Model Of Turbulent Boundary Layer Research Articles

On the challenges of estimating the low-wavenumber wall pressure field beneath a turbulent boundary layer using a microphone array

The low-wavenumber components of the turbulent boundary layer (TBL) wall pressure field (WPF) are known to be the primary cause of structural vibration in low-Mach number flows, despite the maximal energy of the TBL being at the convective wavenumber. Existing semi-empirical TBL models show good agreement in predicting the WPF levels in convective region but differ significantly in the low-wavenumber domain. This study aims to highlight the challenges of estimating the low-wavenumber WPF in a TBL using a microphone array. A regularized Fourier-based approach is proposed to numerically study the estimation of the low-wavenumber WPF. Performance of the proposed method is initially evaluated by comparing the estimated WPF against a closed-form input TBL model. Effects of sensor spacing, co-array factor, and sensor distribution on the estimation of the low-wavenumber WPF levels are then investigated. To mimic experimental measurements a virtual acoustic experiment is proposed, involving the synthesis of snapshots of TBL-induced WPF. It is demonstrated that although with relatively small number of snapshots the convective region can be identified, a significant number of snapshots is required to well estimate the TBL low-wavenumber region.

Numerical study on the estimation of the low-wavenumber wall pressure field using vibration data

It is known that the low-wavenumber components of the wall pressure field beneath a turbulent boundary layer is the main cause of structural vibration in low Mach number flows. This is because the structure filters the convective ridge of the turbulent boundary layer excitation at frequencies well above the aerodynamic coincidence frequency. This work aims to explore the possibility of estimating the low-wavenumber wall pressure filed by obtaining vibration data from a structure excited by a turbulent boundary layer. To achieve this, an analytical model of a simply-supported plate under turbulent boundary layer is developed and the acceleration data obtained from the plate is used to evaluate the wall pressure field in the low-wavenumber domain. The wall pressure field is modelled using the Goody and Mellen models for auto-spectrum density and cross-spectrum density, respectively. Finally, the estimated pressure field is compared with the input turbulent boundary layer to evaluate the accuracy of the proposed method.

Excitation of structures by partially correlated pressures: A review of diffuse acoustic field and turbulent boundary layer models

Structures are sometimes excited by pressure distributions which exhibit complex spatial correlation. This differs from common acoustic excitations since the pressure at one location is only partially correlated with the pressure at another location due to inherent spatial randomness within the forcing function. Two forcing functions which exhibit partially-correlated pressures are the diffuse acoustic field (DAF) and turbulent boundary layer (TBL) flow. A basic model for representing the spatial correlation for these two forcing functions will be reviewed in both the spatial and wavenumber domains. Recent approaches for computing the vibration of structures excited by DAF or TBL flow will then be summarized. Interesting physical effects, such as intermodal coupling, will be highlighted to illustrate the importance of properly modeling partial correlations when they exist.

K2 and Spitzer phase curves of the rocky ultra-short-period planet K2-141 b hint at a tenuous rock vapor atmosphere

K2-141 b is a transiting, small (1.5 R⊕) ultra-short-period (USP) planet discovered by the Kepler space telescope orbiting a K-dwarf host star every 6.7 h. The planet's high surface temperature of more than 2000 K makes it an excellent target for thermal emission observations. Here we present 65 h of continuous photometric observations of K2-141 b collected with Spitzer's Infrared Array Camera (IRAC) Channel 2 at 4.5 μm spanning ten full orbits of the planet. We measured an infrared eclipse depth of ${f_{{{\rm{p}} \mathord{\left/ {\vphantom {{\rm{p}} {{{\rm{f}}_{\rm{*}}}}}} \right. \kern-\nulldelimiterspace} {{{\rm{f}}_{\rm{*}}}}}}} = 142.9_{ - 39.0}^{38.5}$ ppm and a peak to trough amplitude variation of $A = 120.6_{ - 43.0}^{42.3}$ ppm. The best fit model to the Spitzer data shows no significant thermal hotspot offset, in contrast to the previously observed offset for the well-studied USP planet 55 Cnc e. We also jointly analyzed the new Spitzer observations with the photometry collected by Kepler during two separate K2 campaigns. We modeled the planetary emission with a range of toy models that include a reflective and a thermal contribution. With a two-temperature model, we measured a dayside temperature of ${T_{{\rm{p,d}}}} = 2049_{ - 359}^{362}$ K and a night-side temperature that is consistent with zero (Tp,n < 1712 K at 2σ). Models with a steep dayside temperature gradient provide a better fit to the data than a uniform dayside temperature (ΔBIC = 22.2). We also found evidence for a nonzero geometric albedo ${A_{\rm{g}}} = 0.282_{ - 0.078}^{0.070}$. We also compared the data to a physically motivated, pseudo-2D rock vapor model and a 1D turbulent boundary layer model. Both models fit the data well. Notably, we found that the optical eclipse depth can be explained by thermal emission from a hot inversion layer, rather than reflected light. A thermal inversion may also be responsible for the deep optical eclipse observed for another USP, Kepler-10 b. Finally, we significantly improved the ephemerides for K2-141 b and c, which will facilitate further follow-up observations of this interesting system with state-of-the-art observatories such as James Webb Space Telescope.

