arXiv subjects

Dennice F. Gayme

Publications and source records attributed to Dennice F. Gayme.

35 records · Page 2Linked to original sources

arXiv2019

The Role of Strategic Load Participants in Two-Stage Settlement Electricity Markets

Two-stage electricity market clearing is designed to maintain market efficiency under ideal conditions, e.g., perfect forecast and nonstrategic generation. This work demonstrates that the individual strategic behavior of inelastic load participants in a two-stage settlement electricity market can deteriorate efficiency. Our analysis further implies that virtual bidding can play a role in alleviating this loss of efficiency by mitigating the market power of strategic load participants. We use real-world market data from New York ISO to validate our theory.

math.OC↗

arXiv2019

Filtered actuator disks: Theory and application to wind turbine models in large eddy simulation

The actuator disk model (ADM) continues to be a popular wind turbine representation in large eddy simulations (LES) of large wind farms. Computational restrictions typically limit the number of grid points across the rotor of each actuator disk and require spatial filtering to smoothly distribute the applied force distribution on discrete grid points. At typical grid resolutions, simulations cannot capture all of the vorticity shed behind the disk and subsequently over-predict power by upwards of 10%. To correct these modeling errors, we propose a vortex cylinder model to quantify the shed vorticity when a filtered force distribution is applied at the actuator disk. This model is then used to derive a correction factor for numerical simulations that collapses the power curve for simulations at various filter widths and grid resolutions onto the curve obtained using axial momentum theory. The proposed correction therefore facilitates accurate power measurements in LES without resorting to highly refined numerical grids.

physics.flu-dyn↗

arXiv2018

Perturbative expansions of the conformation tensor in viscoelastic flows

We consider the problem of formulating perturbative expansions of the conformation tensor, which is a positive-definite tensor representing polymer deformation in viscoelastic flows. The classical approach does not explicitly take into account that the perturbed tensor must remain positive definite---a fact that has important physical implications, e.g. extensions and compressions are represented similarly to within a negative sign, when physically the former are unbounded and the latter are bounded from below. Mathematically, the classical approach assumes that the underlying geometry is Euclidean, and this assumption is not satisfied by the manifold of positive definite tensors. We provide an alternative formulation that retains the conveniences of classical perturbation methods used for generating linear and weakly nonlinear expansions, but also provides a clear physical interpretation and a mathematical basis for analysis. The approach is based on treating a perturbation as a sequence of successively smaller deformations of the polymer. Each deformation is modelled explicitly using geodesics on the manifold of positive-definite tensors. Using geodesics, and associated geodesic distances, is the natural way to model perturbations to positive-definite tensors because it is consistent with the manifold geometry. Approximations of the geodesics can then be used to reduce the total deformation to a series expansion in the small perturbation limit. We illustrate our approach using direct numerical simulations of the nonlinear evolution of Tollmien-Schlichting waves.

physics.flu-dyn↗

arXiv2018

Geometric decomposition of the conformation tensor in viscoelastic turbulence

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

physics.flu-dyn↗

arXiv2018

Scaling of energy amplification in viscoelastic channel and Couette flow

The linear amplification of disturbances is critical in setting up transition scenarios in viscoelastic channel and Couette flow, and may also play an important role when such flows are fully turbulent. As such, it is of interest to assess how this amplification, defined as the steady-state variance maintained under Gaussian white noise forcing, scales with the main nondimensional parameters: the Reynolds ($Re$) and Weissenberg ($Wi$) numbers. This scaling is derived analytically in the two limits of strong and weak elasticity for when the forcing is streamwise-constant. The latter is the relevant forcing for capturing the overall behaviour because it was previously shown to have the dominant contribution to amplification. The final expressions show that for weak elasticity the scaling retains a form similar to the well-known O($Re^3$) relationship with an added elastic correction. For strong elasticity, however, the scaling is O($Wi^3$) with a viscous correction. The key factor leading to such a mirroring in the scaling is the introduction of forcing in the polymer stress. The results demonstrate that energy amplification in a viscoelastic flow can be very sensitive to the model parameters even at low $Re$. They also suggest that energy amplification can be significantly increased by forcing the polymer stress, thereby opening up possibilities such as flow control using systematically designed polymer stress perturbations.

