Project Advisors: Dr. G.F. Carey and Dr. R.O. Stearman

Project Assistants: Bill Barth, Alexandre Aardelea, Susan Buck

Facilities: CFDLab, Dept. Aerospace Engineering, UT Austin

ASE 363Q – Spring 1999

Department of Aerospace Engineering

The University of Texas at Austin

April 6, 1999

The MicroG Research Group is pleased to present our midterm progress report on the Microgravity Fluid Mechanics and Heat Transfer Computation Project. Our team has been tasked with simulating fluid motion and heat transfer under microgravity conditions using specially-designed software on a parallel-computing cluster. In addition, we are to begin preliminary research into designing boundary conditions and geometries which will create a specified flow and heat transfer. Included in this report is a brief summary of the project background, a detailed discussion of our individual member’s tasks and the theories underlying our methodology. This report is concluded by a description of the future work to be done.

We would like to announce that our team has been making satisfactory progress towards our goals. We have successfully compiled, configured, and run the code which computes the fluid behavior. In addition, we have been able to visualize the results using various graphical software packages. We are well on our way towards our goal of designing boundary conditions and fluid geometries in order to induce a specified flow and heat transfer.

While many challenges lay ahead, we are confident that we will be able to accomplish all of the things that we have set out to do. We hope that our work will serve as an aid to other teams performing research in this area in the future.

Sincerely,

Gary Cox

Oliver Pozo

In a microgravity environment, such as the International Space Station, where the effects of gravity are greatly reduced, scientists can conduct research that achieves results not possible in ground-based laboratories. Computer simulation can help understand the basic fluid physics, as well as help design the experiments or systems for the microgravity situation.

In our research, we are specifically targeting the use of computation in order to simulate coupled fluid flow and heat transfer in a microgravity environment. Through the use of parallel computing facilities at the Computational Fluid Dynamics lab of the Aerospace Engineering Department, UT Austin, we are able to run multiple scenarios in order to find those flows that are the most interesting for physical experimentation. Computer simulations of idealized cases allow us to better understand the physical processes behind many of the observed physical phenomena in a variety of microgravity environments and non-linear flows. Sensitivity studies to various parameters can be carried out and preliminary design studies of fluid thermal systems are feasible.

The MicroG group would like to thank the following individuals and organizations for their assistance and sponsorship of this project:

Dr. C.F. Carey – Project Sponsor/Coordinator

Dr. R.O. Stearman – Team Sponsor

William Barth – Graduate Advisor/Technical Assistant

Alexandre Aardelea – Post-Graduate Advisor/Technical Assistant

Susan Buck – Undergraduate Assistant/Literature Research

NASA – Sponsor of ESS Grand Challenge Project NCCSS-154

DARPA – Sponsor for grant DABT63-96-C-0061

Introduction *

Background Theory *

Progress Made *

References *

Figure 1 -- Drop Canister being Decelerated in the Deceleration Pit. *

Figure 4 -- Surface Tension Driven Flow………………………………………………..16

The "Microgravity Fluid Mechanics and Heat Transfer Computation" senior analysis and design project is related to the UT research work supported by NASA on "Scalable Parallel Finite Element Computations of Rayleigh-Benard-Marangoni Problems in a Microgravity Environment". Dr. G.F. Carey, Director of the Computational Fluid Dynamics (CFD) Lab in the Aerospace Engineering Department at the University of Texas at Austin is supervising the project. There are several other people involved in the larger project that have been of assistance to us during the start-up process. NASA’s grant was awarded to the CFDLab in 1996 and since then they have been working on research related to microgravity applications. This research has made it possible for the project members to develop a finite element code that can be run in parallel processing mode. This code, MGFLO, developed at the CFDLab computes solutions to fluid mechanics and heat transfer equations to solve problems in a microgravity environment. The code allows the user to vary gravity, study different fluids, investigate fundamental fluid mechanics and change the initial conditions, as well as the boundary conditions. Another feature of the code is the possibility to solve the above mentioned equations in either a coupled or uncoupled manner. More information about the formulas and the way the code runs will be provided in the Background Theory section later in the report.

The project we have undertaken is to be able to apply MGFLO to analyze and design fluid/thermal systems in microgravity environments of interest to NASA. This entails first developing an understanding of the fluid/thermal applications.

