Eine Familie stabilitätsbasierter Transitionstransportgleichungsmodelle für die numerische Strömungssimulation

Die vorliegende Arbeit befasst sich mit der physikalischen Modellierung der laminar-turbulenten Transition und stellt eine aus drei Transitionstransportgleichungsmodellen unterschiedlicher Komplexität bestehende neuartige, semi-empirische Modellfamilie zur Transitionsvorhersage für die Außenaerodynamik vor, die auf einer approximierten Form lokaler, linearer Stabilitätstheorie basiert. Durch diese neuen Modelle werden Defizite vorhandener Ansätze bei Tollmien-Schlichting-Transition, die mit positiven und negativen Druckgradienten assoziiert sind, kompensiert und im Verlauf der vorliegenden Arbeit detailliert dokumentiert

General Formulation of the Gradient Richardson Number for RANS Modelling

The present paper deals with a grid-point local and general reformulation of the gradient Richardson number that is used to characterize and quantify mean-streamline curvature and rotation effects inside a fluid flow. In this context, a new computational relation is derived from the classical definition used by Bradshaw. This includes a condition to maintain the directional information which is associated with amplification and damping of turbulence. For this purpose, an in-depth analysis and a comparison with Richardson numbers from the literature are provided. The newly derived equations and terms are eventually verified with the analytical solution using a channel with U-turn test case and a vortex downstream of a delta wing. Moreover, potential areas of applications for the gradient Richardson number in the field of computational fluid dynamics are presented. Besides an application in classical RANS modelling, the usage of the parameter inside the Field Inversion/Machine Learning approach as a flow feature is discussed

Development of a Stability-Based Transition Transport Modeling Framework

The physical process of a laminar boundary layer becoming turbulent is called “laminar­turbulent transition”. Since the flow physics and in particular the skin friction responsible for the drag is significantly influenced by the state of the flow, that is laminar or turbulent, transition plays an important role in external aerodynamics. For example, for rotorcraft computations it was shown that the skin friction was significantly overpredicted (depending on the geometry and the flow state) applying a fully turbulent simulation compared to a simulation that considered laminar­turbulent transition [1]. An overestimation of skin friction leads to an overestimation of power demand which needs to be avoided. However, on complex industrially relevant configurations, like a helicopter rotor, incorporating transition prediction capabilities into the simulation is not straightforward. State­of­the­art streamline­based methods require a great implementation effort, massive user input and a detailed expert knowledge. Additionally, computing helicopter rotors is inherently computationally expensive, requiring unsteady computations on a fine grid (Fig. 1), with a long computation time to establish the flow. The addition of boundary layer transition to the computation requires even finer time­steps and additional effort to compute the transition position. While streamline­based methods are relatively effective, they are not easily parallelizable to a large number of cores. Therefore, in the last decade transition transport models have been developed that aim at simplifying the incorporation and parallelization of the laminar­turbulent transition significantly. These models are only based on information available at each grid point, using transport type partial differential equations

Galilean-Invariant Stability-Based Transition Transport Modeling Framework

A new stability-based transition transport modeling framework for unstructured computational fluid dynamics is introduced. Based on a four-equation model published recently by the authors of this paper, new model formulations are derived being Galilean invariant and fully local. Moreover, the complexity of the four-equation model is reduced, yielding a one-equation model that is based on a local pressure-gradient parameter and a three-equation model that is based on an averaged pressure-gradient parameter considering convection (history) effects. Since the model versions are identical except the pressure-gradient parameter, the implementation effort is reduced. To be able to compute test cases in adverse pressure gradient flow regions at low Reynolds numbers, a method was developed to accelerate the turbulence production (downstream of the point of transition onset) that can also be used inside laminar separation bubbles. The models were implemented into the DLR TAU code, the unstructured compressible finite-volume flow solver of the German Aerospace Center (DLR) for external flows. For verification and validation purposes different test cases are shown capturing a wide range of parameters and flow conditions. This includes a test case verifying that the model yields identical results with and without uniform motion (Galilean invariance). Additionally, industrially relevant three-dimensional test cases were computed. This includes a helicopter rotor in vertical flight