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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

PyAMG: Algebraic Multigrid Solvers in Python

PyAMG is a Python package of algebraic multigrid (AMG) solvers and supporting tools for approximating the solution to large, sparse linear systems of algebraic equations, Ax = b, where A is an n × n sparse matrix. Sparse linear systems arise in a range of problems in science, from fluid flows to solid mechanics to data analysis. While the direct solvers available in SciPy’s sparse linear algebra package (scipy.sparse.linalg) are highly efficient, in many cases iterative methods are preferred due to overall complexity. However, the iterative methods in SciPy, such as CG and GMRES, often require an efficient preconditioner in order to achieve a lower complexity. Preconditioning is a powerful tool whereby the conditioning of the linear system and convergence rate of the iterative method are both dramatically improved. PyAMG constructs multigrid solvers for use as a preconditioner in this setting. A summary of multigrid and algebraic multigrid solvers can be found in Olson (2015a), in Olson (2015b), and in Falgout (2006); a detailed description can be found in Briggs et al. (2000) and Trottenberg et al. (2001).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Engineered Barrier System R&D and International Collaborations – LANL (FY20): Spent Fuel and Waste Disposition

The United States Department of Energy’s Spent Fuel and Waste Disposition (SFWD) program is investigating the design and safety function of generic nuclear geologic repositories in a variety of geologic settings (salt, argillite, and crystalline rock). Different configurations and loadings of spent nuclear fuel and waste within disposal canisters are also being investigated, some of which have the potential to generate repository temperatures higher than previously considered (i.e., temperatures >100ºC) by foreign and domestic concepts. This report expands on engineered barrier material stability in a high temperature crystalline rock repository through high temperature hydrothermal experiments. Experiments were designed to develop engineered barrier system (EBS) concepts in a hightemperature crystalline environment in 1) bentonite-Grimsel Granodiorite interactions, 2) bentonite-cement reactions, and 3) interaction between waste canister materials and bentonite. Experiment results are applied to understanding long-term repository performance in terms of radionuclide isolation. One hydrothermal experiment was completed in the rocking autoclaves at LANL in FY-20: IEBS-6 (Grimsel Granodiorite + Wyoming bentonite + cured ordinary Portland cement + Grimsel Granodiorite synthetic groundwater, 250ºC/150 bar, 8 weeks). Several other experiments were planned but were delayed due to the COVID-19 pause in laboratory work. In addition, some characterization of the reaction products of experiments conducted in FY-20 was prevented by COVID-19. Mineral phase chemistry was not measured via electron microprobe analyses for IEBS-6. Quantitative X-ray diffraction results from IEBS-6 and HBT-1 were not completed. The missing analyses and discussion of the results will be included in next year’s report. New characterization that was completed includes scanning electron microscopy of reaction products from IEBS-6, quantitative X-ray diffraction results are presented from IEBS-1 through IBES-5, preliminary scanning electron microscope images and chemical analyses for IEBS-6, X-ray diffraction of the clay fraction from all experiments, measurement/imaging of mineral growth on the surface of steel coupons. Major observations pertaining to bentonite stability in a Grimsel Granodiorite environment include the stability of Na-montmorillonite at 250°C, the formation of trace CSH phases, and the formation of bentonite colloids on experiment cooling. The addition of a cured chip of Portland cement to the bentonite-Grimsel system results in slightly higher pH values and the formation of diverse secondary mineral phases that were not observed in the previous experiments (e.g., analcime, garronite, CSH phases). The new characterization efforts related to the interaction of stainless-steel coupons and bentonite clay focused on thickness and mineralogy of phases that formed at the steel surface. In Wyoming bentonite + Grimsel Granodiorite systems, newly formed minerals at the bentonitesteel coupon interface included alteration of the outermost steel edge to Fe,Cr-oxide phases, followed by Fe-rich phyllosilicates (Fe-saponite, chlorite) and interbedded Fe,Cr,Ni-sulfide phases (pentlandite). Hydrothermal experiments were completed to assess uranium-carbonate complexation at conditions relevant to high-temperature disposal. Autoclave solubility experiments were conducted at 150 to 250ºC with a range of carbonate and uranium concentrations. The experiment results were characterized via situ UV-Visible spectroscopy and synchrotron-based in situ XAS techniques. Results show a significant decrease in the stability of uranyl-carbonate complexes at temperatures above 100ºC along with the precipitation of uranium oxides. Further, at T > 200ºC, results show that uranyl-hydroxyl complexes control solubility of uranium instead of the previously predicted uranyl-carbonate species. These results are significant for understanding the mobility of uranium in the EBS, which will likely contain carbonate-rich fluids. International research efforts focused on three main areas: 1) participation in international conferences, 2) building collaborations with foreign repository programs, and 3) the initiation of an experimental program to complement the full-scale HotBENT test at the Grimsel test site. This experiment included Wyoming bentonite + low carbon steel + Grimsel Granodiorite synthetic groundwater and was run at the planned maximum temperature of the HotBENT test (200°C). Complete characterization of reaction products was hindered by disruptions to laboratory work but will be reported in the next FY. The experimental results obtained in FY-20 continue to document the wide-ranging effects of bulk composition and pressure-temperature conditions in the mineralogical and geochemical evolution of a high-temperature repository environment. Concepts developed will be used to inform models of long-term material stability in a generic crystalline rock-hosted repository.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Hanford Site Composite Analysis: Comparison of One- and Three-Dimensional Simulation of Vadose Zone Transport and Transfer to Groundwater for Selected Waste Sites