To obtain background information we began by investigating sources via the World Wide Web (Web) and the library for literature research. We read several technical papers, published by CFDLab members and other researchers. Many of these papers and information refer to work NASA is doing in this area. NASA Glenn’s (formerly known as NASA Lewis) Web site provided a valuable source of information on current research activities and on earth-based microgravity experiments. (Actually, the Marshall Space Flight Center is the lead center for NASA’s Microgravity Research, but the microgravity research in fluid physics is implemented at Glenn.)

In addition to their earth-based microgravity physical experiments, NASA Glenn also houses the Computational Microgravity Laboratory (CML) where a lot of experiments similar to the ones we are conducting are being carried out. Some of the more interesting experiments included Bubble Dynamics on a Heated Surface and Protein Crystal Growth. Following the literature study, we began work on applications tests. This involved compiling the code and running test case scenarios with idealized fluids. More information about the project and the progress being made will be discussed in the Progress Report section later in the report.

The objective of the project is to carry out application tests and parametric studies for heated fluids in a microgravity environment. We also plan to investigate control of the flow using applied thermal input. There will also be some related MATLAB finite element/optimization work.

NASA is the main group that conducts experimentation in microgravity in the US. They have several research facilities that can give physical experiments between 2.2 seconds and 14 days of microgravity exposure. In fact in the near future (as early as October and hopefully as late as January 2000) they will be able to house experiments for extended periods of time, by the utilization of the International Space Station.

The most readily available facility for microgravity testing are the drop towers that are located at NASA Glenn. These drop towers range from and exposure time of 2.2 to 5.2 seconds. In the figures below one can appreciate the deceleration of a test canister in the 2.2 second drop tower.

Another research facility that NASA uses for longer periods of microgravity exposure is what is known as the "Vomit Comet". This KC-135 aircraft is housed at NASA Johnson in Houston and is used for experiments that need about 30 seconds of exposure to microgravity. The pilot tries to fly the plane following a parabolic path making the environment inside the airplane between the inflection points to be close to microgravity. Each time the plane flies, about 40 runs of 30 seconds each can be done.

Finally when the experiments being conducted need a semi-extended period of microgravity exposure, NASA puts them in the Space Shuttle inside their USML (United States Microgravity Lab) which is located in the payload bay. Usually there are a lot of scientists that try to get their experiments into the Space Shuttle’s USML schedule, but only a few experiments are selected by NASA each time they fly. In the near future though, once the ISS is habitable and especially after the FCF (Fluids and Combustion Facility) is installed in the US Laboratory module in the Space Station, more complicated and lengthy experiments will be able to be conducted in microgravity. The FCF is composed of there main racks. The first rack is the Combustion Integrated Rack (CIS), and will accommodate combustion science principle investigations. The second rack is the fluids integrated rack (FIR), scheduled to launch in 2002 and will house fluid physics principle investigations. The third rack, still being designed will be launched in 2003, completing the Fluids Combustion Facility on the ISS.

Other facilities that are available to NASA, as mentioned in the previous section of this report are the CML which deals with computer based microgravity research.

The senior project team is composed of two members: Gary Cox and Oliver Pozo. They will collaborate with Dr. Carey and graduate and post-graduate researchers in the project.

Literature research was conducted at the Library as well as on the WEB. Interesting papers and WEB sites that were found and used in this report can be found listed in the Reference section at the end of the report.

The MGFLO code was compiled with the initial conditions pertinent to our project. With that done, the code was ready to run in the parallel cluster at the CFDLab. With the code ready to run, several preliminary and informative tests were run where the boundary conditions were varied. Apart from some fixed temperature and slip/no-slip conditions as well as flux/no-flux conditions in the different walls the parametric constants, such as gravity, surface tension, viscosity and other constants were varied over an application range of interest. For example surface tension was varied from –0.01 to-10.0. For these selections, the code was run in parallel on the Beowulf cluster. Results were visualized and put into a movie format with TekPlot. More interesting flows will be visualized with the more capable visualization program ENSIGHT in future test results.

