Thomas J. Mueller

Low Reynolds Number Aerodynamics of Low-Aspect-Ratio, Thin/Flat/Cambered-Plate Wings

The design of micro aerial vehicles requires a better understanding of the aerodynamics of small low-aspect-ratio wings. An experimental investigation has focused on measuring the lift, drag, and pitching moment about the quarter chord on a series of thin flat plates and cambered plates at chord Reynolds numbers varying between 60,000 and 200,000. Results show that the cambered plates offer better aerodynamic characteristics and performance. It also appears that the trailing-edge geometry of the wings and the turbulence intensity in the wind tunnel do not have a strong effect on the lift and drag for thin wings at low Reynolds numbers. Moreover, the results did not show the presence of any hysteresis, which is usually observed with thick airfoils/wings

Low-aspect-ratio wing aerodynamics at low Reynolds numbers

The recent interest in the development of small unmanned aerial vehicles (UAVs) and micro air vehicles has revealed a need for a more thorough understanding of the aerodynamics of small airplanes flying at low speeds. In response to this need, a study of the lift, drag, and pitching moment characteristics of wings of low aspect ratio operating at low Reynolds numbers are presented. Wind-tunnel tests of wings with aspect ratios between 0.5 and 2.0, four distinct planforms, thickness-to-chord ratios of ≈ 2%, and 5-to-1 elliptical leading edges have been conducted as part of this research. The Reynolds numbers considered were in the range of 7 × × 10 4 to 2 × × 10 5 . Analysis of the data includes comparison of lift-curve slope, nonlinear equation approximations, maximum lift coefficient, and center of lift.

Experimental Studies of Separation on a Two-Dimensional Airfoil at Low Reynolds Numbers

The laminar separation, transition, and turbulent reattachment near the leading edge of a two-dimensional NACA 663 -018 airfoil were investigated using a low-speed, smoke visualization wind tunnel. Lift and drag force measurements were made using an external strain gage balance for a chord Reynolds number range of 40,GOO400,000. An extensive flow visualization study was performed and correlated with the force measurements. Experiments were also conducted with distributed surface roughness at the leading edge and external acoustic excitation to influence the development of the airfoil boundary layer. This study delineates the effects of angle of attack and chord Reynolds number on the separation characteristics and airfoil performance. Nomenclature c = model chord cd = section profile drag coefficient (uncorrected) cf = section lift coefficient (uncorrected) Cp = pressure coefficient / = acoustic frequency, Hz R = reattachment location Rc = Reynolds number based on chord length, U^ civ S = separation location T = location of approximate end of transition £/«, = freestream velocity x/c = nondimensional distance along chord a = angle of attack v - kinematic viscosity

The Influence of Laminar Separation and Transition on Low Reynolds Number Airfoil Hysteresis

An experimental study of the Lissaman 7769 and Miley MO6-13-128 airfoils at low chord Reynolds numbers is presented. Although both airfoils perform well near their design Reynolds number of about 600,000, they each produce a different type of hysteresis loop in the lift and drag forces when operated below chord Reynolds numbers of 300,000. The type of hysteresis loop was found to depend upon the relative location of laminar separation and transition. The influence of disturbance environment and experimental procedure on the low Reynolds number airfoil boundary layer behavior is also presented. The use of potential flow solutions to help predict how a given airfoil will behave at low Reynolds numbers is also discussed.

Measurements in a separation bubble on an airfoil using laser velocimetry

An experimental investigation was conducted to measure the reverse flow within the transitional separation bubble that forms on an airfoil at low Reynolds numbers. Measurements were used to determine the effect of the reverse flow on integrated boundary-layer parameters often used to model the bubble. Velocity profile data were obtained on an NACA 663-018 airfoil at angle of attack of 12 deg and a chord Reynolds number of 140,000 using laser Doppler and single-sensor hot-wire anemometry. A new correlation is proposed based on zero velocity position, since the Schmidt (1986) correlations fail in the turbulent portion of the bubble.

