Turbulent Boundary Layer Theory Research Articles

Using the Boundary Element Method for airfoil trailing edge noise prediction

This study investigates two aspects of the prediction of trailing edge noise from an airfoil using the Boundary Element Method to solve the scattering phenomenon. The first one consists in defining the surface pressure spectrum near the trailing edge as a source for the turbulent boundary layer-trailing edge interaction, using either an empirical model or one-dimensional turbulent boundary layer theory. The second aspect focuses on the capability of the Boundary Element Method to handle general boundary conditions. It is applied to predict the noise emitted by a porous trailing edge. This work is conducted in the context of aerodynamic noise from wind turbine blades, but has a wider range of engineering applications.

Nonlinear input feature reduction for data-based physical modeling

This work introduces a novel methodology to derive physical scalings for input features from data. The approach developed in this article relies on the maximization of mutual information to derive optimal nonlinear combinations of input features. These combinations are both adapted to physics-related models and interpretable (in a symbolic way). The algorithm is presented in detail, then tested on a synthetic toy model. The results show that our approach can effectively construct relevant combinations by analyzing a strongly noisy nonlinear dataset. These results are promising and may significantly help training data-driven models. Finally, the last part of the paper introduces a way to account for the physical dimension of data. The test case is a synthetic dataset inspired by the Law of the Wall from turbulent boundary layer theory. Once again, the algorithm shows that it can recover relevant nondimensional variables for data-base modeling.

Nusselt number correlation for turbulent heat transfer of helium\u2013xenon gas mixtures

A gas-cooled nuclear reactor combined with a Brayton cycle shows promise as a technology for high-power space nuclear power systems. Generally, a helium–xenon gas mixture with a molecular weight of 14.5–40.0 g/mol is adopted as the working fluid to reduce the mass and volume of the turbomachinery. The Prandtl number for helium–xenon mixtures with this recommended mixing ratio may be as low as 0.2. As the convective heat transfer is closely related to the Prandtl number, different heat transfer correlations are often needed for fluids with various Prandtl numbers. Previous studies have established heat transfer correlations for fluids with medium–high Prandtl numbers (such as air and water) and extremely low-Prandtl fluids (such as liquid metals); however, these correlations cannot be directly recommended for such helium–xenon mixtures without verification. This study initially assessed the applicability of existing Nusselt number correlations, finding that the selected correlations are unsuitable for helium–xenon mixtures. To establish a more general heat transfer correlation, a theoretical derivation was conducted using the turbulent boundary layer theory. Numerical simulations of turbulent heat transfer for helium–xenon mixtures were carried out using Ansys Fluent. Based on simulated results, the parameters in the derived heat transfer correlation are determined. It is found that calculations using the new correlation were in good agreement with the experimental data, verifying its applicability to the turbulent heat transfer for helium–xenon mixtures. The effect of variable gas properties on turbulent heat transfer was also analyzed, and a modified heat transfer correlation with the temperature ratio was established. Based on the working conditions adopted in this study, the numerical error of the property-variable heat transfer correlation was almost within 10%.

Wall temperature effects on shock unsteadiness in a reattaching compressible turbulent shear layer

In this study, the effect of heat transfer on the compressible turbulent shear layer and shockwave interaction in a scramjet has been investigated. To this end, highly resolved Large Eddy Simulations (LES) are performed to explore the effect of wall thermal conditions on the behavior of a reattaching free shear layer interacting with an oblique shock in compressible turbulent flows. Various wall-to-recovery temperature ratios are considered, and results are compared to the adiabatic wall. It is found that the wall temperature affects the reattachment location and the shock behavior in the interaction region. Furthermore, fluctuating heat flux exhibits a strong intermittent behavior with severe heat transfer compared to the mean, characterized by scattered spots. The distribution of the Stanton number shows a strong heat transfer and complex pattern within the interaction, with the maximum thermal (heat transfer rates) and dynamic loads (root-mean-square wall pressure) found for the case of the cold wall. The analysis of LES data reveals that the thermal boundary condition can significantly impact the wall pressure fluctuations level. The primary mechanism for changes in the flow unsteadiness due to the wall thermal condition is linked to the reattaching shear layer, which agrees with the compressible turbulent boundary layer theory.

