Fluid Dynamical Systems Research Articles

CFD Systems Level Modeling of a Protonic Ceramic Fuel Cell

There is a critical need for intermediate-temperature fuel cells that offer low-cost, distributed generation both at the system and device levels. Current development work at the Colorado School of Mines is being carried out for a mixed proton and oxygen-ion-conducting electrolyte that enables fuel-cell operation at temperatures less than 500°C. By using a proton- and oxygen-ion-conducting electrolyte, the fuel cell stack is able to reduce coking which clogs anodes with carbon deposits and enhance the process of turning hydrocarbon fuels into hydrogen. Today's solid-oxide fuel cells (SOFCs) are based on oxygen-ion conducting electrolytes and operate at high temperatures. Advanced mixed proton- and oxygen-ion-conducting fuel cells operate at lower temperatures, and have the capacity to utilize hydrogen, ethanol, methanol, or methane fuels. Additionally, an advanced single-step sintering process has been developed to reduce manufacturing costs of these protonic-ceramic fuel cells (PCFC). “Solid-state reactive sintering” reduces the number of manufacturing steps from 15 to 3, drastically decreasing costs. Understanding the systems-level behavior of the PCFC is critical to enable its emergence as a roll-out technology. The team at Calif. State Polytechnic Univ. at Pomona is performing numerical modeling of the PCFC system. The goal of this poster is to present results of Computational Fluid Dynamic (CFD) systems level modeling of a typical PCFC stack having a cylindrical shape factor. The configuration is modeled using commercial CFD software which can easily be benchmarked using experimental data. The flow is H2 on anode side and air on the cathode side. Flow rates are on the order of 100 sccm for each side. The interconnect between each cell is made of ferritic stainless steel (70% Fe, 27% Cr, 1% Y2O3). The operation of a PCFC is fundamentally different than SOFCs due to their ability to conduct protons as well as oxygen ions across a dense ceramic electrolyte. Two global electrochemical reactions are needed since the material is capable of conducting two charged defects. One global reaction is the result of proton conduction across the electrolyte, and the other is the result of oxygen-ion transport across the electrolyte. Similar to SOFCs, heterogeneous internal reforming of hydrocarbons such as methane and water-gas-shift reactions still occur on the nickel phase of the anode. However, since minimal water is generated in the anode from the electrochemical reactions, the reforming reactions must be supplied with an external water source, such as an external waste heat recovery boiler or via anode gas recycle. Additionally, the low temperature operation tends to shift the equilibrium composition of the fuel species toward higher methane content (i.e., lower conversion of internal reforming reaction) where hydrogen partial pressures in the anode will be limited by thermodynamics. The difference in operating temperatures and the removal of hydrogen from the anode via electrochemical oxidation can also influence the optimal steam-to-carbon ratio (S/C) required to avoid solid carbon deposition when compared to SOFCs. The above-described electromechanical kinetics are incorporated into the systems-level CFD model of the PCFC presented in this poster. Results for CFD based Multi-physics of the electro-mechanical PCFC behavior for mole fraction vs. temperature, fuel utilization vs. temperature, voltage potential vs. current density, and power density vs. current density are presented in the poster. Figure 1

On the structure of the two-stream instability–complex G-Hamiltonian structure and Krein collisions between positive- and negative-action modes

The two-stream instability is probably the most important elementary example of collective instabilities in plasma physics and beam-plasma systems. For a warm plasma with two charged particle species, the instability diagram of the two-stream instability based on a 1D warm-fluid model exhibits an interesting band structure that has not been explained. We show that the band structure for this instability is the consequence of the Hamiltonian nature of the warm two-fluid system. Interestingly, the Hamiltonian nature manifests as a complex G-Hamiltonian structure in wave-number space, which directly determines the instability diagram. Specifically, it is shown that the boundaries between the stable and unstable regions are locations for Krein collisions between eigenmodes with different Krein signatures. In terms of physics, this rigorously implies that the system is destabilized when a positive-action mode resonates with a negative-action mode, and that this is the only mechanism by which the system can be destabilized. It is anticipated that this physical mechanism of destabilization is valid for other collective instabilities in conservative systems in plasma physics, accelerator physics, and fluid dynamics systems, which admit infinite-dimensional Hamiltonian structures.

