Gas-Surface Interaction Effect on Aerodynamics of Reentry Vehicles

Transcription

1 International Journal of Educational Research and Information Science 2018; 5(1): Gas-Surface Interaction Effect on Aerodynamics of Reentry Vehicles Zay Yar Myo Myint 1, Sergey Lvovich Gorelov 1, 2 1 Moscow Institute of Physics and Technology, Zhukovsky, Russia 2 The Central Aerohydrodynamic Institute Named After Prof. N.E. Zhukovsky (TSAGI), Zhukovsky, Russia address zayyarmyomyint@gmail.com (Z. Y. M. Myint), gorelovsl@yandex.ru (S. L. Gorelov) To cite this article Zay Yar Myo Myint, Sergey Lvovich Gorelov. Gas-Surface Interaction Effect on Aerodynamics of Reentry Vehicles. International Journal of Educational Research and Information Science. Vol. 5, No. 1, 2018, pp Received: May 6, 2017; Accepted: January 15, 2018; Published: February 12, 2018 Abstract Studying the effects of gas-surface interaction models in rarefied is very important for reentry flights. Gas-surface interaction effects play an important role in rarefied gas dynamics modelling by the direct simulation Monte Carlo (DSMC) method. In the present work, gas-surface interaction models (Maxwell and Cercignani-Lampis-Lord) are described. In rarefied hypersonic flows applying these models have been carried out in a wide range of the momentum and energy accommodation coefficients. In this paper also presented the comparison of the calculation results for reentry vehicles. Keywords Gas-Surface Interaction Models, Rarefied Gas Dynamics, Reentry Vehicle Aerodynamics, DSMC, CLL, Maxwell 1. Introduction It is important to mention an aspect of reentry flight concern with design philosophy. Reentry flight occurs at an altitude 100 kilometers above Earth s atmosphere. The computational simulation of rarefied hypersonic flows plays an essential role in efficient research and development of space flight. The progress of molecular gas dynamics in the last forty years has greatly enhanced the contents of the basic theory and provided information on various interesting and important gas dynamic problems. The paper provides the development of knowledge of typical phenomena in a rarefied gas for future theoretical development and applications. Without the direct simulation of Monte Carlo method (DSMC method) [1, 2], the solution can t be gotten. Aerodynamics is governed by the momentum and energy transferred from the incoming gas flow onto the surface e of the vehicle. These transfers are governed by the collisions between the gas molecules and the solid surface. The collision process between a gas molecule and a solid surface is termed a gas-surface interaction. In kinetic theory, the gassurface interaction forms a boundary condition between the gas molecules and solid surface. For scales relevant to kinetic theory, the gas-surface interactions are usually modeled with parameters having macroscopic character, in order to have manageable and efficient calculations [3-7]. Nowadays, there are various gas-surface interaction models and the validity of these models remains importance in hypersonic rarefied flow condition. The study in this paper employs numerical simulation, using DSMC method, to scrutinize two of the most common gas surface interaction models used with the DSMC method: the Maxwell model, and the Cercignani, Lampis and Lord (CLL) model. In particular, the paper intended to generate a comparison of boundary layer between DSMC and laboratory data of rarefied hypersonic gas flow of spacecraft. These comparisons would be involving the assessment of the prediction capabilities of the gas surface interaction models through parametric analysis of boundary layer velocity profiles. The paper shows a comparison between Maxwell model and CLL model. The results are presented spacecraft aerodynamics simulations using the Maxwell and CLL gassurface interaction models.