A Practical Approach to the Assessment of Waterjet Propulsion Performance: The Case of a Waterjet-Propelled Trimaran

Abstract To obtain a reasonable evaluation of the performance of waterjet propulsion at the design stage, a semi-theoretical and semi-empirical method is used to calculate the fundamental parameters of waterjet propulsion performance using an iterative approach. To calculate the ship’s resistance, a boundary element method based on three-dimensional potential flow theory is used to solve the wave-making resistance, and an empirical approach is used to evaluate the viscous resistance. Finally, the velocity and pressure of the capture area of the waterjet propulsion control volume are solved based on turbulent boundary layer theory. The iteration equation is established based on the waterjet-hull force-balance equation, and the change in the ship’s attitude and the local loss of the intake duct are considered. The performance parameters of waterjet propulsion, such as resistance, waterjet thrust, thrust deduction, and the physical quantity of the control volume, are solved by iteration. In addition, a PID-controlled free-running ship model is simulated using the RANS CFD method as a comparison. We apply the proposed approach and the RANS CFD method to a waterjet-propelled trimaran model, and the simulation process and the results are presented and discussed. Although there are some differences between the two methods in terms of the local pressure distribution and thrust deduction, the relative error in the evaluation results for the waterjet propulsion performance is generally reasonable and acceptable. This indicates that the present method can be used at the early stages of ship design without partial information about the waterjet propulsion system, and especially in the absence of a physical model of the pump.

Heat transfer in the boundary layer in an incompressible fluid in terms of waveguide turbulence model

The possibility of the description of the heat transfer processes in the developed turbulent boundary layer on the flat plate at zero angle attack with zero longitudinal pressure gradient in incompressible fluid is considered as a consequence of the waveguide theory of turbulent boundary layer. It is shown that the logarithmic distribution of temperature along normal coordinates arises in a natural way. It is pointed out the possibility of the intensification of the heat transfer due to generation of own modes of the temperature pulsations. The problem of heat transfer in a boundary layer on a plate flow round an incompressible fluid using the collocation method with Chebyshev polynomial is considered. The dependence of the eigen frequency of the least damped mode on the wave number is obtained. The amplitude of the exicted mode obeys the direct resonance equation if external excitation is applied to the system.

Recurrence quantification analysis of MHD turbulent channel flow

We present Recurrence Plots (RPs) and Recurrence Quantification Analysis (RQA) of time series of velocities in a low-Reynolds-number magnetohydrodynamic turbulent channel flow. The flow was simulated using a fully spectral code with Fourier and Chebyshev decomposition in the periodic and wall bounded directions, respectively. Direct numerical simulations of the flow were performed for Reτ=180, based on the friction velocity and the channel half-height, for the hydrodynamic flow and in the case of a streamwise magnetic field with magnetic interaction number 0.1. The turbulent velocity time series of both cases of the flow were recorded at several positions in the wall-normal direction at fixed spanwise and streamwise positions and analyzed along all directions using RPs and RQA. Using this approach, a number of different flow regions were identified depending on the distance from the channel walls in accordance to the turbulent boundary-layer theory. Different characteristic times were extracted for the various velocity components and related to the dynamics of the flow. Moreover, with the use of Recurrence Plots several distinct system regimes were identified and the effect of the magnetic field was localized.

Theory and application of two-dimension viscous hydraulic design of the ultra-low specific-speed centrifugal pump

Low efficiency and bad cavitation performance restrict the development of the ultra-low specific-speed centrifugal pump (ULSSCP). In this research, combined turbulent boundary layer theory with two-dimension design and two-dimension viscous hydraulic design method has been proposed to redesign a ULSSCP. Through the solution of the displacement thickness in the boundary layer, a less curved blade profile with a larger outlet angle was obtained. Then the hydraulic and cavitation performance of the reference pump and the designed pump were numerically studied. The comparison of performance of the reference pump calculated by the numerical and experimental results revealed a better agreement. Research shows that the average hydraulic efficiency and head of the designed pump improve by 2.9% and 3.3%, respectively. Besides, the designed pump has a better cavitation performance. Finally, through the internal flow analysis with entropy production diagnostic model, a 24.8% drop in head loss occurred in the designed pump.