Study on helium impingement cooling for a sharp leading edge subject to aerodynamic heating

This paper presents numerical studies on a typical actively-cooled thermal protection system (TPS) which turns out to be a potential candidate for the leading edge thermal management. The leading edge is cooled by the impingement jet of gaseous helium. The external aerodynamic heating and radiation, the heat conduction in solid wall, and the internal impingement cooling are coupled in a unified computational fluid dynamics system by using a quasi-coupling method. The thermal-hydraulic performance of internal impingement cooling is particularly highlighted. Four metal alloys are tested in order to find out the impact of the material property on the TPS’s cooling performance. Results show that the reduction of leading edge temperature is remarkable with the impingement cooling scheme and the maximum temperature can be controlled far below the materials’ melting point. However, the thermal stress does not significant decrease and is still a barrier for the application of the actively-cooled TPS. The operation limits of various materials are demonstrated, which may benefit to the future material selection work. Besides, the coolant flow rate requirements for safely operating the TPS under various flight conditions are ascertained.

A maximum entropy approach to the parametrization of subgrid processes in two‐dimensional flow

In numerical models of geophysical fluid systems, parametrization schemes are needed to account for the effect of unresolved processes on processes that are resolved explicitly. Usually, these parametrization schemes require tuning of their parameters to achieve optimal performance. We propose a new type of parametrization that requires no tuning, as it is based on an assumption that is not specific to any particular model. The assumption is that the unresolved processes can be represented by a probability density function that has maximum information entropy under the constraints of zero average time derivatives of key integral quantities of the unresolved processes. In the context of a model of a simple fluid dynamical system, it is shown that this approach leads to definite expressions for the mean effect of unresolved processes on processes that are resolved. The merits of the parametrization, regarding both short‐range forecasting and long‐term statistics, are demonstrated by numerical experiments in which a low‐resolution version of the model is used to simulate the results of a high‐resolution version of the model. For the fluid dynamical system that is studied, the proposed parametrization turns out to be related to the anticipated potential vorticity method with definite values of its parameters.

Predicting bubble size and bubble rate data in water and in froth flotation-like slurry from computational fluid dynamics (CFD) by applying deep neural networks (DNN)

Accurate characterization of two phase bubbly flows is crucial in many industrial processes such as fluidized reactors, ore froth flotation, etc. The bubble size determines the rate at which components present in the gas phase are transferred to the surroundings and vice versa while bubble rate defines the appropriate bubbly flow regime occurring in the heterogeneous system. This research work employs deep neural networks (DNNs) to predict bubble size and bubble rate using data obtained from validated computational fluid dynamics (CFD) computations. Pure water and slurry (in conditions similar to those employed in mineral froth flotation) case studies are evaluated. It is found that the DNN can predict the CFD results accurately when using four hidden layers, describing discontinuities in the bubbly flow regime. The relative errors computed between the CFD data and the prediction obtained by the DNN is as low as 8.8% and 1.8% for bubble size and bubble rate, respectively. These results confirm that the DNN can be applied to sophisticated fluid dynamics systems and allow developing better control process strategies since once the DNN is trained critical variables can be computed very efficiently. The slurry case study, although restricted to the application of mineral froth flotation, can also be generalized to other industrial operations keeping the exact same procedure.

Application of Multidisciplinary Systems‐of‐Systems Optimization to an Aircraft Design Problem

ABSTRACTA generic mathematical formulation for Systems‐of‐Systems (SoS) optimization problems is presented. SoS optimization problems resemble the structure of a tree of Multidisciplinary Design Optimization (MDO) problems with additional unique features. The framework for solving such problems involves features from evolutionary computing, platform‐based design, and evolving design spaces. One important aspect of SoS Engineering, often overlooked, is the role it plays in improving the design of individual systems. In this vein, this work has sought to exemplify such a synergistic approach for aircraft design. A large‐scale SoS optimization problem for designing noise‐optimal aircraft and improved procedures for the approach phase is studied. Modules involving Computational Fluid Dynamics (CFD), noise modeling, multifidelity analysis, topology optimization, and autotuned control systems are used to obtain optimal solutions.

Cooperative path planning with applications to target tracking and obstacle avoidance for multi-UAVs

In this paper, we propose a hybrid approach based on the Lyapunov Guidance Vector Field (LGVF) and the Improved Interfered Fluid Dynamical System (IIFDS), to solve the problems of target tracking and obstacle avoidance in three-dimensional cooperative path planning for multiple unmanned aerial vehicles (UAVs). First, LGVF method is improved for UAV cooperative target tracking in 3D environment by introducing vertical component, with two guidance layers containing steering control and speed control. Second, IIFDS method is presented for UAVs to avoid obstacles or threats in complicated environment, where the local minimum problem is well resolved. Moreover, some cooperative strategies are added into the IIFDS framework to satisfy the constraints of obstacle avoidance and cluster maintenance. Finally, the missions of tracking target and avoiding obstacles can be performed simultaneously, by replacing the original sink fluid of IIFDS with the vector field of LGVF. Besides, the reactive parameters of IIFDS can be adjusted by the rolling optimization strategy to enhance the path quality. The experimental results validate the effectiveness of the hybrid method.

