by Dan Hughes
Larry Ybarrondo suggested that we offer some personal information about how we got to Camp NRTS. Larry and Don Curet have jumped in. Some of my background follows.
I have probably included way too much information here. Scrolling past is easy, however.
I was born September 9, 1941, in Pickens, South Carolina. I was the first born of four boys. Pickens is in the far Northwestern corner of South Carolina, in the Foothills of The Blue Ridge Mountains, near where South Carolina, Georgia and North Carolina meet at Ellicott Rock in the middle of the Chattooga River. I played in those foothills, and the mountains beyond, with my brothers and our friends until I was almost 22 years old.
And play we did. From sunup to sunset off in the woods, down in the streams, walking and biking between play sites, climbing rock faces, and making all kinds of our own adventures. We were Rural Free Range decades before Free Range playing was noticed and encouraged. Our friends and we lived outside of town and seldom had a need to head up that way. Not that the town of Pickens was a major destination for any other than the locals. Almost all our adventures were done on foot, hiking, and exploring the hills and mountains and doing fun stuff; climbing rock faces, pretending that we had found a cave, building shelters out of tree limbs and pine needles, and much more. More information about what we did back in the 1950s can be found at Hughes Boys Memoirs. Making kites with newspaper and sticks we got from bushes and using flour and water ‘glue’, attaching rock-loaded parachutes to the end of kite tails and shaking them off by rapid movements of the kites, letting kites so far away they were out of sight, blowing up stuff with Cherry Bombs and two-inch TNT fireworks, dropping same into streams, launching tin cans with same, riding down the road in a ’57 Chevy and throwing same out the windows, making our own bombs with black powder and discarded cotton mill parts, taking apart things we should not have been taking apart, and lots and lots of other stuff.
In my senior year at Pickens High School my history teacher, Miss Hallum, mentioned that I should consider going to college. So I did and entered Clemson College, just 18 miles down the road in Clemson, South Carolina, from home. Several of my classmates also set off for Clemson, we lived at home and formed a carpool system to commute there. We were called Day Students. It was very cheap way to attend college. I could work during Summer, and school breaks, for small wages, and make almost enough money to cover school expenses.
In my senior year at Clemson, 1963, my Controls professor mentioned that I should consider going to graduate school. I didn’t do that right away, probably because I thought I should finally get a real full-time job. At 21, almost 22, in 1963 I had found a job and left Pickens for more or less forever. Worked for a year at Pratt and Whitney Aircraft in West Palm Beach, Florida. P&W had a research and testing site there for both jet engines and rocket motors. I got into the jet engine part of the business, but I do not recall the details of how that came about.
Generally, the space race was well underway and people were being strongly encouraged to get into what is now called Science, Technology, Engineering, and Math (STEM). Before I left Clemson I actually got a job offer by way of a Telegram from an aerospace company out in California. No interview, no job-site trip, sight unseen, solely the Telegram. Very strange and probably can’t be done these days.
I have wonderful memories of almost all those 22 years. We were a typical USA family of the 1950s and 1960s. Dad worked and Mom stayed home until the youngest of us could make it without adult presence. Dad worked first in a cotton mill and then a woolen mill, with a personal handy-man business on the side. From time to time I got to go to a job with him cutting and threading pipe, pouring molten lead to make cast-iron pipe connections, and general gofer stuff.
I graduated Clemson College (now University) in June 1963 with a B.S. degree in Mechanical Engineering. My undergraduate studies focused on heat transfer (Frank Kreith’s little blue book anyone), fluid flow, and thermodynamics. I immediately went to work at Pratt and Whitney Aircraft at their development and testing site near West Palm Beach, Florida. I was hired to work on heat transfer and fluid flow aspects of the famous JetT 58D engine that powered the first versions of the SR 71 Blackbird aircraft. The fastest airplane that’s ever been built.
All the work was classified and I did not know at the time what the application of the engine was. All we knew was that the sink temperature provided to us was a very big number. During my brief employment there I focused on a heat exchanger and the flow of oil around the various parts of the machine. The heat exchanger cooled the oil with the fuel and the fuel was then dumped into and burned in the combustion section of the engine taking the energy added during the cooling with it.
We were all gathered together in vast rooms with desks shoved up against each other bullpen style, with managers sitting at one end near the lanes between the various groups that were arranged by function. The drafting room had the same arrangement with the drawing boards shoved together as far as the eye could see.
