Constant Dynamic Pressure Research Articles

Interchange instability of a curved current layerconvecting in the magnetosheath from the bow shock towards themagnetopause

Abstract. This paper deals with nonsteady perturbations of the magnetosheath parameters which are related to variations of the interplanetary magnetic field from north to south under a constant solar wind dynamic pressure. The magnetic field changes its direction within a thin layer which is convected with the plasma from the bow shock to the ionopause. In the course of time, this current layer is amplified during its motion towards the magnetopause. The intensity of the current is increasing, the layer thickness is decreasing, and the gradients of parameters are becoming much sharper while the layer is approaching the magnetopause. The curvature radius of this layer is decreasing while it is draping around the magnetopause. This curved layer structure with reversed magnetic field in the magnetosheath is found to be unstable with respect to the interchange instability. The growth rate of the instability is obtained for different positions of the layer. Key words. Magnetospheric physics (magnetosheath)

On the inadequacies of Long's model for steady two-dimensional stratified flows

Nonlinear analysis of two-dimensional steady flows with density stratification in the presence of gravity is considered. Inadequacies of Long's model for steady stratified flow over topography are explored. These include occurrence of closed streamline regions and waves propagating upstream. The usual requirements in Long's model of constant dynamic pressure and constant vertical density gradient in the upstream condition are believed to be the cause of these inadequacies. In this article, we consider a relaxation of these requirements, and also provide a systematic framework to accomplish this. As illustrations of this generalized formulation, exact solutions are given for the following two special flow configurations: the stratified flow over a barrier in an infinite channel; the stratified flow due to a line sink in an infinite channel. These solutions exhibit again closed-streamline regions as well as waves propagating upstream. The persistence of these inadequacies in the generalized Long's model appears to indicate that they are not quite consequences of the assumptions of constant dynamic pressure and constant vertical density gradient in Long's model, contrary to previous belief. 1This aspect was dramatically evident in the experiments of Long (1955) and Davis (1969), in which the upstream effects become prominent when the lee waves began to break internally and become strongly turbulent. The wave breaking and turbulence created a body of fluid essentially at rest with respect to the obstacle which then acted to block the upstream flow in a source-like manner. On the other hand, solutions admitted by the generalized Long's model show that departures from Long's model become small as the flow becomes more and more supercritical. They provide a nonlinear mechanism for the generation of columnar disturbances upstream of the obstacle and lead in subcritical flows to qualitatively different streamline topological patterns involving saddle points, which may describe the lee-wave-breaking process in subcritical flows and could serve as seats of turbulence in real flows. The occurrences of upstream disturbances in the presence of lee-wave-breaking activity described by the present solution are in accord with the experiments of Long (Long, R.R., “Some aspects of the flow of stratified fluids, Part 3. Continuous density gradients”, Tellus 7, 341--357 (1955)) and Davis (Davis, R.E., “The two-dimensional flow of a stratified fluid over an obstacle”, J. Fluid Mech. 36, 127–143 (1969)).

Incomplete Mixing and Off-Design Effects on Shock-Induced Combustion Ramjet Performance

A shock-induced combustion ramjet (“ shcramjet”) model is described to investigate the effects of incomplete fuel/air mixing and off-design e ight conditions on its performance characteristics. A fully implicit, fully coupled, Newton-iteration, lower ‐uppersymmetric Gauss ‐Seidel scheme is employed to solvethe Euler equationsat steady state. This scheme is coupled with a nonequilibrium chemistry model consisting of 33 reactions and 13 species. Axisymmetric and planar shcramjet e owe elds with variable equivalence ratio proe les representing extreme deviations from homogeneous fuel/air mixing are numerically solved for a range of e ight Mach numbers at a constant dynamic pressure of 1400 psf. Results show that incomplete fuel/air mixing gives rise to a combination of detonative combustion and simple shock-induced combustion. Comparison of overall performance characteristics to shcramjets with homogeneous, stoichiometric fuel/air mixtures demonstrates the degree of performance degradation. The propulsive characteristics of mixed-compression ramjets are calculated in off-design operating regimes corresponding to inlet Mach numbers above and below design Mach numbers of 12, 16, and 20; for externalcompression ramjets, the propulsive characteristics are calculated for inlet Mach numbers below design Mach numbers of 12, 16, and 20. It is found that the propulsive properties of the engines deteriorate when they are operated at off-design conditions. For mixed-compression ramjets operating at lower-than-design Mach numbers, the degradation in thrust production is due primarily to reduced heat release in the engine nozzle. At higher-thandesign Mach numbers, thrust production is reduced only slightly due to a modie ed nozzle geometry, required to ensure convergence of the numerical method. Generation of thrust for external-compression ramjets deteriorates at lower-than-design Mach numbers due to a high-pressure zone created in the combustor by the impingement of the detonation wave on the engine surface upstream of the design point. Mixed-compression ramjets are found to provide superior performance to external-compression ramjets at off-design operation. External-compression ramjetsarefound to bemoresensitiveto off-designoperation than mixed-compression ramjets.Itisconcludedthat the engine geometry must be varied as e ight conditions change if degradation in engine performance at off-design conditions is to be avoided.