The impact of ultraviolet heating and cooling on the dynamics and observability of lava planet atmospheres

ABSTRACT Lava planets have non-global, condensible atmospheres similar to icy bodies within the Solar system. Because they depend on interior dynamics, studying the atmospheres of lava planets can lead to understanding unique geological processes driven by their extreme environment. Models of lava planet atmospheres have thus far focused on either radiative transfer or hydrodynamics. In this study, we couple the two processes by introducing ultraviolet (UV) and infrared (IR) radiation to a turbulent boundary layer model. We also test the effect of different vertical temperature profiles on atmospheric dynamics. Results from the model show that UV radiation affects the atmosphere much more than IR. UV heating and cooling work together to produce a horizontally isothermal atmosphere away from the substellar point regardless of the vertical temperature profile. We also find that stronger temperature inversions induce stronger winds and hence cool the atmosphere. Our simulated transmission spectra of the bound atmosphere show a strong SiO feature in the UV that would be challenging to observe in the planet’s transit spectrum due to the precision required. Our simulated emission spectra are more promising, with significant SiO spectral features at 4.5 and 9 $\mu$m that can be observed with the James Webb Space Telescope. Different vertical temperature profiles produce discernible dayside emission spectra, but not in the way one would expect.

Dissipative mathematical model of heat transfer in channels with process intensifiers

A mathematical model is considered and calculated expressions for the average shear stress and the average Nusselt number in channels with surfaces of process intensifiers (wire inserts, annular protrusions, etc.) are obtained. The average shear stress is found using the expression for the energy dissipation rate and the Deisler and Van Driest turbulent boundary layer model. As a result, an equation related to the pressure drop in the channel with process intensifiers was obtained. Using this equation, the Nusselt number is written for channels with heat transfer intensifiers, and the calculation results are given and compared with known experimental data for transformer oil and other media with high viscosity at Reynolds numbers from 200 to 3104. The resulting expression allows calculating the heat transfer coefficients based on the results of experimental studies hydraulic resistance. As a result, the terms and costs of designing or modernizing heat exchangers for various industries are reduced.

Study on Radiated Noise of a Panel under Fluctuating Surface Pressure Due to an Idealized Side Mirror

As traditional automobiles develop towards new energy vehicles, the noise, vibration and harshness (NVH) performance of automobiles is facing new challenges. Without the cover of the traditional engine noise and inlet and exhaust noise, the high-speed wind noise becomes more prominent. Thus, research on the calculation method of vehicle interior noise in high-speed driving condition is needed. However, vehicle body structure is complex, and the external excitation components are complicated. In order to analyze the method of predicting the vehicle interior noise at high speed, an idealized side mirror model is taken as the research object in this paper and the radiated noise of a panel under the fluctuating surface pressure (FSP) due to the idealized side mirror is studied. The FSP of the panel is first studied by the numerical simulations of incompressible and compressible flow field. For the incompressible flow field, the Corcos turbulent boundary layer (TBL) model is established to simulate the convective component and the boundary element method (BEM) is used to extract the acoustic component. Subsequently, the Corcos model coupling BEM method, the random modal force coupling BEM method and the deterministic modal force coupling BEM method are used separately to calculate the noise of the panel under the FSP. For the compressible flow field, the convective and acoustic component in the fluctuating pressure are separated by the wavenumber-frequency spectrum (WFS) method. The radiated noise of the panel under the FSP is calculated again by using the WFS, the method of random modal force and the method of deterministic modal force, respectively. Then, the computational time of the six methods of incompressible and compressible calculation is compared. Finally, a fast and accurate method of calculating the panel radiated noise under FSP is obtained by comparing the computational accuracy with the experimental results and combining the computational time: the method of incompressible random modal force. This method can be used to quickly and accurately analyze the vehicle interior noise at high speed, and to optimize the exterior protrusions and the vehicle sound package for improving the vehicle NVH performance at high speed.

