External Boundary Layer Flow Research Articles

Similarity of length scales in high-Reynolds-number wall-bounded flows

The wall dependence of length scales used to describe large- and small-scale structures of turbulence is examined using highly resolved experiments in zero-pressure-gradient turbulent boundary layers and pipe flows spanning the range $2000< Re_\tau <37\ 700$ . Of particular interest is the influence of external intermittency on the scaling of these length scales. It is found that when suitable scaling parameters are selected and external intermittency is accounted for, the dissipative motions follow inner scaling even into the outer-scaled regions of the flow, and that certain large-scale descriptions follow outer scaling even in the inner-scaled regions of the flow. The wall dependence is the same for both internal pipe and external boundary layer flows, and the different length scales can be related to recognizable features in the longitudinal wavenumber spectrum.

Turbulent Skin Friction Reduction through the Application of Superhydrophobic Coatings to a Towed Submerged SUBOFF Body

Abstract In the present study, the drag-reducing effect of sprayed superhydrophobic surfaces (SHSs) is determined for two external turbulent boundary layer (TBL) flows. We infer the modification of skin friction created beneath TBLs using near-wall laser Doppler velocity measurements for a series of tailored SHSs. Measurements of the near-wall Reynolds stresses were used to infer reduction in skin friction between 8%and 36%in the channel flow. The best candidate SHS was then selected for application on a towed submersible body with a SUBOFF profile. The SHS was applied to roughly 60% of the model surface over the parallel midbody of the model. The measurements of the towed resistance showed an average decrease in the overall resistance from 2% to 12% depending on the speed and depth of the towed model, which suggests a SHS friction drag reduction of 4–24% with the application of the SHS on the model. The towed model results are consistent with the expected drag reduction inferred from the measurements of a near-zero pressure gradient TBL channel flow. Introduction Nature has provided a plethora of materials to be studied and mimicked for everyday applications (Jung & Bhushan 2010). One material pertinent for use in the marine environment is the lotus leaf, which is known for its self-cleansing properties and resistance to wetting (Neinhuis & Barthlott 1997). More specifically, lotus-inspired superhydrophobic surfaces (SHSs) have been biomimetically developed for skin friction reduction in various flow applications (Bhushan et al. 2009; Samaha et al. 2012). Being exhaustively studied in small-scale laminar flows (see Rothstein [2010] for a review of SHS drag reduction and slip on SHSs), advances in the design and fabrication of SHSs have permitted application of these materials in more naval-relevant flows. Previously, it has been shown that in laminar flow, SHSs can reduce drag (Watanabe et al. 1999; Ou et al. 2004; Ou & Rothstein 2005; Zhao et al. 2007; Daniello et al. 2009; Woolford et al. 2009), and in low–Reynolds number turbulent flows, SHS drag reduction has been observed using small-scale, structured surfaces and large air–water interfaces (Henoch et al. 2006; Daniello et al. 2009; Park et al. 2014). However, these surfaces, in higher turbulence flows, can be unstable or become wetted. If the SHS possesses roughness features with small scales compared with the viscous length scale of the flow, researchers have demonstrated SHS friction drag reduction for wall-bounded, high–Reynolds number turbulent flows (Zhao et al. 2007; Aljallis et al. 2013; Bidkar et al. 2014; Golovin et al. 2016; Ling et al. 2016b; Gose et al. 2018a).

Rough Surface Turbulent Boundary Layer Heat Transfer Using Generalized Reynolds Analogies

Abstract Stanton number, St, calculations as a function of position, x, are made for turbulent, external boundary layer flow over aerodynamically rough surfaces and also for a fully developed duct flow with rough top and bottom surfaces. This is accomplished with three different forms of generalized Reynolds analogies from the literature and also with a new data correlation developed with the aid of the thermal inner and outer layers. Comparison of these predicted values of St with experimental data, from the literature, is made for several favorable equilibrium, one nonequilibrium, and a zero pressure gradient as well as a duct flow over “real” roughness patterns. Predictions compare reasonably well with the data for some of the generalized Reynolds analogies.

