Application of OpenFOAM for Rocket Design

Transcription

1 9th OpenFOAM Workshop June 2014 in Zagreb, Croatia Application of OpenFOAM for Rocket Design Marco Invigorito 1, Daniele Cardillo 2 and Giuliano Ranuzzi 3 1 Italian Aerospace Research Centre (CIRA), Capua (CE) Italy, m.invigorito@cira.it 2 Italian Aerospace Research Centre (CIRA), Capua (CE) Italy, d.cardillo@cira.it 3 Italian Aerospace Research Centre (CIRA), Capua (CE) Italy, g.ranuzzi@cira.it Key words: reactingfoam, fluid, combustion, heat-flux, rocketry Computational Fluid Dynamics has the potential to enhance the rocket design and development process in different areas by replacing empiricism in the legacy design tools with a higher fidelity physics based approach. A significant use of a validated CFD tool is able to boost the initial design process by including relevant physical models, it can be further used as guidance for definition and execution of the subscale test campaign reducing the uncertainty of scaling subscale test data to the full scale design. Otherwise CFD models can be used to interpret and understand data when dealing with experimental rebuilding. Within this frame the HYPROB program [1], coherently with CIRA programmatic guidelines in the field of Aerospace Propulsion, aims to improve CIRA design and research capabilities on Liquid and Hybrid Rocket Engines by developing enabling qualified technologies and corresponding high-fidelity simulation tools to support the design of propulsion systems. One of the objectives of the HYPROB-HYBRID program is to develop a high-fidelity simulation tool to perform accurate simulations of hybrid-rocket thrust chambers with suitable numerical and physical models. For this purpose OpenFOAM is chosen for its structure and flexibility as a starting point for building a propulsion oriented CFD software platform to support analysis and design of rocket engines. This paper documents the status of an effort to understand and compare the predictive capabilities and resource requirements of OpenFOAM on a typical rocket design problem, involving compressible reacting flows. Due to the lack of experimental data, especially for hybrid rockets, as a first step a well-documented test on a GO2/GH2 thrust chamber is considered. The selected rocket thrust chamber, including the injector, combustion chamber and nozzle, as target case, is derived from the experiments of Santoro and Pal performed at the Pennsylvania State University s Cryogenic Laboratory [4]. The purpose of the experimental activity was to characterize the chamber wall heat flux for a single element injector using gaseous oxygen (GO2) and gaseous hydrogen (GH2) as propellants with focus

2 on providing benchmark quality data for CFD code validation. This case is simulated with OpenFOAM reproducing mixing, combustion processes and the related thermal environment. Quantitative and qualitative comparisons are performed with available experimental data for wall heat-flux and literature results of several CFD tools implementing different approaches that covers a range of simulation fidelities, including RANS, URANS, and LES [2][3]. The results show a good agreement with the experimental data and significant differences in the flow fields when compared to the other CFD tools, as expected, and are discussed in the paper. The possible degree of OpenFOAM demonstrated accuracy is revealed respect to each level of fidelity found in literature and the computational times to achieve these different levels of accuracy are compared. 1 BACKGROUND The HYPROB program is a major element of CIRA Aerospace Propulsion Program, launched to support the development of Space propulsion, in coherence with the National long-term vision defined by the Italian Aerospace Agency. The strategic objective of the Program is to consolidate national system and technological capabilities on the overall engine system for future space applications, with specific reference to liquid and hybrid propulsion technologies, where Italy can rely upon a significant heritage from previous R&D activities. Hybrid propulsion is receiving more and more attention from the space community because it is able to conjugate operative simplicity, and therefore guarantee reliability, of solid propulsion systems and the versatility and performances of liquid propulsion systems, for the aspects related to thrust throttability and re-ignition capabilities. Proper Computational Fluid Dynamics (CFD) tools are essential to analyze the complex physical-chemical processes that take place in hybrid rocket engines, such as: ignition, flame holding, turbulent mixing, interaction between the main oxidant-stream and the solid fuel grain. A development activity dedicated to design methodologies is foreseen, specifically, a CIRA propulsion oriented CFD software platform to support analysis and design of hybrid rocket engines will be developed, founded on CIRA proprietary numerical code and the open source OpenFOAM code. The general goal of this activity is to improve the simulation models usually available in commercial codes, in terms of accuracy and predictive capabilities. The validation of the CFD software platform, is carried out through available literature data and experimental tests that will be carried out in the frame of R&D activity. As a first step, due to the lack of specific test cases with experimental data, especially for hybrid rockets, a well-documented test on a GO2/GH2 thrust chamber is considered to asses OpenFOAM capabilities and performances