HIGH-RESOLUTION TSUNAMI-BEDLOAD COUPLED COMPUTATION IN AMR ENVIRONMENT

Conventional tsunami computations on coarser grids have employed Manning’s friction coefficients of subgrid equivalent roughness for buildings, vegetation and public facilities (roads, dikes and so on), depending on land-use at the grid location. This equivalent roughness macroscopically models to integrate all effects of resistances against the flow within the computational cells; that is, drag force and pressure reduction behind structures in addition to wall roughness defined in turbulent boundary layer theory. Recently high-resolution land elevation data (2-m resolution), measured by an aerial laser profiler, has been used for computing local inundation of tsunami flood. Since the high-resolution data resolves major buildings and facilities, the mechanical contributions of the structures, such as drag and pressure reduction, are included in the computed result. In this case, conventional equivalent friction may be unacceptable to use.

Roughness height of submerged vegetation in flow based on spatial structure

The classic hydraulic resistance formulas, such as those in the Darcy-Weisbach methods, perform well in the hydraulic design with the characteristic roughness height ks smaller than the flow depth, which can be linked with the momentum roughness height based on the turbulent boundary-layer theory with the log-law formulation. However, when the roughness scale is of the same order as the flow depth, the traditional log-law formulation cannot provide satisfactory results because the flow structure is complicated and the vortices in different layers are dominated by various principles, such as the Karman streets near the channel bed, the mixing layer near the vegetation top, and a canonical turbulent boundary layer above the vegetation layer. Thus, the distribution of the streamwise velocity in the vegetated flow is a combination of the velocity profile linked with the dominant vortex and shows significant differences as compared with the traditional log-law distribution. This paper proposes a new characteristic roughness height of vegetation kv by linking vegetation attributes, especially the characteristics of the cross section in the flow within the vegetation. The power law resistance formula is derived based on a large amount of experimental data. Results show that the new formula is applicable to shallow flows with vegetation.

New friction factor and Nusselt number equations for turbulent convection of liquids with variable properties in circular tubes

Large temperature differences between the wall and bulk fluid in heat exchangers will result in significant property variations in the cross section. Most existing equations use correction factors such as (μw/μb)n or (Prw/Prb)m to take account of property variation effects on heat transfer coefficients and friction factors. The exponents, n or m obtained by regression analysis of experimental data are not consistent in the literature. They are also different for heating and cooling conditions. In the current investigation, velocity and temperature distributions of turbulent convection with variable properties in circular tubes are analyzed using classical turbulent boundary layer theory. The viscosity variation effects on velocity and temperature fields are simplified to the effects on the critical point between the linear and the logarithmic distribution regions. New friction factor and Nusselt number equations for turbulent convection of liquids with variable properties are obtained. The new equations show accurate predictions of experimental data for both heating and cooling conditions and for different kinds of liquids. The new equations show that viscosity variation effects on friction factor decrease with the increasing of Reynolds number, while its effects on Nusselt number almost keep constant with the increasing of Reynolds number.

Instantaneous sediment transport model for asymmetric oscillatory sheet flow.

On the basis of advanced concentration and velocity profiles above a mobile seabed, an instantaneous analytical model is derived for sediment transport in asymmetric oscillatory flow. The applied concentration profile is obtained from the classical exponential law based on mass conservation, and asymmetric velocity profile is developed following the turbulent boundary layer theory and the asymmetric wave theory. The proposed model includes two parts: the basic part that consists of erosion depth and free stream velocity, and can be simplified to the total Shields parameter power 3/2 in accordance with the classical empirical models, and the extra vital part that consists of phase-lead, boundary layer thickness and erosion depth. The effects of suspended sediment, phase-lag and asymmetric boundary layer development are considered particularly in the model. The observed instantaneous transport rate proportional to different velocity exponents due to phase-lag is unified and summarised by the proposed model. Both instantaneous and half period empirical formulas are compared with the developed model, using extensive data on a wide range of flow and sediment conditions. The synchronous variation in instantaneous transport rate with free stream velocity and its decrement caused by increased sediment size are predicted correctly. Net transport rates, especially offshore transport rates with large phase-lag under velocity skewed flows, which existing instantaneous type formulas failed to predict, are predicted correctly in both direction and magnitude by the proposed model. Net sediment transport rates are affected not only by suspended sediment and phase-lag, but also by the boundary layer difference between onshore and offshore.

Existence of the passage to the limit of an inviscid fluid.

