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Heroines; JayVon Muhammad
Education, Health, Higher Consciousness, wisdom May 31, 2017 Leave a comment
JayVon Muhammad
The CEO of the Marin City Health and Wellness Center is a woman of many talents and, seemingly, endless energy.
THE ADDRESS OF the Marin City Health and Wellness Center is 630 Drake Avenue in Marin City. But the best way to find the place is to look for a jam-packed parking lot. Behind that parking lot is a singlestory shingled building that looks a tad tired. But on the inside, the place is full of energy. Phones are ringing, keyboards are clicking and folks of all ages, sizes and colors are asking for assistance. And quickly receiving it.
Within a crowded waiting room, a middleaged man in work clothes is checking in for his dental appointment; a kid in soccer shorts is about to get a sports physical; and a soon-to-be-mom is there for her prenatal care consultation. The Marin City Health and Wellness Center is a FQHC, a federally qualified health center, whose mission is "to provide primary medical, dental and behavioral health care to patients living in Southern Marin and San Francisco." Last year, more than 3,400 patients availed themselves of the center's services in almost 11,300 visits.
In addition to support from the federal government, the Health and Wellness Center receives help from dozens of individual Marin philanthropists, as well as the Marin Community Foundation, Marin General Hospital, Marin Housing Authority, Blue Shield of California, Good Earth and Whole Foods. It was also the only beneficiary this year of a county grant aimed at treating opioid addiction. The center, with 44 employees, operates on an annual budget of just over $5 million.
And in the middle of it all is CEO JayVon Muhammad, an exuberant 44-year-old mother of three and grandmother of three more, who oversees the entire operation. Currently, Muhammad lives in San Pablo but is determined to someday move to Mill Valley.
Can you tell us about your childhood, early years and current family arrangement?
My mother was a drug addict for most of my life; she's been clean now for about six years. And my father was a drug dealer. But that's not as strange as it may sound; in the neighborhood where I grew up, most folks were involved with drugs. In the 1980s, crack cocaine is what devastated most [such] neighborhoods, and Hunters Point, where I spent many of my teen years, was no exception. When I was born, all my family lived in the Fillmore, but when that got gentrified some of my family moved out to the East Bay, some to Sacramento, and my immediate family moved to Hunters Point. I have 11 sisters. They're really half sisters: we all grew up together and knew each other very well, so we're really like "sister sisters"; we just didn't share the same mother. I also had three brothers, but one was murdered, so now it's just the two brothers. Both my mom and dad are still alive and so are all my sisters; it's just that we're scattered between here and Sacramento, and we're hoping to change that. So, it's been a journey and it still is a journey.
What type of education did you receive?
I'm a midwife. I completed three years of a midwifery program and received an Associate Science of Midwifery (ASM) degree. I became pregnant in high school, so I got my GED a few years later than most people [my age], but I got it. Then I attended two years of general college courses in the U.S. and one year of medical school in Mexico. So I have a lot of education; it's just not at the same time or, possibly, in the right location. But when I was in my teens and pregnant, I had the worst experience. I would go to the doctor and it was always really quick. The doctor would listen to my baby and measure my belly but no one would ever ask me,
"Where is the dad?" or
"Who did this to you?"
I was not made to feel like a mother, or a parent. So when I grew older and became a parent and was looking for ways to give back, I decided to become a foster parent to young mothers. I didn't want other girls to go through their pregnancy like I did. At first, they said I couldn't because I was too close in age to the girls who'd be living with me. Then they gave me two psychological assessments and I passed them both and, when I was 21, I had one of only two foster homes in San Francisco for teenage girls who were pregnant. Three girls at a time were living with me until I got married; then it was two girls. By the way, I selected my second husband very discreetly. I knew I did not want to live the way I'd grown up; I knew exactly what I did not want and what I could tolerate. It was always on my mind that things had to change. My husband and I have now been married 21 years and, in addition to my daughter, who has given me three grandchildren, we have a wonderful son who's 18 and a beautiful daughter who's 19. As for foster children, in all, I helped 20 girls through their pregnancies and several of us, children included, are still really close; we often chat on Facebook. So you could say I learned a lot about health and wellness in those years.
How did you acquire the leadership and management skills to be CEO of a $5 million, multitasked organization that employs 44 people?
I think part of it comes from growing up with challenges, like the challenge of poverty and lots of other challenges. I've always had a desire in my gut to do better. And, I want to create something better for poor people. All my life I've wanted to help poor people, create something better for them. But not just poor people; I want something better for all people. Here at work, I try to create a space for each of our employees that makes them healthy and happy, where they can be themselves and not have some rigid environment where a person is standing over them telling them what to do and how to do it. That's how they can do their best to help other people. I've been the CEO at the Health and Wellness Center for three years, but before that I had a year in management with Sutter Health and, before that, in community relations with the Allen Group, which provided community relations services for the Third Street Muni light-rail project in San Francisco. Not having an advanced college degree has never held me back, because I won't let it. And I don't want to go back and get an advanced college degree. I'm not spending another dime to be what I already am, I just want to be a greater version of who I am — and I'll get that by working with others. I learn from everyone. I choose people to work with us because of their passion; if they have leadership skills too, I can train them to do their job. I don't care if they have a college degree; if a person has the skills required for the positions, has a good interview and passes a background check, I hire that person, and then I force [that person] to lead. Personally, I have a good work ethic. I'll show up sometimes when nobody else does and I will stay late until the job is done. I probably work 12 hours a day and can get by with four hours of sleep. And I love my work; it's who I am.
What are your goals for the Marin City Health and Wellness Center?
I think the Marin City Health and Wellness Center can grow into a life-changing clinic. In Marin City, if we have enough time, we will create a clinic that not only improves people's lives through medical doctors, but also improves their economic health. Think about it: economic health is really what makes people healthy. And [the lack of] that's what communities like Marin City suffer from. It's so simple. People with financial resources eat better; they have better schools and parks because they have more tax money. So that's what I want: I want to see the Health and Wellness Center grow into a life-changing clinic, where people become not only medically healthy, but also economically healthy.
The Health and Wellness Center has opened the Marin Family Birth Center. Please tell us about that.
It's in San Rafael, on Las Gallinas near the Northgate mall. We're very excited about it, but it has been very costly to build; we saved up before starting to build it out, and it will be costly to operate, but worth it. It's an alternative birth center that offers the care and support of midwives, doulas, childbirth educators and lactation counselors. This will be Marin's first licensed freestanding birth center; it creates an opportunity for families to deliver their babies in a homelike environment.
You are also a midwife. How many babies have you delivered?
Maybe 300; I haven't really kept count. I was a volunteer midwife in Albania during the war in Kosovo; then I worked a little in Jamaica and I went to medical school in Mexico and to midwifery school in Canada. All the while I was "catching babies." That's what I call being a midwife, catching babies. And I got my license to be a midwife after three years of apprenticeship and two additional years of academic schooling at the National College of Midwifery in Taos, New Mexico. Midwifery means "being with woman," but men can be midwifes too. A man midwifed my second child.
Are all midwifed births natural?
It depends on what we consider natural. Midwives are able to work within many hospitals, but out-ofhospital births are different. Different doesn't mean it's more painful. In fact, I believe it can hurt more when a mother is lying on her back in a hospital bed and pushing against gravity trying to get the baby under a curve and out. A mother working with a midwife decides how she wants to have her baby delivered. A lot of mothers choose the most comfortable way, and for many that means while squatting. That way they're working with gravity, not against it. Many midwifed babies are delivered in water. There are two midwives present at every midwifed birth and emergencies are rare. That's because you the mother must qualify by being healthy (what we call "low-risk") before you can have your baby with a midwife. Because of my job as the CEO, I haven't caught a baby in two years. But last week I helped out when my daughter gave birth to my grandbaby at Kaiser Hospital. The baby wasn't coming out right, so I told my daughter to get up on her hands and knees; she did, and everything went fine. But it was crazy for a while because my daughter is deaf and we had to work through a sign language interpreter who was a 20-year-old boy who'd never experienced childbirth. So for a few minutes, it was really crazy. But, like I said, everything turned out fine.
What else do you have going on this summer?
Well, I'm about to leave on my fourth Quality of Life Road Trip. This year the Health and Wellness Center sponsors seven girls and 11 boys — most are at-risk youth living in public housing — and for 32 days we'll travel in two big vans and visit 26 cities in the United States and we'll even go into Canada, so the kids have to have their passports. It's all about empowerment; many of these children — mostly they're 14 and 15 years old — have never been too far out of Marin City. In Detroit they'll tour Whole Foods; they'll see Niagara Falls; they'll visit a synagogue in Brooklyn; in Washington, D.C., they'll meet Congressman Huffman; and in West Virginia they'll go down into a coal mine. T
They'll hopefully learn two things in those last two stops: one, how to respectfully ask questions, and two, that black people aren't the only ones who are poor. We select the kids who are struggling the most to go on the trip, and they can't bring their cellphones — we provide a phone so they can call home when they want to. Last year we toured Harvard; this year it will be Spellman and Morehouse colleges in Atlanta, Georgia. And we work with the kids while they're in the van.
Like, we list the "Things You Can't Say Anymore." They can't say they don't understand business, because we toured a business in Detroit; they can't say they can't go to college, because in Atlanta they met college students just like them, only a few years older. We'll stay in homes and churches; the Christ Episcopal Church in Sausalito has been so helpful in arranging places for the kids to stay. Once in a while we'll stay in a motel. Each child is asked to bring money, and when that can't happen we quietly slip them a few dollars. The trip costs about $100 a day for each child and we raise that from Marin businesses and individual donors.
We say Quality of Life Road Trip involves 26 cities, two countries, 32 days and 18 changed lives. And it does; it really changes lives — I've seen it happen.
Jesuit World Order Games; Rope-a-Dope-Pope and "The Donald", A Recap
Amerika, Big Brother, child pedophilia, Conspiracy, Education, Higher Consciousness, Jesuit, mind control, money, pedophillia, presidents, Revisionist History, shadow government, vatican May 30, 2017 1 Comment
Operation Mockingbird; How the Jesuit Controlled CIA Control Mainstream News
Amerika, Big Brother, Business, Conspiracy, Education, mind control, Psyops, Revisionist History May 30, 2017 Leave a comment
In 1977, a Rolling Stone magazine article written by Carl Bernstein alleged that over 400 mainstream media journalists were employed by the CIA to parrot their disinformation. He also claimed that one of the most important journalists contracted by Operation Mockingbird was Joseph Alsop (top), who wrote for over 300 different newspapers. Other journalists implicated by the investigation in promoting the tales of the CIA – true or false – were (pictured above, left to right): Stewart Alsop (NewYork HeraldTribune), Ben Bradlee (Newsweek), James Reston (The New York Times), Charles Douglas Jackson (Time), Walter Pincus (Washington Post) and Charles Bartlett (Chattanooga Times). At far right is Carl Bernstein, pictured about the time of his Rolling Stone expose.
http://foodbitsandbites.com/newsletters/FBB167-mockingbird-url.shtml
According to Bernstein and other investigators, the CIA worked closely with CBS, Time magazine, The New York Times, ABC, NBC, the Associated Press, United Press International, Reuters, Hearst Newspapers, Newsweek magazine, The Miami Herald, and many other media outlets in America and abroad. In many cases, the CIA's involvement and collaboration with major American media outlets was done with the full knowledge, consent and complicity of the management of these corporations.
The CIA's primary purpose in infiltrating and collaborating with the major mass media outlets in America was twofold: to gather and assess information gleaned from its many contacts, operatives and sources in the mass media and to spread information (or misinformation) that ostensibly advanced American national interests, at least as perceived by the forces of the Deep State.
Many journalists who wrote propaganda stories on behalf of the CIA viewed their collaboration as patriotic justifying their actions as serving national interests against communism. "I'm proud they asked me and proud to have done it," Joseph Alsop, a noted American journalist and syndicated columnist, unabashedly crowed after it was discovered he (along with many other top journalists) engaged in clandestine operations on behalf of the CIA. "The notion that a newspaperman doesn't have a duty to his country is perfect balls."
In congressional investigations into the CIA's relationship and cooperation with major American media corporations, which included both House and Senate committee investigations in the 1970s, the agency acknowledged utilizing journalists to gather and spread information. However, as Bernstein notes in his report, "The CIA's use of the American news media has been much more extensive than agency officials have acknowledged publicly or in closed sessions with members of Congress."
The Deep State's "special relationship" with the major media outlets in America "enabled the CIA to post some of its most valuable operatives abroad without exposure for more than two decades," according to Bernstein. "In most instances, agency files show, officials at the highest levels of the CIA (usually director or deputy director) dealt personally with a single designated individual in the top management of the cooperating news organization. The aid furnished often took two forms: providing jobs and credentials ('journalistic cover' in agency parlance) for CIA operatives about to be posted in foreign capitals; and lending the agency the undercover services of reporters already on staff, including some of the best known correspondents in the business."
Suffice it to say, the CIA and other Deep State actors had successfully infiltrated the major American media outlets, establishing a base of operations in which information could be gathered and spread to advance the agency's clandestine agenda. "The CIA owns everyone of any significance in the major media," William Colby, who served as director of the CIA from 1973 to 1976, once remarked.
And although the extent of the CIAs involvement with and infiltration of major American media outlets was not entirely revealed, the fact the agency engaged in these type of operations was becoming clear and well established.
CDC: Death rate from Alzheimer's up 55%
Amerika, Big Brother, climate chaos, Conspiracy, Die Off Watch, Education, Health, Higher Consciousness, mind control, Radiation, Revisionist History, scientism, shadow government, WWIII May 30, 2017 Leave a comment
The burden on families and care takers is/will be overwhelming going forward, maybe this is why driverless cars will be such a hit. Our family just lost a loved one at 68 years young with a new type of frontal lobe dementia. Our toxic world by endless consumption and non-consequence living as well as humanities avarice are to blame.
US death rate from Alzheimer's rose dramatically over 15 years. Why? (Can you Say "Geoengineering with aluminum???)
The rate of deaths from Alzheimer's disease increased 55% between 1999 and 2014, according to CDC data recently published in MMWR.
The same data indicated the number of deaths at home attributable to the disease also increased from 14% to 25% during the same time period.
"Millions of Americans and their family members are profoundly affected by Alzheimer's disease. Our new study reveals an increase in the incidence of Alzheimer's disease-related deaths." CDC Acting Director Anne Schuchat, MD, said in a press release. "As the number of older Americans with Alzheimer's disease rises, more family members are taking on the emotionally and physically challenging role of caregiver than ever before. These families need and deserve our support."
According to the CDC, this is the first study to provide county-level rates for deaths caused by Alzheimer's disease.
Chemtrails as "art" How sick can we get???
A team led by Christopher A. Taylor, PhD, of the CDC's division of scientific education and professional development, determined mortality rates using population estimates produced by the U.S. Census Bureau in collaboration with CDC's National Center for Health Statistics. Age-adjusted mortality rates were calculated using the 2000 U.S. standard population. Researchers used joinpoint regression to test the significance of trends in age-specific rates from 1999 to 2014.
Other notable findings included in the report, which is the first to provide county level rates for deaths caused by Alzheimer's disease, include:
•age-adjusted rates of Alzheimer's mortality significantly increased in 41 states and the District of Columbia from 1999 to 2014;
•most Alzheimer's deaths still occur in a nursing home or long-term care facility, but fewer in 2014 (54%) than in 1999 (68%);
•counties with the highest death rates were primarily in the Southeast; other areas with high rates included the Midwest and West Coast; and
•only one state, Maine, had a significant decrease in age-adjusted Alzheimer's disease deaths.
Researchers suggested that their findings indicate caregivers need greater support to care for patients with the disease.
"Significant increases in Alzheimer's deaths coupled with an increase in the number of persons with Alzheimer's dying at home have likely added to the burden on family members or other unpaid caregivers," Taylor and colleagues wrote. "Caregivers might benefit from interventions such as education, respite care, and case management that can lessen the potential burden of caregiving and can improve the care received by persons with Alzheimer's."
Previous CDC data show that Alzheimer's disease is the most common cause of dementia, affecting an estimated 5.5 million adults in the United States and is expected to affect 13.8 million U. S. adults aged 65 years and older by 2050.
Modifiable risk factors associated with an increased risk for dementia include CVD, obesity and years of education, have been identified as factors associated with an increased risk for dementia, according to the CDC. – by Janel Miller
Disclosure: Healio Family Medicine was unable to determine researchers' relevant financial disclosures prior to publication.
"From terminators to teddy bears, anything or any toy can be weaponised."
Amerika, Business, Conspiracy, Higher Consciousness, mind control, Psyops, shadow government May 30, 2017 1 Comment
Cyber kid stuns experts showing toys can be 'weapons'
An 11-year-old "cyber ninja" stunned an audience of security experts Tuesday by hacking into their Bluetooth devices to manipulate a teddy bear and show how interconnected smart toys "can be weaponised".
American wunderkind Reuben Paul, may be still only in 6th grade at his school in Austin, Texas, but he and his teddy bear Bob wowed hundreds at a timely cyber security conference in The Netherlands.
"From airplanes to automobiles, from smart phones to smart homes, anything or any toy can be part of the" Internet of Things (IOT)," he said, a small figure pacing the huge stage at the World Forum in The Hague.
To demonstrate, he deployed his cuddly bear, which connects to the iCloud via WiFi and Bluetooth smart technology to receive and transmit messages.
Plugging into his laptop a rogue device known as a "raspberry pi" — a small credit card size computer — Reuben scanned the hall for available Bluetooth devices, and to everyone's amazement including his own suddenly downloaded dozens of numbers including some of top officials.
Then using a computer language programme, called Python, he hacked into his bear via one of the numbers to turn on one of its lights and record a message from the audience.
"Most internet-connected things have a blue-tooth functionality … I basically showed how I could connect to it, and send commands to it, by recording audio and playing the light," he told AFP later.
"IOT home appliances, things that can be used in our everyday lives, our cars, lights refrigerators, everything like this that is connected can be used and weaponised to spy on us or harm us."
They can be used to steal private information such as passwords, as remote surveillance to spy on kids, or employ a GPS to find out where a person is.
More chillingly, a toy could say "meet me at this location and I will pick you up," Reuben said.
– 'Timebombs' –
His father, information technology expert Mano Paul, told how aged about six Reuben had revealed his early IT skills correcting him during a business call.
Using a simple explanation from dad on how one smart phone game worked, Reuben then figured out it was the same kind of algorithm behind the popular video game Angry Birds.
"He has always surprised us. Every moment when we teach him something he's usually the one who ends up teaching us," Mano Paul told AFP.
But Paul said he been "shocked" by the vulnerabilities discovered in kids toys, after Reuben first hacked a toy car, before moving onto more complicated things.
"It means that my kids are playing with timebombs, that over time somebody who is bad or malicious can exploit."
Now the family has helped Reuben, who is also the youngest American to have become a Shaolin Kung Fu black belt, to set up his CyberShaolin non-profit organisation.
Its aim is "to inform kids and adults about the dangers of cyber insecurity," Reuben said, adding he also wants to press home the message that manufacturers, security researchers and the government have to work together.
Reuben also has ambitious plans for the future, aiming to study cyber security at either CalTech or MIT universities and then use his skills for good.
Failing that maybe he could become an Olympian in gymnastics — another sport he excels in.
Weather Wars Atmo Rivers & Too Hot Now- Earth Frying ~Judas Amigo Blues
Amerika, Big Brother, climate chaos, Conspiracy, Die Off Watch, drought, Education, fracking, Geoengineering, Health, Higher Consciousness, love, mind control, NASA Hoax, Psyops, Radiation, Revisionist History, scientism May 24, 2017 Leave a comment
Must Watch. Critical New Information about Geoengineering and Mis-Deception by members of the Geoengineering movement to keep us from knowing what is really going on and why the very life giving system of Earth is completely manufactured by land and ocean Wet Surface Air Coolers (WSAC)_making massive amounts of steerable water vapor into weather when combined with Aerosol spraying of chemtrails.
Anniversary Thank You and a Favorable Review
Amerika, Big Brother, Business, Education, Flat Earth, Geoengineering, Health, hemp oil, Heroes, Higher Consciousness, Jesuit, language, love, mind control, NASA Hoax, presidents, Revisionist History, scientism, sex slaves, shadow government May 24, 2017 Leave a comment
Hi Dear Readers who read this here and now.
Thank you all who have supported this effort to alert, educate, and inform all to alternative thought and truths. It's been quite the journey.
I have been blessed to have just gone over 4 million views on my blogs and You Tube as to viewership numbers. I began Tabublog.com in 2008 and the definitive and very first Flat Earth website back in January of 2015.
Probably my most important vid/doc ever is about to be released and I hope you all watch/research and get to comprehend the meaning of what I will be presenting. It has been a very profound and deep search into our real state of affairs regarding Earth's life support system that sustains all.
It is a Geoengineered world for sure, I just did not realize to the depth and extent everything has been controlled.. over a large period of land and time, but now the manufactured life support system is out of any man or machine control.
On a more pleasant note, I am asking anyone that can, to go on Amazon's book site and give one or both of my books a review, if you bought the book. They are not allowing any non buyers to comment, just like I cannot just use music on my videos any longer. There all of the sudden protected, along with profit margins for producers, but it's not about the money,
it's about getting the word out and so far my few reviews have been very, very favorable and informative.
Amazon link for comment
https://www.amazon.com/James-W.-Lee/e/B06XBXMGP2/ref=sr_ntt_srch_lnk_1?qid=1491940524&sr=8-1
Amor Russell
This book is a amazing… (I ordered it from Barnes and Nobel and picked it when it came in) This book is the most direct approach to what we now know about our geocentric plane cosmology. This book is for everyone, no matter what your religion. I had a miracle experience with the book as soon as I got it… About 30 minutes after buying this book I walked across the parking lot to the mall, and went in to a T shirt department that customizes T shirts. It was run by 2 Arab Muslims. I told them I wanted a shirt made with "Research Flat Earth" on the back and "The Earth is not a Globe' on the front… with large print so everyone can read it…. they told me the shirt would cost $65 dollars with Large print…… I really wanted the T shirt so I said, "yes." It took them an hour to make, and so stood on the side reading my new book and I flipped through the pages. Every now and then one of the Muslims would look at the cover of the book and smile at me, and I would just hold the book up and point to the cover and smile back. As I was flipping through the pages I hit page 60 with the title "Flat Earth Quran" and I was still reading that page when one of the Muslims walked over and asked me, so "What is Flat Earth?" and I just handed him the book with that page still open and he read all the Flat Earth verses from the Quran that where listed out loud to the other Muslim making my T shirt, and they were really excited. And now they were really interested in hearing about Flat Earth, and overjoyed to make the shirt, and said that they would defiantly be researching "Flat Earth' online. When I got ready to pay for the shirt the Muslim that made it said" Look since you are using this T shirt to advertise Gods Cosmology, I want to pay for most of it … so he only charged me 15 bucks for the shirt and they both hugged my neck when I left. – I thought to myself, "man my next stop is a Hindu Indian restaurant" because there is a chapter in this book on Vedic Flat Earth cosmology as well. – This book is for everyone, no matter what your religion.
RMY Titsinaringer ~
I don't think I have ever found a more profound book to understand Flat Earth legend and theory. That is most likely because there are very few, maybe two books written in modern day on the ever growing topic of geocentrism vs. heliocentrism.
This book is laid out in a colorful introduction about whether we live on a ball or are reconnecting back to over 5,000 years of Theocosmology of our ancestral heritage. I find it strange that this rich history has never been presented in modern day education learning. Why hide 5,000 years of our ancestral history?
The religions all have Flat Earth reference and citation as well including hundred's of KJV bible quotes as well as dozens of firmament and waters above in the Qu'ran as well.
I recommend the color book because the memes are priceless! I will keep this book on my coffee table. It as already stirred many debates in our family and my son even brought up the subject with his school teacher.
Jesus Saves Gretzky Scores
I LOVE THIS BOOK and how it shows what I've always felt about our world. I knew that the Roman Catholic Church had been controlling our world but I had no idea how long they've controlled the world until I made the connection in this heavenly world book of knowledge and Christ's teachings.
Buy this book, you will not be disappointed. It's a keeper. Blessings All.
At first I did not want to read Mr. Lee's book on Chemtrails and Geoengineering. In fact he wanted to send me a free copy because I write often about the subject, but I said "no thanks". Yet the other day someone handed me his book and said it was the scariest book he had ever read in his life, yet was grateful for the knowledge.
So last night I read his book, "Geo-engineering aka Chemtrails; Investigations Into Humanity's 6th Great Extinction Event". I could not put it down. I learned more about why chemtrails occur and who is making the weather than any top website I could learn about I know on the subject.
Who knows how long the internet will allow us to talk about these subjects. Buy the book, it's worth the money.
Oh yea, and sound the alarm to geoengineering the globe for our children's sake.
Smiley T. Wigilton


