Three-dimensional Boundary Layer Research Articles

Effect of Radiation on MHD Convective Flow and Heat Transfer of a Viscoelastic Fluid Over a Stretching Surface

The Problem of three-dimensional MHD convective boundary layer flow and heat transfer of a viscoelastic fluid in the presence of radiation was examined. A similarity transformation is used to reduce the governing non-linear partial differential equations into ordinary differential equations and then they are solved using homotopy analysis method (HAM). Graphical results for the velocity and temperature profiles are displayed and discussed. Numerical results for the local Nusselt number is tabulated for various values of the parameters.

Computational study of a complex three-dimensional shock boundary-layer interaction

Shock boundary–layer interactions occur in many high-speed aerodynamic flows and they can have a notable impact on design considerations due to the aerodynamic and heat transfer effects. Consequently there is a notable interest in understanding the ability of computational tools to calculate the complex flow fields that can arise in a range of engineering applications. Three-dimensional complex shock boundary layer interaction studies are expensive in both time and computational resources. Although recent studies have begun to focus on the use of more complex computational methods such as large eddy simulations, the aim of this research is to assess the ability of steady Reynolds averaged Navier Stokes turbulence models to simulate the interaction of a planar shock impinging on a cylindrical body under supersonic conditions and to determine if these models have a role to play in engineering design applications. The performance of both eddy viscosity and Reynolds stress models are evaluated relative to an established experimental test case. The impact of Reynolds number and impinging shock strength are also considered. Of the eddy viscosity models it was shown that the Spalart-Allmaras model is unsuitable for this complex interaction and that the k- and Reynolds stress methods both gave notably better agreement with the measured surface static pressures. Overall it was considered that the Reynolds stress method was the best model as it also provided better agreement with the measured surface flow topology. It was concluded that, although a steady Reynolds averaged Navier Stokes approach has known limitations for this type of complex interaction, within an engineering context it can also provide useful results when applied appropriately.

Non-Parallel-Flow Effect on Compressible Boundary Layer on a Flat Plate

Instability of boundary layers is an important aspect of laminar flow - turbulence transition. A local, simple and non-perturbative approach to spatial instability of three-dimensional compressible boundary layers, referred to as ‘extended eigenvalue’ or ‘EEV’ approach, is presented, in which both the streamwise variation of the mean flow and the shape distortion of the disturbance are taken into account. In the case of compressible Blasius boundary layer on a flat plate, the predictions are verified and confirmed by direct numerical simulation results, and the non-parallel effects on eigenvalues, eigenfunctions and neutral curves for different Mach numbers are discussed.

Bypass Transition in Three-dimensional Time-dependent Boundary Layers

The influence of spanwise wall oscillation on transition in boundary layers exposed to free-stream turbulence is examined. Results from direct numerical simulations show that for moderate amplitudes of the wall motion, transition to turbulence can be consider- ably delayed. On the other hand, high-amplitude forcing leads to breakdown to turbulence upstream of the unforced reference flow configuration. Flow visualizations and statistical results show that the stabilization of the flow at the optimal forcing parameters is the result of a substantial weakening of the low-frequency boundary layer streaks. On the other hand, the early breakdown at high forcing amplitudes is associated with the amplification of new high-frequency instabilities in the pre-transitional flow.

Modeling Three Dimensional Effects on Cross Flow Instability from Leading Edge Dimples

The formation of shallow dimples near the leading edge of natural laminar flow wings can occur during operation due to impact by hail, potentially changing the stability characteristics and causing an early transition to turbulence downstream of the dimple. Changes in the base flow will be strongly three-dimensional in character putting this problem beyond the capability of the standard strip based approaches founded on conical flow assumptions that are routinely used in the aerospace industry. This paper describes the application of a fully 3d method to a dimple on a wing for flow resembling that on a natural laminar flow wing. Solving the three-dimensional compressible boundary layer equations for the base flow and using a point to point marching scheme for solving the 3d PSE equations, it is shown that high wave-number stationary cross-flow modes can become unstable and grow rapidly in the dimple wake in a region well beyond the leading edge where stationary cross-flow modes would normally be decaying.

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer

A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundary-layer flow over a rotating disk is described. Surface roughness is modelled using a partial-slip approach, which yields steady-flow profiles for the relevant velocity components of the boundary-layer flow which are a departure from the classic von Kármán solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or cross-flow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for three-dimensional disturbances to the undisturbed three-dimensional boundary-layer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.