Background information prior to the more detailed literature research consisted of several meetings with Bill Barth and Alexandre Aardelea. During these meetings we were able to visit the Non-Linear Dynamics Lab in the RLM building at the University of Texas at Austin. During this visit we were exposed to several physical experiments that were being conducted on Rayleigh-Benard-Marangoni effects in thin layer fluids. Bill Barth gave us a presentation on the CFDLab’s computer cluster and also on the MGFLO code that we were going to use during part of our senior design project. This stage was important in order to know what kind of technical papers to look for and where to start looking in the library and on the WEB.

With the rapid expansion of the Internet for technical transfer and discussion of experimental results, it is important that all presentations and technical reports be accessible from the internet. This important feature is what is referred to as WEB design in the above list. All the memos and progress reports are available in HTML format as well as the original format they were written in. Links to interesting sites on the internet as well as a comprehensive bibliography can be found in the MigroG site, which can be found at http://www.cfdlab.ae.utexas.edu/nasa_hpcc/microG/ .

Other people that are involved in this project are Bill Barth and Alexandre Aardelea, who have assisted whenever we had problems compiling the code and/or visualizing the results. They also helped guide us in the preliminary literature research and in understanding how to use the simulator. Bill Barth also gave us a comprehensive tutorial of the MGFLO code.

The understanding of the behavior of heated fluids in microgravity conditions is important for designing useful experiments for the space shuttle and the international space station. In addition, such understanding is important for the future design of thermo-fluid systems and machinery that might be employed in microgravity environments. There is a wealth of knowledge of terrestrial behavior heated of fluids, with experimental data that spans generations. However, very little is known of the microgravity behavior of fluids due to the relative difficulty of obtaining experimental data under such conditions.

Some examples of coupled heat and fluid flow of which we are interested includes hot-forming manufacturing, crystal growth, chemical flow processes for pharmaceuticals, volcanic lava flows, and natural and forced convection systems. In a terrestrial setting, these flows are characterized by natural convection. In natural convection, buoyancy is the dominant factor driving the flow. Benard performed a series of experiments in the early 1900’s on heated fluid layers. These experiments later became known as the Rayleigh-Benard problem after Rayleigh provided a mathematical analysis of buoyancy-driven flow.

The role of thermocapillary surface tension in influencing fluid flow wasn’t appreciated until later. Usually surface tension is associated with the curvature of the surface as in the minimal surface problem for soap films, droplets, and interfaces between fluids. Because the surface tension coefficient can vary significantly with temperature, variations of temperature on the surface will cause surface tension gradients which will then produce shear stresses that move the fluid. This effect, called the Marangoni effect, is now known to be a much more significant contributor than buoyancy to the effects first observed by Benard in the thin fluid layers, so now the problem is called the Rayleigh-Benard-Marangoni (R-B-M) problem. [1]

In microgravity conditions, buoyancy effects are negligible. Therefore the thermocapillary surface tension effects become the primary driving force behind the fluid flow. Control of the fluid behavior can be exercised by the application of direct or indirect surface heating. This heating causes controlled changes in the surface tension properties of the fluid, and therefore the shear forces inside the fluid which will direct its movement. In addition, thermocapillary shear flow plays a key role in the propagation of flame and other combustion fronts in microgravity conditions.

Terrestrial experiments in thermocapillary effects have been limited to the study of thin fluid layers. In thin layers, buoyancy forces become less important with respect to the surface tension effects. While much valuable research has been done using such setups, it is obvious that restricting experiments to thin-layer geometry limits the applicablity to general geometry cases. Mathematical modeling and computer simulations, on the other hand, are not restricted to such thin layers, so any arbitrary geometry can be simulated in addition to thin layers.

In the following section we follow precisely the formulation in. [1]

In describing how we go about modeling fluid flows, it is necessary to briefly develop the mathematical framework involved in thermo-fluid flow. Consider 3-dimensional transient fluid flow and heat transfer for a viscous incompressible fluid with a free surface. The mathematical model for such flow is described by the Navier-Stokes equations with the Boussinesq approximation, and the convective heat transfer equation. Due to the variations in surface tension from temperature gradients, there is a shear stress at the free surface. We only consider a fluid geometry with flat surfaces, as a deformable free surface is not currently implemented in the model. The governing viscous incompressible flow equations are as follows:

[1]

[2]

In flow domain W where u is the velocity field, t is the stress tensor and is specified by Stokes hypothesis for a Newtonian fluid, f is an applied body force, g* is the microgravity vector, T* is the reference external temperature, T is the fluid temperature and b is the thermal coefficient. The no-slip condition applies at the walls, so that u equals u_wall at the boundaries.