The purpose of this document is to compare 1D and 3D technetium-99 (Tc-99) VZ transport and transfer rates to groundwater for five selected waste sites (two tanks, two cribs, and one trench) to demonstrate the need to consider 3D flow and transport mechanisms and commingling of contaminant plumes originating from adjacent waste sites. The waste sites selected for the comparison evaluation are the 241-A-105 Tank in the A Farms Area model, the 216-B-18 Crib and the 216-B-25 Trench in the BC Cribs and Trenches model, the 216-B-49 Crib in the B Complex model, and the 241-SX-115 Tank in the S Farms Area model. The selected waste sites all represent different disposal or leak conditions, with and without potential impacts due to release-fluid commingling, occurring at the Hanford Site Central Plateau.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Dilute Combustion Control Using Spiking Neural Networks

Dilute combustion with exhaust gas recirculation (EGR) in spark-ignition engines presents a cost-effective method for achieving higher levels of engine efficiency. At high levels of EGR, however, cycle-to-cycle variability (CCV) of the combustion process is exacerbated by sporadic occurrences of misfires and partial burns. Previous studies have shown that temporal deterministic patterns emerge at such conditions and certain combustion cycles have a significant influence over future events. Due to the complexity of the combustion process and the nature of CCV, harnessing all the deterministic information for control purposes has remained challenging even with physics based 0-D, 1-D, and high-fidelity computational fluid dynamics (CFD) models. In this study, we present a data-driven approach to optimize the combustion process by controlling CCV adjusting the cycle-to-cycle fuel injection quantity. Readily available data from in-cylinder pressure was used to train a spiking neural network (SNN) which learns the optimal way to manage fuel injection in order to reduce CCV while maintaining acceptable levels of fuel consumption. SNNs are particularly well suited for powertrain control applications due to their ability to be deployed on FPGA-based neuromorphic hardware which are small, inexpensive, and have a low power demand. The high-performance computing (HPC) resources of Oak Ridge National Laboratory were used to run an evolutionary-based training approach for choosing the best SNN configuration that minimizes the size of the network while achieving the desired goal. The neuromorphic hardware with the optimized SNN deployed was connected to the rapid prototyping engine control system for real-time control implementation and tested on a single cylinder version of a GM LNF 4-cylinder engine. The results show a significant reduction of CCV with a small percentage of additional fuel used to stabilize the charge.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1975

Characterization of typical platelet injector flow configurations

A study to investigate the hydraulic atomization characteristics of several novel injector designs for use in liquid propellant rocket engines is presented. The injectors were manufactured from a series of thin stainless steel platelets through which orifices were very accurately formed by a photoetching process. These individual platelets were stacked together and the orifices aligned so as to produce flow passages of prescribed geometry. After alignment, the platelets were bonded into a single, 'platelet injector', unit by a diffusion bonding process. Because of the complex nature of the flow associated with platelet injectors, it was necessary to use experimental techniques, exclusively, throughout the study. Large scale models of the injectors were constructed from aluminum plates and the appropriate fluids were modeled using a glycerol-water solution. Stop-action photographs of test configurations, using spark-shadowgraph or stroboscopic back-lighting, are shown.

