Numerical Simulation of Rolling Stability of Flight Vehicle

LV Meng,SU Cheng,SHI Xiaotian

China Academy of Aerospace Aerodynamics,Beijing 100074

Abstract:Large lift-to-drag ratio,high maneuverability,and good controllability are the basic performance for flight vehicles.Studying the rolling stability problems of a high lift-to-drag ratio aircraft is of great significance to the safety and control in maneuvering flight.The research on the static stability in the rolling direction of a HTV-2 like shape under a typical Mach number and attack angle was carried out.Similarly,by using Euler,laminar,turbulence and transition models,investigations of the dynamic stability in a single degree of freedom rolling motion of the same shape structure were executed.The numerical results show that the dynamic derivative of Euler is the largest,and the dynamic derivatives resulting from laminar,turbulence,and transition models are not much different.

Key words:CFD,free rolling,rolling stability

1 INTRODUCTION

In order to improve the lift-to-drag ratio,most hypersonic vehicles are designed with a symmetrical,non-circular cross-section aerodynamic shape,resulting in a large distance between the yawing pressure center and the pitching pressure center.The yawing restoring moment,rolling restoring moment and damping moments are small.At the same time,its mass is concentrated on the body axis,and the moment of inertia around the body axis is much smaller than the moments of inertia in the other two directions perpendicular to the body axis.As long as there is an asymmetrical moment in the lateral direction,it will cause rolling.So the rolling problem related to flying is particularly prominent[1].

Gao Qing[1]studied the lateral stability of a HTV-2 like shape through wind tunnel tests,model analysis and parameter sensitivity analysis.Li qian[2]studied the stability with two degrees of freedom dynamic coupled motion through numerical simulations and wind tunnel tests.

Through static and dynamic numerical simulations,the static stability of the rolling direction and the dynamic stability of the single degree of freedom rolling motion of the aircraft were studied.

2 NUMERICAL METHODS

2.1 N-S Equations

The three-dimensional compressible integral N-S equation can be expressed as[3]:

Q=[ρ,ρu,ρv,ρw,ρE]Tare conserved variables,FandFvare inviscid flux and viscous flux.Their expressions are:

2.2 Dynamic Derivatives Identification Methods

The vibration equation of the single-degree-of-freedom vibration of an aircraft around a fixed axis is as follows (taking pitching as an example):

Usually,Izz1,Mza＜0,for the above equation,the general solution is:

A1andA2are arbitrary constants,r1andr2are two roots of the characteristic equation.

the general solution can be approximated as:

When cos(ω0·t-?)=1,the envelope equation of the peak value of the vibration curve can be obtained as:

Assuming that after N oscillation decay cycles,the theoretical value of the curve peak envelope is:

Each peak value satisfies the theoretical formula of each peak envelope,and the peak values,Ni,N0are solved separately,then the dynamic derivative is:

3 NUMERICAL SIMULATION RESULTS OF FINNER

The geometry dimensions of finner are shown in Figure 1.Its surface grid is shown in Figure 2.

Figure 1 The geometry dimensions of finner

Figure 2 The surface grid of finner

Firstly,a steady numerical simulation was performed,the flow conditions were:

Figure 3 is a picture of pressure distribution.The shock waves at the head and tail of the flight vehicle are obvious.

Figure 3 Pressure distribution

After the steady flow field calculation converged,the model was released for single degree freedom pitch motion.The dynamic derivative calculated by free vibration is -317.815.The error with the result (-341.93) in the literature [4] is 7.04%.The accuracy meets the engineering application requirement.

4 HTV-2 LIKE SHAPE AND GRID

The simulated model is shown in Figure 4.Its surface grid is shown in Figure 5.

Figure 4 The 3D model of the HTV-2 like shape

Figure 5 The surface grid of the HTV-2 like shape

5 NUMERICAL SIMULATION RESULTS AND ANALYSIS

5.1 Steady Simulation

Firstly,a steady numerical simulation was performed on the HTV-2 like shape in this paper,the flow conditions were:

Figure 6 is a picture of the aircraft’s extreme surface streamlines (α=15°).Figure 7 is a picture of the aircraft’s pressure distribution (α=15°).There is lateral flow at small angles of attack.

Figure 6 Extreme surface streamlines

Figure 7 Pressure distribution

Figure 8 The relationship between the rolling moments and the sideslip angles at different angles of attack

Figure 8 is the relationship between the rolling moments and the sideslip angles at different angles of attack.At small angles of attack,the aircraft is rolling statically unstable.When the angle of attack is 10°,the rolling direction is statically stable,but the stability is low.When the angle of attack is 15°,the rolling direction is statically stable,and the aircraft is more stable.

5.2 Unsteady Simulation

On the basis of the static stability analysis of the aircraft,Euler,laminar,turbulence and transition models were used to simulate the single degree of freedom rolling motion respectively.Table 1 is the rolling dynamic derivatives simulated by different models.

Table 1 The rolling dynamic derivatives simulated by different models

Figure 9 is a graph of the rolling angles varying with time.From Table 1 and Figure 9,the results show that dynamic derivative of Euler is the largest and dynamic derivatives simulated by laminar,turbulence,and transition models are not much different.

Figure 9 The rolling angles varying with time

Figures 10 to 13 are pictures of streamlines simulated by different models.The streamlines show that the flows are different at the bottom of the aircraft.

Figure 10 The streamlines at the bottom of the aircraft simulated by Euler

Figure 11 The streamlines at the bottom of the aircraft simulated by turbulence

Figure 12 The streamlines at the bottom of the aircraft simulated by laminar

Figure 13 The streamlines at the bottom of the aircraft simulated by transition

6 CONCLUSIONS

Through static and dynamic numerical simulations,the research on the static stability of the rolling direction and the dynamic stability of the single degree of freedom rolling motion of the HTV-2 like shape under the typical Mach number and angle of attack was carried out.The results show that:

(1) At small angles of attack,the aircraft is rolling statically unstable.At large angles of attack,the aircraft is rolling statically stable.

(2) Dynamic derivative of Euler is the largest and the dynamic derivatives simulated by laminar,turbulence,and transition models are not much different.