In the dynamics of a viscous fluid, the case of vanishing kinematic viscosity is actually equivalent to the Reynolds number tending to infinity. Hence, in the limit of vanishing viscosity the fluid flow is essentially turbulent. On the other hand, the Euler equation, which is conventionally adopted for the description of the flow of an inviscid fluid, does not possess proper turbulent behaviour. This raises the question of the existence of the passage to the limit of an inviscid fluid for real low-viscosity fluids. To address this question, one should employ the theory of turbulent boundary layer near an inflexible boundary (e.g., rigid wall). On the basis of this theory, one can see how the solutions to the Euler equation become relevant for the description of the flow of low-viscosity fluids, and obtain the small parameter quantifying accuracy of this description for real fluids.

A Simple Model for the Turbulence Intensity Distribution in Atmospheric Boundary Layers

In the current work, we examine the distribution of turbulence intensity (TI) in simulations of atmospheric boundary layers (ABL) for wind turbine applications. We relate the turbulent fluctuations to the mean wind shear profile for neutrally stable ABL based on turbulent boundary layer theory. The results are then compared to corresponding LES data for various shear conditions. From this, a model for the TI distribution across a rotor disc is devised and calibrated. In addition, a second simpler version of the model is derived by assuming a power law for the velocity profile. The models are related to the Mann model and shown to have a similar scaling, however they are simpler and based on assumptions for turbulent boundary layers rather than homogeneous turbulence. The models are then tested for a range of stability conditions and shear values of the ABL including waked conditions from upstream wind turbines that stretch the assumptions made.

О существовании предельного перехода к невязкой жидкости

With the dynamics of viscous fluid, the case of vanishing kinematic viscosity is actually the case of Reynolds number tending to infinity. Hence, in the limiting case of vanishing viscosity the fluid flow is essentially turbulent. On the other hand, the Euler equation, which is conventionally adopted for description of flow of inviscid fluid, does not possess proper turbulent behaviour. The latter rises the question of existence of the passage to the limit of inviscid fluid for real weakly-viscous fluids. To address this question, one should employ the theory of turbulent boundary layer near an uninflectable boundary (e.g., rigid wall). On the basis of this theory, one can see how the solutions to the Euler equation become relevant for the description of flow of weakly-viscous fluids, and derive the small parameter quantifying accuracy of this description for real fluids. Received 16.05.2016 ; accepted 30.06.2016

A new drag force model for the wake acceleration effect and its application to simulation of bubbly flow

Prediction accuracy of dispersed gas–liquid multiphase flow is strongly dependent on modeling of drag force. In this paper, a new drag force model was proposed to predict the relative velocity of bubbly flow. The proposed model considers the wake acceleration effect under large bubble diameter and high volume fraction conditions. Key relation of the new drag force model is the modeling of the relationship between the increased bubble rising velocity and the velocity profile of unstable wake, for which the concept of defining a proper reference fluid velocity is applied. It is found that there is a strong dependency of the increased bubble rising velocity on bubble aspect ratio and wake velocity. A systematic CFD simulation covering a wide range of bubble diameter was carried out, with which the velocity profiles of unstable wake in both radial and vertical directions were investigated in detail. Based on turbulent boundary layer theory, correlations were proposed to describe the velocity profile of unstable wake in terms of bubble terminal velocity and bubble diameter. Finally, the new drag force model was employed to predict the relative velocity in bubbly flow for validation calculation with selected test cases conducted in pipes of different sizes.

PYFLOW: A computer code for the calculation of the impact parameters of Dilute Pyroclastic Density Currents (DPDC) based on field data

PYFLOW is a computer code designed for quantifying the hazard related to Dilute Pyroclastic Density Currents (DPDC). DPDCs are multiphase flows that form during explosive volcanic eruptions. They are the major source of hazard related to volcanic eruptions, as they exert a significant stress over buildings and transport significant amounts of volcanic ash, which is hot and unbreathable. The program calculates the DPDC׳s impact parameters (e.g. dynamic pressure and particle volumetric concentration) and is founded on the turbulent boundary layer theory adapted to a multiphase framework. Fluid-dynamic variables are searched with a probabilistic approach, meaning that for each variable the average, maximum and minimum solutions are calculated. From these values, PYFLOW creates probability functions that allow to calculate the parameter at a given percentile. The code is written in Fortran 90 and can be compiled and installed on Windows, Mac OS X, Linux operating systems (OS). A User׳s manual is provided, explaining the details of the theoretical background, the setup and running procedure and the input data. The model inputs are DPDC deposits data, e.g. particle grainsize, layer thickness, particles shape factor and density. PYFLOW reads input data from a specifically designed input file or from the user׳s direct typing by command lines. Guidelines for writing input data are also contained in the package. PYFLOW guides the user at each step of execution, asking for additional data and inputs. The program is a tool for DPDC hazard assessment and, as an example, an application to the DPDC deposits of the Agnano–Monte Spina eruption (4.1ky BP) at Campi Flegrei (Italy) is presented.

