Estimation of damping derivatives for delta wings in hypersonic flow for straight leading edge

Accurate estimation of the aerodynamic stability derivatives of airplanes is essential to evaluate the performance of the aircraft, whether civilian or military. Theoretical prediction methods for the dynamic stability derivatives at high angles of attack have not advanced, and in the present paper, an attempt has been made to study the effect of damping derivatives for delta wings for different angles of incidence, and the Mach number for a wing whose leading edge is straight. In this paper, the flow is considered to be unsteady flow and also considering the effect of the Leeward surface along with the shock waves and the expansion waves. The theory developed in the present paper considering the unsteady effects, the results have been estimated for speed flows for air assuming the air to behave as perfect gas for a range of angle of incidence and the inertia level. The results show that for Mach number M = 7 and above the damping derivatives become independent of inertia level. Increase in the damping derivatives is substantial when the angle δ is increased from 5 to 10 degree

Analysis of damping derivatives for delta wings in hypersonic flow for curved leading edges with full sine wave

In this study, an attempt is made to evaluate the effect of first arched ends on the damping derived due to the pitch rate aimed at the variable sine wave bounty, flow deflection angle δ, pivot position, and the Mach numbers. Results show that with the escalation in the bounty of the complete sine wave (i.e., positive amplitude) there is an enlightened escalation in the pitch damping derivatives from h = 0, later in the downstream in the route of the sprawling verge it decreases till the location of the center of pressure and vice versa. At the location where the reasonable force acts, when we consider the stability derivatives in damping for the rate of pitch q, there is a rise in the numerical tenets of the spinoffs. This increase is non-linear in nature and not like for position near the leading edges. The level of the stifling derivatives owing to variations in Mach numbers, flow bend approach δ, and generosity of the sine wave remained in the same range

The computation of stiffness derivative for an ogive in the hypersonic flow

Expression for Stiffness derivative for an Ogive is derived with the suppositions of the arc on the nose of the cone from the air is being considered as perfect gas and the viscosity being neglected, the motion is quasi-steady, and the nose deflection angle of the Ogive θ is in such a way that the M2 after the shock is > 2.5. It is seen that due to the increment in angle θ, the stiffness derivative increases linearly due the progressive increase in the plan form area of the nose shape. The results indicate that there is a 38 percent increase in the stability derivative when the flow deflection θ was enhanced in the range of 5 to 10 degrees. With the further enhancement in the flow deflection angle θ from ten degrees and above, does not yield substantial increase in the stability derivative. Due to this change in the surface pressure distribution will lead to shift the location of centre of pressure, from the hinged position h = 0.5 to 0.8. The centre of pressure also has shifted towards the downstream, which lies in the range from h = 0.72 to 0.85

Estımatıon of hypersonıc unsteady and qausı-steady dampıng derıvatıves for a delta wings at large incıdence

This paper presents results of quasi-steady and unsteady damping derivatives of a delta wing whose leading edge is straight. Results are computed for a wide range of Mach numbers and angles of attack. Here the contribution to the damping derivatives due to the rate of change of angle of attack is estimated separately. The results show that with the increase in Mach number, there is a progressive decrease in the damping derivatives for both the cases (i.e., unsteady and quasi-steady). With the further rise in the Mach values, the magnitude of decline has diminished for Mach number M = 10 and above the state of steady-state is achieved. For the entire range of the Mach number, the location of the center of pressure remained unchanged for a fixed value of the flow deflection angle δ. For the lower flow deflection angle of the wing, the magnitude of the damping derivatives is smaller as compared to the higher values of δ. The contribution to the damping derivatives from the rate of change of angle of attack is around 20 percent of the quasi-steady one. The results for flow deflection angles of ten degrees and twenty degrees show a different trend. When we compare the results of the damping derivatives for a fixed pivot position, it is seen that the damping derivatives show different behavior for two different values of the flow deflection angle δ. The steady-state varies for two values of δ. When we look at the damping derivatives at hinge point k = 0.6, the magnitude is small. The steady-state is attained early for quasi-steady in comparison to the unsteady damping derivatives

Analytical estimation of stability derivatives of wing with curved leading edges at hypersonic mach number