Noise radiated from a periodically stiffened cylindrical shell excited by a turbulent boundary layer

This work proposes a semi-analytical method to model the vibroacoustic behavior of submerged cylindrical shells periodically stiffened by axisymmetric frames and excited by a homogeneous and fully developed turbulent boundary layer (TBL). The process requires the computation of the TBL wall-pressure cross spectral density function and the sensitivity functions for stiffened cylindrical shells. The former is deduced from an existent TBL model and the latter are derived from a wavenumber-point reciprocity principle and a spectral formulation of the problem. The stiffeners' dynamic behavior is introduced in the formulation through circumferential admittances that are computed by a standard finite element code using shell elements. Four degrees of freedom are taken into account for the coupling between the shell and the stiffeners: three translation directions and one tangential rotation. To investigate the effect of the stiffeners on the radiated noise, two case studies are considered. The first one examines a fluid-loaded cylindrical shell with regularly spaced simple supports. The influence of Bloch-Floquet waves and the support spacing on the noise radiation are highlighted. The second case study inspects the fluid-loaded cylindrical shell with two different periodic ring stiffeners, namely stiffeners with T-shaped and I-shaped cross-sections. Their influence on the vibroacoustics of the shell is thoroughly analyzed.

Aerodynamic validation studies on the performance analysis of iced wind turbine blades

Ice accretion on wind turbine blades distorts blade profiles and causes degradation in the aerodynamic characteristic of the blades. In this study ice accretion on turbine blades are simulated under various icing conditions, and the resulting power losses are estimated. The Blade Element Momentum method is employed together with an ice accretion prediction methodology based on the Extended Messinger model in a parallel computing environment. The predicted iced profiles are first validated with the experimental and numerical data available in the literature. 2D flow solutions and aerodynamic loads over iced blade profiles are obtained with 3 different flow solvers of increasing fidelity; XFOIL, an open-source panel code coupled with a turbulent boundary layer model, SU2, an open-source RANS solver, and METUDES, an in-house DDES solver. The power production losses of a 30 kW wind turbine operating with iced blades are then investigated in detail. It is shown that the XFOIL-based tool developed for the performance analysis of iced wind turbines successfully predicts ice profiles on turbine blades under various icing conditions and the consequent power losses. About 20% power loss is predicted for a 30 kW wind turbine exposed to icing conditions for an hour.

The importance of capturing late melt season sea ice conditions for modeling the western Arctic ocean boundary layer

To better understand the response of the western Arctic upper ocean to late summer ice-ocean interactions, a range of surface, interior, and basal sea ice conditions were simulated in a 1-D turbulent boundary layer model. In-ice and under-ice autonomous observations from the 2014 Marginal Ice Zone Experiment provided a complete characterization of the late melt-season sea ice and were used to set initial conditions, update boundary conditions, and conduct model validation studies. Results show that underestimates of open water and melt pond fraction at the sea ice surface had the largest influence on ocean-to-ice turbulent heat fluxes reducing basal melt rates by as much as 32%. This substantial reduction in latent heat loss was attributed to underestimates of open water areas and the exclusion of melt ponds by low-resolution synthetic aperture radar imagery. However, the greatest overall effect on the ice-ocean boundary layer came from mischaracterizations of basal roughness, with smooth ice scenarios resulting in 7 m of summer halocline shoaling and preservation of the near-surface temperature maximum. Rough ice conditions showed a 23% deepening of the mixed layer and erosion of heat storage above 40 m. Adjustments of conductive heat fluxes had little effect on the near-interface heat budget due to small internal thermal gradients within the late summer sea ice. Results from the 1-D boundary layer simulations highlight the most influential components of sea ice structure during late summer conditions and provide the magnitude of errors expected when ice conditions are mischaracterized.

Analysis of Turbulence Characteristics in Two Large Concentric Annular Ducts Through Particle Image Velocimetry