There is a shear stress due to surface tension effects at the free surface. On the horizontal free surface, the tangential shear stress is given by

[3]

with a similar expression for t zy where g (T) is the surface tension coefficient and T is the temperature.

The relationship describing the heat transfer within the fluid is given by the following:

[4]

where k is the thermal conductivity of the fluid, r is the density, c_p is the heat capacity, and Q is a heat source term.

Taking the above equations, integrating by parts, introducing Stokes Theorem, and performing additional mathematical manipulation yields the following result:

[5]

Now, we introduce the discretization of elements and the finite element basis functions. The resulting pressure and temperature expansions are given by the following:

[6]

[7]

[8]

where k is the velocity component index and u_j^k , p_j and T_j are the nodal values. Taking the previous results and converting to matrix form yields the following relations:

[9]

[10]

[11]

With the base relations now written in a form easily dealt with in a numerical manner, a standard q method for numerical integration is used. This method employs forward, midstep, and backward-Euler integrators. Both coupled and decoupled algorithms can be utilized, either solving temperature and velocity fields in parallel or in serial fashion.

In the present work a simple non-overlapping decomposition of the finite mesh is used. This means that the processor interfaces coincide with a subset of element faces and the nodes on those faces are shared by adjacent processors. This in turn implies that the element calculations can be easily parallelized over the processor partitions. Such a method provides an efficient parallel strategy, as it allows for communication requests to be initiated for the subdomain border element calculations while computation begins on the interior subset. With that initiated, the border element computations can be completed. Taken as a whole, the strategy will permit complete communication overlap provided that there are sufficient elements in the interior subset.

When the global mesh is partitioned across processors, the "send list" of nodes is also set up. These are nodes on the subdomain boundaries and therefore are shared by neighboring processors. A local and global numbering system is used for identification of each node. The implicit equivalence of local node values avoids sending global node numbers across the network, which saves valuable bandwidth. However, it also complicates the forming of the send lists. Fortunately, since the send lists only need to be generated once for the static processor partitions, it is not a major concern for the current implementation of the program.

The program is designed for fast scalable parallel computation of steady and transient solutions to coupled incompressible viscous flow with heat and mass transfer. Parallel efficiency is achieved by careful implementation of MPI (Message Passing Interface) and customized communication software. Most of the computation time is spent solving large sparse systems, so much time has been spent in optimizing the solver. Matrix-vector (MATV) products are repeatedly needed throughout the solving process, therefore special consideration was given in this area. The optimized assembly-language solver BLAS MATV product routines are used, which result in roughly doubling the performance of the computations.

The resulting software is called MGFLO, which is designed for unstructured mesh finite-element simulations on irregular partitions. While designed to run on many different parallel-computing platforms, continued work has been done with a Beowulf-type cluster comprised of 16 Intel Pentium-II processors for the investigation of parallel computing on workstation clusters. Each node is equipped with a single processor, 128 MB of RAM, and a dedicated 100 Mb Fast Ethernet network connection. These workstations comprise a relatively-low-cost cluster built from commodity of parts. In various applications, the cluster’s performance has been shown to scale linearly with the number of processors utilized up to the maximum of 16 that are present in the cluster. The investigation of workstation parallel-computing has shown that a low-cost alternative to dedicated supercomputers exists for preliminary studies, and that the investigation of smaller fluid problems via software such as MGFLO on these low-cost clusters is viable.

In this section the progress made by the MigroG team will be discussed. The schedule that the MicroG project has been following can be found in the following figure.

Background Research: February 1 – February 10, 1999

Literature Research: February 10 – April 28, 1999

Compiling/Running of Code: February 15 – May 1, 1999

Visualization of Results: March 8 – May 3, 1999

Mid Term Presentation: March 31, 1999

Mid Term Report: April 6, 1999

Studies of Underlying Methodology: April 5 – May 3, 199

Parametric Studies/Applications

'Matrix': April 5 – May 3, 199

Supporting Studies on Finite

Elements and Optimization ToolKits:April 5 – May 3, 199

MATLAB Design phase: April 5 – May 3, 1999

Final Presentation: April 28, 1999

Final Report: May 3, 1999

Background research was first conducted at the library and on the WEB from sources provided by Dr. Carey, the supervising faculty member as well as Bill Barth and Alexandre Ardelea from the CFDLAB research group.

