## The Enigma of Turbulence – Part I

which description would you choose describe turbulence best: Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity… Lewis Fry Richardson Turbulence is a phenomenon which sets in in a viscous fluid for values of viscosity, hence its purest, limiting form may be interpreted as asymptotic, …

Continue reading The Enigma of Turbulence – Part I

## From Reynolds Transport Theorem to Navier-Cauchy to Navier-Stokes Voyage: Part I

There are certain fundamental principles of conservation that govern the implementation of CFD. These principles are Conservation of mass, momentum & energy. We will see how we can represent these principles evolve in a mathematical form that expresses the dynamics of fluid flow by preserving mass, momentum and energy conservation. The Need of Reynolds Transport …

Continue reading From Reynolds Transport Theorem to Navier-Cauchy to Navier-Stokes Voyage: Part I

## SIMPLE Algorithm: Way to solve incompressible NV-Stokes Equation

Introduction Transport equations for each velocity component – momentum equations – can be derived from the general transport equation by replacing the variable φ with u, v and w respectively. The above equations govern a two-dimensional laminar steady ﬂow. The Main Problem! The velocity ﬁeld obtained from the momentum equation must also satisfy the continuity …

Continue reading SIMPLE Algorithm: Way to solve incompressible NV-Stokes Equation

## Eddy Viscosity Concept & Turbulent Kinetic Energy Equation

Turbulence flow exhibits randomness but it is possible to approach them via statistical methods. It fluctuates in time and space. It is possible to do spatial and time averaging. In RANS approach, we time average the turbulent quantities to extract the mean flow properties from the fluctuating ones. Now, we have to find some way …

Continue reading Eddy Viscosity Concept & Turbulent Kinetic Energy Equation

## Navier-Stokes Equation in Moving Reference Frame (MRF)

Most of the cfd applications consist of stationary objects around/inside which fluid will be flowing. So meshes are stationary. If the flow is incompressible, Incompressible Steady Navier-Stokes equations are solved. Very common applications are – Flow around Aerofoil, Flow inside Pipe. In both cases aerofoil and pipe are stationary hence meshes are stationary & solved …

Continue reading Navier-Stokes Equation in Moving Reference Frame (MRF)

## Wall Function: Boundary Layer Modelling Approach

When the flow approaches solid surface, steep gradient would form due to the no slip condition at the surface. This is known as Boundary Layer that develops near the solid surface in contact with the flow. Thickness of this boundary layer affects the wall heat flux and wall shear stress. In order to estimate wall …

Continue reading Wall Function: Boundary Layer Modelling Approach

## Classification of 2nd Order PDE in Fluid Flow Application

Partial Differential Equation based on their mathematical behavior can exhibit totally different solution in the flow field. The different and unique behavior of PDEs depends on their characteristics. It is very important to study these characteristics of PDEs so that we can make an assessment of the kind of numerical method should be applicable for …

Continue reading Classification of 2nd Order PDE in Fluid Flow Application

## From Kolmogorov to Wilcox to BSL to SST – The k-ω Family of Turbulence Models… Then we’re going to slide on ANSYS paradigm – GEKO.

“Every mathematician believes that he is ahead of the others. The reason none state this belief in public is because they are intelligent people” – Andrey Kolmogorov Abstract Three versions of the k-omega two-equation turbulence model will be presented. The first is the original David d. Wilcox model. In contrast to what we learned about …

Continue reading From Kolmogorov to Wilcox to BSL to SST – The k-ω Family of Turbulence Models… Then we’re going to slide on ANSYS paradigm – GEKO.

## TOP POSTS – February 2021

We’ve decided to gather for our “All About Cfd” followers our top ten read posts for February. I found the list kinda cool, maybe Some of my own favorites do not appear this month, but nonetheless it’s a wonderful list of posts: All About Turbulence Modeling – The “All You Can Eat” Menu Predictions for CFD …

Continue reading TOP POSTS – February 2021

## “All About CFD” – Tom’s Blog: The All Inclusive Turbulence Guide – Call to join 🤍🤍🤍

“All About CFD” – Tom’s Blog: The All Inclusive Turbulence Guide Following payment a password shall be granted, and the protected post content shall be fully exposed. Password and Learning Spot are available upon confirming payment at EMAIL: AVR.TOMER@GMAIL.COM

## The Transition Series: Part I – Mathematical Perspective

MOTIVATION MY FIRST  IN A LONG SET ABOUT THE PHENOMENA OF TRANSITION – SO EXCITED… The set shall certainly be for me the most important set of posts I’ve ever posted (I’m focused but it will take time…), based on my own messy scribbled writing, and the very new advances published lately in the works …

Continue reading The Transition Series: Part I – Mathematical Perspective

## TOP POSTS – July 2020 / AND / Two New Upcoming Zoom Sets of Ongoing Sessions

next month would bring fresh and new posts on topics like: Transition Phenomenology, Large Eddy Simulations (LES), and a set of weekly zoom ongoing sessions:
1) My “Recipe” for learning how to become a CFD self sustaining practitioner.
2) A PRIMER TO LARGE EDDY SIMULATIONS (LES).

