Far-field drag decomposition using hybrid formulas and vorticity based area sensors

Numerical simulation of flow-field has become an indispensable tool for aerodynamic design. Usually, wall surface integration is a tool used to calculate values of pressure drag and skin friction drag, but the aerodynamic mechanism of drag production is still confusing. In present work, in order to decompose the total drag into viscous drag, wave drag, induced drag, and spurious drag, a far-field drag decomposition (FDD) method is developed. This method depends on axial velocity defect and area sensor functions. The present work proposes three hybrid formulas for velocity defect to tackle the negative square root issue by analyzing the existing axial velocity defect formulas. For dealing with the issue of detection failure for near-wall cells, a novel vorticity based viscous area sensor function is proposed. The new area sensor function is also independent of the turbulence model, which ensures easy application to general simulation methods for flow-field. Three tests cases are there to validate the proposed FDD method. The three dimensional transonic CRM test case shows that the present improvement is crucial for accurate drag decomposition. Excellent agreement between total decomposed drags and results from the near-field method or experimental data further confirms the correctness.

Aerodynamic Design and Shape Optimization with the Far-Field Drag Decomposition Approach

In the aerodynamic shape design, the drag prediction has always been an extremely challenging mission for the exploration of a configuration. As for the more complex configurations, it is especially desired to the availability of a highly accurate and reliable aerodynamic numerical solution. For improving the drag prediction accuracy and promoting the aerodynamic shape designs, firstly, the characteristics of drag prediction based on far-field drag method and near-field drag method is analyzed and compared. Also, the merits and demerits of defining axial velocity defect with the current main far-field drag prediction approaches is summarized, which promotes the building of the improved method of axial velocity defect and the improved far-field drag prediction and decomposition approach. Moreover, during the establishment of the drag decomposition method, it is necessary to judge and decide on the selection of the drag region. Therefore, the discussions on the sensitivity of the relevant parameters are fulfilled. Furthermore, based on the far-field drag prediction and decomposition method constructed, the aerodynamic performance research of Common Research Model wing-body configuration is launched. The results show that it can effectively observe and analyze the changes in drag components, their impact on the total drag and the contribution percentage. Finally, combining the far-field drag prediction and decomposition method proposed in this paper with a gradient-based aerodynamic shape optimization design system, the aerodynamic shape optimization designs are studied with CRM wing-body configuration. The results can not only directly analyze the detailed change of the visualized drag region, but also can obtain the more accurate total drag and lift-to-drag ratio of the optimized configuration by removing the spurious drag.

Theoretical Modeling of Vertical-Axis Wind Turbine Wakes

In this work, two different theoretical models for predicting the wind velocity downwind of an H-rotor vertical-axis wind turbine are presented. The first model uses mass conservation together with the momentum theory and assumes a top-hat distribution for the wind velocity deficit. The second model considers a two-dimensional Gaussian shape for the velocity defect and satisfies mass continuity and the momentum balance. Both approaches are consistent with the existing and widely-used theoretical wake models for horizontal-axis wind turbines and, thus, can be implemented in the current numerical codes utilized for optimization and real-time applications. To assess and compare the two proposed models, we use large eddy simulation as well as field measurement data of vertical-axis wind turbine wakes. The results show that, although both models are generally capable of predicting the velocity defect, the prediction from the Gaussian-based wake model is more accurate compared to the top-hat counterpart. This is mainly related to the consistency of the assumptions used in the Gaussian-based wake model with the physics of the turbulent wake development downwind of the turbine.

Can a turbulent boundary layer become independent of the Reynolds number?

