A Simplified CFD Model for Radiative Heat Transfer in Engines

Transcription

1 International Multidimensional Engine Modeling User s Group Meeting at the SAE Congress Detroit, MI, 9 April 2018 A Simplified CFD Model for Radiative Heat Transfer in Engines D.C. Haworth and C. Paul Department of Mechanical & Nuclear Engineering, The Pennsylvania State University, University Park, PA, USA Abstract: There has been renewed interest in radiative heat transfer in engines, in light of current trends towards higher operating pressures and higher levels of exhaust-gas recirculation (EGR), for example, both of which enhance molecular gas radiation. Detailed CFD-based spectral radiation models including photon Monte Carlo/line-by-line (PMC/LML) have provided new insight into in-cylinder energy redistribution and heat losses due to radiative transfer, but are computationally expensive. Here, guided by results from recent PMC/LBL simulations, a simplified stepwise-gray spectral model in combination with a first-order spherical harmonics (P1) radiative transfer equation (RTE) solver is presented for engine-relevant conditions. Radiative emission, reabsorption and radiation reaching the walls are computed for a heavy-duty compression-ignition engine at part-load and full-load operating conditions with different levels of EGR and soot. The results are compared with those from PMC/LBL and other radiation models to assess the simplified model s accuracy and computational cost. The results show that the P1/StepwiseGray model can calculate reabsorption locally and globally with less than 10% error (with respect to PMC/LBL) at a small fraction of the computational cost (a factor of 30 smaller). In contrast, error in computed reabsorption using a P1/Gray model is as high as 60%. It is expected that the simplified model should be broadly applicable to high-pressure hydrocarbon-air combustion systems, with or without soot. Introduction Recent applications of high-fidelity spectral radiation models (including photon Monte Carlo/line-by-line PMC/LBL and full-spectrum k-distributions FSK) in engine-relevant environments and in engines [1-3] have shown that radiation redistributes energy (through reabsorption) in the combustion chamber in addition to contributing to heat losses. Soot emits and absorbs over a broad wavenumber spectrum, while gas molecules emit and absorb over discrete bands of wavenumbers. It has been found that CO 2 dominates the total radiative emission in engines, but most of the emitted CO 2 radiation is reabsorbed before reaching the walls. On the other hand, most soot radiation reaches walls, but for the levels of soot in modern engines, H 2 O dominates the radiation reaching walls. More specifically: 1) the in-cylinder system is relatively optically thin with respect to broadband soot radiation; 2) the system is optically thick at the primary CO 2 band (~4.2 µm), and little CO 2 radiation reaches the walls; and 3) the system is of intermediate optical thickness at the primary CO 2 /H 2 O overlap band (~2.8 µm), and most of the radiation that reaches the walls is from H 2 O. Here a simple stepwise gray model for spectral radiation properties is presented that captures these key features. The spectral model is coupled with a simple radiative transfer equation solver (a P1 method), and applied to simulate radiative heat transfer in a heavy-duty diesel engine for several different operating conditions. Results from the P1/StepwiseGray model are compared 1

2 with those from a full line-by-line photon Monte Carlo method (PMC/LBL) and with a gray spectral model (P1/Gray). Radiation Modeling Radiative properties for participating molecular gases (CO 2, H 2 O and CO) have been calculated using the HITEMP2010 spectral database [4] for temperatures from 300 K to 3000 K and pressures from 0.1 bar to 80 bar; pressure-based scaling is used to extrapolate to higher pressures. The spectral absorption coefficient for soot is evaluated using the small-particle limit (Rayleigh theory) with the complex index of refraction from [5]; scattering is neglected. From these underlying radiation properties, a hierarchy of spectral models is constructed. These range from full line-by-line (LBL), to narrowband-based and tabulated full-spectrum k-distributions (FSK), to gray-gas models with Planck-mean absorption coefficients [1,6]. Multiple radiative transfer equation (RTE) solvers have been implemented to calculate the local radiative intensity for conditions where absorption is considered. These include the stochastic photon Monte Carlo (PMC) method where no intrinsic assumptions are invoked regarding the directional distribution of radiative intensity, spherical-harmonics methods, and discrete-ordinates methods [1,6]. In the lowest-order spherical-harmonics implementation (the P1 method), a single elliptic PDE must be solved. A stepwise-gray model is a simple and convenient wide-band spectral model where the entire wavenumber spectrum is divided into discrete bands, and an average absorption coefficient is calculated for each band [6]. Figure 1 shows that CO 2 has a strong emission peak at approximately 2300 cm -1 (~4.2 μm) and that there is a strong overlap of CO 2 and H 2 O emission spectra near 3700 cm -1 (~2.8 μm). The idea behind the simplified stepwise-gray model is to divide the wavenumber spectrum into five bands, giving special attention to these two peaks, and to solve the RTE s assuming constant absorption coefficient (calculated by Planck-functionweighted averaging) in each of the bands. Because of the relatively high optical thickness of the system in the two key spectral bands, it is expected that a simple P1 RTE solver should suffice. Details can be found in [7]. 2

