Nilabh Srivastava

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.

A Two Zone Model of a Single Cylinder HCCI Engine for Control Applications

This paper presents a first step towards developing a physics-based two-zone model of a single cylinder HCCI engine. Previously control laws were derived by using single zone mathematical models of HCCI combustion; although certain multi-zone models were reported, they were found too complex and unwieldy for the development of fast and efficient controllers for HCCI engines. The present work outlines the modeling approach of a single-cylinder two-zone HCCI engine by incorporating the first law of thermodynamics and temperature and concentration inhomogeneities within the cylinder in order to better predict peak pressures and combustion timings. The results showed good conformity when compared with the computationally intensive multi-zone models. A comparative analysis between the single zone and two-zone models, in the context of predicting cylinder pressures, temperatures, ignition timing is also discussed. Moreover, the effect of external parameters such as speed, and EGR were also evaluated.Copyright

TRANSIENT-DYNAMIC MODEL OF A METAL V-BELT CVT FOR RATIO SHIFT CONTROL APPLICATIONS

A continuously variable transmission (CVT) enhances the fuel economy and acceleration performance of a vehicle by allowing the engine to operate at or near its best specific fuel consumption rate for variable driving scenarios. A large volume of work has been reported on the dynamic modeling a metal V-belt CVT system. Most of the models mentioned in literature are steady-state quasi-static equilibrium based or multibody-formalism based, thereby being unsuitable for CVT control applications. Since steady state models fail to accurately capture inertial effects and multibody models present a challenge for control applications due to the large number of bodies involved, the focus of the current work has been to develop a simulation model relatively quick and accurate enough to predict the power transmission behavior and inertial dynamics of a metal pushing V-belt CVT at transient states. The objective of this research is to develop a detailed continuous one-dimensional transient-dynamic model of a metal V-belt CVT system for control applications. The model presented in this work is able to capture the dynamic correlation between the required pulley axial forces and the corresponding transmission ratio. In addition to this, it takes into account detailed inertial effects and predicts the slip behavior and torque capacity of the CVT system under both transient and steady-state regimes. The model proposed in this work would serve as a powerful tool to develop fast, reliable, and accurate controllers for a CVT-equipped driveline to meet the objectives of reduced losses, higher torque capacity, higher vehicle fuel economy and better acceleration performance. The results from the present model subsequently discuss in detail the transient performance of a metal V-belt CVT drive for high torque loading conditions. Various control strategies can be readily implemented with this detailed transient-dynamic model of a metal V-belt CVT system to achieve minimum slip loss and maximum fuel economy and torque capacity.Copyright

LQR-Based Control of a Two Zone HCCI Engine Model

With growing environmental concern, automobile energy consumption has become a key element in the current debate on global warming. Over the last two decades, significant research effort has been directed towards developing advanced engine technologies such as HCCI (Homogeneous Charge Compression Ignition) that not only lower the exhaust emissions from an automobile, but also offers reprieve from conventional gasoline/diesel usage by promising fuel-flexibility. HCCI offers better engine performance and reduced emissions by emulating the best features of both CI (compression-ignition) and SI (spark-ignition) engines. However, accurate and reliable combustion control of an HCCI engine is an inherently challenging task. Many single-zone control-oriented HCCI models reported in literature fail to accurately estimate the peak pressures, ignition timings, and especially cylinder temperatures. Although certain multi-zone models of HCCI engines based on detail chemical kinetics and fluid mechanics have been developed, such models are too complex for the synthesis of fast and reliable control laws. Thus, considerable research effort has been directed in the present work to develop a physics-based two-zone model of a single-cylinder HCCI engine accounting for temperature and concentration inhomogeneities within the cylinder for better prediction of peak pressures, combustion timings, and exhaust temperatures. The results obtained were in consonance with the computationally intensive multi-zone models. The nonlinear model for peak pressure, ignition timing and exhaust temperature was linearized about an operating point to facilitate the development of an effective LQR (linear quadratic regulator). The model inputs include variable valve timings to effectively control peak pressures, exhaust temperatures and ignition timings.Copyright

A Control-Oriented Two Zone Thermo-Kinetic Model of a Single Cylinder HCCI Engine

