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Transonic Flight and Aerofoils
Published in Rose G. Davies, Aerodynamics Principles for Air Transport Pilots, 2020
Modern jet airliners can travel much higher and faster than ever before. They are transonic flights. A transonic flight faces issues caused by shockwaves, and aerodynamic limitations. The features of transonic aircraft have been designed to overcome the extra drag caused by shockwaves, control difficulties, and to improve aerodynamic limitations in transonic flights.
Some Fluid Flows and D’Arcy Equation
Published in Prem K. Kythe, An introduction to BOUNDARY ELEMENT METHODS, 2020
A purely subsonic or purely supersonic flow is governed by the potential equation () (1−M∞2)∂2ϕ∂x2+∂2ϕ∂y2+∂2ϕ∂z2=0,M∞≠1, where M∞ is the Mach number of the incident flow, and the velocity v = (u, υ, w) is defined in terms of the velocity potential ϕ, viz., u = ∂ϕ/∂x, υ = ∂ϕ/∂y, and w = ∂ϕ/∂z. Eq (8.5) is of the elliptic type for purely subsonic flows, and of the hyperbolic type for purely supersonic flows. A transonic flow results when the Mach number M = 1; in this case the undisturbed flow velocity is equal to the speed of sound. The governing equation for a transonic flow is () −γ+1U∞∂ϕ∂x∂2ϕ∂x2+∂2ϕ∂y2+∂2ϕ∂z2=0, where U∞ is the incident flow velocity along x-axis, and γ = cp/cυ is the isentropic exponent (in compressible flows). Eq (8.6) is nonlinear in f, and numerical computation is required in transonic flows.
Equilibrium and Non-Equilibrium Flows, Compressible Flows, and Choke Flows
Published in Robert E. Masterson, Nuclear Reactor Thermal Hydraulics, 2019
Thus, the Mach number depends on the speed of sound, and the speed of sound depends on the state of the fluid. For any fluid that can be treated as an ideal gas, the propagation speed is a function of the temperature only (see Equation 29.29). The flow of fluid through a reactor can then be described in terms of the Mach number of the flow. The flow is called subsonic when Ma < 1, transonic when Ma ≅ 1, supersonic when Ma > 1, and hypersonic when Ma ≫ 1. Fluid flow during reactor accidents can be described in this way. For water at 1 atm and 30°C, the speed of sound is c = 1,512 m/s; for water at 8 MPa and 270°C, it is c = 1,082 m/s; and for water at 15.5 MPa and 300°C, it is c = 977 m/s. Conversely, for air at 30°C, it is 349 m/s. Now, let us discuss the relationship between the speed of sound and various types of orifice flow. In general, flows through devices like nozzles, diffusers, and orifices behaves differently at sonic speeds than they do at subsonic ones. In each device, the flow area changes as a function of position, and the pressure falls at the location where the flow area is least because this is the location where the velocity is highest. In nozzles, the flow area is smallest at the exit of the nozzle, and the flow area at this point is called the throat (see Figure 29.2c). In diffusers, which are designed to perform the opposite function of nozzles, the flow area is greatest at the exit and least at the entrance. Hence, the throat of a diffuser can usually be found at the entrance. Finally, in a nozzle that suddenly converges and then diverges, the throat can be found somewhere near the center of the device. Nozzles of this type are called converging–diverging nozzles, and these nozzles are sometimes used to accelerate gases to supersonic speeds (see Chapter 34). However, they should not be confused with Venturi nozzles, which are used strictly for fluids that are incompressible. Orifice flow is similar to converging–diverging nozzle flow except that the edges are sharper and the L/D ratio at the throat is lower. The fluid velocity is greatest at the point of maximum contraction if the density is constant. Hence, the fluid velocity reaches the sonic velocity at the location of the throat first as the flow rate is increased. The size of the Mach number in the throat then determines whether the flow is sonic or subsonic. The flow through an orifice becomes restricted or choked when the discharge speed at the throat of the orifice becomes equal to the sonic speed. Hence, when the Mach number of the flow becomes equal to unity (Ma = 1.0), the flow reaches its maximum possible speed and this speed then becomes known as the critical speed. Increasing the pressure difference between the inlet and the outlet then has no further effect on the speed at which the flow exits the opening. Only in this case, the length of the channel (or pipe) through which the fluid is flowing determines the point at which the critical flow speed is reached. Whether the flow becomes critical or choked depends on how the actual velocity compares to the critical velocity. Example Problem 29.5 illustrates how this can be determined for a gas reactor.
