Stochastic modeling of random roughness in shock scattering problems: theory and simulations
Random rougness is omnipresent in engineering applications and may often affect performance in unexpected way. Here, we employ synergistically stochastic simulations and second-order stochastic perturbation analysis to study supersonic flow past a wedge with random rough surface. The roughness (of length $$d$$) starting at the wedge apex is modeled as stochastic process (with zero mean and correlation length $$A$$) obtained from a new stochastic differential equation. A multi-element probabilistic collocation method (ME-PCM) based on {\em sparse grids} is employed to solve the stochastic Euler equations while a WENO scheme is used to discretize the equations in two spatial dimensions. The perturbation analysis is used to verify the stochastic simulations and to provide insight for small values of $$A$$, where stochastic simulations become prohibitively expensive. % We show that the random roughness enhances the lift and drag forces on the wedge beyond the rough region, and this enhancement is proportional to $(d/A)^2$. The effects become more pronounced as the Mach number increases. These results can be used in designing smart rough skins for airfoils for maxiumum lift enhancement at a minimum drag penalty.
- Research Organization:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-76RL01830
- OSTI ID:
- 947458
- Report Number(s):
- PNNL-SA-57556; KJ0101010
- Journal Information:
- Computer Methods in Applied Mechanics and Engineering, 197(43-44):3420-3434, Journal Name: Computer Methods in Applied Mechanics and Engineering, 197(43-44):3420-3434 Journal Issue: 43-44 Vol. 197; ISSN 0045-7825; ISSN CMMECC
- Country of Publication:
- United States
- Language:
- English
Similar Records
Effect of Surface Roughness on Wind Turbine Performance
An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media