Peter Thomas Tkacik

Color Schlieren imaging of high-pressure overexpanded planar nozzle flow using a simple, low-cost test apparatus

Complex flow features within rocket nozzles can exert significant influence on both the dynamics and safety of rockets during flight. Specifically, under over-expanded flow conditions, during, low altitude flight, random, often large side loads can appear within nozzles. While significant research has focused on this classical problem, due to the high nozzle pressure ratios (NPR) extant across rocket nozzles, most experimental work: (1) has focused on measuring wall pressure distributions under conditions when side loads appear, (2) has been carried out in large government or industrial test facilities, and (3) has only provided limited, though crucially important, visualization data. This short paper describes the construction and operation of a very simple, low cost test apparatus that allows imaging of flow features within planar nozzles, under the high NPR conditions characteristic of medium-to-large rockets. Representative color Schlieren images of flow shock structure obtained within the test apparatus are also presented and briefly described.Graphical abstract

Influence of nozzle random side loads on launch vehicle dynamics

It is well known that the dynamic performance of a rocket or launch vehicle is enhanced when the length of the divergent section of its nozzle is reduced or the nozzle exit area ratio is increased. However, there exists a significant performance trade-off in such rocket nozzle designs due to the presence of random side loads under overexpanded nozzle operating conditions. Flow separation and the associated side-load phenomena have been extensively investigated over the past five decades; however, not much has been reported on the effect of side loads on the attitude dynamics of rocket or launch vehicle. This paper presents a quantitative investigation on the influence of in-nozzle random side loads on the attitude dynamics of a launch vehicle. The attitude dynamics of launch vehicle motion is captured using variable-mass control-volume formulation on a cylindrical rigid sounding rocket model. A novel physics-based stochastic model of nozzle side-load force is developed and embedded in the rigid-body model...

Stochastic rocket dynamics under random nozzle side loads: Ornstein-Uhlenbeck boundary layer separation and its coarse grained connection to side loading and rocket response

A long-standing, though ill-understood problem in rocket dynamics, rocket response to random, altitudedependent nozzle side-loads, is investigated. Side loads arise during low altitude flight due to random, asymmetric, shock-induced separation of in-nozzle boundary layers. In this paper, stochastic evolution of the innozzle boundary layer separation line, an essential feature underlying side load generation, is connected to random, altitude-dependent rotational and translational rocket response via a set of simple analytical models. Separation line motion, extant on a fast boundary layer time scale, is modeled as an Ornstein-Uhlenbeck process. Pitch and yaw responses, taking place on a long, rocket dynamics time scale, are shown to likewise evolve as OU processes. Stochastic, altitude-dependent rocket translational motion follows from linear, asymptotic versions of the full nonlinear equations of motion; the model is valid in the practical limit where random pitch, yaw, and roll rates all remain small. Computed altitude-dependent rotational and translational velocity and displacement statistics are compared against those obtained using recently reported high fidelity simulations [Srivastava, Tkacik, and Keanini, J. Appl. Phys. 108, 044911 (2010)]; in every case, reasonable agreement is observed. As an important prelude, evidence indicating the physical consistency of the model introduced in the above article is first presented: it is shown that the study’s separation line model allows direct derivation of experimentally observed side load amplitude and direction densities. Finally, it is found that the analytical models proposed in this paper allow straightforward identification of practical approaches for: i) reducing pitch/yaw response to side loads, and ii) enhancing pitch/yaw damping once side loads cease.

Macroscopic liquid-state molecular hydrodynamics

Experimental evidence and theoretical modeling suggest that piles of confined, high-restitution grains, subject to low-amplitude vibration, can serve as experimentally-accessible analogs for studying a range of liquid-state molecular hydrodynamic processes. Experiments expose single-grain and multiple-grain, collective dynamic features that mimic those either observed or predicted in molecular-scale, liquid state systems, including: (i) near-collision-time-scale hydrodynamic organization of single-molecule dynamics, (ii) nonequilibrium, long-time-scale excitation of collective/hydrodynamic modes, and (iii) long-time-scale emergence of continuum, viscous flow. In order to connect directly observable macroscale granular dynamics to inaccessible and/or indirectly measured molecular hydrodynamic processes, we recast traditional microscale equilibrium and nonequilibrium statistical mechanics for dense, interacting microscale systems into self-consistent, macroscale form. The proposed macroscopic models, which appear to be new with respect to granular physics, and which differ significantly from traditional kinetic-theory-based, macroscale statistical mechanics models, are used to rigorously derive the continuum equations governing viscous, liquid-like granular flow. The models allow physically-consistent interpretation and prediction of observed equilibrium and non-equilibrium, single-grain, and collective, multiple-grain dynamics.

Laboratory-Scale Flight Characterization of a Multitethered Aerostat for Wind Energy Generation

Tethered lifting bodies have attracted significant attention from surveillance, communications, and (most recently) wind energy domains. As with many aerospace systems, the costs of full-scale test...

