# Numerical Study of Heat Transfer Around the Small Scale Airfoil Using Various Turbulence Models

24 Dec 2009-Numerical Heat Transfer Part A-applications (Taylor & Francis Group)-Vol. 56, Iss: 12, pp 946-969

TL;DR: In this article, a numerical investigation of low-Reynolds number flows with thermal effect around the MAV airfoils using various turbulence models, including an algebraic Baldwin-Lomax model, Spalart-Allmaras one equation, and two equation (k-ω and SST-kω) turbulence models were presented.

Abstract: A numerical investigation of low-Reynolds number flows with thermal effect around the MAV airfoils using various turbulence models, including an algebraic Baldwin-Lomax model, Spalart-Allmaras one equation, and two equation (k-ω and SST-k-ω) turbulence models, is presented. First, the thermal effect on the aerodynamic efficiency is studied for flow around a rectangular MAV wing, based on the NACA0012 airfoil section at low-aspect ratio (AR = 2) and an angle of attack equal to 0°. Second, details of the thermal effect are limited to the two-dimensional NACA0012 airfoil with chord length of 3.81 cm. This study shows that the improvement of aerodynamic efficiency (increase lift and reduce drag) is achieved by the generation of a temperature difference between extrados and intrados of the airfoil (by cooling the upper surface and heating the lower surface). The numerical results obtained with various turbulence models are in good agreement with experiment data, except the k-ω turbulence model. These results a...

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TL;DR: In this paper, the aerodynamic problems that must be addressed in order to design a successful small aerial vehicle are described, including the effects of Reynolds number and aspect ratio (AR) on the design and performance of fixed-wing vehicles.

Abstract: In this review we describe the aerodynamic problems that must be addressed in order to design
a successful small aerial vehicle. The effects of Reynolds number and aspect ratio (AR) on the design and
performance of fixed-wing vehicles are described. The boundary-layer behavior on airfoils is especially important
in the design of vehicles in this flight regime. The results of a number of experimental boundary-layer studies,
including the influence of laminar separation bubbles, are discussed. Several examples of small unmanned
aerial vehicles (UAVs) in this regime are described. Also, a brief survey of analytical models for oscillating and
flapping-wing propulsion is presented. These range from the earliest examples where quasi-steady, attached flow
is assumed, to those that account for the unsteady shed vortex wake as well as flow separation and aeroelastic
behavior of a flapping wing. Experiments that complemented the analysis and led to the design of a successful
ornithopter are also described.

102 citations

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TL;DR: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted by as mentioned in this paper, where the authors conducted a comprehensive survey.

Abstract: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted Due to the immenseness of the literature volume, the survey

58 citations

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TL;DR: In this paper, wind-tunnel experiments performed to investigate the aerodynamic and mechanical characteristics of micro air vehicles with flexible wings in different conditions of propeller type, motor power, and elevator deflections.

Abstract: The field of micro air vehicles is relatively immature; consequently, high-fidelity simulations do not yet exist for a generic aircraft. The fidelity of flight dynamic simulations is closely correlated to the reliability of models representing the vehicle's aerodynamic and propulsion characteristics in the entire flight envelope, including the nonlinear region. This paper discusses wind-tunnel experiments performed to investigate the aerodynamic and mechanical characteristics of micro air vehicles with flexible wings in different conditions of propeller type, motor power, and elevator deflections. Visual image correlation was used to measure the deformation of the flexible wings to quantify general features such as variations in aerodynamic and geometric twist angle. Aerodynamic and propulsion results were used to formulate empirical models of the relevant coefficients in the form of multiple linear regressions and to estimate the effectors' functional dependencies and interactions. High-order nonlinear interactions were confirmed between the coefficients of lift, drag, and pitching moment with the independent variables. The rates of the dependencies with elevator deflections and angle of attack were found, to some extent, to be motor voltage and dynamic pressure dependent, evincing a strong coupling with the propeller speed.

24 citations

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TL;DR: In this paper, a dynamic model and drag coefficient calculations of a temperature probe descent into ocean water are presented to predict the depth of the probe during descent into the ocean during a measurement of ocean temperatures.

Abstract: Computational fluid dynamics techniques have been applied to model fluid flow in the vicinity of oceanographic temperature probes A major goal of the modeling effort is the determination of drag coefficients for probe descent into ocean water These drag coefficients can be used, in conjunction with a dynamic model of the probe, to predict the depth of the probe during descent Accurate depth information is essential for the proper measurement of ocean temperatures and, consequently, ocean heating associated with climate change Until recently, probe depths were predicted with the use of experimental calibrations which relate time-of-flight and depth Those calibrations are limited in their accuracy, they are confined to conditions that match the experiments from which the calibrations were determined, and they are unable to account for variations in quantities such as the drop height or initial probe mass The dynamic model and drag coefficient calculations presented here are, to the best knowledge of t

20 citations

### Additional excerpts

...It is expected that the quality of the results would be maintained even if less sophisticated turbulence models were used [ 35 ]....

