Boundary Layer Calculation Research Articles

Foreword to the Special Issue on Computational Heat Transfer

Foreword to the Special Issue on Computational Heat Transfer

Improved numerical simulations of incompressible flows based on viscous/inviscid interaction procedures

Viscous/inviscid interaction procedures consist usually of coupling potential flow and boundary layer calculations. In this study, the interaction is modeled using Helmholtz-type velocity decomposition where the gradient of the potential is augmented with a correction accounting for the vorticity effects in the viscous layers. Different ways to calculate the rotational components are discussed and methods to systematically improve the model are studied. Numerical results are compared with standard Navier–Stokes calculations to justify the present approach.

Assessment and Modification of One-Equation Models of Turbulence for Wall-Bounded Flows

This work assesses the performance of two single-equation eddy viscosity transport models that are based on Menter’s transformation of the k-ε and the k-ω closures. The coefficients of both models are set exactly the same and follow directly from the constants of the standard k-ε closure. This in turn allows a cross-comparison of the effect of two different destruction terms on the performance of single-equation closures. Furthermore, some wall-free modifications to production and destruction terms are proposed and applied to both models. An assessment of the baseline models with and without the proposed modifications against experiments, and the Spalart-Allmaras turbulence model is provided via several boundary-layer computations. Better performance is indicated with the proposed modifications in wall-bounded nonequilibrium flows.

Influence of the geometry of the nozzle on the characteristics of an exhaust jet

Two solutions for the parameters of a turbulent exhaust jet of a dual-duct engine — the traditional solution within the framework of Prandtl equations of the type of boundary-layer equations and calculation of the near-range field within the framework of the Navier-Stokes equations with subsequent calculation within the framework of the Prandtl equations for large distances — have been compared. It has been shown that the influence of the real geometry of the nozzle exit section, including the shift of the center body and the main duct forward from the exit section of the cold secondary duct, can be allowed for by correcting the constant of the source term in the differential equation for turbulent kinematic viscosity.

Shape Optimization of Stratosphere Airship

PRESENTLY, there is a strong interest in developing unmanned stratospheric airship platforms to be utilized as telecommunication relays, for environmental monitoring or surveillance purposes. Because of the large surface area of the hull, an airship shows high drag, which roughly increases with the square of the airspeed. The required propulsion power is proportional to the third power of the airspeed. Therefore, it is of essential interest to minimize the aerodynamic drag and to maximize the propulsion efficiency. The propulsive power required depends mainly on the aerodynamic drag of the airship hull, which accounts for about 2 of the total drag. Even a small reduction in hull drag can result in a significant saving of fuel, which in turn will lead to a greater payload capacity or an increased range of the airship. During the aerodynamic design of an airship, it is therefore especially important to find a drag-minimized envelope for the intended range of missions. The investigations on the shape optimization of airship were conducted by Th. Lutz et al. 1 and Nejati et al. 2 A source distribution on the body axis was chosen to model the body contour and the corresponding inviscid flowfield, with the source strengths and the lengths of respective segments being used as design variables for the optimization process. Boundary-layer calculation is performed by means of a proved integral method for attached laminar or turbulent boundary layers. To determine the transition location, Lutz used a semi-empirical method based on linear stability theory (e n method), Nejati applied forced transition criterion and concluded that the e n -method is desirable for determining the transition location. A commercial optimizer as well as an evolution strategy with covariance matrix adaption of the mutation distribution were applied as optimization algorithm in Lutz’ paper. Nejati used the genetic algorithm as the optimization algorithm and found that genetic algorithm is a powerful method for such a multidimensional, multimodel, and nonlinear objective function. In this Note, we developed a new method for shape optimization of airship body in terms of the previous investigations of shape optimization. 1−11 The airship geometry is expressed analytically as a polynomial function of eight parameters. The inviscid flow

Hydraulics of skimming flows on stepped chutes: The effects of inflow conditions?

