Small perturbation expansions in unsteady aerofoil theory

1977 ◽  
Vol 83 (2) ◽  
pp. 209-224 ◽  
Author(s):  
J. M. R. Graham ◽  
I. Kullar
Keyword(s):  
Turbulent Flow ◽  
Small Perturbation ◽  
Second Order ◽  
Perturbation Expansions ◽  
Approximate Methods ◽  
Unsteady Forces ◽  
Unsteady Lift

Perturbation expansions are derived to second order in a wavenumber parameter for the unsteady lift induced on an aerofoil by disturbances convected past it at subsonic speeds. The results are used to discuss other approximate methods which have been used to predict the unsteady forces and noise generated by an aerofoil in turbulent flow.

Radiant Heat Transfer From Isothermal Dispersions With Isotropic Scattering

1967 ◽  
Vol 89 (4) ◽  
pp. 300-308 ◽  
Author(s):  
R. H. Edwards ◽  
R. P. Bobco
Keyword(s):  
Heat Transfer ◽  
Approximate Solutions ◽  
Radiant Heat ◽  
Second Order ◽  
Isotropic Scattering ◽  
Radiant Heat Transfer ◽  
Approximate Methods ◽  
First Order ◽  
Order Solution ◽  
Radiant Transfer

Two approximate methods are presented for making radiant heat-transfer computations from gray, isothermal dispersions which absorb, emit, and scatter isotropically. The integrodifferential equation of radiant transfer is solved using moment techniques to obtain a first-order solution. A second-order solution is found by iteration. The approximate solutions are compared to exact solutions found in the literature of astrophysics for the case of a plane-parallel geometry. The exact and approximate solutions are both expressed in terms of directional and hemispherical emissivities at a boundary. The comparison for a slab, which is neither optically thin nor thick (τ = 1), indicates that the second-order solution is accurate to within 10 percent for both directional and hemispherical properties. These results suggest that relatively simple techniques may be used to make design computations for more complex geometries and boundary conditions.

Study on Conditional Statistics in Two-Dimensional Liquid Jet With the Second-Order Chemical Reaction

2011 ◽  
Author(s):  
Tomoaki Watanabe ◽  
Hiroki Yasuhara ◽  
Yasuhiko Sakai ◽  
Takashi Kubo ◽  
Kouji Nagata ◽  
...  
Keyword(s):  
Turbulent Flow ◽  
Chemical Reaction ◽  
Mixture Fraction ◽  
Spectroscopic Method ◽  
Second Order ◽  
Moment Closure ◽  
Liquid Jet ◽  
Two Dimensional ◽  
Conditional Moment ◽  
Conditional Moment Closure

It is important in engineering to elucidate the mechanism of a chemical reaction in turbulent flow. But there are still few studies on reacting turbulent flow in a liquid phase. In this study, the two-dimensional liquid jet with the second-order reaction (A+B←R) is investigated. The concentrations of the species R and the conserved scalar (which is the concentration of other species independent of the above chemical reaction) are measured simultaneously by the optical fiber probe based on light absorbtion spectroscopic method. The concentrations of species A and B are obtained from the conserved scalar theory. Regarding the velocity field, the streamwise velocity is measured by the hot-film anemometer. The moment closure methods are often used for the prediction of turbulent flow. But it is difficult to apply it to the reacting turbulent flow because of the high non-linearity of the reaction rate terms. It is commonly known that the values of concentrations depend strongly on the mixture fraction (which is a conserved scalar) defined as the normalized concentration of the species which is independent of reaction. Hence, Conditional moment closure (CMC) methods are useful for the prediction of the turbulent flow with chemical reactions. In this study, conditional scalar statistics are investigated by using the conditional moment closure methods and experimental data. It is shown that the conditional averages of concentration of reactant and product species approach the equilibrium limit (which correspond to the limiting case of the fast chemical reaction) in the downstream direction and the value of the conditional scalar (mixture fraction) dissipation decreases and its distribution varies in the downstream direction and comes to show the local minimum value near the point η = ξS (which is the stoichiometric value of the mixture fraction).

scholarly journals Structure of turbulent flow over regular arrays of cubical roughness

2007 ◽  
Vol 589 ◽  
pp. 375-409 ◽  
Author(s):  
O. COCEAL ◽  
A. DOBRE ◽  
T. G. THOMAS ◽  
S. E. BELCHER
Keyword(s):  
Turbulent Flow ◽  
Order Statistics ◽  
Spatial Organization ◽  
Second Order ◽  
Quadrant Analysis ◽  
Simple Estimate ◽  
Second Order Statistics ◽  
Ejections And Sweeps ◽  
Conditional Averaging ◽  
Regular Arrays

