Velocity Distribution In Boundary Layer Research Articles

Physics-informed deep learning cascade loss model

The design procedure of aero-engine compressor requires empirical models such as cascade loss model and deviation model. With accurate predictions of basic cascade performance by empirical model, better designs would be obtained and the cost would be reduced. A number of empirical models have been developed and most of them build mathematical equations based on experimental data. It is difficult to modify and broaden the scope of application for empirical models because of its inadequate ability to fit strong nonlinear function relationship and lack of data. Neural networks, which are widely used nowadays, are applied to solve this problem but a simple end-to-end neural network only slightly improves the model performance due to the neglect of flow field details and the similarity of different samples. A promising way to solve the problems is to embed the physics mechanism or flow field details into neural networks as intermediate variables to guide the learning of models. A physics-informed deep learning cascade loss model is proposed. By adjusting the architecture of neural network and the data structure, model can build the relationship of input and output in a more reasonable way while providing a prediction of flow fields. This paper verified the superiority of deep learning model, which has no physics informed, with a 22.3% error reduction when compared to empirical models. A physics-informed model is built and trained with the velocity distribution in boundary layer is chosen as intermediate variable and the influencing factors of physics-informed models are explored. The error of physics-informed model decreases 57.4% overall, and over 60% at high Mach numbers and high incidences compared to empirical model. The physics informed deep learning model is promising to replace the empirical models in compressor design since it shows better performance and gives a local description of the cascade flow field, which can be utilized in subsequent cascade design.

Generalized Bed-Load Function Based on Empirical Data

There exist many bed-load functions in the literature to calculate bed-load transport rates, but none of them fit data from low to high shear stress conditions. This research presents a generalized bed-load function based on empirical data. Specifically, the classic power law in high shear stress conditions is extended to low shear stress conditions by applying a complimentary error function (or logistic function) and using Coles’ mathematical idea for the wake law in turbulent boundary layer velocity distribution. The resulting generalized bed-load function agrees well with the classic data sets; it reduces to Huang’s 5/3 power law in the very low and the high shear stress conditions, and it is numerically close to Paintal’s 16th power law in the transitional regime. It is found that the maximum turbulence-induced lift force and the minimum critical shear stress in the Shields diagram correspond to the inflection point (in terms of logarithmic scale) in the Einstein bed-load diagram, resulting in the most efficient bed-load transport rate. After that, this paper discusses the effects of turbulence-induced lift force, critical shear stress, viscosity, nonlinearity, and uncertainty on bed-load transport. Finally, an example with uncertainty analysis is illustrated for applications.

Assessment of turbulence models for the boundary layer transition flow simulation around a hydrofoil

Boundary layer transition is a typical phenomenon in flows around hydrofoils and has a large influence on the hydrodynamic characteristics such as lift & drag, and vortex shedding. The purpose of this paper is to assess the predictive capability of different turbulence models in computational fluid dynamics (CFD) on boundary layer transition along a hydrofoil. Two typical sub-grid scale (SGS) stress models (LES WALE and LES Smagorinsky), as well as DDES γ-Reθt, DDES, SSTCC γ-Reθt, SST γ-Reθt, and SST k−ω are selected. The boundary layer and wake flow calculated by different models are analyzed in detail and compared with the experimental data. The results show that large eddy simulation is more accurate than other models in terms of boundary layer velocity distribution, vortex shedding and wake structure prediction at the same grid conditions. The transition model considering curvature correction influences the predictive capability in the near-wall region compared with SST γ-Reθt. The flow fields calculated by different curvature correction coefficients are quite different. In this paper, the prediction in the front of the transition end point (0.85L) has achieved good results as scaling coefficient is equal to 75 or 100. The transition model considering curvature modification improves the prediction of boundary layer transition by decreasing the turbulence intensity and increasing the pressure gradient of the aft part of the curvature hydrofoil leading. It is found that the LES model is the first choice in the case of enough computing resources. However, for engineering problems, it is highly efficient to adopt SSTCC γ-Reθt model by adjusting the curvature correction coefficient.

