Boundary Layer Calculation Research Articles

A Simple Prediction Method for the Form Factor of Full Form Ships

An efficient hull form design needs to incorporate some prediction methods which will be able to predict the influence of hull form modification on the ship performance. This paper presents a new and simple prediction method for the form factor which relates directly to the hull form. Six flow-field parameters which have influences on the form factor are proposed on the basis of the result of double-model flow calculation and 3-dimensional boundary layer calculation around the hull form. A regression equation to predict the form factor is made by using 7 parameters (6 flow-field parameters and displacement-length ratio) and model test results in a towing tank. In order to adopt the minimum Akaike Information Criterion (AIC) estimate method in a regression analysis, 7 parameters are selected among many variations.Predicted results for the form factor of full form ship at full load condition by the present regression equation show good agreement within 2% with tank test results. At ballast condition, predicted results show good agreement within 3%. Since flow-field parameters in the present regression equation act as intermediary between actual hull form and ship performance, a designer can easily obtain an information of how to modify the hull form according to the flow-field parameter in order to improve ship performance.

The martian diurnal water cycle

Near-surface water (both in the regolith and atmosphere) represents a potentially important resource for the exploration of Mars. However, most analyses of these resources (cf. Mellon and Jakosky, 1993, and references therein) hearken back to the seminal discussion of Martian volatiles by Leighton and Murray (1966) which assumed a planetwide average water vapor column of about 10 precipitable micrometers (pr-μm). This ignores considerable latitude, seasonal, and diurnal variations in water vapor. Similarly, previous high-resolution boundary-layer modeling of the diurnal water cycle (Zent et al., 1993) regarded the atmospheric column as controlling the soil conditions. Thus, the soil was initialized with some 2 kg m −3 (corresponding to 20 pr-μm cm −1) of water, causing the assumed atmospheric column to be filled in a matter of days. Global modeling of the Martian water cycle over a period of several decades (Houben et al., 1997), on the other hand, gives strong indications that the regolith water inventory is much smaller and that adsorption of water on this regolith dominates the lower atmospheric column. Presented here are diurnal boundary-layer calculations utilizing the one-dimensional Zent et al. (1993) model but which are initialized with the smaller Houben et al. (1997) estimated soil water inventories, for a variety of locations and seasons on Mars.

A Time-Marching Method for the Calculation of Nonsimilar 3D Boundary Layers on Turbomachinery Blades

A method is presented for the computation of three-dimensional boundary layers on turbomachinery blades. The method is based on a finite difference approach on a body-fitted curvilinear coordinate system, in which the time-dependent 3D boundary layer equations are marched in time until the steady-state solution is found. The method does not employ a similarity law and can therefore be applied to nonsimilar boundary layers. The method not only enables one to compute the skin friction and displacement of the boundary, but also provides information on the sources of entropy generation on the blades. The entropy generation is in fact split into three main components, which correspond to heat conduction, streamwise shear stress, and cross-flow shear stress. By considering each of the components of shear stress, at the design stage considerable insight can be found on the best way of modifying the blade geometry in order to reduce blade losses. The method is validated by comparison with analytical data for a laminar flat plate, experimental results for a helical blade in turbulent flow, and an axial compressor blade. Finally, the method is applied to the prediction of boundary layers on a subsonic centrifugal compressor impeller blade.

A New Model for Free-Stream Turbulence Effects on Boundary Layers

A model has been developed to incorporate more of the physics of free-stream turbulence effects into boundary layer calculations. The transport in the boundary layer is modeled using three terms: (1) the molecular viscosity, ν; (2) the turbulent eddy viscosity, εT, as used in existing turbulence models; and (3) a new free-stream-induced eddy viscosity, εf. The three terms are added to give an effective total viscosity. The free-stream-induced viscosity is modeled algebraically with guidance from experimental data. It scales on the rms fluctuating velocity in the free stream, the distance from the wall, and the boundary layer thickness. The model assumes a direct tie between boundary layer and free-stream fluctuations, and a distinctly different mechanism than the diffusion of turbulence from the free-stream to the boundary layer assumed in existing higher order turbulence models. The new model can be used in combination with any existing turbulence model. It is tested here in conjunction with a simple mixing length model and a parabolic boundary layer solver. Comparisons to experimental data are presented for flows with free-stream turbulence intensities ranging from 1 to 8 percent and for both zero and nonzero streamwise pressure gradient cases. Comparisons are good. Enhanced heat transfer in higher turbulence cases is correctly predicted. The effect of the free-stream turbulence on mean velocity and temperature profiles is also well predicted. In turbulent flow, the log region in the inner part of the boundary layer is preserved, while the wake is suppressed. The new model provides a simple and effective improvement for boundary layer prediction.