What a treasure trove the British Newspaper Archive is!
I have just searched my maternal grandfather's name (Henry Fotheringham Ferguson) and discovered the Dundee Evening Telegraph's report of my aunt's wedding in August 1945. Aunty Joan was an actress (using the stage name Joanna Derrill) and this does read a bit like a celebrity report with details of what both my aunt and her bridesmaid (my Mum to be) were wearing.
"The wedding of Miss Joanna Derrill and Mr Antony Groser – two members of Dundee Repertory Company – took place in Edinburgh to-day.
The bride, whose own name is Miss Joan Ferguson, is the elder daughter of Dr and Mrs Henry Fotheringham Ferguson, 21 Inverleith Row, Edinburgh, and the bridegroom is the younger son of Rev. St John Beverley Groser, St George's-in-the-East, London E1, and of Mrs Groser.
Ceremony, which was in St John's Episcopal Church, was conducted by the bridegroom's father, assisted by the rector of the church, Rev. S Harvie Clark.
A beautiful Elizabethan gown of white moire silk taffeta was worn by the bride, whose father gave her away. The full skirt swept into a small train over which rippled her veil, surmounted by a wreath of orange blossom. Deep red roses composed her bouquet.
Miss Margaret Ferguson, sister of the bride, was bridesmaid. Her graceful gown of silver and pale blue brocaded satin was cut on princess lines and showed large puff sleeves. Her pastel tinted hair wreath toned with the sweet peas in her Victorian posy.
Mr Michael Groser, brother of the groom, was best man, and the ushers were Dr Kinnier Ferguson (uncle of the bride), and Mr George Beith (cousin of the bride).
The reception was in the bride's home.
This one newspaper report also answered a question that had bugged me a few years back. On a London Historians' tour of the Royal Foundation of St Katharine in E14 a few years ago I noticed the name "Groser" on a list of names on the wall. I remember wondering if this was a relation to my Uncle Tony married to Mum's sister Joan. The Dundee newspaper article gives my uncle's father's name and on a quick internet search I have discovered that St John Beverley Groser was described both as "the best-known priest in the East End [of London]" and "one of the most significant Christian socialist figures in twentieth-century Britain". He also had a separate career as an actor and played Thomas Becket in the 1951 film Murder in the Cathedral.
As far as I know I never met Uncle Tony's father and he died in March 1966 when I wasn't even 4 years old.
Sadly it was only after my Mum's death in 2016 that I discovered that her sister had a stage name – Joanna Derrill. Mum had talked about Joan meeting Agatha Christie and once I knew her stage name I found more information. Agatha Christie attended the premiere of Hidden Horizons at the Dundee Repertory Theatre in 1944. When it arrived at the Ambassadors Theatre in London it then became Murder on the Nile. Aunty Joan (Joanna Derrill) performed in both the Dundee and London productions. The Ambassadors later became the first home of the Mousetrap until it moved in the 1970s around the corner to St Martin's Theatre.
Tatler 3rd April 1946. Review of Murder on the Nile at the Ambassadors.
The author of this blog (Joanna Moncrieff) leads walks in the West End, Islington and further afield.