## Zoom/Webinar: From Jones-Launder 1972 to ANSYS Turbulence Modules 2020 Team. Broadcasted: 20.7.20 – THE UNABRIDGED RECORDING

Zoom/Webinar: From Jones-Launder 1972 to ANSYS Turbulence Modules 2020 Team TODAY, 20.6.20, 20:00-21:30 – WE ARE HOAXED!

## Zoom: CFD Best Practice Guidelines 15/7/2020 20:00-21:30 (IDT) + Unabridged Recordings

Zoom: CFD Best Practice Guidelines 15/7/2020 20:00-21:30 (IDT)…
Zoom participants are the only ones who enjoy shred material I raise as important, and it’s a lot of material, this is why Registration is mandatory.

## Large Eddy Simulation – The Challenge of Filters That Commute With Differentiation – PART I – HOPE

Background Computational Fluid Dynamics (CFD) progress has been tremendous in the past half a decade. Moore’s Law vision of an exponential growth in computational resources lived up to its expectation and it’s predicted to keep doing so (at least) for  the next 20 years. Moore’s Law applied to CFD Scientists and engineers have developed models of many levels of …

Continue reading Large Eddy Simulation – The Challenge of Filters That Commute With Differentiation – PART I – HOPE

## Private Mentoring – Zoom Sessions – Going Official

Private and dedicated mentoring which includes an hour of private Zoom lesson, tailored to the students interest and level, rare (my…) resources and tutorials for self learning during the session, a final project of the students choice conducted in collaboration with Tom Avraham

## Zoom-Webinar: Transition Modeling and Phenomenology – 9.7.2020, 20:00-22:00 (IDT) + Unabridged Recording

A webinar on my favorite topic 💕 – Transition.

### I am always amazed over and over again when you participants find the time to watch me talk, I feel a wholeheartedly flattered but mostly grateful. Thank you! 🙏💕

There is quite a lot of research and known facts about turbulent flows and of course the laminar ones, yet the transition between them was always  a lacking in knowledge and enigmatic phenomena.

It doesn’t matter which kind you prefer in the above video…

In this short webinar we really really flew at a fast pace around very deep topics like the history of transition beginning with Reynolds and Orr-Sommerfeld, but also after noting ?Rayleigh and Fjo’rtof and 2D inviscid laminar flows criterions moved to 3D base flows and saw indications for baseflow profiles which arrive to a turbulent state without having an inlection point, that led us to the option of searching an answer in interacting mechanism of both Orr-Sommerfeld and Squire equation, and not stick with modal groth, with Ellingsen and Palm (1983) we have found transient algebraic growth, and introduced the reynolds-Orr Equation and learned firmly that the grothh rate of a final inviscid flow transition and and the inflection point and Fj’ortof Criterion. Modal stability analysis and the Orr-Sommerfeld/Squire equations, Landahl’sLift-up effect (1980 MIT school), and its huge contribution.

(highly) non-normal linearity Vs.non-linear normality where explained in a couple of ways,

“bootstrapping debate” (Fabian Walleffe clearly quite harshly criticizing the school of thought originating in MIT and spreading to KTH). At the time was fully engrossed with non-normal operators and linear transient growth mechanisms… Than it hit me that Walleffe has it very nicely explained, a rush of confusion went through my body. It made me review how much we do not notice our tendency for confirmation bias (in a big way unconsciously).

I think that if one listens well the concepts of streaks becomes almost fully explained.

secondary instability theory and Floquet analysis, the concept of pseudospectra “(read

with the amazing conceptuality and relevence to transition flow of the Pseudospectra

and the behaviour of a resolvent when a non-normal or better yet HIGHLY non-normal

operator is where we aim to investigate. that the level of non-normality could be

represented represented by a condition number, of which the non-normal matrix

behaviour dependents strongly, we simply don’t have the same behaviour for the

resolvent of a normal Vs. a non-normal operator… and if we understood the essence we

MUST acknowledge that in the case of transient growth of non-normal operators things

like shpe (the obliqueness of Dan Henningson (KTH), the Landahl’s effect, and

‘bootstraping” redistributing energy in orthogonal direction back and forth) play a huge

role and it is not the exponentially modal eigenvalue that is not most susceptible to

growth just enough to excite non-linear mechanisms.