Three spacecraft observations of the geomagnetic tail during moderately disturbed conditions: Structure and evolution of the current sheet

On April 22, 1979, from 0840 to 1018 UT, ISEE 1 and ISEE 2 stayed in the tail current sheet at 17 RE, crossing the current sheet center several times while the initially northward interplanetary magnetic field Bz turned southward under conditions of constant solar wind velocity and dynamic pressure. An overview of the period from 0840 to 1050 UT, discussing the solar wind conditions, the tail magnetic field response at ISEE 1, ISEE 2 and IMP 8, and the ground electrojet activities has been presented in an accompanying paper. Herein under the assumption that the magnetic field is antisymmetric about the current sheet center, the hyperbolic tangent current sheet model of Harris has been used to calculate the current sheet thickness from these two close spacecraft measurements of the tail magnetic field. The thickness varied from 2.5 to 0.5 RE during this period. The current sheet thinned just prior to a rapid poleward expansion of the auroral electrojet and just after the arrival of a southward turning of the IMF Bz and apparent tail field reconnection at ISEE 1 and 2. The plasma density and temperature distribution in the vertical direction appears to be close to adiabatic at this time and the total pressure is roughly constant through the lobe. In this case study, the polytropic index of the tail plasma is found to be 5/3 on the average. This implies that the plasma convection at 17 RE in tail was steadily adiabatic over the period of about 100 min.

Aerospace Plane Ascending Trajectories with Heat Consideration

This is a study of performance and control for transatmospheric (TAV) aerospace planes, that use air-breathing propulsion. The study is structured in two parts and considers the heat load near the stagnation point. The first part is analytical and consists of two cases, it seeks closed form solutions for the non-linear feedback controls (aerodynamic and thrust), which are necessary to transfer the (TAV) from one specified state to another specified state, while satisfying pairs of equality constraints (that is, Case I: constant acceleration with constant dynamic pressure and Case II: constant rate of climb with constant dynamic pressure). This leads to closed form solutions for the controls in feedback form and also for the heat rate and load. The analytical approach gives a reasonable approximation of the general ascent trajectory to orbit, where the two cases can be used in combination with different constant values of the constraints in different levels of the hypersonic trajectory. The analytical results were a useful guide in the numerical studies. The second part describes numerical simulation and optimization. The control laws, which minimize the heat load, are found in feedback form. A numerical example is worked out for illustration. The trajectory corridor and, in general, all the constraints are satisfied for heat load ≤ 350 kJ/cm2 using feasible controls.

Flutter of an infinitely long panel in a duct

The aeroelastic stability is examined of an infinitely long panel of finite width enclosed in a duct such that both the upper and lower surfaces of the panel are exposed to an inviscid, and compressible flow. The panel behavior is accounted for by small deflection plate theory, whereas the aerodynamic forces acting on the panel are described by the classical linearized small disturbance potential theory. As such, a self-consistent theoretical model is constructed for the asymptotic behavior of the panel. Two panel boundary conditions are considered; the panel is assumed to be either simply supported, or clamped along the side edges. For the simply supported case, rather extensive numerical results have been obtained. The effects of Mach number, air/panel mass ratio, and duct dimension on the flutter velocity are determined. a a* b c CQ c* D E h h* hp L / /* M m P t U U* U*T W x y z y Nomenclature speed of sound a/c0 panel width wave speed reference wave speed, 2n(D/pmhb2)1/2 C/CQ plate stiffness modulus of elasticity height of duct nondimensional height of duct, h/b panel thickness panel length wavelength nondimensional wavelength, l/b Mach number, U*/a* number of modes pressure time flow velocity U/CQ critical flutter velocity panel deflection streamwise coordinate spanwise coordinate coordinate perpendicular to plane of panel separation constant nondimensional dynamic pressure, /x£/*2

Magnetosphere Inflation due to Equatorial Ring Current.

