The present research is aimed at developing analytical procedures for predicting the performance and stability characteristics of chemical propulsion engines. Specific emphasis is being placed on understanding the physical and chemical processes in the small engines that are used for applications such as spacecraft attitude control and drag make-up. The small thrust sizes of these engines lead to low nozzle Reynolds numbers with thick boundary layers which may even meet at the nozzle centerline. For this reason, the classical high Reynolds number procedures that are commonly used in the industry are inaccurate and of questionable utility for design. A complete analysis capability for the combined viscous and inviscid regions as well as for the subsonic, transonic, and supersonic portions of the flowfield is necessary to estimate performance levels and to enable tradeoff studies during design procedures

Merkle, Charles L.

English

NASA Technical Reports Server

PRESENTATION 2.3.6 
CFD APPLICATION8 IN 
CHEMICAL PROPWLBION ENGINES 
https://ntrs.nasa.gov/search.jsp?R=19910018920 2020-03-19T17:28:34+00:00Z
CFD APPLICATIONS IN CHEMICAL PROPULSION ENGINES 
Charles L. Merkle 
Department of Mechanical Engineering 
1. Research Objectives and Potential Impact on Propulsion 
The present research is aimed at developing analytical procedures for 
predicting the performance and stability characteristics of chemical propulsion 
engines. Specific emphasis is being placed on understanding the physical and 
chemical processes in the small engines that are used for applications such as 
spacecraft attitude control and drag make-up. The small thrust sizes of these engines 
lead to low nozzle Reynolds numbers with thick boundary layers which may even meet 
at the nozzle centerline. For this reason, the classical high Reynolds number 
procedures that are commonly used in the industry are inaccurate and of questionable 
utility for design. A complete analysis capability for the combined viscous and inviscid 
regions as well as for the subsonic, transonic and supersonic portions of the flowfield 
is necessary to estimate performance levels and to enable trade-off studies during 
design procedures. 
Most engines that are used for auxiliary propulsion operate at efficiencies that 
are considerably below those reached by larger engines. Although a portion of this 
efficiency decrement is due to the reduced Reynolds number conditions, a substantial 
fraction can also be attributed to the design processes which fail to take into account 
properly the viscous nature of the flow. Improved design and analysis capabilities 
should allow considerable performance improvements in these small engines. Higher 
performance in turn means that a reduced amount of propellant is needed to keep the 
spacecraft on orbit, thus leading to longer spacecraft life without increased launch 
weight. This potential for increased on-orbit time is the justification for the present 
research effort. Additional areas that are being considered include CFD modeling of 
combustion instability. These efforts are directed, for the most part at larger engines, 
but again, the application of CFD here promises to provide increased understanding of 
the physics that control engine design. 
The numerical analyses of compressible flows has progressed rapidly in the 
past two decades,and it is presently routine to compute two-dimensional steady flows, 
while two-dimensional unsteady and three-dimensional flows are feasible in a 
research environment. Although two-dimensional computations are within the reach 
of day-to-day design procedures, no particular attention has been given to the 
computation of rocket flowfields and care must be taken to develop a procedure that is 
accurate and efficient enough for design use. Similarly, the areas of combustion 
instability is one that has received little attention from full CFD formulations. In addition 
to the computational aspects, major modeling issues exist with regard to the spray 
atomization and vaporization processes as well as the turbulent combustion 
processes and the heat release rates in the combustor. Three-dimensional and 
unsteady flows are also of downstream interest. The present effort is directed towards 
these issues. 
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II. Current Status and Results 
At present, coordinated efforts are going on in several areas. The first has to do 
with the application of CFD methods to the prediction of mixing and combustion in 
auxiliary propulsion engines . Our efforts here have started from an existing code for 
hypersonic reacting flows. This code uses an LU-SSOR central-difference algorithm 
with a complete chemistry and physical properties formulation for hydrogen-oxygen 
reactions and kinetics. Turbulence is modeled by the simple Baldwin-Lomax mixing 
