Two-scale momentum theory for time-dependent modelling of large wind farms

This paper presents a theory based on the law of momentum conservation to define and help analyse the problem of large wind farm aerodynamics. The theory splits the problem into two sub-problems; namely an 'external' (or farm-scale) problem, which is a time-dependent problem considering large-scale motions of the atmospheric boundary layer (ABL) to assess the amount of momentum available to the ABL's bottom resistance (due to wind turbines and land/sea surface) at a certain time; and an 'internal' (or turbine-scale) problem, which is a quasi-steady (in terms of large-scale motions of the ABL) problem describing the breakdown of the ABL's bottom resistance into wind turbine drag and land/sea surface friction. The two sub-problems are coupled to each other through a non-dimensional parameter called 'farm wind-speed reduction factor,' for which a simple analytic equation is derived that can be solved iteratively using information obtained from both sub-problems. This general form of coupling allows us to use the present theory with various types of flow models at each scale, such as a numerical weather prediction (NWP) model for the external problem and a computational fluid dynamics (CFD) model for the internal problem. The theory is presented for a simplified wind farm situation first, followed by a discussion on how the theory can be applied (in an approximate manner) to real-world problems; for example, how to estimate the power loss due to the so-called 'wind farm blockage effect' for a given large wind farm under given environmental conditions.Comment: Under consideration for publication in J. Fluid Mech. (16 pages, 5 figures

An analytical model of momentum availability for predicting large wind farm power

Turbine-wake and farm-atmosphere interactions influence wind farm power production. For large offshore farms, the farm-atmosphere interaction is usually the more significant effect. This study proposes an analytical model of the `momentum availability factor' to predict the impact of farm-atmosphere interactions. It models the effects of net advection, pressure gradient forcing and turbulent entrainment, using steady quasi-1D flow assumptions. Turbulent entrainment is modelled by assuming self-similar vertical shear stress profiles. We used the model with the `two-scale momentum theory' to predict the power of large finite-sized farms. The model compared well with existing results of large-eddy simulations (LES) of finite wind farms in conventionally neutral boundary layers. The model captured most of the effects of atmospheric boundary layer (ABL) height on farm performance by considering the undisturbed vertical shear stress profile of the ABL as an input. In particular, the model predicted the power of staggered wind farms with a typical error of 5% or less. The developed model provides a novel way of instantly predicting the power of large wind farms, including the farm blockage effects. A further simplification of the model to analytically predict the 'wind extractability factor' is also presented. This study provides a novel framework for modelling farm-atmosphere interactions. Future studies can use the framework to better model large wind farms.Comment: 22 pages, 12 figures, 4 table

An analytical model of momentum availability for predicting large wind farm power

Turbine–wake and farm–atmosphere interactions influence wind farm power production. For large offshore farms, the farm–atmosphere interaction is usually the more significant effect. This study proposes an analytical model of the ‘momentum availability factor’ to predict the impact of farm–atmosphere interactions. It models the effects of net advection, pressure gradient forcing and turbulent entrainment, using steady quasi-one-dimensional flow assumptions. Turbulent entrainment is modelled by assuming self-similar vertical shear stress profiles. We used the model with the ‘two-scale momentum theory’ to predict the power of large finite-sized farms. The model compared well with existing results of large-eddy simulations of finite wind farms in conventionally neutral boundary layers. The model captured most of the effects of atmospheric boundary layer (ABL) height on farm performance by considering the undisturbed vertical shear stress profile of the ABL as an input. In particular, the model predicted the power of staggered wind farms with a typical error of 5 % or less. The developed model provides a novel way of predicting instantly the power of large wind farms, including the farm blockage effects. A further simplification of the model to predict analytically the ‘wind extractability factor’ is also presented. This study provides a novel framework for modelling farm–atmosphere interactions. Future studies can use the framework to better model large wind farms

Data‐driven modelling of turbine wake interactions and flow resistance in large wind farms

Turbine wake and local blockage effects are known to alter wind farm power production in two different ways: (1) by changing the wind speed locally in front of each turbine and (2) by changing the overall flow resistance in the farm and thus the so-called farm blockage effect. To better predict these effects with low computational costs, we develop data-driven emulators of the ‘local’ or ‘internal’ turbine thrust coefficient as a function of turbine layout. We train the model using a multi-fidelity Gaussian process (GP) regression with a combination of low (engineering wake model) and high-fidelity (large eddy simulations) simulations of farms with different layouts and wind directions. A large set of low-fidelity data speeds up the learning process and the high-fidelity data ensures a high accuracy. The trained multi-fidelity GP model is shown to give more accurate predictions of compared to a standard (single-fidelity) GP regression applied only to a limited set of high-fidelity data. We also use the multi-fidelity GP model of with the two-scale momentum theory (Nishino & Dunstan 2020, J. Fluid Mech. 894, A2) to demonstrate that the model can be used to give fast and accurate predictions of large wind farm performance under various mesoscale atmospheric conditions. This new approach could be beneficial for improving annual energy production (AEP) calculations and farm optimization in the future

Data‐driven modelling of turbine wake interactions and flow resistance in large wind farms

