Beating Betz: Energy Extraction Limits in a Constrained Flow Field

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Peter M. Jamieson
Keyword(s):  
Kinetic Energy ◽  
Flow Field ◽  
Wind Energy ◽  
Recent Analysis ◽  
Energy Extraction ◽  
Power Performance ◽  
Fluid Stream ◽  
Extraction Device ◽  
Ideal Limit ◽  
Constrained Flow

Experiments with diffusers and other flow concentrating devices have shown that the power performance coefficient Cp of an energy extraction device, defined in relation to the area of flow intercepted at the device, may exceed the Betz limit. “Beating Betz,” in that sense, has been long established but no theory has existed to define in a generalized way what ideal limit may apply to Cp in such situations. Recent analysis has resolved this. This indicates that, irrespective of the presence of flow concentration systems or other influences that perturb the flow but do not in themselves extract energy, there is a universal ideal limit of energy extraction. This is found to be 89 of the upstream kinetic energy in the streamtube associated with the energy extraction. Moreover, the familiar Betz equations for power and thrust coefficients can be generalized in a simple way to express this. Although this work has been developed in the context of wind energy, it will be apparent that the results are of general significance for any application of ducted rotors or propellers in a fluid stream.

Preliminary Analysis and Testing of the AWOG: A Novel Non-Rotational Wind Energy Extraction Device

2011 ◽  
Author(s):  
Jesse J. French ◽  
Colton T. Sheets
Keyword(s):  
Wind Tunnel ◽  
Wind Energy ◽  
Turbulent Flows ◽  
Power Output ◽  
Energy Extraction ◽  
Stored Energy ◽  
Practical Applications ◽  
Micro Scale ◽  
Aspect Ratios ◽  
Extraction Device

This paper highlights the work done by the authors to develop and test a novel, biologically inspired, non-rotational wind energy extraction device. This device capitalizes on the principles of a wind deflected shaft and vortex induced vibrations to generate micro-scale power. Piezoelectric and magnetic flux methods are explored as options to convert the stored energy of mechanical deflection to electrical power. The device is modeled after long-stemmed grasses, grains, and bamboos and geometrically mimics their aspect ratio in order to replicate their movement in low altitude, turbulent flows. This design is based on a significant sampling of the shaft aspect ratios and head shapes of naturally occurring biological samples collected in the field. This concept has been affectionately christened the AWOG (Amber Waves of Grain) and shows promise for use in highly turbulent, low-level air flows close to the ground or mounting surface. Potential operating sites of the AWOG, include locations very close to ground level, along building rooflines, and in urban settings. To determine the efficiency and power output of a single AWOG unit, wind tunnel testing and in-situ field testing were performed. Power stored in a single deflected AWOG has been experimentally determined to be 430 w/m^2, which is comparable to existing wind turbine designs. Initial tests outlined in this paper are only able to recover a fraction of the stored energy. Practical applications of AWOG units would be to use them in formation and examinations are included for several proposed grouping methods. Analysis is performed to determine the ideal arrangement for grouped AWOG units based on experimental and field data from biological specimens and wind tunnel tests. This includes analyzing the effect that different configurations have on individual power output and efficiency of the formation as a whole. Recommendations are made as to the feasibility of use in a variety of settings and consideration is given concerning scaling of the AWOG to the micro-scale and to larger scales.

scholarly journals A New Method to Determine the Impact of Individual Field Quantities on Cycle-to-Cycle Variations in a Spark-Ignited Gas Engine

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4136
Author(s):  
Clemens Gößnitzer ◽  
Shawn Givler
Keyword(s):  
Kinetic Energy ◽  
Flow Field ◽  
Turbulent Kinetic Energy ◽  
Negative Impact ◽  
Operating Conditions ◽  
Engine Operation ◽  
Gas Engine ◽  
Cycle Simulation ◽  
Simulation Results ◽  
The Impact

