Reynolds Number Boundary Layer Research Articles

The differential precession of Earth’s fluid and solid cores

The Earth’s spin axis is inclined by ∊=23.4° with respect to the ecliptic normal and precesses in space with a period of 26 kyr. The fluid core and solid inner core precess at slightly different angles. Here, we compute their differential precession angles on the basis of an elastically deforming Earth and dissipative torques inferred from nutation observations. We show that the precession angle of the fluid core is larger than that of the mantle by 1.714 arcsec and lags behind it by 0.0124 arcsec. The precession angle of the spin (and figure) axis of the inner core is smaller than that of the mantle by 1.861 arcsec and trails behind it by 3.660 arcsec. These correspond to differential velocities (Δv) at the core mantle boundary (CMB) and inner core boundary (ICB) of 2.11 and 2.21 mm/s, to associated boundary layer Reynolds (Re) numbers of 247 and 258, and to dissipations D of 4.6 and 14.5 GW. At such Re values the flow in the core should feature wavelike instabilities but should not be in a fully developed turbulent regime. Δv and Re at the CMB have remained approximately constant in the past 4 Gyr, and D has been steadily decreasing from a maximum of approximately double its present-day value. At the ICB, Δv,Re and D have all increased since inner core formation. Future projections indicate that Re and D at the ICB may reach 500 and 100 GW, respectively, in a few Gyr. Our results suggest that, for the whole of Earth’s history, dissipation from the misaligned precession of the fluid and solid cores has contributed only a small fraction of the total heat flux out of the core and has not provided an important power source for maintaining the geodynamo.

대형 비행갑판을 갖는 함정과 풍동시험 결과를 활용한 고신뢰도 함정 Airwake 예측

Developing high-fidelity Computational Fluid Dynamics (CFD) simulation methods used to evaluate the airwake characteristics along a flight deck of a large ship, the various kind of data such as actual ship measurement and wind tunnel results are required to verify the accuracy of CFD simulation. Inflow velocity profile at the bow, local unsteady flow field data around the flight deck, and highly reliable wind tunnel data which were measured after reviewing Atmospheric Boundary Layer (ABL) simulation and Reynolds Number effects were also used to determine the key parameters such as turbulence model, time resolution and accuracy, grid resolution and type, inflow condition, domain size, simulation length, and so on in STAR CCM+. Velocity ratio and turbulent intensity difference between Full-scale CFD and actual ship measurement at the measurement points show less than 2% and 1.7% respectively. And differences in velocity ratio and turbulence intensity between wind tunnel test and small-scale CFD are both less than 2.2%. Based upon this fact, the selected parameters in CFD simulation are highly reliable for a specific wind condition.

150USRT Class R-513A Refrigerant Two-Stage Centrifugal Compressor Design Point and Separation Point Flow Field Simulation Analysis

This study used computational fluid dynamics for low greenhouse effect refrigerant (R-513A) simulation analysis in the two-stage 150 USRT class oil-free centrifugal refrigerant compressor using integrated part load value (IPLV) and internal flow field. The compressor rotor speed and mass flow rate for the IPLV working conditions with various loads were planned using Stage 1 and Stage 2 simulations, respectively. The performance and flow field numerical simulation analyses for the two-stage centrifugal compressor is discussed. This study used Ansys-CFX software for numerical simulation analysis and the conservation form of a 3D steady-state Navier–Stokes equation set with the finite volume discretization method for computation. The computing mode produced better computing efficiency and flexible mesh setting using the k-omega (k-ω) model, which has better computational performance in the near wall boundary layer and low Reynolds number flow field (used as the turbulence model) for simulation. The R-513A refrigerant property setting was calculated using the Soave–Redlich–Kwong gas equation. This study discusses the shaft work, pressure ratio, and isentropic efficiency and also describes the main research findings with the meridional pressure, isentropic efficiency contour maps, and flow field velocity vector diagrams. According to the numerical simulation results, in Stage 1 and Stage 2 simulations, the isentropic efficiency produced the highest numerical results in the 75% load case, which are 88.19% and 89.06%, respectively. The isentropic efficiency decreased to 75.93% and 82.26%, respectively, in the 25% load case. The flow field velocity vector diagram shows that in the 25% load case, there was back-flow field distribution near the impeller shroud. The compressor performance was also analyzed.

