Modelling and Simulation of Entry Objects (Space Debris and Asteroids) Dr Edmondo Minisci Department of Mechanical and Aerospace Engineering University of Strathclyde, Glasgow, Scotland, UK Outline Entry Flows • (Re-)Entry and Hypersonic Flows Hyper. Flows – Introduction to flow regimes and hypersonic phenomena (shock waves and heating) Space Debris • Re-entry and evolution of Space Debris Intro – Introduction (statistics, hazard & risk assessment) Tools&Met. – Main tools and used methods Our Activ. – Our activities • Entry and evolution of Asteroids/Comets Asteroids Intro – Introduction Methods – Main methods and some recent advances Our Activ. – Our activities 23-June-15 Second talk at University of Cagliari 2 Introduction Entry Flows • “A space vehicle/object entering the atmosphere of Hyper. Flows a planet passes different flow regimes”, that is “The flow field surrounding a vehicle/object evolves as it descends to the surface of a planet.” Space Debris Intro Tools&Met. • The reason for that lies in: Our Activ. – large entering velocity of the vehicles/objects (≈ 7.5 km/s for re-entry from Earth orbits and 10 km/s for planetary Asteroids entries … up to 20-70 km/s for asteroids/comets), and Intro ≥ Methods – wide range of density and pressure with the altitude. Our Activ. 23-June-15 Second talk at University of Cagliari 3 Introduction – the large velocity of the entering vehicle/objects (≈ 7.5 km/s for Entry Flows re-entry from Earth orbits and 10 km/s for planetary entries Hyper. Flows … up to 20-70 km/s for asteroids/comets), means evolution ≥ from Space Debris Intro Tools&Met. Hypersonic flow Our Activ. to Supersonic (not always …) Asteroids and finally Intro Methods Subsonic (not always …) Our Activ. 23-June-15 Second talk at University of Cagliari 4 Introduction The wide range of density and pressure with the Entry Flows altitude, means evolution Hyper. Flows from Space Debris Free molecular flow Intro to Tools&Met. Our Activ. Disturbed molecular flow (Transition regime) to Asteroids Continuum flow with slip Intro effects Methods to Our Activ. Continuum flow 23-June-15 Second talk at University of Cagliari 5 Introduction Entry Flows • The degree of rarefaction is defined by the Knudsen Hyper. Flows number = Space Debris 휆 Intro • is the molecular mean퐾퐾 free path (average value of Tools&Met. the path length between two퐿 collisions with other Our Activ. molecules)휆 • is the characteristic length scale of the considered Asteroids system Intro 퐿 Methods Our Activ. C. White, 2013. 23-June-15 Second talk at University of Cagliari 6 Introduction The wide range of The two regimes with continuum Entry Flows density and pressure flow, can be treated with the Hyper. Flows with the altitude, means Navier-Stokes equations and evolution from differ only with respect to the formulation of the wall boundary Space Debris conditions. Free molecular flow Intro In the nominal case of continuum Tools&Met. to flow no-slip conditions at the wall Our Activ. Disturbed molecular flow are prescribed, whereas in the (Transition regime) second case the flow slips on the to surface Asteroids Continuum flow with slip and the temperature of the wall is Intro effects different from the temperature of the gas at the wall (temperature Methods to Our Activ. jump condition). Continuum flow 23-June-15 Second talk at University of Cagliari 7 Introduction The wide range of The two molecular regimes Entry Flows density and pressure require the application/solution of Hyper. Flows with the altitude, means the Boltzmann equations evolution from describing the gas kinetic behaviour of flows. Boltzmann Space Debris equations, in the context of the Free molecular flow Intro re-entry flow problem, are usually Tools&Met. to solved by methods such as the Our Activ. Disturbed molecular flow Direct Simulation Monte-Carlo (Transition regime) method (DSMC method) to Asteroids Continuum flow with slip Intro effects Methods to Our Activ. Continuum flow 23-June-15 Second talk at University of Cagliari 8 Introduction Entry Flows Definition/characterisation of Hyper. Flows hypersonic flows < 1 , subsonic flow (perturbations in the flow propagate both Space Debris 푀downstream∞ and upstream) Intro > 1 , supersonic flow Tools&Met. (perturbations in the flow propagate Our Activ. only푀∞ downstream) 0.8 < < 1.2 , transonic region Asteroids ∞ Intro 푀 Methods Our Activ. M = speed to sound speed ratio (Mach number) 23-June-15 Second talk at University of Cagliari 9 Introduction Entry Flows Definition/characterisation of Hyper. Flows hypersonic flows Shock waves generated for Space Debris > 0.8: Intro Tools&Met. 푀∞ Our Activ. Shock waves are very small regions in the gas where the gas Asteroids properties change by a large Intro amount. Methods Our Activ. 