A main part of the plant was an engine testing site. A jet engine and rocket motor testing site as Pratt and Whitney developed and tested rocket engines there, too. The control and observation rooms were built with solid concrete because from time to time a compressor or turbine row would separate from the engine and go bouncing all around the test area. I never did see that. But I did see a test engine that had all the plumbing and components exterior to the engine gold plated. The idea was to minimize the radiative heat transfer to the cooling oil and fuel. Some of the rocket motors produced products of combustion that were highly toxic. I heard tales of birds flying into the exhaust plumes and then dropping to the ground. Never did see that either.
I lasted only a year there and in August, 1964, moved to Raleigh, North Carolina, to attend graduate school in Mechanical Engineering at North Carolina State University, NCSU. My graduate studies focused on heat transfer, fluid flow, and mathematics, with Dr. M. N. Ozisik as my main advisor. Dr. Ozisik was a great teacher and totally focused on theoretical and analytical approaches to conduction heat transfer, radiative energy transport, and conjugate problems in these main areas. He wrote several books, including one on numerical methods in conduction heat transfer. His Heat Conduction book, a classic, has been updated and revised by Professor David Hahn of the University of Florida. He was also a great believer in validation of theoretical results with experimental data. My PhD dissertation was an example of his philosophy. My first presentation at a technical meeting was based on that work and presented at the 1969 American Nuclear Society (ANS) meeting in Seattle, Washington. A paper eventually appeared in Nuclear Science and Engineering. My career has to this day focused on fundamental aspects of heat transfer and fluid flow, almost all in the multi-phase thermal sciences.
I still remember that Dr. Ozisik hand wrote drafts of his books and papers using a real fountain pen and ink on that green-lined engineering plotting paper. We were decades away from personal computers on everybody’s desk, but I suspect he never got into that approach to writing. He used a physical realization of the cut and paste method for moving text around. A pair of scissors was always at hand so he would cut the paper and then tape it in the new place with clear Scotch tape. He didn’t use white-out, either. A single-edge razor blade was also at hand so he would gently rub the offending words right off the paper. I attempted to follow his method for writing drafts, but I quickly learned that a ball-point pen makes a too large impression on that green-lined paper. You need a light hand to pull of his correction method.
How I got to Camp NRTS
In 1968, some nine years after Miss Hallum, history teacher at Pickens High School, had mentioned that I should consider college, I was nearing the end of my graduate studies. Larry Ybarrondo, representing the Atomic Energy Division of Phillips Petroleum Company, the operating contractor at the National Reactor Testing Station (NRTS) in Idaho Falls, Idaho, visited the campus for interviews with graduate students who were looking to soon join the workforce. I was one of those he interviewed and was fortunate to be offered a visit to the company and interviews with potential co-workers.
Later in 1968, I am not certain of the date but it was cold and snow season when I arrived in Idaho Falls, I went out for an interview. The flight schedule included a layover and plane change in Salt Lake City. That layover was sufficiently long for me to rent a car and ride up one of the canyons, probably Emigration Canyon, or up Interstate 80. Having spent my entire life in the southeast, I had never seen so much snow. Flying over the snow covered Rocky Mountains was an unforgettable experience.
I do not now recall if I took the infamous last flight to Idaho Falls from Salt Lake City. A flight that I took many times in the following years, usually arriving close to midnight and a very, very quiet town. In the olde days, the 5 pm traffic rush in Idaho Falls was over at 5:15 pm. We could always count on Western Air Lines (We’re Always Late) to hold the flight in Salt Lake for all late-arriving flights that had connecting passengers. At the time, the plane was a propeller-driven DC-6. During my flight the pilot walked back through the cabin to check something, maybe checking the door, maybe to check with a stewardess, and they were all young women back then, about activities later that night, if you get my drift, maybe to score a few of those little bottles liquid refreshment to accompany the evening, and he was wearing sunglasses. I thought it was somewhat unusual for a pilot to be flying a plane full of people in the darkness of night while wearing sunglasses. I finally figured out that he was probably wearing the sunglasses to assist his adjustment to the dark outside when he returned to the flight controls.
Larry’s group that I interviewed was located out on the semi-arid high plains about 60 miles from Idaho Falls on the NRTS at Test Area North, TAN. I do not recall who I chatted with other than I’m sure that Carl Hocevar was among them. And possibly Jay Larson, George Brockett, and Don Curet.