Determination of Non-Eroding Discharge Based on the Threshold Velocity of Particle Motion and Soil Texture Triangle in Irrigation Furrows

One of the common methods to prevent the erosion of the furrows’ bed is to enter the water flow with a discharge less than the maximum of eroding discharge. Accordingly, it is important to determine the threshold velocity of the bed particle motion. In the current study, the average diameter of particles in each soil class was determined using 12 available classes in the soil texture triangle and then in an irrigation furrow with a fixed bed and triangular cross section, the threshold velocities were calculated using the equations provided by El-Zaemey, Novak, Nalluri and Charles Heinz Bong and compared them with proposed values of Walker et al and the US Department of Soil Conservation. The results were also compared with the Shields graph by determining the Shields parameter and boundary layer Reynolds number in the slope range of 0.5% to 1% for each soil texture class. A graph was presented based on all the above mentioned methods to simplify the use of the results. In addition to specifying the difference in velocity values predicted ​​by different methods, the graph can be also used to determine the maximum permissible velocity in furrows.

Compressible modification of boundary-layer momentum thickness localized method in transition model

In current transition models, Menter’s correlation between the maximum vorticity Reynolds number Revmax in the boundary layer and momentum thickness Reynolds number Reθ has been widely used in the localization of the boundary layer length scale. However, the existing correlations have problems in correctly reflecting compressibility effects and only relying on local variables. In this paper, the similarity solutions of laminar compressible boundary layer equations are adopted to study the relation between Revmax and Reθ. Through extracting the local Mach number Malocal and the ratio of wall temperature to the local temperature Tw/Tlocal right at the position where Revmax happens, the influences of the Mach number effect and wall heat transfer effect are characterized, meanwhile a new correlation only relying on local variables between Revmax and Reθ is proposed. For plat-plate boundary layers, the relative error is tiny within a large Mach number and wall-to-adiabatic temperature ratio range and the error caused by the streamwise pressure gradient is not of great concern for general pressure gradients. Furthermore, numerical results over common geometries, including wedges, sharp cones and blunt cones, demonstrate that the proposed correlation could give much better predictions of the relation between Revmax and Reθ than previous correlations. At last, the present correlation is applied to the γ-Reθ transition model as an application presentation.

Three-dimensional flow of nanofluid with heat and mass flux boundary conditions

This article presents magnetohydrodynamic three-dimensional flow of nanofluid over an exponentially stretching surface with prescribed heat flux (PHF) and prescribed concentration flux (PCF) conditions. An exponentially stretching surface is used to generate the flow. Effects of Brownian motion, thermophoresis, viscous dissipation and Joule heating are also taken into account. Boundary layer and small magnetic Reynolds number assumptions are considered in the mathematical modeling. The conversion from nonlinear partial differential equations to nonlinear ordinary differential equations is taken into place by using suitable transformations. The resulting nonlinear system is solved via convergent homotopic approach. Graphs are sketched in order to analyze that how the temperature and concentration profiles are affected by distinct physical flow parameters. Skin-friction coefficients and local Nusselt and Sherwood numbers are also computed and analyzed.

A revised model for Jeffrey nanofluid subject to convective condition and heat generation/absorption

Here magnetohydrodynamic (MHD) boundary layer flow of Jeffrey nanofluid by a nonlinear stretching surface is addressed. Heat generation/absorption and convective surface condition effects are considered. Novel features of Brownian motion and thermophoresis are present. A non-uniform applied magnetic field is employed. Boundary layer and small magnetic Reynolds number assumptions are employed in the formulation. A newly developed condition with zero nanoparticles mass flux is imposed. The resulting nonlinear systems are solved. Convergence domains are explicitly identified. Graphs are analyzed for the outcome of sundry variables. Further local Nusselt number is computed and discussed. It is observed that the effects of Hartman number on the temperature and concentration distributions are qualitatively similar. Both temperature and concentration distributions are enhanced for larger Hartman number.

An analytical solution for magnetohydrodynamic Oldroyd-B nanofluid flow induced by a stretching sheet with heat generation/absorption

This article provides an analytical investigation of magnetohydrodynamic (MHD) three-dimensional flow of an Oldroyd-B nanofluid in the presence of heat generation/absorption and convective surface boundary condition. Flow is induced by stretching surface considering the effects of Brownian motion and thermophoresis. The process of heat transfer is examined through the convective boundary condition. Oldroyd-B fluid is taken electrically conducting in the presence of a uniform applied magnetic field. A condition associated with nanoparticles mass flux at the surface is utilized. Problem formulation is made for boundary layer and low magnetic Reynolds number approximations. Suitable transformations are employed to construct the nonlinear ordinary differential equations. The strongly nonlinear differential equations are solved analytically through the optimal homotopy analysis method (OHAM). Effects of various interesting parameters on the temperature and nanoparticles concentration are studied and discussed. The local Nusselt number is also computed and analyzed. Our computations reveal that the temperature distribution has a direct relationship with Biot number and magnetic parameter.