physics.flu-dyn↗

arXiv2017

Effects of turbine spacing on the power output of extended wind-farms

We present results from large eddy simulations (LES) of extended wind-farms for several turbine configurations with a range of different spanwise and streamwise spacing combinations. The results show that for wind-farms arranged in a staggered configuration with spanwise spacings in the range $\approx[3.5,8]$D, where $D$ is the turbine diameter, the power output in the fully developed regime depends primarily on the geometric mean of the spanwise and streamwise turbine spacings. In contrast, for the aligned configuration the power output in the fully developed regime strongly depends on the streamwise turbine spacing and shows weak dependence on the spanwise spacing. Of interest to the rate of wake recovery, we find that the power output is well correlated with the vertical kinetic energy flux, which is a measure of how much kinetic energy is transferred into the wind-turbine region by the mean flow. A comparison between the aligned and staggered configurations reveals that the vertical kinetic energy flux is more localized along turbine rows for aligned wind-farms than for staggered ones. This additional mixing leads to a relatively fast wake recovery for aligned wind-farms.

physics.flu-dyn↗

arXiv2017

Generalized coupled wake boundary layer model: applications and comparisons with field and LES data for two wind-farms

We describe a generalization of the Coupled Wake Boundary Layer (CWBL) model for wind-farms that can be used to evaluate the performance of wind-farms under arbitrary wind inflow directions whereas the original CWBL model (Stevens et al., J. Renewable and Sustainable Energy 7, 023115 (2015)) focused on aligned or staggered wind-farms. The generalized CWBL approach combines an analytical Jensen wake model with a "top-down" boundary layer model coupled through an iterative determination of the wake expansion coefficient and an effective wake coverage area for which the velocity at hub-height obtained using both models converges in the "deep-array" portion (fully developed region) of the wind-farm. The approach accounts for the effect of the wind direction by enforcing the coupling for each wind direction. Here we present detailed comparisons of model predictions with LES results and field measurements for the Horns Rev and Nysted wind-farms operating over a wide range of wind inflow directions. Our results demonstrate that two-way coupling between the Jensen wake model and a "top-down" model enables the generalized CWBL model to predict the "deep-array" performance of a wind-farm better than the Jensen wake model alone. The results also show that the new generalization allows us to study a much larger class of wind-farms than the original CWBL model, which increases the utility of the approach for wind-farm designers.

physics.flu-dyn↗

arXiv2016

A statistical state dynamics approach to wall-turbulence

This paper reviews results from the study of wall-bounded turbulent flows using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure which isolates the interaction between the streamwise mean and the equivalent of the perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean together with nonlinear interactions between the mean and the perturbation covariance. This dynamical restriction, in which explicit perturbation-perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems in which an ensemble of a finite number of realizations of the perturbation equation share the same mean flow provide tractable approximations to the equivalently infinite ensemble RNL system. The infinite ensemble system, referred to as the S3T, introduces new analysis tools for studying turbulence. The RNL with a single ensemble member can be alternatively viewed as a realization of RNL dynamics. RNL systems provide computationally efficient means to approximate the SSD, producing self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations (DNS) despite its greatly simplified dynamics. Finally, we show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support, or "band-limiting", can be used to improve quantitative accuracy of RNL turbulence. The results suggest that the SSD approach provides new analytical and computational tools allowing new insights into wall-turbulence.

physics.flu-dyn↗

arXiv2016

Performance metrics for droop-controlled microgrids with variable voltage dynamics