Following the interviews I was offered employment and at the time I was wrapping up my studies and my dissertation. The latter would prove to almost be a show stopper. Larry called me a couple of times over the months to find out my status and to remind me that I had an opportunity for full-time gainful employment waiting. These calls made me very anxious because I did not have a back-up employer; I had put all-in for the NRTS job.
I finally left Raleigh in February 1969, now almost 10 years after Miss Hallum’s suggestion, after passing my prelim exams in math, and completing, defending, and getting approval of my dissertation. I think it was February, but nonetheless it was early in 1969. By this time, Larry’s group had moved into Idaho Falls and had access to an IBM 370 mainframe computer that was located in the same building on the northern edge of the town. The IBM 370 was damn near cutting-edge technology at the time. I think the building was named the Computer Science Center (CSC)??
My initial assignments including getting to know what was going on in an organization, unknown at the time, that would prove to be the nucleus of the world-wide water reactor safety industry. The projects underway included development of mathematical models, numerical solution methods, and computer software for transient, compressible two-phase flows of water in complex engineered equipment, and several experimental projects. The combination of theoretical and analytical developments with corresponding experimental projects is to this day considered to be the standard approach for attacking inherently complex physical problems.
I left NRTS in mid-1975 to go to work at Energy Incorporated (EI). The situation surrounding the decision to leave has been described in a few post on this blog. Some of my work at Camp NRTS and EI in the early-to mid 1970s is also the subject of posts on this blog and this summary by Bob Lyczkowski.
I left EI in 1987 and returned to Camp NRTS and managed to stay there until ca. 1992. Lance Agee needed help getting non-condensable gases in RETRAN, so I went to work, saving his butt again, at CSAi which had spun out of EI taking RETRAN with them. After developing the model equations and modifying the numerical solution methods, I started self-employed consulting from a base in Idaho Falls.
I left Idaho Falls in 1996 to take a position through a contractor at LANL, working on the TRAC-P code. At the time I had spent one-half of my life in Idaho Falls after spending the first half in the Southeast. I again did some self-employed consulting, this time with Los Alamos as my base. EPRI was a good customer during that time. And tele-commuting was the main method of staying in contact with my customers.
In early 2001 I moved to New York to work at KAPL, again with the TRAC-P code. I had been promised actual models and methods development R & D. Instead I spent all my time catching up with the various versions of TRAC as it evolved from TRAC-P to TRAC/M to TRACE. At that time, the USNRC was about five years into the TRAC/RELAP Advanced Computational Engine (TRACE) development project, having a code run-off back in ca. ’96 or ’97, with TRAC the winner. Near the end of my time at KAPL yet another code run-off meet was going on with KAPL backing TRAC/TRACE and Bettis backing RELAP5. Didn’t need to be a part of another one of those, and the promised R & D never happened, and I could clearly see that it wasn’t going to happen, so I quit in early 2003, and “retired” later that year.
For a couple or three years following retirement I worked at writing a book about calculational aspects of boiling two-phase flows. I finally decided, (1) writing a book is too damn hard, (2) I have nothing new to say about boiling two-phase flows, and (3) I much more enjoy learning about new things than I enjoy re-hashing old stuff. So I dropped that.
Moto Road Trips
In the meantime, Mary and I made a couple of long range tours of our wonderful and beautiful country by motorcycle. You can read all about it. I made what is very likely my last Moto Road Trip cross-country ride in 2016.
Ill-posed IVPs with ODEs
I then got interested in following several online discussions / blogs relating to the effects of the addition of carbon dioxide, CO2, to Earth’s atmosphere. Several aspects of the mathematical modelling, and associated numerical solution methods and software development, are related to my experience and expertise. Along the way, I picked up on the numerical solutions of ill-posed Initial Value Problems (IVPs).
I had first encountered these way back in the early 1980s when we were looking into applying RETRAN, and other codes, to Natural Circulation Loops (NCLs) following the Three Mile Island accident. Stability, or lack thereof, in the physical domain was a major issue. And the accuracy of code calculations relative to stability / instability decisions being the associated concern in the modelling domain. It’s an interesting computational problem in that both false positives and false negatives must be rigorously eliminated. Stability, for example, might be due to the inherent dissipative properties of the discrete approximations and numerical solution methods. Instability might be due to less-than-accurate treatment of distributions along the loops; lack of continuity in any of the variables of the problem can induce instability, for example. As can numerical solution methods.