On magnetohydrodynamic flow of second grade nanofluid over a convectively heated nonlinear stretching surface

Here magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching surface with the convective surface boundary condition is examined. Heat and mass transfer characteristics subject to viscous dissipation, Brownian motion and thermophoresis effects are examined. Second grade fluid is electrically conducted in the presence of non-uniformly applied magnetic field. Mathematical formulation for boundary layer and low magnetic Reynolds number assumptions is presented. Newly proposed condition having a zero nanoparticles mass flux at the surface is employed. The partial differential system has been converted into the nonlinear ordinary differential system by using appropriate transformations. The resulting nonlinear system has been solved via convergent approach. Graphs are sketched to analyze the impacts of various physical parameters on the velocity, temperature and nanoparticles concentration distributions. Numerical values of skin friction coefficient and local Nusselt number are computed and discussed.

Magnetohydrodynamic (MHD) three-dimensional flow of second grade nanofluid by a convectively heated exponentially stretching surface

This article deals with the magnetohydrodynamic (MHD) three-dimensional flow of second grade nanofluid in the presence of convective boundary condition. The flow is induced due to an exponentially stretching surface. An electrically conducting fluid in the presence of uniform magnetic field is taken into account. Problem formulation is developed subject to boundary layer and small magnetic Reynolds number assumptions. The systems of nonlinear ordinary differential equations are obtained by using the appropriate transformations. Solutions of governing systems are first established and then convergence has been verified through plots and numerical data. A detailed parametric study is carried out to explore the effects of various physical parameters on the velocity, temperature and nanoparticles concentration profiles. Skin friction coefficients, local Nusselt and Sherwood numbers are tabulated and discussed. Our findings show that the temperature profile has a direct relationship with the magnetic parameter and Biot number.

Logarithmic Velocity Profile for Turbulent Flow in Straight Rough Pipe and Evaluation of Karman Constant with Boundary Layer Reynolds Number- A Complete Solution

Logarithmic Velocity Profile for Turbulent Flow in Straight Rough Pipe and Evaluation of Karman Constant with Boundary Layer Reynolds Number- A Complete Solution

Ventilated cavity flow over a backward-facing step

Ventilated cavities detaching from a backward facing step (BFS) are investigated for a range of upstream boundary layer thicknesses in a cavitation tunnel. The upstream turbulent boundary layer thickness is varied by artificial thickening of the test section natural boundary layer using an array of transversely injected jets. Momentum thickness Reynolds numbers from 6.6 to 44 x 103 were tested giving boundary layer thickness to step height ratios from 1.25 to 3.8. A range of cavity lengths were obtained by variation of the ventilation flow rate for several freestream Reynolds numbers. Cavity length to step height ratios from 20 to 80 were achieved. Cavity length was found to be linearly dependent on ventilation rate and to decrease with increasing boundary layer thickness and/or Reynolds number. This result may have implications in the practical optimization of these flows which occur in applications such as drag reduction on marine hull forms.

Effect of Reynolds number on compressible convex-corner flows

An experimental study was conducted to investigate the effect of Reynolds number on compressible convex-corner flows, which correspond to an upper surface of a deflected flap of an aircraft wing. The flow is naturally developed along a flat plate with two different lengths, resulting in different incoming boundary layer thicknesses or Reynolds numbers. It is found that boundary layer Reynolds number, ranging from <TEX>$8.04{\times}10^4$</TEX> to <TEX>$1.63{\times}10^5$</TEX>, has a minor influence on flow expansion and compression near the corner apex in the transonic flow regime, but not for the subsonic expansion flow. For shock-induced separated flow, higher peak pressure fluctuations are observed at smaller Reynolds number, corresponding to the excursion phenomena and the shorter region of shock-induced boundary layer separation. An explicit correlation of separation length with deflection angle is also presented.

