Numerical Study on Flow Induced Vibration of LOX Post in Liquid Rocket Engine Preburner
Chihiro Inoue 1 , Toshinori Watanabe 2 and Takehiro Himeno 2
1 School of Engineering The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan E-mail: firstname.lastname@example.org
2 Department of Aeronautics and Astronautics The University of Tokyo
ABSTRACT In a preburner of liquid rocket engines, some liquid-oxygen (LOX) posts, which introduced oxygen into combustion chamber, experienced severe flow-induced vibration due to unsteady cryogenic hydrogen flow. The mechanism of the vibration has not been fully understood because of the complexity of the flow field. In the present study, a new numerical method was developed to analyze the flow field of hydrogen, whose characteristic properties lie in its non-idealness and compressibility. The unsteady hydrogen flow inside the preburner unit was analyzed to investigate the details of hydrogen flow field as well as the mechanism of LOX post vibration. It was clarified that hydrogen flow inside the manifold and fluid dynamic forces on LOX posts were strongly affected by vortices shed from the junction at the upstream of the inlet. A baffle plate put inside the manifold was shown to reduce unsteady fluid forces on the LOX posts. INTRODUCTION In liquid rocket engines, a preburner is equipped at an upstream position of turbines to generate combustion gas for driving turbo pumps. A lot of liquid-oxygen (LOX) posts are arranged in the preburner to lead oxygen and hydrogen into the combustion chamber. A combustion chamber unit, schematically shown in Fig.1, is mainly consisted of a hydrogen manifold, an oxygen manifold, hundreds of LOX posts, and a combustion chamber. Figure 2 shows a cross-sectional view of hydrogen flow channel projected on the plane A-A in Fig.1. During the development of Space Shuttle Main Engine, some LOX posts were reported to experience harmful flow induced vibration (A.Kanmuri, 1983). Since the vibration was thought to be due to the unsteady hydrogen cross flow around the posts, some fluid dynamics studies have been carried out so far to clarify the mechanism of the vibration (S.S.Chen and J.A.Jendrzejczyk, 1984) (M.Williams, 1987). However, the detailed flow field in the preburner and the vibration mechanism have not been understood yet because of the complexity of the hydrogen flow field inside the preburner. The non-ideal characteristics of hydrogen itself inside the manifold also made it difficult to understand them. Recently, some LOX posts in a preburner of Japanese liquid rocket engine experienced a strong vibration, too. In the engine system, the hydrogen flow into the preburner was observed to have significant non-uniformity in the hydrogen manifold, though the details of the flow were still unclear.
To obtain full understanding of the flow and vibration phenomena, detailed flow simulations should be performed in which the effect of all the LOX posts are taken into account and the hydrogen is treated as compressible and non-ideal fluid.
In the present study, a new numerical method has been developed and proposed for simulating the complex flow field of compressible non-ideal hydrogen in the preburner. As a fundamental study, two-dimensional flow field, shown in Fig.2, was analyzed by the developed method to clarify the unsteady complicated flow field, and to investigate the mechanism of the flow induced vibration. The effect of a countermeasure of the strong vibration of LOX posts was also studied. NOMENCLATURE
D tube diameter [m] e internal energy [J/kg] f frequency of shed vortices [Hz] Hs area fraction of solid [ - ] Hv volume fraction of solid [ - ] J Jacobian [ - ] N
normal vector of distance function [ - ] p pressure [Pa] q heat flux [W/m2] R gas constant [m2/s2 K] T temperature [K] Tc temperature at critical point [K] u velocity vector [m/s] v quasi-velocity vector [m/s] Vc volume at critical point [K] W velocity [m/s] density [kg/m3] first viscosity coefficient [Pa s] second viscosity coefficient [Pa s] distance function [m] quasi-time [sec] kinematic viscosity [m2/s]
, , the generalized curved coordinates [m] nabla operator [1/m] Subscripts m main tube b side tube
International Journal of Gas Turbine, Propulsion and Power SystemsOctober 2007, Volume 1, Number 1
Manuscript received on Jan. 9, 2007 Review completed on Sept. 25, 2007
Copyright 2007 Gas Turbine Society of Japan
NUMERICAL METHOD The difficulties in simulating hydrogen flow inside the preburner lie in compressible and non-ideal characteristics of hydrogen, and the complex configuration of the flow channel composed of hundreds of LOX posts. In the developed numerical method, what is called Temperature-based CCUP (TCUP) (T.Himeno et al., 2005) was used to analyze cryogenic hydrogen flow, and Cut-cell technique was incorporated to simulate the complex flow channel with the LOX posts. Basic Equations
The developed TCUP is based on CCUP(T.Yabe et al., 2001).While the combination of independent variables in the original CCUP was selected as ( , , )TQ u p
, the combination was
changed to ( , , )TQ u T p
in TCUP. By solving temperature directly, heat transfer even in the incompressible flow field can be adequately simulated. The following Navier-Stokes equations were computed in the present simulation.
