Typical Aero‐Optical Flows

The flow structure and turbulence in an open cavity shear layer has been investigated experimentally at a Reynolds number of$4. 0\times 1{0}^{4} $, with an emphasis on interactions of the unsteady pressure field with the cavity corners. A large database of time-resolved two-dimensional PIV measurements has been used to obtain the velocity distributions and calculate the pressure by spatially integrating the material acceleration at a series of sample areas covering the entire shear layer and the flow surrounding the corners. Conditional sampling, low-pass filtering and time correlations among variables enable us to elucidate several processes, which have distinctly different frequency ranges, that dominate the shear layer interactions with the corners. Kelvin–Helmholtz shear layer eddies have the expected Strouhal number range of 0.5–3.2. Their interactions with the trailing corner introduce two sources of vorticity fluctuations above the corner. The first is caused by the expected advection of remnants of the shear layer eddies. The second source involves fluctuations in local viscous vorticity flux away from the wall caused by periodic variations in the streamwise pressure gradients. This local production peaks when the shear layer vortices are located away from the corner, creating a lingering region with peak vorticity just above the corner. The associated periodic pressure minima there are lower than any other point in the entire flow field, making the region above the corner most prone to cavitation inception. Flapping of the shear layer and boundary layer upstream of the leading corner occurs at very low Strouhal numbers of ∼0.05, affecting all the flow and turbulence quantities around both corners. Time-dependent correlations of the shear layer elevation show that the flapping starts in the boundary layer upstream of the leading corner and propagates downstream at the free stream speed. Near the trailing corner, when the shear layer elevation is low, the stagnation pressure in front of the wall, the downward jetting flow along this wall, the fraction of shear layer vorticity entrained back into the cavity, and the magnitude of the pressure minimum above the corner are higher than those measured when the shear layer is high. However, the variations in downward jetting decay rapidly with increasing distance from the trailing corner, indicating that it does not play a direct role in a feedback mechanism that sustains the flapping. There is also low correlation between the boundary/shear layer elevation and the returning flow along the upstream vertical wall, providing little evidence that this returning flow affects the flapping directly. However, the characteristic period of flapping, ∼0.6 s, is consistent with recirculation time of the fluid within the cavity away from boundaries. The high negative correlations of shear/boundary layer elevation with the streamwise pressure gradient above the leading corner introduce a plausible mechanism that sustains the flapping: when the shear layer is low, the boundary layer is subjected to high adverse streamwise pressure gradients that force it to widen, and when the shear layer is high, the pressure gradients decrease, allowing the boundary layer to thin down. Flow mechanisms that would cause the flapping-induced pressure changes, and their relations to the flow within the cavity are discussed.

Heat, mass and momentum transfer in separated flows. The simple model of a backward‐facing step in flat plate boundary layers provides basic information on heat, mass and momentum transfer in local separated regions. These new investigations cover nearly the whole range of existence of incompressible separated flows with laminar as well as turbulent boundary layers at separation, including the two main parameters Reδ1 and Res: The Reynolds number Reδ1 represents the boundary layer at separation, the Reynolds number Res the shape of the body. It is demonstrated that independently of the state of the boundary layer at separation, there exist three types of local separated regions. Therefore a new general valid classification of local separated flows is introduced based on the actual state of the separated boundary (shear) layer from separation to reattachement. The new results presented are limited to the case where no temperature or concentration boundary layers exist at separation, i.e. to the case of unheated or inert starting length before separation: Only then can the analogy of heat, mass and momentum transfer give useful results over the whole range of existence of local separated regions. A new shear layer model is introduced to facilitate transfer of the results obtained for backward‐facing steps to arbitrary shaped bodies. A compilation and comparison of available literature values shows that this shear layer model for the step also permits the calculation of heat and mass transfer in separated areas on arbitrarily shaped bodies.

