You might never know when one seemingly minor decision could change your life.
One summer weekend, just before entering my third year in the Civil & Environmental Engineering program at Tufts, I found myself on a whitewater kayaking class for beginners run by volunteer instructors with the Appalachian Mountain Club. A friend recruited me to join at the last minute; they needed more new “boaters” to reach their minimum capacity.
Some combination of perfect weather, good company, and new challenges that weekend got me hooked on the sport. The more time I spent on the river, the more folks I met who had degrees and careers related to hydrology or engineering. That would eventually include me, too – my love for this hobby & fluid dynamics led me to work here at Alden.
When I returned to school in the fall, I took my first fluid dynamics course. The coursework and the new hobby complemented each other – spending time in a boat made it easier for me to understand certain fluid mechanics topics.
One of those topics is the concept of a stagnation point: an obstruction in a flow field, like a rock or bridge abutment in a river, will cause the fluid to slow down to a velocity of zero at the object’s surface, resulting in high static pressure.
For a boater, the stagnation point is a dangerous place to be. You and your boat can get pinned on the upstream side of an obstruction, and if you can’t get free quickly, you could be injured or drown.
What makes the stagnation point so dangerous? Consider conservation of energy and the Bernoulli equation, a key concept in fluid dynamics:
The Bernoulli equation only applies to steady, incompressible, frictionless flow along a streamline. Under these conditions, total mechanical energy per unit mass of water (which is the sum of pressure (p/rho), kinetic (V2/2), and potential (gz) energies) is constant along a streamline. This concept can clearly explain why a kayaker doesn’t want to get stuck at the stagnation point.
Figure 1: Bridge Abutment Stagnation Point
Follow the light blue dotted streamline through the middle of the river in Figure 1. If we estimate negligible friction and minimal change in elevation as the streamline approaches the bridge abutment, Bernoulli’s equation says the energy from a high velocity in the river upstream of the abutment will change to a velocity of zero, along with high static pressure at the stagnation point.
For a boater, this means that if you float head on into an obstruction and become pinned, you will have a velocity of zero, and high water pressure will hold you in place against the obstruction. Yikes! It is best to avoid this situation by navigating around the obstruction, but boaters should always be prepared for the worst by staying up to date on swift water rescue techniques and carrying appropriate safety equipment. Thanks for the safety tip, Bernoulli!
Whitewater kayaking was also helpful in understanding my favorite dimensionless parameter: the Froude number! This parameter compares inertial to gravitational forces. It is also a ratio of the fluid’s velocity to the speed that a surface wave travels across the fluid (AKA wave celerity).
Froude numbers less than 1 indicate subcritical flow: the water is deep and moving relatively slowly. Froude numbers higher than 1 indicate supercritical flow: the water is shallow and moving quickly. At a Froude number of 1, we have critical flow: gravitational and inertial forces are equivalent. Critical flow can be achieved where the slope of the channel or river is zero, such as over the top of a weir. If you measure the depth (L) of water over the top of the weir as well as the width of the river along the weir, you can determine the flow area, flow velocity (using the Froude number), and ultimately the total flow rate of the river. The Froude number also helps us understand how waves form, and why kayakers are able to surf on them.
When conditions are just right in a river, standing waves and holes (shown in Figure 2) can form; they stay in the same place and don’t move with the flow of the water. Kayakers can have fun with these features by surfing on them, balancing on top of the wave or hole, and staying in the same location relative to the river bank in a fast-moving river.
Figure 2: Whitewater Hole & Wave1
In fluid dynamics, this phenomenon is called a hydraulic jump.
Hydraulic jumps suitable for surfing sometimes occur naturally in rivers, and can also be designed and installed where river flow and gradient (along with local stakeholders and regulatory agencies) permit. To create a hydraulic jump, a weir-like structure in a river (shown as a “play feature” in Figure 2) can be used to make the flow to transition from critical to supercritical (i.e., the water is shallow and moving quickly). An abrupt drop leading into the downstream pool creates a discontinuity along the river bed. The flow immediately becomes subcritical, getting deeper and slowing down. This abrupt change is mirrored at the river surface, shown in these pictures as a “seam” in a hole or as a “trough” in a wave, where the green water of the supercritical upstream flow meets the hydraulic jump.