Hundreds of reports and papers have been written, and experiments conducted, on the subject; see Chapter 16 of this book.
In the course of looking into the problem I ran across the Lorenz system of three non-linear ODEs, which is a highly simplified representation of a NCL, Physical Fluid Dynamics. Being three simple ODEs, I fired up an off-the-shelf Runge-Kutta method to see what might come out. My calculated results did not look like those in the book even tho I had set up the same problem. Plus, changing the discrete time step size resulted in curves completely different from the original results.
Well, that was interesting. But being tied to the needs of EPRI’s customers, we had no time to play in the sandbox. Lance was a hard task-master. So, I dropped the work and returned to more pressing needs. Not having time to dig deeper into the problem, I was not aware of the fact that I had just been introduced to ill-posed IVPs for ODEs.
Some 25 years later, in ca.2005, I discovered that the Lorenz concept of chaotic trajectories in the solutions of simple non-liner systems of ODEs plays a very significant role in mathematical modelling of Earth’s atmosphere. Life is a circle.
The models of Earth’s atmosphere are ill-posed in the sense that the solution trajectories are not continuously dependent on the initial data. Infinitely small changes in the initial data result in exponential growth of the difference between the two solutions. In exactly the same way, changes in the discrete time step size used in numerical solution methods leads to the same kind of exponential growth between two solution trajectories. Different solution methods, order of the discrete approximation, for example, also lead to differences in solutions.
I eventually connected with Professor L.S. Yao at Arizona State who had an interest in the matter. In 2008, we submitted a Comment on this paper:
J. Teixeira, C.A. Reynolds, and K. Judd (2007), Time step sensitivity of nonlinear atmospheric models: Numerical convergence, truncation error growth, and ensemble design. Journal of the Atmospheric Sciences, Vol. 64 No.1, pp. 175189.
Our Comment on that paper was published:
L. S. Yao and D. Hughes (2008), Comment on Time step sensitivity of nonlinear atmospheric models: numerical convergence, truncation error growth, and ensemble design Journal of the Atmospheric Sciences, Vol. 65, No. 2, pp. 681-682.
The authors’ Reply.
Subsequently, additional comments and responses about another publication appeared, this one by Lorenz. The paper:
Edward N. Lorenz (2006), Computational periodicity as observed in a simple system, Tellus A, Vol. 58A, pp. 549-557.
L. S. Yao and D. Hughes (2008), Comment on ‘Computational periodicity as observed in a simple system’, by E. N. Lorenz, Tellus A, Vol. 60, No. 4, pp. 803-805.
Response to the comment:
E. N. Lorenz (2008), Reply to comment by L.-S. Yao and D. Hughes, Tellus A, Vol. 60, pp. 806-807.
Following these publications, several appeared that directly addressed the problem of accurate numerical integration of ODE systems that exhibit chaotic response. As frequently occurs on these more or less straight-forward problems a cottage industry builds and lots of people get in on the action. In this case the technical approach is along the lines, “My numbers and integration order are bigger than yours.” Using multi-precision representations of numbers and arithmetic and high order numerical methods, the extent of the reliable range over which the equations can be integrated was significantly extended.
The following papers appeared as the discussions evoloved:
S. Liao (2009), On the reliability of computed chaotic solutions of non-linear differential equations. Tellus A, Vol. 61, No. 4, pp. 550-564.
Kehlet (2010) addressed the problem in a MSc thesis.
B. Kehlet, Analysis and implementation of high-precision finite element methods for ordinary differential equations withapplication to the Lorenz system, MSc thesis, Department of Informatics, University of Oslo, 2010.
And Kehlet and Logg (2010, 2013)
B. Kehlet and A. Logg (2010), A reference solution for the Lorenz system on [0, 1000], American Institute of Physics, ICNAAM, Numerical Analysis and Applied Mathematics, International Conference 2010, Vol. III, Edited by T. E. Simos, G.Psihoyios and Ch. Tsitouras.
B. Kehlet and A. Logg (2013), Quantifying the computability of the Lorenz System, See also Proceedings ofthe VI International Conference on Adaptive Modeling and Simulation (ADMOS 2013), Edited by J. P. Moitinh de Almeida,P. D`ez, C. Tiago and N. Pars. International Center for Numerical Methods in Engineering (CIMNE), 2013.