The paper discusses approaches to the construction of integral models of the convective boundary layer (CBL), based on the concept of complete mixing. To test analytic bulk models and the basic hypotheses of similarity, we use the results of eddy modeling (LES – Large Eddy Simulation). The empirical constants of the CBL integral models obtained according to the LES data for the case of free convection, are in good agreement with the previously published data of laboratory experiments. It is also shown that the flow of kinetic energy from the upper boundary of the CPS, carried out by gravitational waves, is small compared with other components of the balance of turbulent kinetic energy (TKE) in the convective layer. Parametrization of TKE generation for the case of sheared convective boundary layer in terms of the friction velocity and the average wind velocity in the CBL derived; resulting dimensionless constants are obtained from LES data. The results of the work allow us to formulate an integral model of the shear KPS suitable for practical use.

This paper serves as part II of a two-part tutorial on "aero-optical effects." In part I, we provide introductory material with an emphasis on system-level considerations, particularly for those who are new to the field of aero-optics. In part II, we move on to survey several sources of aberrations. For example, we cover foundational sources like boundary layers and shear layers, as well as miscellaneous sources like mechanical contamination, shock waves, and aero acoustics. Throughout part II, we emphasize drivers for system-level performance, which appropriately builds on the system-level considerations covered in part I. This emphasis will inform future efforts looking to develop airborne-laser systems flying at subsonic, supersonic, and hypersonic speeds.

In any application of wall-bounded or shear fluid flows, near-wall boundary layer and shear layer are the places of struggle between viscous and inertial forces.After development and spread of using wall functions for modeling near-wall region of boundary layer in wall-bounded turbulent flows, the importance of accurate prediction and modeling of different layers of boundary layer, particularly the so-called logarithmic layer becomes more crucial in aerodynamics.Due to the intrinsic characteristics of flow structure in log-layer and wide-spread applications of wake flows, the presence of these characteristics in wake flows rather than wall-bounded flows opens a new window to the researchers to investigate the possibility of using log-law within wake regions, particularly on wake centerline for modeling purposes.On the applications of wake modeling and studying, we can point out to wing and blade trailing edge design, exhaust flow of pipes and ducts (e.g.nozzle exhaust or internal flow of polymers in dimpled pipes), and vortex generator design which are just a few examples of the areas with great interest in both fundamental scientific research, that is, developing optimum and accurate Computational Fluid Dynamics (CFD) tools and their industrial applications.In this article, a brief description about different approaches, previous efforts and case studies, and similar analogous problems is presented to give a better perception to the future researchers.

Partial melting in a thermo-chemical boundary layer at the base of the mantle

Slender wing vortex flows at subsonic, transonic, and supersonic speeds were investigated in a 6 x 6 ft wind tunnel. Test data obtained include off-body and surface flow visualizations, wing upper surface static pressure distributions, and six-component forces and moments. The results reveal the transition from the low-speed classical vortex regime to the transonic regime, beginning at a freestream Mach number of 0.60, where vortices coexist with shock waves. It is shown that the onset of core breakdown and the progression of core breakdown with the angle of attack were sensitive to the Mach number, and that the shock effects at transonic speeds were reduced by the interaction of the wing and the lead-edge extension (LEX) vortices. The vortex strengths and direct interaction of the wing and LEX cores (cores wrapping around each other) were found to diminish at transonic and supersonic speeds.

Effects of shear and potential temperature gradient on the formation mechanism and turbulence characteristics of the sheared convective boundary layer are studied through Large-Eddy Simulation (LES) experiments. Four cases with different velocity difference ΔU of 1.5ms−1 and 3.0ms−1 and different potential temperature gradient Γθ of 0.006Km−1 and 0.015Km−1 were conducted in the horizontal homogeneous atmospheric convective boundary layer of 6000m × 6000m × 2000m. The results show that the formation of the entrainment layer is affected integratedly by the horizontal shear effect and the vertical buoyancy effect, in which turbulence shows strong anisotropy and intermittent characteristics, wherein the mixed layer is dominated by stable small eddies, and the entrainment layer by strip-shaped large eddies. Compared with the pure buoyancy boundary layer, the entrainment flux ratio Af is 0.176∼0.385, and the height of the entrainment layer zi is shifted to the side with bigger velocity (U2). ΔU promotes entrainment and Γθ inhibits, especially for the upper limit of the entrainment layer h2. Obviously, the shear-shelter entrainment phenomenon appears under the weak shear and strong potential temperature gradient.