This paper focusses attention on the influence of prominent curved ends to restraining deprived owing to the transverse frequency for the numerous amplitude, flow rebound perspective δ, hinge location, and the inertia. In the current learning by the consequence of expansion fan on the expansion side (i.e., Leeward surface) are neglected. Outcomes of the demonstration are that with the increase of the amplitude of the half-sine wave, there is a progressive increase in the-hampering spinoffs from k = 0, advanced to the TE, it declines up to the whereabouts of the normal force location and just opposite trend. At the place of k = 0.4, while we deliberate the permanence spinoffs in curbing for the pitch q, there is a reduction in the mathematical tenets of the derivatives, and this trend continues till k = 1 towards the trailing edge. This upsurge is not linear and not like for position near the foremost edges. The change in the enormousness of the inhibiting results because of the deviations in the Mach (M), flow deflection angle δ, and the amplitude of the sine wave persisted in the identical kind

An effect of sweep angle on roll damping derivative for a Delta wing with curved leading edges in unsteady flow

This paper presents the results of an analytical study to account the effect of the sweep angle of a delta wing whose leading edges are curved on roll damping derivative at various angles of attack and the amplitude of the full sine waves. In the present theory, the effect of Leeward surface has been taken into consideration with the attached shock case at the leading edge. For a detached shock case, this theory will not be valid. Results have been obtained for the hypersonic flow of perfect gases over a wide range of angle of attack and the Mach number. The results indicate that the roll damping derivative decreases with a sweep angle, but increase with the increase in the flow deflection angle δ as well as with Mach M

Evaluation of stiffness derivative for a delta wing with straight leading edges in unsteady flow

The emphasis of this paper is to examine the Stiffness derivative variation with the pivot position by varying Mach number in unsteady flow and its comparison with quasi-steady the flow of Crasta& Khan for varying angle of attack with different Mach number. From the results, it is evident that Stiffness derivative decreases as the Mach number increases. Comparison with Liu as well as Crasta& Khan theory it is evident that there is an improvement in the present theory being unsteady over quasi-steady theory, in addition to the fact that in the present work the pressure on the leeward surface is taken into account which results in increased value of the stability derivative and the same is clearly visible in result

Computation of stability derivatives of an oscillating cone for specific heat ratio = 1.66

In this paper the expressions for stiffness and Damping derivatives are obtained in a closed form for perfect gas where the flow is quasi-steady and axi-axisymmetric, and the nose semi angle of the cone is such that the Mach number behind the shock . Results are presented for an oscillating cone for gas with , at different Mach numbers and semi cone angles. The Stiffness derivative decreases with pivot position and also with semi vertex angle, there is substantial change in the stiffness derivative when semi-vertex has been increased from 5 degrees to ten degrees, further increase in the semi-vertex angle results in marginal change in the stiffness derivative. Due the marginal change in the Mach number level there is marginal increase in the magnitude of the stability and with further increase in the inertia level the stability derivative conform to the Mach number independence principle. The present theory for Oscillating cone is restricted to quasi-steady case. Viscous effects have been neglected. The expressions so obtained for stability derivative in pitch are valid for a slender ogive which often approximates to the whole fuselage of an aircraft. Keywords: High Speed Flow, Hypersonic Flow, Oscillating cone, Stiffness derivativ

Computation of stiffness derivative for an unsteady delta wing with curved leading edges

An attempt has been made to derive the expressions for stiffness derivative for a delta wing with curved leading edges for an unsteady high speed flow. It is evident from the figures that stiffness derivative decreases as Mach number increases. It is also seen that as amplitude of half sine wave increases the stiffness derivative also increases. This is an improvement of previous theory as the effect of leeward surface are included in the present work

Effect of sweep angle and a half sine wave on roll damping derivative of a Delta Wing

This paper presents the effect of sweep angle on a roll of damping derivative of a delta wing with half-sine wave for an attached shock case in supersonic/hypersonic flow has been studied analytically. The Ghosh Strip theory is replicated. By combining this with the similitude at high-speed flows lead to giving a piston theory. The initial conditions for the applicability of the theory are that the attached wave must be attached with the leading edge of the wing. The results of the present study reveal that with the increments in the sweep angles; it results in continuous decrease in the roll damping derivative, it is also seen that the magnitude of the decrement for lower sweep angle is considerable as compared to the higher values of the sweep angles due to the drastic change in the surface area of the wing. Roll damping derivative progressively increases with the angle of attack; however, with the increase in the inertia level of the flow, it results in the decrement in the damping derivative and later conforms to the Mach number independence principle. Effect of the leading edge bluntness and viscous effects are neglected. Results have been obtained for the supersonic/hypersonic flow of perfect gases over a wide range of angle of attack, planform area for different Mach numbers. In the present study, attention is on the effect of sweep angle of the wing on roll damping derivative at a different angle of attack and inertia level has been studied. In contemporary theory, Leeward surface is taken along with shock waves attached with the leading edge