|| Volume 5 || Issue 10 ||October 2020 || ISO 3297:2007 Certified ISSN (Online) 2456-3293 CFD ANALYSIS FOR SUPERSONIC FLOW OVER A WEDGE 1 PIDATALA KIRAN KUMAR, 2 Smt. T. SUSEELA, 1M.Tech student, Department of Mechanical Engineering, Acharya Nagarjuna University College of Engineering and Technology, Nagarjuna Nagar, Guntur, Andhra Pradesh 2Assistant Professor, Department of Mechanical Engineering, Acharya Nagarjuna University College of Engineering and Technology, Nagarjuna Nagar, Guntur, Andhra Pradesh 1 2 [email protected], [email protected] ------------------------------------------------------------------------------------------------------------ Abstract: A wedge is triangular shaped geometrical structure. It is mostly used as supersonic airfoils and nose of supersonic airplanes. It is typically inclined plane which is at an angle with the horizontal. This project helps in explaining most of the concepts related to wedge. In this project the principle of working of wedges with the variation of half-wedge angle and also with variation of Mach number has been done. Theoretical analysis of supersonic flow over wedge is also done. The variation of flow parameters like Pressure, Temperature and Mach number is visualised using computational fluid Dynamics and it’s contours and graphs has been plotted. The simulation of shockwave (attached and detached) through CFD is also analyzed. To look at the flow qualitatively. You will solve problem in Fluent and hexa mesh in ICEMCFD. We will use online shock calculator to see Mach number after each step and as well as the flow angle. -------------------------------------------------------------------------------------------------------- I INTRODUCTION density-based formulations, which have evolved from methods developed for the solution of the Euler equations. INTRODUCTION OF TUBULENCE They are mostly optimized for tight shock resolution and nonoscillatory behavior near extrema. On the other hand, CFD based on the Reynolds Averaged Navier Stokes general-purpose industrial codes are generally built on (RANS) equations is now widely used in the aeronautical pressurebased formulations like the SIMPLE or SIMPLEC industry during the design process. While a large number of schemes or more recent method like those given by Rhie and studies are concerned with classical aerodynamic simulations Chow . at transonic speeds, an increasing number of auxiliary simulations are required to optimize the entire aircraft. This 1.2 WEDGE: includes flows at low speeds (take-off and landing, cabin A wedge is a triangular shaped or in other words a plane climate), multi-phase flows (icing) as well as “multi-physics” inclined with an angle to the horizontal applications (fluid-structure coupling, aerodynamic noise generation, radar signature). Historically, different codes are used for the different applications. The auxiliary simulations are mostly based on general-purpose codes, while in-house or special purpose codes are used for the external aerodynamics. However, an increasing number of applications require the combination of generality with a high degree of numerical and modelling accuracy. It is therefore essential that general- purpose codes provide a level of accuracy and numerical performance satisfying the requirements of aeronautical design engineers. Aerodynamics codes are typically built on Figure 1 WEDGE WWW.OAIJSE.COM 59 || Volume 5 || Issue 10 ||October 2020 || ISO 3297:2007 Certified ISSN (Online) 2456-3293 1.3 FLOW OF A WEDGE 1.5 OBLIQUE SHOCKWAVE: When a shockwave makes As an object moves through a gas, the gas molecules are an oblique angle with respect to upstream flow, it is termed as deflected around the object. If the speed of the object is much oblique shockwave. Oblique shockwave occurs when a less than the speed of sound of the gas, the density of the gas supersonic flow is encountered at the wedge that effectively remains constant and the flow of gas can be described by turns the flow into itself. Oblique shock is generally created at conserving momentum, and energy. As the speed of the the nose of the wedge. Downstream of the oblique shock the object approaches the speed of sound, we must properties change drastically. consider compressibility effects on the gas. The density of the gas varies locally as the gas is compressed by the object. For compressible flows with little or small flow turning, the flow process is reversible and the entropy is constant. The change in flow properties are then given by the isentropic relations (isentropic means "constant entropy"). But when an object moves faster than the speed of sound, and there is an abrupt decrease in the flow area, shock waves are generated in the flow. Shock waves are very small regions in the gas FIGURE 2 OBLIQUE SHOCKWAVE PROPERTIES where the gas properties change by a large amount. Across a VARIATION shock wave, the static pressure, temperature, and 1.6 BASIC EQUATION: gas density increases almost instantaneously. The changes in Basic equations The