23-June-15 Second talk at University of Cagliari 10 Hypersonic Flows Definition/characterisation of hypersonic flows Entry Flows Hyper. Flows • Across a shock wave, the static pressure, temperature, and gas density increase “very fast”. • Equations for Normal shock waves (shock wave is Space Debris perpendicular to the flow direction) derived by considering the Intro conservation of mass, momentum, and energy for a Tools&Met. compressible gas while ignoring viscous effects. Our Activ. 2 p1 2γM 0 − (γ −1) = p0 γ +1 Asteroids Specific heat ratio, T [2γM 2 − (γ −1)][(γ −1)M 2 + 2] 1.4 Intro 1 = 0 0 (actually 2 2 T0 (γ +1) M 0 function of Methods 훾 ≈ ρ (γ +1)M 2 temperature) Our Activ. 1 = 0 2 ρ0 (γ −1)M 0 + 2 23-June-15 Second talk at University of Cagliari 11 Hypersonic Flows Definition/characterisation of hypersonic flows Entry Flows Hyper. Flows • Since shock waves do no work, and there is no heat addition, the total enthalpy and the total temperature are constant. • Since the flow is non-isentropic, the total pressure downstream Space Debris of the shock is always less than the total pressure upstream of Intro the shock. Tools&Met. • Equations for Normal shock waves (shock wave is Our Activ. perpendicular to the flow direction) derived by considering the conservation of mass, momentum, and energy for a Asteroids compressible gas while ignoring viscous effects. γ 1 Intro p (γ +1)M 2 γ −1 γ +1 γ −1 t1 = 0 Methods 2 2 pt0 (γ −1)M 0 + 2 2γM 0 − (γ −1) Our Activ. T t1 =1 Tt0 23-June-15 Second talk at University of Cagliari 12 Hypersonic Flows Definition/characterisation of hypersonic flows Entry Flows Hyper. Flows • The Mach number and speed of the flow also decrease across a shock wave. • Equations for Normal shock waves (shock wave is Space Debris perpendicular to the flow direction) derived by considering the Intro conservation of mass, momentum, and energy for a Tools&Met. compressible gas while ignoring viscous effects. Our Activ. 2 2 (γ −1)M 0 + 2 Asteroids M1 = 2γM 2 − (γ −1) Intro 0 Methods Our Activ. 23-June-15 Second talk at University of Cagliari 13 Space Debris Re-entry • Aerodynamic loads Entry Flows • Aerodynamic force and torque are the resulting action of Hyper. Flows pressure and shear stress distribution over the object surface ρV 2 = + Space Debris Fa ∫ (cPn cτ t )dS Intro 2 S Tools&Met. ρV 2 = × + × Our Activ. M a ∫ (r cPn r cτ t )dS 2 S 2 • q=pV /2 dynamic free stream pressure, cP = p/q local Asteroids pressure coeff., c = /q local shear stress coeff., , Intro surface unit normal and tangential vectors on local Methods surface element, 휏dS,휏 the vector distance to the centre퐾 of Our Activ. 푡mass.⃗ 푟⃗ 23-June-15 Second talk at University of Cagliari 14 Space Debris Re-entry Entry Flows • Aerodynamic loads Hyper. Flows • Aerodynamic force and torque are the resulting action of pressure and shear stress distribution over Space Debris the object surface (long. plane) Intro Tools&Met. 2 2 Our Activ. ρV ρV L = CL S ; D = CD S 2 2 2 Asteroids ρV M = CM cS Intro 2 Methods Our Activ. 23-June-15 Second talk at University of Cagliari 15 Hypersonic Flows Entry Flows • Definition/characterisation of hypersonic flows Hyper. Flows • Change from subsonic to supersonic conditions is quite sharp. Space Debris Intro Tools&Met. Our Activ. Asteroids Intro Methods Our Activ. 23-June-15 Second talk at University of Cagliari 16 Hypersonic Flows Entry Flows • Definition/characterisation of hypersonic flows Hyper. Flows • Hypersonic aerodynamics is much different than the now conventional and experienced regime of Space Debris Intro supersonic aerodynamic. Tools&Met. • “Rule of thumb”: hypersonic if Mach number >5 Our Activ. • Hypersonic flow is best defined as the regime where certain physical phenomena become progressively Asteroids more important as the Mach number is increased to Intro higher values (some phenomena may become Methods important before reaching 5, other much after … no Our Activ. crisp threshold) J. Anderson, HYPERSONIC AND HIGH TEMPERATURE GAS DYNAMICS, McGraw-Hill Book, 1989. 23-June-15 Second talk at University of Cagliari 17 Hypersonic Flows • Definition/characterisation of hypersonic flows Entry Flows Hyper. Flows • Thin shock layers The flow field between the shock wave and the body is defined as the Space Debris shock layer, and for hypersonic speeds this shock layer can be quite Intro thin. Tools&Met. Some physical complications, such as the merging of the shock wave Our Activ. itself with a thick, viscous boundary layer growing from the body surface. Asteroids Intro Methods Our Activ. 23-June-15 Second talk at University of Cagliari 18 Hypersonic Flows Entry Flows Definition/characterisation of hypersonic flows Hyper. Flows Viscous interaction Viscous dissipation: high kinetic energy is transformed (in part) into internal energy. Space Debris The characteristics of hypersonic boundary layers are dominated Intro by temperature increases. Tools&Met. – The viscosity increases with temperature, and this by itself will make the Our Activ.