Numerical investigation of the generation and growth of coherent flow structures in a triggered turbulent spot

AbstractMultiple mechanisms for the regeneration of hairpin-like coherent flow structures in transitional and turbulent boundary layers have been proposed in the published literature, but a complete understanding of the typical topologies of coherent structures observed in the literature has not yet been achieved. To contribute to this understanding, a numerical study is performed of a turbulent spot triggered in a zero-pressure-gradient laminar boundary layer by a pulsed, transverse jet. Two direct numerical simulations (DNS) capture the growth of the spot into a mature turbulent region containing a large number of coherent vortical flow structures. The boundary-layer Reynolds number based on the test-surface streamwise length is $\mathit{Re}_{L}=309\,200$. The internal structure of the spot is characterized by densely spaced packets of hairpin vortices. Lateral growth of the spot occurs as new hairpin vortices form along the spanwise edges of the spot. The formation of these hairpin vortices is attributed to unstable shear layers that develop in the streamwise–spanwise plane due to the wall-normal motions induced by the streamwise oriented legs of hairpin vortices within the spot. Results are presented that highlight the mechanism by which the instability of such shear layers forms wavepackets of hairpin vortices; how the formation of these vortices produces a flow environment that promotes the creation of new hairpin vortices; and how the newly created hairpin vortices impact the production of turbulence kinetic energy in the flow region surrounding the spot. A quantitative description of the hairpin-vortex regeneration mechanism based on the transport of the instantaneous vorticity vector is presented to illustrate how the velocity and vorticity fields interact with the local strain rates to promote the growth of coherent vortical structures. The simulation results also shed light on a mechanism that seems to have a dominant influence on the formation of the calmed region in the wake of the turbulent spot.

Influence of tank hydrodynamics on vertical oxygen stratification in flatfish tanks

In sole (Solea spp.) culture, like in other flatfish culture, it is likely that a vertical gradient of dissolved oxygen (DO) occurs with the lower concentrations being at the tank bottom. This lower concentration at the tank bottom is a consequence of fish oxygen consumption and of the presence of the boundary layer. This fact generates lower DO concentrations in the near-bottom zone where soles are lying most of the time. The aim of this work was to study the hydrodynamic conditions that determine the oxygen gradient that occurs in the layer of water adjacent to flatfish.Three flow rates were tested in a circular tank and in a rectangular or raceway tank. For each flow rate, water velocities, boundary layer thickness and Reynolds number were calculated. Results showed that the vertical gradient of dissolved oxygen diminishes when water velocity and Reynolds numbers (Re) increase. At the fish density used in this work (11.6kgm−2), when Re decreased under 6000, a large increase in the DO gradient was observed. Guidelines are presented to determine in which situations, as defined by hydraulic parameters, Re>6000 is achieved and DO stratification avoided.The present work shows that in raceways, the flow rate required to avoid DO stratification is higher than that typically needed to maintain water quality (oxygen, ammonia-nitrogen, carbon dioxide and suspended solids). In circular tanks, it can be easier to achieve velocities that are high enough to avoid stratification with low water inlet flow rates, by adjusting the area of the water entry orifices.

Mars Science Laboratory Heat Shield Aerothermodynamics: Design and Reconstruction

The Mars Science Laboratory heat shield was designed to withstand a fully turbulent heat pulse using information from ground testing and computational analysis on a preflight design trajectory. Instrumentation on the flight heat shield measured in-depth temperatures to permit reconstruction of the surface heating. The data indicate that boundary-layer transition occurred at five of seven measurement locations before peak heating. Data oscillations at three pressure measurement locations may also indicate transition. This paper presents the heat shield temperature and pressure data, possible explanations for the timing of boundary-layer transition, and a comparison of reconstructed and computational heating on the actual trajectory. A smooth-wall boundary-layer Reynolds number that was used to predict transition is compared with observed transition at various heat shield locations. A single transition Reynolds number criterion does not uniformly explain the timing of boundary-layer transition observed during flight. A roughness-based Reynolds number suggests that transition due to discrete or distributed roughness elements occurred. However, the distributed roughness height from acreage heat shield material would have needed to be larger than expected. The instrumentation confirmed the predicted location of maximum turbulent heat flux near the lee-side shoulder. The reconstructed heat flux at that location is bounded by smooth-wall turbulent convective heating, indicating that a significant augmentation due to surface roughness did not occur. Turbulent heating on the downstream side of the heat shield nose exceeded smooth-wall convective levels, assuming a supercatalytic surface, indicating that roughness may have augmented heating. The stagnation region heating also exceeded calculated convective heating; the cause of elevated heating may be attributed to a combination of shock-layer radiation and a heating augmentation of unknown origin that was also evident in ground test data.