An experimental study is presented on water single-phase flow in two 10.5 m-long annular ducts, with external pipe's internal diameter (De) of 155 mm and two concentric internal pipes of external diameters (Di) of 60 mm and 125 mm, i.e., radius ratio (α = Ri/e) of 0.39 and 0.80, respectively, with the aim of improving the understanding of flows in annular ducts. Particle image velocimetry (PIV) was applied to obtain instantaneous and averaged velocity measurements of the flow field. A charge-coupled device camera (2448 pixel × 2050 pixel, 5 Mpixel, 12-bit ) recorded pairs of images of the seeding particles and a double-pulsed PIV laser (Nd:YAG, frequency doubled to 532 nm), with a measured pulse intensity of 70 to 75 mJ/pulse, provided the illumination. Laminar flows were analyzed for validation purposes, experimental data on turbulent flows were compared with the classical law of the wall of the turbulent boundary-layer model, and the shear stresses derived from PIV data were compared with those calculated from the measured pressure drop. The effects of the Reynolds number and geometry on turbulent velocity profiles and Reynolds stresses are presented. The results suggest that the law of the wall for annular-duct flow is a function of radius ratio. The new experimental results are of great value for the development of computational fluid dynamics models and more refined pressure-drop prediction tools in annular-duct flow.

Prediction of compressible turbulent boundary layer via a symmetry-based length model

A recently developed symmetry-based theory is extended to derive an algebraic model for compressible turbulent boundary layers (CTBL) – predicting mean profiles of velocity, temperature and density – valid from incompressible to hypersonic flow regimes, thus achieving a Mach number ($Ma$) invariant description. The theory leads to a multi-layer analytic form of a stress length function which yields a closure of the mean momentum equation. A generalized Reynolds analogy is then employed to predict the turbulent heat transfer. The mean profiles and the friction coefficient are compared with direct numerical simulations of CTBL for a range of$Ma$from 0 (e.g. incompressible) to 6.0 (e.g. hypersonic), with an accuracy notably superior to popular current models such as Baldwin–Lomax and Spalart–Allmaras models. Further analysis shows that the modification is due to an improved eddy viscosity function compared to competing models. The results confirm the validity of our$Ma$-invariant stress length function and suggest the path for developing turbulent boundary layer models which incorporate the multi-layer structure.

A Model of Heat and Mass Transfer in Gas Phase in Axial and Turbulent Dispersed Annular Flows

The problem of simulation of heat and mass transfer in the gas phase of film devices in the regime of weak and strong phase interaction has been solved. The Deissler three-layer model of turbulent boundary layer was used. Expressions have been derived for calculating the average Nusselt and Sherwood numbers. Examples of calculations for various conditions of phase interaction and comparison with experimental data are shown.

Modification of turbulent boundary layer model based on wall fluctuations measurement

A modified turbulent boundary layer (TBL) model based the measurement performed in wind tunnel is proposed to investigate the turbulent boundary layer excitation which usually causes serious vibration of the aircraft structure. The Corcos model is the widely used and classical TBL model to simulate the fluctuating pressure excitation over the aircraft structure. However, the assumption of the non-pressure gradient in boundary layer limits its application in a high-speed flow. To extend the classical model to satisfy the high-speed flow, a modified model based on the measurement in wind tunnel is used to modify the Corcos model. To show the superiority of the modified model developed in this study, different TBL models are used to describe theoretical results and experimental results, respectively. The research results demonstrated that the modified model of TBL excitation could make a better agreement with the test results in wind tunnel than that of the classical Corcos model. Meanwhile, such simpler expression of the modified model shows its great convenience to resolve the engineering problems.

Axisymmetric flow in a cylindrical tank over a rotating bottom. Part II. Deformation of the water surface and experimental verification of the theory

The theory of axisymmetric flow in a cylindrical container with a rotating bottom, as described in Part I, is validated against the results of previous and our own laboratory experiments. First, deformation of the water surface is derived using the velocity distribution of the axisymmetric flow obtained by the theory. The form of the water surface is classified into three regimes, and the rotation rates of the transitions between these regimes are determined. The parameters predicted from this theory are compared with the results measured in laboratory experiments and also with data from previous experimental studies. The theory predicts the experimental data well, but a slight difference was found in the narrow region close to the side wall. Corrections estimated by considering the fluid behavior around the side wall boundary layer successfully explain most of the discrepancies. This theory appears to predict the results of the laboratory experiments very well, much better than a theory using an assumption of quadratic drag as a model of turbulent boundary layers.

