On the Comparison of Flow Physics between Minimal and Extended Flow Units in Turbulent Channels

• Main Authors: Ethan A. Davis, Siamak Mirfendereski, Jae Sung Park
• Format: Article
• Language: English
• Published: MDPI AG 2021-05-01
• Series: Fluids
• Subjects: turbulence; flow physics; direct numerical simulation; minimal flow units; extended flow units
• Online Access: https://www.mdpi.com/2311-5521/6/5/192

Direct numerical simulations were performed to study the effects of the domain size of a minimal flow unit (MFU) and its inherent periodic boundary conditions on flow physics of a turbulent channel flow in a range of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>200</mn><mo>≤</mo><mi>R</mi><msub><mi>e</mi><mi>τ</mi></msub><mo>≤</mo><mn>1000</mn></mrow></semantics></math></inline-formula>. This was accomplished by comparing turbulent statistics with those computed in sub-domains (SD) of extended domain simulations. The dimensions of the MFU and SD were matched, and SD dynamics were set to minimize artificial periodicities. Streamwise and spanwise dimensions of healthy MFUs were found to increase linearly with Reynolds number. It was also found that both MFU and SD statistics and dynamics were healthy and in good agreement. This suggests that healthy MFU dynamics represent extended-domain dynamics well up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mi>τ</mi></msub><mo>=</mo><mn>1000</mn></mrow></semantics></math></inline-formula>, indicating a nearly negligible effect of periodic conditions on MFUs. However, there was a small deviation within the buffer layer for the MFU at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mi>τ</mi></msub><mo>=</mo><mn>200</mn></mrow></semantics></math></inline-formula>, which manifested in an increased mean velocity and a tail in the Q2 quadrant of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>u</mi><mo>′</mo></msup></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>v</mi><mo>′</mo></msup></semantics></math></inline-formula> plane. Thus, it should be noted that when considering an MFU domain size, stricter criteria may need to be put in place to ensure healthy turbulent dynamics.