What Is the Reynolds Number?

Reynolds number A dimensionless number that can be used to characterize the flow of a fluid. Re = vd / , where v, , and are the flow velocity, density, and viscosity coefficient of the fluid, respectively, and d is a characteristic length. For example, if fluid flows through a circular pipe, d is the equivalent diameter of the pipe. The Reynolds number can be used to distinguish whether the flow of a fluid is laminar or turbulent. It can also be used to determine the resistance to an object flowing in the fluid.

Reynolds number is

The smaller the Reynolds number is, the more significant the viscous effect is, and the larger the inertia effect is. The flow with a small Reynolds number, such as the drop of fog beads or the flow process in the lubricating film, is characterized by the fact that the viscous effect is important in the entire flow field. The flow with a large Reynolds number, such as the airflow relative to the aircraft when flying near the ground, is characterized by the effect of the viscosity of the fluid on the flow around the object is only important in the boundary layer of the object and the wake behind the object. In the flow where inertia and viscous forces play an important role, to make two geometrically similar flows (geometric similarity ratio n = L _p / L _m , the subscript p represents the real object, m represents the model) to meet the dynamic similarity conditions, the model must be guaranteed It is equal to the Reynolds number in kind. For example, if simulation experiments are performed in the same fluid (that is, is equal), the dynamic similarity condition is v _m = nv _p , that is, the model is reduced by n times, and the speed is increased by n times.

When an object moves in a steady plane in an incompressible viscous fluid, all dimensionless numbers are determined by two parameters: the angle of attack and the Reynolds number Re. In order to achieve similar dynamics, in addition to requiring the model and physical geometry to be similar, the angle of attack and Reynolds number must also be equal. The first condition is always easy to implement, while the second condition is generally difficult to fully meet. In particular, when the size of the object to be flowed is relatively large, the model is many times smaller than the real object, which requires a large change in the flow velocity, density and viscosity of the fluid. This is very difficult in practice, because in low-speed wind tunnels, there is always a limit to the increase in wind speed. Therefore, the law of similarity cannot be strictly met, but can only be approximated. Of course, this will affect the aerodynamic characteristics, for example, the maximum drag coefficient will be reduced, and the minimum drag coefficient will be increased. However, as long as the difference between the physical Reynolds number Re _p and the model Reynolds number Re _m is not too large, some empirical methods can be used to modify it so that the experimental results can still be applied in practice. Of course, the best way is to build a huge wind tunnel in which the real aircraft can be blown, or a closed loop wind tunnel in which compressed air (larger density) acts, in order to increase the model test Reynolds number. .

According to the theory of molecular motion, the dynamic viscosity coefficient vl, where v is the average molecular velocity and l is the average free path of the molecule. Since v and the speed of sound c are of the same magnitude, we can get: Re = kMa / K _n, where Ma is the Mach number; Kn is the Knudsen number; k is a constant; There is an internal connection between them. When the flow velocity is small, Ma is very small, and Kn is also very small. Since the viscous effect is dominant, these two dimensionless parameters appear as a combination of Ma / Kn, that is, as Reynolds numbers. When the flow velocity is high, it can be known from the dimensional theory that both Reynolds number and Mach number play an important role. If the air is thin, Knuth has played a major role.

The solution of viscous fluids is not only related to boundary conditions, but also to Reynolds number. If the Reynolds number is small, the viscous force is the main factor, and the pressure term is mainly balanced with the viscous force term; if the Reynolds number is large, the viscous force term becomes the secondary factor, and the pressure term is mainly balanced with the inertial force term. Therefore, in different ranges of Reynolds number, the fluid flow is different, and the resistance to the object is also different. When the Reynolds number is low, the resistance is proportional to the speed, viscosity, and characteristic length. When the Reynolds number is high, the resistance is roughly proportional to the square of speed, density, and characteristic length.

Reynolds number is also the basis for judging the flow characteristics. For example, in tube flow, the flow with Reynolds number less than 2300 is laminar, Reynolds number equal to 2300 4000 is the transition state, and Reynolds number greater than 4000 is turbulent.

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