<p>Turbulence in the atmospheric boundary layer (ABL) plays an important role in the weather and climate system as it governs the meteorological exchanges of momentum, energy, and moisture between the free atmosphere and the Earth’s surface. Motivated by the need for conceptual physics-based models that parameterize turbulence in the ABL in terms of spectra at all spatio-temporal scales, we explore a linear random advection approach to characterize different scenarios of sheared convective boundary layer flows. As a main result, we obtain the wavenumber–frequency spectrum as a product of the wavenumber spectrum and a Gaussian frequency distribution, whose mean and variance are given by the mean advection and random sweeping velocities, respectively. The applicability of the model is evaluated with direct numerical simulations of the mixed layer and entrainment zone for the streamwise and vertical velocity components as well as buoyancy. To obtain a fully analytical formula for the linear random advection approach, we propose using a von-Kàrmàn wavenumber spectrum parameterized by the characteristic convective velocity and length scales. These scales are height-dependent and vary considerably with the relative balance of buoyancy and shear forces. The comparison of the von-Kàrmàn-based model for velocity and buoyancy to simulation results shows that the main features of the measured spectra are captured by the model. </p>

Predicting the heat flux through a horizontal layer of fluid confined between a hot bottom plate and a cold top one has always spurred theoretical, numerical and experimental work on Rayleigh–Bénard convection. Customarily, the Nusselt number (the heat flux in non-dimensional form) has been modelled in the form of one or several power-laws of three parameters, the Rayleigh, Prandtl and Reynolds numbers. Quantifying the large-scale flow that spontaneously develops in a turbulent Rayleigh–Bénard cell, the Reynolds number, unlike the Rayleigh and Prandtl numbers, is not a control parameter strictly speaking and, depending on the model, is sought as another power-law or introduced as an external input. Whereas balancing the different transport mechanisms can predict the exponents in these power laws, experimental and numerical results are required to adjust the various prefactors. The early and simple model of Malkus (1954) and Howard (1966) assumed that the value of the Nusselt number could be directly deduced from the marginal stability of the two sheared thermal boundary layers along the upper and lower plates, interacting via the large-scale flow. Maintaining this simplicity, this work shows that in the classical regime of turbulent convection, considering the linear critical conditions of absolute (as opposed to convective) thermo-convective instabilities alleviates the flaws of the original model. Revisiting available Direct Numerical Simulations from which a Reynolds number can be unambiguously extracted, the present approach then yields the Nusselt number as a function of the Rayleigh and Prandtl numbers agreeing well with the numerical results.

Numerical simulations of boundary layer evolution in offshore flow of warm air over cool water are conducted and compared with aircraft observations of mean and turbulent fields made at Duck, North Carolina. Two models are used: a two-dimensional, high-resolution mesoscale model with a turbulent kinetic energy closure scheme, and a three-dimensional large-eddy simulation (LES) model that explicitly resolves the largest turbulent scales. Both models simulate general aspects of the decoupling of the weakly convective boundary layer from the surface, as it is advected offshore, and the formation of an internal boundary layer over the cool water. Two sets of experiments are performed, which indicate that complexities in upstream surface conditions play an important role in controlling the observed structure. The first (land–sea) experiments examine the transition from a rough surface having the same temperature as the ambient lower atmosphere, to a smooth ocean surface that is 5°C cooler. In the second (barrier island) experiment, a 4-km strip along the coastline having surface temperature 5°C warmer than the ambient atmosphere is introduced, to represent a narrow, heated barrier island present at the Duck site. In the land–sea case, it is found that the mesoscale model overpredicts turbulent intensity in the upper half of the boundary layer, forcing a deeper boundary layer. Both the mesoscale and LES models produce only a small change in the boundary layer shear and tend to decrease the momentum flux near the surface much more rapidly than the observations. Results from the barrier-island case are more in line with the observed momentum and turbulence structure, but still have a reduced momentum flux in the lower boundary layer in comparison with the observations. The authors find that turbulence in the LES model generated by convection over the heated land surface is stronger than in the mesoscale model, and tends to persist offshore for greater distances because of greater shear in the upper boundary layer winds. Analysis of the mesoscale model results suggests that better estimation of the mixing length could improve the turbulence closure in regions where the surface fluxes are changing rapidly.