Parallel adaptive high-order CFD simulations characterising SOFIA cavity acoustics
Published in International Journal of Computational Fluid Dynamics, 2016
Michael F. Barad, Christoph Brehm, Cetin C. Kiris, Rupak Biswas
Higher order accurate implicit large eddy simulations (ILESs) using NASA's Launch Ascent and Vehicle Aerodynamics (LAVA) CFD solver Kiris et al. (2016) were performed. These simulations become computationally very expensive due to the requirement of accurately capturing a wide range of physically and temporally relevant scales. Numerical methods with high spectral accuracy are required to efficiently simulate these types of problems. The computation of transonic flows is further complicated by the occurrence of shocks which generate discontinuities in the flow field. In order to handle these discontinuities, we applied state-of-the-art higher order shock capturing schemes. LAVA's immersed boundary method was used to circumvent the very time-consuming (e.g. structured curvilinear) volume mesh generation process for the complex SOFIA geometry. The ghost cell=based immersed boundary method is a natural fit with the block-structured Cartesian adaptive mesh refinement (AMR) framework.
A Numerical Investigation of the Dominant Characteristics of A Transonic Flow Over A Hemispherical Turret
Published in International Journal of Computational Fluid Dynamics, 2022
Songxiang Tang, Jie Li, Ziyan Wei
Although both the flow fields and aero-optics of turrets have been studied extensively, detailed studies on the dominant flow field and the relations between the dominant flow field characteristics and aero-optics are still lacking. This is especially true for transonic flow fields, which contain shocks and relevant shock-induced flow structures. As the aero-optics are mainly influenced by the density field according to the Gladstone – Dale relation (Wolfe and Zizzis 1978), the study of the dominant characteristics of the density field is important to future work on flow control to reduce aero-optical effects. As experiments are costly and the data is partially measured, computational fluid dynamics (CFD) is a reasonable strategy with which to study complex flow characteristics. Although directly solving the Navier – Stokes equation using direct numerical simulation (DNS) can effectively capture all the turbulent features, the computational cost is nearly unaffordable (Spalart 2000). The LES method adopts a model to solve the small-scale turbulence and is efficient at solving the larger characteristics (Yang and Voke 2001), but it is also restricted by the Reynolds number. The numerical method of solving the Reynolds-averaged Navier – Stokes (RANS) equations is widely used to solve the averaged flow field. Although the unsteady RANS (URANS) method can also be used to predict temporal flow fields, its failure to accurately estimate turbulence viscosity restricts it in the prediction of separation flows (Szydlowski and Costes 2004; Liu et al. 2014). The DES method (Spalart et al. 1997; Strelets 2001), as a hybrid RANS/LES method, has the advantages of LES and RANS. It is not restricted by the Reynolds number and its resolution of large eddies is also enough for the turret flow field. Because of some weaknesses of DES such as grid-induced separation (GIS) and model stress depletion (MSD), several improved DES-like methods have been developed, namely DDES (Spalart et al. 2006; Menter and Kuntz 2004) and IDDES (Shur et al. 2008). DDES employs a shield function to prevent the RANS region from being prematurely intruded on by the LES region. Compared with DDES, IDDES overcomes the weakness of log layer mismatch, which is induced by an overestimated local turbulent viscosity in the boundary layer because of the shield function of DDES. It should be mentioned that one partial strategy of the DES method called zonal DES (Deck 2012) is also widespread (Zhang et al. 2018). ZDES requires setting RANS and DES regions manually and seems unfeasible for flows whose mechanisms are not very clear. DDES and IDDES should be competitive in turret flow field prediction.