Hickox, C. E.↗
NASA NTRS1991

Frequency effects on the stability of a journal bearing for periodic loading

The stability of a journal bearing is numerically predicted when a unidirectional periodic external load is applied. The analysis is performed using a cavitation algorithm, which mimics the Jakobsson-Floberg and Olsson (JFO) theory by accounting for the mass balance through the complete bearing. Hence, the history of the film is taken into consideration. The loading pattern is taken to be sinusoidal and the frequency of the load cycle is varied. The results are compared with the predictions using Reynolds boundary conditions for both film rupture and reformation. With such comparisons, the need for accurately predicting the cavitation regions for complex loading patterns is clearly demonstrated. For a particular frequency of loading, the effects of mass, amplitude of load variation and frequency of journal speed are also investigated. The journal trajectories, transient variations in fluid film forces, net surface velocity and minimum film thickness, and pressure profiles are also presented.

Vijayaraghavan, D.↗
NASA NTRS1993

Modeling of PCG fluid dynamics: Salient results

Materials processing in space-based laboratories has already yielded higher quality crystals during previous space flights, and opportunities for several fluids experiments are anticipated during the extended duration missions planned for the future. Crystal growth in space benefits not only from its reduced gravity environment but also from the absence of the hydrostatic pressure which assists certain crystal growth and refinement methods. Gravity-driven phenomena are thus reduced in strength, and a purely diffusive fluid's behavior can be attained. In addition, past materials science experiments have shown that microgravity can also help produce larger crystals. While gravity-related effects are definitely curtailed in space, they are nevertheless present to some degree due to the acceleration environment onboard the spacecraft. This residual acceleration level is comprised of quasi-steady, oscillatory, and transient components, and is caused by a variety of mechanisms. For example, gravity gradient forces produce low frequency disturbances, and the operation of machinery, control thrusters, solar panels, human activity, etc. contribute to higher frequency accelerations. These disturbances are collectively referred to as g-jitter, and they can be deleterious to certain experiments where the minimization of the acceleration level is important. Advanced vibration isolation techniques can be utilized to actively filter out some of the detrimental frequencies and help in obtaining optimum results. However, the successful application of this technology requires the detailed analysis of candidate fluids experiments to gauge their response to g-jitter and to determine their acceleration sensitivities. Several crystal growth experiments in the Protein Crystal Growth (PCG) area, besides others, are expected to be carried out on future shuttle flights and on Space Station Freedom. The need for vibration isolation systems or components for microgravity science experiments can be expected to grow as experiments and available hardware becomes more complex. This technology will also find increased application as the science community develops an awareness of their specific needs relative to the environment available in manned space missions. Vibration isolation research strives to develop a microgravity environment requirement that defines tolerance limits on the allowable g-level, and provides the required technology to achieve it. This effort will assist in establishing the tolerable acceleration levels for specific fluids experiments. The primary effort is directed towards modeling PCG and the approach undertaken for this investigation is outlined. The objectives of this research are: (1) to computationally determine vibration sensitivity of protein crystal growth experiments; (2) determine if these experiments can benefit from vibration isolation techniques; and (3) provide realistic requirements for vibration isolation technology.

Ramachandran, N.↗
NASA NTRS1996

Computer Aided Grid Interface: An Interactive CFD Pre-Processor

NASA maintains an applications oriented computational fluid dynamics (CFD) efforts complementary to and in support of the aerodynamic-propulsion design and test activities. This is especially true at NASA/MSFC where the goal is to advance and optimize present and future liquid-fueled rocket engines. Numerical grid generation plays a significant role in the fluid flow simulations utilizing CFD. An overall goal of the current project was to develop a geometry-grid generation tool that will help engineers, scientists and CFD practitioners to analyze design problems involving complex geometries in a timely fashion. This goal is accomplished by developing the Computer Aided Grid Interface system (CAGI). The CAGI system is developed by integrating CAD/CAM (Computer Aided Design/Computer Aided Manufacturing) geometric system output and / or Initial Graphics Exchange Specification (IGES) files (including all the NASA-IGES entities), geometry manipulations and generations associated with grid constructions, and robust grid generation methodologies. This report describes the development process of the CAGI system.

