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The following areas of flight science are discussed in detail; (1) inviscid flow, (2) viscous flow, (3) aircraft aerodynamics, (4) fluid mechanics, (5) propulsion and combustion, and (6) flight dynamics and control.
A new explicit, time splitting algorithm has been developed for finite difference modelling of the full two and three-dimensional time-dependent, compressible, viscous Navier-Stokes equations of fluid mechanics. The scheme is optimal in the sense that the split operators achieve their maximum allowable time step, i.e., the corresponding Courant number. The algorithm allows a conservation-form formulation. Stability is proven analytically and verified numerically. In proving stability it was shown that all nine matrix coefficients of the Navier-Stokes equations are simultaneously symmetrizable by a similarity transformation. Two such transformations and their resulting symmetric matrix coefficients are presented explicitly.
A constitutive lubricant friction model for rolling/sliding concentrated contacts such as gears and cams was developed, based upon the Johnson and Tevaarwerk fluid rheology model developed earlier. The friction model reported herein differs from the earlier rheological models in that very large slide to roll ratios can now be accommodated by modifying the thermal response of the model. Also the elastic response of the fluid has been omitted from the model, thereby making it much simpler for use in the high slide to roll contacts. The effects of this simplification are very minimal on the outcome of the predicted friction losses (less than 1%). In essence then the lubricant friction model developed for the high slide to roll ratios treats the fluid in the concentrated contact as consisting of a nonlinear viscous element that is pressure, temperature, and strain rate dependent in its shear response. The fluid rheological constants required for the prediction of the friction losses at different contact conditions are obtained by traction measurements on several of the currently used gear lubricants. An example calculation, using this model and the fluid parameters obtained from the experiments, shows that it correctly predicts trends and magnitude of gear mesh losses measured elsewhere for the same fluids tested here.
Based on considerations of fluid dynamic simulation appropriate to hypersonic, viscous flow over blunt-nosed lifting bodies, a method was presented earlier for estimating drag coefficients in the transitional-flow regime. The extension of the same method to prediction of lift coefficients is presented. Correlation of available experimental data by a simulation parameter appropriate for this purpose is the basis for the procedure described. The ease of application of the method makes it useful for preliminary studies which involve a wide variety of three-dimensional vehicle configurations or a range of angles of attack of a given vehicle.
The intermediate-wavelength geoid (lambda similar to 2000 km) and sea-floor topography fields in the central Pacific Ocean were studied in terms of static and dynamic compensation models. Topographic features on the sea-floor with lambda less than 1000 km were found to be compensated both regionally, by the elastic strength of the lithosphere, and locally, by displacing mantle material to reach isostatic adjustment. The larger-scale sea-floor topography and the corresponding geoid anomalies with lambda similar to 2000 km cannot be explained by either local or regional compensation. The topography and the resulting geoid anomaly at this wavelength were modeled by considering the dynamic effects arising from viscous stresses in a layer of fluid with a highly temperature-dependent viscosity for the cases of: (1) surface cooling, and (2) basal heating. In this model, the mechanical properties of the elastic part of the lithosphere were taken into account by considering an activation energy of about 520 kJ/mol in the Arrhenius law for the viscosity. Numerical predictions of the topography, total geoid anomaly, and admittance were obtained, and the results show that the thermal perturbation in the layer, which accounts for the mass deficit, must be located close to the surface to compensate the gravitational effect of the surface deformation. For the case of basal heating, the temperature dependence of viscosity results in a separation of the upper, quasi-rigid lid from the lower mobile fluid, hence inhibiting the development of a compensating thermal perturbation at shallow depths. The results clearly rule out small-scale, upper-mantle convection as the source of these anomalies. Instead, the geophysical observables can be well explained by a shallow, transient thermal perturbation.
Recently, NASA, FAA, and other organizations have focused their attention upon the possible effects of rain on airfoil performance. Rhode carried out early experiments and concluded that the rain impacting the aircraft increased the drag. Bergrum made numerical calculation for the rain effects on airfoils. Luers and Haines did an analytic investigation and found that heavy rain induces severe aerodynamic penalties including both a momentum penalty due to the impact of the rain and a drag and lift penalty due to rain roughening of the airfoil and fuselage. More recently, Hansman and Barsotti performed experiments and declared that performance degradation of an airfoil in heavy rain is due to the effective roughening of the surface by the water layer. Hansman and Craig did further experimental research at low Reynolds number. E. Dunham made a critical review for the potential influence of rain on airfoil performance. Dunham et al. carried out experiments for the transport type airfoil and concluded that there is a reduction of maximum lift capability with increase in drag. There is a scarcity of published literature in analytic research of two-phase boundary layer around an airfoil. Analytic research is being improved. The following assumptions are made: the fluid flow is non-steady, viscous, and incompressible; the airfoil is represented by a two-dimensional flat plate; and there is only a laminar boundary layer throughout the flow region. The boundary layer approximation is solved and discussed.