We saw that a spectra of an undisturbed initial flow to a infinitesimal disturbance is

modaly stable or perhaps unstable by way such a way that we shall find the flow

turbulent way before the representing Reynolds number of the unstable orthogonal

mode happens (such as waiting for orszag (1971) to find that at 5777.2 while in actuality

transition arrives whey before distabilation…). trying to communicate the essence

without deriving (albeit sometimes getting a glimpse at the frightening equations to stay

attached to the core)…

Then get a short but well posed acquaintance with types of transition mechanisms, (K-H-

O-N-TS…) the evolving literature in the studying fine grained coherent structures and self

sustained turbulence cycles, and watch cool KTH (by one of my favorite dissertations

It was really hard to organize communicating such an intrinsically intricate topic in two

hours. So I must admit I had some live difficult time… 🙏 (Forgive me if I got a little

confusion, you know this rarely happens to me… Love me 😋)…

### ✨There is room for a second webinar on the topic. Next week seems cool…✨

The webinar presented many recommended resources that I find most valuable. Resources shall are shared as per request with participants, and it is always said they may always reach out tome without thinking a second time, helping you is never time wasted. that  and the webinar shall be unabridged recorded.

The webinar, as all of my webinar is interactive, always asking participants not to unmute themselves, still ending with a dedicated Q&A.

## Understanding The Detached Eddy Simulation From DES to IDDES

Understanding The Detached Eddy Simulation From DES to IDDES

## Ask Me Anything – 2 (17.6.20 IDT) – ANSWERS + UNABRIDGED RECORDING + RESOURCES

Ask Me Anything – 2 (17.6.20 19:00 IDT) – The Answers + Recordings + Resources

More Than TWO(!) hours of raw unabridged recording

## All About Turbulence Modeling – The “All You Can Eat” Menu

I love turbulence. Knowing how to model it in just the right fidelity is an art imho. An art I fell in love with 💕 The intention of this set of posts is to embark on a journey of connecting the dots between CFD and turbulence modeling with the phenomenological and practical concepts of …

## Webinar 10.6: Thermal Analysis and CFD of Electronic Equipment: My Resource + Unabridged Recording

❤️❤️❤️Thank you dear participants, it aleays amazes me that people rather join me with their precious time ❤️❤️❤️                                     💥Thermal Analysis and CFD of Electronic Equipment💥   The webinar shall give the attendee the full view of top to …

Continue reading Webinar 10.6: Thermal Analysis and CFD of Electronic Equipment: My Resource + Unabridged Recording

## Webinar 27.5: Near Wall Turbulence Modeling and the k-ω Turbulence Models family

❤️❤️❤️Thank you dear participants ❤️❤️❤️ Open Zoom webinar about near wall modeling and the k-ω family of turbulence models: heuristic reasoning, ad-hoc assumption in the derivation, the shear-stress concept, certain corrections such as compressibility or curvature, wall insensitivity Vs. Wall sensitivity, GEKO approach and its different choices of parameters effect, and best practice guidelines for …

Continue reading Webinar 27.5: Near Wall Turbulence Modeling and the k-ω Turbulence Models family

## The “Ask Me Anything” (AMA) Webinar series No. 1 – Turbulence and a little ROMs (20.5.2020)…

The Ask Me Anything series shall be going on about as I follow my  private messages and emails pile up and think it’s best to address some of the resembling questions on a kind of open share zoom/webinar format. So I guess every every two weeks a new AMA shall be renounced.

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

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

## “All About Entropy…” – Part II – Claude Shannon in a glimpse

“This duality can be pursued further and is related to a duality between past and future and the notions of control and knowledge. Thus we may have knowledge of the past but cannot control it; we may control the future but have no knowledge of it…” Claude Elwood Shannon In Part I of “All About …

Continue reading “All About Entropy…” – Part II – Claude Shannon in a glimpse

## All About Entropy… – Part I – Beginnings

If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations – then much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of …

## Turbulence Modeling – Near Wall Treatment

Most of nowadays CFD simulations are conducted with the Reynolds Averaging approach. Reynolds Averaged Navier-Stokes (RANS) simulation, the “working horse” of industrial CFD is based on the Reynolds decomposition according to which a flow variable is decomposed into mean and fluctuating quantities. When the decomposition is applied to Navier-Stokes equation an extra term known as the Reynolds …