Non-equilibrium Thermodynamics of Rayleigh–Taylor Instability

Here, the fundamental problem of Rayleigh–Taylor instability (RTI) is studied by direct numerical simulation (DNS), where the two air masses at different temperatures, kept apart initially by a non-conducting horizontal interface in a 2D box, are allowed to mix. Upon removal of the partition, mixing is controlled by RTI, apart from mutual mass, momentum, and energy transfer. To accentuate the instability, the top chamber is filled with the heavier (lower temperature) air, which rests atop the chamber containing lighter air. The partition is positioned initially at mid-height of the box. As the fluid dynamical system considered is completely isolated from outside, the DNS results obtained without using Boussinesq approximation will enable one to study non-equilibrium thermodynamics of a finite reservoir undergoing strong irreversible processes. The barrier is removed impulsively, triggering baroclinic instability by non-alignment of density, and pressure gradient by ambient disturbances via the sharp discontinuity at the interface. Adopted DNS method has dispersion relation preservation properties with neutral stability and does not require any external initial perturbations. The complete inhomogeneous problem with non-periodic, no-slip boundary conditions is studied by solving compressible Navier–Stokes equation, without the Boussinesq approximation. This is important as the temperature difference between the two air masses considered is high enough ( $$\Delta T = 70$$ K) to invalidate Boussinesq approximation. We discuss non-equilibrium thermodynamical aspects of RTI with the help of numerical results for density, vorticity, entropy, energy, and enstrophy.

Local conservative regularizations of compressible magnetohydrodynamic and neutral flows

Ideal systems like magnetohydrodynamics (MHD) and Euler flow may develop singularities in vorticity (w=∇×v). Viscosity and resistivity provide dissipative regularizations of the singularities. In this paper, we propose a minimal, local, conservative, nonlinear, dispersive regularization of compressible flow and ideal MHD, in analogy with the KdV regularization of the 1D kinematic wave equation. This work extends and significantly generalizes earlier work on incompressible Euler and ideal MHD. It involves a micro-scale cutoff length λ which is a function of density, unlike in the incompressible case. In MHD, it can be taken to be of order the electron collisionless skin depth c/ωpe. Our regularization preserves the symmetries of the original systems and, with appropriate boundary conditions, leads to associated conservation laws. Energy and enstrophy are subject to a priori bounds determined by initial data in contrast to the unregularized systems. A Hamiltonian and Poisson bracket formulation is developed and applied to generalize the constitutive relation to bound higher moments of vorticity. A “swirl” velocity field is identified, and shown to transport w/ρ and B/ρ, generalizing the Kelvin-Helmholtz and Alfvén theorems. The steady regularized equations are used to model a rotating vortex, MHD pinch, and a plane vortex sheet. The proposed regularization could facilitate numerical simulations of fluid/MHD equations and provide a consistent statistical mechanics of vortices/current filaments in 3D, without blowup of enstrophy. Implications for detailed analyses of fluid and plasma dynamic systems arising from our work are briefly discussed.

Superrelativity

Did any physics experts expect SUPERRELATIVITY paper, a physics revolution producing the EINSTEIN-RODGERS RELATIVITY EQUATION, producing the HAWKING-RODGERS BLACK HOLE RADIUS, and producing the STEFAN-BOLTZMANN-SCHWARZSCHILD-HAWKING-RODGERS BLACK HOLE RADIATION POWER LAW, as the author gave a solution to The Clay Mathematics Institute’s very difficult problem about the Navier-Stokes Equations? The Clay Mathematics Institute in May 2000 offered that great $million prize to the first person providing a solution for a specific statement of the problem: “Prove or give a counter-example of the following statement: In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier-Stokes Equations.” Did I, the creator of this paper, expect SUPERRELATIVITY to become a sophisticated conversion of my unified field theory ideas and mathematics into a precious fluid dynamics paper to help mathematicians, engineers and astro-physicists? [1]. Yes, but I did not expect such superb equations that can be used in medicine or in outer space! In this paper, complicated equations for multi-massed systems become simpler equations for fluid dynamic systems. That simplicity is what is great about the Navier-Stokes Equations. Can I delve deeply into adding novel formulae into the famous Schwarzschild’s equation? Surprisingly, yes I do! Questioning the concept of reversibility of events with time, I suggest possible 3-dimensional and 4-dimensional co-ordinate systems that seem better than what Albert Einstein used, and I suggest possible modifications to Maxwell’s Equations. In SUPERRELATIVITY, I propose that an error exists in Albert Einstein’s Special Relativity equations, and that error is significant because it leads to turbulence in the universe’s fluids including those in our human bodies. Further, in SUPERRELATIVITY, after I create Schwarzschild-based equations that enable easy derivation of the Navier-Stokes Equations, I suddenly create very interesting exponential energy equations that simplify physics equations, give a mathematical reason for turbulence in fluids, give a mathematical reason for irreversibility of events with time, and enable easy derivation of the Navier-Stokes Equations. Importantly, my new exponential Navier-Stokes Equations are actually wave equations as should be used in Fluid Dynamics. Thrilled by my success, I challenge famous equations by Albert Einstein and Stephen Hawking [2] [3].

