Robert J. Moffat

Describing the Uncertainties in Experimental Results

Abstract It is no longer acceptable, in most circles, to present experimental results without describing the uncertainties involved. Besides its obvious role in publishing, uncertainty analysis provides the experimenter a rational way of evaluating the significance of the scatter on repeated trials. This can be a powerful tool in locating the source of trouble in a misbehaving experiment. To the user of the data, a statement (by the experimenter) of the range within which the results of the present experiment might have fallen by chance alone is of great help in deciding whether the present data agree with past results or differ from them. These benefits can be realized only if both the experimenter and the reader understand what an uncertainty analysis is, what it can do (and cannot do), and how to interpret its results. This paper begins with a general description of the sources of errors in engineering measurements and the relationship between error and uncertainty. Then the path of an uncertainty analysis is traced from its first step, identifying the intended true value of a measurement, through the quantitative estimation of the individual errors, to the end objective—the interpretation and reporting of the results. The basic mathematics of both single-sample and multiple-sample analysis are presented, as well as a technique for numerically executing uncertainty analyses when computerized data interpretation is involved. The material presented in this paper covers the method of describing the uncertainties in an engineering experiment and the necessary background material.

Structure of transitionally rough and fully rough turbulent boundary layers

Structural characteristics of transitionally rough and fully rough turbulent boundary layers are presented. These were measured in flows at different roughness Reynolds numbers developing over uniform spheres roughness. Inner regions of the longitudinal component of normal Reynolds stress profiles and log regions of mean profiles continuously change in the transitionally rough regime, as the roughness Reynolds number, R ek , varies. These properties asymptotically approach fully rough behaviour as R ek increases, and smooth behaviour at low R ek Profiles of other Reynolds-stress tensor components, turbulence kinetic energy, turbulence-kinetic-energy production, and the turbulence-kinetic-energy dissipation are also given, along with appropriate scaling variables. Fully rough, one-dimensional spectra of longitudinal velocity fluctuations from boundary-layer inner regions are similar to smooth-wall results for k 1 y > 0.2 when non-dimensionalized using distance from the wall y as the lengthscale, and (τ/ρ) ½ as the velocity scale, where τ is local shear stress, ρ is static density, and k 1 is one-dimensional wavenumber in the flow direction.

Illuminant invariant calibration of thermochromic liquid crystals

Abstract A video-based system is described for using thermochromic liquid crystals (TLCs) to make highly accurate, full-field, surface temperature measurements, independent of the illuminant spectrum, background lighting, angle of incidence, and optical path. The system is comprised of three parts: (1) mixing, filtering, and spraying protocols that produce uniform TLC surfaces; (2) on-axis, cross-polarized primary lighting; and (3) correction algorithms for the optical path, the intensities, and spectra of both the primary illuminant and the background lighting, based on CIE Illuminant C—referenced color specimens placed in both the application and calibration fields of view. When 30 frames (1 seconds worth of data) are averaged, the uncertainty is less than ±0.25°C (with 95% confidence) even in the presence of various combinations of sunlight and fluorescent/incandescent room lighting, as long as the viewing angle is within ±25° of the normal.

The turbulent boundary layer on a porous plate: Experimental heat transfer with uniform blowing and suction

Abstract There exists a need for additional experimental work in the field of heat transfer through a turbulent boundary layer with blowing and suction. An apparatus has been constructed which allows the determination of Stanton number to within 0·0001 units over most of the range between the asymptotic suction layer and the apparent “blow off” of the boundary layer. Data are presented for the case of uniform blowing and suction, constant free stream velocity, and essentially constant properties. Stanton numbers ranged from 0·0080 (asymptotic suction layer behavior; blowing fraction of −0·00765) to a value of 0·0001 (near “blow off”; blowing fraction of + 0·00955). The Reynolds number range is 1·3 × 105−2·3 × 106. Tabular and graphical results are presented.

The turbulent boundary layer on a porous plate: Experimental skin friction with variable injection and suction

Abstract Experimental skin friction results from constant free-stream velocity boundary layers are reported for a variety of constant and slowly varying injection and suction wall conditions. A description is given of the flow characteristics of these air experiments. The uniform injection results are in good agreement with the results of Kendall and the Stevenson, Rotta, and Kinney results from the Mickley-Davis data. For all turbulent flows examined, C f 2 is found to be a a function of local Reθ and B. The friction factor ratio C f C fo |Reθ is found to be a function of B alone, and is given as an empirical function of B. Of seven theories examined, the theories of Rubesin and of Torii et al. are in best agreement with all of the results when considered on a local Ree and B basis. A simple calculation method of C f 2 vs. Rex is suggested for slowly varying Vw(X).