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TL;DR: In this article, the effect of heat transfer upon the aerodynamic performance of a pitching and plunging NACA0012 airfoil in the low Reynolds number flow regime with particular emphasis upon the airfoils's lift and drag coefficients was investigated.

Abstract: The unsteady low Reynolds number aerodynamics phenomena around flapping wings are addressed in several investigations. Elsewhere, airfoils at higher Mach numbers and Reynolds numbers have been treated quite comprehensively in the literature. It is duly noted that the influence of heat transfer phenomena on the aerodynamic performance of flapping wings configurations is not well studied. The objective of the present study is to investigate the effect of heat transfer upon the aerodynamic performance of a pitching and plunging NACA0012 airfoil in the low Reynolds number flow regime with particular emphasis upon the airfoil's lift and drag coefficients. The compressible Navier–Stokes equations are solved using a finite volume method. To consider the variation of fluid properties with temperature, the values of dynamic viscosity and thermal diffusivity are evaluated with Sutherland's formula and the Eucken model, respectively. Instantaneous and mean lift and drag coefficients are calculated for several temperature differences between the airfoil surface and freestream within the range 0–100 K. Simulations are performed for a prescribed airfoil motion schedule and flow parameters. It is learnt that the aerodynamic performance in terms of the lift C L and drag C D behavior is strongly dependent upon the heat transfer rate from the airfoil to the flow field. In the plunging case, the mean value of C D tends to increase, whereas the amplitude of C L tends to decrease with increasing temperature difference. In the pitching case, on the other hand, the mean value and the amplitude of both C D and C L decrease. A spectral analysis of C D and C L in the pitching case shows that the amplitudes of both C D and C L decrease with increasing surface temperature, whereas the harmonic frequencies are not affected.

10 citations

##### References

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TL;DR: In this article, it is shown that these features can be obtained by constructing a matrix with a certain property U, i.e., property U is a property of the solution of the Riemann problem.

Abstract: Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded and that only certain features of the exact solution are worth striving for. It is shown that these features can be obtained by constructing a matrix with a certain “Property U.” Matrices having this property are exhibited for the equations of steady and unsteady gasdynamics. In order to construct them, it is found helpful to introduce “parameter vectors” which notably simplify the structure of the conservation laws.

8,174 citations

### "Numerical Study of Heat Transfer Ar..." refers methods in this paper

...For the RANS equations, two different spatial discretization schemes are available: Roe’s flux difference splitting scheme [42] and Van Leer’s flux vector splitting scheme [43]....

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TL;DR: In this article, the local turbulent viscosity is determined from the solution of transport equations for the turbulence kinetic energy and the energy dissipation rate, and the predicted hydrodynamic and heat-transfer development of the boundary layers is in close agreement with the measured behaviour.

Abstract: The paper presents a new model of turbulence in which the local turbulent viscosity is determined from the solution of transport equations for the turbulence kinetic energy and the energy dissipation rate. The major component of this work has been the provision of a suitable form of the model for regions where the turbulence Reynolds number is low. The model has been applied to the prediction of wall boundary-layer flows in which streamwise accelerations are so severe that the boundary layer reverts partially towards laminar. In all cases, the predicted hydrodynamic and heat-transfer development of the boundary layers is in close agreement with the measured behaviour.

3,999 citations

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01 Jan 1978

TL;DR: In this article, an algebraic turbulence model for two-and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer, and compared with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil.

Abstract: An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.

3,701 citations

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01 Jan 1982TL;DR: When approximating a hyperbolic system of conservation laws w t + {f(w)} t = 0 with so-called upwind differences, one must determine in which direction each of a variety of signals moves through the computational grid.

Abstract: When approximating a hyperbolic system of conservation laws w t + {f(w)} t = 0 with so-called upwind differences, we must, in the first place, establish which way the wind blows. More precisely, we must determine in which direction each of a variety of signals moves through the computational grid. For this purpose, a physical model of the interaction between computational cells is needed; at present two such models are in use.

1,648 citations

### "Numerical Study of Heat Transfer Ar..." refers methods in this paper

...For the RANS equations, two different spatial discretization schemes are available: Roe’s flux difference splitting scheme [42] and Van Leer’s flux vector splitting scheme [43]....

[...]