Figure 3: Me, trying to throw a loop, in Tariffville CT. Photo credit goes to Andrew Nitchske.
The velocity of the subcritical flow is very low, and can in some cases reverse so the water is flowing upstream, which makes it possible to surf and do tricks in a wave or hole without floating downstream.
The flow is critical at the seam or trough, which means that the Froude number is equal to 1. The wave/hole will not move around too much since the flow velocity is equal to the wave celerity.
Kayak surfing (made possible by the Froude number) is my favorite thing to do!! Check it out:
Figure 4: Katelyn Green (yellow kayak) and me (blue kayak), surfing in Tariffville CT.
So… what’s the difference between a wave and a hole? Tune in next time for a post from my colleague Ben Mater!
Remember to use the comment field to share your favorite fluid dynamics hobbies with us.
 McLaughlin Whitewater Design Group, Ben Nielsen, April 15, 2014 Presentation “Recreational Whitewater: Keys to Successful Management”, available online at https://www.slideshare.net/rshimoda2014/nielsen-ben-rms-recwwworkshop2014submittededit (slide 38 of 66). McLaughlin is one of a small number of companies that create whitewater parks for surfing, and Alden has been lucky enough to collaborate with McLaughlin on occasion!
For many employees at Alden, fluid dynamics is part of their life outside the office--in the sports they choose for their free time. In many cases, a sport was what came first and later helped inform a career choice in fluids and fluid flow. This ongoing series will feature some of the various and unique ways our employees spend some of their non-working hours and how CFD and fluid flow analysis is being used to improve techniques used in those sports.
Part II: Sailing - Dave Schowalter and Kimbal & Becca Hall
Sailing is all about using fluid dynamic forces to propel and control a boat. There is the fluid dynamics of the water against the rudder and the keel or centerboard, which allows the skipper to steer the boat and and to sail upwind. Then there is the aerodynamics of the wind against the sails, and maximizing the lift on the sails. As with an airplane, balancing the fluid dynamics forces is a key element to boat design and making a boat responsive and easily controllable.
At least three current Alden employees enjoy sailing as a hobby.
Dave Schowalter grew up sailing with his family on Chesapeake Bay and Long Island Sound. From the moment his father explained that the principals of a sail were the same as that of an airplane wing, he was hooked. Today, he can be found sailing whenever he gets a chance, anywhere from tiny Indian Lake in Worcester, to the Caribbean.
Dave Schowalter at the helm of two very differently sized sailboats. Guess which one he owns!
Kimbal Hall also learned to sail from his father. While Dave grew up cruising and relaxing on boats, Kimbal was fueled by the spirit of competition, ending up on the sailing team at Tufts University, and even sailing in the 2000 Olympic trials in his day. Kimbal met Becca (also an Alden employee) during their senior year at Tufts, and after college they started sailing together. Now they share a sailboat on Narragansett Bay with Kimbal’s father, where they do some light racing and family cruising.
Kimbal and Becca racing on the Columbia River (#2278, top) and sailing with kids (bottom)
Some of the interesting fluid dynamics of sailing can be visualized in this computational fluid dynamics (CFD) video of an America’s Cup Yacht. The included effects are wind, relative current, and waves.
With the America’s Cup competition coming up in Bermuda, Kimbal looks forward to covering associated CFD and design work in more detail as part of a future blog post.
Remember to send us links of your own fluid dynamics hobbies!
For many employees at Alden, fluid dynamics is part of their life outside the office--in the sports they choose for their free time. In many cases, a sport was what came first and later helped inform a career choice in fluids and fluid flow. This ongoing series features some of the various and unique ways our employees spend some of their non-working hours and how CFD and fluid flow analysis is being used to improve techniques used in those sports.
Part IV: Archery - Duncan Phyfe
Duncan Phyfe, a senior CFD engineer at Alden, started enjoying archery thanks to his mother. She was one of the riflery coaches at Choate-Rosemary Hall prep school. When the school needed an archery instructor, they assumed she could do it, since she already knew how to get one type of projectile to hit a target! So Duncan has been shooting arrows since he was about 6 years old.
When Duncan was 10 years old, he started attending The World Archery Center (TWAC), and that is when he started to learn the physics and aerodynamics of archery. The mentor for the instructors at TWAC was Dr. Clarence Hickman, an archery buff, and physicist who worked on rockets with Robert Goddard.