This paper investigates the performance of a microgrid with droop-controlled inverters in terms of the total power losses incurred in maintaining synchrony under persistent small disturbances. The inverters are modeled with variable frequencies and voltages under droop control. For small fluctuations from a steady state, these transient power losses can be quantified by an input-output H2 norm of a linear system subject to distributed disturbances. We evaluate this H2 norm under the assumption of a dominantly inductive network with identical inverters. The results indicate that while phase synchronization, in accordance with previous findings, produces losses that scale with a network's size but only weakly depend on its connectivity, the losses associated with the voltage control will be larger in a highly connected network than in a loosely connected one. The typically higher rate of convergence in a highly interconnected network thus comes at a cost of higher losses associated with the power flows used to reach the steady state.

math.OC↗

arXiv2015

Coupled wake boundary layer model of wind-farms

We present and test the coupled wake boundary layer (CWBL) model that describes the distribution of the power output in a wind-farm. The model couples the traditional, industry-standard wake model approach with a "top-down" model for the overall wind-farm boundary layer structure. This wake model captures the effect of turbine positioning, while the "top-down" portion of the model adds the interactions between the wind-turbine wakes and the atmospheric boundary layer. Each portion of the model requires specification of a parameter that is not known a-priori. For the wake model, the wake expansion coefficient is required, while the "top-down" model requires an effective spanwise turbine spacing within which the model's momentum balance is relevant. The wake expansion coefficient is obtained by matching the predicted mean velocity at the turbine from both approaches, while the effective spanwise turbine spacing depends on turbine positioning and thus can be determined from the wake model. Coupling of the constitutive components of the CWBL model is achieved by iterating these parameters until convergence is reached. We illustrate the performance of the model by applying it to both developing wind-farms including entrance effects and to fully developed (deep-array) conditions. Comparisons of the CWBL model predictions with results from a suite of large eddy simulations (LES) shows that the model closely represents the results obtained in these high-fidelity numerical simulations. A comparison with measured power degradation at the Horns Rev and Nysted wind-farms shows that the model can also be successfully applied to real wind-farms.

physics.flu-dyn↗

arXiv2015

A minimal model of self-sustaining turbulence

In this work we examine the turbulence maintained in a Restricted Nonlinear (RNL) model of plane Couette flow. This model is a computationally efficient approximation of the second order statistical state dynamics (SSD) obtained by partitioning the flow into a streamwise averaged mean flow and perturbations about that mean, a closure referred to herein as the RNL$_\infty$ model. The RNL model investigated here employs a single member of the infinite ensemble that comprises the covariance of the RNL$_\infty$ dynamics. The RNL system has previously been shown to support self-sustaining turbulence with a mean flow and structural features that are consistent with DNS. This paper demonstrates that the RNL system's self-sustaining turbulent state is supported by a small number of streamwise varying modes, which form the natural support for the self-sustaining process maintaining RNL turbulence. Remarkably, truncation of the RNL system's support to a single streamwise varying mode can suffice to sustain the turbulent state. The close correspondence between RNL simulations and DNS that has been previously observed along with the results presented here suggest that the fundamental mechanisms underlying wall-turbulence can be analyzed using these highly simplified RNL systems.

physics.flu-dyn↗

arXiv2014

Standard logarithmic mean velocity distribution in a band-limited restricted nonlinear model of turbulent flow in a half-channel

Numerical simulations of wall-turbulence using the restricted nonlinear (RNL) model generate realistic mean velocity profiles in plane Couette and channel flow at low Reynolds numbers. The results are less accurate at higher Re, and while a logarithmic region is observed, its von-Kármán constant is not consistent with the standard logarithmic law. In half-channel flow we show that limiting the streamwise-varying wavenumber support of RNL turbulence to one or few empirically determined modes improves its predictions considerably. In particular, the mean velocity profiles obtained with the band-limited RNL model follow standard logarithmic behavior for the higher Reynolds numbers in this study.