2 2 Zay Yar Myo Myint and Sergey Lvovich Gorelov: Gas-Surface Interaction Effect on Aerodynamics of Reentry Vehicles 2. Gas-Surface Interaction Models The effect of the form of the boundary conditions on the aerodynamic characteristics of the reentry vehicle is investigated under the assumption of the diffusion-mirror law of the reflection of molecules from the surface, when the distribution function of the molecules reflected from the element (in the case of a monatomic gas). The most popular gas-surface interaction model for kinetic theory is specular and diffuse reflection model developed by Maxwell. This model is based on the assumption that the portion (1 σ τ ) of molecules reflected specularly from the surface, and the rest part σ τ of the molecule diffusely. The density of distribution of reflected molecules is set as follows: f ( ξ) = (1 σ) f ( ξ) + σ f ( ξ, T, n ) w specular M axwell r r Here, f specular (ξ) distribution function of mirror reflected molecules from the surface of reentry vehicle, f Maxwell (ξ, T r, n r ) Maxwell distribution function, n r, T r the density and temperature of reflected molecules, σ - the diffusivity coefficient. Diffuse reflection with complete momentum and energy accommodation is most frequently used in DSMC method. In a diffuse reflection, the molecules are reflected equally in all directions usually with a complete thermal accommodation. The problem of gas-surface interaction takes an essential place in aerodynamics. The role of laws of molecular interaction with surfaces is shown more strongly, than more gas is rarefied [3]. The accommodation coefficients are defined in terms of incident and reflected fluxes as follows P P ni nr τi τr σn =, στ Pni Pnw Pτi P P Ei Er =, σe = E E here E w - energy which would be carried out the reflected molecules if gas is in equilibrium with a wall (T r = T w ). In work [8] is proposed phenomenological model of Cercignani-Lampis (CL) which also satisfies the principle of reciprocity and is reported improvement of the Maxwell models [8]. The model is based on the introduction of two parameters which represent accommodation coefficient of kinetic energy connected with normal momentum σ n = σ En, and tangential momentum accommodation coefficients σ τ, respectively. Cercignani, Lampis model well corresponds to the results of laboratory researches with high-speed molecular beams. Although a comparison is limited by laboratory conditions, Cercignani, Lampis model has theoretically justified and relatively simple. Later, there were modification of scattering kernel of Cercignani, Lampis model; however, they give slight improvement in comparison with laboratory experiments. Generally the interaction model has some arbitrary physical parameters that allow achieving the reasonable agreement with results of laboratory researches in a range of conditions. In this sense, original Cercignani, Lampis model is enough physically and suitable for i w theoretical research. The universal model should use the scattering kernel received on the basis of physical experiment in a wide range of Knudsen numbers and velocity of the stream. In Cercignani, Lampis model, the diffusion kernel of velocity of surface normal has the following form 2ξ ξ ξ nr ni nr K(ξni ξ nr) = I σ n σ σ n n, 2 2 2π ξ nr + (1 σ n)ξ ni 1 exp, I0( x) = exp( xcos φ) dφ σn 2π 0 1 K(ξτi ξ τr) = πσ (2 σ ) τ τ ( ξ ) 2 τr (1 σ τ)ξτi σ (2 σ ) τ τ. here I 0 first type Bessel function, ξ ni, ξ nr molecular velocities of surface normal for the incident and reflected molecules. ξ τi, ξ τr molecular velocities of tangent to surface for the incident and reflected molecules. The model in this form is called as Cercignani-Lampis-Lord model (CLL). Usage of Cercignani, Lampis model transformation expands to account for rotational energy exchange between gas and surface. Then, updating Cercignani- Lampis-Lord model in the form of [9, 10] is to account for vibrational energy exchange and extend range of states of the scatted molecule. Cercignani-Lampis-Lord model is widely recognized examples of its application are presented in multiple works [11-20]. In order to simulate the partial surface accommodation, the Cercignani-Lampis-Lord model was implemented into this DSMC calculation. The Cercignani- Lampis-Lord model is derived assuming momentum components. The two adjustable parameters appearing in the Cercignani-Lampis-Lord model are the normal component of translational energy σ n and the tangential component of momentum σ τ. However, in the implementation of the Cercignani-Lampis-Lord model in the DSMC method, Bird has shown that it is equivalent to specify the normal σ n and tangential σ τ components of translational energy σ E, assuming that σ τ lies between 0 and Results and Discussion The results are presented in terms of the drag coefficient C x ; lift coefficient C y and pitching moment m z using the reentry vehicles Orion and Mars Pathfinder [20] in figure 2-4, figure 6, 7. In order to compare between Maxwell and Cercignani-Lampis-Lord model in free molecular flow are agree with the analytical solutions within the statistical error in the DSMC sample. The calculation was carried out in a range of angles of attack. Parameters of the problem as follows: velocity relationship s = V / 2RT = 15, the ratio of specific heat γ = 1.4, the values of the temperature factor t w = T w /T = 0.001, 0.1, 1; total particles were used particles. The tangential accommodation coefficient σ = 0.5 and 1.

3 International Journal of Educational Research and Information Science 2018; 5(1): Figure 1. Geometry description of reentry vehicle Orion. Figure 2. Drag coefficient C x of reentry vehicle in various accommodation coefficients.

4 4 Zay Yar Myo Myint and Sergey Lvovich Gorelov: Gas-Surface Interaction Effect on Aerodynamics of Reentry Vehicles Figure 3. Lift coefficient C y of reentry vehicle in various accommodation coefficients. Figure 4. Pitching moment m z of reentry vehicle in various accommodation coefficients.

5 International Journal of Educational Research and Information Science 2018; 5(1): The results are presented for a Maxwell model with various accommodation coefficients, and various temperature factors. With the Maxwell model, scattered molecules consist of a combination of specularly reflected molecules which have the same velocity distribution as the incoming molecules which have Maxwellian velocity distribution characteristics of the surface temperature. The CLL model provides a much more complex description of the velocity distribution of scattered molecules in which the overall mean velocity, temperature and mean scattering angle are complex functions of the incoming velocity, the surface temperature and the normal and tangential accommodation coefficients. Figure 5. Geometry description of reentry vehicle Mars Pathfinder. Figure 6. Drag coefficient C x of reentry vehicle in various accommodation coefficients.