Mathematical Modelling of Hydromagnetic Casson non-Newtonian Nanofluid Convection Slip Flow from an Isothermal Sphere

Abstract In this article, the combined magnetohydrodynamic heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid from an isothermal sphere surface with convective condition under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. magnetic parameter (M), Buoyancy ratio parameter (N), Casson fluid parameter (β), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr) and thermal slip (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Increasing viscoplastic (Casson) parameter decelerates the flow and also decreases thermal and nano-particle concentration. Increasing Brownian motion accelerates the flow and enhances temperatures whereas it reduces nanoparticle concentration boundary layer thickness. Increasing thermophoretic parameter increasing momentum (hydrodynamic) boundary layer thickness and nanoparticle boundary layer thickness whereas it reduces thermal boundary layer thickness. Increasing magnetohydrodynamic body force parameter decelerates the flow whereas it enhances temperature and nano-particle (species) concentrations. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

Mathematical analysis of non-Newtonian nanofluid transport phenomena past a truncated cone with Newtonian heating

In the present study, we analyze the heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid past a truncated cone surface with Biot Number effect is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer Biot Number effect. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via. Appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. Casson fluid parameter (?), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Buoyancy ratio parameter (N ), Prandtl number (Pr) and Biot number (Bi) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Validation of solutions with a Nakamura tri-diagonal method has been included. The study is relevant to enrobing processes for electric-conductive nano-materials of potential use in aerospace and other industries.

Numerical Study of Hydromagnetic Non-Newtonian Nanofluid Transport Phenomena from a Horizontal Cylinder with Thermal Slip: Aerospace Nanomaterial Enrobing Simulation

In this article, the combined magnetohydrodynamic heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid from a horizontal circular cylinder surface with convective condition under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. magnetic parameter (M), Casson fluid parameter (β), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr) and thermal slip (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Validation of solutions with a Nakamura tridiagonal method has been included. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

A Relatively Simple Integral Method for Turbulent Flow Over Rough Surfaces

The integral form of the equation for x momentum is solved for the skin friction coefficient, in external thin boundary layer flow, on surfaces whose technical roughness elements' size is given. This is done by using a “roughness depression function” in the law of the wall and wake which serves as the needed velocity profile. The method uses the equivalent sand grain size concept in its calculations. Predictions are made of the friction coefficient, Cf, as a function of momentum thickness Reynolds number and also, of Cf's dependence on the ratio of momentum thickness to the size of the technical (actual) roughness elements. In addition, boundary layer thicknesses and velocity profiles on rough surfaces are calculated and, when available, comparisons are made with the experimental data from a number of sources in the literature. Also, comparisons are made with the results of another major predictive scheme which does not use the equivalent sand grain concept.

Hydromagnetic non‐Newtonian nanofluid transport phenomena from an isothermal vertical cone with partial slip: Aerospace nanomaterial enrobing simulation

AbstractIn this article, the combined magneto‐hydrodynamic heat, momentum, and mass (species) transfer in external boundary layer flow of Casson nanofluid from a vertical cone surface with convective conditions under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multidegree, nonsimilar PDEs consisting of the momentum, energy, and concentration equations via appropriate nonsimilarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second‐order, accurate finite difference method of the implicit type. The influences of the emerging parameters, that is, magnetic parameter (M), Casson fluid parameter (β), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr), velocity slip (Sf) and thermal slip (ST) on velocity, temperature, and nanoparticle concentration distributions is illustrated graphically and interpreted at length. Validation of solutions with a Nakamura tridiagonal method has been included. The study is relevant to enrobing processes for electrically conductive nanomaterials, of potential use in aerospace and other industries.

Computational analysis of nonnewtonian boundary layer flow of nanofluid past a vertical plate with partial slip

In the present study, the heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid over a vertical plate surface with multiple slip effect is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. Casson fluid parameter (β), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Buoyancy ratio parameter (N ), Lewis number (Le), Prandtl number (Pr), Velocity slip factor (Sf) and Thermal slip factor (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Validation of solutions with a Nakamura tridiagonal method has been included. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

Role of cross-drilled holes in enhanced cooling of ventilated brake discs

As constructive guidance for brake design engineers to improve brake disc cooling, understanding of thermo-fluidic behaviors associated with ventilated brake discs has attracted much attention. In this study, a systematic comparison of the thermo-fluidic characteristics between standard and cross-drilled ventilated brake discs incorporating radial vanes is carried out using numerical simulations. Mechanisms for heat transfer enhancement by the cross-drilled holes are clarified. To validate the numerical model, a series of experiments are also conducted. The gradient of axial pressure is found to drive the cooling air into the ventilated channel through cross-drilled holes. Such a special flow accelerates external boundary layer flow over the rubbing surface, enhancing therefore local heat transfer. Additionally, the through-hole flow removes heat via the surfaces of the holes while air jets issuing from the cross-drilled holes deflect to suction sides of the vanes, improving further local heat transfer. However, blockage by the jets not only reduces the pumping capacity through ventilated channel inlet but also causes a low-momentum wake downstream each jet. Hence, local heat transfer on the inner surface of each rubbing disc is deteriorated. Eventually, relative to the standard brake disc, the cross-drilled brake disc exhibits a 22–27% higher overall Nusselt number within the typical operating range of 200–1000 RPM. The contribution of each mechanism to overall heat transfer enhancement is quantified.