Bed Shear Stresses Parameterization in Wave–Current Interaction by k − ω Turbulence Model

For a flow generated by the wave–current interaction (WCI), an accurate estimate of the maximum ([Formula: see text]) and the mean ([Formula: see text]) bed shear stresses is important for the sediment transport calculation. These two parameters are usually estimated by numerical modeling which can prove to be difficult to implement and very costly in CPU time. This paper then proposes analytic parameterization of [Formula: see text] and [Formula: see text] by simple relationship depending on the current and wave shear stresses ([Formula: see text] and [Formula: see text]).The proposed parameterization was performed in two steps: the first step is to build a numerical database of [Formula: see text] and [Formula: see text] for different combinations of flow variables. This step was carried out by an one-dimensional vertical (1DV) model of turbulent bottom boundary layer using the [Formula: see text] turbulence model. The second step is to represent this database by predefined analytical relations. This step was performed by an optimization procedure adopting the GlobalSearch (GS) (function of Matlab software).The proposed parameterization based on the “[Formula: see text]/GS” combination provides very good estimations of [Formula: see text] and [Formula: see text]. These estimations are similar to those proposed by other authors who have studied the WCI by analytical models widely used by the marine science community.

Modal forcing functions for structural vibration from turbulent boundary layer flow

In this paper, several approaches for combining large-scale finite-element structural vibration models with turbulent boundary layer (TBL) forcing functions are evaluated. The objective is to determine an efficient method to predict the surface displacement and radiated acoustic power. The overall formulation is based on a standard modal summation approach, and the focus of this work is the calculation of the modal force matrix. Direct numerical integration of the modal force is shown to be very computationally intensive and requires overly resolved structural models. However, an asymptotic approximation to the TBL model provides a very efficient method to compute the modal force at high frequencies. The asymptotic results are equivalent to full numerical integration when the TBL correlation lengths are roughly an order of magnitude smaller than the structural wavelengths. Additionally, the asymptotic solution also removes any dependence of the structural mesh resolution. Analytical formulas using this approach are derived for structures with and without free edges. Example results are shown for a simple isotropic plate and for a complex rib-stiffened plate at low speed in water.

Field observations and results of a 1-D boundary layer model for developing near-surface temperature maxima in the Western Arctic

Summer sea ice extent in the Western Arctic has decreased significantly in recent years resulting in increased solar input into the upper ocean. Here, a comprehensive set of in situshipboard, on-ice, and autonomous ice-ocean measurements were made of the early stages of formation of the near-surface temperature maximum (NSTM) in the Canada Basin. These observations along with the results from a 1-D turbulent boundary layer model indicate that heat storage associated with NSTM formation is largely due to the absorption of penetrating solar radiation just below a protective summer halocline. The depth of the summer halocline was found to be the most important factor for determining the amount of solar radiation absorbed in the NSTM layer, while halocline strength controlled the amount of heat removed from the NSTM by turbulent transport. Observations using the Naval Postgraduate School Turbulence Frame show that the NSTM was able to persist despite periods of intermittent turbulence because transport rates were too small to remove significant amounts of heat from the NSTM layer. The development of the early and late summer halocline and NSTM were found to be linked to summer season buoyancy and wind events. For the early summer NSTM, 1-D boundary layer model results show that melt pond drainage provides sufficient buoyancy to the summer halocline to prevent subsequent wind events from mixing out the NSTM. For the late summer NSTM,limited freshwater inputs reduce the strength of the summer halocline making the balance between interfacial stresses and buoyancy more tenuous. As a result, the late summer NSTM is an ephemeral feature dependent on local wind conditions, while the early summer NSTM is more persistent and able to store heat in the near-surface ocean beyond the summer season.

A Generalized Corcos model for modelling turbulent boundary layer wall pressure fluctuations

A turbulent boundary layer (TBL) can be an important source of noise and vibration and its simulation is still an open research challenge. The stochastic pressure distribution associated with turbulence can significantly excite a structure that radiates acoustic power. In such a situation, a good description of the wall pressure field is necessary for an accurate prediction of the vibration and noise propagation. In order to tackle this issue, many TBL models have been developed since the 50s. Among others, the Corcos model has been widely used, especially because of its advantageous mathematical features. However, a major drawback is the small rate of decay for wavenumbers below the coincidence frequency.This paper presents a novel Generalized Corcos model that allows controlling the decay in the wavenumber domain below the convective peak, yet preserving similar mathematical advantages. Such a model is built on a two-dimensional Butterworth filter, whose orders allow to modify the shape of the TBL and possibly to adapt it to different flow configurations. The main aim of this work is to compare and position the Generalized Corcos model with respect to the existing models and to highlight its possible applications.

Математическое моделирование интенсифицированного теплообмена при турбулентном течении в продольно омываемых пучках труб с поперечными кольцевыми канавками с применением компаундной трёхслойной модели турбулентного пограничного слоя

Математическое моделирование интенсифицированного теплообмена при турбулентном течении в продольно омываемых пучках труб с поперечными кольцевыми канавками с применением компаундной трёхслойной модели турбулентного пограничного слоя