition of ADN and the oxidization of methanol do not happen synchronously in the chamber. The decomposition of ADN takes place near the inlet while methanol is oxidized downstream of the porous media. The establishment of pressure in the thruster depends on the evaporation and reaction processes and the temperature changes relatively slowly because the porous media increases the thermal inertia of the whole system.
Conference Paper
PRECISE focuses on the research and development of a MEMS-based monopropellant micro chemical propulsion system for highly accurate attitude control of satellites. The availability of such propulsion systems forms the basis for defining new mission concepts such as formation flying and rendezvous manoeuvres. These concepts require propulsion systems for precise attitude and orbit control manoeuvrability. Application-oriented aspects are addressed by two end-users who are planning a formation flying mission for which the propulsion system is crucial. Basic research is conducted aiming at improving crucial MEMS technologies required for the propulsion system. Research and development also focuses on the efficiency and reliability of critical system components. System analysis tools are enhanced to complement the development stages. Finally, the propulsion system will be tested in a simulated space vacuum environment. These experiments will deliver data for the validation of the numerical models.
Contenido: Vectores y tensores; Propiedades de equilibrio; Mecánica estadística; La ecuación del estado de los gases a densidad baja y moderada; La ecuación del estado de gases densos y líquidos; Equilibrio del líquido-vapor y fenómenos críticos; Teoría cuántica y la ecuación de estado; La teoría cinética de los gases; Fenómenos de transporte y gases; Propiedades de transporte de gases densos y líquidos; Teoría cuántica y fenómenos de transporte; Aplicaciones hidrodinámicas de las ecuaciones de cambio; Bases electromagnéticas de las fuerzas intermoleculares; La teoría de las fuerzas intermoleculares; Cálculos de mecánica cuántica de fuerzas intermoleculares.
This paper introduces a new model for real gas thermodynamics, with improved accuracy, performance, and robustness compared to state-of-the-art models. It is motivated by the physical insight that in non-premixed flames, as encountered in high pressure liquid propellant rocket engines, mixing takes place chiefly in the hot reaction zone among ideal gases. We developed a new model taking advantage of this: When real fluid behavior only occurs in the cryogenic oxygen stream, this is the only place where a real gas equation of state (EOS) is required. All other species and the thermodynamic mixing can be treated as ideal. Real fluid properties of oxygen are stored in a library; the evaluation of the EOS is moved to a preprocessing step. Thus decoupling the EOS from the runtime performance, the method allows the application of accurate high quality EOS or tabulated data without runtime penalty. It provides fast and robust iteration even near the critical point and in the multiphase coexistence region. The model has been validated and successfully applied to the computation of 0D phase change with heat addition, and a supercritical reactive coaxial LOX/GH2 single injector.
This book can be described as a student's edition of the author's Dynamical Theory of Gases. It is written, however, with the needs of the student of physics and physical chemistry in mind, and those parts of which the interest was mainly mathematical have been discarded. This does not mean that the book contains no serious mathematical discussion; the discussion in particular of the distribution law is quite detailed; but in the main the mathematics is concerned with the discussion of particular phenomena rather than with the discussion of fundamentals.