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Violence by Hong Kong Protesters Won't Advance Their Cause
Thomas Kellogg
I have watched with growing concern as violence has intensified in Hong Kong. I have been deeply dismayed to see escalating police violence, which has fundamentally damaged the reputation of a police force once known as among Asia's best. And I have...
Who's to Blame for Hong Kong's Weakening Rule of Law?
Alvin Y.H. Cheung
Rimsky Yuen, Hong Kong's third Secretary for Justice, stepped down in early January. He leaves his department, and the city's reputation for rule of law, markedly worse than they were when he took office in July 2012.According to the Department of...
Joshua Wong Sentenced in Hong Kong for Role in Umbrella Movement
Mr. Wong had pleaded guilty to contempt of court for refusing to obey a court order to leave a protest site in the last days of demonstrations, known as the Umbrella Movement, that paralyzed parts of Hong Kong without winning any political...
Worries Grow in Hong Kong as China Pushes Its Official Version of History in Schools
The new proposed curriculum for city schools is missing key parts of modern Chinese history, like Hong Kong's 1967 pro-Communist riots against British rulers and the Tiananmen Square massacre of 1989, when Chinese troops killed hundreds of unarmed...
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redpajama_set_name: RedPajamaCommonCrawl


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Virtu Financial CEO Douglas A. Cifu to Present at the Goldman Sachs U.S. Financial Services Conference on December 7, 2022
Virtu Financial, LLC
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About Virtu Financial, Inc.
Virtu is a leading provider of financial services and products that leverages cutting-edge technology to deliver liquidity to the global markets and innovative, transparent trading solutions to its clients. Leveraging its global market making expertise and infrastructure, Virtu provides a robust product suite including offerings in execution, liquidity sourcing, analytics and broker-neutral, multi-dealer platforms in workflow technology. Virtu's product offerings allow clients to trade on hundreds of venues across 50+ countries and in multiple asset classes, including global equities, ETFs, foreign exchange, futures, fixed income, cryptocurrency and myriad other commodities. In addition, Virtu's integrated, multi-asset analytics platform provides a range of pre-, intra-, and post-trade services, data products and compliance tools that clients rely upon to invest, trade and manage risk across global markets.
Investor Relations and Media Relations
investor_relations@virtu.com
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text:
\section{Introduction}
\label{sec:intro}

Unsteady flow over streamlined surfaces produces interesting but usually
undesirable phenomena such as flutter, buffeting, gust response, and dynamic
stall~\cite{McCroskey_1982}. Dynamic stall is a nonlinear fluid dynamics
phenomenon that occurs frequently on rapidly maneuvering
aircraft~\cite{brandon_1991}, helicopter rotors~\cite{ham_1968}, and wind
turbines~\cite{fujisawa_2001,larsen_2007}, and is characterized by large
increases in lift, drag, and pitching moment far beyond the corresponding
static stall values.  Carr~\cite{Carr_1988} presents an excellent review on
dynamic stall. Dynamic stall can be divided into two categories based on the
degree to which the angle of attack, $\alpha$ increases beyond the static-stall
value. Denoting the maximum $\alpha$ reached during the unsteady motion by
$\alpha_{max}$, these categories are: (1) {\em Light stall:} when
$\alpha_{max}$ is small, the viscous, separated flow region is small (of the
order of the airfoil thickness), and (2) Deep stall: for large $\alpha_{max}$,
the viscous region becomes comparable to the airfoil chord. A prominent feature
of deep stall is the presence of the dynamic stall vortex (DSV) that is
primarily responsible for the large overshoots in aerodynamic forces and
moments.

Many fundamental aspects of flutter, buffeting, and gust response can be
explained using linearized theory. Pioneering work in this area was done by
Theodorsen~\cite{theodorsen_1935} and Karman and Sears~\cite{karman_1938}. The
linearized approach however is limited to small perturbations and the highly
nonlinear phenomenon of dynamic stall requires other approaches. Semi-empirical
methods~\cite{leishman_1989,ericsson_1988} have been developed to model dynamic
stall. These methods are invaluable for preliminary design and analysis, but
they do not provide insight into the physical mechanisms.  Computational
investigations have included Reynolds Averaged Navier-Stokes (RANS)
computations~\cite{visbal_1990} and large eddy simulations
(LES)~\cite{garmann_2011,visbal_2011}. Recent computational efforts have
focused on using highly resolved LES to investigate dynamic stall on flat
plates~\cite{garmann_2011} and airfoils~\cite{visbal_1990}. All of these
simulations have focused on relatively thin airfoils operating at
low-to-moderate chord-based Reynolds numbers, $10^4 < Re_c < 5\times10^5$. In
this paper, we explore the effects of airfoil geometry on the onset of dynamic
stall at $Re_c=2\times 10^5$ using large eddy simulations. In particular, we
focus on the mechanism of stall onset as airfoil thickness is varied.