Dr. Hickman developed an explanation for “the archer’s paradox,” by which an arrow must apparently move around the bow but still moves towards the target. An episode of “Smarter Every Day” explains this paradox with some nice high speed video:
It was through learning about the aerodynamics and mechanics of archery that Duncan realized he wanted to be a fluids engineer. He continues to shoot (both guns and bows) to this day, and also teaches archery in the local middle school.
Duncan Phyfe teaching archery (above), and as a young archer (left, below).
This video shows the support sculling technique used to propel a swimmer's legs out of the water while upside down.
Some computational studies specific to synchronized swimming have been conducted of various ways to improve lift and power and therefore height. In one study conducted by Shinichiro Ito of the National Defense Academy in Yokosuka, Japan, the hydrodynamic hand characteristics of five hand shapes were investigated in a steady-state flow field to determine the configuration resulting in the maximum force and therefore the best performance. It was determined that the most buoyant lift was produced from a cupped hand (rather than flat), straight fingers (rather than naturally bent) and no gaps between the fingers.
Amie and her teammates competing at the 2010 U.S. Masters Synchronized Swimming Championships in La Mirada, California.
Please share photos or videos of yourself involved in fluid dynamics related hobbies, and stay tuned for more.
To better illustrate this phenomenon, we captured a video of this beautiful dance between gas and liquid. The close-up view shows off the complex wavy motion of the liquid draining down the edge of the glass after a pour, while the bubbles collectively drive, and are driven by the liquid circulation.
Figure 1: The flow patterns after pouring a pint of Guinness are mesmerizing.
Now it’s our turn
Our curiosity was piqued. However, because Guinness is a mostly opaque liquid, we can only see what’s happening near the outer edge of the glass. We can’t see all those bubbles rising in the middle of the glass—unless we use CFD, of course. Challenge accepted.
Instead of showing the liquid flow patterns as in some of the previous studies, we chose to use computation fluid dynamics (CFD) to show the motion of the bubbles – that is what we are looking at in the glass after all.
Figure 2: Each bubble is color coded. That color stays with the bubble throughout the entire simulation; this color coding helps to visualize the circulation patterns within the glass.
Besides being more visually interesting for this experiment, simulating bubbly flows is useful for a number of our client’s applications. For instance, fermentation tanks, bioreactors, and waste water treatment plants often use bubbles to stir up the liquid, keeping all the cells and solids in suspension. Simulating bubbles helps us see what’s happening inside the tank to make sure things stay well mixed. The bubbles also provide an incredible amount of surface area for mass transfer—they allow a mixture to breathe.
Bubbles can also cause problems — like with spillways for high head dams. Water flowing over the spillway plunging into a pool of water from great heights will entrains air bubbles deep underwater. The pressure deep down in the water turns the air bubbles into high levels of dissolved nitrogen and oxygen in the water. When fish breathe in water down deep and then come to the surface, they end up with bubbles in their blood just like a SCUBA diver getting the bends. Not good. By using CFD, we can determine if dissolved gas concentrations are too high, and then design modifications to the spillway to better protect the fish.
Why did we model the bubbles in a pint of a Guinness? We did it because we can. Previous work had set a high bar, but we tapped into our experience and hopped on this project. We poured over the literature and immersed ourselves in the problem, knowing we could handle the pressure and rise to the challenge. And maybe because we like beer also. We’re always looking for ways to improve our understanding of flow related phenomena so we can stay ahead of the curve, and continue to help our clients solve whatever flow related problems they can brew up. Happy St. Patrick’s Day.
Sloshing is something that everyone is familiar with on a very basic level. The classic example is trying not to spill a full cup of coffee – but I’ve had a similar experience with enthusiastic children at bath time.
The basic idea is that you have liquid in some sort of a container with a free surface. When there is a force applied to the liquid – like walking with the coffee cup, or kids splashing around in the tub – the liquid starts moving. The container confines the motion of the liquid, and sets up a back-and-forth oscillation, which we know as sloshing.
Spilling your coffee is usually just a minor inconvenience, but with larger containers sloshing can have real consequences. Some bigger examples of sloshing include:
The consequence comes from the force that is generated by the large mass of liquid moving quickly – anything standing in the way of the onrushing liquid will be subject to loads that it may not have been designed for.