physics.flu-dyn↗

arXiv2014

Large Eddy Simulation studies of the effects of alignment and wind farm length

Large eddy simulations of wind farms are performed to study the effects of wind turbine row alignment with respect to the incoming flow direction. Various wind farms with fixed stream-wise spacing (7.85 rotor diameters) and varying lateral displacements and span-wise turbine spacings are considered, for a fixed inflow direction. Simulations show that, contrary to common belief, a perfectly staggered (checker-board) configuration does not necessarily give the highest average power output. Instead, the highest mean wind farm power output is found to depend on several factors, the most important one being the alignment that leads to minimization of wake effects from turbines in several upstream rows. This alignment typically occurs at significantly smaller angles than those corresponding to perfect staggering. The observed trends have implications for wind farm designs, especially in sites with a well-defined prevailing wind direction.

physics.flu-dyn↗

arXiv2014

Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow

This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier Stokes equations and permits computationally tractable studies of the dynamical system obtained using stochastic structural stability theory (S3T), which is a second order approximation of the statistical state dynamics of the flow. The RNL model shares the dynamical restrictions of the S3T model but can be easily implemented through reducing a DNS code to the equations governing the RNL system. Comparisons of turbulence arising from DNS and RNL simulations demonstrate that the RNL system supports self-sustaining turbulence with a mean flow as well as structural and dynamical features that are consistent with DNS. These results demonstrate that the simplified RNL/S3T system captures fundamental aspects of fully developed turbulence in wall-bounded shear flows and motivates use of the RNL/S3T system for further study of wall turbulence.

physics.flu-dyn↗

arXiv2012

Quadratically constrained quadratic programs on acyclic graphs with application to power flow

This paper proves that non-convex quadratically constrained quadratic programs can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a certain technical condition. When this condition is not satisfied, we propose a heuristic to obtain a feasible point. We demonstrate this approach on optimal power flow problems over radial networks.

math.OC↗

arXiv2012

The Price of Synchrony: Resistive Losses due to Phase Synchronization in Power Networks

We investigate the total resistive losses incurred in returning a power network of identical generators to a synchronous state following a transient stability event or in maintaining this state in the presence of persistent stochastic disturbances. We formulate this cost as the input-output $H^2$ norm of a linear dynamical system with distributed disturbances. We derive an expression for the total resistive losses that scales with the size of the network as well as properties of the generators and power lines, but is independent of the network topology. This topologically invariant scaling of what we term the price of synchrony is in contrast to typical power system stability notions like rate of convergence or the region of attraction for rotor-angle stability. Our result indicates that highly connected power networks, whilst desirable for higher phase synchrony, do not offer an advantage in terms of the total resistive power losses needed to achieve this synchrony. Furthermore, if power flow is the mechanism used to achieve synchrony in highly-distributed-generation networks, the cost increases unboundedly with the number of generators.

nlin.CD↗

arXiv2010

Amplification and Nonlinear Mechanisms in Plane Couette Flow

We study the input-output response of a streamwise constant projection of the Navier-Stokes equations for plane Couette flow, the so-called 2D/3C model. Study of a streamwise constant model is motivated by numerical and experimental observations that suggest the prevalence and importance of streamwise and quasi-streamwise elongated structures. Periodic spanwise/wall-normal (z-y) plane stream functions are used as input to develop a forced 2D/3C streamwise velocity field that is qualitatively similar to a fully turbulent spatial field of DNS data. The input-output response associated with the 2D/3C nonlinear coupling is used to estimate the energy optimal spanwise wavelength over a range of Reynolds numbers. The results of the input-output analysis agree with previous studies of the linearized Navier-Stokes equations. The optimal energy corresponds to minimal nonlinear coupling. On the other hand, the nature of the forced 2D/3C streamwise velocity field provides evidence that the nonlinear coupling in the 2D/3C model is responsible for creating the well known characteristic "S" shaped turbulent velocity profile. This indicates that there is an important tradeoff between energy amplification, which is primarily linear and the seemingly nonlinear momentum transfer mechanism that produces a turbulent-like mean profile.

physics.flu-dyn↗