Modern stepped spillways are typically designed for large discharge capacities corresponding to a skimming flow regime for which flow resistance is predominantly form drag. The writer demonstrates that the inflow conditions have some effect on the skimming flow properties. Boundary layer calculations show that the flow properties at inception of free-surface aeration are substantially different with pressurized intake. The re-analysis of experimental results highlights that the equivalent Darcy friction factor is f ∼ 0.2 in average on uncontrolled stepped chute and f ∼ 0.1 on stepped chute with pressurized intake. A simple design chart is presented to estimate the residual flow velocity, and the agreement of the calculations with experimental results is deemed satisfactory for preliminary design

A source wake model for cascades of axial flow turbomachines

This work presents a computational model for the viscous flow through rectilinear cascades of axial turbomachinery. The model is based on modifications of the classical Hess & Smith panel method. The viscous effect of the attached flow portion is introduced by means of normal transpiration velocities obtained from the boundary layer calculations on the airfoil contour. At the separated flow portion, fictitious velocities semi-empirical normal velocities are introduced assuming a constant pressure in the wake. When the separation is not detected, it is possible to simulate the effect of the small wake near the trailing edge by using an injected flow on a distance based on the Gostelow (1974) fairing-in procedure. The numerical model presents two iteration cycles: the first one to find the separation point, and the second one to accomplish the viscous-inviscid interaction, in which the transpiration velocities and the flow injection are submitted to a relaxation process in order to guarantee the convergence of the method. Results for the pressure distributions, flow turning angles and lift coefficients are compared with experimental data for the model validation.

Response of a Laminar Separation Bubble to an Impinging Wake

Laminar separation and transition phenomena were investigated experimentally in the wake-disturbed flow over a 2.4 m long flat plate. A controlled diffusion pressure distribution, representative of that on a compressor blade, was imposed but with sufficiently strong loading to cause laminar separation. Boundary layer velocity traverses were performed at several longitudinal stations. Wakes were generated upstream by a single rod, parallel to the leading edge, attached to a rotating disk mounted flush in the sidewall of the working section. Data are presented in the form of velocity traces and contours of velocity and turbulent intermittency. The results highlight the interaction between the incoming wake and the natural boundary layer, which features a long and thin laminar separation bubble; they demonstrate that wind tunnel experiments provide a good representation of boundary layer behavior under wake disturbances on turbomachinery blading. The calmed region behind the disturbance is a feature that is even stronger behind a wake interaction than behind a triggered turbulent spot. Intermittency values for the undisturbed flow in the separation bubble reattachment region are well represented by Narasimha’s universal intermittency distribution, lending support to the use of intermittency-based predictive routines in calculations of blade boundary layers.

Observations of plan-view sand ripple behavior and spectral wave climate on the inner shelf of San Pedro Bay, California

Concurrent video images of sand ripples and current meter measurements of directional wave spectra are analyzed to study the relations between waves and wave-generated sand ripples. The data were collected on the inner shelf off Huntington Beach, California, at 15 m water depth, where the sea floor is comprised of well-sorted very fine sands ( D 50=92 μm), during the winter of 2002. The wave climate, which was controlled by southerly swells (12–18 s period) and westerly wind waves (5–10 s period), included three wave types: (A) uni-modal, swells only; (B) bi-modal, swells dominant; and (C) bi-modal, wind-wave dominant. Each wave type has distinct relations with the plan-view shapes of ripples that are classified into five types: (1) sharp-crested, two-dimensional (2-D) ripples; (2) sharp-crested, brick-pattern, 3-D ripples; (3) bifurcated, 3-D ripples; (4) round-crested, shallow, 3-D ripples; and (5) flat bed. The ripple spacing is very small and varies between 4.5 and 7.5 cm. These ripples are anorbital as ripples in many field studies. Ripple orientation is only correlated with wave directions during strong storms (wave type C). In a poly-modal, multi-directional spectral wave environment, the use of the peak parameters (frequency, direction), a common practice when spectral wave measurements are unavailable, may lead to significant errors in boundary layer and sediment transport calculations.