This paper assesses the importance of viscothermal effects for acoustics calculations in lined ducts, both inside and outside of a finite-thickness compressible boundary layer using a combination of asymptotics and numerics. Viscosity is always present, even at the high Reynolds numbers associated with aeroacoustics. The large majority of aeroacoustic calculations are performed inviscidly, however. Existing inviscid impedance boundary conditions (e.g. Myers) have failed in predicting experimental results, and it is suggested that viscosity is the key to accurate computations. Here, numerical solutions of the Linearized Navier–Stokes equations are compared to inviscid numerics inside a sheared boundary layer to quantify the errors associated with neglecting viscosity. It is found that invisicd errors are strongly dependent on frequency, with normalised errors of over 10% common at low frequencies. It is suggested that errors increase with Mach number, though the dependence is weaker than that of frequency. Viscothermal effects are also shown to be as important as shear. Existing impedance boundary conditions rely on the assumption that the acoustics outside the boundary layer are the same as they would be in a completely uniform inviscid flow. This assumption, that the near-wall effects of shear and viscous dissipation do not penetrate far into the duct, is tested here by comparing analytic expressions for the uniform acoustics with viscous numerics. It is found that errors outside a 99% boundary layer are on average 0.006% for the pressure and 0.1% for the radial velocity, validating this assumption Three existing impedance boundary conditions are tested against full viscous numerics and are found to be inadequate for modelling the possibly unstable surface modes. A new asymptotic boundary condition is derived that combines the regularising effect of a finite-thickness shear layer with viscosity and thermal conduction to accurately capture the physics of a boundary layer over an acoutic lining. Comparisons of the new boundary condition with viscous numerics are extremely positive, and due to the decoupling of the Reynolds number and boundary layer thickness in the derivation the condition may be used for any flow. The new condition correctly predicts the stability of modes as parameters vary. Though an analytic form of the new condition is not found, it is suggested that it could be incorporated into a boundary solver at minor computational cost.

Although erosion during high-energy passage of a pyroclastic density current (PDC) causes great damage, analyses of the effects of such erosion are sparse in scientific literature compared to observations and interpretations of depositional processes. In this paper, we review observations of surfaces where PDCs have eroded sets of grooves that provide information on the erosion process. We postulate that in some cases, the grooves were carved by streamwise vortices in the boundary layer of the PDC and review possible fluid dynamic instabilities that can give rise to such vortices. For the prominent grooves at Volcán Bárcena, Mexico, we propose that a fluid dynamic instability, which we dub the “groovy instability,” occurred and caused formation of erosive counter-rotating vortices. This instability occurs when the particle concentration boundary layer thickness, δc, is larger than the velocity (shear) boundary layer thickness, δu, i.e., L=δc /δu>1. In subaqueous turbidity currents, these vortices have a typical wavelength of ~25*δc. If this relation is applied to the grooves formed on Volcán Bárcena, the inferred particle concentration boundary layer is estimated to have been <1 m thick. We postulate that a transition between erosion of grooves and deposition of dunes at Volcán Bárcena occurred when hydraulically supercritical flow on the upper flanks changed to subcritical flow about halfway down the mountain. We call attention to boundary layer dynamics in erosive pyroclastic density currents at a dimension that is difficult to scale quantitatively in laboratory experiments and is usually not resolved computationally and to the need for incorporating such dynamics into models of PDC dynamics.

