# Scale-Resolving Simulation (SRS) as Part of Daily Engineering Routine

“Science is the study of what Is, Engineering builds what Will Be. The scientist merely explores that which exists, while the engineer creates what has never existed before…” – Theodore von Karman

First, before getting to the post issue, a remark I’m quite proud of is in order. I’ve been approached by many (and I mean a lot) of CFD practitioners who attended Dr. Florian Menter’s ANSYS Simulation World Lecture, telling me there is quite a remarkable correspondence between what you are about to read and the lecture.

## WHY SRS?

### Direct Numerical Simulation (DNS)

My first actual encounter with DNS  was while researching for my thesis relating to the role of hairpins in transition and turbulence (specifically originating from bypass transition mechanism). ChannelFlow code as simple as it was made me feel ever so powerful in my direct confrontation with turbulence… 😉 Turbulence phenomena is very precisely described by a seemingly simple set of equations, the Navier-Stokes equations, their nature is such that analytic solutions to even the most simple turbulent flows can not be obtained and resorting to numerical solutions seems like the only hope. But the resourcefulness of the plea to a direct numerical description of the equations is a mixed blessing as it seems the availability of such a description is directly matched to the power of a dimensionless number reflecting on how well momentum is diffused relative to the flow velocity (in the cross-stream direction) and on the thickness of a boundary layer relative to the body – The Reynolds Number. It is found that the computational effort in Direct Numerical Simulation (DNS) of the Navier-Stokes equations rises as Reynolds number in the power of 9/4 which renders such calculations as prohibitive for most engineering applications of practical interest and it shall remain so for the foreseeable future, its use confined to simple geometries and a limited range of Reynolds numbers  in the aim of supplying significant insight into turbulence physics that can not be attained in the laboratory.

Turbulent Boundary Layer (P. Schlatter and D. Henningson of KTH)

Saying all that, it is not expected that DNS will take on vital role in the engineering design process, where many designs are to be evaluated working through a repetitive cycle of obtaining a CAD geometry–> grid generation–>Solving the equation–>post-processing the results–>optimization decisions. Nonetheless, DNS shall find its place in the industrial CFD community for specialized research as it does in the academy, where on the line of an academic study which lasts up to approximately 5 years only a few high-fidelity simulations are conducted

The above presents a three dimensional direct numerical simulation using high-order methods has been performed to study the flow around the asymmetric NACA-4412 wing at a moderate chord Reynolds number (Rec = 400,000), with an angle of attack of 5 degrees. This flow regime corresponds approximately to the flow around a small glider. In addition to providing highly accurate data, high-order methods produce massive amount of data enabling proper flow visualization. For instance, in this study vortical structures emerging from tripping the flow to turbulence are visualized using the lambda2 criterion:

It is interesting to see how interaction of such vortical structures from the turbulent boundary layer and the turbulent wake creates a natural art of its own. a great source for some of the advancements in the DNS is found in Center for Turbulence Research – Stanford University”, directed by Parviz Moin. But as it seems A DNS of complete engineering application such as an airplane wing shall keep be quoted in publications as “not in the foreseeable future”.

### The incorporation of SRS in engineering process

In order for SRS to be best incorporated in engineering design process there are some challenges to overcome, most of which are related to LES rather than second generation URANS, based on RANS methodology which is very mature and well-tested as RANS has truly been the work horse for most large-scale engineering applications, in contrast with LES closures which are mostly algebraic and suffer from lack of complex engineering applications validity.

#### OPTIMIZATION AND SENSITIVITY ANALYSIS

Engineering design process is based on an iterative design achieving the best product through assessing a current design by optimization methodologies such as local sensitivity analysis, by which gradients of design parameters are calculated subsequently to be employed in gradient-based optimization algorithms. In order to being able to use LES in such quantification of design parameters it needs to be incorporated with tools of sensitivity analysis to measure how uncertainty factors affect the performance of the design. The problem is that LES is a non-linear dynamical system, hence suffers from chaotic behavior. Local calculations of quantities of interest of which initial conditions slightly depart, exponentially diverge as time advances. A robust methodology to avoid uncertainty calculations divergence is mandatory if LES is to participate in the engineering design process.

