On the mixed Cauchy problem with data on singular conics

We consider a problem of mixed Cauchy type for certain holomorphic partial differential operators whose principal part $Q_{2p}(D)$ essentially is the (complex) Laplace operator to a power, $\Delta^p$. We pose inital data on a singular conic divisor given by P=0, where $P$ is a homogeneous polynomial of degree $2p$. We show that this problem is uniquely solvable if the polynomial $P$ is elliptic, in a certain sense, with respect to the principal part $Q_{2p}(D)$

Maneuver of fixed-wing combat aircraft

Introduction: The ability to maneuver is an important consideration for fixed wing combat aircraft and is required for both aggressive and evasive maneuvers. Small differences in maneuver performance can be significant in determining which aircraft will win a combat engagement. For example, pilots often regard a difference of 2–3◦ s−1 in turn rate as being significant. The required maneuver performance will be determined by the aircraft’s role. For instance, an air combat aircraft designed to engage enemy fighters is likely to require high instantaneous turn rates, whilst a beyond visual range interceptor armed with long range missiles is more likely to be concerned with acceleration at high altitude and good climb to height characteristics

Use of wall suction in half model wind tunnel testing

The half model wind tunnel technique suffers from aerodynamic loses due to the interaction of the tunnel wall boundary layer with the flow over the model and the formation of a horseshoe vortex in the model-floor junction. The vortex is believed to contribute to the degradation of the half model aerodynamic performance. An attempt was made to reduce the aerodynamics losses by modifying the junction horseshoe vortex through the use of localized suction just upstream of the model leading edge. Wind tunnel tests on a rectangular and untwisted, wing only, modified LS(1)-0413 half model were conducted at Reynolds numbers of 0.44 x 10(6), 0.88 x 10(6) and 1 x 10(6). Without suction the force and moment balance measurements of the half model showed the anticipated deviation from full model values, e.g. lower lift curve slope and higher drag values. Effects of localized suction were limited to Reynolds number of 0.44 x 10(6) and improvements were seen only near stall angles of attack. Flow visualization for the no suction case showed that a horseshoe vortex did not exist over much of the incidence range for this particular model and hence there was little room for suction to effect junction flow. Near stall, suction removed the horseshoe vortex around the upper surface of the model and significantly reduced flow separations occurring in the model-floor junction, leading to the improved stall characteristics

The influence of hole orientation on the aerodynamics of battle damaged wings

Wind tunnel tests were carried out on an NASA LS(1)-0417MOD aerofoil with a circular hole simulating gunfire damage. To represent different attack directions, the inclination of the hole axis relative to the aerofoil chord was varied. The hole had a diameter of 20% of the aerofoil chord and its axis was centred at half chord. The aerofoil spanned the wind tunnel to create approximate two-dimensional conditions and balance measurements were carried out at a Reynolds number of 500, 000. Surface flow visualisation and pressure measurements were also carried out. The aerofoil model incorporated a cavity to represent the internal geometry of an aircraft’s wing. Compared to an undamaged wing the addition of damage increased drag, reduced lift and gave a more negative pitching moment. The effects increased with incidence. Adding negative obliquity, where the upper surface hole was moved forward and the lower hole rearwards, increased the magnitude of these effects. Except when combined with extreme negative obliquity, adding skew, where the holes were offset in a spanwise direction, had little measurable effect in terms of aerodynamic coefficients. However, adding skew introduced asymmetry to the flow through the damage

A technique to predict the aerodynamic effects of battle damage on an aircraft's wing

A technique is developed that can be used to predict the effects of battle damage on the aerodynamic performance of an aircraft’s wing. The technique is based on results obtained from wind tunnel tests on a NASA LS(1)-0417MOD aerofoil with simulated gunfire damage. The wind tunnel model incorporated an internal cavity to represent typical aircraft construction and this was located between 24% and 75% of chord. The damage was simulated by circular holes with diameters between 20% and 40% of chord. To represent different attack directions, the inclination of the hole axis relative to the aerofoil chord was varied between ±60o pitch and 45o of roll. The aerofoil spanned the wind tunnel to create approximate two-dimensional conditions and balance measurements were carried out at a Reynolds number of 500,000 for incidences, increased in 2o increments, from -4o to 16o. Surface flow visualization and pressure measurements were also carried out. For a given hole size, the increments in lift, drag and pitching moment coefficients produced trends when plotted against the difference between the upper and lower surface pressure coefficients on the undamaged aerofoil taken at the location of the damage. These trends are used as the basis of the predictive technique. The technique is used to predict the effects of a previously untested damage case, and these are compared with wind tunnel tests carried out on a half model finite aspect ratio wing. For all coefficients the trends in the predicted data are similar to experiment, although there are some discrepancies in absolute values. For the drag coefficient these discrepancies are partly accounted for by limitations in the technique, whilst discrepancies in the lift and pitching moment coefficients are attributed to limitations in the aerofoil test arrangements

