Under a NASA MSFC SBIR Phase 1 effort an interactive software package has been developed for the analysis of discrete (particulate) phase dynamics in two-phase flows in which the discrete phase does not significantly affect the continuous phase. This package contains a Graphical User Interface (based on the X Window system and the Motif tool kit) coupled to a particle tracing program, which allows the user to interactively set up and run a case for which a continuous phase grid and flow field are available. The software has been applied to a solid rocket motor problem, to demonstrate its ease of use and its suitability for problems of engineering interest, and has been delivered to NASA Marshall Space Flight Center

Dejong, Frederik J.

Thoren, Stephen J.

English

NASA Technical Reports Server

N95- 23641
AN INTERACTIVE TOOL FOR DISCRETE PHASE ANALYSIS IN TWO-PHASE FLOWS
Frederik J. de Jong and Stephen J. Thoren
Scientific Research Associates, Inc.
Glastonbury, CT
Presented at the
Workshop for Computational Fluid Dynamics Applications
in Rocket Propulsion
April 20-22, 1993
/ +. +
Abstract
Under a NASA MSFC SBIR Phase I effort an interactive software package has been developed
for the analysis of discrete (particulate) phase dynamics in two-phase flows in which the discrete
phase does not significantly affect the continuous phase. This package contains a Graphical User
Interface (based on the X Window system and the Motif"tool kit) coupled to a particle tracing
_rogram, which allows the user to interactively set up and run a case for which a continuous phase
grid and flow field are available. The software has been applied to a solid rocket motor problem, to
demonstrate its ease of use and its suitability for problems of engineering interest, and has been
delivered to NASA Marshall Space Flight Center.
I. Introduction
Multiphase flow effects in liquid and solid propulsion systems have profound implications on
performance and durability. For example, the dynamics of aluminum oxide particulates in an SRM
affects the slag accumulation, thereby affecting the performance. A second example is particulate
impingement on the motor casing and nozzle affecting durability via its influence on the thermal load
on the insulator. The effect of the discrete phase on performance and durability can be very
significant even when the concentration of the discrete phase is low enough to not alter the
continuous phase flow field in a significant manner. Under the present effort a workstation-based
analysis tool has been developed which can be used by analysts and designers to interactively
assess the discrete phase effects during the development and testing of rocket propulsion systems.
The workstation based software uses a Lagrangian analysis for the discrete phase motion and
includes a Graphical User Interface allowing the user to interactively change the relevant parameters
to conduct parametric studies. To demonstrate the suitability of the interactive software and its ease
of use, it has been successfully applied to a two-dimensional solid rocket motor test problem.
The software consists basically of two pads: (i) the Graphical User Interface for input/output,
and (ii) the computational analysis for the discrete phase dynamics. As description of these is given
below.
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II. Discrete Phase Analysis and Governina Eauations
The present analysis is based on the Lagrangian analysis described by de Jong et al. [1].
Although originally part of a fully coupled two-phase flow analysis (see, for example, Madabhushi
et al. [2] or de Jong and Sabnis [3]), this analysis has been adapted for stand-alone use, and
does not, in its current form, depend on any flow solver. For a _ computational grid and
continuous phase flow field, the stand-alone particle code integrates a Lagrangian equation of motion
for each particle. A brief description of its relevant features is presented below.
I1.1 Eauation of Motion
The equation of motion for a particle can be written in the form
d2X F
d--_ = m (1)
where X is the position vector of the particle, m is the particle mass, and F is the total force acting on
the particle. In general, F contains "body" forces, such as those due to gravity or electro-magnetic
fields, and the force acted upon the particle by the fluid (Fp). Integration of Eqo (1) yields
dX It F dT + dX I (2)
d--t= to m _ to
At this stage a coordinate transformation Y = Y(X) is introduced to transform the equation of
motion into the computational coordinate space corresponding to the grid used for the continuous
phase analysis, i.e.
