Team Name: WunderWasser

Names: Jaimie Carlson, Brian Wright

Contact: jaimiec@seas.upenn.edu, brwr@seas.upenn.edu

Learning Description

The discipline of fluid mechanics is vitally important for engineers — key to designing tiny microfluidics and enormous dams alike. However, it is often presented much later in an educational curriculum than solid mechanics and seems less intuitive to most students, who have better physical intuition about the movement of everyday solid objects like balls or cars. These students may be able to master the mathematical techniques of fluid dynamics but have trouble connecting the abstract formalism of the hydrostatic equation or Navier-Stokes equations to the forces, velocities, and pressures actually experienced inside a fluid.

Connecting the Navier-Stokes equations to important everyday phenomena can be difficult

Visual simulations here can assist students to some degree, adding information to spoken lectures and written mathematics by creating a virtual fluid environment. The addition of haptic feedback to this environment makes fluid mechanics more accessible to a wider audience. Even if students do not yet have the necessary mathematical background to comprehend the Navier-Stokes equations fully, they can explore environments commonly used as Navier-Stokes examples and gain an intuitive understanding of how pressure and velocity vary through these regions. Hopefully, this natural approach will supplement a more mathematical course of study, or even serve alone as a less rigorous introduction to fluid mechanics for high school students.

When using WunderWasser, a student first chooses an environment from several choices: parallel plates, pipe, Couette flow, annular pipe, or randomly generated obstacles. Then, they adjust fluid or environment properties (viscosity; pressure gradient; environment dimensions) using interactive sliders. Then, the student uses one hand to control the Haply linkage, placed over a laptop, and places the other hand on the Hapkit paddle. The fluid dynamic visual simulation appears on the laptop screen, and the student uses the Haply linkage to navigate over it. In the Haply linkage, the student should feel a force proportional to the velocity vector at the point directly below the Haply linkage on the laptop screen. In the Hapkit paddle, the student should feel a force proportional to the pressure at the point directly below the Haply linkage on the laptop screen. The student can continue to explore different locations within an environment, restart the same environment with different fluid properties, or switch environments entirely.

The visual component of a pipe environment students can experience

This experience is intended as a supplement to common Navier-Stokes problems. For instance, a common problem for students might be to derive the axial velocity of fluid flow within a pipe as a function of radius. A student could not simply plug in their problem’s given parameters to our environment to receive an instant answer and avoid calculation, but they could set up the environment given in their problem and explore it to get a broad idea of the solution’s form (linear/parabolic/other).

WunderWasser uses Haply and Hapkit to allow students to immerse themselves in an interactive, tactile fluid environment, linking mathematical knowledge to a visio-haptic model.

System Description

To support this learning environment, we built a system to allow students to navigate positions within a two-dimensional environment, feel 2-DoF velocity vectors, and feel 1-DoF pressures. To that end, we used the hAPI with Haply to input two-dimensional positions, as well as to output two-dimensional velocity vectors. We used the hAPI with Hapkit to output 1-DoF pressures as well. Thus, the user can interact with the environment in many ways (in addition to changing parameters with laptop input and viewing a visual simulation with laptop screen output).

Hapkit 1-DoF paddle used to simulate fluid pressure
Haply 2-DoF linkage used to input position and output fluid velocity
Algorithm for WunderWasser system


Both the 2-DoF Haply and the 1-DoF Hapkit were used as hardware for this demonstration. No major changes were made to either.

Hapkit (left) and Haply (right) used to interact with an on-screen fluid simulation


The software implementation has a front-end allowing the user to input parameters into a particle-based fluid dynamics simulation and displaying that simulation, and a back-end continually polling data from the Haply linkage, using that data to find coordinates within the simulation, and writing outputs to the Hapkit paddle and Haply linkage based on the simulation’s data at those coordinates.

Different fluid simulations possible with software front-end (From left to right: parallel plates; annular flow; Couette flow with moving top plate)

The platform front-end uses the PixelFlow library in Processing (https://github.com/diwi/PixelFlow) to display left-to-right fluid flow through various environments, including parallel plates, pipe, Couette flow, annular pipe, and random obstacles. Users control environment type, viscosity, pipe radius, starting velocity, and pressure gradient. The fluid flow simulation uses color to reveal the intensity of the fluid pressure or velocity at each spatial location: above, white is high velocity, blue is medium velocity, and orange is low velocity. There are also velocity vectors shown at each position.

The platform back-end retrieves data using the Haply Arduino-based microcontroller. Forward kinematics use angle data from quadrature encoders to compute the linkage tip position. This end effector position is converted to an (x, y) location on the screen. By moving the tip, the user actively explores different regions of the fluid simulation. The velocity vector at the (x, y) location is scaled to a force vector output by the Haply. The pressure at the (x, y) location is calculated with PixelFlow and used to apply a uniform, scaled force to the Hapkit paddle.

Link to full code: https://github.com/jaimiecarlson/WunderWasser


Any fluid environment can be simulated with both velocity (left) and pressure (right)

The incorporation of more fluid environments would improve this display. This system’s design allows it to be extremely scalable; any new fluid environment which can be created with the PixelFlow library can be simulated in the same way as existing environments. Thus, we will seek to add more fluid environments, as well as creating a new mode to let students design their own environments, using the Haply linkage as a drawing tool for further customization.

Additionally, the visual and haptic aspects of the demonstration might augment traditional learning reinforcement methods, including practice problems and conceptual quizzes, which could be easily alternated with demonstration stages to create a full tutorial. Further development may enable three-dimensional environments with fully adjustable viewing angles and cross-sections.

In addition, hardware could be modified to press fit a push button into the Hapkit paddle and use it with the Hapkit board to allow students to control sliders, and thus fluid parameters, with the paddle and simplify the user experience.

In addition to providing a supplement for students learning fluid dynamics, another stated goal of this assignment was to make fluid dynamics accessible for students not otherwise learning it, such as high school students who might have limited resources. Providing this platform for mobile devices like phones or tablets, as well as for computers, will help achieve this goal. A mobile application will make the platform accessible to a broader audience and facilitate learning outside the classroom and independent study.

This system lets users feel velocities and pressures of moving fluids to stimulate a visceral understanding of various fluid dynamics concepts, augmenting conventional methods of studying abstract implementations of the Navier-Stokes mathematical model. With this setup, students gain an enhanced understanding of the geometries, boundary conditions, and simplifications necessary to find closed-form solutions to Navier-Stokes equations. A student using WunderWasser augments traditional study methods through the experiential memory of tactile interactions and links mathematic knowledge to an intuitive, visio-haptic model.