Soni, Bharat K.↗
NASA NTRS1997

Computer Aided Grid Interface: An Interactive CFD Pre-Processor

NASA maintains an applications oriented computational fluid dynamics (CFD) efforts complementary to and in support of the aerodynamic-propulsion design and test activities. This is especially true at NASA/MSFC where the goal is to advance and optimize present and future liquid-fueled rocket engines. Numerical grid generation plays a significant role in the fluid flow simulations utilizing CFD. An overall goal of the current project was to develop a geometry-grid generation tool that will help engineers, scientists and CFD practitioners to analyze design problems involving complex geometries in a timely fashion. This goal is accomplished by developing the CAGI: Computer Aided Grid Interface system. The CAGI system is developed by integrating CAD/CAM (Computer Aided Design/Computer Aided Manufacturing) geometric system output and/or Initial Graphics Exchange Specification (IGES) files (including all the NASA-IGES entities), geometry manipulations and generations associated with grid constructions, and robust grid generation methodologies. This report describes the development process of the CAGI system.

Soni, Bharat K.↗
NASA NTRS1999

PAR Analysis of HSR Nozzles

Only recently has computational fluid dynamics (CFD) been relied upon to predict the flow details of advanced nozzle concepts. Computer hardware technology and flow solving techniques are advancing rapidly and CFD is now being used to analyze such complex flows. Validation studies are needed to assess the accuracy, reliability, and cost of such CFD analyses. At NASA Lewis, the PARC2D/3D full Navier-Stokes (FNS) codes are being applied to HSR-type nozzles. This report presents the results of two such PARC FNS analyses. The first is an analysis of the Pratt and Whitney 2D mixer-ejector nozzle, conducted by Dr. Yunho Choi (formerly of Sverdrup Technology-NASA Lewis Group). The second is an analysis of NASA-Langley's axisymmetric single flow plug nozzle, conducted by the author.

Georgiadis, Nicholas J.↗
NASA NTRS2003

A Eulerian-Lagrangian Model to Simulate Two-Phase/Particulate Flows

Figure 1 shows a snapshot of liquid fuel spray coming out of an injector nozzle in a realistic gas-turbine combustor. Here the spray atomization was simulated using a stochastic secondary breakup model (Apte et al. 2003a) with point-particle approximation for the droplets. Very close to the injector, it is observed that the spray density is large and the droplets cannot be treated as point-particles. The volume displaced by the liquid in this region is significant and can alter the gas-phase ow and spray evolution. In order to address this issue, one can compute the dense spray regime by an Eulerian-Lagrangian technique using advanced interface tracking/level-set methods (Sussman et al. 1994; Tryggvason et al. 2001; Herrmann 2003). This, however, is computationally intensive and may not be viable in realistic complex configurations. We therefore plan to develop a methodology based on Eulerian-Lagrangian technique which will allow us to capture the essential features of primary atomization using models to capture interactions between the fluid and droplets and which can be directly applied to the standard atomization models used in practice. The numerical scheme for unstructured grids developed by Mahesh et al. (2003) for incompressible flows is modified to take into account the droplet volume fraction. The numerical framework is directly applicable to realistic combustor geometries. Our main objectives in this work are: Develop a numerical formulation based on Eulerian-Lagrangian techniques with models for interaction terms between the fluid and particles to capture the Kelvin- Helmholtz type instabilities observed during primary atomization. Validate this technique for various two-phase and particulate flows. Assess its applicability to capture primary atomization of liquid jets in conjunction with secondary atomization models.

Apte, S. V.↗
NASA NTRS2016

Overview of the NASA Glenn Flux Reconstruction Based High-Order Unstructured Grid Code

A computational fluid dynamics code based on the flux reconstruction (FR) method is currently being developed at NASA Glenn Research Center to ultimately provide a large- eddy simulation capability that is both accurate and efficient for complex aeropropulsion flows. The FR approach offers a simple and efficient method that is easy to implement and accurate to an arbitrary order on common grid cell geometries. The governing compressible Navier-Stokes equations are discretized in time using various explicit Runge-Kutta schemes, with the default being the 3-stage/3rd-order strong stability preserving scheme. The code is written in modern Fortran (i.e., Fortran 2008) and parallelization is attained through MPI for execution on distributed-memory high-performance computing systems. An h- refinement study of the isentropic Euler vortex problem is able to empirically demonstrate the capability of the FR method to achieve super-accuracy for inviscid flows. Additionally, the code is applied to the Taylor-Green vortex problem, performing numerous implicit large-eddy simulations across a range of grid resolutions and solution orders. The solution found by a pseudo-spectral code is commonly used as a reference solution to this problem, and the FR code is able to reproduce this solution using approximately the same grid resolution. Finally, an examination of the code's performance demonstrates good parallel scaling, as well as an implementation of the FR method with a computational cost/degree- of-freedom/time-step that is essentially independent of the solution order of accuracy for structured geometries.