yJ = yJ (Xl,X2,X3) (j = 1,2,3)
where yJ are the computational coordinates (the components of Y) used in the continuous phase
analysis and x i are the physical coordinates (the components of X). Let J be the inverse of the
transformation matrix, i.e. let J be the matrix with elements Jij, where
oy i
Jij =
oxj
Then
d¥ dX
-- = J -- (3)
dt dt
Substituting Eq. (2) into Eq. (3) yields
d¥ It F dX I (4)
= J m dT+ toto
598
This equation can be integrated (assuming that J, F, and m are constant over the integration interval
at) to yield
AM = ½At2J _F + AtJOpl
m t O
(s)
where AY is the change in the coordinate space position vector (i.e. Y) during the period at. Equation
(5) then provides the change in particle location (in computational space) for a given time interval at
and starting location corresponding to t -- t0.
The transformation of the Lagrangian equations of motion from the physical coordinates to the
computational, body-fitted coordinates used for the continuous phase analysis offers some very
significant advantages. Since the motion of a particle is tracked in the computational coordinate
space (via Eq. (5)), no searching is needed for the mesh cell in which a computational particle
resides. This facilitates the computation of the force on the particle in the Lagrangian equation of
motion. Also, tracking the motion in the computational space allows the estimation of the time taken
by the particle to cross the boundaries of the grid cell where it currently resides. This estimate is used
in the selection of sub-time steps (described below) used in integrating the equation of motion.
Finally, the search for boundaries is simplified, which makes it easier to determine whether a particle
has reached a solid boundary and should be reflected, or a particle has left the computational
domain and should be omitted. This latter advantage is of major importance when the number of
boundaries is large (see de Jong et al. [1] and McConnaughey et al. [4] for an interesting
application).
Each particle is moved through the domain by integrating its Lagrangian equation of motion
using a sequence of "sub-time steps" _t s. These sub-time steps are chosen as the minimum time
for the particle to cross the nearest cell boundary and a kinematic time scale defined as a fraction
(e.g. 0.1) of the ratio of particle velocity to acceleration. It should be noted that, for accuracy
reasons, the maximum allowable sub-time step could be significantly different for different
particles depending upon their location, mass, etc. The sub-time step approach has been adopted
to provide an accurate representation of the particle motion, since at the end of each sub-time
step the force on the particle is updated using the particle attributes and the continuous phase
values corresponding to the new particle locations.
11.2 Force on a Particle
In Equation (1), the force F on the particle has been assumed to consist of a drag force, a
gravitational acceleration force, and a force due to the pressure gradient in the liquid,
m
F = F D + mg Vp (6)
Pp
where g is the (gravitational) acceleration vector, pp is the particle density, p is the local pressure in
the continuous phase and where the drag force FD =sgiven by
1
FD = _" CDP_rDp2IURIUR (7)
Here p is the density of the continuous phase, Dp is the particle diameter and U R is the velocity of
the particle relative to the continuous phase velocity. C D is the drag coefficient, which is related
to the particle Reynolds number
599
PURDp
Rep ---- F
(where ju is the viscosity of the continuous phase) via the expression
(8)
24 [i + 1CD = _-_p 6 Rep 2/3] for Rep < 1000 (9)
= 0. 424 for Rep > 1000
The second term on the right hand side of Eq. (6) represents the gravitational (or other acceleration)
effects, which could be significant for solid particles or liquid droplets in a gaseous continuous phase.
The effect of buoyancy, on the other hand, which is included in the last term of Eq. (6), may not
always be of importance.
11.3 DiscrQtQ Phase Turbulent Dispersion
In two-phase flows, the continuous phase turbulence results in dispersion of the discrete phase.