Continue reading Turbulence Modeling – Near Wall Treatment

## The CFD Bare Minimum – An Initial Roadmap To Begin Practicing CFD

Here’s a set of CFD online resources regarding basic CFD related concepts which are unnecessarily linked to a specific commercial code but goes all the way to basics with respect to CFD (numerical schemes, modified equation, CFL, Von Neumann analysis, numerical diffusion, pressure-velocity coupling, types of meshing, turbulence modelling, etc’…), along with application-specific resources, and some “hands on” practical resources. I highly recommend to follow all types of routes, if one wants to achieve both the breadth and the depth CFD has to offer…

## Large Eddy Simulation (LES) of Tunnel Pool Fire and calculation Infra Red absorption Coefficients of Soot Particles

1. Introduction Tunnel development is proceeding to reduce transportation time and to achieve efficient use of space. Maintenance and management of these tunnels are now important, due to increased demand for greater use and the needs for construction of tunnels [1]. Therefore, because of increased usability of tunnels, the prevention of fire and emergency evacuation …

Continue reading Large Eddy Simulation (LES) of Tunnel Pool Fire and calculation Infra Red absorption Coefficients of Soot Particles

## Discretization Schemes – Upwinding

✨✨UPWINDING✨✨

In what follows a problem which arises as a consequence of specific properties of solutions to difference equations shall be presented. In contrary to what is often thought, the phenomena which manifests itself as non-physical oscillation of the numerical solution from one grid point to the next does not arise simply from nonlinearities of Navier–Stokes equations (NSE).

After exploring communicatively the above presented problem we shall delve to an approach developed by a the one and only S. V. Patankar.
Patankar had taken an ad-hoc “physical reasoning” arguing that as it is clear from the representation of centered difference approximation to the velocity gradient both upstream and downstream flow behavior are sensed. Hence a least biased difference approximation, using only information carried in the flow direction in its simplest form is offered.

So… let’s go Upwinding together 🤙🏻

https://lnkd.in/dc4cY5C

#discretization #Patankar #CellRe #cfd #engineering #technology #innovation #FREEonlinelearning #FREEeducation blogging

## CFD SIMULATION OF ETHANOL STEAM REFORMING FOR MARINE STIRLING ENGINE

1. INTRODUCTION  External combustion engines, like the Stirling engine, have benefits over their internal combustion counterparts due to their ability to remain completely sealed from the elements and their nearly silent operation. Stirling engines are inherently robust, quiet, and only require an external heat source for operation. These characteristics make these engines ideal candidates for …

Continue reading CFD SIMULATION OF ETHANOL STEAM REFORMING FOR MARINE STIRLING ENGINE

## CFD Design of Hydrogenation Reactor for Producing GVL from LA -Levulinic Acid

1. Introduction Levulinic acid (LA) is considered as one of the “Top 10” building blocks for future bio-refineries as proposed by the US Department of Energy. It is  one of the most important platform molecules for the production of fine chemicals and fuels based on its compatibility with existing processes, market economics, and industrial ability …

Continue reading CFD Design of Hydrogenation Reactor for Producing GVL from LA -Levulinic Acid

## Going Dynamic – Part I

“Big whorls have little whorls that feed on their velocity, and little whorls have lesser whorls and so on to viscosity” – Lewis Fry Richardson The above quote, an almost epic description by Lewis Fry Richardson captures the horrific cartoon presented by Navier-Stokes equations. Although seemingly a fairly simple set of equations, analytic solutions to even the most simple turbulent …

Continue reading Going Dynamic – Part I

## “Turbulence Modeling Best Practice Guidelines: Task specific EVMs – PART III”

“Turbulence Modeling Best Practice Guidelines: Task specific EVMs – PART I“ presented a general description of the Standard EVMs along with meshing guidance.The next post, “Turbulence Modeling Best Practice Guidelines: Standard EVMs – PART II”, discusses what is arguably the important topic – V&V, along with some in-depth model specific practical best guidelines on near-wall …

Continue reading “Turbulence Modeling Best Practice Guidelines: Task specific EVMs – PART III”

## Know Your Mesh – Basic Methodologies

Consider the simulation of flow field past a solid obstruction. Generating a grid to solve a discretization scheme shall proceed in one of few routes. First a surface grid covering the boundaries of the solid body may be generated. In subsequent step, If a finite-difference scheme is employed, then a curvilinear coordinate system aligned with the grid lines shall be …

## Turbulence Modeling Best Practice Guidelines: Standard EVMs – PART II

In Part II we delve into topics which are of no less importance such as V&V, and near-wall treatment. Tip No. 3: Always V&V Some would claim that this should have been the first tip on the list, and I am not sure I disagree. It is best to not rely on CFD at all, …