Based on considerations of fluid dynamic simulation appropriate to hypersonic, viscous flow over blunt-nosed lifting bodies, a method was presented earlier for estimating drag coefficients in the transitional-flow regime. The extension of the same method to prediction of lift coefficients is presented in this paper. Correlation of available experimental data by a simulation parameter appropriate for this purpose is the basis of the procedure described. Under low-density, hypersonic flow conditions, the overriding importance of projected and wetted areas, rather than details of body configuration, support this approach for finding aerodynamic forces. The ease of application of the method makes it useful for preliminary studies that involve a wide variety of three-dimensional vehicle configurations or a range of angles of attack of a given vehicle. It is also easy to examine the influence of different assumptions regarding gas/surface interaction parameters.
The objective of this study is to propose a computational methodology that can effectively anchor the base flowfield of a four-engine clustered nozzle configuration. This computational methodology is based on a three-dimensional, viscous flow, pressure-based computational fluid dynamics (CFD) formulation. For efficient CFD calculation, a Prandtl-Meyer solution treatment is applied to the algebraic grid lines for initial plume expansion resolution. As the solution evolves, the computational grid is adapted to the pertinent flow gradients. The CFD model employs an upwind scheme in which second- and fourth-order central differencing schemes with artificial dissipation are used. The computed quantitative base flow properties such as the radial base pressure distributions, model centerline static pressure, Mach number and impact pressure variations, and base pressure characteristic curve agreed reasonably well with those of the measurement.
The objective of this study is to validate a computational methodology for the aerodynamic performance of an advanced conical launch vehicle configuration. The computational methodology is based on a three-dimensional, viscous flow, pressure-based computational fluid dynamics formulation. Both wind-tunnel and ascent flight-test data are used for validation. Emphasis is placed on multiple-engine power-on effects. Computational characterization of the base drag in the critical subsonic regime is the focus of the validation effort; until recently, almost no multiple-engine data existed for a conical launch vehicle configuration. Parametric studies using high-order difference schemes are performed for the cold-flow tests, whereas grid studies are conducted for the flight tests. The computed vehicle axial force coefficients, forebody, aftbody, and base surface pressures compare favorably with those of tests. The results demonstrate that with adequate grid density and proper distribution, a high-order difference scheme, finite rate afterburning kinetics to model the plume chemistry, and a suitable turbulence model to describe separated flows, plume/air mixing, and boundary layers, computational fluid dynamics is a tool that can be used to predict the low-speed aerodynamic performance for rocket design and operations.
A straightforward procedure has been developed to quickly determine an inviscid design of a hypersonic wind tunnel nozzle when the test crash is both calorically and thermally imperfect. This real gas procedure divides the nozzle into four distinct parts: subsonic, throat to conical, conical, and turning flow regions. The design process is greatly simplified by treating the imperfect gas effects only in the source flow region. This simplification can be justified for a large class of hypersonic wind tunnel nozzle design problems. The final nozzle design is obtained either by doing a classical boundary layer correction or by using this inviscid design as the starting point for a viscous design optimization based on computational fluid dynamics. An example of a real gas nozzle design is used to illustrate the method. The accuracy of the real gas design procedure is shown to compare favorably with an ideal gas design based on computed flow field solutions.
A space shuttle and a competitive swimmer have a lot more in common than people might realize: Among other forces, both have to contend with the slowing influence of drag. NASA s Aeronautics Research Mission Directorate focuses primarily on improving flight efficiency and generally on fluid dynamics, especially the forces of pressure and viscous drag, which are the same for bodies moving through air as for bodies moving through water. Viscous drag is the force of friction that slows down a moving object through a substance, like air or water. NASA uses wind tunnels for fluid dynamics research, studying the forces of friction in gasses and liquids. Pressure forces, according to Langley Research Center s Stephen Wilkinson, dictate the optimal shape and performance of an airplane or other aero/hydro-dynamic body. In both high-speed flight and swimming, says Wilkinson, a thin boundary layer of reduced velocity fluid surrounds the moving body; this layer is about 2 centimeters thick for a swimmer.