Optimal control problems for the Navier–Stokes system coupled with the [formula omitted]-[formula omitted] turbulence model

Optimal control of fluid-dynamics systems has gained attention in the last several years from the scientific community because of its potential use in design of new engineering devices and optimization of existing ones. Many research works have extensively studied the optimal control for the system of Navier–Stokes but the problem of turbulence in these works is usually not taken into account because of the many difficulties arising from the numerical implementation and solution of the optimality system. In this work turbulence is considered by coupling the k-ω two-equation turbulence model with the averaged Navier–Stokes system. The complete optimality system is derived and the existence of a weak solution proven. Some numerical examples are reported.

Gauge symmetries and Noether charges in Clebsch-parameterized magnetohydrodynamics

It is shown that the Clebsch parameterization, upon canonizing the Hamiltonian system of ideal fluid or plasma dynamics, converts the Casimir invariants (mass and helicities) in the original noncanonical formulation into the Noether charges pertinent to the gauge symmetries of the parameterization. The problem is addressed in the context of magnetohydrodynamics. The concrete forms of the gauge symmetries of Clebsch parameterization are worked out.

Global existence and asymptotic stability of smooth solutions to a fluid dynamics model of biofilms in one space dimension

In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [3] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in an open neighborhood of the physical parameters, the system is totally dissipative near its unique non-vanishing equilibrium point. Using this property, we are able to prove existence and uniqueness of global smooth solutions to the Cauchy problem on the whole line for small perturbations of this equilibrium point and the solutions are shown to converge exponentially in time at the equilibrium state.

Real-time path planning of unmanned aerial vehicle for target tracking and obstacle avoidance in complex dynamic environment

According to the tactical requirements of unmanned aerial vehicle (UAV) for tracking target and avoiding obstacle in complex dynamic environment, a three-dimensional (3D) real-time path planning method is proposed by combing the improved Lyapunov Guidance Vector Field (LGVF), the Interfered Fluid Dynamical System (IFDS) and the strategy of varying receding-horizon optimization from Model Predictive Control (MPC). First, in order to track the moving target in 3D environment, the LGVF method is improved by introducing flight height into the traditional Lyapunov function, and the generated velocity can guide UAV converge gradually to the limit cycle in horizontal plane and the optimal height in vertical plane. Then, the IFDS method imitating the phenomenon of fluid flow is utilized to plan the collision-free path. To achieve the mission of tracking moving target and avoid static or dynamic obstacle at the same time, the guidance vector field by LGVF is taken as the original fluid of IFDS. As the fluid system still remains stable under the influence of obstacles, the disturbed streamline from the interfered fluid can be regarded as the planned path. Third, as the quality of route is mainly influenced by the repulsive and tangential parameters of IFDS, the real-time suboptimal route can be planned by the varying receding-horizon optimization according to the predicted motion. The experimental results prove that the proposed hybrid method is applicable to various dynamic environments.

Thermal creep flow for the Boltzmann equation

It is known that the Boltzmann equation has close relation to the classical systems in fluid dynamics. However, it provides more information on the microscopic level so that some phenomena, like the thermal creep flow, can not be modeled by the classical systems of fluid dynamics, such as the Euler equations. The author gives an example to show this phenomenon rigorously in a special setting. This paper is completely based on the author’s recent work, jointly with Wang and Yang.

