Tianjun Han

I am an assistant professor at Tennessee Tech University. I lead the Flow Physics for Robotic Propulsion and Flight Laboratory at TN Tech. I earned my PhD from Lehigh University in 2023, advised by Dr. Keith Moored. I am from Wuhan, Hubei. I also earned my bachelor's degree from Wuhan University. After work, I enjoy playing drums and basketball.

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Research

My research focuses on robotic propulsion and flight. Through a fusion of simulations and experiments, I develop scaling laws to predict the optimal kinematics and material and structural properties of unmanned flapping vehicles for maximizing their performance. My research guides the design and control of underwater and aerial drones.

My thoughts on scaling laws: I am always fascinated by the beauty and power of scaling laws in uncovering underlying physics and solving engineering problems. Scaling laws identify and quantify the dominant physical factors, enabling them to inform design optimization, guide Model Predictive Control (MPC), and directly advise the training of Deep Reinforcement Learning (DRL) for underwater and aerial vehicles.

The distinctions between scaling laws and curve fitting: 1. Scaling laws are derived from physical principles, such as Newton’s second law, the Kutta-Joukowski theorem, and the Euler-Bernoulli beam equation. 2. In scaling laws, units are consistent between the left- and right-hand sides, as well as among all the terms on the right-hand side. 3. Each term on the right-hand side has a clear physical meaning. 4. Scaling laws’ validity is independent of datasets. 5. Scaling laws are valid in asymptotic conditions. For example, a scaling law that predicts the thrust of oscillating propulsors should yield zero thrust as the amplitude or frequency approaches zero. In contrast, curve fitting does not satisfy all of these conditions simultaneously.

Here are the highlights of selected completed research projects:

We found that the propulsive efficiency of flexible pitching propulsors can be increased by more than 70% by simply tailoring their bending patterns.

We presented a scaling law that predicts the resonant condition of non-uniformly flexible propulsors from their frequencies, bending stiffness, and flexion ratios:
\[\Pi_{k} = f(f,\, EI, \,\lambda)\]

We found that the equilibrium altitude in unsteady ground effect is generated by a balance between positive wake-induced lift and negative quasi-steady lift while the added mass lift does not play a role.

We presented a scaling law that predicts the equilibrium altitude of pitching propulsors from their Strouhal numbers and reduced frequencies:
\[D^* = f(St,\, k)\]

We found that in-line stable formations scale with the actual wake wavelength of the leader, rather than the nominal wake wavelength that is the ratio of velocity over oscillating frequency. Leveraging mismatched amplitudes, unconstrained propulsors can settle into the high-efficiency zone identified by previous constrained studies of in-line schooling.

We presented a scaling law that predicts the actual wake wavelength of the leader from its chord length, Strouhal number, and reduced frequency:
\[\lambda = f(c,\,St,\, k)\]

We developed a single-actuator turning strategy for the Tunabot by introducing a frequency asymmetry between the left and right half strokes of each tail-beat cycle.

We presented a scaling law that predicts the turning radius of the Tunabot from its base frequency and frequency asymmetry:
\[r = f(f,\, \Delta f)\]

Here are the highlights of selected ongoing research projects:

We are examing the energetics of a bio-robot school that consist of two independently free-swimming tuna-like robots.

We are developing a scaling law that predicts the cost of transport of the school from its lateral spacing, tail-beat frequency and amplitude, and phase synchrony:
\[CoT = f(Y^*,\, f,\,A,\,\phi)\]

We are developing a pectoral fin-based vertical maneuver that enable the Tunabot to climb and dive without introducing additional pitch angle or angular velocity.

We are developing a scaling law that predicts the vertical trajectory of the Tunabot from its pectoral fin pitch angle and tail-beat frequency:
\[H^* = f(\theta,\, f)\]

We are investigating the performance of pitching propulsor schools of more than ten swimmers.

We are developing a scaling law that predicts the thrust enhancement of propulsors in the school from their vertical and lateral spacings, Strouhal number, and reduced frequency:
\[T^* = f(X^*,\,Y^*,\, St,\,k)\]

Publication List:

Teaching

I have experience in teaching both theoretical and experimental courses. Additionally, I am skilled at developing experimental setups and numerical tools that engage students in hands-on work and connect classes to real-world problems.

Here are the highlights of my teaching experience:

I guided students in experiments of vortex shedding.

I developed an experimental setup to study vortex ring propagation, and I gave class recitations on thin airfoil theory, lifting line theory, potential flow simulations, and shock waves.

I guided students in using vortices to simulate real-world problems, such as flying, swimming, and energy harvesting.

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