The period of the slosh depends on the size and shape of the container – big containers like lakes have longer periods than small containers like coffee cups. Things get interesting, though, when we start looking at higher mode frequencies of containers. Consider a large cylindrical tank 20-ft in diameter, and 10-ft deep – a scaled up version of a coffee cup. The sloshing mode everyone is familiar with in their coffee cup has one wavelength around the perimeter (i = 1), and no waves across the diameter (j = 0). We can use some way-cool Bessel functions for this simple shape to determine the period of the primary sloshing mode, which is 4.28 seconds. This is a long period because the tank is fairly large, and so is unlikely to interact with any structural frequencies.
However, if we start packing more waves around the circumference of the vessel, or we start putting some waves across the diameter of the vessel (or both!), the wavelength shrinks, the speed that the wave travels shrinks, and the period of that wave mode shrinks. Table 1 shows the resonant periods for various wave modes, and the liquid surface for each wave mode is shown at the bottom of the post. Some of the higher modes start to get pretty wild!
Table 1: Sloshing Periods for different wave modes in a tank that is 20-ft in diameter, and 10-ft deep tank
Interestingly, as you get to higher frequency modes, there are many modes that end up having very nearly the same period. This becomes important if you have a forcing frequency that aligns with several modes at once. In a reactor tank, excitation could come from gas injection into the liquid that excites the liquid surface, or a long agitator shaft that excites a surface wave at the shaft’s natural frequency, or flow periodically distorting the flexible container wall.
In the case of jet fuel in a wing tank, sloshing in the wing tank can cause changes in the flight behavior, which recover at the same period as the sloshing, forcing feedback that eventually leads to bad things for the airplane. The solution for airplanes is to put several restrictive baffles that break the large tank into many smaller tanks with higher frequencies that don’t interact with the plane’s flight response. In the case of the circular tank, putting baffles in the tank can turn into a game of whack-a-mole where you might block one wave mode, only to have the energy move to a different mode with a similar period.
If possible, sometimes the best answer is to identify that you might have a sloshing problem early in the design process, and do your best to avoid it.
Click to Enlarge
Mixing between fluids of different properties goes on all around us every day (e.g., think of stirring milk into your coffee or smoke billowing from a chimney). In many flows of engineering relevance, velocity differences between fluid bodies generate turbulent motions that, in turn, greatly enhance the mixing process; small-scale chaotic eddies that characterize the turbulence are much more effective than molecular diffusion at mixing fluid properties such as momentum, heat, salinity, sediment load, or pollution concentration.
When fluid bodies are of different densities the effects of gravity weigh heavily on the turbulent mixing process (pun intended). For example, when warm air escapes from a chimney it accelerates upward in a turbulent billow because it is lighter (less dense) than the cooler air around it, and gravity acts to drive turbulence through buoyant convection. On the other hand, in a stably-stratified lake, gravity acts to suppress turbulence at the thermocline where lighter, warm water overlies heavier cold water.
The signatures of turbulent mixing in stratified flows are perhaps most obvious in the sky above us. Clouds provide a convenient flow visualization method! An anvil-shaped thunder head reveals convectively-generated turbulence in an unstably-stratified environment, whereas rolling billows – think of the sky in van Gogh’s Starry Night – indicate shear-generated turbulence in a stably-stratified environment. A great example of the latter type of cloud was recently observed outside Alden's Fort Collins office (Figure 1).
Figure 1: Lenticular cloud bands forming at the crests of atmospheric gravity waves in the lee of the Rocky Mountain Front Range (flow is toward camera).
The two parallel cloud bands seen in the photograph are occurring at the crests of atmospheric waves that are occurring in the lee of Colorado’s Front Range Mountains (wind is coming toward you in the picture). Flow over the mountains disturbs the stably-stratified atmosphere and generates a train of gravity waves similar to surface waves in a ship's wake. Low pressure at the wave crests causes water vapor to condense and form the "lenticular" cloud bands you see in the picture. Air is actually moving through the clouds rather than the clouds moving with the air! A good cross-section schematic of mountain lee waves is show in Figure 2 from Durran (2013).
Figure 2: Schematic of mountain lee waves and lenticular clouds (from Durran, 2013). Flow is from left to right.