length model. Although this procedure is effective for hypersonic flows, it has some 
shortcomings in the low-speed subsonic regime that is characteristic of the heat 
release regions in chemical propulsion engines. Several enhancements are being 
investigated to increase the robustness and efficiency of the code in this lower speed 
regime. 
The first enhancement in the code was to switch from the LU solution algorithm 
to a fourth-order, explicit Runge-Kutta procedure with an implicit treatment for the 
axisymmetric and chemical kinetics source terms. The implicit treatment of the source 
terms enables larger time steps in applications where the source terms are stiff. All 
terms are still centrally differenced on a finite volume grid in a manner identical to the 
original LU formulation. Some representative results comparing the new RK4 
procedure with the LU method are presented on Fig. 1. These results show that the 
Runge-Kutta method converges approximately twice as fast as the LU procedure in 
terms of iterations, in addition to showing faster CPU times per iteration. The LU 
procedure requires about 135 psec. per grid point per iteration on the CRAY-YMP, 
while the RK method requires only 98 psec. 
Other enhancements to the code include the implementation of characteristics- 
based boundary conditions on the inflow and outflow boundaries (which also enhance 
the convergence of the original LU method as Fig. 1 shows). In addition to 
implementing characteristic techniques, boundary procedures were also added to 
enable the specification of the incoming mass flow rather than only stagnation 
quantities. This enhancement enables the user to mimic the experimental procedure 
where upstream conditions control the incoming flow rates of fuel and oxidizer while 
the choked throat in the noule sets the chamber pressure. Experience to date with 
the RK method shows that it is more robust than the LU method for this problem, and, 
in addition, requires smaller amounts of artificial viscosity to be added, thus enhancing 
the accuracy of the results, particularly in the steep gradient regions near the wall. 
Some representative solutions for a gaseous hydrogen-oxygen engine are 
shown on Figs. 2 to 4. Figure 2 shows the overall geometry of the proposed station- 
keeping engine for the Space Station, while Fig. 3 shows the computed temperature 
contours and Fig. 4 the corresponding Mach number contours in the downstream 
mixing region of the low Reynolds number combustor. The computational grid used 
for these results is given in Fig. 5. The results show that the hydrogen stream from the 
outer periphery of the noule undergoes little reaction with the internal oxygen-rich 
core stream. Although these predictions could be correct, the present turbulence 
model is not sufficient to predict accurately the mixing and combustion processes in 
this complex boundary-layerlfree-shear-layer region. For this reason we are currently 
adding a k-E turbulence model to the code to enhance these predictions. 
At the present time the k-E model has been coded and is being debugged and 
validated. The model is presently working for the boundary layer in the outer 
hydrogen stream alone, and current efforts are directed toward demonstrating it for the 
shear layer region as well. The model is formulated with low Reynolds number terms 
to enable the profiles to be computed all the way to the wall. Preliminary results 
suggest that this more complex turbulence model will predict substantially faster 
mixing and combustion processes than the present mixing length model, although 
comparison of the code predictions with hydrogen-oxygen flame measurements 
obtained from the literature is necessary to verify its accuracy. Downstream plans 
include extension to a complete PDF model of the turbulent combustion process. 
Additional efforts on the low Reynolds number nozzle problem include the 
implementation of a flux-difference-split, upwind-biased, finite volume method with 
TVD capabilities for the flowfield. Results to date show that the upwind-finite volume 
method is considerably more robust than the centrally differenced methods, and 
should result in a more reliable code. The use of third-order biased differencing 
provides accuracy that is similar to that obtained with central differences. All results to 
date are for air chemistry, and again for the Baldwin-Lomax turbulence model, and are 
based on an alternating direction implicit (ADI) solution procedure. Modifications for 
the chemistry and physical properties of hydrogen-oxygen mixtures is nearly complete 
and results should be available shortly. The incorporation of an LU time marching 
procedure, that is also underway, should provide a further improvement in 
computational efficiency over the RK4 method. Although the LU procedure is not 
efficient for centrally differenced schemes, it is quite effective for upwind schemes, and 
