Analysis of a turbulent round jet based on direct numerical simulation data at large box and high Reynolds number

We have conducted a direct numerical simulation of a turbulent round jet at a previously unattained Reynolds number of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mtext>Re</a:mtext><a:mo>=</a:mo><a:mn>3500</a:mn></a:mrow></a:math> based on the jet diameter <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>D</b:mi></b:math> and jet-inlet bulk velocity <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>U</c:mi><c:mtext>b</c:mtext></c:msub></c:math> in a particularly long box of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>75</d:mn><d:mi>D</d:mi></d:mrow></d:math>. To achieve very fast convergence to self-similarity, we used a turbulent pipe flow at the same Reynolds number and length <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mn>5</e:mn><e:mi>D</e:mi></e:mrow></e:math> as the upstream inflow boundary condition. This indeed results in a very rapid emergence of self-similarity already at very small axial distances <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>z</f:mi></f:math> compared to all turbulent jet data published so far. Not only for the mean velocities and the Reynolds stresses as well as the budgets of the Reynolds stress tensor and the turbulent kinetic energy, a nearly perfect classical scaling based on the normalized radius <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>η</g:mi><g:mo>=</g:mo><g:mi>r</g:mi><g:mo>/</g:mo><g:mi>z</g:mi></g:mrow></g:math> in the range <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>z</h:mi><h:mo>/</h:mo><h:mi>D</h:mi><h:mo>=</h:mo><h:mn>25</h:mn><h:mo>−</h:mo><h:mn>65</h:mn></h:mrow></h:math> is shown, but also for the probability density function (PDF) of the axial velocity <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi>U</i:mi><i:mi>z</i:mi></i:msub></i:math> as well as the associated skewness and kurtosis. All budget terms have been calculated directly, resulting in a marginal error in the balance. An almost completely Gaussian behavior of the PDF for the axial velocity is observed on the jet axis, while a clear deviation with increasingly heavy tails is evident with increasing distance from the axis. Published by the American Physical Society 2024