Effect of Initial Temperature Profile on Recovery Factor Computations

Effect of Initial Temperature Profile on Recovery Factor Computations

Transition Prediction on the Slat of a High-Lift System

In this paper, a transition prediction approach for the slat of a high-lift system is presented. Accurate mean flows over a multi-element airfoil at various angles of attack have been calculated by using a Navier‐Stokes code. Linear parabolized stability equations have been used to analyze these mean flows and to generate the database for simplified transition prediction correlations. The slat transition prediction module, constituting these correlations, is then used to analyze low-disturbance wind-tunnel data for transition onset in the slat boundary layer. Good agreement is found when Ntr =9 is used as the transition criterion for the two-dimensional flow on the slat of a three-element high-lift system for a range of angle of attack. Comparison of velocity profiles from Navier‐Stokes and boundary-layer computations indicates significant departure from the assumptions associated with the first-order boundary-layer theory.

Advanced High-Turning Compressor Airfoils for Low Reynolds Number Condition—Part II: Experimental and Numerical Analysis

Part I of this paper describes the design and optimization of two high turning subsonic compressor cascades operating as an outlet guide vane (OGV) behind a single stage low pressure turbine at low Reynolds number condition Re=1.3×105. In the numerical optimization algorithm, the design point and off-design performance has been considered in an objective function to achieve a wide low loss incidence range. The objective of the present paper is to examine some of the characteristics describing the new airfoils as well as to prove the reliability of the design process and the applied flow solver. Some aerodynamic characteristics for the two new airfoils and a conventional controlled diffusion airfoil (CDA), have been extensively investigated in the cascade wind tunnel of DLR Cologne. For an inlet Mach number of 0.6 the effect of Reynolds number and incidence angle on each airfoil performance is discussed, based on experimental and numerical results. For an interpretation of the airfoil boundary layer behavior, results of some boundary layer calculations are compared to oil flow visualization pictures. The design goal of an increased low loss incidence range at low Reynolds number condition could be confirmed without having a negative effect on the high Reynolds number region.

High-Speed Trimaran Drag: Numerical Analysis and Model Tests

A numerical technique for high-speed trimaran resistance calculation is developed. The technique is based on the modified viscous-inviscid interaction concept and quasi-linear theory of wave resistance (Amromin et al 1984). The key element of this technique, which is called modified quasi-linear theory (MQLT), is an account of Froude number influence on the ship trim, transom drag, and wetted surface. This influence leads to appearance of a drag component that significantly depends on both Reynolds number and Froude number. This component has been traditionally included in residuary drag in the model test data. The presented preliminary numerical results were obtained with simplifications of the boundary layer theory that are acceptable for slender hulls. Calculated drag is in sufficient accordance with results of model tests. The MQLT computations of boundary layers are also compared with the Reynolds averaged Navier-Stokes (RANS) calculations(one-equation turbulence model by Spalart and Allmaras 1992) at model and ship scale Reynolds numbers. An analysis of the model-ship scale correlation factor for high-speed slender hulls with transom sterns and diverse mutual position of the trimaran hulls is done.

Aerodynamic Entropy Generation Rate in a Boundary Layer With High Free Stream Turbulence

Aerodynamic Entropy Generation Rate in a Boundary Layer With High Free Stream Turbulence

Numerical Experiment of Flow around a Self-Oscillating Circular Cylinder by a Vortex Method Combined with Boundary Layer Calculation. (The Flow Features and the Motion of Circular Cylinder in the Initial Stage of Self-Oscillation)

In this study, the flow features of vortex shedding from a self-oscillating circular cylinder and the characteristics of fluid force were examined using a vortex method simulation combined with boundary layer calculation in a uniform flow at high Reynolds number in order to investigate validity and applicability to the analysis of the flow-induced vibration problems. The calculations were performed for the parameters of the mass ratio M (=1.78, 5.15), the damping factor C (=0.0, 0.0153) and the reduced velocity Vr (=1.38-4.13) at the Reynolds number Re=1×105 based on the uniform flow velocity U and the cylinder diameter D. As a result of the calculations, two typical patterns of vortex shedding were observed, one of which is symmetric twin vortex shedding and the other is antisymmetric twin vortex shedding. It was confirmed that the calculated flow patterns and the free-oscillation motions of the cylinder, were in reasonable agreement with experimental results. The relationship between the fluid force and the resultant cylinder's displacement was investigated.

