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Correction of linear functional differential equations with time delay showing error due to incorrect interchange of order of integration involving Stieltjes integral
Based on an optimization formulation, a procedure has been developed to evaluate Mach number and angle-of-attack corrections. The Euler equations are assumed to be the flow governing equations. To obtain efficient solutions for the optimization problem, the iterative solutions for the flow variables and the design parameters are simultaneously updated. In addition to the model lift and geometry, the procedure requires pressure measurements near the tunnel walls. The accuracy and efficiency of several optimization techniques are investigated. The effect of perturbing certain test conditions on the residual interference is investigated.
The analysis is based on a primary secondary velocity decomposition in a given coordinate system, and leads to approximate governing equations which correct an a priori inviscid solution for viscous effects, secondary flows, total pressure distortion, heat transfer, and internal flow blockage and losses. Solution of the correction equations is accomplished as an initial value problem in space using an implicit forward marching technique. The overall solution procedure requires significantly less computational effort than Navier-Stokes algorithms. The solution procedure is effective even with the extreme local mesh resolution which is necessary to solve near wall sublayer regions in turbulent flow calculations. Computed solutions for both laminar and turbulent flow compared very favorably with available analytical and experimental results. The overall method appears very promising as an economical procedure for making detailed predictions of viscous primary and secondary flows in highly curved passages.
Numerical solutions are presented for three-dimensional laminar and turbulent flow in curved ducts of rectangular cross section and significant curvature. The analysis is based on a primary-secondary velocity decomposition in a given coordinate system, and leads to approximate governing equations which correct an a priori inviscid solution for viscous effects, secondary flows, total pressure distortion, heat transfer, and internal flow blockage and losses. Solution of the correction equations is accomplished as an initial-value problem in space using an implicit forward-marching technique. The overall solution procedure requires significantly less computational effort than Navier-Stokes algorithms. The present solution procedure is effective even with the extreme local mesh resolution which is necessary to resolve near-wall sublayer regions in turbulent flow calculations. Computed solutions for both laminar and turbulent flow compare very favorably with available analytical and experimental results.
Front-end stray light baffles for optical imaging systems are used to limit the amount of out-of-field light that reaches the entrance pupil of the optical system. From star tracker baffles to the outer barrel of the Hubble Space Telescope, it is vital to design the locations and apertures of baffle vanes so that the inner walls of the baffle are not simultaneously visible to both stray light sources and the optical entrance pupil. Various designs have been presented for arbitrary cylindrical baffle tubes and explicitly specified conical tubes, but no working generalized algorithm has been presented where the baffle tube can take an arbitrary conical form. Haghshenas and Johari presented what should be a working recursive algorithm, but the published equations have two errors that result in incorrect output. Corrections to their equations are presented here. Additionally, tolerancing in the field of baffle design has typically been accomplished by slightly increasing the field-of-view of the baffle system to avoid clipping the optical field due to mechanical tolerance errors. A new way of incorporating fabrication, alignment, and environmental tolerancing is presented that is more consistent with typical mechanical engineering practice. Furthermore, it is included in the recursive equations with some demonstration of their impact.
Front-end stray light baffles for optical imaging systems are used to limit the amount of out-of-field light that reaches the entrance pupil of the optical system. From star tracker baffles to the outer barrel of the Hubble Space Telescope, it is vital to design the locations and apertures of baffle vanes so that the inner walls of the baffle are not simultaneously visible to both stray light sources and the optical entrance pupil. Various designs have been presented for arbitrary cylindrical baffle tubes and explicitly specified conical tubes, but no working generalized algorithm has been presented where the baffle tube can take an arbitrary conical form. Haghshenas and Johari presented what should be a working recursive algorithm, but the published equations have two errors that result in incorrect output. Corrections to their equations are presented here. Additionally, tolerancing in the field of baffle design has typically been accomplished by slightly increasing the fieldof-view of the baffle system to avoid clipping the optical field due to mechanical tolerance errors. A new way of incorporating fabrication, alignment, and environmental tolerancing is presented that is more consistent with typical mechanical engineering practice and margin against those fabrication errors is included in the recursive equations with demonstration of their benefit.
This article [Opt. Eng. 51, 011002 (2012)] was originally published on 8 February 2012 with an error in Eq. (13). The corrected equation appears below. The manuscript was corrected online on 15 February 2012. The article appears correctly in print.
A control-volume based finite difference method to solve the Reynolds averaged Navier-Stokes equations is presented. A pressure correction equation valid at all flow velocities and a pressure staggered grid layout are used in the method. Example problems presented herein include: a developing laminar channel flow, developing laminar pipe flow, a lid-driven square cavity flow, a laminar flow through a 90-degree bent channel, a laminar polar cavity flow, and a turbulent supersonic flow over a compression ramp. A k-epsilon turbulence model supplemented with a near-wall turbulence model was used to solve the turbulent flow. It is shown that the method yields accurate computational results even when highly skewed, unequally spaced, curved grids are used. It is also shown that the method is strongly convergent for high Reynolds number flows.
A control-volume based finite difference computation of a turbulent transonic flow over an axisymmetric curved hill is presented. The numerical method is based on the SIMPLE algorithm, and hence the conservation of mass equation is replaced by a pressure correction equation for compressible flows. The turbulence is described by a k-epsilon turbulence model supplemented by a near-wall turbulence model. In the method, the dissipation rate in the region very close to the wall is obtained from an algebraic equation and that for the rest of the flow domain is obtained by solving a partial differential equation for the dissipation rate. The other flow equations are integrated up to the wall. It is shown that the present turbulence model yields the correct location of the compression shock. The other computational results are also in good agreement with experimental data.