The structure of turbulent flow over large roughness consisting of regular arrays of cubical obstacles is investigated numerically under constant pressure gradient conditions. Results are analysed in terms of first- and second-order statistics, by visualization of instantaneous flow fields and by conditional averaging. The accuracy of the simulations is established by detailed comparisons of first- and second-order statistics with wind-tunnel measurements. Coherent structures in the log region are investigated. Structure angles are computed from two-point correlations, and quadrant analysis is performed to determine the relative importance of Q2 and Q4 events (ejections and sweeps) as a function of height above the roughness. Flow visualization shows the existence of low-momentum regions (LMRs) as well as vortical structures throughout the log layer. Filtering techniques are used to reveal instantaneous examples of the association of the vortices with the LMRs, and linear stochastic estimation and conditional averaging are employed to deduce their statistical properties. The conditional averaging results reveal the presence of LMRs and regions of Q2 and Q4 events that appear to be associated with hairpin-like vortices, but a quantitative correspondence between the sizes of the vortices and those of the LMRs is difficult to establish; a simple estimate of the ratio of the vortex width to the LMR width gives a value that is several times larger than the corresponding ratio over smooth walls. The shape and inclination of the vortices and their spatial organization are compared to recent findings over smooth walls. Characteristic length scales are shown to scale linearly with height in the log region. Whilst there are striking qualitative similarities with smooth walls, there are also important differences in detail regarding: (i) structure angles and sizes and their dependence on distance from the rough surface; (ii) the flow structure close to the roughness; (iii) the roles of inflows into and outflows from cavities within the roughness; (iv) larger vortices on the rough wall compared to the smooth wall; (v) the effect of the different generation mechanism at the wall in setting the scales of structures.

Comparison of Real-Time Hybrid Model Testing of a Braceless Semi-Submersible Wind Turbine and Numerical Simulations

2017 ◽  
Author(s):  
Madjid Karimirad ◽  
Erin E. Bachynski ◽  
Petter Andreas Berthelsen ◽  
Harald Ormberg
Keyword(s):  
Wind Turbine ◽  
Real Time ◽  
Hybrid Model ◽  
Low Frequency ◽  
Ocean Basin ◽  
Model Testing ◽  
Second Order ◽  
Experimental Results ◽  
Scaled Model ◽  
Approximate Methods

In this paper, integrated analyses performed in SIMA are compared against experimental results obtained using real-time hybrid model testing (ReaTHM®) carried out in the ocean basin facilities of MARINTEK in October 2015. The experimental data is from a 1:30 scaled model of a semi-submersible wind turbine. Coupled aero-hydro-servo-elastic simulations are performed in MARINTEK’s SIMA software. The present work extends previous results from Berthelsen et al. [1] by including a blade element/momentum (BEM) model for the rotor forces in SIMA and comparing the coupled responses of the system to the experimental results. The previously presented hydrodynamic model is also further developed, and the importance of second order loads (and applicability of approximate methods for their calculations) is examined. Low-frequency hydrodynamic excitation and damping are seen to be important, but these loads include a combination of viscous and potential forces. For the selected concept, the second order potential flow forces have limited effects on the responses.

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: Transition From Laminar to Turbulent Flow

2010 ◽  
Author(s):  
K. M. Akyuzlu ◽  
M. Chidurala
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Turbulent Flow ◽  
Numerical Study ◽  
Second Order ◽  
Working Fluid ◽  
Two Dimensional ◽  
Rectangular Enclosure ◽  
Circulation Patterns ◽  
Vertical Walls

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature stratification inside a rectangular enclosure. One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for turbulent compressible flows), and energy equations for the enclosed fluid subjected to appropriate boundary conditions. A standard two equation turbulence model is used to model the turbulent flow in the enclosure. The compressibility of the working fluid is represented by an ideal gas relation. The conservation equations are discretized using an implicit finite difference technique which employs second order accurate central differencing for spatial derivatives and second order (based on Taylor expansion) finite differencing for time derivatives. The linearized finite difference equations are solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Numerical experiments were then carried out to simulate the development of the buoyancy driven circulation patterns inside rectangular enclosures (with aspects ratios 0.5, 1 and 1.5) filled with a compressible fluid (Pr = 0.72). Experiments were repeated for various wall temperature differences which corresponded to Rayleigh numbers between 104 and 106. Changes in unsteady circulation patterns, temperature contours, and vertical and horizontal velocity profiles were predicted while the flow inside the enclosure transferred from laminar to turbulent flow due to the sudden temperature change imposed on the vertical walls of the enclosure. Only the results of the enclosure with aspect ratio one is presented in this paper. These results indicate that this transition is characterized by unicellular circulation patterns breaking up in to multicellular formations and increase in the values of the predicted wall heat fluxes and Nusselt number as flow becomes turbulent.

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