Development of a performance prediction method for centrifugal compressor channel diffusers

A hybrid performance prediction method is proposed in the present study. A channel diffuser is divided into four subregions: vaneless space, semi-vaneless space, channel, and channel exit region. One-dimensional compressible core flow and boundary layer calculation of each region with an incidence loss model and empirical correlation of residuary pressure recovery coefficient of a channel predict the performance of diffusers. Three channel diffusers are designed and tested for validating the developed prediction method. The pressure distributions from an impeller exit to the channel diffuser exit are measured and discussed for various operating conditions from choke to nearly surge conditions. The strong non-uniform pressure distribution which is caused by impeller-diffuser interaction is obtained over the vaneless and semi-vaneless spaces. The predicted performance shows good agreement with the measured performance of diffusers at a design condition as well as at off-design conditions.

A three‐dimensional boundary layer scheme: stability and accuracy analyses

AbstractWe present a numerical scheme for the calculation of incompressible three‐dimensional boundary layers (3DBL), designed to take advantage of the 3DBL model's overall hyperbolic nature, which is linked to the existence of wedge‐shaped dependence and influence zones. The proposed scheme, explicit along the wall and implicit in the normal direction, allows large time steps, thus enabling fast convergence. In order to keep this partly implicit character, the control volumes for the mass and momentum balances are not staggered along the wall. This results in a lack of numerical viscosity, making the scheme unstable. The implementation of a numerical diffusion, suited to the local zone of influence, restores the stability of the boundary layer scheme while preserving second‐order space accuracy. The purpose of this article is to present the analytical and numerical studies carried out to establish the scheme's accuracy and stability properties. Copyright © 2002 John Wiley & Sons, Ltd.

Numerical studies of wall effects with laminar methane flames

Wall effects in the combustion of lean methane mixtures have been studied numerically using the CHEMKIN software. To gain a deeper understanding of the flame-wall interaction in lean burn combustion, and in particular the kinetic and thermal effects, we have simulated lean and steady methane/air flames in a boundary layer flow. The gas-phase chemistry is modeled with the GRI mechanism version 1.2. Boundary conditions include an inert wall, a recombination wall and catalytic combustion of methane. Different pressures, wall temperatures and fuel-air ratios are used to address questions such as which part of the wall effects is most important at a given set of conditions. As the results are analyzed it can be seen that the thermal wall effects are more significant at the lower wall temperature (600 K) and the wall can essentially be modeled as chemical inert for the lean mixtures used. At the higher wall temperature (1,200 K), the chemical wall effects become more significant and at the higher pressure (10 atm) the catalytic surface retards homogeneous combustion of methane more than the recombination wall because of product inhibition. This may explain the increased emissions of unburned fuel observed in engine studies, when using catalytic coatings on the cylinder walls. The overall wall effects were more pronounced for the leaner combustion case (φ = 0.2). When the position of the reaction zone obtained from the boundary layer calculations is compared with the results from a one-dimensional premixed flame model, there is a small but significant difference except at the richer combustion case (φ = 0.4) at atmospheric pressure, where the boundary layer model may not predict the flame position for the given initial conditions.

Transport phenomena

Transport phenomena

Calculation of a two-phase dynamic laminar boundary layer and a thermal laminar boundary layer on a plate

The approximate method of calculation of a bubble boundary layer based on the integral relations for momentum and energy is proposed. The corresponding equations are derived and results of the numerical investigation of heat exchange are given.