substantial improvements in speed are expected. 
A third effort in developing robust procedures for the small rocket engine 
application is adaptation of a parabolic Navier-Stokes (PNS) based algorithm to fully 
elliptic flow in the supersonic portion of the nozzle. This method has been 
demonstrated for perfect gas flows and is currently being extended to the full 
hydrogen-oxygen kinetics scheme, again using the same kinetics package that was 
used above. Our current efforts here are on the development of the space-marching 
PNS procedure. Later extensions will add a reverse iterative sweep to incorporate the 
complete elliptic Navier-Stokes effects. Some representative results for the perfect 
gas case in a contoured, high expansion nozzle, including the effects of expansion to 
a non-ideal back pressure are shown on Figs. 6 and 7. The PNS method, being a 
single pass method, is much faster than iterative methods, and the forward-backward 
sweeping procedure for the full Navier-Stokes equations is again much faster than 
classical time-marching algorithms. 
Other efforts include the addition of a time derivative preconditioning method for 
enhancing convergence in low speed regimes such as occur in rocket combustors and 
the development of an Eulerian-Lagrangian method for oxidizer droplets. The 
convergence rates of most time-marching procedures scale inversely with the flow 
Mach number because of the stiff eigenvalues in the low speed regime. Because most 
rocket combustion occurs at these low Mach numbers, it is imperative that methods be 
developed to retain fast convergence rates especially when complex chemistry 
models are in use. The present effort is based on extending earlier preconditioning 
methods by the author for inviscid flows to flows where diffusion is significant. Figure 8 
compares the convergence rates with and without preconditioning for typical low 
speed conditions. 
The work on two phase flows is in an early stage with efforts currently focussed 
on reviewing current state-of-the-art modeling procedures for liquid spray combustion. 
At present a first generation liquid propellant model has been developed and applied 
to one-dimensional flows. Our immediate plans are to extend this analysis to two 
dimensions by combining our existing Eulerian methods for the gas phase with 
Lagrangian droplet models developed elsewhere. 
Finally as a last effort, a CFD-based combustion instability model is being 
developed for predicting finite amplitude waves in rocket combustors. At present, 
efforts are concentrated on developing accurate procedures and we are therefore 
employing simple combustion models (equivalent to n-.r: models) with perfect gas 
conditions. Later extension to more realistic combustion models is planned. The 
model is based on an iterative, implicit time-marching method with capabilities similar 
to those described above for low speed flows. At present we are comparing one and 
two-dimensional oscillatory wave calculations with test cases based on linearized 
stability results that have been recommended by the current JANNAF Combustion 
Instability Panel as the result of recent JANNAF workshops. 
Ill.  Proposed Work for Coming Year 
For the coming year our efforts are to be divided among several fronts. Primary 
emphasis is to be placed on enhancing and upgrading the turbulent combustion 
model and validating the code. Of secondary interest is a continuing effort to make the 
algorithm more robust and reliable both through day-to-day running, and through the 
addition of algorithm enhancements. Additional improvements are also planned to 
enable a wider, choice of wall boundary conditions and geometrical configurations. 
Low level efforts are also planned for the continued development of a liquid spray 
capability in the code. The final item to be addressed is the continued development of 
a combustion instability model based on CFD procedures. 
The efforts on improved turbulent combustion models will focus on completing 
the incorporation of a two-equation model of turbulence to enable us to represent the 
boundary-layer-shear-layer more realistically. This model will then be augmented by 
a turbulent combustion model, most likely of the PDF variety using existing techniques 
from the literature. The validation of the code by comparison with experimental data 
will also be an area of focus. In conjunction with advanced turbulence modeling, we 
will also look for methods for enhancing the mixing and combustion processes in the 
rocket combustor. This will probably necessitate the use of three-dimensional 
phenomena, and, in particular, will include an assessment of the effect of discrete hole 
injection of hydrogen fuel (as is presently being done in the experimental 
configuration) on the mixing and combustion of the Space Station engine. These 
