Critical transition Reynolds number for plane channel flow

The determination of the critical transition Reynolds number is of practical importance for some engineering problems. However, it is not available with the current theoretical method, and has to rely on experiments. For supersonic/hypersonic boundary layer flows, the experimental method for determination is not feasible either. Therefore, in this paper, a numerical method for the determination of the critical transition Reynolds number for an incompressible plane channel flow is proposed. It is basically aimed to test the feasibility of the method. The proposed method is extended to determine the critical Reynolds number of the supersonic/hypersonic boundary layer flow in the subsequent papers.

Critical Transition Reynolds Number for the Incompressible Flat-plate Boundary Layer as Searched by Numerical Simulation

The critical transition Reynolds number is the lowest value at which the turbulent flow can hold in real flows.The determination of the critical transition Reynolds number not only is a scientific problem,but also is important for some engineering problems.However,there is no available theoretical method to search the critical value.For the hypersonic boundary layer with significant importance for engineering problems,there is no available experimental method to search the critical value so far.Consequently,it is imperative to take numerical method to search it.In this paper,direct numerical simulations(DNS)method is employed to determine the critical transition Reynolds number for the incompressible flat-plate boundary layer.Firstly,under the assumption of parallel flow,the temporal mode DNS is performed to determine the critical value as Re_(xpcr)=43767,which is quite close to the numerical results of other people.Secondly,under the condition of nonparallel flow,the spatial mode DNS is performed to determine the critical transition Reynolds number as Re_(xcr)=3×10^(5),which is well consistent with the experimental results.In principle,the proposed method in this paper can be extended to the supersonic/hypersonic boundary layer,and that problem will be discussed in the subsequent papers.

Locating the QCD critical end point through peaked baryon number susceptibilities along the freeze-out line

We investigate the baryon number susceptibilities up to fourth order along different freeze-out lines in a holographic QCD model with a critical end point（CEP）, and we propose that the peaked baryon number susceptibilities along the freeze-out line can be used as a clean signature to locate the CEP in the QCD phase diagram.On the temperature and baryon chemical potential plane, the cumulant ratio of the baryon number susceptibilities（up to fourth order） forms a ridge along the phase boundary, and develops a sword-shaped ＂mountain＂ standing upright around the CEP in a narrow and oblate region. The measurement of baryon number susceptibilities from heavy-ion collision experiments is along the freeze-out line. If the freeze-out line crosses the foot of the CEP mountain, then one can observe the peaked baryon number susceptibilities along the freeze-out line, and the kurtosis of the baryon number distributions has the highest magnitude. The data from the first phase of the beam energy scan program at the Relativistic Heavy Ion Collider indicates that there should be a peak of the kurtosis of the baryon number distribution at a collision energy of around 5 Ge V, which suggests that the freeze-out line crosses the foot of the CEP mountain and the summit of the CEP should be located nearby, around a collision energy of 3–7 GeV.