Cycle-to-cycle variations (CCV) in spark-ignited (SI) engines impose performance limitations and in the extreme limit can lead to very strong, potentially damaging cycles. Thus, CCV force sub-optimal engine operating conditions. A deeper understanding of CCV is key to enabling control strategies, improving engine design and reducing the negative impact of CCV on engine operation. This paper presents a new simulation strategy which allows investigation of the impact of individual physical quantities (e.g., flow field or turbulence quantities) on CCV separately. As a first step, multi-cycle unsteady Reynolds-averaged Navier–Stokes (uRANS) computational fluid dynamics (CFD) simulations of a spark-ignited natural gas engine are performed. For each cycle, simulation results just prior to each spark timing are taken. Next, simulation results from different cycles are combined: one quantity, e.g., the flow field, is extracted from a snapshot of one given cycle, and all other quantities are taken from a snapshot from a different cycle. Such a combination yields a new snapshot. With the combined snapshot, the simulation is continued until the end of combustion. The results obtained with combined snapshots show that the velocity field seems to have the highest impact on CCV. Turbulence intensity, quantified by the turbulent kinetic energy and turbulent kinetic energy dissipation rate, has a similar value for all snapshots. Thus, their impact on CCV is small compared to the flow field. This novel methodology is very flexible and allows investigation of the sources of CCV which have been difficult to investigate in the past.

scholarly journals Characteristics, Energetics, and Origins of Agulhas Current Meanders and Their Limited Influence on Ring Shedding

2015 ◽  
Vol 45 (9) ◽  
pp. 2294-2314 ◽  
Author(s):  
Shane Elipot ◽  
Lisa M. Beal
Keyword(s):  
Kinetic Energy ◽  
Single Mode ◽  
Cyclonic Circulation ◽  
Recent Analysis ◽  
Altimeter Data ◽  
Western Boundary ◽  
Mean Flow ◽  
Current Time ◽  
Agulhas Current ◽  
The Mean

AbstractThe Agulhas Current intermittently undergoes dramatic offshore excursions from its mean path because of the downstream passage of mesoscale solitary meanders or Natal pulses. New observations and analyses are presented of the variability of the current and its meanders using mooring observations from the Agulhas Current Time-Series Experiment (ACT) near 34°S. Using a new rotary EOF method, mesoscale meanders and smaller-scale meanders are differentiated and each captured in a single mode of variance. During mesoscale meanders, an onshore cyclonic circulation and an offshore anticyclonic circulation act together to displace the jet offshore, leading to sudden and strong positive conversion of kinetic energy from the mean flow to the meander via nonlinear interactions. Smaller meanders are principally represented by a single cyclonic circulation spanning the entire jet that acts to displace the jet without extracting kinetic energy from the mean flow. Synthesizing in situ observations with altimeter data leads to an account of the number of mesoscale meanders at 34°S: 1.6 yr−1 on average, in agreement with a recent analysis by Rouault and Penven (2011) and significantly less than previously understood. The links between meanders and the arrival of Mozambique Channel eddies or Madagascar dipoles at the western boundary upstream are found to be robust in the 20-yr altimeter record. Yet, only a small fraction of anomalies arriving at the western boundary result in meanders, and of those, two-thirds can be related to ring shedding. Most Agulhas rings are shed independently of meanders.

scholarly journals Development of a two zone turbulence model and its application to the cycle-simulation

2014 ◽  
Vol 18 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Momir Sjeric ◽  
Darko Kozarac ◽  
Rudolf Tomic
Keyword(s):  
High Pressure ◽  
Kinetic Energy ◽  
Flow Field ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Combustion Process ◽  
Progress Variable ◽  
Cycle Simulation ◽  
Pressure Cycle ◽  
Turbulent Flow Field