Continue reading Turbulence Modeling Best Practice Guidelines: Standard EVMs – PART II

## Turbulence Modeling Best Practice Guidelines: Standard EVMs – PART I

In the following set of posts I shall present what I find as the most effective best practice guidelines to the challenge of modeling turbulence. I shall try to keep the posts as practical as I can from an engineering standpoint, and as pointed as I can towards the best practice guidelines themselves. To be …

Continue reading Turbulence Modeling Best Practice Guidelines: Standard EVMs – PART I

## Some Fundamental Thoughts About Emergent Theories…

As far as we know, there is only one objective physical reality, but there are many ways of describing it. Usually, we refer to these ways as “theories” or sometimes “models”. Ever since the days of Aristotle and his contemporaries, science has discovered many such theories or models, some may be harder to perceive but …

## Define Turbulence… PART I

Big whorls have little whorls that feed on their velocity, and little whorls have lesser whorls and so on to viscosity”– Lewis Fry Richardson Explaining the nature of turbulence, is hard, as all through history the greatest of minds couldn’t quite capture a satisfactory definition Well, easier said than done. The understanding of turbulent behavior in …

Continue reading Define Turbulence… PART I

## Engineering Turbulence – Part II: Lifting The Wright Way!

“It’s easy to explain how a rocket works, but explaining how a wing works takes a rocket scientist…” – Philippe Spalart (senior technical fellow – the Boeing company) The intention of this set of posts is to embark on a journey of connecting the dots between CFD and turbulence modeling with the phenomenological and practical …

Continue reading Engineering Turbulence – Part II: Lifting The Wright Way!

## Engineering Turbulence – Part I: Phenomenology

“If you want to be a Millionaire, start with a billion dollars and launch a new airline …” – Richard Branson The intention of this set of posts is to embark on a journey of connecting the dots between CFD and turbulence modeling with the phenomenological and practical concepts of engineering aerodynamics. Even though it …

Continue reading Engineering Turbulence – Part I: Phenomenology

## GEKO – And Then There Were Six…

“with four parameters I can fit an elephant, with five I can make him wiggle his trunk…” – John von Neumann Most of nowadays CFD simulations of engineering applications are conducted via the Reynolds Averaging approach. Reynolds-Averaged Navier-Stokes (RANS) simulation is based on the Reynolds decomposition according to which a flow variable is decomposed into …

Continue reading GEKO – And Then There Were Six…

## Turbulence Modeling – The Gist

The attached presentation is a concise description of turbulence modeling approaches, based on the portion of Turbulence Modeling of past CFD courses I have had the opportunity to lead. It has many links to more elaborated blog posts relating to specific turbulence models and its foundations. Update 29/3/18: Stress-Blended Eddy Simulation (SBES) (slides 86-87) Update …

Continue reading Turbulence Modeling – The Gist

## Know Thy Mesh – Mesh Quality – Part I

Many would argue that your CFD solution is as good as the mesh behind it. Many aspects of the mesh have a vital contribution to simulation accuracy, and include among others the type of physics models simulated, the details of the solution to the particular simulation, chosen discretization scheme and geometric mesh properties …

Continue reading Know Thy Mesh – Mesh Quality – Part I

## Numerical Schemes in CFD: Upwinding and The Cell-Reynolds Problem

Numerical Schemes in CFD: Upwinding and The Cell-Reynolds Problem

## Know Thy Solver – Part III: Pressure Equation Methodologies for Incompressible Flow

In compressible flows the continuity equation can be used to determinethe density and the pressure can be calculated from an equation of state. This approach is not appropriate for incompressible or low Mach number flows. When considering the incompressibility assumption as valid, Navier-Stokes equations supplemented by continuity take the following recognizable form (body forces …

Continue reading Know Thy Solver – Part III: Pressure Equation Methodologies for Incompressible Flow

## Law of the Wall

We begin our discussion by noting that there are three quite general and distinct types of turbulent flows: namely, Homogeneous and/or isotropic turbulence, free shear flows and wall-bounded shear flows. Homogeneous and/or Isotropic Turbulence Homogeneous turbulence is such that statistics are invariant under spatial translations, while isotropic turbulence is invariant under rotations and reflections. As rotations and reflections can …

Continue reading Law of the Wall

## A Forest of Hairpins – on the quest for turbulence coherent structures (updated)

“Mathematics is the language in which God has written the universe”… Galileo Galilei, Italian astronomer & physicist (1564 – 1642) Recent studies, suggest a dominant role for hairpin shaped vortices of various sizes throughout the boundary layer in transitional stages. Hairpins are well-known structures in transitional flows, appearing as a result of shear-layer roll-up. …

