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

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

Performance of an ideal turbine in an inviscid shear flow

Although wind and tidal turbines operate in turbulent shear flow, most theoretical results concerning turbine performance, such as the well-known Betz limit, assume the upstream velocity profile is uniform. To improve on these existing results we extend the classical actuator disc model in this paper to investigate the performance of an ideal turbine in steady, inviscid shear flow. The model is developed on the assumption that there is negligible lateral interaction in the flow passing through the disc and that the actuator applies a uniform resistance across its area. With these assumptions, solution of the model leads to two key results. First, for laterally unbounded shear flow, it is shown that the normalised power extracted is the same as that for an ideal turbine in uniform flow, if the average of the cube of the upstream velocity of the fluid passing through the turbine is used in the normalisation. Second, for a laterally bounded shear flow, it is shown that the same normalisation can be applied, but allowance must also be made for the fact that non-uniform flow bypassing the turbine alters the background pressure gradient and, in turn, the turbines ‘effective blockage’ (so that it may be greater or less than the geometric blockage, defined as the ratio of turbine disc area to cross-sectional area of the flow). Predictions based on the extended model agree well with numerical simulations approximating the incompressible Euler equations. The model may be used to improve interpretation of model-scale results for wind and tidal turbines in tunnels/flumes, to investigate the variation in force across a turbine and to update existing theoretical models of arrays of tidal turbines

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

Convolutional Analysis Operator Learning: Dependence on Training Data

Convolutional analysis operator learning (CAOL) enables the unsupervised training of (hierarchical) convolutional sparsifying operators or autoencoders from large datasets. One can use many training images for CAOL, but a precise understanding of the impact of doing so has remained an open question. This paper presents a series of results that lend insight into the impact of dataset size on the filter update in CAOL. The first result is a general deterministic bound on errors in the estimated filters, and is followed by a bound on the expected errors as the number of training samples increases. The second result provides a high probability analogue. The bounds depend on properties of the training data, and we investigate their empirical values with real data. Taken together, these results provide evidence for the potential benefit of using more training data in CAOL.Comment: 5 pages, 2 figure

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

A study of the types of interlace on Northumbrian sculpture

The introductory material of this thesis is concerned with building up a form of analysis whereby interlace might be described or compared. This is therefore involved with what can be discovered about the construction of interlace, the measurements and techniques used from the primary material. Also a system of categorising designs is put forward; by this the patterns with similar elements and the patterns with like variations of different elements may be compared. Northumbrian sculptured interlace is thus examined by taking into account factors of measurement technique and pattern types but keeping in mind the part played by the interlace in the whole ornamental programme of each work. Several groups of work become clearly defined, others remain nebulous because of their more fragmentary nature. There are found to be some very early works associated with Wearmouth-Jarrow and Hexham-Ripon. There are groups of mature interlace existing around Ripon and Lastingham in Deira and others in Bernicia, more difficult to associate with a centre but having expression at Lindisfarne and Norham, while Wearmouth, Jarrow and Tynemouth also appear to be centres of importance. The work of the late Anglian and Viking era is only followed in part. The study is specifically directed to the later work of Lindisfarne and Chester-le-Street to discover how the Anglian style of interlace survived, developed or changed through the troubled era. The study ends with a review of the best great expression of sculptured interlace of Northumbria, that belonging to the Durham revival