Turbulence Ingestion Noise, Part 2: Rotor Aeroacoustic Response to Grid-Generated Turbulence

This is the second of two papers that discuss an experimental investigation of the aeroacoustic response characteristics of a 10-bladed rotor to grid-generated turbulence. To characterize empirically the rotor response, both the ingested velocity field and resulting far-field sound were measured. In part 1, an empirical velocity characterization of the grid- generated turbulence field was presented. This characterization culminated in a semi-empirical model of the ingested small-scale turbulence field and a modal decomposition of the circumferentially varying mean velocity field in the rotor inlet plane. This detailed velocity model is now used to investigate the aeroacoustic response of a 10-bladed rotor ingesting the grid-generated turbulence field. In particular, the semi-empirical turbulence model is used, in conjunction with theoretical spectral analysis techniques, to predict the far-field sound generated by the 10-bladed rotor. These predictions are compared to corresponding measured data to assess the fidelity of the spectral analysis methods and the semi-empirical turbulence model

Turbulence Ingestion Noise, Part 1: Experimental Characterization of Grid-Generated Turbulence

Results are presented of an experimental investigation into the aeroacoustic response characteristics of rotor turbulence ingestion. To fully characterize the rotor response, both the ingested velocity field and the resulting far-field sound were measured. The results are presented of a detailed velocity characterization, which was performed upstream of the rotor. The velocity measurements included an evaluation of the streamwise development of turbulence characteristics downstream of the grid, a high-resolution mapping of the spatial distribution of the mean velocity and rms turbulence fluctuations in the rotor inlet plane, and the development of a semi-empirical, functional representation of the three-dimensional wave number spectral density of the ingested turbulence

Analysis of low Reynolds number separation bubbles using semiempirical methods

The formation and growth of transitional separation bubbles can significantly affect boundary-layer development on airfoils operating at low chord Reynolds numbers. Of primary concern is the change in boundary-layer thickness between laminar separation and turbulent reattachment. This can be estimated using semiempirical methods, such as the one devised by H. P. Horton, which are based on solutions to the integral forms of the boundary-layer equations. The applicability of these methods at low Reynolds numbers was investigated using hot-wire measurements of bubbles formed on an NACA 663-018 airfoil at chord Reynolds numbers of 50,000-200,000. Analysis of the data revealed significant Reynolds number effects on the evolution of separated laminar flow. The momentum thickness growth between separation and transition was found to be similar to that predicted for a laminar half-jet and appears to be influenced by the momentum thickness Reynolds number at separation. This parameter also was found to have a noticeable effect on the Reynolds number based on the length of a bubbles laminar portion. In the turbulent portion of the bubbles, no Reynolds number effects were evident. This was true for both the momentum thickness growth and for Hortons reattachment criterion.

Experimental study of a low Reynolds number tandem airfoil configuration

Experiments were concluded with two identical Wortmann FX63-137 airfoils in closely coupled tandem configurations at a Reynolds number of 8.5 x 10 4. For the data presented here, the values of the stagger and gap were 1.5 and 0, respectively. The decalage angles were 0 and ±10 deg. Direct measurement of lift, drag, and 1/4-chord pitching moment, as well as static pressure distributions, were acquired for each airfoil. Flow visualization using kerosene smoke was performed to complement the experimental data. The total drag reduction and lift increase resulted in a significant increase in the lift-to-drag ratio for a number of configurations. Nomenclature Aw = wing area Cd = section drag coefficient, D/(Awqx) Ci = section lift coefficient, L/(AwqJ) Cm = section 1/4-chord moment coefficient, Cp = pressure coefficient, l-q/qx c = chord length D = drag force G = gap, \y\lc L = lift force M = 1/4-chord pitching moment q = dynamic pressure, \pU2 Rc = Reynolds number based on chord, Uxc/v St = stagger, x/c (positive when upstream airfoil is above the downstream airfoil) U = flow velocity x = distance in streamwise direction y - distance normal to streamwise directions a = angle of attack 8 = decalage, aua - ada

Effect of Endplates on Two-Dimensional Airfoil Testing at Low Reynolds Number

The presence of endplates (or sideplates ) in two-dimensional wind-tunnel force measurements on airfoils has a strong effect on lift and drag coefe cients at low Reynolds numbers. Results on an Eppler 61 airfoil indicate that the endplates are responsible for a sharp decrease in the airfoil performance. The lift coefe cient is reduced and the drag coefe cient is increased due to the interaction of the airfoil boundary layer with the sideplate boundary layer. Nomenclature b = span Cd = section proe le drag coefe cient Cl = section lift coefe cient c = chord length eQ = quantization error M = resolution of A/D converter Rec = chord Reynolds number Rex = Reynolds number based on distance x along endplate U1 = freestream velocity x = distance from leading edge of endplate ® = angle of attack ± = boundary-layer thickness