A General Relativistic Calculation of Boundary Layer and Disc Luminosity for Accreting Non-magnetic Neutron Stars in Rapid Rotation

We calculate the disc and boundary layer luminosities for accreting rapidly rotating neutron stars with low magnetic fields in a fully general relativistic manner. Rotation increases the disc luminosity and decreases the boundary layer luminosity. A rapid rotation of the neutron star substantially modifies these quantities as compared with the static limit. For a neutron star rotating close to the centrifugal mass shed limit, the total luminosity has contribution only from the extended disc. For such maximal rotation rates, we find that well before the maximum stable gravitational mass configuration is reached, there exists a limiting central density, for which particles in the innermost stable orbit will be more tightly bound than those at the surface of the neutron star. We also calculate the angular velocity profiles of particles in Keplerian orbits around the rapidly rotating neutron star. The results are illustrated for a representative set of equation of state models of neutron star matter.

Drag Reduction and Shape Optimization of Airship Bodies

A tool for the numerical shape optimization of axisymmetric bodies submerged in incompressible flow at zero incidence has been developed. Contrary to the usual approach, the geometry of the body is not optimized in a direct way with this method. Instead, a source distribution on the body axis was chosen to model the body contour and the corresponding inviscid flowfield, with the source strengths being used as design variables for the optimization process. Boundary-layer calculation is performed by means of a proved integral method. To determine the transition location, a semiempirical method based on linear stability theory (e n method) was implemented. A commercially available hybrid optimizer as well as an evolution strategy with covariance matrix adaption of the mutation distribution are applied as optimization algorithms. Shape optimizations of airship hulls were performed for different Reynolds number regimes. The objective was to minimize the drag for a given volume of the envelope and a prescribed airspeed range

Numerical Simulation of Turbulent Boundary Layer over Complex Rough Surfaces

The simulation method of numerical calculation of turbulent boundary layer over complex rough surfaces was reviewed. Turbulent boundary flows over rough surfaces calculated by different methods were examined. Firstly, the handling of roughness as a surface boundary condition and the modeling of roughness effect were discussed. Secondly, the generation methods of turbulent fields at the inflow boundary were presented and the effect of the inflow boundary condition was discussed.

Computations of periodic turbulent boundary layers with moderate adverse pressure gradient

Computations of periodic turbulent boundary layers with moderate adverse pressure gradient

Computations of periodic turbulent boundary layers with moderate adverse pressure gradient

In this computational study a two-equation eddy-viscosity model of turbulence is used to predict the development of boundary layers with periodic variation of the free-stream velocity and time-mean adverse pressure gradient. Transport equations are solved for q, the square root of the turbulence kinetic energy and ζ, its dissipation rate. Comparisons with reliable experimental data on such flows verified that the model can satisfactorily reproduce the time-average prime variables as well as their amplitudes. The predicted boundary-layer integral parameters were also found to be in good agreement with comparable data in the literature. Additional comparisons are made with the computed development of the same flow at constant pressure. The effects of the pressure gradient isolated and studied in this way were generally found to be similar to those of nonperiodic flow in similar conditions.

Prediction of Transpired Turbulent Boundary Layers With Arbitrary Pressure Gradients

An integral method, using Coles combined inner and outer law as the velocity profile, is developed for calculation of turbulent boundary layers with blowing or suction and pressure gradients. The resulting ordinary differential equations are solved numerically for the distribution of skin friction coefficient and integral thickness along the surface. Comparisons of predicted skin friction coefficients with experimental data are made for a wide range of blowing and suction rates and for various pressure gradients, including adverse, zero and a strong favorable gradient. In addition to good agreement with experimental data for constant blowing fractions F, the method is also successfully tested on cases where the blowing fraction is variable with position. Predictions, in general, exhibit satisfactory agreement with the data. The integral method predictions are comparable to, or better than, a number of finite difference procedures in a limited number of cases where comparisons were made.

Heat Transfer Committee and Turbomachinery Committee Best Paper of 1996 Award: The Path to Predicting Bypass Transition

A theory is presented for calculating the fluctuations in a laminar boundary layer when the free stream is turbulent. The kinetic energy equation for these fluctuations is derived and a new mechanism is revealed for their production. A methodology is presented for solving the equation using standard boundary layer computer codes. Solutions of the equation show that the fluctuations grow at first almost linearly with distance and then more slowly as viscous dissipation becomes important. Comparisons of calculated growth rates and kinetic energy profiles with data show good agreement. In addition, a hypothesis is advanced for the effective forcing frequency and free-stream turbulence level that produce these fluctuations. Finally, a method to calculate the onset of transition is examined and the results compared to data.