Remote Measurement of Heat Flux from Power Plant Cooling Lakes

AbstractLaboratory experiments have demonstrated a correlation between the rate of heat loss q″ from an experimental fluid to the air above and the standard deviation σ of the thermal variability in images of the fluid surface. These experimental results imply that q″ can be derived directly from thermal imagery by computing σ. This paper analyses thermal imagery collected over two power plant cooling lakes to determine if the same relationship exists. Turbulent boundary layer theory predicts a linear relationship between q″ and σ when both forced (wind driven) and free (buoyancy driven) convection are present. Datasets derived from ground- and helicopter-based imagery collections had correlation coefficients between σ and q″ of 0.45 and 0.76, respectively. Values of q″ computed from a function of σ and friction velocity u* derived from turbulent boundary layer theory had higher correlations with measured values of q″ (0.84 and 0.89). This research may be applicable to the problem of calculating losses of heat from the ocean to the atmosphere during high-latitude cold-air outbreaks because it does not require the information typically needed to compute sensible, evaporative, and thermal radiation energy losses to the atmosphere.

Airfoil 주변에서의 층류 및 난류경계층 이론에 대한 수치해석

본 논문에서는 층류 및 난류 유동 특성 중 경계층 두께와 배제 두께, 그리고 모멘텀 두께에 대한 기존의 이론값과 실제 CFD 해석을 통한 수치해석의 데이터를 비교하였다. Freestream velocity는 Reynolds 수에 영향을 주게 되고, airfoil 주변에서의 유동의 층류 및 난류에 영향을 주게 된다. 층류 및 난류의 경우 유동특성이 달라 경계층 두께 및 배제두께, 그리고 모멘텀 두께가 달라지게 되고, 결국 airfoil의 공력특성인 양력과 항력, 그리고 pitching moment에 영향을 주며, separation point도 다양한 angle of attack에서 바뀌게 된다. 이번 연구에서의 목적은 비점성 유동과, 층류 및 난류 각 경우에 대한 유동특성에 대해 알아보는 것이다. 연구에서 사용된 airfoil의 경우 c=1인 Joukowski airfoil을 사용하였으며, CFD는 상용 프로그램인 Fluent 6.0을 통해 NACA-0012 airfoil을 사용하였다. 층류 및 난류에서의 $Re_c$ 는 $Re_c$ =3,000 3,000, 700,000이며 각각에 해당하는 속도는 0.045, 10 m/s이다. 본 연구를 통해 기존의 실험값과 수치해석의 결과가 잘 일치함을 알 수 있으며, 이를 통해 다양한 airfoil의 형상을 모델링할 수 있는 근거를 마련하였다. 【In the present study, we compared the theory with CFD data about the boundary layer thickness, displacement thickness and momentum thickness. According to the freestream velocity, larminar and turbulent is decided and affect to the flow patterns around the airfoil The boundary layer thickness, displacement thickness and momentum thickness affect to the aerodynamic characteristics of the airfoil(e.g. lift, drag and pitching moment). The separation point is affected by varying angle of attack. In the present study, we used the Joukowski airfoil(c=1), and NACA0012 airfoil was used at CFD. The chord Reynolds number is $Re_c$ =3,000 3,000, 700,000, respectively and the freestream velocity is 0.045, 10 m/s, respectively. In this paper, the data was a good agreement with that of experimental results, so we can analyze the various airfoil models.】

Wall-Pressure Spectral Model Including the Adverse Pressure Gradient Effects

4, in both internal (channel) and external (airfoil) flows. A review of the boundary-layer parameters characterizing the pressure gradient effects is provided, and the more relevant ones are introduced as new variables in the model. The method is then compared to the zero pressure gradient model it is derived from. The influence of the pressure gradient on the wall-pressure spectrum is discussed.Finally,themethodisappliedtoprovideinputdataofaradiatedtrailing-edge noisemodelbymeansofan aeroacoustic analogy, namely Amiet’s theory of turbulent boundary layer past a trailing edge. The results are compared to experimental data obtained in an open-jet anechoic wind tunnel.