Specific cooling capacity of liquid nitrogen

The assumed cooling process and the method used to calculate the specific cooling capacity of liquid nitrogen are described, and the simple equation fitted to the calculated specific cooling capacity data, together with the graphical form calculated values of the specific cooling capacity of nitrogen for stagnation temperatures from saturation to 350 K and stagnation pressures from 1 to 10 atmospheres, are given

Recovering piecewise smooth functions from nonuniform Fourier measurements

In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to ensure high accuracy we employ reconstruction spaces consisting of splines or (piecewise) polynomials. We analyze the relation between the dimension of the reconstruction space and the bandwidth of the nonuniform samples, and show that it is linear for splines and piecewise polynomials of fixed degree, and quadratic for piecewise polynomials of varying degree

Effect of Reynolds Number and Mach Number on flow angularity probe sensitivity

Preliminary calibrations were performed on nine flow angularity probes in the Langley 7- by 10-Foot High-Speed Tunnel (7 x 10 HST) and the Langley 0.3-Meter Transonic Cryogenic Tunnel (0.3-m TCT). These probes will be used in surveying the test section flows of the National Transonic Facility (NTF). The probes used in this study have a pyramid head with five pressure orifices. The calibrations consisted of both isolated probe measurements and rake-mounted multiprobe measurements that covered a range of subsonic Mach numbers up to 0.90 and Reynolds numbers per foot up to 40 X 10 to the 6th power. The preliminary calibration in the 7 x 10 HST included testing the probes both individually and in a rake. The 0.3-m TCT calibration tested two probes singly at varying Reynolds numbers. The results from these tests include Mach number, Reynolds number, and rake-mounting effects. The results of these tests showed probe sensitivity to be slightly affected by Mach number. At Reynolds numbers per foot above 10 x 10 to the 6th power, the probe did not exhibit a Reynolds number sensitivity

Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit

We show the potential of greedy recovery strategies for the sparse approximation of multivariate functions from a small dataset of pointwise evaluations by considering an extension of the orthogonal matching pursuit to the setting of weighted sparsity. The proposed recovery strategy is based on a formal derivation of the greedy index selection rule. Numerical experiments show that the proposed weighted orthogonal matching pursuit algorithm is able to reach accuracy levels similar to those of weighted $\ell^1$ minimization programs while considerably improving the computational efficiency for small values of the sparsity level

Simulation of flight test conditions in the Langley pilot transonic cryogenic tunnel

The theory and advantages of the cryogenic tunnel concept are briefly reviewed. The unique ability to vary temperature independently of pressure and Mach number allows, in addition to large reductions in model loads and tunnel power, the independent determination of Reynolds number, Mach number, and aeroelastic effects on the aerodynamic characteristics of the model. Various combinations of Reynolds number and dynamic pressure are established to represent accurately flight variations of aeroelastic deformation with altitude changes. The consequences of the thermal and caloric imperfections of the test gas under cryogenic conditions were examined and found to be insignificant for operating pressures up to 5 atm. The characteristics of the Langley pilot transonic cryogenic tunnel are described and the results of initial tunnel operation are presented. Tests of a two-dimensional airfoil at a Mach number of 0.85 show identical pressure distributions for a chord Reynolds number of 8,600,000 obtained first at a stagnation pressure of 4.91 atm at a stagnation temperature of 322.0 K and then at a stagnation pressure of 1.19 atm at a stagnation temperature of 116.5 K

Full-scale aircraft simulation with cryogenic tunnels and status of the National Transonic Facility

The effect of thermal and caloric imperfections in cryogenic nitrogen on boundary layers was determined to indicate that in order to simulate nonadiabatic laminar or turbulent boundary layers in a cryogenic nitrogen wind tunnel, the flight enthalpy ratio, rather than the temperature ratio, should be reproduced. The absence of significant real gas effects on both viscous and inviscid flows makes it unlikely that there will be large real gas effects on the cryogenic tunnel simulation of shock boundary layer interactions or other complex flow conditions encountered in flight. Condensation effects were studied to determine the minimum usable temperature and indicated that under most circumstances free stream Mach number rather than maximum local Mach number determines the onset of condensation effects

The cryogenic wind tunnel concept for high Reynolds number testing

Theoretical considerations indicate that cooling the wind-tunnel test gas to cryogenic temperatures will provide a large increase in Reynolds number with no increase in dynamic pressure while reducing the tunnel drive-power requirements. Studies were made to determine the expected variations of Reynolds number and other parameters over wide ranges of Mach number, pressure, and temperature, with due regard to avoiding liquefaction. Practical operational procedures were developed in a low-speed cryogenic tunnel. Aerodynamic experiments in the facility demonstrated the theoretically predicted variations in Reynolds number and drive power. The continuous-flow-fan-driven tunnel is shown to be particularly well suited to take full advantage of operating at cryogenic temperatures

Analysis of validation tests of the Langley pilot transonic cryogenic tunnel

A pilot transonic cryogenic pressure tunnel has recently been developed and proof tested at the NASA Langley Research Center. In addition to providing an attractive method for obtaining high Reynolds number results at moderate aerodynamic loadings and tunnel power, this unique tunnel allows the independent determination of the effects of Reynolds number, Mach number, and dynamic pressure (aeroelasticity) on the aerodynamic characteristics of the model under test. The proof of concept experimental and theoretical studies are briefly reviewed. Experimental results obtained on both two- and three-dimensional models have substantiated that cryogenic test conditions can be set accurately and that cryogenic gaseous nitrogen is a valid test medium

A Phenomenological Study of Counseling Students’ Experiences with Ambiguity

Six master’s-level counseling students were interviewed about their phenomenological experiences of ambiguity in counselor preparation. Analysis revealed five themes: students’ preparation for ambiguous experiences, ambiguities of counselor preparation, accompanying overwhelming feelings, coping approaches, and self-assurance gained from facing ambiguity. These findings have implications for counselor education and supervision

Beta lives - some statistical perspectives on the capital asset pricing model

This note summarizes some technical issues relevant to the use of the idea of excess return in empirical modelling. We cover the case where the aim is to construct a measure of expected return on an asset and a model of the CAPM type is used. We review some of the problems and show examples where the basic CAPM may be used to develop other results which relate the expected returns on assets both to the expected return on the market and other factors