Sarra and Meador (2011) also addressed the problem.
Scott A. Sarra and Clyde Meador (2011), On the numerical solution of chaotic dynamical systems using extend precision floating point arithmetic and very high order numerical methods, Nonlinear Analysis: Modelling and Control, Vol. 16, No. 3, pp. 340-352.
S. Liao and co-workers, especially really got into it and summarized their calculations in this preprint as follows:
In 2009, Liao  first successfully implemented [Clean Numerical System] CNS to obtain a convergent chaotic solution of the Lorenz equation in the time interval [0,1000], with 400th-order Taylor series and 800-digit MP data. The reliability of this CNS result has been confirmed  by CNS with 1000th-order Taylor series and 2100-digit MP data in a longer time interval [0,2500]. Currently, using 1200 CPUs at the National Supercomputer TH-A1 (in Tianjin, China) and a parallel CNS algorithm with a 3500th-order Taylor expansion and 4180-digit MP data, Liao and Wang  have successfully obtained, for the first time, a convergent and reliable solution of the Lorenz equation in a rather long interval [0,10000], which is several hundred times longer than those from the traditional numerical algorithms (such as the Runge-Kutta method). This brand-new simulation result, never reported in open literature before, provides us a numerical benchmark for mathematically reliable long- term prediction of chaos. [Bold by EDH]
(Their numbers and integration order are bigger than anybody’s.)
 S. J. Liao, Tellus-A 61, 550 (2009).
 P. F. Wang, J. P. Li, and Q. Li, Numer. Algorithms, 59, 147 (2012).
 S. J. Liao, and P. F. Wang, Sci. China – Phys. Mech. Astron. 57, 330 (2014).
Well, enough about that. It was fun.
On-the-Clock Consulting Work
In ca. 2009 I signed up as a part-time, on-call employee of Information Systems Laboratories, inc. (ISL). There is very little playing in the sandbox R&D remaining in my end of the business these days, so the work has for the most part has been straightforward. I did have a small part in helping Glen Mortensen get a flexible-wall model into a version of RELAP5. Glen did all the heavy lifting, and in his usual rigorous and thorough manner. It’s a beauty to see.
One unusual business trip occurred in 2015 when I spent my birthday in Abu Dhabi, UAE, enjoying the spectales of that place along with the immense heat. And working hard, of course.
I think there will be no more On-the-Clock Consulting work forever. That makes stashing away gas money for Moto Road Trips kind of difficult.
Flexible Wall Modelling and Analytical Solutions
As spinoff from the flexible wall modelling work I developed the same capability for RETRAN. This led to some analytical solutions that can be used for Verification by the Method of Exact Solutions. The solutions can be used to determine; (1) that Boundary Conditions are correctly handled in the solutions of the FDEs, (2) the pure inherent dissipation of the numerical solutions, and (3) conservation of mass and energy by the numerical solution methods. The results are documented in the following reports:
These are given as a pair of URLs. The first leads to basically text, and the second gives the detailed developments. This approach is used because I have not studied MML. Plus, I suspect that your typical equation editor makes equation handling easier than MML.
Introduction to implicit function theory Part 0.
Details of introduction to implicit function theory.
Part 1 Introduction to the one node one link case.
Details of the one node one link case.
Introduction to improved documentation of Part 1.
Details of the improved documentation of Part 1.
Introduction of the case of fluid systems mechanically coupled through a flexible wall
Details of the case of fluid systems mechanically coupled through a flexible wall.
Introduction for the case of two nodes coupled by a single link.
Details of the case of two nodes coupled by a single link.
As I do not have access to RETRAN, the modelling remains a possible approach that hasn’t been tested. Review and checking the algebra of these will be appreciated. Any system analysis code results will be especially appreciated. We can very likely get it published.
Natural Circulation Loops
Because of the interest in Natural Circulation Loops (NCLs) relative to Small Modular Reactors (SMRs) I have dabbled in mathematical modelling of these systems.
The results are documented in the following:
here for the case of coupled NCLs with simple Boundary Conditions,
here for the case of HEX Boundary Conditions at both ends of a single loop, and
here for the case of HEX Boundary Conditions at both ends of coupled loops .
I think, based on my literature review for the Handbook, that some of these results have not appeared in the literature. The algebra is long and very tedious. All corrections will be appreciated.
I’m wondering if anyone made it this far./a>