A technique to predict the aerodynamic losses of battle damaged wings

Development of a technique to predict the effects of simulated battle damage on the aerodynamics of a three dimensional wing is described. A methodology for converting two dimensional lift, drag and pitching moment data to three dimensional values is developed. To test this methodology, wind tunnel testing was carried out on a three dimensional half model of the NASA LS(1)-0417MOD aerofoil, with simulated battle damage. The effective aspect ratio of the model was 6. A circular hole with a diameter of 20% of wing chord was used to simulate gunfiretype battle damage. To model different attack directions the axis of the hole was inclined along the chord and span. Three spanwise locations for the damage were tested. Testing was undertaken at a Reynolds Number of 1,000,000. Compared to an undamaged wing, the addition of damage caused an increase in drag, a decrease in lift and a more negative pitching moment. The effects increased with incidence and changed with hole orientation. These effects were reduced as the damage was moved towards the wing tip. Results from the predictive technique were compared with those from half model testing. The predicted lift loss was seen to be in close agreement with wind tunnel results, but the drag increase was under predicted. The biggest errors in the prediction occurred for the pitching moment, although the relatively low aspect ratio is believed to have an adverse effect on the comparison

Analysis of single hole simulated battle damage on a wing using particle image velocimetry

Particle Image Velocimetry (PIV) has been used to map the complex flow field generated by simulated battle damage to a two-dimensional wing. Previous studies have relied on surface flow visualisation techniques to study the flow but here PIV data has enabled the flow field away from the surface to be analysed for the first time. Damage was simulated by a single hole with a diameter equal to 20% of the chord, located at mid-chord. Wind tunnel tests were conducted at a Reynolds number of 500,000 over a range of incidences from 0-10 with two-component PIV measurements made on three span-wise planes; on the damage centre line and o set by 0.5 and 1.0 hole radii. The PIV data was seen to be in good agreement with existing surface flow visualisation showing strong evidence of the formation of a horse shoe vortex, a counter-rotating vortex pair and reverse flow regions. Large variations in the flow structure were observed over the range of incidences tested as the jet transitioned from weak at lower angles to strong at higher angles. The data also revealed some significant differences in the flow compared to classic Jets In Cross-Flow (JICF) behaviour. Notably in the case of battle damage the jet never fully occupies the hole and jet velocity pro le is highly skewed towards the rear of the hole. Additionally, the measured velocity ratios are much less than would be expected for typical JICF. For example, strong jet behaviour is observed at a velocity ratio as low as 0.22 whereas JICF studies would suggest a much higher ratio (> 2) is required. Increasing velocity ratio has been related to a reduction in lift and an increase in drag. At the highest incidence tested (10 ) the velocity ratio of 0.32 resulted in a reduction of the lift coe fficient by 0.18 and an increase in the drag coeffi cient of 0.035

Manual pages for SAGA software tools, appendix H

Several pages from the SAGA UNIX programmer's manual are presented. These pages are for SAGA software tools

Design methodology and performance of an indraft wind tunnel

The design methodology and performance of Loughborough University’s new 1·9m × 1·3m, indraft wind tunnel is discussed in the following paper. To overcome severe spatial and financial constraints, a novel configuration was employed, with the inlet and exit placed adjacent to each other and opened to atmosphere. Using a fine filter mesh, honeycomb, two turbulence reduction screens and a contraction ratio of 7·3, flow uniformity in the working area of the jet at 40ms-1 is shown to be within 0·3% deviation from the mean velocity, with turbulence intensity in the region of 0·15%. Working section boundary layer characteristics are shown to be consistent with that of a turbulent boundary layer growing along a flat plate, which originates at the point of inflection of the contraction. A maximum velocity of 46ms-1 was achieved from a 140kW motor, compared to a prediction of 44ms-1, giving an energy ratio of 1·42. Comparison between theoretical and measured performance metrics indicate differences between the way modules perform when part of a wind tunnel system compared to data gathered from test rigs