While the lee waves themselves are not breaking into turbulence, it appears that a crosswind acting perpendicular to the main flow is doing something interesting to the cloud bands. See those curling billows in the photograph (close up picture in Figure 3)? Those are caused by shear between the lighter air above the cloud and the heavier air below. The fancy name for these shear-driven billows is Kelvin Helmholtz instabilities. "K-H" instabilities can be observed in many natural flows with density stratification and are common in thermally-stratified flows of oceans, lakes, and rivers. As the billows roll up, they lift heavy fluid up and push light fluid down – working against gravity. Eventually, the coherent billows collapse into smaller-scale, chaotic, turbulent motions that mix the two fluid bodies.
Figure 3: Zoomed photograph of Kelvin Helmholtz instabilities due to shear generated by a cross wind.
The computational fluid dynamics (CFD) models used at Alden can capture K-H instabilities as demonstrated in Figure 4 which shows a snapshot from a simple two-dimensional simulation of warm, lighter water (red) moving across cold heavy water (blue). In many cases of engineering relevance, however, domain size and complexity often preclude the resolution needed to explicitly model the flow structures such as K-H billows that ultimately drive mixing. Instead, numerical models rely on assumptions about what’s going on at the unresolved scales of the turbulence. These assumptions form the basis for turbulence models that approximate the mixing process.
Figure 4: Kelvin Helmholtz instabilities occurring on a density and shear interface between warm water (red) and cold water (blue) as captured in a highly-resolved (Δx = 0.50 cm) two-dimensional simulation. Each billow is approximately 10 cm tall.
Because no model is perfect, keys to a successful modeling effort include calibration and validation. A promising approach to calibration and validation using field data comes in the form of airborne thermal imaging. Alden is currently developing a drone-mounted infrared camera system that will provide overhead snapshots of mixing of water bodies of different temperatures – an application of focus being thermal plumes discharged from power plants. IR images taken recently from a power plant discharging cooling water into a major river are shown in Figure 5. IR imagery provides a valuable check on the lateral mixing predicted by a given CFD model and serves as yet another tool in Alden’s arsenal for understanding and solving mixing-related problems.
Figure 5: Aerial infrared image taken by Alden of a thermal plume discharged from a power plant on a major river.
Flow is from top to bottom of the image. Note the complex structure of the mixing/shear line and dilution of the plume in the downstream direction.
Durran, D.R. (2013, Jan. 29) Trapped lee waves over the western U.S. http://www.youtube.com/watch?v=P84WoxbDXCg.
I was also thinking this might have to do with weight distribution in the boat. I have noticed an instability like this when sitting up sledding in a one person toboggan. Because most of the weight is in the back, the drag on the front of the sled will create a higher moment than the drag in back, and the sled will want to go backwards, where the drag moments are in a stable configuration. I would think the drag on the bottom of the boat from the water surface could cause a similar phenomenon.
Richard, I'm not sure about the oscillation you mentioned (I'll have to pay attention for that this weekend!!), but the sudden spinning around when you're trying to go straight on flat water is just like catching an edge or carving around a turn on moving water. This is something folks might be familiar with from other sport like skiing or snowboarding. Even on flat water (or flat, snow-covered ground if you've ever tried cross country skiing), many of the factors that contribute to carving or catching an edge are still present: the boat will probably not be level laterally as the paddler leans to the side to put in a stroke; the paddle stroke (even a good forward stroke) will generate a small amount of rotation and a slight difference in water velocity relative to the boat from one side to the other (causing water to flow under the hull at angle!); the shape of the boat/ski/vehicle as well as the center of mass will also impact the dynamics of the turn. Whitewater kayaks are generally not designed to travel in a straight line - they are shorter (as compared to a sea kayak), and often have sharp edges to allow the boater to make quick maneuvers around obstacles. However, with good technique (e.g., maintaining the angle between the hull and water surface while putting in good forward strokes), more experienced whitewater enthusiasts are able to keep moving in a relatively straight line without spinning around on flat water.
New kayakers often complain that they can't make their boats go straight. I have noticed that ww kayaks, especially in flat water, tend to suddenly start to spin and once they begin that turn, they are very hard to stop. If you let them go, they often seem to spin almost 180 deg, then oscillate like a pendulum. Could this be the result of water flowing under the hull at an angle?