Continue reading A Forest of Hairpins – on the quest for turbulence coherent structures (updated)

## Going Hybrid

Nothing is as beneficiary for the flight industry as the ability to cut substantially on fuel budget. From a CFD perspective, such a goal could potentially be achieved by high fidelity simulation for a detailed design full airborne vehicle . A naive approach for the highest physical fidelity could be a Direct Numerical Simulation (DNS) of Navier-Stokes equations. …

## Know Thy Solver- PART II: Projection Methods

Hopefully upon finishing reading Know Thy Solver- PART I, we have consolidated the logic and motivation behind NSE solver segregated algorithms. Our task now is to present an important cornerstone which serves as a building block for ANSYS Fluent pressure-based algorithms as in most other commercial CFD codes – Projection Methods. It is important to note …

Continue reading Know Thy Solver- PART II: Projection Methods

## Know Thy Solver- PART I: Introduction to NSE Algorithms

A successful CFD analysis workflow consists of the following key elements (sometimes by repeating cycles, and sometimes with additional elements as-per-cause): Definition CFD modeling goals according to the model problem at hand: Physics gives us a description of reality or in other words, a model, by such CFD modeling goals should conform to the level …

Continue reading Know Thy Solver- PART I: Introduction to NSE Algorithms

## Modeling Transition…

Turbulence prediction has an enormous impact airliners fuel budget, weather information, automotive industry, turbomachinery, biomedical industry and could be easily linked to many other aspects of our daily lives. A lot of focus has been given to the prediction of turbulence through numerical modeling to level of physical fidelity depending on the goal of …

## Understanding The Realizable k-ε Turbulence Model

Most of nowadays CFD simulations are conducted with the Reynolds Averaging approach. Reynolds Averaged Navier-Stokes (RANS) simulation, the “working horse” of industrial CFD is based on the Reynolds decomposition according to which a flow variable is decomposed into mean and fluctuating quantities. When the decomposition is applied to Navier-Stokes equation an extra term known as the Reynolds …

Continue reading Understanding The Realizable k-ε Turbulence Model

## Predictions for CFD in 2030

“Prediction is very difficult, especially if it’s about the future…” – Niels Bohr Growing up as the child of two software engineers, mathematics and computers were an inseparable part of my life. My father always had these wonderful science-related stories and the patience to follow up on each and every question I had. I remember …

Continue reading Predictions for CFD in 2030

## Thermal Analysis and Cooling Solutions for Electronic Equipment – a comprehensive guide

In order to reduce development time, electronic equipment manufacturers and PCB designers need to ascertain the thermal aspects at the earliest possible stage of the design process. In the early days of thermal management thermal analysis to supply such information was conducted mainly by thumb ruling and simplified correlation-based calculations, rendering somewhat of an expected …

Continue reading Thermal Analysis and Cooling Solutions for Electronic Equipment – a comprehensive guide

“Turbulence is the most important unsolved problem of classical physics…” – Richard Feynman. Nothing would be as cost-effective for the flight industry as the ability to cut substantially on fuel budget. From a CFD perspective, such a goal could be achieved in a much more straightforward manner if a full airborne vehicle simulation could be supplied, still keeping high fidelity of the physics. …

## Scale Resolving Simulation – Overview

It’s quite amazing how Computational Fluid Dynamics (CFD) progress has been tremendous in the past half a decade. Moore’s Law vision of an exponential growth in computational resources lived up to its expectation and it’s by many predicted to keep doing so for  the next 20 years if not more. Moore’s Law applied to CFD One huge leap forward …

Continue reading Scale Resolving Simulation – Overview

## Understanding the Boussinesq Hypothesis and the Eddy-Viscosity Concept

The two levels of descriptions, the microscopic-molecular and that of the macroscoping-continuum assumption are totally autonomous, but also, they have a different range of applicability, manifested in their different vocabularies. For example, we are not allowed to talk about the temperature of an atom, or about the pressure exerted on it. This is described …

Continue reading Understanding the Boussinesq Hypothesis and the Eddy-Viscosity Concept

## Understanding Reynolds Stress Models (RSM) for Turbulence Modeling

The earliest steps to use of second-moment closure (also known as Reynolds stress models, RSMs) could be traced back to Rotta’s work at the early 50’s, although most of the advancement in the field took hold in mid seventies by Launder et al. and came to light shortly after introduction of the modern two equation eddy-viscosity models.