\section{Methodology}
\label{sec:methodology}
The extensively validated compressible Navier-Stokes solver,
FDL3DI~\cite{visbal_2002} is used for the fluid flow simulations. FDL3DI solves
the full, unfiltered Navier-Stokes equations on curvilinear meshes. The solver
can work with multi-block Overset (Chimera) meshes with high order
interpolation methods that extend the spectral-like accuracy of the solver to
complex geometries. The solver can be run in a large eddy simulation (LES) mode
with the effect of sub-grid scale stresses modeled implicitly via spatial
filtering to remove the energy at the unresolved scales. {\em Discriminating},
high-order, low-pass spatial filters are implemented that regularize the
procedure without excessive dissipation.

\subsection{Governing Equations}
\label{sec:geqs}
The governing fluid flow equations (solved by FDL3DI), after performing a
time-invariant curvilinear coordinate transform from physical coordinates
$(x,y,z,t)$ to computational coordinates $(\xi, \eta, \zeta, \tau)$, are
written in a strong conservation form as
\begin{equation}
  \pd{}{t}\left( \frac{\bf Q}{J} \right) + \pd{\hat{\bf F}_I}{\xi} + \pd{\hat{\bf G}_I}{\eta} + \pd{\hat{\bf H}_I}{\zeta}
  = \frac{1}{Re}
  \left[
    \pd{\hat{\bf F}_v}{\xi} + \pd{\hat{\bf G}_v}{\eta} + \pd{\hat{\bf H}_v}{\zeta}
  \right],
  \label{eq:geq_FDL}
\end{equation}
where $J=\partial(\xi,\eta,\zeta,\tau)/\partial(x,y,z,t)$ is the Jacobian of
the coordinate transformation, ${\bf Q}= \{\rho, \rho u, \rho v, \rho w, \rho
E\}$; the inviscid flux terms, $\hat{\bf F}_I,\hat{\bf G}_I,\hat{\bf H}_I$ are
\begin{equation}
  \hat{\bf F}_I  =
      \begin{bmatrix}
        \rho \hat{U} \\
        \rho u \hat{U} + \hat{\xi}_x p  \\
        \rho v \hat{U} + \hat{\xi}_y p  \\
        \rho w \hat{U} + \hat{\xi}_z p  \\
        (\rho E + p) \hat{U} - \hat{\xi}_t p \\
      \end{bmatrix}, \;
  \hat{\bf G}_I =
      \begin{bmatrix}
        \rho \hat{V} \\
        \rho v \hat{V} + \hat{\eta}_x p  \\
        \rho v \hat{V} + \hat{\eta}_y p  \\
        \rho w \hat{V} + \hat{\eta}_z p  \\
        (\rho E + p) \hat{V} - \hat{\eta}_t p \\
      \end{bmatrix}, ~{\rm and} \;
  \hat{\bf H}_I =
      \begin{bmatrix}
        \rho \hat{W} \\
        \rho u \hat{W} + \hat{\zeta}_x p  \\
        \rho v \hat{W} + \hat{\zeta}_y p  \\
        \rho w \hat{W} + \hat{\zeta}_z p  \\
        (\rho E + p) \hat{W} - \hat{\zeta}_t p \\
      \end{bmatrix},
      \label{eq:inviscidFluxes}
\end{equation}
where,
\begin{align}
  \hat{U} &= \hat{\xi}_t   + \hat{\xi}_x u   + \hat{\xi}_y v   + \hat{\xi}_z w,             \nonumber \\
  \hat{V} &= \hat{\eta}_t  + \hat{\eta}_x u  + \hat{\eta}_y v  + \hat{\eta}_z w,            \nonumber \\
  \hat{W} &= \hat{\zeta}_t + \hat{\zeta}_x u + \hat{\zeta}_y v + \hat{\zeta}_z w,~{\rm and} \nonumber \\
  \rho E  &= \frac{p}{\gamma-1} + \frac{1}{2}\,\rho \,(u^2+v^2+w^2).
\end{align}
In the above, $\hat{\xi}_{(x,y,z)} = J^{-1} \partial \xi/\partial {(x,y,z)}$,
and $u,v,w$ are the components of the velocity vector in Cartesian coordinates,
and $\rho,p,T$ are respectively the fluid density, pressure, and temperature.
The gas is assumed to be perfect, $p = \rho T/\gamma M^2_\infty$. The viscous
flux terms, $\hat{\bf F}_v,\hat{\bf G}_v,\hat{\bf H}_v$ are provided in
Ref.~\cite{visbal_2002a}.

\subsection{Numerical Scheme}
\label{sec:numerics}
Finite differencing is used to discretize the governing equations. Space is
discretized using high-order (up to sixth order) compact difference
schemes~\cite{lele_1992}. Time integration is performed using an implicit,
approximately-factored procedure described in Ref.~\cite{visbal_2002}. Spatial
derivatives of any scalar, $\phi$ are obtained in the computational space
($\xi,\eta,\zeta$) by solving the tri-diagonal system -
\begin{equation}
   \alpha \phi'_{i-1} + \phi'_i + \alpha \phi'_{i+1}
 = \beta \frac{\phi_{i+2}-\phi_{i-2}}{4} + \gamma \frac{\phi_{i+1}-\phi_{i-1}}{2}.
 \label{eq:spderiv}
\end{equation}
Spatial derivatives of different orders of accuracy can be obtained by choosing
different combinations of $\alpha, \beta$, and $\gamma$.  A sixth-order scheme,
obtained by setting $\alpha=1/3,~\gamma=14/9,$ and $\beta=1/9$, is used in this
paper. Equation~\ref{eq:spderiv} is a central scheme which works in the
interior of the domain; for points near the physical and inter-processor
boundaries, one-sided differences are used. Neumann boundary conditions, such
as $\partial p/\partial n=0$, are implemented using fourth-order one-sided
differences. Inviscid fluxes are computed at the node points using
Eq.~\ref{eq:spderiv}. Viscous terms are computed by differentiating the
primitive variables, constructing the viscous flux terms, and then
differentiating the flux terms using Eq.~\ref{eq:spderiv} at the node points.

Since the grid is designed to resolve large, energy-containing eddies (and not
for Direct Numerical Simulations), the content not resolved by the grid (high
wavenumbers) has to be removed from the solution. In traditional LES, this is
achieved via sub-grid scale (SGS) models. In the current simulations, this
objective is achieved by filtering the solution at every sub-iteration during
time integration using the following low-pass, high-order filtering procedure.
Denoting a component of the solution vector (a conserved flow variable) by
$\phi$, its filtered value, $\hat{\phi}$ is obtained by solving the following
system of equations
\begin{equation}
  \alpha_f \hat{\phi}_{i-1} + \hat{\phi}_i + \alpha_f \hat{\phi}_{i+1}
  = \sum_{n=0}^{N} \frac{a_n}{2}\left( \phi_{i+n} + \phi_{i-n} \right),
  \label{eq:filter}
\end{equation}
where a proper choice of the coefficients, $a_n$ as functions of $\alpha_f$,
with $n$ ranging from $1$ to $N$, results in a $2N^{th}$-order accurate
filtering scheme with a $2N+1$-size stencil. $\alpha_f$ is a free variable that
provides additional control on the degree of filtering achieved for a given
order.  Similar to the implementation of spatial derivatives, one-sided
filtering formulae are used near the boundaries. While the central scheme of
Eq.~\ref{eq:filter} is always dissipative, care needs to be exercised with
one-sided filtering formulae as these can amplify certain wave numbers and make
the solution unstable. In the current simulations, an $8^{th}$-order filter
with $\alpha_f=0.4$ is used in the interior points.

\section{Meshing}
\label{sec:mesh}

The simulations are carried out at a chord-based Reynolds number, $Re_c =
200,000$ and a flow Mach number, $M_\infty = 0.1$. The span length of the
airfoil model in the simulations is 10\% of the airfoil chord.
A planar, single-block O-mesh is generated around the airfoil, which is
repeated with uniform grid spacing in the span direction. The mesh is highly
refined over the suction side to resolve the viscous flow phenomena expected
during the airfoil pitch up motion.  Figure~\ref{fig:mesh} shows three
cross-sectional views of the computational mesh for one of the airfoils. The
boundary layer on the pressure side stays laminar and attached through most of
the pitch-up maneuver. A relatively coarse mesh is therefore sufficient to
discretize the pressure side. Besides, the dynamic stall phenomenon is
relatively unaffected by the pressure-side flow in the pitch-up maneuver
considered in this study.

\begin{figure}[htb!]
  \centering
  \centering\includegraphics[width=\columnwidth]{./figures/figure1}
  \caption{Three views of the mesh used for the NACA 0012 simulation: (a) full
    computational domain, (b) zoom view of the grid around the airfoil, and (c)
    zoom view showing the trailing edge geometry and resolution. Every fifth-
    and every fourth point in the radial and circumferential
    directions respectively are shown for clarity.}
  \label{fig:mesh}
\end{figure}

The O-grid in the physical space ($x,y,z$) maps to an H-grid in the
computational domain ($\xi,\eta,\zeta$). The following orientation is used:
$\hat{\bm e}_{\xi}$ points radially out, $\hat{\bm e}_{\eta}$ is in the
circumferential direction. Figure~\ref{fig:mesh} (b) shows the orientation of
$\hat{e}_{\xi}$ and $\hat{e}_{\eta}$; $\hat{\bm e}_{\zeta}$ is along the span
direction such that the right hand rule, $\hat{\bm e}_{\zeta} = \hat{\bm
e}_{\xi} \times \hat{\bm e}_{\eta}$ is obeyed.

Periodic boundary conditions on the $\eta$ boundaries simulate the continuity
in the physical space around the airfoil. Periodicity is also imposed at the
boundaries in the span direction ($\hat{\bm e}_{\zeta}$). Periodic boundary
conditions are implemented using the Overset grid approach in FDL3DI. A minimum
of five-point overlap is required by FDL3DI to ensure high-order accurate
interpolation between individual meshes. A five-point overlap is therefore
built into the mesh. Similar overlaps are created automatically in FDL3DI
between sub-blocks when domain decomposition is used to split each block into
multiple sub-blocks for parallel execution. The airfoil surface is a no-slip
wall. Freestream conditions are prescribed at the outer boundary which is about
100 chords away from the airfoil. The filtering procedure removes all
perturbations as the mesh becomes coarse away from the airfoil to the farfield
boundary.

The same distribution of points around the airfoil is used for the four
airfoils simulated. The same stretching ratios are used to extrude the airfoil
surface grid (along the surface normal direction) to obtain a 2-D O-grid. This
grid is then repeated in the span direction to obtain the final 3-D grid for
each airfoil.