#### GEOMETRY, GRID GENERATION AND NUMERICAL SCHEMES

In order for LES to come forth on its future vital role, many adjustments and advancements to current dominating LES approaches should be conducted. In essence, what differs practical engineering applications from their academic counterparts is the level of geometry complexity. Unstructured meshing for complex geometries has been dominating industrial CFD and from an LES standpoint this means that large errors due to commutation of non-commutative operations may hamper results accuracy substantially. Advancements of Immersed Boundary Method (IBM), in which the boundaries of the body do not conform to the grid, the governing equations are discretized on fixed meshes and applying boundary conditions requires modifying the equations in the vicinity of the solid boundary by means of a forcing function that reproduces the effect of the boundary, are promising as far of high fidelity simulations of complex geometry and especially for moving meshes are concerned.

A snapshot of Large Eddy Simulation of a 5-bladed rotor wake in hover with a novel multiblock IBM (by Technion CFD Lab – S. Frankel)

#### Mixed SGS LES Models

Some new advancements in mixed-models (such dynamic and Smagorinsky) based on the integral formulation of the LES equation (F. M. Denaro) alleviate some of commutation problematic issues and allow for a much more accurate filtering. Moreover, of true importance is the increasing the level of automation. As HPC shall keep obeying Moore’s law in its advancement, CFD workflows shall suffer tremendously from the “human-in-the-loop” syndrome, where the practitioner is too much involved, especially in the geometry accommodation and grid generation phases of the design and analysis.

A great challenge concerning SRS is adaptive grid-generation, this is of course especially prevalent in wall bounded flows where slight grid changes of the order of magnitude of the kolmogorov scale may revile or hide coherent structures extremely important for the understanding of the phenomenolgy and the route of sustained turbulent. Besides that subtle point, what stands out is the fact that while in RANS grid adaptation is aimed only on reducing numerical error, for LES it is intended also to improve SGS model errors and  increase the fraction of resolved motions. Suggestions to alleviate the difficulty are strongly related to the fact that standard algebraic eddy-viscosity modeling approach render LES as “not complete” (in the same sense the we call 2-eq RANS models as “complete”) in the sense that the filter to be applied is not grid-independent. One exciting route of such by SB Pope  suggesting adaptation aiming on resolving a user-deﬁned fraction of the kinetic energy, and also presented an incorporation of such in dynamic modeling. There is still harsh problems to resolve in dynamic mesh model as LES closure is “incomplete”, a LES filter in its essence acts on a fully developed energy spectrum such as in homogeneous isotropic turbulence. A dynamic model would like to achieve some kind of scale separation between resolved and modeled scales, yet this is of course impossible, so what is usually done is placing the filter width very close to the dissipative scale, though still in very near the Taylor microscale to achieve (almost) universality. as the filter is always related to the grid size there are certain estimations for the length scale but these get harder to predict for complex flows (e,g, the presence of several length scales with strong dependence of the wall distance. The incorporation of higher order numerical methods in commercial CFD packages (by high I mean third order and above) shall also possibly be on the focus as the increase in computational power shall make them quite attractive for problems of which highly dissipative schemes are problematic such as vortex dominated flows and problems of wave propagation conducted in large scale and exploiting SRS.

#### CONSISTENCY OF SUB-GRID SCALE MODELS

It is highly desirable and possibly a step towards increasing the physical fidelity if SGS models are consistent with the Navier-Stokes equations in a mathematical and physical standpoint. Properties like symmetry requirements, near wall scaling (such as eddy-viscosity cubed), Realizability, production of turbulence kinetic energy, zero subgrid dissipation for laminar ﬂow, consistency with the second law of thermodynamics and some others are to be explored while developing new or revised SGS methodologies.