Centerline instabilities on the hypersonic international flight research experimentation HIFiRE-5 elliptic cone model

Linear instability of the three-dimensional boundary-layer over the Hypersonic International Flight Research Experimentation 5 (HIFiRE-5) flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, is analyzed through spatial BiGlobal linear instability analysis, in an effort to understand transition and accurately predict local heat loads on this model of next-generation flight vehicles. The base flow conditions are selected for a Mach 7 flow at altitude of 33.0km and unit Reynolds number Re′=1.89×106m. The base flow is computed using the US3D solver. The three-dimensionality of the boundary-layer on the elliptic cone produces spanwise pressure gradients, inducing crossflow from the leading edge (major-axis meridian) to the centerline (minor-axis meridian) and producing lift-up of low momentum boundary-layer fluid at the centerline. The present analysis focuses on the resulting mushroom-like structure formed near the minor-axis meridian. An unstable fluid structure, which is composed of a low-velocity streak surrounded by a three-dimensional high-shear layer, is thus generated. Results show that this complex fluid structure can sustain linear growth of a number of instability modes, thus confirming earlier analyses which identified such modes without taking surface curvature of the geometry in question into consideration. These so-called centerline modes are associated with varicose or sinuous deformations of the low-velocity streak and are found to have similar growth rates in the frequency range studied, between 50 and 300kHz. Furthermore, unstable boundary-layer modes, identified as oblique second Mack modes, are unraveled in the vicinity of the centerline. At the conditions studied, Mack modes are found to be less amplified that the centerline modes.

Entropy Generation through a Deterministic Boundary-Layer Structure in Warm Dense Plasma

The computational prediction of nonlinear interactive instabilities in three-dimensional boundary layers is obtained for a warm dense plasma boundary layer environment. The method is applied to the Richtmyer–Meshkov flow over the rippled surface of a laser-driven warm dense plasma experiment. Coupled, nonlinear spectral velocity equations of Lorenz form are solved with the mean boundary-layer velocity gradients as input control parameters. The nonlinear time series solutions indicate that after an induction period, a sharp instability occurs in the solutions. The power spectral density yields the available kinetic energy dissipation rates within the instability. The application of the singular value decomposition technique to the nonlinear time series solution yields empirical entropies. Empirical entropic indices are then obtained from these entropies. The intermittency exponents obtained from the entropic indices thus allow the computation of the entropy generation through the deterministic structure to the final dissipation of the initial fluctuating kinetic energy into background thermal energy, representing the resulting entropy increase.

A remark on similarity analysis of boundary layer equations of a class of non-Newtonian fluids

A similarity analysis of three-dimensional boundary layer equations of a class of non-Newtonian fluid in which the stress, an arbitrary function of rates of strain, is studied. It is shown that under any group of transformation, for an arbitrary stress function, not all non-Newtonian fluids possess a similarity solution for the flow past a wedge inclined at arbitrary angle except Ostwald-de-Waele power-law fluid. Further it is observed, for non-Newtonian fluids of any model only 90° of wedge flow leads to similarity solutions. Our results contain a correction to some flaws in Pakdemirli׳s [14] (1994) paper on similarity analysis of boundary layer equations of a class of non-Newtonian fluids.

Method for solving the equations describing the triple-deck interaction of a three-dimensional boundary layer with an outer inviscid transonic flow

An approach is developed for solving boundary value problems describing three-dimensional steady flows in the region where a laminar boundary layer interacts with an outer inviscid transonic flow. By applying the method, the flow over a roughness element is computed within the classical triple-deck theory, the asymptotic height of the roughness element corresponding to nonseparated flow is determined, and separated flow patterns are constructed.

Three-dimensional boundary layers with short spanwise scales

AbstractWe investigate three-dimensional (laminar) boundary layers that include a spanwise scale comparable to the boundary-layer thickness. A forcing of short spanwise scales requires viscous dissipation to be retained in the two-dimensional cross-section, perpendicular to the external flow direction, and in this respect the flows are related to previous work on corner boundary layers. We use two examples to highlight the main features of this category of boundary layer: (i) a flat plate of narrow (spanwise) width, and (ii) a narrow (spanwise) gap cut into an otherwise infinite flat plate; in both cases the plate is aligned with a uniform oncoming stream. We find that a novel feature arises in connection with the external flow; the presence of a narrow gap/plate (or indeed any comparable short-scale feature of long streamwise extent) necessarily modifies the streamwise mass flux in that vicinity, which in turn induces an associated boundary-layer transpiration on the same short spanwise length scale. This (short-scale) transpiration region leads to a half-line-source/sink correction to the outer inviscid, irrotational flow. Crucially, the volumetric flux associated with this line-source/sink must be explicitly included as part of the computational procedure for the leading-order boundary layer, and as such there is a weak interaction between the outer (inviscid) flow and the boundary layer. This is a generic feature of boundary layers that are forced through the presence of short-scale spanwise variations.