The Corcos wall pressure model was modified to incorporate surface roughness effects. The longitudinal cross-spectral density part of the Corcos model was modeled from rough wall data taken from the literature. The wall pressure frequency spectrum was nondimensionalized by the wall shear stress and boundary layer displacement thickness and shown to fit both smooth and rough wall data. The boundary layer parameters were obtained from a finite-difference boundary layer code developed by the author to account for surface roughness effects by the discrete roughness approach [G. H. Christoph and R. H. Pletcher, AIAA J. 21, 509–515 (1983)]. The blockage of the roughness height, shape and spacing is explicitly accounted for in this approach. Flow noise was calculated for a variety of roughness element heights and spacings in air and in water. The calculations clearly show that element spacing as well as height is important and that the viscous sublayer height, not the boundary layer thickness, determines the influence of roughness on flow noise. Thus roughness is typically more important in water than in air because of the thinner viscous sublayer. Also, the effect of transducer size and viscoelastic layer thickness are shown for rough surfaces.

Experiments examining the effect of surface roughness on vortex-induced vibration (VIV) and drag of flexible cylinders at critical and supercritical Reynolds numbers have been conducted. Four levels of surface roughness were tested for their effect on VIV and drag of a circular cylinder that was 20 diameters upstream of a downstream cylinder (i.e. effectively an isolated cylinder). The rougher cylinders experienced vibrations of up to 3rd mode (in transverse bending). A surprising discovery was that the smooth cylinder experienced low drag and virtually no VIV as the boundary layers became turbulent in the critical Reynolds number range. Introduction and Background The study of flow separation and vortex shedding past a circular (or approximately circular) cylinder has a long history. Simple observation of flow past a vertical stick or reed in a stream indicates that man has probably observed this phenomenon well before recorded history. Similarly, vortexinduced vibration (VIV), which results when something free to move experiences vortex shedding, has an equally long history. The vibration felt when attempting to move one's arm through the water as fast as possible is evidence that VIV was also observed in antiquity. A parameter that strongly influences flow past a circular cylinder is the Reynolds number (Re), which represents the ratio of the convective forces to the diffusive forces, defined as Re=V*D/?. Another important parameter, for the purposes of this paper, is the surface roughness k/D, where k is the average "peak to trough" height of the surface protrusions. Figure 1 illustrates the basics of flow past a circular cylinder. As the fluid approaches the cylinder, a thin boundary layer (exaggerated in the figure for illustration purposes) forms on each side of the cylinder (shown on only one side). The fluid closest to the cylinder wall is impeded by friction on the cylinder's surface, hence the region between the wall and where the velocity is close to that of the free stream is known as the boundary layer. As the boundary layer fluid proceeds around the cylinder surface, the retardation of the fluid near the surface eventually causes it to come to a halt, thereby resulting in separation of the boundary layer into a "shear layer". Because the outer fluid in the shear layer is moving faster than the inner fluid of the shear layer, the layer rolls up into a vortex. For Reynolds numbers larger than about 40, the vortex pattern is unstable, and thus there is an alternating vortex street that is shed from the cylinder. Numerous studies have been made of flow past a stationary circular cylinder, most of these with air as the flowing fluid1–6. These studies have covered Reynolds numbers well exceeding 1×107. Figure 2 illustrates the general relationship that these studies have found between drag coefficient (defined as Cd = Fd/(0.5*?*V2*D*L) and Reynolds number for flow past a stationary cylinder. This figure shows that, at a Reynolds number of about 1×105 (the "critical" Reynolds number range), the drag coefficient diminishes dramatically, a phenomenon known as the "drag crisis". This corresponds to a change in the boundary layers from laminar to turbulent.