Validation of a Model for Estimating the Strength of a Vortex Created from the Bound Circulation of a Vortex Generator

A hypothesis was tested and validated for predicting the vortex strength induced by a vortex generator in wall-bounded flow by combining the knowledge of the Vortex Generator (VG) geometry and the approaching boundary layer velocity distribution. In this paper, the spanwise distribution of bound circulation on a vortex generator was computed by integrating the pressure force along the VG height, calculated using Computational Fluid Dynamics (CFD). It was then assumed that all this bound circulation was shed into a wake to fulfill Helmholtz’s theorem which then curls up into one primary tip vortex. To validate this, the trailed circulation estimated from the distribution of the bound circulation was compared to the one in the wake behind the vortex generator, determined directly from the wake velocities at some downstream distance. In practical situations, the pressure distribution on a vane is unknown and consequently other estimates of the spanwise force distribution on a VG must instead be applied, such as using 2D airfoil data corresponding to the VG geometry at each wall-normal distance. Such models have previously been proposed and used as an engineering tool to aid preliminary VG design. Therefore, it is not the purpose of this paper to refine such engineering models, but rather to validate their assumptions, such as applying a lifting line model on a VG that has a very low aspect ratio and is placed in a wall boundary layer. Herein, high Reynolds number boundary layer measurements of VG-induced flow were used to validate the Reynolds-Averaged Navier–Stokes (RANS) model circulation results, which were used for further illustration and validation of the hypothesis.

Numerical model on the flow dynamics around the sediment-water interface in the tidal coastal area

Investigating flow dynamics around the sediment-water interface is one of difficult issues in marine environment. It has important significance to study the physical, chemical and biological activities between the overlying water and sedimentary layer with tidal forcing. In this study, we established a numerical model to investigate the flow dynamics around the sediment-water interface in the tidal coastal area. The model reflected the hydrodynamics of periodic reciprocating unsteady flow in the overlying water layer and the fully coupled simulation of flow movement between the overlying water layer and sedimentary layer. A sedimentary layer, an overlying water layer, and an air layer were all treated as the fluid zone. The unsteady Reynolds-averaged Navier-Stokes equations, and the Reynolds stress model with porosity, were solved by the finite volume method. Moreover, the drag source term in the momentum equation was modified as the Darcy-Forchheimer extended form. The model showed a strong performance in simulating the hydrodynamics of coupled flow around the sediment-water interface with tidal forcing in a coastal area. With considering the sedimentary layer, the benthic boundary layer velocity distributions were more accurate than those obtained by a wall function model. Around the sediment-water interface, there was inertial loss in the flow. Furthermore, velocity increased with increasing porosity, and velocity gradient became larger. Compared with models with Darcy's Law, the numerical model in this study had better performance in the turbulent characteristics of sediment-water interface layer. The model can lead to better understanding of the exchange mechanisms of oxygen, nitrogen and nutrient between overlying water and sediment.

A hydrodynamic fragmentation model based on boundary layer stripping

Fuel Coolant Interactions (FCIs) are important issues in nuclear reactor severe accident analysis, which have drawn much attention by experts all over the world for many years. The boundary layer stripping is one of the mechanisms that result in hydrodynamic fragmentation during FCIs, and has been studied for many years. However, the results and trends predicted by the existing fragmentation rate models based on such a mechanism are still very different from the experimental data. In this study, in order to develop a fragmentation rate model of a liquid droplet, induced by boundary layer stripping, a new velocity distribution in boundary layer is proposed, which covers two very significant parameters. Then, based on theoretical modeling and experimental data, semi-empirical correlations which can predict the fragmentation rate and the average size of fragments are established, which are verified by typical experimental data and are compared with previous model predictions. The result shows that the fragmentation rate calculated by the present model and the certain range of average fragment size are in good agreement with the experimental data, which proves that the two new parameters involved can reflect the velocity distribution in boundary layers of both the melt and coolant more appropriately and reliably. With the help of the model from IFCI and CULDESAC codes, there is reason to believe the present hydrodynamic fragmentation model could be applied in FCI codes in the future.