Dynamic Roughness as a Means of Leading-Edge Separation Flow Control

The aircraft industry, as a whole, has been deeply concerned with improving the aerodynamic efficiency of current and future flight vehicles, particularly in the commercial and military markets. However, of particular interest to the field of aerodynamics is the elusive concept of a workable flow control mechanism. Effective flow control is a concept which if properly applied can increase aerodynamic efficiency. Various concepts and ideas to obtain successful flow control have been studied in an attempt to reap these rewards. Some examples include boundary layer blowing (steady and periodic), suction, and synthetic jets. The overall goal of flow control is to increase performance. The specific objectives of flow control include: 1) delay or eliminate flow separation, 2) delay boundary layer transition or 3) reduce skin friction drag. The purpose of this research is to investigate dynamic surface roughness as a novel method of flow control technology for external boundary layer flows. As opposed to standard surface roughness, dynamic roughness incorporates small time dependent perturbations to the surface of the airfoil. These surface perturbations are actual humps and/or ridges that are on the scale of the laminar boundary layer, and oscillate with an unsteady motion. Research has shown that this can provide a means to modify the instantaneous and mean velocity profile near the wall and favorably control the existing state of the boundary layer. The results of this study have shown that dynamic roughness can be a viable alternative in delaying and/or eliminating the leading edge laminar separation bubble and hence reaping some of the rewards of an effective flow control system, while also maintaining some physical advantages over other techniques.

Acoustic Properties of Porous Coatings for Hypersonic Boundary-Layer Control

Numerical simulations are performed to investigate the interaction of acoustic waves with an array of equally spaced two-dimensional microcavities on an otherwise flat plate without external boundary-layer flow. This acoustic scattering problem is important in the design of ultrasonic absorptive coatings for hypersonic laminar flow control. The reflection coefficient, characterizing the ratio of the reflected wave amplitude to the incident wave amplitude, is computed as a function of the acoustic wave frequency and angle of incidence, for coatings of different porosities, at various acoustic Reynolds numbers relevant to hypersonic flight. Overall, the numerical results validate predictions from existing theoretical modeling. In general, the amplitude of the reflection coefficient has local minima at some specific frequencies. A simple model to predict these frequencies is presented. The simulations also highlight the presence of resonant acoustic modes caused by coupling of small-scale scattered waves near the coating surface. Finally, the cavity depth and the porosity are identified as the most important parameters for coating design. Guidelines for the choice of these parameters are suggested.

Computational study on the internal layer in a diffuser

We report an internal layer found in the turbulent flow through an asymmetric planar diffuser using large-eddy simulation; we discuss five issues relevant to the internal layer: definition and identification, conditions for occurrence, connection with its outer flow, similarity with other equilibrium flows, and growth. The present internal layer exists in a region with stabilized positive skin friction downstream of a sharp reduction. The streamwise pressure gradient changes suddenly from slightly favourable to strongly adverse at the diffuser throat, and relaxes in a prolonged mildly adverse region corresponding to the skin friction plateau. Development of the internal layer into the outer region is slow, in contrast to the internal layers previously identified from certain external boundary-layer flows where the sudden change in streamwise pressure gradient is from strongly adverse to mildly favourable. Signatures of the internal layer include an inflectional point in the wall-normal profiles of streamwise turbulence intensity, and a well-defined logarithmic slope in the mean streamwise velocity underneath a linear distribution extending to the core region of the diffuser. Some of these characteristics bear a certain resemblance to those existing in the C-type of Couette–Poiseuille turbulent flows. Frequency spectrum results indicate that application of strong adverse pressure gradient at the diffuser throat enhances the low-frequency content of streamwise turbulent fluctuations. Inside the internal layer, the frequency energy spectra at different streamwise locations, but with the same wall-normal coordinate, nearly collapse. Two-point correlations with streamwise, wall-normal and temporal separations were used to examine connections between fluctuations inside the internal layer and those in the core region of the diffuser where the mean streamwise velocity varies linearly with distance from the wall. Galilean decomposition of instantaneous velocity vectors reveals a string of well-defined spanwise vortices outside the internal layer. The internal layer discovered from this study provides qualified support for a conjecture advanced by Azad & Kassab some years ago (Phys. Fluids A, vol. 1, 1989, p. 564).