Over the past two decades, homogeneous charge compression ignition engine technology (HCCI) has aroused a great deal of interest in the automotive sector owing to its ability to generate ultra-low exhaust emissions and to be fuel-flexible. The current work proposes a control-oriented two-zone thermo-kinetic model of such a single cylinder HCCI engine. Earlier control laws were derived by using single zone mathematical models of HCCI combustion; however, these models fail to accurately capture the combustion dynamics of an HCCI engine owing to the assumption of homogeneous composition and temperature in the cylinder. Certain multi-zone models of HCCI engines emphasizing the shortcomings of these single zone models have also been reported in literature. However, such models are far too complex and unwieldy for the development of fast and efficient controllers for HCCI engines. The present work outlines the modeling approach of a single-cylinder two-zone HCCI engine by incorporating the first law of thermodynamics and the temperature and concentration inhomogeneities. The results showed good conformity to those obtained from literature-based multi-zone models. A comparative analysis between the single zone and two-zone models, in the context of predicting cylinder pressures, exhaust gas temperatures, emission concentrations, and start of combustion (SOC), is also discussed.Copyright

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 .

Ascending rockets as macroscopic self-propelled Brownian oscillators

High-fidelity numerical experiments and theoretical modelling are used to study the dynamics of a sounding-rocket-scale rocket, subject to altitude-dependent random wind and nozzle side loads and deterministic aerodynamic loading. This paper completes a series of studies that showed that Ornstein–Uhlenbeck (OU) rotational dynamics arise when random nozzle side loads dominate wind and aerodynamic loading. In contrast to the earlier work, this paper elucidates that under conditions where aerodynamic, wind and nozzle side loads are comparable, the rocket behaves as stochastic Brownian oscillator. The Brownian oscillator model allows straightforward interpretation of the complex rotational dynamics observed: three dynamical regimes—each characterized by differing balances between nozzle-side-load-induced torques, spring-like aerodynamic torques and mass flux damping torques—characterize rocket ascent. Further, the paper illuminates that in the limit where wind and aerodynamic loads are small, random mass flux variations exponentially amplify side-load-induced rotational stochasticity. In this practical limit, pitch/yaw dynamics are described by a randomly damped OU process; an exact solution of the associated Fokker–Planck equation can be obtained and used to compute, e.g. time-dependent pitch/yaw rate means and variances.

Dynamic Analysis of a Gearless Wind Turbine Coupled to a DFIG

Most modern wind turbines use power electronic converters to maintain voltage phase, frequency, and magnitude at the grid-dictated values. However, such converters have often been reported to have high failure rates and cost. Further, failure of conventional wind turbine gearboxes adds to the overall cost and downtime. One remedy to limit the size of these converters is to implement a continuously variable transmission (CVT) which has fewer moving parts, e.g. a belt/chain CVT. Further, a CVT may completely eliminate the conventional gearbox architecture used in current wind turbine drivetrains. However, several dynamical issues related to CVTs prevent their widespread use. Current dynamical understanding of the most common CVTs (i.e. a belt/chain CVT) is limited by formulations of shift speed, belt-pulley friction torques, as well as belt-pulley slip. This paper aims to redress the shift speed formulation which has been widely based on quasi-static equilibrium analyses and, surprisingly, on slip definitions that provide minimal detail on the inertial interactions between the belt and the pulleys. Consequently, the paper proposes a new definition of slip to capture such interactions and uses it to develop more accurate representations of belt-pulley friction torques. Using MATLAB/Simulink, the CVT model is incorporated into a wind turbine model with a doubly-fed induction generator (DFIG). Further, the entire turbine/rotor-CVT-generator model is coupled to the grid through the conventional grid- and rotor-side converters (i.e. GSC and RSC respectively). The results for the overall integrated powertrain are presented and discussed in detail with the CVT operated in open-loop and the DFIG in closed-loop. The intent is to study how control inputs of a CVT affect power flow through the entire drivetrain to meet the objectives of a) maximal power extraction from the wind and b) tracking the grid demands without degrading the CVT performance (with regard to slip, torque capacity, etc.). Further, the results presented herein examine the ability of a CVT to provide speed control (which traditionally is achieved via RSC), thereby, offering the potential to downsize RSC and thus the overall converter.Copyright