An experimental study of the turbulent prandtl number of air with injection and suction

Experimental values for Prt from blown, unblown, and sucked turbulent incompressible air boundary layers (Pr = 0·71) have been obtained from the mean velocity and temperature profile data of Simpson [5]and Whitten [6]. A description is given of the procedure used in obtaining these results. In the inner similarity region, Prt 1 in the outer similarity region. These results are in agreement with Ludwiegs [2]pipe results and show no effect of blowing or suction on Prt. The Jenkins model [21], which accounts for the unequal loss of momentum and thermal energy from an eddy in flight for Pr = 1 fluids, is found to describe the variation of Prt in the inner region within experimental uncertainty of the data. Using Hinzes [14]suggestion that the diffusion of heat might be a combination of gradient and large eddy transport, a new model is developed to account for Prt < 1 in the outer region. Predictions based on these models lie within the uncertainty band of the experimental results and indicate no effect of blowing or sucking on Prt.

Thermoregulation and the determinants of heat transfer in Colias butterflies

SummaryAs a means of exploring behavioral and morphological adaptations for thermoregulation in Colias butterflies, convective heat transfer coefficients of real and model butterflies were measured in a wind tunnel as a function of wind speed and body orientation (yaw angle). Results are reported in terms of a dimensionless heat transfer coefficient (Nusselt number, Nu) and a dimensionless wind speed (Reynolds number, Re), for a wind speed range typical of that experienced by basking Colias in the field. The resultant Nusselt-Reynolds (Nu-Re) plots thus indicate the rates of heat transfer by forced convection as a function of wind speed for particular model geometries.For Reynolds numbers throughout the measured range, Nusselt numbers for C. eurytheme butterflies are consistently lower than those for long cylinders, and are independent of yaw angle. There is significant variation among individual butterflies in heat transfer coefficients throughout the Re range. Model butterflies without artificial fur have Nu-Re relations similar to those for cylinders. Heat transfer in these models depends upon yaw angle, with higher heat transfer at intermediate yaw angles (30–60°); these yaw effects increase with increasing Reynolds number. Models with artificial fur, like real Colias, have Nusselt numbers which are consistently lower than those for models without fur at given Reynolds numbers throughout the Re range. Unlike real Colias, however, the models with fur do show yaw angle effects similar to those for models without fur.The independence of heat loss from yaw angle for real Colias is consistent with field observations indicating no behavioral orientation to wind direction. The presence of fur on the models reduces heat loss but does not affect yaw dependence. The large individual variation in heat transfer coefficients among butterflies is probably due to differences in fur characteristics rather than to differences in wing morphology.Finally, a physical model of a butterfly was constructed which accurately simulates the body temperatures of basking Colias in the field for a variety of radiation and wind velocity conditions. The success of the butterfly simulator in mimicking Colias thermal characteristics confirms our preliminary understanding of the physical bases for and heat transfer mechanisms underlying thermoregulatory adaptations in these butterflies.

Experimental results for the transpired turbulent boundary layer in an adverse pressure gradient

The fluid mechanics of transpired incompressible turbulent boundary layers under zero and adverse pressure gradient conditions is investigated using an open-ended wind tunnel with a porous floor in the test section and a secondary air system for supply and metering of the transpiration air. All velocity profiles and turbulence profiles are obtained by linearized constant-temperature hot-wire anemometry. The wall shear stress is determined by measuring the shear stress away from the wall and extrapolating to the wall by integrating the boundary layer equations for the shear-stress profile. Equilibrium boundary layers are obtained when the transpiration velocity is varied such that the blowing parameter and the Clauser pressure gradient parameter are held constant. The experimental results obtained are presented in tabular and graphical forms.

What's new in convective heat transfer?

Abstract This paper describes the quest for invariant descriptors of the convective process, and the new requirements those descriptors put on quantitative full-field thermal imaging. There is increasing need, in applications, for heat transfer descriptors which can deal with non-uniform thermal boundary conditions, including those induced by conjugate effects. This paper discusses two approaches which have arisen within the past 10 years: (1) the use of h adiabatic and T adiabatic to describe the convective process and more recently, (2) the emergence of discretized Greens functions for convection. Both of these approaches acknowledge the effects of upstream heat transfer on local behavior but both do so using coefficients which, themselves, are invariant with respect to changes in the thermal boundary conditions. Thus measurements made in the lab can be applied in the field, under different thermal boundary conditions. Both approaches can be used in complex flow fields, such as flows on surfaces with obstructions. To realize the full potential of either approach, the uncertainties in full-field optical data acquistion techniques must be reduced by about a factor of 3.

The accelerated fully rough turbulent boundary layer

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity. An appropriate acceleration parameter K r for fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fraction F greater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state when K r is held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant. Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (for F equal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.