3 for rocket modeling in a design environment. 2 SCOPE OF THE CURRENT EFFORT The scope of this effort is focused on the simulation and evaluation of the results of modeling the test case titled "Penn State Pre-burner Combustor" using OpenFOAM. The main details of this test case are described in the following section and further details are reported in [4] and [5]. The specific goals of this study are a) to achieve steady state solutions and demonstrate iteration and solution convergence; b) to compare the results of the chamber wall heat flux with experimentally determined values and c) provide a comparison of relevant CFD results from literature; d) compare the computational time to achieve solutions for different levels of accuracy. In the accomplishments of these goals the available OpenFOAM solver for combustion with chemical reactions, reactingfoam, is used. 3 EXPERIMENTAL DESCRIPTION The simulation presented in this paper is based on the experiments of Santoro and Pal [4] performed at the Pennsylvania State University s Cryogenic Laboratory. The activity was conducted as part of a NASA funded effort titled, Focused Validation Data for Full Flow Staged Combustion Injectors. The purpose of the experimental effort was to characterize the chamber wall heat flux for a single element injector using gaseous oxygen and gaseous hydrogen as propellants with the focus on providing benchmark quality data for CFD code validation. The test rig, shown in Figure 1, is comprised of oxidizer and fuel pre-burners, a single element shear coaxial injector, an instrumented heat sink main combustion chamber for wall temperature and heat flux measurements and a water cooled nozzle. The chamber diameter is 38.1 mm and its length mm. Two upstream pre-burners produce oxidizer-rich and fuel-rich gases, respectively. The oxidizer-rich gas is fed to the combustion chamber through the inner tube of the coaxial injector with a diameter of 5.26 mm and is recessed 0.43 mm with respect to the combustion chamber face plane. The annular fuel feed has an inner diameter of 6.30 mm and an outer diameter of 7.49 mm. More details on the experimental apparatus can be found in [4]. The composition, key reference properties, and flow characteristics of the oxidizer and fuel streams are listed in Table 1.

4 Figure 1: Schematic of integrated pre-burners/main chamber rocket assembly. Oxidizer Preburner Fuel Preburner Pressure MPa Temperature K Total mass flow rate kg/s 9.04E e-2 Composition by mass 0.945(O 2 )/0.0550(H 2 O) 0.402(H 2 )/0.598(H 2 O) Main Chamber Pressure MPa 5.17 Table 1. Operating condition of the Penn State pre-burner combustor test case. 4 CONFIGURATION AND NUMERICAL SETUP Among the available OpenFOAM solvers for combustion modeling, reactingfoam solver is chosen for its capability to perform unsteady Reynolds-average simulation including appropriate models for the effect of turbulence and gas phase reaction schemes. The Menter Shear Stress Transport (SST) k-omega model is used in the current study for its essential feature of accurate and robust near wall treatment and its effectiveness in heat transfer prediction, [7].

5 This model, in combination with a formulation that will automatically shift from wall functions to a low-re formulation, based on the near wall grid density offers two important advantages. The model does not involve the complex non-linear damping functions required for the low-re model and is therefore more accurate and more robust. Furthermore the automatic wall treatment overcomes the strict grid requirement in terms of cell count of a low- Re number model, and avoids the deterioration of the results typically seen if low-re models are applied on under-resolved grids. A 9 species, 23 reaction step chemical kinetics model is used to represent combustion of hydrogen and oxygen and reaction rates are determined by laminar finite-rate model. Additional details about chemical kinetics model are given in [8]. All numerical computations are performed using second-order accurate numerical scheme in space and time. 4.1 Grids and boundary conditions The simulations are performed as 2D axisymmetric calculations. The computational domain and the experimental set of boundary conditions used in the calculations are shown in Figure 2. The overall domain is cylindrical and includes the injector, main chamber and nozzle. All three sections match the geometric profiles of the experimental apparatus. Figure 2. Computational domain, measured wall temperature for the Penn State pre-burner combustor. The injector post tip wall and the injector faceplate are assumed isothermal with a assigned temperature of 755 K. For the combustion chamber wall a temperature distribution corresponding to a least squares fit of the measured data points is set as boundary condition. The nozzle is water-cooled and is considered isothermal with a temperature of 510 K. All other walls are assumed to be adiabatic. Both inlet boundary conditions for the oxidizer and the fuel are specified as fixed mass flow rate and temperature values according to the operating condition in Table 1. Unfortunately no