The library research proved useful in finding technical papers as well as technical descriptions of fluids and their governing parameters. The WEB research was useful to find out what other universities and institutions are doing in this same field and to point to related interesting papers that could be found at the library or on the web site.

An important first step towards the technical goal was to become familiar with the code and to compile it for a test problem. We had accounts set up in the CFDLAB and with the code running and two meetings with Bill Barth, we were ready to run our own cases of idealized flow. At this point the boundary conditions and the fluid flow and heat transfer governing parameters were varied in order to get a better understanding of the fluid flow and heat transfer interactions. The main parameters that where changed were the gravity, the surface tension and the viscosity of the idealized fluid. At this stage the fluid in use was set to have governing parameters equal to one. By changing the gravity vector, between –10.0 and –0.01 we were able to see the flow pass from a buoyancy driven flow to a surface tension driven flow (this happens as gravity is reduced to microgravity values). The surface tension parameter was also varied from values ranging also from –0.01 to –10. The greater (or more negative) the surface tension was, the stronger the flow was driven by surface tension. For example in the figures below one can see a case of low gravity (-0.01 gravity units) and high surface tension (-10.0 surface tension units). If this figure is compared to the same gravity units and to –0.01 surface tension units one can see that the velocity vectors in the flow are at least 35 times stronger in the figure with greater surface tension.

The reason the vortex is created in a low gravity environment is due to the surface tension effects with the difference in temperature on the surface being the driving force. The reason that the vortex is formed at the top of the figure is because the driving horizontal traction due to thermocapillary surface tension sets here. Furthermore, the lower wall has a no-slip condition which makes all velocities zero. The reason for the flow to turn clockwise is because the surface tension of the hotter flow (left wall) has a lower surface tension (or skin-pull) and there fore the colder flow (right wall) has a higher surface tension (or stronger skin-pull). These cold/hot effects determine how the flow is pulled from the hot (left) section to the colder (right) section in the figure. Now that we understand why the flow is, at the early stages, going from left to right it will be obvious that the flow is going to move through the upper part of the figure. The reason for this is that the upper wall has a no-flux condition, allow any kind of horizontal velocities, while the lower wall has a no-slip condition, making all the velocities locally zero. When the hotter fluid gets to the right side of the figure the flow continues to complete the vortex by going down on the right side and is pushed back up on the left side. This is the same effect for both of the figures shown above. The difference comes in the intensity of the surface tension pull.

For other test cases that were run, similar effects to these were found. In cases where the gravity is high and the surface tension is low, the actual drive of the flow is not the surface tension, as described above, but is due to buoyancy. It is interesting to note that the buoyancy driven flows that we tested had a similar vortex in the upper region.

For the next few weeks before the final presentation and report are due, the design project team is going to conduct a set of test cases with real fluids: water and silicone oil (instead of the idealized fluid that was used in the preliminary studies given here). Also a MATLAB script will be written in order to attempt a preliminary control process for design of a coupled fluid/thermal system. Also studies of the underlying methodology will be undertaken as well as parametric studies and applications, which will be done in a "matrix" fashion. This "matrix" will be composed of 27 runs (or maybe more) where the gravity, surface tension and fluid properties will be changed in such a way that they are al interlaced and can be compared to one another. In the MATLAB programming, elements of optimization will also be included. With this initial preliminary design and the several tasks we have set forth before the final project is due, we will have accomplished our main goal in this senior design project course. The final presentations and reports are due at the beginning of May, 1999.

1. Carey, G.F., H. Swinney, R. McLay, S. van Hook, A. Pehlivanov, G. Bicken, W. Barth, "Thermocapillary Surface Tension Driven Flows", AIAA conference paper, Reno, NV, 1999.
2. NASA Microgravity Research Division, "Fluid Physics" general information sheet.
3. NASA Microgravity Research Division, "Materials Science" general information sheet.
4. NASA Microgravity Research Division URL, "http://zeta.lerc.nasa.gov"