The development of a two zone k-? turbulence model for the cycle-simulation software is presented. The in-cylinder turbulent flow field of internal combustion engines plays the most important role in the combustion process. Turbulence has a strong influence on the combustion process because the convective deformation of the flame front as well as the additional transfer of the momentum, heat and mass can occur. The development and use of numerical simulation models are prompted by the high experimental costs, lack of measurement equipment and increase in computer power. In the cycle-simulation codes, multi zone models are often used for rapid and robust evaluation of key engine parameters. The extension of the single zone turbulence model to the two zone model is presented and described. Turbulence analysis was focused only on the high pressure cycle according to the assumption of the homogeneous and isotropic turbulent flow field. Specific modifications of differential equation derivatives were made in both cases (single and two zone). Validation was performed on two engine geometries for different engine speeds and loads. Results of the cyclesimulation model for the turbulent kinetic energy and the combustion progress variable are compared with the results of 3D-CFD simulations. Very good agreement between the turbulent kinetic energy during the high pressure cycle and the combustion progress variable was obtained. The two zone k-? turbulence model showed a further progress in terms of prediction of the combustion process by using only the turbulent quantities of the unburned zone.

Simulation of Flow Field on a Large Scale Wind Turbine

2008 ◽  
Author(s):  
I. Janajreh ◽  
C. Ghenai
Keyword(s):  
Flow Field ◽  
Wind Energy ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Cross Sections ◽  
Large Scale ◽  
Wind Farms ◽  
Operating Characteristics ◽  
Cross Sectional ◽  
Capital Costs

Large scale wind turbines and wind farms continue to evolve mounting 94.1GW of the electrical grid capacity in 2007 and expected to reach 160.0GW in 2010 according to World Wind Energy Association. They commence to play a vital role in the quest for renewable and sustainable energy. They are impressive structures of human responsiveness to, and awareness of, the depleting fossil fuel resources. Early generation wind turbines (windmills) were used as kinetic energy transformers and today generate 1/5 of the Denmark’s electricity and planned to double the current German grid capacity by reaching 12.5% by year 2010. Wind energy is plentiful (72 TW is estimated to be commercially viable) and clean while their intensive capital costs and maintenance fees still bar their widespread deployment in the developing world. Additionally, there are technological challenges in the rotor operating characteristics, fatigue load, and noise in meeting reliability and safety standards. Newer inventions, e.g., downstream wind turbines and flapping rotor blades, are sought to absorb a larger portion of the cost attributable to unrestrained lower cost yaw mechanisms, reduction in the moving parts, and noise reduction thereby reducing maintenance. In this work, numerical analysis of the downstream wind turbine blade is conducted. In particular, the interaction between the tower and the rotor passage is investigated. Circular cross sectional tower and aerofoil shapes are considered in a staggered configuration and under cross-stream motion. The resulting blade static pressure and aerodynamic forces are investigated at different incident wind angles and wind speeds. Comparison of the flow field results against the conventional upstream wind turbine is also conducted. The wind flow is considered to be transient, incompressible, viscous Navier-Stokes and turbulent. The k-ε model is utilized as the turbulence closure. The passage of the rotor blade is governed by ALE and is represented numerically as a sliding mesh against the upstream fixed tower domain. Both the blade and tower cross sections are padded with a boundary layer mesh to accurately capture the viscous forces while several levels of refinement were implemented throughout the domain to assess and avoid the mesh dependence.

Numerical Simulation of Flow Field in Burnt Lime Hydrator

2011 ◽  
Vol 383-390 ◽  
pp. 2206-2210
Author(s):  
Ming Hua Bai ◽  
Yu Zhang ◽  
Qiu Fang Wang
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Flow Field ◽  
Velocity Gradient ◽  
Rotational Speed ◽  
Fugitive Dust ◽  
Work Condition ◽  
Burnt Lime ◽  
Stirring Effect ◽  
Recirculation Zones

