Scaling patch analysis of turbulent planar plume

Journal Article · Mon May 03 00:00:00 EDT 2021 · Physics of Fluids

DOI:https://doi.org/10.1063/5.0050189· OSTI ID:1804439

Wei, Tie  ^[1]; Livescu, Daniel  ^[2]

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1. New Mexico Institute of Mining and Technology, Socorro, NM (United States)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Proper scaling in turbulent planar plumes is investigated in this study using a scaling patch approach. Based on the scaled boundary conditions, a proper velocity scale for the mean axial flow is the plume centerline velocity $U_{\text{ref}}=U_{\text{ctr}}$, and a proper temperature scale for the temperature excess is ${\Theta }_{\text{ref}}=T_{\text{ctr}}–T_{\infty }$, where T_ctr is the plume centerline temperature and $T_{\infty }$ is the ambient fluid temperature. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity, mean momentum, and mean energy equations, respectively, the following is found: (1) a proper scale for the mean transverse flow is $V_{\text{ref}}=(d\delta /dx)U_{\text{ctr}}$, where $d\delta /dx$ is the growth rate of the plume width. (2) A proper scale for the Reynolds shear stress is $R_{\text{vu},\text{ref}}=U_{\text{ctr}}{V}_{\text{ref}}=(d\delta /dx)U_{\text{ctr}}^2$, a mix of the scales for the mean axial and transverse flows. (3) A proper scale for the turbulent heat flux is $R_{\mathrm{v}\theta ,\text{ref}}=V_{\text{ref}}{\Theta }_{\text{ctr}}$, a mix of the scales for the mean transverse flow and mean temperature excess. The mean transverse flow thus plays a critical role in the scaling of turbulent planar plumes. Approximate functions are developed for the scaled mean transverse flow, Reynolds shear stress, and turbulent temperature flux, and are found to agree favorably with experimental and numerical simulation data. The integral analysis of the mean momentum equation yields a Richardson number Ri, which remains invariant in the axial direction. The Richardson number is defined as $\text{Ri}\stackrel{\text{def}}{=}g\beta {\Theta }_{\text{ctr}}{\delta }_t/\left(U_{\text{ctr}}{V}_{\text{ref}}\right)\approx 1/\sqrt{2}$, where g is the gravitational acceleration, β is the thermal expansion coefficient, and δ_t is the plume half-width based on the mean temperature profile. This Richardson number arises directly from the scaling patch analysis of the mean momentum equation, including both the streamwise and transverse velocity scales.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: 89233218CNA000001; 20210298ER
• OSTI ID: 1804439
• Alternate ID(s): OSTI ID: 1970599
• Report Number(s): LA-UR-21-23862; TRN: US2212668
• Journal Information: Physics of Fluids, Vol. 33, Issue 5; ISSN 1070-6631
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
equations of fluid dynamics
energy equations
thermal effects
turbulent flows
Newtonian mechanics
volumetric flow rates
Navier Stokes equations