An inflation of the magnetosphere due to the magnetic field of an equatorial ring current is estimated. It is suggested that the inflation of the magnetosphere is determined by an equivalent magnetic dipole of the ring current which is approximated by half a Dst variation of the geomagnetic field multiplied by a cube of an effective radius of the equatorial ring current. It is also suggested that a 100-200 nT Dst causes a 7-20% inflation of the dayside magnetosphere, 10-30% in the distant tail radius, and as large as 40-170% of the tail length under the constant dynamic pressure of the solar wind. In this connection, it is also shown that the Dst magnitude is limited below a certain value with a certain effective radius of the ring current, for example about 450 nT with the effective radius of 5 RE. An increase in the flaring angle of the tail magnetopause is also expected to occur as a Dst field develops.

Signatures of flux erosion from the dayside magnetosphere

The rate of merging and the strength of the region 1 Birkeland currents increase during periods of southward interplanetary magnetic field (IMF). Fringe fields of the Birkeland currents depress dayside magnetospheric magnetic field strengths and remove magnetic flux from the dayside magnetosphere, thereby allowing the dayside magnetopause to move inward and the cusp equatorward. We use previously derived fits to the magnetopause location as a function of IMF Bz, the condition of pressure balance at the magnetopause, and an idealized model of region 1 Birkeland currents to estimate that strong southward IMF turnings will produce ∼13‐ to 26‐nT depressions in the geosynchronous magnetic field strength over periods of 30‐60 min. We then present three case studies of geosynchronous magnetic field strength variations during periods of nearly constant solar wind dynamic pressure and southward IMF. The dayside magnetospheric magnetic field strength was depressed ∼10 nT during a period of strongly southward IMF (Bz = −6 nT), but only ∼5 nT during two more typical periods of slightly southward IMF (Bz = −2 to −3 nT). The depressions correspond to periods of enhanced AL index, which we interpret as evidence for directly driven solar wind‐magnetosphere interaction rather than the unloading of energy stored within the magnetotail. Dayside geosynchronous magnetic field strengths are weakly correlated with IMF Bz.

The oblique impact of a hard ball against ductile, semi-infinite target materials—experiment and analysis

Six ductile target materials were impacted with hardened steel balls over a range of impact velocities (50–200 m s −1) and impact angles (15–90°). The dimensions of the resulting impact craters and also the rebound velocity and angle were experimentally measured. These experimental values were compared with the predictions of a simplified model which assumes a constant dynamic yield pressure and friction coefficient. The model correctly predicts the magnitude of the crater dimensions and volume and also their variation with impact angle and velocity. In contrast, the rebound angle and the energy absorbed per impact are not predicted correctly by the simple model.

Entry flow in a curved pipe

This paper deals with the development of the flow in a curved tube near the inlet. The solution is obtained by the method of matched asymptotic expansions. Two inlet conditions are considered: (i) the condition of constant dynamic pressure at the entrance, which may be of practical interest in applications to blood flow in the aorta; and (ii) a uniform entry condition. It is shown that the geometry and the nature of the entry condition appreciably influence the initial development of the flow. The effect of the secondary flow due to the curvature on the wall shear is discussed and it is shown that the cross-over between shear maxima on the inside and the outside of the tube occurs at a downstream distance which is 1·9 times the radius of the tube for entry condition (i) while in the case of entry condition (ii) it is 0·95 times the radius, which is half the distance required in case (i). It is found that the pressure distribution is not significantly influenced by the secondary flow during the initial development of the motion. The analysis, which is developed for steady motion, can be extended to pulsatile flows, which are of greater physiological interest.

VARIABLE-LIFT RE-ENTRY AT SUPERORBITAL AND ORBITAL SPEEDS

Analytical solutions have been obtained for a type of variable-lift modulation applicable to a lifting body entering the atmosphere from superorbital and orbital speeds. The variablelift modulation analyzed here results in nonoscillatory trajectories and achieves a smooth transition into a nominal glide phase such as constant flight path angle, constant altitude, constant dynamic pressure, or any other glide desired. Simple closed-form formulas were derived which permit quick estimation of 1) the peak deceleration and the altitude where it occurs, and 2) the required lift modulation necessary for any set of prescribed transition conditions. These approximate formulas show the explicit dependence of trajectory quantities in terms of re-entry conditions, vehicle aerodynamic characteristics, and parameters defining the lift modulation. It can be shown that the analytical solutions obtained in this report include the constant lift-drag solutions obtained by Lees, Hartwig, and Cohen in the orbital case and by Ting and Wang in the superorbital case. Furthermore, in the case of variable lift, this report deals with a continuous lift modulation program instead of a stepwise change of lift-drag considered by Lees, Hartwig, and Cohen.