6 experimental data is available for turbulent quantities so that estimations is used. Different grid resolutions with an increasing number of cells are studied and three levels of cell density are defined: coarse, medium and fine. The wall-normal size of the chamber walladjacent cell is calculated for each grid to achieve different y+ values with the applied turbulence model. Details of grids are listed below in Table 2. Coarse Medium Fine Cell number Chamber wall y + <3 <2 <1 Table 2. Details of grid resolutions. Sensitivity analysis is performed on the three different grid levels and the results show a good agreement for the surface heat flux distribution; in particular the results on the medium and fine grids appear comparable and the agreement is satisfactory within the design application framework, hence, the medium grid density is used for all further investigation. As shown in Figure 3. Figure 3. Grid sensitivity analysis results: a) chamber wall y + ; b) chamber wall heat fluxes for different grid densities: coarse, medium and fine. 4.2 Flow field initialization Unsteady RANS simulation of propellant ignition and combustion initiation in rocket typical trust chamber assembly is a challenging task. In computational terms, combustion can be initiated by several means such as adding energy at a given location, but a correct ignition procedure requires placing the adequate amount of energy at the proper location at the right time in the flow field. If the energy source is too small or the local O/F concentration is inappropriate, a small kernel of flame may be ignited but can burn itself out before becoming

7 established. If too much energy is added or too much premixing has taken place, an explosion can occur that can either destroy the simulation or create large pressure perturbations that continue to reverberate for long periods of time. The resulting trial and error procedure is very difficult to establish, either experimentally or computationally. For these reasons the simulation employs a robust and effective initialization and combustion initiation process based on the study of Merkle et al. [6]. The initial conditions for the problem are shown schematically in Figure 4 and are specified as follows. The first three-fourth of oxidizer and fuel passages were filled with propellant at the appropriate temperatures and composition from the experiments. The remainder of the propellant inlet passages and chamber were filled with hot nitrogen. The nitrogen initial temperature was set to 1500K. All velocity component was set to zero throughout the domain. The initial pressure was set to 3.24 MPa, which corresponds to pressure generated in the chamber with 1500 K nitrogen passing through the choked throat at the same mass flow rate as the incoming propellants. Ignition occurs spontaneously when initial hydrogen and oxygen come into contact upon mixing. The heated inert fluid in the chamber provides sufficient pre-heat to initial portions of incoming fluid to allow ignition. This results in a very smooth and well controlled ignition process that avoids large acoustic oscillations caused by ignition of a finite mass of propellant. A sequence of snapshots of the flow field development during the ignition process is shown in Figure 5. It is worth to note that the initial nitrogen in the chamber and inlet tubes serves another important purpose. Since neither the incoming fuel nor oxidizer contain nitrogen, the amount of residual nitrogen in the computational domain immediately indicates the degree to which the initial condition still impacts the prediction. Unambiguous results clearly require that the nitrogen concentration be reduced to a negligible magnitude at every point throughout the domain. Figure 4. Initial conditions. a) temperature; b) fuel concentration; c) oxidizer concentration.

8 Figure 5. Instantaneous snapshots of ignition process. Temperature (K) at a) t = 0.5 ms; b) t =1.0 ms; c) t = 1.5 ms. 4.3 Convergence criteria Solution convergence is evaluated by a combination of net mass flow rate convergence defined as the difference between the integrated mass at inlet and outlet, temperature and pressure behavior at selected probe point locations throughout the flow field as a function of solution time. A characteristic flow-through time τ = 8.3 ms is defined as that required for a particle to traverse the entire length of the camber at a bulk velocity, based on the total mass flow entering the system, theoretical combustion products and chamber diameter. The solution is obtained using an integration step of microseconds to simulate about seven chamber flow-through times. This amounts to approximately 60 ms of injection operation, the simulation ran for five flow-through times or 40 ms to reach a statistically steady solution, after which was run for another flow-through time until 60 ms to ensure convergence. Convergence history is shown in Figure 6: a) shows the overall mass conservation as a function of solution time, mass conservation is typically achieved to levels below 1.5% after 40 ms and 0.1% at 60 ms when solution is deemed to be well converged; b) average chamber pressure is monitored and when flow field approaches stationary conditions, just after 40 ms, its value is 5.1 MPa against the specified pressure 5.17 MPa from the experiment; c) the temperature from a flow field probe located just downstream of the injector post tip is plotted

