 Good morning, everyone. My name is Wei Gao, and the topic today is the large-edged simulations of the turbulent flow past the aero-spatial airfoil at a high-velocity number. Since it is a high-velocity number, we're bound to the turbulent flows. So our work is focusing on the war model. The outline of my presentation is as follows. Following the introduction, the governing equations, and the numerical methods to solve the equations are described. After that, the physical model to close these equations is involved. Then finally, I will show some numerical methods to verify and validate our war model area code. And then the conclusion will be drawn. As we know, the eternal flow past an isolated airfoil is relevant for a variety of engineering applications, such as aircrafts, small wind turbines, or water mines. There are many different methods used to study these kind of flows, such as equipment tools. But equipment guys just focusing on the lift and drag coefficient. If we want to know the exact turbulent structures and the flow structures around the airfoil, we need the numerical tools. And these tools could be classified into the following four types, DNS, LES, DES, and RANS. RANS just solved the equation in the time average sense. Others, for LES and DES, they resolved the large scales and the model, the effect of small scales with some models. DNS resolved all the scales. So the computational cost of this method is different. For DNS and a war with OVS, the computational cost scale with Reynolds number with some equivalent. And according to NASA CFD vision, by 2030, we could be expected to perform this type of calculations on the leadership HPC machine. That means for war-bounded turbulent flows, Reynolds number as high as millions, it is now impossible to perform the war with OVS and DNS on such kind of flows. So we put our site to the world model is DNS and DES. So DES is just a kind of, I mean, hyper advanced LES. And both war model ES and DES, the computational cost is weakly dependent on the Reynolds number. So the basic approach for the war model ES is to compute the outer layer using a coarse LES while modeling the effect of momentum and heat transfer from the inner layer to the outer layer in the war model region. And there are many war models for simple geometry developed, for example, for turbulent boundary layer flows, channel flows, pipe flows. And most of these models just assume the velocity profile is low-glow. And sometimes the information from the outer ES is not coupled into the war region. So once this model is applied to the complexity military, there will be some problems. When it comes to the complexity military, most of the war model is just in the literature, just hyper advanced LES and DES. It is solving the simplified or full-Rens equation in the war model region. And this we are offered the Dirichlet or Newman boundary condition for the outer LES region. But there are some challenges for such kind of method. First is that there are more or less some free parameters in the Rens model. And another problem is that there's a so-called scale disparity at the Rens LES interface. And our contribution is to develop the virtual war model in the porting fitted carbon linear coordinates. That means there's no Rens and no free parameters in our model. The governing equations in the generalized carbon linear coordinates is in the table. It should be mentioned that without the blue term, then the equation degenerated to the governing equation for DINS. If we included the blue term, that means the SGS term inside into the F, then it is the governing equation for LES. To solve these equations, I use the fraction-save method. And for the spatial declarizations, I use the energy conservative force order find a different scheme. For the temporal declarations, I use the adiabatic force scheme for the convective and SGS term and a fairly implicit for the viscose term. For the pressure Poisson equation, I solve this with the martyquery method with line relaxed Gauss-Seider as the smoother. Then finally, all the code is parallel with MPI. The mesh is divided into blocks of equal size. And each of them is assigned to a unique processor. To close this model, I have to involve two physical models. One is the SGS model to compute the subgrade scale stress. Another one is the war model that will offer the boundary condition near the solid war. The subgrade scale model we choose, it is the stretch-spirited model. This is originally developed by Dale Pooley and the coworkers and also intended to channel flow simulations. It is a structure-based approach. And from the table, we can see that it will let the SGS stress with the subgrade kinetic energy. It assumes that in each computational cell, the subgrade motion is dominant by a vortex with a de-vegation. And this de-vegation is determined from a delta function PDF. The virtual war model in Cartesian coordinate was developed by Chou and Pooley for channel flow simulations. The most promising feature of this model is there's no free parameters. And this model has achieved many successful applications in kinematic flows. For example, turbulent boundary layer flow with or without adverse pressure gradient. Pipe flow with roof effects. That we also reproduce the Moody diagram very well. And then the turbulent boundary layer with or without separation and attachment. It captures a separation bubble on the turbulent boundary layer. The essential idea of this model is to combine the inner scaling with the world parallel and the normal integration filter and dividing an ODE for this friction velocity. So follow this approach. We developed, intended this model to the generalized coronary coordinate. First, we define the resultant velocity Q. It is composed by the three-wise velocity and the span-wise velocity. And after that, define two filter rings and using the inner scaling. In the inner scaling, the Q is related by the friction velocity and function F. But we don't need to know the exact form of the F because after integration, the F function would be canceled out. So finally, we can get the ODE for eta 