Modeling Flow and Heat Transfer During Freezing of Foods in Forced Airstreams

ABSTRACT: Mathematical modeling of food freezing has been limited to the modeling of the internal heat transfer where the external convective heat‐transfer coefficients are assumed or empirically estimated. Previous procedures followed to solve the external boundary layer in tandem with the internal heat transfer were constrained by numerical complexities due to the transient nature of the heat transfer, requiring unsteady formulation for the flow. In this article, attempts have been made to decouple the flow and heat transfer equations for the external boundary layer flow over a food product being frozen. The flow equations have been solved as a steady‐state problem using Falker‐Skan transformations of the boundary layer equation. The heat‐transfer equation for fluid flow is solved as an unsteady‐state problem in conjunction with the internal heat transfer and phase change inside the product undergoing freezing. The model is validated for a case of air‐impingement freezing.

Revisited results about the theory of steady laminar forced convection for 2D external boundary layer flows

Revisited results about the theory of steady laminar forced convection for 2D external boundary layer flows

Revisited results about the theory of steady laminar forced convection for 2D external boundary layer flows

This paper is inspired by the observation in the literature that there was a lack of data about the knowledge of semi-analytical solutions of steady thermal state applied to laminar boundary layer flows in the case of forced convection. Thus, we have made a complete analysis and synthesized the results on both the surface temperature and the surface flux problems, from the development of integral and differential methods, in the range 10 −3 ≤ Pr ≤ 10 2. Moreover, it has been shown that the same ratio, δ T δ = 20 traduces the transition between boundary layer and slug flows, whatever the thermophysical considered case. Finally, we present a warning about the use of 2 and 3-order polynomial shapes by Pohlhausen method which induce a non-unicity of steady state thermal solutions.

Heating and partial cooling problems in unsteady forced convection

The study of thermoconvective problems in a laminar external boundary layer flow is theoretically presented for both partial heating and cooling situations after that the fluid/wall system has already reached a first steady heating state. The 4th order Karman-Pohlhausen integral approach is used under the hypothesis that the thermal boundary layer thickness is assumed to be steady during the transient phase. The final mathematical equation for both cooling and heating problems is proposed and exemples of space and time corresponding thermograms are given.

Wavenumber Selection for Small‐Wavelength Gertler Vörtices in Curved Channel Flows

We consider the problem of wavenumber selection for fully nonlinear, small‐wavelength Görtler vortices in a curved channel flow. These type of Görtler vortices were first considered by Hall and Lakin [1] for an external boundary layer flow. They proved particularly amenable to asymptotic description, it was possible to consider vortices large enough that the mean flow correction driven by them is as large as the basic state, and this prompted us to consider them in a curved channel flow as an initial application of the phase‐equation approach to Görtler vortices. This involves the assumption that the phase variable of these Görtler vortices varies on slow spanwise and time scales, then an analysis of both inside and outside the core region, to which vortex activity is restricted, leads to a system of partial differential equations, which we can solve numerically for the wavenumber. We consider in particular the effect on the wavenumber of the outer channel wall varying on the same slow spanwise scale as the phase variable.

Skin Friction following BLADE manipulation in a turbulent pipe flow

This study attempts to analyze the measured wall shear stress distribution downstream of single and tandem BLADEs in fully developed pipe flow. Previous works have indicated the adverse effect of overall drag increase with the single BLADE in both channel and pipe flows, and an even larger drag increase with the tandem BLADES. This is contrary to that observed for external boundary layer flow. Extensive comparisons are then made to the wall shear stress distribution following BLADEs in boundary layer flow, leading to the conclusion of little or no potential in the application of BLADEs alone to pipe flow.

Simulating Boundary Layer Transition With Low-Reynolds-Number k–ε Turbulence Models: Part 1—An Evaluation of Prediction Characteristics

An analysis and evaluation of the capability of k–ε low-Reynolds-number turbulence models to predict transition in external boundary-layer flows subject to free-stream turbulence is presented. The similarities between the near-wall cross-stream regions in a fully turbulent boundary layer and the progressive stages through which developing boundary layers pass in the streamwise direction are used to describe the mechanisms by which the models simulate the transition process. Two representative models (Jones and Launder, 1972; Lam and Bremhorst, 1981) are employed in a series of computational tests designed to answer some specific practical questions about the ability of these models to yield accurate, reliable answers over a range of free-stream turbulence conditions.