The following poTenzorTenzor”All About CFD” blog presents a review of the Reynolds Stress Modeling (RSM) approach for Reynolds Averaged Navier-Stokes (RANS) equations, followed by Part II where a reduced form of RSM shall be presented along with its valuable features – the Algebraic Reynolds Stress Model (ASM), with special emphasis on its attractive explicit form (i.e. EASM).

## LET’s LES IV

“…the smallest eddies are almost numberless, and large things are rotated only by large eddies and not by small ones, and small things are turned by small eddies and large” – Leonardo di ser Piero da Vinci Following the anticipated approach for LES simulation setup, as presented thoroughly in LET’s LES I, LET’s LES II and …

## Second Generation URANS – Get Your LES-Like Content Resourcefully

The post shall present a fascinating route to achieving resourceful Scale Resolving Simulation (SRS – P. Moin, F. Menter, P.G Tucker, NASA Report by J. Slotnick, etc’…), all of which aim to provide a road Second Generation URANS – extracting your LES-like content (along with TENZOR insight and conclusions on the subject). Scale-Resolving Simulations (SRS) Computational Fluid Dynamics …

## Democratization of CFD and Scale Resolving Simulation (SRS)

There is a powerful movement nowadays supporting the “democratization of CFD”. Far and fore most I want to declare that I would be ultimately happy when the day shall come and it appears that it is just around the corner. Nonetheless, lately I read quite an interesting post (by Keith Hanna – Mentor Graphics) about the …

Continue reading Democratization of CFD and Scale Resolving Simulation (SRS)

## Direct Numerical Simulation Part III – The Reynolds Number Limitation

“To mechanical progress there is apparently no end: for as in the past so in the future, each step in any direction will remove limits and bring in past barriers which have till then blocked the way in other directions; and so what for the time may appear to be a visible or practical limit …

Continue reading Direct Numerical Simulation Part III – The Reynolds Number Limitation

## Direct Numerical Simulation Part II – Boundary Conditions for Incompressible DNS

The specification of boundary conditions for open boundaries of the numerical space is a subtlety in DNS. One must consider that given the turbulent flow, the only boundary conditions for a specific DNS realization is the solution itself, on that is of course unknown a-priori… The major difficulty (considering incompressible flow) is posed in inflow …

Continue reading Direct Numerical Simulation Part II – Boundary Conditions for Incompressible DNS

## Direct Numerical Simulation Part I – Spectral Methods

A plea for 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 …

Continue reading Direct Numerical Simulation Part I – Spectral Methods

## “All About CFD…” List of Recommended CFD and Fluid Mechanics Books

In the following a partial list of my favorite books on your way to mastery of CFD: Doug McLean’s presentation “Common Misconceptions in Aerodynamics” is actually a preview for a seminal and intuitive book “Understanding Aerodynamic” I especially recommend: some more amazing CFD material is posted on behalf of J.M. McDonough (university of Kentucky). The fascinating lecture notes …

Continue reading “All About CFD…” List of Recommended CFD and Fluid Mechanics Books

## “The Grey Area” – Interfacing RANS and LES and Hybrid Subtleties

While the ultimate goal is a model that may work in the RANS limit, LES limit and smoothly connect them at their interface (might it be zonal or monolithic formulation), it seems that in particular the interface termed “the grey area” stands problematic although in the focus of the CFD community for some time. …

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## Kolmogorov Route Employed by Uriel Frisch – Part II

U. Frisch treatment of Kolmogorov’s raw assumptions was a foundation to many research and analysis in the 80-90’s of the previous century. The origin for this treatments are three hypothesis devised by Frisch which are not as simple and straight forward as Kolmogorov’s original assumptions: Hypothesis 1:  In the Re → ∞ limit, all …

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## Understanding the v2f Model – Part I

Computational Fluid Dynamics (CFD) in the industry had gone through tremendous advancements in the past 50 years and cientists and engineers have developed models of increasing fidelity. Lifting-surface Methods that model only the camber lines of lifting surfaces, not the thickness, vortex wakes that must of course be paneled. Linear Panel Methods that solve either the incompressible potential-flow …

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## Kolmogorov’s Route Part I – Universality Assumptions

“An individual tends to absorb the surrounding spirit and to radiate the acquired lifestyle and worldview to anyone around, not just to a select friend.” Andrei Kolmogorov contribution to the field of turbulence was not less than astonishing.  The original Kolmogorov  papers were difficult to read as some of the assumptions made are not implicitly stated and …