u u ut
[ ]e u e u qt
The stress tensor consisted of pressure tensors pI and viscous force T is described as follows: p I T (4)
( ) [( ) ( ) ]Tu u u T I (5)
Eq.(1)-(3) are solved with TCUP scheme, the algorithm of which is schematically illustrated in Fig.3. The change in the flow field during a computational time step t is divided into an advection phase and a non-advection phase. The advection equation is solved by CIP(T.Yabe and E.Takei, 1988). The non-advection phase is divided into a diffusion phase and an acoustic phase again.
The applicability of TCUP is not limited to ideal gas flow. It can treat any fluids whose state equations are known. In order to calculate density from temperature and pressure, the state equation is necessary. In the present study, Redlich-Kwong equation (O.Redrich and J.N.S.Kwong, 1949) (R-K eq.) was used, which is written as follows;
0.51 (1 )RT apb T b
where the values of a and b are calculated from the condition at critical point as
( / ) 0Tcdp dV (7) 2 2( / ) 0Tcd p dV (8) Specific heat, coefficient of viscosity, coefficient of thermal
conductivity and sound speed are calculated based on Eq.(6)(Y.Wakamatu et al., 1987). The variation of the sound speed by temperature is shown in Fig.4 at the pressure of 30MPa. As shown in Fig.4, the calculated values based on Eq.(6) show good agreement with the experimental data(McCarty, R.D, 1975) for higher value of temperature than 100K, while the calculated values from the equation of state for ideal gas do not agree. It means that the cryogenic hydrogen should be computed as non-ideal fluid. Since hydrogen temperature and pressure are around 160K and 30MPa, respectively, in the present study, R-K eq. is judged to be applicable for computation.
Cut-cell Technique with Distance Function
In order to simulate the flow field inside the complex channel, Cut-cell technique was utilized in which the governing equations were discretized on the orthogonal grid system. The surface configuration of each object, such as the LOX post and the triangular baffle, were expressed as the iso-contour surface where the value of distance function was zero. The distance function at an arbitrary point in the domain was defined as the signed distance from surface of the nearest object to the point. The sign corresponds to fluid or solid portion as follows.
Fig. 2 Hydrogen flow channel inside preburner
Fig. 1 Schematic of combustion chamber
Fig.3 Algorithm of TCUP scheme
50 100 150 2000
experimentR-K equationideal gas
Fig.4 Hydrogen sound speed at 30MPa
JGPP Vol. 1, No. 1
0 outside objects(fluid) 0 surface of objects 0 inside objects(solid) Figure 2 shows the preburner configuration, that is, the iso-contour of the zero distance function, while Fig.5 shows the contours of the distance function defined inside the preburner. Both Fig.2 and Fig.5 are illustrated in an orthogonal cross grid. Compared with a body fitted grid, the complex objects are easily expressed by representing the surfaces implicitly as the contours of zero distance function. Though, of course, this method is not able to analyze flow inside surface boundary layers precisely because of lack of grid fineness near objects, the advantage of Cut-cell technique is to avoid the pre-process of mesh generation and to compute flow field with a small computational cost.
Since each object is represented implicitly in the computational domain, the viscous surface boundary condition was imposed by zero-velocity fix method (M.Watanabe et al., 2003) as follows. Normal vector of distance function is calculated as /N
A variable v is defined as /v u (10) v is transferred into solid by the following advection equation by CIP.
0v N v
Where is quasi-time and Eq.(11) is iterated several times. Then v is transformed into u inside solid as u v (12) As the result of