Turbine wake and local blockage effects are known to alter wind farm power production in two different ways: (1) by changing the wind speed locally in front of each turbine and (2) by changing the overall flow resistance in the farm and thus the so-called farm blockage effect. To better predict these effects with low computational costs, we develop data-driven emulators of the ‘local’ or ‘internal’ turbine thrust coefficient C_{*}^{T} as a function of turbine layout. We train the model using a multi-fidelity Gaussian process (GP) regression with a combination of low (engineering wake model) and high-fidelity (large eddy simulations) simulations of farms with different layouts and wind directions. A large set of low-fidelity data speeds up the learning process and the high-fidelity data ensures a high accuracy. The trained multi-fidelity GP model is shown to give more accurate predictions of C_{*}^{T} compared to a standard (single-fidelity) GP regression applied only to a limited set of high-fidelity data. We also use the multi-fidelity GP model of C_{*}^{T} with the two-scale momentum theory (Nishino & Dunstan 2020, J. Fluid Mech. 894, A2) to demonstrate that the model can be used to give fast and accurate predictions of large wind farm performance under various mesoscale atmospheric conditions. This new approach could be beneficial for improving annual energy production (AEP) calculations and farm optimization in the future

Analysing momentum balance over a large wind farm using a numerical weather prediction model

This study attempts to better understand the mechanisms of wind farm blockage effect by analysing momentum balance in realistic atmospheric flow over an idealised large offshore wind farm. The analysis is performed following the two-scale momentum theory, which predicts the importance of three different terms in the farm-scale momentum balance, namely the streamwise pressure gradient, Coriolis force and acceleration/deceleration terms. A numerical weather prediction (NWP) model is used as a realistic farm-scale flow model in this study to investigate how these three terms tend to change in time. Initial results suggest that the streamwise pressure gradient may be enhanced substantially by the resistance caused by the wind farm, whereas its influence on the other two terms appears to be relatively minor. These results suggest the importance of modelling the farm-induced pressure gradient accurately for various weather conditions in future studies of wind farm blockag

Incidence of diabetic retinopathy in people with type 2 diabetes mellitus attending the Diabetic Retinopathy Screening Service for Wales: retrospective analysis

Objectives To determine the incidence of any and referable diabetic retinopathy in people with type 2 diabetes mellitus attending an annual screening service for retinopathy and whose first screening episode indicated no evidence of retinopathy

Patterns of skeletal fractures in child abuse: systematic review

Objectives To systematically review published studies to identify the characteristics that distinguish fractures in children resulting from abuse and those not resulting from abuse, and to calculate a probability of abuse for individual fracture types

Cost analysis of large-scale implementation of the ‘Helping Babies Breathe’ newborn resuscitation-training program in Tanzania

Background: Helping Babies Breathe (HBB) has become the gold standard globally for training birth-attendants in neonatal resuscitation in low-resource settings in efforts to reduce early newborn asphyxia and mortality. The purpose of this study was to do a first-ever activity-based cost-analysis of at-scale HBB program implementation and initial follow-up in a large region of Tanzania and evaluate costs of national scale-up as one component of a multi-method external evaluation of the implementation of HBB at scale in Tanzania. Methods: We used activity-based costing to examine budget expense data during the two-month implementation and follow-up of HBB in one of the target regions. Activity-cost centers included administrative, initial training (including resuscitation equipment), and follow-up training expenses. Sensitivity analysis was utilized to project cost scenarios incurred to achieve countrywide expansion of the program across all mainland regions of Tanzania and to model costs of program maintenance over one and five years following initiation. Results: Total costs for the Mbeya Region were $202,240, with the highest proportion due to initial training and equipment (45.2$4,000,000 (around $600 per facility). Following sensitivity analyses, the estimated total for all Tanzania initial rollout lies between$2,934,793 to $4,309,595. In order to maintain the program nationally under the current model, it is estimated it would cost$2,019,115 for a further one year and $5,640,794 for a further five years of ongoing program support. Conclusion: HBB implementation is a relatively low-cost intervention with potential for high impact on perinatal mortality in resource-poor settings. It is shown here that nationwide expansion of this program across the range of health provision levels and regions of Tanzania would be feasible. This study provides policymakers and investors with the relevant cost-estimation for national rollout of this potentially neonatal life-saving intervention

Structured on-the-job training to improve retention of newborn resuscitation skills: a national cohort Helping Babies Breathe study in Tanzania

Background: Newborn resuscitation is a life-saving intervention for birth asphyxia, a leading cause of neonatal mortality. Improving provider newborn resuscitation skills is critical for delivering quality care, but the retention of these skills has been a challenge. Tanzania implemented a national newborn resuscitation using the Helping Babies Breathe (HBB) training program to help address this problem. Our objective was to evaluate the effectiveness of two training approaches to newborn resuscitation skills retention implemented across 16 regions of Tanzania. Methods: An initial training approach implemented included verbal instructions for participating providers to replicate the training back at their service delivery site to others who were not trained. After a noted drop in skills, the program developed structured on-the-job training guidance and included this in the training. The approaches were implemented sequentially in 8 regions each with nurses/ midwives, other clinicians and medical attendants who had not received HBB training before. Newborn resuscitation skills were assessed immediately after training and 4–6 weeks after training using a validated objective structured clinical examination, and retention, measured through degree of skills drop, was compared between the two training approaches. Results: Eight thousand, three hundred and ninety-one providers were trained and assessed: 3592 underwent the initial training approach and 4799 underwent the modified approach. Immediately post-training, average skills scores were similar between initial and modified training groups: 80.5 and 81.3%, respectively (p-value 0.07). Both groups experienced statistically significant drops in newborn resuscitation skills over time. However, the modified training approach was associated with significantly higher skills scores 4–6 weeks post training: 77.6% among the modified training approach versus 70.7% among the initial training approach (p-value \u3c 0.0001). Medical attendant cadre showed the greatest skills retention. Conclusions: A modified training approach consisting of structured OJT, guidance and tools improved newborn resuscitation skills retention among health care providers. The study results give evidence for including on-site training as part of efforts to improve provider performance and strengthen quality of care