Non‐uniform velocity distribution effect on the Betz–Joukowsky limit

ABSTRACTA simple analytic correction is derived for the maximum efficiency of an ideal wind turbine rotor, the Betz–Joukowsky limit. The analytic correction accounts for the effect that the non‐uniform atmospheric boundary layer velocity distribution has on the Betz–Joukowsky derivation. The maximum power coefficient predicted by using the atmospheric boundary layer velocity profile is slightly higher than that predicted by using a uniform velocity distribution. The application of the correction to a 100 m rotor diameter at 80 m hub height in a neutrally stratified boundary layer flow predicts a maximum power increase of 1–2%, depending on the approach terrain. Copyright © 2012 John Wiley & Sons, Ltd.

Experimental investigation of separation and transition processes on a high-lift low-pressure turbine profile under steady and unsteady inflow at low Reynolds number

The effects induced by the presence of incoming wakes on the boundary layer developing over a high-lift low-pressure turbine profile have been investigated in a linear cascade at mid-span. The tested Reynolds number is 70000, typical of the cruise operating condition. The results of the investigations performed under steady and unsteady inflow conditions are analyzed. The unsteady investigations have been performed at the reduced frequency of f +=0.62, representative of the real engine operating condition. Profile aerodynamic loadings as well as boundary layer velocity profiles have been measured to survey the separation and transition processes. Spectral analysis has been also performed to better understand the phenomena associated with the transition process under steady inflow. For the unsteady case, a phase-locked ensemble averaging technique has been employed to reconstruct the time-resolved boundary layer velocity distributions from the hot-wire instantaneous signal output. The ensemble-averaging technique allowed a detailed analysis of the effects induced by incoming wakes-boundary layer interaction in separation suppression. Time-resolved results are presented in terms of mean velocity and unresolved unsteadiness time-space plots.

Viscous Damping of Cnoidal Waves Over Fluid‐Mud Seabed

The heights of water waves propagating over fluid-mud bottom can be significantly reduced due to the viscous energy dissipation occurring in the mud bottom. In some cases, exceptionally high rates of attenuation are possible whereby waves are almost completely damped within several wavelengths. This phenomenon has been observed both in field investigation and in laboratory experiment action. In this paper, the viscous damping of cnoidal waves progressing over fluid-mud seabeds is investigated, in which fluid mud is assumed to be a viscous fluid. The theoretical model adopted here is a two-layer viscous fluid model modified with three boundary layers at the water-mud interface and at the rigid bottom beneath mud layer. Viscosities of both water and fluid mud are taken into consideration. For a nonlinear shallow wave progressing over a viscous mud bed, the first-order analytical solutions are derived for the velocity distributions in boundary layers and for the attenuation rate of wave heights with distance. The attenuation coefficients are larger than those predicted on the basis of linear shallow wave theory and unlike the case of linear shallow waves, they are not independent of wave height. The viscous damping of solitary and sinusoidal waves, which are two extreme cases of cnoidal wave, are also discussed according to the present solution.

Heat Transfer Downstream of a Leading Edge Separation Bubble

Experiments for flow about a two-dimensional blunt body with a circular leading edge are described. Measurements of the free-stream and boundary-layer velocity distributions are presented and indicate that a small separation “bubble” existed where the leading edge joined the body. In particular, it was found that the laminar leading edge boundary layer separated and reattached shortly downstream as a turbulent boundary layer with a low-momentum thickness Reynolds number. Heat transfer measurements around the body are also presented and show almost an order of magnitude increase across the bubble. Downstream of the bubble, however, the heat transfer could be correlated by a slightly modified turbulent flat plate equation using the separation point as the virtual origin of the heated turbulent boundary layer.