This paper examines the Reynolds number ($Re$) dependence of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) which develops over a two-dimensional rough wall with a view to ascertaining whether this type of boundary layer can become independent of $Re$. Measurements are made using hot-wire anemometry over a rough wall that consists of a periodic arrangement of cylindrical rods with a streamwise spacing of eight times the rod diameter. The present results, together with those obtained over a sand-grain roughness at high Reynolds number, indicate that a $Re$-independent state can be achieved at a moderate $Re$. However, it is also found that the mean velocity distributions over different roughness geometries do not collapse when normalised by appropriate velocity and length scales. This lack of collapse is attributed to the difference in the drag coefficient between these geometries. We also show that the collapse of the $U_{\unicode[STIX]{x1D70F}}$-normalised mean velocity defect profiles may not necessarily reflect $Re$-independence. A better indicator of the asymptotic state of $Re$ is the mean velocity defect profile normalised by the free-stream velocity and plotted as a function of $y/\unicode[STIX]{x1D6FF}$, where $y$ is the vertical distance from the wall and $\unicode[STIX]{x1D6FF}$ is the boundary layer thickness. This is well supported by the measurements.

Pressure Gradient Effects on Smooth- and Rough-Surface Turbulent Boundary Layers—Part II: Adverse Pressure Gradient

An experimental investigation has been conducted to identify the effects of pressure gradient and surface roughness on turbulent boundary layers. In Part II, smooth- and rough-surface turbulent boundary layers with and without adverse pressure gradient (APG) are presented at a fixed Reynolds number (based on the length of flat plate) of 900,000. Flat-plate boundary layer measurements have been conducted using a single-sensor, hot-wire probe. For smooth surfaces, compared to the zero pressure gradient (ZPG) boundary layer, the APG boundary layer has a higher mean velocity defect throughout the boundary layer and lower friction coefficient. APG decreases the streamwise normal Reynolds stress for y less than 0.4 times the boundary layer thickness and increases it slightly in the outer region. For rough surfaces, APG reduces the roughness effects of increasing the mean velocity defect and normal Reynolds stress for y less than 23 and 28 times the average roughness height, respectively. Consistently, for the same roughness, APG decreases the integrated streamwise turbulent kinetic energy. APG also decreases the roughness effect on the friction coefficient, roughness Reynolds number, and roughness shift. Compared to the ZPG boundary layers, the roughness effects on integral boundary layer parameters—boundary layer thickness and momentum thickness—are weaker under APG. Thus, contrary to the favorable pressure gradient (FPG) in part I, APG reduces the roughness effects on turbulent boundary layers.

Pressure Gradient Effects on Smooth and Rough Surface Turbulent Boundary Layers—Part I: Favorable Pressure Gradient

The effects of the pressure gradient and surface roughness on turbulent boundary layers have been experimentally investigated. In Part I, smooth- and rough-surface turbulent boundary layers with and without favorable pressure gradients (FPG) are presented. All of the tests have been conducted at the same Reynolds number (based on the length of the flat plate) of 900,000. Streamwise time-mean and fluctuating velocities have been measured using a single-sensor hot-wire probe. For smooth surfaces, the FPG decreases the mean velocity defect and increases the wall shear stress; however, the friction coefficient hardly changes due to the increased freestream velocity. The FPG effect on the streamwise normal Reynolds stress has been examined. The FPG increases the streamwise normal Reynolds stress for y less than 0.6 times the boundary layer thickness. With the zero pressure gradient (ZPG), the roughness increases the mean velocity defect throughout the boundary layer and increases the normal Reynolds stress for y greater than twice the average roughness height. The roughness effect on the mean velocity defect is stronger under the FPG than under the ZPG for y less than 30 times the average roughness height. For y less than 25 times the average roughness height, the roughness effect of increasing normal Reynolds stress is also stronger under the FPG than under the ZPG. Consequently, for a rough surface, the FPG increases the integrated streamwise turbulent kinetic energy, friction coefficient, roughness Reynolds number, and roughness shift. Furthermore, the FPG increases the roughness effects on the integral boundary layer parameters—the boundary layer thickness, momentum thickness, ratio of the displacement thickness to the boundary layer thickness, and shape factor. Thus, the FPG augments the roughness effects on turbulent boundary layers.