High-Order Methods↗
NASA NTRSDate not supplied

Recent Langley Aerothermodynamic Laboratory Testing (2019-2022)

In support of flight programs, multiple wind tunnel entries were conducted on reentry vehicle configurations to investigate blunt body aeroheating environments. Blunt body block thermal protection system (TPS) roughness, the Low-Earth Orbit Flight Test of an Inflatable Decelerator aeroshell scalloping, and a woven TPS all were tested to determine the effects of those parameters on increased surface heating to the vehicle. Commercial Crew Program studies also utilized the speed and ease of testing in the LAL to analyze parametric databases of low-earth reentry configurations, like the Boeing CST-100, and vehicles designed to travel to the moon or Mars, such as the SpaceX Starship. LAL wind tunnel investigations also supported several DoD and AFRL flight projects, such as HIFiRE 6 and BOLT. External customers leveraged the LAL testing capability to advance their research programs, including UPSTAR, RocketLab, and Lawrence Livermore National Laboratory. Academia groups benefitted from the inexpensive cost to test in the tunnels for many university collaborations, such as studies conducted in partnership with the University of Maryland on a flat plate, using a pressure rake and investigating fluid structure interactions. Multiple studies in collaboration with Purdue considered boundary layer transition on various cone configurations. Another study was conducted using a cone with shaped roughness elements borrowed from the Arnold Engineering Development Complex. Internal testing included studies using a phosphor thermography system that can measure higher temperatures than the current LAL phosphor capability and a characterization study of the noise in the wind tunnel flow. The breadth of testing across research and commercial paradigms, both internal and external to NASA, different configurations, a variety of test techniques and aerodynamic and aerothermal environments will be discussed in this overview presentation of the recent work conducted in the LAL.

wind tunnel test↗
DOE OSTI2016

Numerical Study of Critical Role of Rock Heterogeneity in Hydraulic Fracture Propagation

Log and seismic data indicate that most shale formations have strong heterogeneity. Conventional analytical and semi-analytical fracture models are not enough to simulate the complex fracture propagation in these highly heterogeneous formation. Without considering the intrinsic heterogeneity, predicted morphology of hydraulic fracture may be biased and misleading in optimizing the completion strategy. In this paper, a fully coupling fluid flow and geomechanics hydraulic fracture simulator based on dual-lattice Discrete Element Method (DEM) is used to predict the hydraulic fracture propagation in heterogeneous reservoir. The heterogeneity of rock is simulated by assigning different material force constant and critical strain to different particles and is adjusted by conditioning to the measured data and observed geological features. Based on proposed model, the effects of heterogeneity at different scale on micromechanical behavior and induced macroscopic fractures are examined. From the numerical results, the microcrack will be more inclined to form at the grain weaker interface. The conventional simulator with homogeneous assumption is not applicable for highly heterogeneous shale formation.

Dual Lattice Discrete Element Method↗
NASA NTRSDate not supplied

Validation of Gas-Liquid Sharp Interface Model in Loci-Stream for Propellant Tank Self-pressurization under Normal Gravity

Deep space missions require advances in cryogenic fluid management (CFM) for long term storage of propellants. One of the important phenomena is self-pressurization due to heat leakages into the tank. Managing self-pressurization is one of the key technologies for deep space exploration and long-term space missions. The complex interactions involving natural convection, thermal gradients, turbulence, and phase change near the gas-liquid interface cannot be modeled using reduced order or nodal analysis models, and 3-D CFD analyses are necessary to fully characterize the dynamics. CFD analyses pose their own difficulties. The requisite CFD tool to tackle this problem need to be modular with the ability to incorporate various physics models, efficient, and computationally scalable for simulating flight size tanks. In this paper, we discuss modeling approach for self-pressurization in situations where the liquid interface is static and validate NASA MSFC’s Loci-Stream CFD solver for predicting self-pressurization in a test tank in normal gravity. This tank was designed to capture quantifiable and accurate data for understanding various two-phase fluid phenomena and to validate modeling tools. Specifically, we demonstrate the capability of the Loci-Stream solver with a two-phase sharp-interface treatment to predict self-pressurization of a tank with an unperturbed gas-liquid interface. This validation highlights the reliability of our modeling approach and our solver to serve as a design and analysis tool for NASA’s CFM application needs.