9 as a function of time to control ignition and flame stabilization. The probe temperature is steady at about 3500 K after 20 ms; d) average chamber nitrogen concentration is plotted to ensure that all the effects of the initial conditions, used to initiate combustion, are washed out the computational domain. Typically the amount of the hot nitrogen reaches ideally zero value at 20 ms, when combustion is well established. Figure 6. Convergence history: a) net mass flow rate; b) averaged chamber pressure; c) near injector post tip temperature; d) chamber nitrogen mass fraction; as a function of solution time. 5 RESULTS Figure 7 shows instantaneous fields of temperature and hydroxyl radicals mass fraction of the overall thrust chamber assembly flow field. The oxidizer stream flows toward the chamber in the center tube, the fuel stream flow in the surrounding annulus. The streams are separated by

10 Figure 7. Instantaneous snapshots of temperature contour (top) and hydroxyl radicals mass fraction distribution (bottom) at t = 60 ms. the oxidizer post, then mix and began to combust in the oxidizer post tip wake where the flame is anchored. A significant feature of the flow are the large recirculation zones between the flame and the chamber wall that dominates the flow field. As can be seen in Figure 8 hot combustion products are carried even into the upstream corners of the combustion chamber by this the recirculation zones. Figure 8. Instantaneous snapshot of streamlines and water vapor contours at t = 60 ms. 5.1 Wall heat flux prediction The heat flux prediction on the chamber wall of rocket assembly from OpenFOAM simulation is analyzed respect to the experimental data of Santoro et al., [4].

11 OpenFOAM prediction is further compared to three literature results selected from the study of Tucker et al. [2] with the objective of evaluate its level of accuracy respect to other CFD methodologies ranging from RANS to LES. The three methodologies chosen represent a hierarchy in terms of accuracy and computational expense, with the highest accuracy tools being the most computationally expensive. The methodologies are listed below in Table 3, here we will refer to the respective approaches using the authors names. Author Affiliation Tool Level of Accuracy Oefelein Sandia LES State of the art Merkle Purdue URANS Intermediate Tucker MSFC RANS Production/design Table 3. Computational modeling techniques adopted in [2]. The LES simulation of Oefelein et al. represents the state of the art and matches the available experimental data extremely well, so it is used to gauge the other results. The MSFC (RANS) simulation performed by Tucker represents the state of production/design and comparison to this result on the opposite end of the accuracy spectrum is necessary as well. The result from Merkle is also compared as it performs URANS simulation and offer further term of comparison. Looking at more detailed trends in Figure 9 according to the experimental data the heat flux rises very rapidly in the head end of the chamber as the propellants begin to react. The heat flux has an almost flat peak from 0.03 meters to 0.09 meters downstream of the injector face at a value of approximately 16 MW/m 2. From the peak, the heat flux value gradually decreases with axial distance until the last measured value of just over 5 MW/m 2 near the chamber exit. Respect to the experimental measurements the OpenFOAM prediction is able to capture the initial heat flux rise rate, although it is shifted somewhat downstream. However results under predicts the heat flux in the head-end of combustion chamber and slightly under predicts the peak of about 10%, but overestimate the heat flux by approximately the 25-40% in the downstream region. Interestingly the Merkle (URANS) prediction exhibits the opposite trend, the initial head end heat flux is over predicted by approximately 30% and then slightly under predicted near the peak, but is essentially identical to Oefelein (LES) prediction downstream. Similarities between OpenFOAM and Tucker s results are evident; these probably depend on the turbulence model wall treatment, since both the simulation employs the Menter s k- Omega SST model and it is widely recognized that wall heat flux prediction accuracy and

12 turbulence model are strictly dependent. At this stage, with the current numerical setup, OpenFOAM offers a comparable level of accuracy respect to the production/design CFD tool developed by Tucker (MSFC), in estimating the chamber wall heat flux for the Penn State pre-burner combustor test case. Figure 9. Heat flux predictions from respective calculations compared with corresponding experimental data of Santoro et al. [4]. 5.2 Resource requirement Recall that the objectives of the overall effort are to determine the trades between predictive capability and resource requirement of OpenFOAM and to determine how to use this information to provide results with sufficient accuracy, but computationally affordable in a rocket design environment. To achieve these goals, as first step, OpenFOAM computational performance is compared with the data of a progressive hierarchy in term of fidelity of 5 computational techniques applied to Penn State pre-burner test case, studied in [2]. For sake of clarity should be underlined that every CFD calculation from literature is the result of different methodologies ranging from RANS to LES using different spatial or temporal accuracies, convergence strategies and above all a variety of hardware architectures with different powers of computing. For these reasons a direct comparison between the performances of the different techniques is not strictly correct, but a general indication of resource requirements is obtained. In Table 4 for completeness are reported for each CFD tool the main features, grid dimension, iterations number, cumulative CPU time and CPU time per cell is introduced for clearer