Aerodynamic optimum design of transonic turbine cascades using Genetic Algorithms

This paper presents an aerodynamic optimum design method for transonic turbine cascades based on the Genetic Algorithms coupled to the inviscid flow Euler solver and the boundary-layer calculation. The Genetic Algorithms control the evolution of a population of cascades towards an optimum design. The fitness value of each string is evaluated using the flow solver. The design procedure has been developed and the behavior of the genetic algorithms has been tested. The objective functions of the design examples are the minimum mean-square deviation between the aimed pressure and computed pressure and the minimum amount of user expertise.

Asymptotic defect boundary layer theory applied to thermochemical non-equilibrium hypersonic flows

Viscous flow computations are required to predict the heat flux or the viscous drag on an hypersonic re-entry vehicle. When real gas effects are included, Navier–Stokes computations are very expensive, whereas the use of standard boundary layer approximations does not correctly account for the ‘entropy layer swallowing’ phenomenon. The purpose of this paper is to present an extension of a new boundary layer theory, called the ‘defect approach’, to two-dimensional hypersonic flows including chemical and vibrational non-equilibrium phenomena. This method ensures a smooth matching of the boundary layer with the inviscid solution in hypersonic flows with strong entropy gradients. A new set of first-order boundary layer equations has been derived, using a defect formulation in the viscous region together with a matched asymptotic expansions technique. These equations and the associated transport coefficient models as well as thermochemical models have been implemented. The prediction of the flow field around the blunt-cone wind tunnel model ELECTRE with non-equilibrium free-stream conditions has been done by solving first the inviscid flow equations and then the first-order defect boundary layer equations. The numerical simulations of the boundary layer flow were performed with catalytic and non-catalytic conditions for the chemistry and the vibrational mode. The comparison with Navier–Stokes computations shows good agreement. The wall heat flux predictions are compared to experimental measurements carried out during the MSTP campaign in the ONERA F4 wind tunnel facility. The defect approach improves the skin friction prediction in comparison with a classical boundary layer computation.

Experimental and theoretical investigations of low-pressure CVD of Cu using CuI as precursor

For the first time Cu was deposited on SiO 2 using CuI as precursor. CuI is generated in a reactor by flowing gaseous I 2 and N 2 or He as inert carrier gas through a hot copper bed. The growth chamber is a vertical stagnation point reactor. The resistivity of Cu layers deposited at a total pressure of 400 Pa and a substrate temperature of 970 K was 1.9 μΩ·cm. Impurities, in particular I 2, have not been detected with EDX in the films. The spatial CuI concentration distribution above the substrate on the stagnation point line was determined by the method of laser-induced fluorescence spectroscopy for several deposition conditions. The experimental results were compared with the results of a boundary layer computation, simulating the reactant flow at the stagnation point. First simulations show acceptable agreement with experiments for the growth rate and the CuI gas-phase concentration.

Numerical prediction of pressure loss coefficient and induced mass flux for laminal natural convective flow in a vertical channel

The natural convection heat transfer and ventilation characteristics of heated and vented parallel wall channels have been studied numerically. The flow is assumed to be laminar and steady, and the governing two-dimensional Navier-Stokes equations are solved by a finite volume formulation to calculate the chimney effect that draws cooler ambient air from the lower opening. The fluid-dynamic and heat-transfer characteristics of vented vertical channels are investigated for both symmetric isothermal and constant heat-flux boundary conditions for the Rayleigh number ranging from 10 3 to 10 5 and the aspect ratio in the 5–20 range. The non-dimensional entrance and exit pressure losses and the induced mass-flow are correlated with the Rayleigh number. The results indicate that although inlet- and exit-loss coefficients may vary significantly with Rayleigh number and aspect ratio, the total pressure-loss coefficient is a weak function of Rayleigh number. It is also shown that the total pressure loss coefficient and non-dimensional mass-flow rate results are better correlated with the modified Rayleigh number that is obtained by dividing the Rayleigh number by the aspect ratio. The elliptic flow results, obtained from the present procedure, are compared with fully developed flow results and with boundary-layer calculations of previous authors. Numerical results also yielded important information regarding the placement of the free pressure boundary. The results for the present geometry indicate that the effect of free-boundary location is negligible if it is placed at a distance of four times the channel width or greater.

Analysis of rarefied compressible boundary layers in transition regime

Results of flat plate compressible boundary layer calculation, based on discrete formulation of DSMC method, are presented in low Mach number and low Knudsen number range. The free stream is a uniform flow of pure nitrogen at various Mach numbers in low pressures (i.e. rarefied gas). Complete thermal accommodation and diffuse molecular reflections are used as the wall boundary condition, replacing unreal no-slip condition used in continuum calculations. In the discrete formulation of DSMC method, there is no need to use ad hoc assumptions on transport properties like viscosity and thermal conductivity, instead viscosity is calculated from values of other field variables (velocity and shear stress). Also the results are compared with existing self-similar continuum solutions. In all Mach number cases computed, velocity slip is most pronounced in regions near the leading edge where continuum formulation renders the solution singular. As the boundary layer develops further downstream, velocity slips asymptote to values that are between 10 to 20% of the magnitude of free stream velocity. When the free stream number density is reduced, so the gas more rarefied, the velocity slip increases as expected.