We discuss techniques for calculating the amount of crustal assimilation possible in lunar magma chambers and dikes based on thermal energy balances, kinetic rates, and simple fluid mechanical constraints. Assuming parent magmas of picritic compositions, we demonstrate the limits on the capacity of such magmas to melt and dissolve wall rock of anorthitic, troctolitic, noritic, and KREEP (quartz monzodiorite) compositions. Significant melting of the plagioclase-rich crustal lithologies requires turbulent convection in the assimilating magma and an efficient method of mixing in the relatively buoyant and viscous new melt. Even when this occurs, the major element chemistry of the picritic magmas will change by less than 1-2 wt %. Diffusion coefficients measured for Al2O3 from an iron-free basalt and an orange glass composition are 10(exp -12) sq m/s at 1340 C and 10(exp -11) sq m/s at 1390 C. These rates are too slow to allow dissolution of plagioclase to significantly affect magma compositions. Picritic magmas can melt significant quantities of KREEP, which suggests that their trace element chemistry may still be affected by assimilation processes; however, mixing viscous melts of KREEP composition with the fluid picritic magmas could be prohibitively difficult. We conclude that only a small part of the total major element chemical variation in the mare basalt and volcanic glass collection is due to assimilation/fractional crystallization processes near the lunar surface. Instead, most of the chemical variation in the lunar basalts and volcanic glasses must result from assimilation at deeper levels or from having distinct source regions in a heterogeneous lunar mantle.
We discuss techniques for calculating the amount of crustal assimilation possible in lunar magma chambers and dikes based on thermal energy balances, kinetic rates, and simple fluid mechanical constraints. Assuming parent magmas of picritic compositions, we demonstrate the limits on the capacity of such magmas to melt and dissolve wall rock of anorthitic, troctolitic, noritic, and KREEP (quartz monzodiorite) compositions. Significant melting of the plagioclase-rich crustal lithologies requires turbulent convection in the assimilating magma and an efficient method of mixing in the relatively buoyant and viscous new melt. Even when this occurs, the major element chemistry of the picritic magmas will change by less than 1-2 wt %. Diffusion coefficients measured for Al2O3 from an iron-free basalt and an orange glass composition are 10(exp -12) m(exp 2) s(exp -1) at 1340 C and 10(exp -11) m(exp 2) s(exp -1) at 1390 C. These rates are too slow to allow dissolution of plagioclase to significantly affect magma compositions. Picritic magmas can melt significant quantities of KREEP, which suggests that their trace element chemistry may still be affected by assimilation processes; however, mixing viscous melts of KREEP composition with the fluid picritic magmas could be prohibitively difficult. We conclude that only a small part of the total major element chemical variation in the mare basalt and volcanic glass collection is due to assimilation/fractional crystallization processes near the lunar surface. Instead, most of the chemical variation in the lunar basalts and volcanic glasses must result from assimilation at deeper levels or from having distinct source regions in a heterogeneous lunar mantle.
Microgravity processes must rely on mechanisms other than bouyancy to move bubbles or droplets from one region to another in a continuous liquid phase. One suggested method is thermocapillary migration in which a temperature gradient is applied to the continuous phase. When a fluid particle contacts this gradient, one pole of the particle becomes warmer than the opposing pole. The interfacial tension between the drop or bubble phase and the continuous phase usually decreases with temperature. Thus the cooler pole is of higher interfacial tension than the warmer pole, and the interface is tugged in the direction of the cooler end. This thermocapillary or thermally induced Marangoni surface stress causes a fluid streaming in the continuous phase from which develops a viscous shear traction and pressure gradient which together propel the particle in the direction of the warmer fluid. In this paper, we provide a theoretical basis for remobilizing surfactant retarded fluid particle interfaces in an effort to make viable the use of thermocapillary migrations for the management of bubbles and drops in microgravity,
Viscous and bluntness induced pressures for flat plates, wedges, cylinders and cones at Mach 41
Viscous and bluntness induced pressures for flat plates, wedges, cylinders and cones at Mach 41
Some physical, analytical, and computational aspects of viscous flow are examined with reference to examples of computed flows. The discussion of the physical aspects covers the development of important scales used to reference flow phenomena in laminar and turbulent shear layers; the usefulness of the concepts of circulation and vorticity; and some relatively large-scale organized structures that have recently been identified in transitional and fully developed turbulent flows. Among the analytical aspects discussed are a compact presentation of the compressible Navier-Stokes equations, the Reynolds-averaged form of these equations, and a simplified description of some forms of turbulent models. Finally, results of a simulation of the onset of transition, direct turbulence simulations, and large-eddy simulations are given.
The advantage of vortex methods for inviscid flows of several fluids separated by interfaces is that problems of this kind may be posed and solved numerically entirely on the interface surface. For free surface problems, where one of the fluids has negligible inertia, a small amount of viscosity produces a thin, weak rotational layer adjacent to the potential flow vortex sheet. Here, a method is described for including this weak viscous effect as a modification of the boundary conditions for the potential part of the flow, thus allowing this slightly viscous flow to be formulated as a vortex method on the free surface. This is important for unsupported free drops where the viscosity at the free surface is the only source of damping for oscillations, and for gas-filled bubbles, where it provides both drag and damping. Small applied shear stresses from aerodynamic, electrostatic, or other sources may be included provided they are of the same order as the potential flow shear stress or smaller.