Approximate solutions to the initial value problem for some compressible flows

For the natural initial conditions L 1 in the density field (more generally a positive bounded Radon measure) and L ∞ in the velocity field, we obtain global approximate solutions to the Cauchy problem for the 3-D systems of isothermal and isentropic gases and the 2-D shallow water equations. We obtain a sequence of functions which are differentiable in time and continuous in space and tend to satisfy the equations in the sense of distributions in the space variables and in the strong sense in the time variable. The method of construction relies on the study of a specific family of two ODEs in a classical Banach space (one for the continuity equation and one for the Euler equation). Standard convergent numerical methods for the solution of these ODEs can be used to provide concrete approximate solutions. It has been checked in numerous cases in which the solutions of systems of fluid dynamics are known that our construction always gives back the known solutions. It is also proved that it gives the classical analytic solutions in the domain of application of the Cauchy–Kovalevskaya theorem.

A fluid dynamics multidimensional model of biofilm growth: stability, influence of environment and sensitivity.

In this article, we study in detail the fluid dynamics system proposed in Clarelli et al. (2013, J. Math. Biol., 66, 1387-1408) to model the formation of cyanobacteria biofilms. After analysing the linear stability of the unique non-trivial equilibrium of the system, we introduce in the model the influence of light and temperature, which are two important factors for the development of a cyanobacteria biofilm. Since the values of the coefficients we use for our simulations are estimated through information found in the literature, some sensitivity and robustness analyses on these parameters are performed. All these elements enable us to control and to validate the model we have already derived and to present some numerical simulations in the 2D and the 3D cases.

High accuracy differential pressure measurements using fluid-filled catheters – A feasibility study in compliant tubes

High accuracy differential pressure measurements are required in various biomedical and medical applications, such as in fluid-dynamic test systems, or in the cath-lab. Differential pressure measurements using fluid-filled catheters are relatively inexpensive, yet may be subjected to common mode pressure errors (CMP), which can significantly reduce the measurement accuracy. Recently, a novel correction method for high accuracy differential pressure measurements was presented, and was shown to effectively remove CMP distortions from measurements acquired in rigid tubes. The purpose of the present study was to test the feasibility of this correction method inside compliant tubes, which effectively simulate arteries. Two tubes with varying compliance were tested under dynamic flow and pressure conditions to cover the physiological range of radial distensibility in coronary arteries. A third, compliant model, with a 70% stenosis severity was additionally tested. Differential pressure measurements were acquired over a 3cm tube length using a fluid-filled double-lumen catheter, and were corrected using the proposed CMP correction method. Validation of the corrected differential pressure signals was performed by comparison to differential pressure recordings taken via a direct connection to the compliant tubes, and by comparison to predicted differential pressure readings of matching fluid–structure interaction (FSI) computational simulations. The results show excellent agreement between the experimentally acquired and computationally determined differential pressure signals. This validates the application of the CMP correction method in compliant tubes of the physiological range for up to intermediate size stenosis severity of 70%.

Running interfacial waves in a two-layer fluid system subject to longitudinal vibrations.

We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of quasistationary states of free interface in fluid dynamical systems subject to vibrations, revealed the existence of standing periodic waves and solitons in this system. However, this approach does not provide regular means for dealing with evolutionary problems: neither stability problems nor ones associated with propagating waves. In this work, we rigorously derive the evolution equations for long waves in the system, which turn out to be identical to the plus (or good) Boussinesq equation. With these equations one can find all the time-independent-profile solitary waves (standing solitons are a specific case of these propagating waves), which exist below the linear instability threshold; the standing and slow solitons are always unstable while fast solitons are stable. Depending on initial perturbations, unstable solitons either grow in an explosive manner, which means layer rupture in a finite time, or falls apart into stable solitons. The results are derived within the long-wave approximation as the linear stability analysis for the flat-interface state [D.V. Lyubimov and A.A. Cherepanov, Fluid Dynamics 21, 849 (1986)] reveals the instabilities of thin layers to be long wavelength.

Firedrake-Fluids v0.1: numerical modelling of shallow water flows using an automated solution framework

Abstract. This model description paper introduces a new finite element model for the simulation of non-linear shallow water flows, called Firedrake-Fluids. Unlike traditional models that are written by hand in static, low-level programming languages such as Fortran or C, Firedrake-Fluids uses the Firedrake framework to automatically generate the model's code from a high-level abstract language called Unified Form Language (UFL). By coupling to the PyOP2 parallel unstructured mesh framework, Firedrake can then target the code towards a desired hardware architecture to enable the efficient parallel execution of the model over an arbitrary computational mesh. The description of the model includes the governing equations, the methods employed to discretise and solve the governing equations, and an outline of the automated solution process. The verification and validation of the model, performed using a set of well-defined test cases, is also presented along with a road map for future developments and the solution of more complex fluid dynamical systems.