0. As the previous said, the eta 0, it is the velocity gradient on the wall. So using this equation, we can get a solution to eta 0. Then, after some assumptions, we get the analytical solutions to the ODE. So this ODE is solved locally and dynamically. And we don't need to solve that with some numerical methods after the assumption. The assumption that follows first is that the A beta is independent of time of T in the very small dt integral. And the velocity angle doesn't change in the securities from the solid war to the virtual war. Wang Chen devised the governing equation for velocity angle in turbulent boundary layer simulations and found that there's very little difference between a dynamic theta model and a fixed theta. So here, for simplicity, we also use the fixed theta assumption in our war model AS code. So finally, adopting the idea of a constant shear stress of permeations, the velocity on the virtual war is developed as follows. For here, in the separation zone, we use the linear profile for the velocity. And in the attached zone, it follows the linear log profile. There are many LES work on airfoils. But most of the work, I could find some arguments. For example, most of the work, the span-wide domain size is very small. But according to some papers, they argue that the span-wide domain size is very important to resolve all the turbulent scales. And another one is that for the war model AS results, some papers, they didn't approach the CF. But it's very important because CF it is given by the war model. So if CF could not be reproduced correctly, then how can we say our result is reliable? And the last point is that the finest mesh size for the LES of airfoils is about 90 million. So our computational domain size is in the figure. The wake length is 10 code lengths. And the radius is a C code length. And the span-wide domain size is 0.8 code lengths. This is also recommended by Sun and Samtani in their computer and fluid paper. Only the first and this mesh is generated by the software point-wise. Only the first mesh layer on the virtual world is forced to be orthogonal. Then we have to verify and validate our war model AS code. The verification is using the NACA-12 airfoil. Venus number 10,000, attack angle 5. And the war units is as follows. In the world normal units, it's about 14. And then we compare our war model, yes, results with the DNS results. The validation, it is the aerospatial airfoil. Venus number 2.1 million and attack angle 13.3. And the world normal units, it is about 21. To save our competition costs for these high Venus number simulations, we first get the 2D DNS fields and let these 2D DNS fields as the initial field for the small war model, yes, simulations. The smallest war model, yes, it is that in the span-wise direction, we use 32 mesh points. Then switch to the first 3D war model, yes. Only the last four convective time scale results is used to analyze. And this results would be compared with the LES foil impairment. These two figures, it is a time and span-wise L-ish pressure coefficient around the airfoil and friction coefficient on the suction side. We can find that both of them compare well with the DNS results. Only small difference is exiting near the trailing edge. This is the contour of the new velocity. We can find our war model, yes, code could capture the separation bubble on the suction side very well, comparing with the DNS results. And this is the velocity distribution along the suction surface. And the velocity profile separated just with a displacement of 2 for that. And we also find the velocity profile compare well with the DNS, even in the separated zone. And this is the venous trace contour. And we use the transition creation 10 to minus 3 as the transition creation. And find that the transition by our war model, yes, also compare well with our DNS. This is the airfoil results. Also, we find that this pressure coefficient and the friction coefficient compare well with the impairment. This is the streamline velocity distribution along the suction surface. The left one is very close to the airfoil. The other one is far away from that. And we find that in the attached zone, left it compare very well, only small difference existing in the separation zone. And this is the UU prime along the suction surface. Also, in the attach zone, it compare well. In the separation zone, not well, but acceptable. Also, this is the VV profile, the same conclusion as before. And then it is venous trace along the suction surface and these five locations. And we also find that even in the separation zone, the comparison is not very good, but the maximum value of the UU prime compare well with the impairment. So finally, we come to the conclusions. First is that we develop the fourth order incompressible DNS and the war model, yes, called in the generalized carbon linear coordinate. This war model could be also attended to the unstructured mesh. The second, the virtual war model originally developed in the Cartesian coordinate, you get attended to the carbon linear coordinate. And the devolved equation for eta 0 is solved analytically and dynamically. Third one is this code is reflected and validated compare well with boating S and the impairment. Last one is the venous trace in the attach zone compare very well with the impairment data where some derivation writes in the separation zone. So this requires further inviscations. So all the simulation is carried out on Shaheen XC40 at cost. So thank you, everyone. Talk to us all the time, please. Is this the high Reynolds number? Yes. You don't have the Reynolds number on your slide. OK. So this is Reynolds number 2.1 by 10 to the 6. Is that correct? Yes. Yeah. And what about transition? Where does transition happen? Because in the impairment, he didn't specify the exact location. So we didn't compare that. But we can found the CF plot. We can find this transition. Almost here, yeah. In the impairment, it didn't use any trip. It's a free transition. There's free transition. Yes. With no blowing, nothing. Nothing. Yes. Do you use the trip sub-sort? No. Thank you again.