This process is modeled by some researchers (see Abbas et al. [5]) by adding a "diffusion" velocity
obtained from some phenomenological model to the particle velocity. In the present analysis, this
effect is modeled by evaluating the fluid force on a particle using an instantaneous continuous phase
velocity field rather than a mean velocity field. The instantaneous velocity components are obtained
by adding stochastically generated turbulent velocity components to the mean velocity field for the
continuous phase. If the continuous phase turbulence is assumed to be isotropic, and the random
turbulent velocity components are assumed to have a Gaussian probability distribution with standard
deviation o, then
G = _-- (9)
where k is the turbulent kinetic energy, and the random turbulent velocity components can be
obtained as
4k ] 1/2_--- erf-l(2x- i) (I0)
where x is random variable with uniform probability distribution between 0 and 1 (i.e. x is a random
number between 0 and 1). This latter result follows from the observation that if x is random variable
with uniform probability distribution between 0 and 1, then F "l(x) is a random variable whose
cumulative probability function is F. This technique offers a way to treat the effect of gas phase
turbulence on the particulate phase dispersion in a manner which is less empirical than the
techniques traditionally used with Eulerian-Eulerian analyses. Similar techniques for modeling the
discrete phase turbulent dispersion have been used by, for example, Dukowicz [6], Gosman and
Ioannides [7], and Hotchkiss [8].
If the turbulent energy k is not directly available, but an eddy viscosity/_T and a mixing length 1
are (for example, when a mixing length turbulence model is used in the continuous phase analysis),
then k can be obtained from the relation
/zT = C/_¼pk½1 (12)
600
where C/j
C_
is a function of/JTthat can be determined from the expression
= 0.09 exp .... /_T
1 + 0.02 --
(cf. Launder and Spalding [10]).
(13)
III. Grsphical User Interface
The Graphical User Interface (GUI) developed under the present effort is based on the X
Window system and the MotiP' tool kit. Some advantages to using X and Motif" include improved
code portability, maintaining a consistent look and feel between applications and the ability to run the
interface on one machine and to display it on another. Its portability was verified by compiling and
running the GUI both on SGI 4D/25TG and IBM RS/6000 Workstations. The main window of the GUI
contains a menubar with several pull-down menus (Fig. 1) that allow the user to perform functions
associated with file I/O, problem specification, or output display. In most cases, selection of a menu
item from a pull-down menu opens up a property window that provides the userwith the requested
input items. Depending on the item, user input is possible via type-ins, toggle buttons, selection from
lists, or graphically by using the mouse. Some of the features of the GUI are:
@ Grid and flow field files can be used in standard PLOT3D-type format.
(ii) Boundaries can be defined in the computational domain by adding or deleting "zones" or
"blocks'. Here a "zone" is defined as a region inside which there is a flow field, while a "block" is
defined as a solid region (without a flow field). These "zones" or "blocks" can be specified
graphically by using the mouse (Figs. 2-3). This approach allows the user to define complex
(2-D) geometries without the need for code modifications.
(iii) To define the boundary type (such as inlet/exit, wall, or symmetry line) and the properties
(restitution and friction coefficients) of a solid wall, this boundary can be selected by "clicking"
on it. The boundary type can then be set by choosing the appropriate one from a menu (Fig.
4), while the relevant properties can be typed in.
(iv) The injection locations can be specified graphically by clicking on the desired grid points in
the computational domain (Fig. 5). The particle properties at these locations (such as the
particle velocity, its radius and its density) can be specified via type-ins. By defining default
properties, only those properties that change from one particle to the next have to be typed in.
(v) Wherever possible, error and consistency checks are performed by the interface on user input
prior to running the particle code. This helps to produce a more accurate input file and
prevents needless execution of the particle code.
The Graphical User Interface is coupled to the particle code, so that it can be used both to set
up and to run a particular problem. Execution of the particle tracking program under the GUI displays
the particle traces while they are being computed; once the program is finished, the image can be
manipulated interactively. A complete description of all the functions included in the GUI and
601
guidelines for setting up and running a new case can be found in the User's Manual; on-line help is
available for most functions.