INVESTIGATION OF SCALE EFFECTS ON WAKE DISTRIBUTION USING GEOSIM MODELS

The scale effect on the wake distribution of a full form ship model was studied experimentally and theoretically on a geosim series of a tanker . Wake as well as boundary layer velocity distributions were measured by 5 hole Pitot tubes at several stations for each model in towing tanks. The measurements were compared with theoretical results by three methods for predicting scale effects of the wake and boundary layer. The results obtained were: 1> the width of the wake becomes narrower as the dimensions of the model increase, 2> the value of the wake fraction becomes smaller in the wake-peak regions as the dimensions of the model increase, and 3> prediction methods which consider the scale effect in velocity defect as well as in wake width are superior to those which do not consider the scale effect in velocity defect.

Heat Transfer from a Flat Plate in Two-Component Mist Flow

An experimental study concerning the characteristics of heat transfer from a dry isothermal flat plate in two-component (water-air) mist flow has been performed for lower water-air mass flow ratios up to 2.3 percent. Heat transfer coefficients in mist flow increase several times corresponding to single phase coefficients with increasing mass flow ratio and free stream velocity, and with decreasing wall temperature. The measurements of droplet velocity employing laser Doppler anemometry indicate the similarity of velocity distributions in boundary layer of mist flow, which approximately fit the laminar single phase one. It is confirmed that an augmentation of heat transfer is attributable to a latent heat due to evaporation of water droplets within the boundary layer, and that, at a constant Reynolds number and wall temperature, the enhanced rates of heat transfer coefficients are linearly correlated to water mass flow rates for unit cross-sectional area.

Application of a “Radiation-Type” Boundary Condition to the Wave, Porous Bed Problem

Abstract The problem of a small-amplitude wave propagating over a flat porous bed is reanalyzed subject to the bottom boundary conditionwhere u represents the horizontal velocity in the fluid,ũs represents the horizontal velocity within the bed as predicted by Darcey's law, K is the permeability and the subscript 0 denotes evaluation at the bottom (z=0). The term α is a constant whose value depends on the porosity of the bed at the interface and must be determined experimentally. The boundary condition is of the form of a “radiation-type” condition commonly encountered in heat conduction problems. The important physical quantities (velocity, velocity potential, streamfunction, shear stress and energy dissipation) have been derived and are presented, subject to natural conditions. The bottom boundary layer is represented by the linearized Navier-Stokes equations under the usual boundary layer approximation. It is found that the boundary layer velocity distribution and shear stress can be greatly altered fr...

A Boundary-Layer Theory for Transient Viscous Losses in Turbulent Flow

A laminar boundary-layer model is proposed to account for viscous losses during the transient turbulent flow of a liquid in a tube. In this model, inviscid slug flow is assumed for the core and all viscous effects are assumed to occur in the boundary layer. The transient boundary-layer velocity distribution is determined as a function of a prescribed variation in core velocity and the associated pressure gradient. Both analytical and numerical solutions are presented. This transient flow information is used to calculate local and integrated energy dissipation rates which are then combined, with one-dimensional energy analyses. The result is a prediction of the decrease in pressure-wave magnitude due to viscous dissipation, and a comparison is made with experimental data for rapid flow extinction. Good agreement between the observed and predicted results is obtained.

Comparison of Velocity Distribution in the Boundary Layer between Ship and Model

Comparative tests on the velocity distribution in boundary layer were carried out on a large tanker and her 6.25 meter model.Measurements were made at a point about 0.1 Lpp forward of A. P. and 0.3× (design draft) above base line. Velocity distribution in boundary layer on the ship agrees approximately with the 1/7th power law. Profile of velocity distribution on the model shows more remarkable drop, near the hull surface than that of the ship and is very close to separation. Considerable difference in flow direction in the boundary layer can be seen between on ship and model.

A further comment on the relationship between static hole error and boundary layer velocity distribution

A further comment on the relationship between static hole error and boundary layer velocity distribution