cryogenic fluid management↗
NASA NTRSDate not supplied

Validation of Gas-Liquid Sharp Interface Model in Loci-Stream for Propellant Tank Self-pressurization under Normal Gravity

Deep space missions require advances in cryogenic fluid management (CFM) for long term storage of propellants. One of the important phenomena is self-pressurization due to heat leakages into the tank. Managing self-pressurization is one of the key technologies for deep space exploration and long-term space missions. The complex interactions involving natural convection, thermal gradients, turbulence, and phase change near the gas-liquid interface cannot be modeled using reduced order or nodal analysis models, and 3-D CFD analyses are necessary to fully characterize the dynamics. CFD analyses pose their own difficulties. The requisite CFD tool to tackle this problem need to be modular with the ability to incorporate various physics models, efficient, and computationally scalable for simulating flight size tanks. In this paper, we discuss modeling approach for self-pressurization in situations where the liquid interface is static and validate NASA MSFC's Loci-Stream CFD solver for predicting self-pressurization in a test tank in normal gravity. This tank was designed to capture quantifiable and accurate data for understanding various two-phase fluid phenomena and to validate modeling tools. Specifically, we demonstrate the capability of the Loci-Stream solver with a two-phase sharp-interface treatment to predict self-pressurization of a tank with an unperturbed gas-liquid interface. This validation highlights the reliability of our modeling approach and our solver to serve as a design and analysis tool for NASA's CFM application needs.

cryogenic fluid management↗
DOE OSTI2016

Optimization of micropillar sequences for fluid flow sculpting

Inertial fluid flow deformation around pillars in a microchannel is a new method for controlling fluid flow. Sequences of pillars have been shown to produce a rich phase space with a wide variety of flow transformations. Previous work has successfully demonstrated manual design of pillar sequences to achieve desired transformations of the flow cross section, with experimental validation. However, such a method is not ideal for seeking out complex sculpted shapes as the search space quickly becomes too large for efficient manual discovery. We explore fast, automated optimization methods to solve this problem. We formulate the inertial flow physics in microchannels with different micropillar configurations as a set of state transition matrix operations. These state transition matrices are constructed from experimentally validated streamtraces for a fixed channel length per pillar. This facilitates modeling the effect of a sequence of micropillars as nested matrix-matrix products, which have very efficient numerical implementations. With this new forward model, arbitrary micropillar sequences can be rapidly simulated with various inlet configurations, allowing optimization routines quick access to a large search space. We integrate this framework with the genetic algorithm and showcase its applicability by designing micropillar sequences for various useful transformations. We computationally discover micropillar sequences for complex transformations that are substantially shorter than manually designed sequences. We also determine sequences for novel transformations that were difficult to manually design. Finally, we experimentally validate these computational designs by fabricating devices and comparing predictions with the results from confocal microscopy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Odd surface waves in two-dimensional incompressible fluids

We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress) boundary conditions. We first find the free surface wave solutions of hydrodynamics in the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral and even exist in the absence of gravity and vanishing shear viscosity. In this limit, we derive effective nonlinear Hamiltonian equations for the surface dynamics, generalizing the linear solutions to the weakly nonlinear case. Within the small surface angle approximation, the equation of motion leads to a new class of non-linear chiral dynamics governed by what we dub the chiral Burgers equation. The chiral Burgers equation is identical to the complex Burgers equation with imaginary viscosity and an additional analyticity requirement that enforces chirality. We present several exact solutions of the chiral Burgers equation. For generic multiple pole initial conditions, the system evolves to the formation of singularities in a finite time similar to the case of an ideal fluid without odd viscosity. We also obtain a periodic solution to the chiral Burgers corresponding to the non-linear generalization of small amplitude linear waves.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