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## LET’s LES III

“…the smallest eddies are almost numberless, and large things are rotated only by large eddies and not by small ones, and small things are turned by small eddies and large” – Leonardo di ser Piero da Vinci Spatial and Temporal Resolution In LES, especially for complex flows as the large-scale anisotropic features are to be accurately …

## LET’s LES II

“…the smallest eddies are almost numberless, and large things are rotated only by large eddies and not by small ones, and small things are turned by small eddies and large” – Leonardo di ser Piero da Vinci Being so passionate for the subject of turbulence modelling I shall kick off with my favorite, SGS… 😉 LES …

## Immersed Boundary Method (IBM)

Although found some reemergence in the past few years, the general concept was actually developed by Peskin in 1972 for the simulation of blood flow and cardiac mechanics coupling. In IBM a non-body conformal Cartesian grid is employed. The immersed boundary would still be represented by a surface grid, but the Cartesian volume grid is generated …

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## NSE and a Taste of Cause-and-Effect Relations

As much as I think a matter of interpretation should always have its place in science, even if just for the matter of a straightforward explanation it may be expressed as such, the view that the curl of the velocity (i.e. vorticity) inducing a velocity field is clearly misleading and o n the harsh side, it’s …

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## Vorticity, Vortex Streching and Turbulence

“Big whorls have little whorls that feed on their velocity, and little whorls have lesser whorls and so on to viscosity” – Lewis Fry Richardson After reading Is velocity induction by vorticity a fallacy?, we clearly understood that although vorticity is an extremely important topic, and has already considered to be a key ingredient of turbulent flow, it …

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## Understanding The v2-f Turbulence Model – Part II

The v2-f Turbulence Model In the v2−f model, the variable v^2, and its source term f , as variables in addition to the  k and ε (turbulence kinetic energy and turbulence dissipation) parameters of the k−ε eddy-viscosity turbulence model. The model hence solves for three transport equations for the turbulence kinetic energy, turbulence dissipation and the …

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## High Vs. Low Order Numerical Methods in CFD

High Vs. Low Order Numerical Discretizations in CFD

## Understanding The Spalart-Allmaras Turbulence Model

“It’s easy to explain how a rocket works, but explaining how a wing works takes a rocket scientist…” – Philippe Spalart Most of nowadays CFD simulations are conducted with the Reynolds Averaging approach. Reynolds-Averaged Navier-Stokes (RANS) simulation  is based on the Reynolds decomposition according to which a flow variable is decomposed into mean and fluctuating …

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## Understanding The k-ε Turbulence Model

“To mechanical progress there is apparently no end: for as in the past so in the future, each step in any direction will remove limits and bring in past barriers which have till then blocked the way in other directions; and so what for the time may appear to be a visible or practical limit …

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## Let’s LES I

“…the smallest eddies are almost numberless, and large things are rotated only by large eddies and not by small ones, and small things are turned by small eddies and large” – Leonardo di ser Piero da Vinci The remarkably modern quote dated a few hundreds of years ago, generally envision the apparent frustration from the “order …

## Pots and PANS

“predictions are very difficult, especially about the future…” – Richard Feinmann Turbulence modelling is considered by many as witchcraft, by others as the art of producing physics out of chaos. The above quote by Niels Bohr, generally to remind the impossibility in predicting future events in life, ever so affected by and coupled with our surrounding …

## Milton Van Dyke: “An Album of Fluid Motion”

Milton Van Dyke’s “An Album of Fluid Motion” is a rich historical contribution of flow visualisation. A note about CFD stems from a photo that appears on page 23 for streaklines marked by dye released from upstream in a water tunnel for a NACA 64A015 airfoil at zero incidence, Re=7000 (laminar and steady flow). Van Dyke …

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## That’s a Big W(h)ALE…

“I am an old man now, and when I die and go to Heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics and the other is the turbulent motion of fluids. And about the former I am rather more optimistic…” – Sir Horace Lamb The above quote by Sir …

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## V. Flow by VORCAT – how to simulate turbulence mesh free…

The software is one of the most sophisticated vortex method commercial software I came across during my thesis. Peter Bernard’s (and partners) Vorcat is based upon Alexandre Chorin publications of some fascinating ideas concerning numerical modelling with mesh free methods. Chorin proposed a discretization of the vorticity equation by vortex entities, linking them to the …

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## Is velocity induction by vorticity a fallacy?

Each and every engineering student finds himself confronted with the Biot-Savart law at one point or another of their undergraduate studies whether it is related to fluid mechanics or classical electromagnetics. The Biot-Savart carries along the qualitative idea that knowing the curl of a vector field at one point allows us to infer something about …

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