A detailed mesh sensitivity for a constant-rate pitching airfoil has been
presented by Visbal and Garmann~\cite{visbal_2017}. and hence is not repeated
here. The meshes used in the simulations presented here correspond to the
``Fine'' mesh of Ref.~\cite{visbal_2017} with the grid dimensions and first
cell size in wall units ($\Delta x^+, \Delta y^+, \Delta z^+$) presented in
Table~\ref{tab:mesh}.
\begin{table}[htb!]
  \centering
  \caption{Grid dimensions and non-dimensional cell sizes in wall units.
  Averages and max values are over the entire airfoil; the suction side of the
  airfoil is more refined than the pressure side.}
  \label{tab:mesh}
  \begin{tabular}{l|c|c|c|c}
    \hline \hline
    Grid & $N_\xi \times N_\eta \times N_\zeta$ & $\Delta y^+$ (avg, max) & $\Delta x^+$ (avg, max) & $\Delta z^+$ (avg, max) \\
    \hline \hline
    Fine   & $410 \times 1341 \times 134$ &  $0.19,~0.50$  &  $10.6,~87.2$  &  $7.0,~24.5$ \\
    \hline \hline
  \end{tabular}
\end{table}

\section{Results}
\label{sec:results}
The simulations are performed in two steps. In the first step, a statistically
stationary solution is obtained with the airfoil set at $\alpha= 4^\circ$. A
positive $\alpha$ is selected to ensure that the boundary layer on the bottom
surface (pressure side) stays laminar. Dynamic simulations with airfoil motion
are simulated in the second step. A constant-rate pitch-up motion is simulated
with the pitching axis located at the quarter-chord point of the airfoil.
Results of `static' simulations for all three airfoils are presented first.

\subsection{Static Simulations}
\label{sec:static_results}
For the static simulations, the $x$ axis of the coordinate system is aligned
with the airfoil chord and constant inflow is prescribed at the desired angle
of attack ($\alpha=4^\circ$ here). In order to minimize the computation time, a 2-D
viscous solution is first obtained by removing the span dimension.  The
two-dimensional solution is computed on a grid that is reduced in the span
direction to three cells, which is the minimum required by FDL3DI to compute an
effectively 2-D solution. Potential flowfield, obtained using an in-house
vortex panel code, is prescribed as the initial condition for the 2D viscous
simulation (see Fig.~\ref{fig:panelInitialization}). The potential solution
sets the pressure and velocity distribution in the farfield to be reasonably
close to the final viscous solution, and avoids large pressure waves that would
otherwise develop if a uniform flowfield is prescribed as the initial
solution. The 2D simulation is run until integrated aerodynamic lift and drag
forces converge.

\begin{figure}[htb!]
  \centering\includegraphics[width=0.35\columnwidth]{./figures/figure2}
  \caption{Potential flowfield (NACA-0015 case shown) used to initialize the
    static 2-D viscous simulations.}
  \label{fig:panelInitialization}
\end{figure}

Static, three-dimensional simulations are then performed with the 2-D viscous
solution repeated in span to generate the initial solution. The simulation is
run until statistical convergence is reached for integrated airfoil loads, as
well as for static pressure at a few point probes placed in the suction side
boundary layer. Surface properties, such as aerodynamic pressure coefficient
($C_P$) and skin friction coefficient ($C_f$) are extracted and compared
against XFOIL predictions. XFOIL~\cite{xfoil} is a panel method code that
simultaneously solves potential flow equations with boundary integral
equations. It uses the $e^{N}$-type amplification formulation to determine
boundary layer transition.

Figures~\ref{fig:Cp} and~\ref{fig:Cf} compare the FDL3DI predicted $C_P$ and
$C_f$ distributions against those obtained using XFOIL for the four airfoils.
The XFOIL simulations are performed with the $N_{crit}$ parameter set equal to
11. $N_{crit}$ is the log of the amplification factor of the most-amplified
wave that triggers transition. A value of 11 for $N_{crit}$ is appropriate for
use with airfoil models tested in a ``clean'' wind tunnel (i.e., with very low
inflow turbulence). Since the inflow in FDL3DI simulations is uniform with zero
turbulence, $N_{crit}=11$ is deemed appropriate.

The overall agreement between XFOIL and FDL3DI is good; the similarities and
the differences are identified here with their possible causes. The peak
suction pressure predictions by the two codes are in good agreement. Highest
peak suction pressure is observed for the thinnest (NACA-0009) airfoil due to
the smallest radius of curvature and the correspondingly high local
acceleration. The transition location can be identified by a sudden drop in
suction pressure; this drop is subtle, especially for the NACA-0009 airfoil.
Transition location is identified more readily with a sudden increase in $C_f$
as seen for all four airfoils in Fig.~\ref{fig:Cf}. Both methods predict nearly
the same location for transition; the largest mismatch is for the NACA-0009
airfoil.  FDL3DI predicts a longer transition region than XFOIL - the $C_f$
curve rises abruptly (a little earlier than XFOIL) marking transition, then
plateaus, and then rises again to its local peak value corresponding to a fully
turbulent boundary layer. A similar, ``two-stage'' transition is seen in FDL3DI
prediction for the NACA-0012 airfoil as well. Similar behavior has been
observed by Barnes and Visbal~\cite{barnes2016}. XFOIL simulations do not
exhibit this two-stage transition, likely because of the simple transition
model, which ensures a monotonic increase in $C_f$ once transition is
triggered. FDL3DI simulations show a large difference between airfoils in $C_f$
distribution around the transition location - the thicker airfoils show a very
steep spatial gradient in chordwise direction ($\partial C_f/\partial x$)
compared to the thin airfoils. This behavior is not predicted by XFOIL, which
shows almost no change in $\partial C_f/\partial x$ with airfoil thickness. In
all the cases simulated here, the laminar boundary layer separates ($C_f<0$),
transition occurs in the shear layer, and the turbulent boundary layer then
reattaches to the surface.

\begin{figure}[htb!]
  \centering\includegraphics[width=\columnwidth]{./figures/figure3}
  \caption{Comparison of coefficient of pressure, $C_P$ between predictions by
    FDL3DI and XFOIL. XFOIL is run with $N_{crit}=11$ to simulate very low
    inflow turbulence.}
  \label{fig:Cp}
\end{figure}

\begin{figure}[htb!]
  \centering\includegraphics[width=\columnwidth]{./figures/figure4}
  \caption{Comparison of skin friction coefficient, $C_f$ between predictions
    by FDL3DI and XFOIL ($N_{crit}=11$).}
  \label{fig:Cf}
\end{figure}

To investigate the two-stage transition observed in FDL3DI simulations for
NACA-0009 and NACA-0012, the flow structure near transition location is
investigated. Figure~\ref{fig:transition_structures} shows iso-surfaces of
Q-criterion colored by contours of streamwise velocity. The spanwise coherent
2-D vortex structures (seen clearly for NACA-0009 and NACA-0012) are the
instability waves that breakdown and transition the boundary layer to
turbulence. It is apparent from the figure that the transition region is much
longer for NACA-0009 and NACA-0012 airfoils, while transition occurs over a
much smaller region for NACA-0015 and NACA-0018 airfoils. The long transition
region for the relatively thinner airfoils is the reason why the time averaged
$C_f$ distributions show a two-stage transition, with the plateau representing
the region where the boundary layer is transitional. The higher adverse
pressure gradients in the aft portion of the thicker airfoils is possibly the
reason why the flow breaks down faster and transition occurs abruptly for these
airfoils.
\begin{figure}[htb!]
  \subfloat[NACA-0009]{\centering\includegraphics[width=0.9\columnwidth]{figures/figure5a}} \\
  \subfloat[NACA-0012]{\centering\includegraphics[width=0.9\columnwidth]{figures/figure5b}} \\
  \subfloat[NACA-0015]{\centering\includegraphics[width=0.9\columnwidth]{figures/figure5c}} \\
  \subfloat[NACA-0018]{\centering\includegraphics[width=0.9\columnwidth]{figures/figure5d}}
  \caption{Iso-surfaces of Q-criterion to visualize vortical structures near
    the transition region. The transitional region is long for thin airfoils and
    short for thick airfoils.}
  \label{fig:transition_structures}
\end{figure}

\subsection{Dynamic Simulations}
\label{sec:dynamic_results}
In the second step, the airfoil pitch-up motion is simulated via grid motion.
A constant-pitch rate motion, with the pitching axis located at the airfoil
quarter-chord point, is investigated. The non-dimensional rotation (pitch) rate
is $\Omega^+_0 = \Omega_0 c/u_\infty = 0.05$.  An abrupt change of rotation
rate from zero to a finite value would result in a very large acceleration
(limited only by the time step). A ramp function, defined by Eq.~\ref{eq:ramp},
is therefore employed to smoothly transition $\Omega^+ (t)$ from zero at $t=0$
to $\Omega^+_0$ at $t=t_0$. In Eq.~\ref{eq:ramp}, `$s$' is a scaling parameter
that determines the steepness of the ramp function.
\begin{equation}
  \Omega^+ (t) = \frac{\Omega^+_0}{2} \left(\frac{\tanh \left(s
  \left(2t/t_0-1\right)\right)}{\tanh (s/t_0)}+1\right)
  \label{eq:ramp}
\end{equation}

Figure~\ref{fig:ramp} plots the ramp function (Eq.~\ref{eq:ramp} with $s=2.0$
and $t_0=1.0$) used in the dynamic simulations. The objective is to
transition from $\Omega^+=0$ to the final value $\Omega^+=-0.05$ quickly
without introducing large perturbations due to inertial acceleration.  A
hyperbolic tangent function provides a smooth transition at both end points,
and hence is selected to specify the pitch rate. The transition (ramp) region
is limited by $t_0$ and scaled by $s$; the higher the $s$ value, the quicker
the pitch rate transitions to its final value, but the inertial acceleration is
also high. Since the final pitch rate of $-0.05$ is relatively small, the
effects of inertial acceleration are small and can be ignored.

\begin{figure}[htb!]
  \centering\includegraphics[width=0.4 \columnwidth]{figures/figure6}
  \caption{Ramp function used to transition $\dot{\theta} (=\Omega^+)$ from $0$
  to $0.05$, and the associated variations in pitch angle ($\theta$) and
  acceleration ($\ddot{\theta}$); Eq.~\ref{eq:ramp} with $s=2$ and $t_0=1.0$.}
  \label{fig:ramp}
\end{figure}

For $t>t_0$, the airfoil continues to pitch at the constant pitch rate,
$\Omega^+(t)=0.05$, and the angle of attack increases linearly with the pitch
angle, $\theta$. The airfoil goes through various flow stages in the following
sequence during the pitch-up motion:
\begin{enumerate}
  \item The laminar-to-turbulent boundary layer transition point on the suction
    surface moves upstream towards the leading edge.