13 estimation of computational resource requirements. Looking at the Table 4, it is not unexpected that methodologies based on large eddy simulations require the highest overall effort in terms of computational time and hardware requirements and although these are able to generate the most accurate representation of the rocket flow field and heat flux estimation, see Figure 9, their application is not feasible as design tool. For this reason comparison between performances of RANS/URANS approaches is necessary and the analysis is focused on the cumulative CPU time per cell that every CFD tool employs to perform a complete simulation, this parameter gives a general information about the pure code performances and computing efficiency, independent from the grid resolution. This direct comparison shows that OpenFOAM performances are comparable with URANS code developed by Merkle at Purdue University, while MSFC code is faster, since it is a RANS code with local time stepping technique. The second step of the analysis centered its attention to CPU times to define general guidelines about OpenFOAM ability to complete a simulation of the Penn State pre-burner combustor as design tool with proven convergence, conservation and demonstrated accuracy. Using reactingfoam solver, as stated in 4.3, is observed that 60 ms of unsteady simulation, corresponding to about 1.71E+06 iterations with the current numerical setup, is a sufficient time to approach stationary conditions. The entire computation required approximately 1.44E+03 hours of cumulative CPU time. This data scaled on HPC cluster using 32 Intel Xeon E5 processors with 2.7 GHz clock frequency results in about 45 hours of computation time and accomplishes the design process needs in a reasonable time with affordable resource requirement. Author Affiliation Tool Grid cells Simulated time [ms] Iterations 1 CPU Time [h] 1 CPU Time [h]/cell Oefelein Sandia LES/3D 255.0E E E Menon GT LES/3D 3.160E E E Yang Penn State LES/2D 2.625E E E Merkle Purdue URANS/2D 2.500E E E Tucker MSFC RANS/2D 4.000E E E OpenFOAM URANS/2D 3.000E E E Table 4. Computational performance, methodologies adopted in [2] versus OpenFOAM. 6 CONCLUSION This study has highlighted the results obtained in the simulation of the Penn State pre-burner combustor case in the contest of the evaluation by CIRA of OpenFOAM software as CFD tool

14 for rocket design. Important conclusion from this effort can be drawn on two aspects. The first aspect focuses on evaluating the accuracy of the current approach in capturing flame dynamics and accurate heat flux prediction respect to the experimental measurements. In this aspect OpenFOAM has the potential to meet the requirements of a design tool as its solver offers great flexibility in setting reasonably precise geometry and boundary conditions from experiments, reproducing an adequate level of fidelity respect to the physics of the problem. Furthermore, the initialization strategy employed in the calculation has proved to produce a smooth ignition and combustion initiation processes with beneficial consequences on convergence history and resulting increased numerical robustness and reliability. Comparison of the heat flux prediction with the experimental data has revealed the level of accuracy that OpenFOAM is able to achieve and further confrontation with calculations found in literature, ranging from RANS to LES, has consented to collocate its fidelity in a close position respect to the state of design. The second aspect is specific to the computational cost and the consequent resource requirements necessary to achieve the aforementioned level of accuracy. In fact it is not surprising that LES methodologies return the highest fidelity simulations and represent the best comparison of all attempts respect to the experimental data, but in a design context this level of fidelity is obviously not possible due to a sensible boost of the computational cost. OpenFOAM has proved affordable performances in terms of computational cost, comparable with other RANS/URANS codes for propulsion application from research and university and, furthermore, has demonstrated its effectiveness and reliability to comply with design requirements in terms of fidelity and computational cost, accomplishing a complete simulation task in a reasonable computation time, with affordable hardware requirement. 7 FUTURE WORKS The results and discussion presented above have provided a first attempt to understand and compare the predictive capabilities and resource requirements of OpenFOAM for rocket application. In terms of overall effort, more detailed analysis of the Penn State pre-burner combustor is required. The additional work consists of evaluation of the influence of different turbulence models on heat flux prediction, assessment on the effect of turbulent combustion models and the understanding the impact of improved models in terms of computational cost.

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