Heat addition effect on the instability of the crossflow in a three-dimensional boundary layer

The heat addition effect on the stability characteristics of the crossflow in the swept-wing boundary layer is investigated. The physical mechanism of the effect is established. The calculations performed illustrate the variation in the instability mode growth rates under the heating of the surface in a flow and at bulk energy addition.

Miniature Four Hole Probe for Three Dimensional Boundary Layer Measurements

The design, fabrication and calibration details of a miniature four hole probe for three-dimensional boundary layer measurements are presented in this paper. The probe has a nominal measuring area of 1 mm2 and has a nominal dimension of 0.4 mm in the boundary layer direction thus minimizing pressure and velocity gradient errors and wall vicinity errors. The probe is calibrated in an open jet calibration tunnel at a velocity of 50 m/s in the yaw and pitch angle range of + 40O at 5O interval. The calibration coefficients are defined, calculated and presented. The sensitivity of the calibration coefficients is also calculated and presented.

Simplified system of equations for calculating the stability of the boundary layer gas flow on a swept wing

A composite system of equations for calculating the stability of a compressible flow in a three-dimensional boundary layer is developed. A comparison with the calculations in accordance with the complete system of equations shows that the system proposed almost accurately predicts the growth rates of both the Tollmien-Schlichting mode and the transverse flow instability mode over a wide range of frequencies and transverse wavenumbers at moderate Mach numbers. At the same time, the computation time reduces by an order.

Topological evolution of laminar juncture flows under different critical parameters

Horseshoe vortex topological structure has been studied extensively in the past, traditional “saddle of separation” and new “attachment saddle point” topologies found in literature both have theoretical basis and experimental and computational evidences for support. The laminar incompressible juncture flows at low Reynolds numbers especially are observed to have new topology. Studies concerning the existence of the new topology though found in literature, the topological evolution and its dependency on various critical flow parameters require further investigation. A Particle Image Velocimetry based analysis is carried out to observe the effect of aspect ratio, δ*/D and shape of the obstacle on laminar horseshoe vortex topology for small obstacles. Rise in aspect ratio evolves the topology from the traditional to new for all the cases observed. The circular cross section obstacles are found more apt to having the new topology compared to square cross sections. It is noted that the sweeping effect of the fluid above the vortex system in which horseshoe vortex is immersed plays a critical role in this evolution. Topological evolution is observed not only in the most upstream singular point region of horseshoe vortex system but also in the corner region. The corner vortex topology evolves from the traditional type to new one before the topological evolution of the most upstream singular point, resulting in a new topological pattern of the laminar juncture flows “separation-attachment combination”. The study may help extend the understanding of the three-dimensional boundary layer separation phenomenon.

Transition on a Wing with Spanwise Varying Crossflow and Linear Stability Analysis

A new test case for challenging current transition prediction methods for three-dimensional boundary layers is designed with special focus on the effect of spanwise varying mean flow. The wind-tunnel model of this test case has a sickle-shaped planform. It is equipped with pressure taps and a special skin layup to increase the contrast of infrared transition measurements. The wing is designed to generate three-dimensional boundary layers with increasing crossflow toward the wingtip. The sickle-shaped planform with distinct kinks creates spanwise gradients, and the assumptions of linear local stability theory are therefore challenged. It is found that, at locations of high spanwise gradients, the transition location moves upstream, due to strong amplification of stationary crossflow vortices. Hot-film measurements are used to identify and characterize traveling modes, and to quantify disturbance amplifications. The wing exhibits areas of rapidly growing Tollmien–Schlichting modes, which behave in good agreement with linear stability theory, whereas crossflow-dominated regions display both stationary and traveling crossflow modes.