On the Singular Nature of Turbulent Boundary Layers

An estimate is derived for the rate at which, with increasing Reynolds number, the vorticity in turbulent boundary layers is confined to a diminishing fraction of the overall flow domain. For laminar boundary layers this rate is reflected in the self-similar coordinate stretching that determines the Reynolds number scalings for boundary layer growth and skin friction. For the turbulent boundary layer this rate is shown to also derive from an underlying similarity structure. An accounting of the magnitude ordering of terms in the mean dynamical equation for the turbulent boundary layer reveals a four layer structure. This structure forms during the transitional regime, persists for all subsequent Reynolds numbers, and provides a framework for describing the evolution of the boundary layer vorticity and momentum fields. Multiscale analyses that exploit the four layer ordering reveal that two kinds of self-similarities are formally admitted. With increasing Reynolds number, these are shown to be associated with two kinds of scale-separation between the motions characteristic of the velocity and vorticity fields. One pertains to the near-wall spatial confinement of the vorticity field owing to vorticity stretching, and the other pertains to the advective transport of decreasingly smaller scale vortical motions over a domain that approaches the overall flow width as the Reynolds number becomes large. The scalings associated with the self-similar structure indicate that slightly greater than 50% of the total vorticity content is, with increasing Reynolds number, confined to a near-wall layer of diminishing thickness, with the remainder attributable to a domain that approaches the total layer thickness. Within the larger domain at least 50% of the vorticity is concentrated in narrow vortical fissures that also decrease in relative scale with Reynolds number. Spanwise vorticity measurements in laboratory boundary layers and the atmospheric surface layer are shown to be in agreement with the theoretical predictions, but also provide evidence that at sufficiently high Reynolds number, the vortical fissures develop an intermittent internal structure. Collectively, these results indicate that, on average at any given instant, at least 75% of the boundary layer circulation (per unit length) is confined to a region that diminishes like ▪ as the boundary layer Reynolds number, δ += δ uτ/ν →∞.

1042 AN EXPERIMENTAL STUDY ON THE WAKE OF A RECTANGULAR FOREBODY WITH SUCTION APPLIED OVER THE SURFACES

Previous studies have shown that a modification of the boundary layer of a bluff body can change the wake properties like the vortex shedding frequency and the base drag. In the present study the boundary layer has been modified by applying suction over the top and bottom surfaces of a bluff body. A level of suction above a certain threshold has been shown to give an asymptotic suction boundary layer. For the asymptotic suction boundary layer the boundary layer properties become independent of the free stream velocity and hence the boundary layer Reynolds number. The bluff body studied can be described as a rectangular forebody with a smooth leading edge and a blunt trailing edge. Hot-wire anemometry measurements have been carried out in the boundary layer of the forebody. For four different Reynolds numbers, all within the laminar regime, the suction coefficient has been varied in the range from the neutral case to the case for which the asymptotic suction boundary layer is reached. It is observed that as the suction coefficient approaches the asymptotic suction boundary layer threshold, the Strouhal number based on the shedding frequency approaches a constant value. The base pressure decreases as the boundary layer thickness decreases. Furthermore it is shown that the Strouhal number does not always decrease for an increase of the displacement thickness.

The wave-induced boundary layer under long internal waves

The boundary layer formed under the footprint of an internal solitary wave is studied by numerical simulation for waves of depression in a two-layer model of the density stratification. The inviscid outer flow, in the perspective of boundary-layer theory, is based on an exact solution for the long wave-phase speed, yielding a family of fully nonlinear solitary wave solutions of the extended Korteweg–de Vries equation. The wave-induced boundary layer corresponding to this outer flow is then studied by means of simulation employing the Reynolds-averaged Navier–Stokes (RANS) formulation coupled with a turbulence closure model validated for wall-bounded flows. Boundary-layer characteristics are computed for an extensive range of environmental conditions and wave amplitudes. Boundary-layer transition, identified by monitoring the eddy viscosity, is correlated in terms of a boundary-layer Reynolds number. The frictional drag is evaluated for laminar, transitional, and turbulent cases, and correlations are presented for the friction coefficient plus relevant measures of the boundary-layer thickness.

Bleed Interactions in Supersonic Flow

A parametric study is conducted to characterize the flow throughout supersonic flow bleed regions and to investigate the effects of free stream Reynolds number and incoming boundary layer thickness. Numerical solutions of the compressible Navier-Stokes equations are obtained in a domain that includes the passages within a bleed-hole row and plenum in addition to the external flow. A turbulence model based on the two-equation SST model is employed to enable the resolution of large separated flow regions inside the normal bleed holes. Computational results are presented to show the effects of free stream Reynolds number on the external flow above and downstream of the bleed region. Stagnation pressure contours are compared at various stream-wise locations for different incoming boundary layer thicknesses as well. The results show that the freestream Reynolds number has a strong influence on the total pressure distortion and on the secondary flow in the cross sectional planes downstream of the bleed region.