  \item A laminar separation bubble (LSB) forms on the suction surface and
    moves closer to the leading edge while simultaneously reducing in size with
    increasing angle of attack. The suction peak ahead of the LSB continues to
    rise; most of the boundary layer on the suction side is turbulent at this
    time.

  \item The LSB ``bursts'' and the suction peak collapses, leading immediately
    to the development of the dynamic stall vortex (DSV).

  \item The DSV convects with the flow. The flow entrainment induced by the DSV
    causes the vorticity in the shear layer in the aft portion of the airfoil to
    roll up into a shear layer vortex (SLV).

  \item As the DSV moves downstream, the airfoil pitch-down moment ($-C_M$)
    increases sharply as the lift distribution becomes aft dominant, and moment
    stall occurs.

  \item When the DSV gets close to the trailing edge, the additional lift due to
    the velocity induced by the DSV reduces dramatically, causing lift stall.
\end{enumerate}

This sequence of events can be seen in the snapshots of the FDL3DI predicted
flowfield for the NACA-0012 airfoil in Fig.~\ref{fig:Qcrit_0012}. Each plot in
the figure shows iso-surfaces of the Q-criterion colored by the value of the
$x-$component of flow velocity. The boundary layer transition location can be
clearly seen to have moved upstream in plot (b) compared to plot (a). The LSB
then settles at $x/c \sim 0.06$ and lift continues to increase with $\alpha$.
The LSB bursts somewhere between plots (d) and (e) in Fig.~\ref{fig:Qcrit_0012}
leading to the formation of the DSV, which is seen centered at $x/c \sim 0.2$
in plot (e).  Entrainment of flow by the DSV can be interpreted from the
streamwise elongated eddies seen in plot (f); these are formed because of the
large velocity induced by the DSV impinging on the airfoil and pushing the
residual turbulent boundary layer further downstream, rolling it up into a
shear layer vortex. Plot (f) also marks the beginning of moment stall as the
suction peak moves downstream with the DSV. In plot (h), the DSV is nearing the
trailing edge, marking the onset of lift stall.

\begin{figure}[htb!]
  \centering\includegraphics[width=\columnwidth]{figures/figure7}
  \caption{Iso-surfaces of Q-criterion with colored contours of $x-$component
    of flow velocity of the NACA-0012 simulation at various stages of dynamic
    stall.}
  \label{fig:Qcrit_0012}
\end{figure}

\subsubsection{Boundary Layer Transition}
\label{sec:transition}
The transition location is investigated in detail using time accurate pressure
data sampled at several stations along the airfoil suction surface. Pressure
and velocity data is collected at one cell height away from the surface. The
data is collected with a sampling rate of $\Delta f = 25,000\times u/c$, which
is approximately 80,000 data points for each degree of blade rotation.
Aerodynamic pressure coefficient ($C_P$) is averaged along the span to obtain
$\langle C_P \rangle$, which is further low-pass filtered, and the filtered
quantity is denoted by $\langle \widetilde{C_P} \rangle$. Considering $\langle
\widetilde{C_P} \rangle$ as a quantity averaged locally in time, and following
Visbal~\cite{visbal_2014}, we define rms of pressure fluctuations with respect
to this filtered value as ${C_P}_{rms} = \left[ \langle C_P \rangle - \langle
\widetilde{C_P} \rangle \right]^{1/2}$. Early experiments~\cite{lorber_1988}
and some recent measurements at very high sampling rates~\cite{ansell_2017},
have used rms pressure to identify transition location during dynamic stall.
Transition location is identified by a sharp increase in wall pressure
fluctuations.

Figure~\ref{fig:trans_locs} plots ${C_P}_{rms}$, $\langle \widetilde{C_P}
\rangle$, and $\langle C_f \rangle$ for the four airfoils at $x/c=0.02$ as they
go through the pitch-up maneuver. A large increase in ${C_P}_{rms}$ (defined
w.r.t. $\langle \widetilde{C_P} \rangle$ is clearly visible for each airfoil,
which coincides with the angle of attack where $\langle C_f \rangle$ increases
sharply. For the simulations considered, the $\langle C_f \rangle$ dips
negative before the transition location, which is due to the reverse flow
inside the LSB. The sharp jumps observed in ${C_P}_{rms}$ and $\langle C_f
\rangle$ are consistent with the increase in fluctuations due to the boundary
layer turning turbulent. At the transition location, a dip in suction pressure
($\langle \widetilde{C_P} \rangle$) is also observed, consistent with the
measurements reported in Ref.~\cite{ansell_2017}.

\begin{figure}[htb!]
  \subfloat[NACA-0009]{\centering\includegraphics[width=0.47\columnwidth]{figures/figure8a}}\;
  \subfloat[NACA-0012]{\centering\includegraphics[width=0.47\columnwidth]{figures/figure8b}}\\
  \subfloat[NACA-0015]{\centering\includegraphics[width=0.47\columnwidth]{figures/figure8c}}\;
  \subfloat[NACA-0018]{\centering\includegraphics[width=0.47\columnwidth]{figures/figure8d}}
  \caption{Identification of transition location using
    ${C_P}_{rms}$, $\langle \widetilde{C_P} \rangle$, and $\langle C_f \rangle$.}
  \label{fig:trans_locs}
\end{figure}

\subsubsection{Lift, Drag, and Moment Variations}
\label{sec:clcdcm}
The four airfoils tested here more-or-less follow the same general pattern as
the pitch angle is increased through stall, although there are considerable
differences in the unsteady lift increase, local pressure peaks, and the amount
of trailing edge separation before stall occurs. These differences are
discussed next.

Figure~\ref{fig:dyn_ClCdCm} compares the dynamic section lift-, drag-, and
moment coefficients for the four simulated airfoils as they undergo the
constant-rate pitching motion. We focus first on the NACA-0012 simulation. The
slope of the $c_l-\alpha$ curve increases around $\alpha=18^\circ$, which is due to
the strengthening of the DSV and the associated increase in lift. This is
immediately followed by moment stall, marked by the strong divergence in the
$c_m-\alpha$ curve. As explained earlier, the sharp increase in pitch-down
moment is due to the progressive aft propagation of loading induced by the DSV.
At around $\alpha=25^\circ$ the DSV has propagated close to the trailing edge and
away from the airfoil. As a result the lift induced by the DSV reduces
dramatically and lift stall occurs.

Comparing the sectional lift, drag and moment for the four airfoils (see
Fig.~\ref{fig:dyn_ClCdCm} and Table~\ref{tab:alpha_SSvsDS}) shows that the
largest increase in lift and pitch-down moment due to airfoil motion (dynamic
stall), is observed for the NACA-0009 airfoil; the smallest increase in lift is
observed for the NACA-0015 airfoil; while the NACA-0018 experiences the
smallest increase in pitch-down moment. The increase in unsteady lift is
measured as the difference of $c_{l,max}$ between dynamic- and static stall.
The values for dynamic stall are obtained using FDL3DI while the corresponding
static values are obtained using XFOIL. The angle of attack beyond which the
drag coefficient increases rapidly, increases monotonically with airfoil
thickness -- the thinnest airfoil showing the divergence at much smaller
$\alpha$ than the thick airfoils. While unsteady loads reduce with increasing
airfoil thickness, stall delay (as measured by the difference in $\alpha$ where
dynamic stall occurs versus where static stall occurs) remains nearly
unchanged. The static stall $\alpha$ values for the four airfoils are also
obtained using XFOIL.

\begin{figure}[htb!]
  \centering
  \subfloat[$c_l$]{\centering\includegraphics[width=0.32\columnwidth]{figures/figure9a}}\;
  \subfloat[$c_d$]{\centering\includegraphics[width=0.32\columnwidth]{figures/figure9b}}\;
  \subfloat[$c_m$]{\centering\includegraphics[width=0.32\columnwidth]{figures/figure9c}}
  \caption{Sectional lift-, drag-, and moment coefficients as functions of angle of
  attack during a constant pitch-rate maneuver.}
  \label{fig:dyn_ClCdCm}
\end{figure}

\begin{table}[htb!]
\centering
\caption{Angle of attack values at which static stall and dynamic stall occurs
  (denoted by $\alpha_{SS}$ and $\alpha_{DS}$ respectively) for different
  airfoils.  Moment stall and lift stall values are indicated separately.
  Static stall values are obtained using XFOIL whereas dynamic stall values are
  from FDL3DI simulations.}
\label{tab:alpha_SSvsDS}
\begin{tabular}{r|c|l|l|l}
\multirow{2}{*}{} & \textbf{Moment Stall} & \multicolumn{3}{c}{\textbf{Lift Stall}} \\ \cline{2-5}  \cline{2-5}
                  &                   $\alpha^{(M)}_{DS}$ & $\alpha^{(L)}_{DS}$ &                   $\alpha^{(L)}_{SS}$ & $\Delta \alpha^{(L)} = \alpha^{(L)}_{DS} - \alpha^{(L)}_{SS}$  \\ \hline  \hline
        NACA 0009 & \cellcolor[HTML]{EFEFEF}15.0           &   22.2               & \cellcolor[HTML]{EFEFEF}  10.7         &    11.5                                        \\ \hline
        NACA 0012 & \cellcolor[HTML]{EFEFEF}18.7           &   24.6               & \cellcolor[HTML]{EFEFEF}  13.7         &    10.9                                        \\ \hline
        NACA 0015 & \cellcolor[HTML]{EFEFEF}23.5           &   25.5               & \cellcolor[HTML]{EFEFEF}  15.0         &    10.5                                        \\ \hline
        NACA 0018 & \cellcolor[HTML]{EFEFEF}22.0           &   26.0               & \cellcolor[HTML]{EFEFEF}  17.0         &     9.0                                        \\ \hline \hline
\end{tabular}
\end{table}

\subsubsection{Effect of Finite Span in Simulations}
\label{sec:coherence}
The span of the simulated airfoil geometries is equal to 10 percent of the
airfoil chord length. Periodic boundary conditions are employed in the span
direction. The impact of using finite span length is assessed by investigating
spanwise coherence at different stages during the pitch-up maneuver. Magnitude
squared coherence $\gamma^2(\Delta z)$ is defined as
\begin{align}
  \gamma^2(\Delta z) &= \frac{\langle \abs{S_{xy}}^2 \rangle}{\langle S_{xx}\rangle \langle S_{yy} \rangle}
  \label{eq:coherence}
\end{align}
where $S_{xy}=\int_{-\infty}^{\infty} \exp(-i \omega \tau) R_{xy}(\tau)\,{\rm
d} \tau$ is the cross-spectral density of pressures between two points along
the span separated by $\Delta z$, at a fixed chord-wise location of $x/c=0.5$;
$S_{xx} = \int_{-\infty}^{\infty} \exp(-i \omega \tau) R_{xx}(\tau)\,{\rm d}
\tau$ and $S_{yy} = \int_{-\infty}^{\infty} \exp(-i \omega \tau) R_{yy}(\tau)
\,{\rm d} \tau$ are power spectral densities at each of the two points.  The
cross-spectral and power spectral densities are respectively the Fourier
transforms of the cross-correlation ($R_{xy}(\tau)$) and auto-correlation
($R_{xx}(\tau)$) functions of the signals (pressure time history). The angular
brackets in Eq.~\ref{eq:coherence} denote ensemble average, which is reduced to
time averaging here by assuming ergodicity.