Three-dimensional magnetohydrodynamics axisymmetric stagnation flow and heat transfer due to an axisymmetric shrinking/stretching sheet with viscous dissipation and heat source/sink

The present work is concerned with the effects of viscous dissipation and heat source/sink on a three-dimensional magnetohydrodynamic boundary layer axisymmetric stagnation flow, and the heat transfer of an electrically conducting fluid over a sheet, which shrinks or stretches axisymmetrically in its own plane where the line of the symmetry of the stagnation flow and that of the shrinking (stretching) sheet are, in general, not aligned. The governing equations are transformed into ordinary differential equations by using suitable similarity transformations and then solved numerically by a shooting technique. This investigation explores the conditions of the non-existence, existence and uniqueness of the solutions of the similar equations numerically. It is noted that the range of the velocity ratio parameter, where the similarity solution exists, is increased with the increase of the value of the magnetic parameter. Furthermore, the study reveals that the non-alignment function affects the shrinking sheet more than the stretching sheet. In addition, the numerical results of the velocity profile, temperature profile, skin-friction coefficient, and rate of heat transfer at the sheet are discussed in detail with different parameters.

Transitional Intermittency Exponents Through Deterministic Boundary-Layer Structures and Empirical Entropic Indices

A computational procedure is developed to determine initial instabilities within a three-dimensional laminar boundary layer and to follow these instabilities in the streamwise direction through to the resulting intermittency exponents within a fully developed turbulent flow. The fluctuating velocity wave vector component equations are arranged into a Lorenz-type system of equations. The nonlinear time series solution of these equations at the fifth station downstream of the initial instabilities indicates a sequential outward burst process, while the results for the eleventh station predict a strong sequential inward sweep process. The results for the thirteenth station indicate a return to the original instability autogeneration process. The nonlinear time series solutions indicate regions of order and disorder within the solutions. Empirical entropies are defined from decomposition modes obtained from singular value decomposition techniques applied to the nonlinear time series solutions. Empirical entropic indices are obtained from the empirical entropies for two streamwise stations. The intermittency exponents are then obtained from the entropic indices for these streamwise stations that indicate the burst and autogeneration processes.

Years devoted to development of aerodynamics in Siberia

April 29, 2014 is the 100th anniversary of Vladimir V. Struminskii. He was born in Orenburg in a family of a school teacher Vasilii Ya. Struminskii (1880–1967) and his wife Mariya F. Dmitrovskaya (1884−1972). After studying at school for seven years, he worked as a turner at a factory in Kazan and then at the Dinamo plant in Moscow. In 1933, without leaving his work, Vladimir Struminskii graduated from the school for working youth and entered the Physical Faculty of the Lomonosov Moscow State University. After graduating from the university cum laude, V.V. Struminskii became a post-graduate student at the Institute of Physics at the Moscow State University; in 1941, he defended the candidate’s thesis entitled “Electron theory of solids,” where he presented a solution of the Schroedinger equation for the crystal lattice of alloys. On the eve of the Great Patriotic War, Vladimir V. Struminskii was appointed to the Central Aerohydrodynamic Institute named after Academician N.E. Zhukovskii (TsAGI), where he started to study some problems new for him: aerodynamic investigations of finitespan wings. Several years later, he developed a method for calculating the maximum lift force of the wing and the distribution of stall zones over the wing span. A series of experiments with finite-span wings in the full-scale wind tunnel based at TsAGI at high Reynolds numbers confirmed the efficiency of the proposed method of aerodynamic design of the wing. In 1947, Struminskii together with other TsAGI researchers was awarded with the State Prize for the development of new wings for high-velocity airplanes and preparation for their batch production. V. V. Struminskii made a significant contribution to the progress in aeronautics by developing a method of aerodynamic design of the wing from a set of airfoils with a nonseparated flow at the wing tip, which ensured high reliability and safety of flight at high angles of attack; this method was developed during the Great Patriotic War. Before that, a large amount of theoretical activities were performed. Exact solutions of three-dimensional boundary layer equations

Physical implication of two problems in transition prediction of boundary layers based on linear stability theory

Up to now, the most widely used method for transition prediction is the one based on linear stability theory. When it is applied to three-dimensional boundary layers, one has to choose the direction, or path, along which the growth rate of the disturbance is to be integrated. The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable. However, unlike the saddle point method applied to water waves, here its physical meaning is not so obvious, as the frequency and wave number may be complex. And on some occasions, in advancing the integration of the growth rate of the disturbance, up to a certain location, one may not be able to continue the integration, because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number. In this paper, these two problems are discussed, and suggestions for how to do transition prediction under the latter condition are provided.