The challenge for future consistency is to match physical and mathematical consistency while also preserving important features such as locality for example, to match expected sharp increase in parallelism and to support hierarchical memory architectures having numerous graphical processing units (GPUs) and co-processors.

#### HIGH POWER COMPUTING (HPC)

The effectiveness and impact of CFD on the engineering design process is extremely dependent on the power and availability of modern HPC systems. During the last decades, CFD codes were formulated using message passing (MPI) software models which match nowadays parallelism efficiently. As future route and prevailing computing hardware, memory architecture (hierarchical not supported by MPI) and network connecting is not a-priori known new algorithms have to be supportive and advance hand to hand with computing resources. Numerical schemes such must also support tremendous parallelism in future exascale computing. Schemes involving global operations shall not prevail do to obvious bottlenecking.

The computational time can be estimated if we assume that the turbulent Reynolds number is proportional to the mean flow Reynolds number Rt = ζ Re, where ζ is an empirical coefficient usually close to 1/10 in confined flows (and in usual Reynolds numbers range). It is then proportional to the Reynolds number according to the law t ∝ 64ζ Rt 11/4 . These numerical order of magnitudes clearly show that DNS (or even highly resolved LES) implies a huge numerical task and still remains difficult to reach in practice at the present time even if considering the Moore’s law suggesting that the number of transistors of a processor doubles every second years (10 years = factor 32) and of top nowadays supercomputers : The second issue relates to the fact that in order to utilize such computational advancements, methodologies for SRS should be developed as to be also used outside the academy. As much as it is important that novel modelling techniques shall be validated and tested on simple canonical problems (e.g. ZPGBL/couette/channel/pipe flows) which lend themselves to detailed assessment, they should be developed to be also applied to real engineering problems. It is no coincidence that the k-ω SST 2-equation turbulence model (F. Menter) Detached-Eddy Simulation (DES) (P. Spalart) and WALE LES model (F. Nicoud and F. Ducros) have gained such popularity. It is the fact that each of them was devised intentionally to perform well for industrial applications, that made them such.  A good example is non-local operations which find their way to many LES formulations. Their use in commercial CFD code environment is near to impossible.

#### DEMOCRATIZATION OF SRS

I read quite an interesting post (by Keith Hanna – Mentor Graphics) about the “Democratization of CFD“. Referring to SRS, it is quite obvious that in order for LES to be widespread in the design process, it clearly needs to be much more accessible to non-proficient practitioners. In my post “Let’s LES” I have reviewed some of LES mandatory set of tools without which the credibility of the simulation is doubtful at best.

When a non-proficient practitioner tries to perform an LES, there are many instances of which being able to construct an animation of a time-varying flow that looks like a turbulent flow seems very satisfying. However, this offers no guarantee that the appropriate grid resolution has been used, spatial and temporal schemes have been selected, boundary conditions (especially time-varying, turbulent containing inflow conditions) are proper, etc’… CFD practitioners have to be educated to control a much different set of tools than those they were used to with RANS (and other low fidelity methodologies) to actually achieve the added benefit that LES could provide.

#### In Sum…

Even though it’s safe to predict that SRS (and especially LES) shall not replace RANS in the near future, the level of physical fidelity achieved by SRS shall have a growing impact on engineering design process. Returning to Moore’s law prediction it could be assumed that LES is going to take more and more of a vital role in engineering design process, being ever so attractive as its level of fidelity is such that it combines the advantages of simulations along with reliability features of experiments. This allows the engineer to build up his confidence while extracting high fidelity realizable results, such that the margin of safety could be tightening for the few more percentages of quantitative, qualitative and HPC which are the hardest to achieve. For this forecast to become reality, the one conclusion shared by most authors was that sincere confrontation with SRS challenges should be conducted while also taking under consideration its practicality to engineering design process.