Stochastic modeling of random roughness in shock scattering problems: theory and simulations

Journal Article · Fri Aug 01 04:00:00 EDT 2008 · Computer Methods in Applied Mechanics and Engineering, 197(43-44):3420-3434

DOI:https://doi.org/10.1016/j.cma.2008.02.025· OSTI ID:947458

Lin, Guang; Su, Chau-Hsing; Karniadakis, George E

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

Related Subjects

42 ENGINEERING
AIRFOILS
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
MACH NUMBER
PERFORMANCE
RANDOMNESS
ROUGHNESS
SCATTERING
STOCHASTIC PROCESSES
SUPERSONIC FLOW