The entire pitch-up maneuver is divided into three time intervals. The left
plots in Fig.~\ref{fig:coherence} plot the pressure signal in the time domain
at a reference point on the airfoil suction surface ($x/c=0.5; z/c=0$) for
these three intervals. Magnitude square coherence, $\gamma^2(\Delta z)$ plots
for each of these intervals are shown on the right in Fig.~\ref{fig:coherence}.
The first interval is characterized by strong instability modes that ultimately
cause boundary layer transition on the suction surface. These instability modes
are highly correlated in the span direction; they are essentially
two-dimensional. The coherence plot for this time interval shows high spanwise
correlation at several high frequencies corresponding to these essentially 2-D
modes.

In the second interval, the boundary layer is turbulent at the selected
chord-wise location, and dynamic stall onset occurs towards the very end
of the interval ($\alpha \sim 20^\circ$). The corresponding coherence plot shows
relatively small spanwise coherence, suggesting that the simulated span length
is sufficient to investigate onset of dynamic stall.

In the third time interval, the DSV convects over the chordwise location,
$x/c=0.5$ and the airfoil experiences deep stall. Very large coherence is
observed at low frequencies corresponding to the large-scale, slow-moving DSV.
The span length of 10\% chord is therefore not sufficient to study post-stall
airfoil behavior, however simulation of interval 2, where stall onset occurs,
can be carried out on this finite-span geometry model. This conclusion is
corroborated by the results for simulations performed for different span
lengths.~\cite{visbal_2017}

\begin{figure}[htb!]
  \subfloat[Interval 1]{\centering\includegraphics[width=0.9\columnwidth]{figures/figure10a}} \\
  \subfloat[Interval 2]{\centering\includegraphics[width=0.9\columnwidth]{figures/figure10b}} \\
  \subfloat[Interval 3]{\centering\includegraphics[width=0.9\columnwidth]{figures/figure10c}}
  \caption{Spanwise coherence of $C_P$ at $x/c=0.5$ (shown for the NACA 0015
    airfoil) during pitch-up maneuver. The entire maneuver is divided into three
    intervals to assess adequacy of the span length in the simulations.}
  \label{fig:coherence}
\end{figure}

\subsubsection{Onset of Dynamic Stall}
\label{sec:stallMechanisms}
Based on the nature of the boundary layer separation leading to dynamic stall,
McCroskey~{\em et al.}~\cite{mccroskey1981} classified dynamic stall (see
Fig.~4 in Ref.~\cite{mccroskey1981}) into the following categories:
\begin{enumerate}

  \item {\em Leading edge stall} can occur in one of two ways - (a) the LSB may
    ``burst'' as the adverse pressure gradient becomes too high and the
    separated shear layer fails to re-attach, leading to formation of the DSV,
    or (b) via an abrupt forward propagation of flow reversal to the leading
    edge.

  \item {\em Trailing edge stall} initiates with flow reversal near the
    trailing edge. The reverse flow region gradually expands as the separation
    location moves upstream with increasing angle of attack. Once the
    separation point reaches close to the leading edge, the reverse flow region
    covers most of the airfoil. The DSV then forms at the leading edge and
    convects downstream and away from the airfoil.

  \item {\em Thin airfoil stall} is said to occur when the LSB progressively
    lengthens and covers the entire airfoil.

  \item {\em Mixed stall} can occur in two ways: (a) flow separation occurs
    simultaneously near the leading and trailing edges and the separation
    points move toward each other and merge near mid-chord, or (b) flow
    separation occurs near mid-chord, the separation point subsequently
    bifurcates with one branch moving upstream and the other downstream.
\end{enumerate}
\clearpage

We investigate the mechanism of stall onset for the cases considered here by
analyzing the details of the flowfield over the suction surface for each
airfoil. Figures~\ref{fig:Cp_contours} and~\ref{fig:Cf_contours} respectively
plot spanwise averaged contours of $-C_P$ and $C_f$ (denoted by -$\langle C_P
\rangle$ and $\langle C_f \rangle$ respectively) on the suction side of the
airfoil as functions of chordwise distance and angle of attack, $\alpha$. This
representation is similar to $x-t$ diagrams with $\alpha$ representing time
($t$) scaled by the pitch rate (since the pitch rate is constant). $x-t$
diagrams are useful to identify characteristics of hyperbolic equations.
Contour plots are shown for all four cases. The sequence of flow events
identified earlier in Section~\ref{sec:dynamic_results} are clearly seen in the
contour plots. The transition location is identified by the boundary where the
2D instability modes (seen clearly in Fig.~\ref{fig:Cf_contours} as alternating
blue and red spots) start to appear. The transition location moves upstream
with increasing $\alpha$. The speed at which the transition location moves
upstream reduces with increasing airfoil thickness. The LSB forms near the
leading edge (marked by leveling off of chordwise variation of $\langle C_P
\rangle$) and is sustained up to approximately $\alpha =
11^\circ,~15^\circ,~19^\circ$, and $23^\circ$ for the 9\%,12\%, 15\%, and 18\%
thick airfoils respectively.
\begin{figure}[htb!]
  \subfloat[NACA-0009]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure11a}} \qquad
  \subfloat[NACA-0012]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure11b}} \\
  \subfloat[NACA-0015]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure11c}} \qquad
  \subfloat[NACA-0018]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure11d}} \;
  \caption{Contours of span-averaged pressure coefficient ($\langle C_P
    \rangle$) on the suction side of the four airfoils through the constant-rate
    pitch-up motion.}
  \label{fig:Cp_contours}
\end{figure}
\begin{figure}[htb!]
  \subfloat[NACA-0009]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure12a}} \qquad
  \subfloat[NACA-0012]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure12b}} \\
  \subfloat[NACA-0015]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure12c}} \qquad
  \subfloat[NACA-0018]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure12d}}
  \caption{Contours of span-averaged skin friction coefficient ($\langle C_f
    \rangle$) on the suction side of the four airfoils through the constant
    pitch-rate motion.}
  \label{fig:Cf_contours}
\end{figure}

Figure~\ref{fig:LSB_Cp} (a) plots the variation of $C_P$ with arc length
measured from the leading edge for each airfoil just before the LSB collapses.
The abscissa is plotted on a logarithmic scale to zoom in on the LSB. The size
of the LSB is clearly seen to reduce with airfoil thickness. It is also
observed that the thickest airfoil (NACA-0018) experiences the largest increase
in peak $-\langle C_P \rangle$, quite in contrast with integrated lift increase due to dynamic
stall, which is observed to be highest for NACA-0009 (see
Fig.~\ref{fig:dyn_ClCdCm} (a)). This is due to larger leading edge radius of
curvature in thicker airfoils which alleviates the increase in adverse pressure
gradient due to airfoil pitch up motion, hence sustaining the LSB to higher
$\alpha$. A similar observation has been reported in
Ramesh~{\em et al.}~\cite{ramesh2011augmentation}, which defines a leading edge
suction parameter (LESP) and identifies the critical value of LESP for a given
airfoil geometry at which the flow separates at the leading edge. The LESP is
defined in an inviscid sense as the flow velocity at the leading edge of the
airfoil; a viscous equivalent of LESP would be static pressure with opposite
sign. Ramesh~{\em et al.}~\cite{ramesh2011augmentation} remark that the critical LESP
should increase with increasing airfoil thickness.
\begin{figure}[htb!]
  \centering
  \subfloat[Variation of $\langle C_P \rangle$ with arc length on the suction side before LSB burst]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure13a}} \qquad
  \subfloat[$\langle C_P \rangle$ variation with $\alpha$ at $x/c=0.005$]                           {\centering\includegraphics[width=0.45\columnwidth]{figures/figure13b}}
  \caption{Span-averaged aerodynamic pressure coefficient (-$\langle C_P
    \rangle$) variation: (a) with arc length measured from the airfoil leading
    edge just before the LSB bursts, and (2) with angle of attack at $x/c=0.005$ as
    each airfoil is pitched up at a constant rate.}
  \label{fig:LSB_Cp}
\end{figure}

The LSB ``burst'' is marked by a sudden loss in suction near the leading edge
with increasing $\alpha$. Figure~\ref{fig:LSB_Cp} (b) plots the variation with
$\alpha$ of $-\langle C_P \rangle$ on the suction side of each airfoil at
$x/c=0.005$. The suction pressure peak collapse is more sudden for the thicker
airfoils.  The collapse of the suction peak is followed immediately by the
formation of the dynamic stall vortex (DSV). These events are notated in the
plots in Figs.~\ref{fig:Cp_contours} and~\ref{fig:Cf_contours}. The locus of
the DSV is clearly visible in Fig.~\ref{fig:Cp_contours} as a hotspot streak
running from left to right at an angle (marked with a blue arrow); the angle
determined by the speed at which the DSV convects along the airfoil chord, and
the color intensity signifying the additional suction induced by the DSV. The
{\em chordwise} convection speeds of the DSVs, computed using the slopes of the
hotspot streaks, are: 0.15, 0.18, 0.24, and 0.30 for the 9\%,12\%, 15\%, and
18\% thick airfoils respectively.  Note that the freestream flow speed is 1.0.
The apparent increase in convection speed with airfoil thickness is due to the
fact that the DSV formation and propagation occur at higher pitch angles with
increasing thickness. This is because, at higher pitch angles, the flow speed
over the entire airfoil is higher for thicker airfoil corresponding to the
higher suction ($-\langle C_P \rangle$) seen in Fig.~\ref{fig:LSB_Cp} (a) for
thicker airfoils.  A small contribution to the difference in chordwise
convection speed of the DSV also arises from the following. The DSV does not
actually convect along the airfoil chord; it moves approximately in the
direction of the freestream velocity vector. The DSV convection speed measured
using the slopes of the hot streaks in Fig.~\ref{fig:Cp_contours} is the
projection of the actual speed onto the direction of the chord line. Since the
airfoil pitch angle at the point when the DSV forms increases with airfoil
thickness, the projected chordwise convection speed would be higher for thicker
airfoils even if the actual (physical) convection speeds are the same.