A numerical investigation of transonic turbulent flows separated by curvature and shock wave - boundary layer interaction is presented. The free stream Mach numbers considered are 0.4, 0.5, 0.6, 0.7, 0.8, 0.825, 0.85, 0.875, 0.90, and 0.925. In the numerical method, the conservation of mass equation is replaced by a pressure correction equation for compressible flows and thus incremental pressure is solved for instead of density. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. The present numerical results show that there exists a reversed flow region at all free stream Mach numbers considered whereas various k-epsilon turbulence models fail to predict such a reversed flow region at low free stream Mach numbers. The numerical results also show that the size of the reversed flow region grows extensively due to the shock wave - turbulent boundary layer interaction as the free stream Mach number is increased. These numerical results show that the turbulence model can resolve the turbulence field subjected to extra strains caused by the curvature and the shock wave - turbulent boundary layer interaction and that the numerical method yields a significantly accurate solution for the complex compressible turbulent flow.
A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.
A numerical investigation of incompressible and compressible turbulent flows over strongly curved surfaces is presented. The turbulent flow equations are solved by a pressure based Navier-Stokes equations solver. In the method, the conservation of mass equation is replaced by a pressure correction equation applicable for both compressible and incompressible flows. The turbulence is described by a multiple time scale turbulence model supplemented with a near-wall turbulence model. The numerical results show that the internal layer is a strong turbulence field which is developed beneath the external boundary layer and is located very close to the wall. The development of the internal layer is attributed to the enormous mean flow strain rate caused by the streamline curvature. The external boundary layer flow responds rather slowly to the streamline curvature. Thus, the turbulence field of the forward corner of the curved hill is characterized by two turbulence fields interacting with each other. The turbulence intensity of the internal layer is much stronger than that of the external boundary layer, so that the development of a new boundary layer in the downstream region of the curved hill depends mostly on the internal layer. These numerical results are in good agreement with the measured data, and show that the turbulence model can resolve the turbulence field subjected to the strong streamline curvature.
A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.
Optical measurements of range and elevation angle are distorted by the earth's atmosphere. High precision refraction correction equations are presented which are ideally suited for surveying because their inputs are optically measured range and optically measured elevation angle. The outputs are true straight line range and true geometric elevation angle. The 'short distances' used in surveying allow the calculations of true range and true elevation angle to be quickly made using a programmable pocket calculator. Topics covered include the spherical form of Snell's Law; ray path equations; and integrating the equations. Short-, medium-, and long-range refraction corrections are presented in tables.
A system for geometrically correcting LANDSAT MSS imagery includes all phases of processing, from receiving a raw computer compatible tape (CCT) to the generation of a corrected CCT (or UTM mosaic). The system comprises modules for: (1) control of the processing flow; (2) calculation of satellite ephemeris and attitude parameters, (3) generation of uncorrected files from raw CCT data; (4) creation, management and maintenance of a ground control point library; (5) determination of the image correction equations, using attitude and ephemeris parameters and existing ground control points; (6) generation of corrected LANDSAT file, using the equations determined beforehand; (7) union of LANDSAT scenes to produce and UTM mosaic; and (8) generation of output tape, in super-structure format.
A new empirical atmospheric density model is developed using the CIRA72 (Jacchia 71) model as the basis for the diffusion equations. New solar indices based on orbit based sensor data are used for the solar irradiances in the extreme and far ultraviolet wavelengths. New exospheric temperature and semiannual density equations are employed to represent the major thermospheric density variations. Temperature correction equations are also developed for diurnal and latitudinal effects, and finally density correction factors are used for model corrections required at high altitude (1500-4000 km). The new model, Jacchia-Bowman 2006, is validated through comparisons of accurate daily density drag data previously computed for numerous satellite. For 400 km altitude the standard deviation of 16% for the standard Jacchia model is reduced to 10% for the new JB2006 model for periods of low geomagnetic storm activity.
Soil moisture in the 0-cm to 4-cm layer could be estimated with 1-mm soil temperatures throughout the growing season of a rainfed barley crop in eastern South Dakota. Empirical equations were developed to reduce the effect of canopy cover when radiometrically estimating the soil temperature. Corrective equations were applied to an aircraft simulation of HCMM data for a diversity of crop types and land cover conditions to estimate the soil moisture. The average difference between observed and measured soil moisture was 1.6% of field capacity. Shallow alluvial aquifers were located with HCMM predawn data. After correcting the data for vegetation differences, equations were developed for predicting water table depths within the aquifer. A finite difference code simulating soil moisture and soil temperature shows that soils with different moisture profiles differed in soil temperatures in a well defined functional manner. A significant surface thermal anomaly was found to be associated with shallow water tables.
The quantum electrodynamic correction to the equation of state of a plasma at finite temperature is applied to the areas of solar physics and cosmology. A previously neglected, purely quantum term in the correction is found to change the equation of state in the solar core by -0.37%, which is roughly estimated to decrease the calculated high energy neutrino flux by about 2.2%. We also show that a previous calculation of the effect of this correction on big bang nucleosynthesis is incomplete, and we estimate the correction to the primordial helium abundance Y to be Delta A= 1.4 x 10(exp -4). A physical explanation for the correction is found in terms of corrections to the dispersion relation of the electron, positron, and photon.