6 6 Zay Yar Myo Myint and Sergey Lvovich Gorelov: Gas-Surface Interaction Effect on Aerodynamics of Reentry Vehicles Figure 7. Lift coefficient C y of reentry vehicle in various accommodation coefficients. Figure 8. Drag coefficient C x of aerospace vehicle in various temperature factors (t w = 0.1, 1) at accommodation coefficient (σ τ = 0.9, 1).

7 International Journal of Educational Research and Information Science 2018; 5(1): For accommodation coefficients less than one but greater than zero, the CLL model gives a somewhat higher average velocity of scattered molecules and a more continuous distribution of molecules scattered near a specular angle. The comparisons between the results of the Maxwell model at various temperature factors are shown in figure (8-10) for aerospace vehicle [21-24]. In figure 8 can see sensitively when the temperature factor increase, the drag coefficient are increasing. For cold object shows C x almost symmetrical and hot object not symmetric. When the cold body object the drag coefficient C x = 0.45 at an angle of attack α = 0 and C x = 2 at an angle of attack α = 90 and 90. Lift coefficient also increase with the increasing of temperature. Maximum Lift coefficient C y = at an angle of attack α = 45 for a very hot body object. For the pitching moment m z less sensitive to the value of the temperature factor, its value suggests that this factor must be taken into account when analyzing the orientation of the body under the action of the strongly rarefied gas flow. The two models were compared at an angle of attack 90 to 90. In Maxwell model σ τ = 0.9, 1 in CLL model with temperature factor t w = 0.1. The drag and lift coefficient results of CLL model less than the Maxwell model as expected. For pitching moment the result shows that Maxwell and CLL model inversely between at an angle of attack 90 <α<0 and 0 >α>90. The Maxwell model and CLL model predict the same lift, drag and heat transfer when the accommodation coefficients are equal to zero or one. In fact, for σ τ = 1 in Maxwell model and σ τ = σ n = 1 in the CLL model, the two models give precisely the same. For accommodation coefficients not equal to zero or one, the CLL model gives higher aerodynamic forces than the Maxwell model for the same value of their respective accommodation coefficients. Varying σ n, however, has the opposite effect on drag than that caused by varying σ τ. When σ n is increased from 0.0 to 1.0 the drag coefficient decreased by approximately the same rate as the lift. When σ τ is increased from 0.0 to 1.0, however, the drag coefficient increases at approximately the same rate as the lift coefficient decreases. Figure 9. Lift coefficient C y of aerospace vehicle in various temperature factors (t w = 0.1, 1) at accommodation coefficient (σ τ = 0.9, 1).

8 8 Zay Yar Myo Myint and Sergey Lvovich Gorelov: Gas-Surface Interaction Effect on Aerodynamics of Reentry Vehicles Figure 10. Pitching moment m z of aerospace vehicle in various temperature factors (t w = 0.1, 1) at accommodation coefficient (σ τ = 0.9, 1). 4. Conclusions The DSMC method is commonly used to simulate rarefied flow problems, and the accuracy of the method depends directly on the accuracy of the gas-surface interaction model. The Maxwell model is the most widely used and is based on classical thermodynamics in which it is assumed that molecules will either reflect diffusely from a surface with complete energy accommodation or will reflect specularly with no change in energy. An accommodation coefficient α τ is defined which specifies the fraction of molecules that will be scattered diffusely, with α τ = 0 giving complete specular reflection, and α τ = 1 giving complete diffuse reflection. In the CLL model, the transformations of the normal and tangential components of velocity are assumed to be manually independent. They give similar predictions of aerodynamic forces and heat transfer coefficients on difference object though the gassurface interaction models have fundamental differences. The models differ in their predictions of the flow field around the object. The calculation presented in this work has only covered a limited number of parametric variations. The calculations with normal, tangential accommodation coefficients are provided more sensitivity of the aerothermodynamics quantities of hypersonic technologies. Further investigation into this behavior is required to provide better understanding of the effects of gas-surface models in DSMC calculations and ultimately a better understanding of the accommodation coefficients of materials. References [1] O. M. Belotserkovskii and Yu. I. Khlopkov Monte Carlo Methods in Mechanics of Fluid and Gas. World Scientific Publishing Co. N-Y, London, Singapore, Beijing, Hong Kong [2] G. A. Bird Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford University Press [3] N. M. Kogan Rarefied Gas Dynamic. New York, Plenum [4] R. G. Wilmoth, G. J. Le Beau and A. B. Carlson DSMC grid methodologies for computing low density hypersonic flows about reusable launch vehicles. AIAA Paper No [5] G. Koppenwallner Satellite Aerodynamics and Determination of Thermospheric Density and Wind. 27th international symposium on rarefied gas dynamics. AIP Conference Proceedings, Vol P

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