Optimization of hypersonic power law derived waverider using TLBO

In hypersonic flow regime high lifting bodies are of special interest to scientific community. Waverider is a lifting body tailored to create high lift to drag ratio in high speed flow. The tailoring is done in such a manner that the shock formed is attached to the leading edge of the configuration leading to no pressure leakage. The objective of the present study is to choose an optimized waverider geometry from a vast design space based on following design parameters - n (power law exponent), δ (wedge angle) and λ (aspect ratio). Two objective functions are considered (a) L/D and (b) L/D*V^(2/3)/S. S is the wetted area of the waverider which is also a representation of heat flux. Thus second objective function considers maximum volume, minimum heat flux along with higher L/D.

Analytical model developed by Ryan Starkey [1] is used to calculate planform area, wetted area, volume and lift to drag ratio in terms of n, δ and λ. This model calculates lift and drag values based on shock and expansion relations along with Eckerts reference temperature method (for viscous drag). This model was tested by comparing lift to drag ratios obtained by 3D CFD simulations using HiFUN CFD solver. CFD validation with experimental results [2] is also carried out to gain confidence over the analytical model (see Table 1). Teacher-Learner-Based Optimization (TLBO) [3] is used in this study to get optimized waverider geometry parameters. Unlike other evolutionary and swarm intelligence algorithms, TLBO requires only common controlling parameters like population size and number of generations, making it an algorithm-specific parameter-less algorithm.

The optimisation is carried out for a design altitude corresponding to dynamic pressure of 0.3 bar at zero angle of attack at various design Mach numbers ranging from 5 to 8. Optimised waverider geometry parameters for inviscid, laminar and turbulent cases are compared for the respective objective functions. Dependence of n, δ and λ on lift to drag ratio is discussed in detail. Finally the variation of force coefficients and L/D with angle of attack are studied for all the optimized configurations. Despite having some limitations, this model serves as a valuable design tool in the conceptual phase to arrive at optimised waverider configurations in quick turn around time.

Table 1: Comparison of force coefficients.

Figure 1: Comparison of L/D with alpha for waverider geometry with the design parameters M=7, n=0.3, δ=5 degree and λ =1 [4].

References:

1. Starkey, R. P., and Lewis, M. J., “Analytical Off-Design Lift-to-Drag Ratio Analysis for Hypersonic Waveriders.” AIAA Journal of Spacecraft and Rockets, Volume 37, Number 5, September-October 2000, pages 684-691.
2. K. Hemanth, G. Jagadeesh, S. Saravanan, K. Nagashetty and K.P.J. Reddy, ““Shock tunnel testing of a Mach 6 hypersonic waverider”.” Proceedings of 26th International Symposium on Shock Waves, Gottingen, Germany, 2007.
3. R. Venkata Rao and Vivek Patel, “An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problem.” International Journal of Industrial Engineering Computations 3 (2012) 535-560.
4. S. Pradeep Roy, et al “High angle of attack characteristics of power law derived hypersonic waveriders - computational study.” Proceedings of the 16th annual CFD symposium, Bangalore, India, 2014.