Design and Performance Prediction of Centrifugal Impellers

This study presents a simple method for designing the blade geometry of a centrifugal compressor impeller. In this method, instead of giving the mean swirl distribution on the meridional surface, the blade angle distribution is specified and the blade shape is derived, making it easier to perform the design. The quasi-three-dimensional potential flow field inside the impeller is obtained using the streamline curvature method, which solves the Euler equation along arbitrary quasi-orthogonals. The viscous effect is incorporated indirectly into the inverse design of the impeller via the simplified three-dimensional boundary layer calculation and the performance prediction. A three-dimensional centrifugal impeller was designed using this inviscid-viscous method and eventually manufactured. The newly designed impeller (B) and another impeller (A) designed previously were tested on a standard apparatus for model impellers. With the aid of three-hole probes and thermocouples, the flow parameters downstream of the exit of the impellers were measured along the axial direction of the impellers. A viscous loss model related to the boundary parameters is developed and used for the performance predictions of the impellers together with other loss models. From both the boundary layer analysis and the performance prediction, it is concluded that impeller B is superior to impeller A, which is in close accordance with the measurements.

Terminal structure of unsteady classical and interacting boundary layers

The terminal structure of the unsteady boundary-layer equations is investigated for the problem of impulsive flow past a circular cylinder. It is known that both the classical and interacting boundary-layer equations for this problem are singular and the singular structure for the interacting boundary layer on a circular cylinder has not been properly resolved using the classical finite difference approach within an Eulerian framework. The objective of this paper is to resolve the singular structure for both the classical and interacting boundary layers for the impulsively started flow past a cylinder. An adaptive-grid scheme, coupled to a panel method for the interacting case, is employed to resolve the extremely small time and length scales associated with a terminal structure defined by the emergence of a singularity. Calculations performed in an Eulerian coordinate system show that interacting boundary-layer calculations terminate sooner than the classical boundary-layer calculation, and as the Reynolds number decreases, the singularity occurs earlier in time and closer to the rear stagnation point of the circular cylinder. Comparisons with previous Lagrangian and fixed-grid Eulerian results are discussed.

Computation and Simulation of Wake-Generated Unsteady Pressure and Boundary Layers in Cascades: Part 2—Simulation of Unsteady Boundary Layer Flow Physics

The unsteady pressure and boundary layers on a turbomachinery blade row arising from periodic wakes due to upstream blade rows are investigated in this paper. Numerical simulations are carried out to understand the effects of the wake velocity defect and the wake turbulence intensity on the development of unsteady blade boundary layers. The boundary layer transition on the blade is found to be strongly influenced by the unsteady wake passing. Periodic transitional patches are generated by the high turbulence intensity in the passing wakes and transported downstream. The time-dependent transition results in large unsteadiness in the instantaneous local skin friction coefficient and a smoother time-averaged transition curve than the one observed in the steady boundary layer. A parametric study is then carried out to determine the influence of wake parameters on the development of the unsteady blade boundary layers. It is shown that the unsteadiness in the blade boundary layer increases with a decrease in the axial gap, an increase in wake/blade count ratio, or an increase in the wake traverse speed. The time-averaged boundary layer momentum thickness at the trailing edge of the blade is found to increase significantly for higher wake/blade count ratio and larger wake traverse speed. Increase of the wake/blade count ratio also results in higher frictional drag of the blade.

Computation and Simulation of Wake-Generated Unsteady Pressure and Boundary Layers in Cascades: Part 1—Description of the Approach and Validation

The unsteady pressure and boundary layers on a turbomachinery blade row arising from periodic wakes due to upstream blade rows are investigated in this paper. A time-accurate Euler solver has been developed using an explicit four-stage Runge–Kutta scheme. Two-dimensional unsteady nonreflecting boundary conditions are used at the inlet and the outlet of the computational domain. The unsteady Euler solver captures the wake propagation and the resulting unsteady pressure field, which is then used as the input for a two-dimensional unsteady boundary layer procedure to predict the unsteady response of blade boundary layers. The boundary layer code includes an advanced k–ε model developed for unsteady turbulent boundary layers. The present computational procedure has been validated against analytic solutions and experimental measurements. The validation cases include unsteady inviscid flows in a flat-plate cascade and a compressor exit guide vane (EGV) cascade, unsteady turbulent boundary layer on a flat plate subject to a traveling wave, unsteady transitional boundary layer due to wake passing, and unsteady flow at the midspan section of an axial compressor stator. The present numerical procedure is both efficient and accurate in predicting the unsteady flow physics resulting from wake/blade-row interaction, including wake-induced unsteady transition of blade boundary layers.