A case study in experimentally-infused plant and controller optimization for airborne wind energy systems

This paper presents a combined plant and controller optimization process for airborne wind energy systems (AWEs) that fuses numerical optimization with lab-scale experimental results. The methodology introduced in this paper, referred to as experimentally-infused optimization, addresses several challenges faced by AWE system designers, including a strong coupling between the controller and plant design, significant modeling uncertainties (which require the use of experiments), and high costs associated with full-scale experimental prototypes. This paper presents an initial case study of the proposed experimentally-infused optimization, where experiments were conducted on a 1/100th-scale model of Altaeros Buoyant Air Turbine (BAT), which was tethered and flown in the University of North Carolina at Charlotte 1m × 1m water channel. The lab-scale experimental platform reduced the cost of evaluating flight dynamics and control by more than two orders of magnitude, while resulting in substantially improved flight performance, quantified by a 15.2 percent improvement in an objective function value, as compared to a purely numerical optimization.

Lab-Scale Characterization of a Lighter-Than-Air Wind Energy System - Closing the Loop

Airborne Wind Energy systems (AWEs), which replace conventional systems’ towers with tethers and a lifting body, can provide inexpensive and clean energy to remote locations that have traditionally relied on expensive diesel fuel as their principal fuel source. However, many AWEs have not been implemented because of the lack of flight dynamic characterization that has resulted from the high costs of full-scale models. This paper presents recent developments in a lab-scale, water channel-based test platform for the characterization of AWEs, focusing on the flight dynamics of the Buoyant Airborne Turbine (BAT) of Altaeros Energies, which uses a lighter-than-air shell to elevate a horizontal-axis turbine to altitudes as high as 600 m. Specifically, the paper describes the lab-scale testing framework implemented in the UNC-Charlotte water channel, which includes real-time motion capture, closed-loop control of tethers, and rapid variability over a variety of model parameters (including tether attachment location, center of mass location, and fin geometry), which represent significant advances with respect to the authors’ previous work. The research specifically focused on the impact of center of mass location, trim pitch angle, and horizontal stabilizer pitch angle on flight dynamics, demonstrating the sensitivity of flight dynamic performance on these parameters both in the openand closed-loop setting.

Millisecond-scale shock-train evolution in high-pressure ratio nozzles: Schlieren imaging and qualitative analysis of shock-boundary layer interaction

The classical picture of shock evolution in nozzles holds that under over-expanded flow conditions, a single, nominally normal shock exists within the nozzle. Focusing on the highly dynamic flow produced during blow-down of an experimental, high-nozzle pressure ratio, planar nozzle, this article presents visual evidence that shock-trains – here, a pair of parallel, nominally normal shocks – dominate the rapidly evolving flow field. Three principal results are presented in this study. First, high-speed schlieren images of the evolving nozzle flow are reported. Second, a simple qualitative model of shock–boundary layer/recirculation zone interaction is proposed and used to explain observed millisecond-scale shock-train structure. Third, limited wall pressure measurements and schlieren images are combined to propose a second qualitative model of shock-train–boundary layer/recirculation zone evolution on the longer blow-down process time-scale. The results provide insight into millisecond-scale compressible flow dynamics within high-nozzle pressure ratios .

Human Sensitivity in Forced Feedback Systems as a Function of Frequency and Amplitude of Steering Wheel Vibrations

A warning system is described as, that improves safety in an over the road truck application by warning the driver with steering wheel vibration of impending roll over. This work focuses on creating a Haptic feedback and the corresponding driver response to a range of frequencies and amplitudes of vibration at the steering wheel. The haptic feedback system is the endpoint of the entire warning system. An experimental road going system is designed, presented, and tested. The experimental data reveals information about the response of the human subject to the frequency of steering wheel vibration, while driving a vehicle. Data variability is investigated through sampling of a population of drivers. The experimental setup probing the amplitude and frequency information is analyzed. Objective measurement anomalies in the data were seen in the subjective tests as well. Some conclusions are given about the applicability of laboratory tests to moving vehicle tests.

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An analog, macroscopic method for studying molecular-scale hydrodynamic processes in dense gases and liquids is described. The technique applies a standard fluid dynamic diagnostic, particle image velocimetry (PIV), to measure: i) velocities of individual particles (grains), extant on short, grain-collision time-scales, ii) velocities of systems of particles, on both short collision-time- and long, continuum-flow-time-scales, iii) collective hydrodynamic modes known to exist in dense molecular fluids, and iv) short- and long-time-scale velocity autocorrelation functions, central to understanding particle-scale dynamics in strongly interacting, dense fluid systems. The basic system is composed of an imaging system, light source, vibrational sensors, vibrational system with a known media, and PIV and analysis software. Required experimental measurements and an outline of the theoretical tools needed when using the analog technique to study molecular-scale hydrodynamic processes are highlighted. The proposed technique provides a relatively straightforward alternative to photonic and neutron beam scattering methods traditionally used in molecular hydrodynamic studies.