IV. Application and Results
To demonstrate the suitability of the software package developed under the present effort and
its ease of use for solid rocket motor applications, the Particle Trace Interface was used to set up and
run particle trajectories in the so-called super BATES motor. The geometry of this motor is shown in
Fig. 6. The flow field in this motor was computed with SRA's MINT code, on the grid shown in Fig. 6.
This grid contains two "cut-out" regions, adjacent to the grain surface and the nozzle wall. The "full"
grid is shown in Fig. 7. This grid, and the flow field, were then used as input to the Particle Trace
Interface (PTI). Using the PTI, the boundaries of the computational domain were constructed by
putting two "blocks" into the "zone" that comprised the full grid (cf. Fig. 5). Altematively, it would have
been possible to build up the domain as the union of three "zones', corresponding to the combustion
chamber, the slot region, and the nozzle region. At this point it should be noted that Fig. 7 was
actually obtained by displaying the grid in the PTI after it had been read in, while Fig. 6 was obtained
by displaying the grid after the boundaries had been specified. Next, the PTI was used to define the
"boundary conditions" (insofar as these are needed to determine the behavior of a particle when it
reaches a boundary) and a set of particle injection locations (the solid circles in Fig. 5). Particle and
flow field information was specified to complete the problem setup, after which the PTI was used to
(interactively) execute the particle tracing code. Figs. 8 and 9 show the resulting particle traces
(again obtained from the PTI). The whole operation was completed without exiting from the PTI.
Acknowledgements
This research was supported by the NASA George C. Marshall Space Flight Center under
Contracts NAS8-39337 and NAS8-38959.
References
° De Jong, F. J., Sabnis, J. S., and McConnaughey, P. K.: "A Combined Eulerian-Lagrangian
Two-Phase Flow Analysis of SSME HPOTP Nozzle Plug Trajectories: Part I - Methodology',
AIAA Paper 89-2347, AIAA/ASME/SAE/ASEE 25th Joint Propulsion Conference, July 1989.
. Madabhushi, R.K., Sabnis, J.S., de Jong, F.J. and Gibeling, H.J.: "Calculation of Two-Phase
Aft-Dome FIowfield in Solid Rocket Motors," J. Propulsion and Power, Vol. 7, 1991, pp. 178-184.
_o de Jong, F.J. and Sabnis, J.S.: "Simulation of Cryogenic Liquid Flows with Vapor Bubbles,"
AIAA Paper 91-2257, AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, June 1991.
. McConnaughey, P. K., Garcia, R., de Jong, F. J., Sabnis, J. S., and Pribik, D.A.: "A Combined
Eulerian-Lagrangian Two-Phase Flow Analysis of SSME HPOTP Nozzle Plug Trajectories: Part
II - Results', AIAA Paper 89-2348, AIAA/ASME/SAE/ASEE 25th Joint Propulsion Conference,
July 1989.
602
.°
.
o
.
Abbas, A. S., Kousa, S. S. and Lockwood, F. C.: "The Prediction of the Particle Laden Gas
Flows," Proc. 18th Symposium on Combustion, Combustion Institute, 1981, pp. 1427-1438.
Dukowicz, J. K.: "A Particle-Fluid Model for Liquid Sprays', J. Computational Physics, Vol.
35, 1980, pp. 229-253.
Gosman, A. D. and Ioannides, E.: "Aspects of Computer Simulation of Liquid-Fueled
Combustors," J. Energy, Vol. 7, 1983, pp. 482-490.
Hotchkiss, R. S.: "The Numerical Modeling of Air Transport in Street Canyons', Report
LA-UR-74-1427, Los Alamos Scientific Laboratory, 1974.
Launder, B.E. and Spalding, D.B.: "The Numerical Computation of Turbulent Flows," Computer
Methods in Applied Mechanics and Engineering, Vol. 3, 1974, pp. 269-289.
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An Interactive Tool for Discrete Phase Analysis in Two-Phase Flows

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