The flow field distribution in burnt lime hydrator has been investigated by a software FLUENT, with k-ε turbulence model and MRF method. The simulation result shows that when four blades deflect 30°, the whole velocity gradient of flow reduces and the recirculation zones also diminish; when the rotational speed is 75r/min, the turbulence kinetic energy of stir zone between two axes becomes larger, which can raise stirring effect and reduce fugitive dust, so it is easy to achieve the purpose of improving the environment of work condition.

scholarly journals Lidar arc scan uncertainty reduction through scanning geometry optimization

2016 ◽  
Vol 9 (4) ◽  
pp. 1653-1669 ◽  
Author(s):  
Hui Wang ◽  
Rebecca J. Barthelmie ◽  
Sara C. Pryor ◽  
Gareth. Brown
Keyword(s):  
Theoretical Model ◽  
Wind Speed ◽  
Wind Energy ◽  
Turbulence Intensity ◽  
Wind Direction ◽  
Energy Production ◽  
Elevation Angle ◽  
Relative Standard Error ◽  
Power Performance ◽  
Relative Standard

Abstract. Doppler lidars are frequently operated in a mode referred to as arc scans, wherein the lidar beam scans across a sector with a fixed elevation angle and the resulting measurements are used to derive an estimate of the n minute horizontal mean wind velocity (speed and direction). Previous studies have shown that the uncertainty in the measured wind speed originates from turbulent wind fluctuations and depends on the scan geometry (the arc span and the arc orientation). This paper is designed to provide guidance on optimal scan geometries for two key applications in the wind energy industry: wind turbine power performance analysis and annual energy production prediction. We present a quantitative analysis of the retrieved wind speed uncertainty derived using a theoretical model with the assumption of isotropic and frozen turbulence, and observations from three sites that are onshore with flat terrain, onshore with complex terrain and offshore, respectively. The results from both the theoretical model and observations show that the uncertainty is scaled with the turbulence intensity such that the relative standard error on the 10 min mean wind speed is about 30 % of the turbulence intensity. The uncertainty in both retrieved wind speeds and derived wind energy production estimates can be reduced by aligning lidar beams with the dominant wind direction, increasing the arc span and lowering the number of beams per arc scan. Large arc spans should be used at sites with high turbulence intensity and/or large wind direction variation.

Performance of a Wave-Energy-Converter Array Operating Under Model-Predictive Control Based on a Convex Formulation

2018 ◽  
Author(s):  
Qian Zhong ◽  
Ronald W. Yeung
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Wave Energy ◽  
Reactive Power ◽  
Optimal Solution ◽  
Energy Output ◽  
Control Input ◽  
Energy Extraction ◽  
Power Performance ◽  
Point Absorbers

Economics decision drives the operation of ocean-wave energy converters (WEC) to be in a “farm mode”. Control strategy developed for a WEC array will be of high importance for improving the aggregate energy extraction efficiency of the whole system. Model-predictive control (MPC) has shown its strong potential in maximizing the energy output in devices with hard constraints on operation states and machinery inputs (See Ref. [1–3]). Computational demands for using MPC to control an array in real time can be prohibitive. In this paper, we formulate the MPC to control an array of heaving point absorbers, by recasting the optimization problem for energy extraction into a convex Quadratic Programming (QP) problem, the solution of which can be carried out very efficiently. Large slew rates are to be penalized, which can also guarantee the convexity of the QP and improve the computational efficiency for achieving the optimal solution. Constraints on both the states and the control input can be accommodated in this MPC method. Full hydro-dynamic interference effects among the WEC array components are taken into account using the theory developed in [4]. Demonstrative results of the application are presented for arrays of two, three, and four point absorbers operating at different incident-wave angles. Effects of the interacting waves on power performance of the array under the new MPC control are investigated, with simulations conducted in both regular and irregular seas. Heaving motions of individual devices at their optimal conditions are shown. Also presented is the reactive power required by the power takeoff (PTO) system of the array to achieve optimality. We are pleased to contribute this article in celebration of our collegiality with Professor Bernard Molin on the occasion of his honoring symposium.

Sign in / Sign up

Export Citation Format

Share Document