February 2005Generation of Dynamic Grids and Computation of Unsteady Transonic Flows around Assemblies· 1 ·
Generation of Dynamic Grids and Computation of Unsteady Transonic Flows around Assemblies
Cai Fei1,*, Zhang Liping2
1Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2School of Electronic and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract
The coupled numerical simulation of flow field, solid temperature field, species concentration field and gas radiation transfer/energy field based on statistical narrow-band correlated-k (SNBCK) model, is employed to accurately predict aerothermodynamic characteristic of aircraft exhaust system. A series of methods to increase computational efficiency and descend computational resources make it possible to finish the calculation in PC. The parameters of narrow-band model are evaluated by HITEMP line-by-line database. Three examples have proved the accuracy of using these methods to solve flow heat transfer coupled problem and radiation transfer/energy equation, which are the calculation of temperature distribution of water-cooling nozzle in rocket engine, the calculation of carbon dioxide absorptivity at 4.3 micron band, and the gas radiation heat transfer evaluation of the cylindrical furnace. Finally, the inner flaps temperature distribution of ejecting nozzle with floating outer flaps is computed, under high-altitude, high-speed and afterburning conditions. Two completely different air-inlet schemes of ejecting channel almost achieve the same effect in cooling inner flaps.（英文摘要应在150-200词左右；包含研究的目的、方法、结果和结论；通常用一般现在时，除非有明显的过去时间指示词出现Abstract should be about 150 to 200 words, including purpose, method, results and conclusion, present tense is preferred）
Keywords:transonic flow; unsteady flow; full-potential equation（5-8个，建议其中1-2个选自EI controlled term 词表About 5-8 words. Selection of 1-2 from EI controlled term list is preferred）
1. Introduction[1]
The computation method of unsteady transonic flow based on N-S equations should be best accurate, but to three-dimensional complex problems, it can be achieved only on large computers, and moreover, the resultsare not ideal sometimes[1]. A viscous/inviscid interaction method is an applicable one and the computation time can be reduced by two orders.
The method to solve the full-potential equation over transonic unsteady forces on wings has been developed[2-3], but to assemblies, it is not mature, and the research worksare continuously carried on[4-5].
The key to compute the unsteady aerodynamic forces is to generate dynamic grids efficiently. In the present paper, an algebraic method and rapid deforming technique are used to generate three-dimensional boundary-fitted dynamic grids for assemblies. The conservative full-potential equation is solved by a time-accurate approximate factorization algorithm and internal Newton iterations. An integral boundary layer method based on the dissipation integral is used to account for viscous effects. The computational results about unsteady transonic forces on wings, bodies and control surfaces are in agreement with experimental data. （前言一般不要放图、表、公式Equations, figures and tables are usually not supposed to appear in this part.）
2. Computation Scheme
2.1. Governing equation
The unsteady full-potential equation written in a body fitted coordinate system is given by
(1)
where is density,U, V, and W are the contravariant velocity components in the , , and directions,means time, and Jis Jacobian. （正文中不要用公式编辑器插入符号，直接敲入即可do not use Equation Editor to insert symbols but type them directly）
（公式编辑器中的行距不要改动，默认值即可Do not change the line-width in the Equation Editor）
(公式中用到小括号时，不要用公式编辑器中的括号，如，直接用键盘敲入即可如When there is parenthesis in an equation, do not use the parenthesis in the Equation Editor but type it through keyboard. For instance, use instead of .)
where is velocity potential.
2.2. Generation of grids
The algebraic method is used to generate three-dimensional boundary-fitted grids for a wing.The height of the firstgrid next to the body is controlled, and the grids near to the body are normalized.
To wing/missile combination, the H-H boundary-fitted grids for a single wing are generated at first in order to simulate the aerodynamic forces on missiles accurately. The section at the position of pylon is changed into two overlapping layers.A partial deforming technique is used in the area of pylon/launching/missile to get the static grids for the combination.
When with fuselage, the deforming technique is used at the symmetric section to get the static grids also.
To simplify the equation, the dynamic grids where the far field is fixed and the body is dynamic are applied to unsteady flows. As it will consume much time to generate grids once a time-step, to aerodynamic elasticity movement of small amplitude, ordinarily, the grids are obtained by solving the balance equation based on last time-step, but that is still not economic.
Taking the incompressible potential flow round a cylinder for example, the stream function is
(2)
where ais radius,is the velocity of free stream. Magnifying its radius to , then the previous streamline passing point (r, )will yield a normal displacement r
(3)
That is difficulty directly to generate dynamic grids. Simplifying further, the coordinates (represented by subscriptu) of the dynamic grids are
(4)
where subscript s represents the boundary-fitted static grids which are used as the initial values,r represents the instantaneous coordinate that the static grids move to with bodies,gis the function about the serial number of the grid lines.
(5)
where b represents the corresponding boundary points, f represents the far field points.
3.Presentation of Result
F5 wing/missile and HARW wing/fuselageare taken for examples in the present paper. Fig.1 shows the sketches of F5 wing/missile and HARW wing/fuselage with control surfaces. The missile is located at 73.5 percent of half-span. The trailing edge control surface of HARW wing/fuselage takes up 20 percent of the chord; control surface I is located at a position from 58.9% to 79.4% of half span; control surface IIis located from 9.6% to 23.9%. Fig.2 is the H-H surface grids for F5 wing/missile.Fig.3 shows the overlooking view of HARW wing/fuselage assembles’ C-H grids.
Fig.4 Comparison between computation result and experimental data[24] for temperature distribution of inner wall of nozzle.
Table 5CPU time ratio of each term
Computational term / CPU time/%Flow field / 32.6
Solid temperature field / 2.2
Species concentration field / 4.3
Radiation transfer/energy field / 60.9
4.Conclusions
(1) A rapid method of the generation of boundary-fitted dynamic grids is developed in this paper, and the method of Viscous/Inviscid Interaction is used to compute the unsteady aerodynamic forces on wing/missiles and wing/body with control surfaces.
(2) The computation results are in agreement with experimental data. To unsteady flows, it takes nearly one hour to carry out three time cycles with 140 thousand nodes, so this method is powerful. This method presented in this paper provides an applicable, efficient tool for the aerodynamic elasticity analysis in the transonic aspect.（分点总结，只写结论，其他背景、方法都不必赘述only conclusions, no background information and methods）
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*Corresponding author. E-mail address:
Foundation item: National Natural Science Foundation of China (基金号)
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