relevant equations of motion for the flow properties are irreversible and the entropy of the aerodynamic flows are the mass, momentum and energy entire system increases. Because a shock wave does no work, equations: and there is no heat addition, the total enthalpy and the total temperature are constant. But because the flow is non- isentropic, the total pressure downstream of the shock is always less than the total pressure upstream of the shock. There is a loss of total pressure associated with a shock wave. On this page, we consider the supersonic flow of air past a two-dimensional wedge. If the Mach number is high enough and the wedge angle is small enough, an oblique shock wave is generated by the wedge, with the origin of the shock attached to the sharp leading edge of the wedge. If we think where ρ is density, i u is velocity, P is pressure, µ is of the oblique shock as a normal shock inclined to the flow at the fluid viscosity, H is total enthalpy / 2 i i H= h + u u , h is some shock angle s, then the normal shock relations can be the static enthalpy, T is temperature and ij τ is the stress applied across the shock in a direction perpendicular to the tensor. These equations are supplemented by an equation of shock, and the flow component parallel to the shock remains state, ρ = ρ(P,T) , a stress-strain relation for ij τ as a function unchanged. The resulting Mach number and speed of the flow of viscosity, µ , and the strain rate, the thermal conductivity, decrease across the shock wave. For the Mach number change k, and a thermodynamic enthalpy definition, h = h(P,T) . For across an oblique shock there are two possible solutions; one turbulent flows, an eddy-viscosity is typically added and the supersonic and one subsonic. In nature, the supersonic ("weak equations are solved for the Reynolds averaged quantities. shock") solution occurs most often. However, under some The general form of the equations stays the same. conditions the "strong shock", subsonic solution is possible. 1.7 DISCRETIZATION OF THE EQUATIONS: For a given upstream Mach number, there is a maximum The present method uses an implicit pressure-based wedge angle for which the shock remains attached to the formulation, where the primary dependent variables are (P, i u leading edge. For wedge angles greater than the maximum, ,H). This is a typical choice for general-purpose codes, as it a detached normal shock occurs. The conditions for an allows an efficient treatment of incompressible flows, which attached shock is shown on the slide. are frequently encountered in industrial CFD simulations. 1.4 SHOCKWAVE : A shockwave is an extremely thin Provisions, which have to be taken to ensure a proper region, typically on the order of 10-5 cm across which the coupling between the pressure and the velocity fields for flow properties can change drastically. flows with strong variations in density, will be described below. The control volume is constructed around an element WWW.OAIJSE.COM 60 || Volume 5 || Issue 10 ||October 2020 || ISO 3297:2007 Certified ISSN (Online) 2456-3293 vertex as the dual element mesh, as shown in Figure 1. The modeling of LES is provided by the more computing power procedure is the same for all element types (hex, tet, wedge, demanding Direct Numerical Simulation (DNS). pyramid) The numerical accuracy of the simulation is Nevertheless, RANS calculations will continue for many determined by the accuracy of the representation of the years to support the aerospace industry. Even when LES surface integrals (fluxes) at the integration points in terms of reach the level of application in aerospace components or the nodal variables. complete configurations, it will be more economic to apply 1.8 SHOCK WAVE IN AERODYNAMIC FLOWS: RANS in an optimization procedure and subsequently to simulate the optimum configuration by LES. Object of the Shock wave phenomenon present study is the turbulence modeling of flows with Shock waves can be generally classified into four categories: extensive crossflow separation, i.e., three-dimensional flows (1) Attached shock wave, e.g. when a supersonic in which the separated boundary layer rolls up into flowencountersan inward corner longitudinal vortices. This type of separation appears in many practical aerospace configurations; for example, (2) Detached shock wave, e.g. for a supersonic flow past subsonic/supersonic flow about slender bodies or delta wings ablunt body at high incidence or in components of supersonic/hypersonic (3) Recompression shock wave, generated to adjust to farfield air vehicles when swept shock waves interact with boundary pressure, e.g. for a transonic flow past the uppersurface of an layers airfoil or for a supersonic noz-zle flow with high back pressure. (4) Secondary induced shock wave, due to e.g. shock reflec- tion shock–shock interaction shock-wave/boundary-layer interaction lateral jet flow interaction showssome typical examples with shock/boundary-layer interactions in the vicinity of a high-speed vehicle.