Flow reversal on the airfoil suction surface is investigated to find out if it
plays a role in dynamic stall onset.  Region of flow reversal are identified in
Fig.~\ref{fig:Cf_contours} by negative values of $\langle C_f \rangle$. A
two-color scheme is chosen for the contour plots in Fig.~\ref{fig:Cf_contours}
to aid in visually identifying the reverse-flow regions. It is seen that for
NACA-0009, there is virtually no flow reversal near the trailing edge by the
time the DSV forms and stall occurs. In the NACA-0012 case, there is a hint of
flow reversal (faint blue contours between $12^\circ < \alpha < 18^\circ$;
region between the dashed black and green lines in Fig.~\ref{fig:Cf_contours}
(b)) localized near the trailing edge. The NACA-0015 case however shows a
moderate size flow separation region that reaches almost up to 30\% chord when
the LSB bursts and dynamic stall begins. In these three cases, the dynamic
stall onset is clearly triggered by the bursting of the LSB and hence can be
categorized as leading edge stall. For the thickest airfoil tested (NACA-0018)
however, the flow reverse flow region in the turbulent boundary layer reaches
the location of the LSB ($x/c \sim 0.18$) exactly at the time when the LSB
collapses. In this case, it is difficult to isolate the mechanism that triggers
dynamic stall. The trailing edge separation region interacting with the LSB
could be the mechanism that causes the airfoil to stall.

Another characteristic, that is readily observed in Fig.~\ref{fig:Cf_contours}
(c), is the left-to-right running line that starts at the LSB-burst location
and convects at a speed greater than that of the DSV (shallower angle in the
plot). This characteristic is denoted by the green dashed line with an
arrowhead in the figure. The $\langle C_f \rangle$ changes sign across this characteristic -
from negative to positive as $\alpha$ is increased. A moderate drop in suction
pressure is also observed across this characteristic
(Fig.~\ref{fig:Cp_contours}). As the DSV grows, some of the viscous boundary
layer vorticity rolls up into it. The remaining vorticity rolls up further
downstream into a shear layer vortex (SLV). The DSV and the LSV are visualized
in Fig.~\ref{fig:SLV} using vorticity contours and streamlines. In between the
DSV and the LSV, there is a region of positive $\langle C_f \rangle$ due to the interplay
between the freestream and the velocity induced by the DSV. This is also seen
in Fig.~\ref{fig:Qcrit_0012} (e \& f) where the region between the DSV and the
LSV shows turbulent eddies stretched in the streamwise direction due to the
flow locally accelerated by the DSV. The characteristic referred to above,
marks the trailing end of the SLV. The propagation speed of this characteristic
is nearly equal to unity as the SLV convects with the local flow speed along
the chord.
\begin{figure}[htb!]
  \centering
  \centering\includegraphics[width=0.7\columnwidth]{figures/figure14}
  \caption{Vorticity contours for NACA-0015 airfoil at $\alpha=22.41^\circ$ identifying
  the shear layer vortex (SLV) and the DSV.}
  \label{fig:SLV}
\end{figure}

Figure~\ref{fig:flow_reversal} plots instantaneous contours of chordwise blade
relative velocity for each airfoil immediately prior to onset of dynamic stall.
The contours are cutoff above the zero value to show only the reverse flow
regions. Reverse flow region is clearly visible in the aft portion of the
relatively thick airfoils (NACA-0015 and NACA-0018), while the 9\% and 12\%
thick airfoils show almost no flow reversal. While these plots provided a good
qualitative view of how far upstream the reverse flow region reaches at the
onset of dynamic stall, the skin friction coefficient is examined next for a
quantitative assessment.
\begin{figure}[htb!]
  \subfloat[NACA 0009]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure15a}} \qquad
  \subfloat[NACA 0012]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure15b}} \\
  \subfloat[NACA 0015]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure15c}} \qquad
  \subfloat[NACA 0018]{\centering\includegraphics[width=0.45\columnwidth]{figures/figure15d}} \\
  \caption{Contours of blade-relative chord-wise flow velocity for the four
  airfoils immediately before onset of dynamic stall. The contours are cut-off
  above 0 to identify reverse flow regions.}
  \label{fig:flow_reversal}
\end{figure}

Figure~\ref{fig:NACA-0015_CpCf} shows line plots of $-\langle C_P \rangle$ and
$\langle C_f \rangle$ along the NACA-0015 airfoil chord at five different
angles of attack ($\alpha$) during the pitch-up maneuver. The $\alpha$ values
are selected to illustrate a few interesting stages in the pitch up maneuver.
At $\alpha=9.23^\circ$, the laminar boundary layer over the airfoil locally
separates (see $\langle C_f \rangle$ plot) and transitions; the transition
region shows oscillations corresponding to the instability modes in both
$\langle C_P \rangle$ and $\langle C_f \rangle$. At $\alpha=13.81^\circ$, the LSB
is securely positioned close to the airfoil leading edge and the boundary layer
transitions abruptly right behind the LSB. Some evidence of the turbulent
boundary layer separating near the trailing edge is also visible. Further
increase in $\alpha$ to $19.31^\circ$ causes the LSB to move upstream and shrink in
size. At this time, the turbulent boundary layer is separated beyond mid-chord
($\langle C_f \rangle <0$). The LSB bursts as $\alpha$ is increased beyond
$19.31^\circ$ and the DSV forms. The DSV is seen as locally increased $C_P$ value
in the curves for $\alpha=20.69^\circ$ and $22.98^\circ$. As the DSV forms and convects
downstream, some part of the turbulent boundary layer reattaches (as seen in
the $C_f$ curve for $\alpha=22.98^\circ$) due to the large induced velocity by the
DSV. This is marked as ``flow reversal boundary'' in
Figs.~\ref{fig:Cp_contours} and~\ref{fig:Cf_contours}.
\begin{figure}[htb!]
  \subfloat[-Span-averaged pressure coeff., $-\langle C_P \rangle$]    {\centering\includegraphics[width=0.45\columnwidth]{figures/figure16a}} \qquad
  \subfloat[Span-averaged skin friction coeff., $\langle C_f \rangle$] {\centering\includegraphics[width=0.45\columnwidth]{figures/figure16b}} \\
  \caption{Distributions of $-\langle C_P \rangle$ and $\langle C_f \rangle$
    along the NACA-0015 chord at five angles of attack during the pitch up
    maneuver.}
  \label{fig:NACA-0015_CpCf}
\end{figure}

Figure~\ref{fig:Cf_cmp} compares $C_f$ distributions between the four airfoils
taken immediately prior to the bursting of the LSB. No flow separation is seen
near the trailing edge for the thinnest airfoil. The NACA-0012 simulation shows
reverse flow in a very small region near the trailing edge. More than 50\% of
the NACA-0015 airfoil experiences reverse flow before LSB burst, while for
NACA-0018, the turbulent flow separation point reaches the edge of the LSB
before onset of stall. The close proximity of the turbulent flow separation
with the LSB suggests that the stall onset could be caused either by the
bursting of the LSB or by the separated turbulent boundary layer interacting
with the LSB for the NACA-0018 airfoil.
\begin{figure}[htb!]
  \centering\includegraphics[width=0.6\columnwidth]{figures/figure17}
  \caption{$\langle C_f \rangle$ distributions on the suction surfaces of the
    four airfoils immediately before onset of dynamic stall.}
  \label{fig:Cf_cmp}
\end{figure}

\section{Conclusions}
\label{sec:conclusions}
Onset of dynamic stall is investigated at $Re_c=2\times10^5$ for four symmetric
NACA airfoils of varying thickness -  9\%, 12\%, 15\%, and 18\%. A constant
rate pitch-up airfoil motion about the quarter-chord point is investigated
using wall-resolved large eddy simulations. Comparisons are drawn against XFOIL
for static simulations at angle of attack, $\alpha=4^\circ$. Overall, the
agreement between FDL3DI and XFOIL in predicting $C_P$ and $C_f$ distributions
is quite good. XFOIL however does not capture the two-stage transition process
observed in FDL3DI for relatively thinner (9\% and 12\%) airfoils. XFOIL also
does not show any significant change in $\partial C_f/\partial x$ with airfoil
thickness, whereas FDL3DI predicts a large increase with thickness.

The effect of finite span size is evaluated by investigating spanwise coherence
of pressure. It is found that while the solution is highly correlated along the
entire span in the post-stall region, the correlation is rather small in the
stall incipience region and hence onset of stall can be investigated with the
span length of 10\% chord utilized in this study.

Dynamic simulations show the following sequence of events: (1) upstream
movement of the transition location, (2) formation of a laminar separation
bubble (LSB) and rise in suction peak pressure, (3) LSB burst followed by
formation of the dynamic stall vortex (DSV), (4) roll up of boundary layer
vorticity into a vortex (shear layer vortex or SLV), (5) sharp increase in
pitch-down moment (moment stall), and (5) precipitous drop in airfoil lift
(lift stall). While all the airfoils undergo the same sequence of events, the
duration of each event and the associated aerodynamics differ substantially
with airfoil thickness. The thinnest airfoil tested (NACA-0009) experiences the
largest increase in sectional lift coefficient whereas the highest peak suction
pressure is obtained for the thickest airfoil (NACA-0018).

Comparisons of ${C_P}_{rms}$, where mean $C_P$ is obtained via low-pass
filtering the solution, show high correlation between increase in ${C_P}_{rms}$
and sharp increase in $C_f$, thus verifying that ${C_P}_{rms}$ measurements can
be effectively used to locate boundary layer transition.

Spatio-temporal diagrams of span-averaged $-C_P$ and $C_f$ clearly show the
different stages of dynamic stall, and highlight the differences between the
different airfoils. The $\alpha$ up to which the LSB is sustained increases
with airfoil thickness. The peak value of $-C_P$ near airfoil leading edge,
increases with airfoil thickness. In all cases, the LSB bursts is followed by
the formation of the DSV, however the characteristics of the DSV and its
convection speed vary with airfoil thickness, with the highest speed for the
thickest airfoil.

Investigation of skin friction coefficient on the suction surface shows that
while turbulent boundary layer separation is nearly non-existent for NACA-0009,
the separation (flow reversal) region for NACA-0018 extends from the trailing
edge all the way up to the LSB location immediately before dynamic stall
occurs. This observation suggests that stall onset could have been triggered by
the turbulent separation region reaching up to and interacting with the LSB for
NACA-0018, and the possibility that mechanism of stall onset gradually changes
with airfoil thickness from that due solely to LSB burst to that due to
interaction of trailing edge separation with the LSB.

\begin{acknowledgments}
\label{sec:acknowledgement}
Funding for this research is provided by the AFOSR Summer Faculty Fellowship
program and by the National Science Foundation under grant number NSF/
CBET-1554196. Computational resources are provided by NSF XSEDE (Grant
\#TG-CTS130004) and the Argonne Leadership Computing Facility, which is a DOE
Office of Science User Facility supported under Contract DE-AC02-06CH11357.

The second author would like to acknowledge support by AFOSR under a task
monitored by Dr. D. Smith, and by a grant of HPC time from the DoD HPC Shared
Resource Centers at AFRL and ERDC. Technical support for the FDL3DI software
provided by Dr. Daniel Garmann of the Air Force Research Laboratory is
acknowledged.
\end{acknowledgments}

\bibliographystyle{aiaa}

redpajama_set_name: RedPajamaArXiv


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