discrete holes are presently being modeled in two-dimensional fashion as a slot, and 
this simplified treatment may be underestimating the degree of mixing and 
combustion. Improved methods for treating this three-dimensional injector pattern 
without going completely to three-dimensions will also be sought, including efforts for 
estimating the errors introduced by the use of the current two-dimensional predictions 
instead of the more realistic three-dimensional geometry. 
In terms of a continued upgrade of the code, the results of other companion 
studies concerning various methods for enhancing the present algorithm will be 
integrated into the model as appropriate. Specific issues to be considered include the 
efficacy of switching to the flux-difference-split method, the enhancements to be 
gained through the use of low Mach number preconditioning, and the desirability of 
incorporating the PNS-based Navier-Stokes algorithm for the supersonic portion of the 
nozzle flowfield. The emphasis in these code improvement issues will be to evolve the 
code steadily into a more reliable procedure, as capabilities dictate. In addition, the 
extension of the method to other chamber geometries will also be undertaken, with the 
purpose of determining the capabilities of the method for predicting thrust and specific 
impulse accurately. 
Additional capabilities to be included in the analysis include the addition of 
regenerative and radiation wall cooling procedures so the nozzle flowfield calculations 
will predict both the wall temperature and the heat flux distribution. The accurate 
prediction of wall heat transfer is an important issue in the design of small rocket 
engines, and requires an adequate model of turbulent wall heat transfer as well as 
some estimate of the locations of transition to turbulence. The improved turbulence 
model should provide some help in this area also. 
Efforts to model the two-phase liquid spray combustion process will continue, 
although at a lower level of effort than the above topics. The purpose here will 
continue to be focussed on identifying the appropriate levels of technology and 
assessing the degree to which the spray combustion process can be predicted. Only 
representative solutions of simpler combustion processes are expected to be 
completed this year. A major emphasis will be placed on assessing the degree of 
reliability that can be expected as a stepping stone for planning the following year's 
effort. 
In the related area of combustion instability, primary emphasis will be placed on 
demonstrating the accuracy that can be expected from a CFD analysis of combustion 
instability using a global model for the combustion process. Emphasis will be placed 
on estimating the effect of distributed heat release on disturbance growth, the effects of 
finite nozzle lengths of representative size, and other similar analyses based on 
simple phenomenological combustion models. These calculations will center around 
two-dimensional, radial-tangential modes, but additional studies of complete three- 
dimensional models based on the numerical solution of the linearized equations will 
be obtained as a precursor to incorporating three-dimensional disturbances in the 
complete nonlinear solution. Additional emphasis will be placed on the effect of finite 
amplitude disturbances on the growth of waves. An assessment of the advantages of 
CFD analyses over classical linear stability procedures will also be a goal of this 
research along with a comparison of the relative merits of the CFD predictions. 


111. Proposed Work for Coming Year 
1. Complete the development of the droplet temperature measurement technique 
and its integration with the droplet size and velocity techniques in order to obtain 
the capability to make simultaneous droplet size, velocity and temperature 
measurements in liquid hydrocarbon sprays. 
2. Complete the fabrication, assembly and testing of the 70 atm, 300.C turbulent 
flow system and single droplet generator. 
3. Obtain a set of simultaneous droplet size and velocity measurements in a 
vaporizing liquid hydrocarbon spray, at atmospheric pressure and room 
temperature, and at one laminar and one turbulent flow condition. 
I 
4. Obtain a set of droplet size and temperature versus time measurements for the 
case of individual liquid hydrocarbon droplets injected into the same two flow 
conditions used in task 3. 
5. Make a preliminary study of the behavior of individual liquid hydrocarbon 
droplets injected into a supercritical environment using high speed, back lit 
photography. 
6. Make a preliminary investigation of the feasibility of using two-dimensional 
Raman scattering to visualize supercritical liquid hydrocarbon droplets. 


CFD applications in chemical propulsion engines

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