3 Figure 1: Stepwise-gray model bands, for pressures from 1 bar to 80 bar and temperatures from 300 K to 3000 K. Engine Configuration and Operating Conditions A simplified model of a Volvo 13L production six-cylinder heavy-duty diesel truck engine has been built using OpenFOAM v2.3.x [8], and unsteady Reynolds-averaged simulations (URANS) have been performed for four operating conditions: a part-load condition and a full-load condition, each with and without EGR. The liquid fuel injection and spray evolution are modeled using a stochastic Lagrangian parcel method, turbulence is modeled using a two-equation k-ε model with wall functions, skeletal chemical mechanisms are used for gas-phase chemistry, and a semi-empirical two-equation model is used for soot. The engine configuration and operating conditions (15.8:1 compression ratio, engine speed 1213 r/min, and swirl ratio of 0.3) are the same as those in an earlier modeling study [9]. Simulations begin after intake-valve closure at 60 before top-dead-center (btdc), and continue until 120 after top-dead-center (atdc) (before exhaust-valve opening). A 60-degree sector mesh with 85,650 cells is used, centered on one of the six spray plumes, with cyclic symmetry conditions on the lateral faces. A computational time step of 3.4 μs (0.025 crank-angle-degrees CAD) is used. For radiation post-processing, the solution fields (pressure, temperature and species concentrations) are saved every 2.5 CAD. The peak pressure for the part-load and full-load EGR operating conditions are approximately 85 bar and 200 bar, respectively. Results and Discussion Computed total radiative emission, reabsorption and radiation reaching walls for part-load EGR and no-egr operating conditions are shown in Fig. 2, and the final quantities for all four cases 3

4 are tabulated in Table 1. To simplify the plots, P1/FSK results are not shown there, but are tabulated in Table 1. Computed radiative emission is essentially the same for all four radiation models. This is expected, as there are no assumptions for radiative emission, and the same underlying spectral database has been used for all models. On the absorption side, P1/FSK matches PMC/LBL closely. This confirms the appropriateness of using the P1 RTE solver. However, the maximum error in computed reabsorption by the P1/Gray model is as much as 61% (compare to PMC/LBL) for the part-load no-egr case. For the same operating condition, the P1/StepwiseGray model error is only 8%. The P1/StepwiseGray model predicts reabsorption with significantly better accuracy in comparison to the P1/Gray model, and within 10% of PMC/LBL for all operating conditions. Figure 2: Cumulative radiative emission, reabsorption and radiation reaching walls as functions of crank-angle degrees. (a) Part-load with EGR. (b) Part-load with no EGR. Table 1: Total radiative emission, reabsorption and radiation reaching walls. The (%) in the reabsorption column is the percent difference with respect to PMC/LBL. 4

5 The computational cost of the different radiation models in coupled runs is tabulated in Table 2. These runs have been carried out for the full-load EGR case, using 24 processors. The P1/StepwiseGray model requires 3.0 hrs, less than 10% of the time required for P1/FSK (43 hrs) and approximately 3% of the time required for PMC/LBL (96 hrs). This is a significant gain in efficiency, with less than 10% loss of accuracy. Table 2: Simulation time for coupled radiation runs for the full-load EGR case. The (%) after the radiation time is the percent of total simulation time required for the radiation calculation. Conclusions Results from a P1/StepwiseGray radiation model have been compared with those from simpler (P1/Gray) and more detailed (PMC/LBL and P1/FSK) radiation models for a heavy-duty diesel engine. In the stepwise gray model, the wavenumber spectrum is divided into five bands, emphasizing the CO 2 peak at ~4.2 μm and the strong CO 2 /H 2 O overlap band at ~2.8 μm. The P1 RTE equation is solved for each band using the band s Planck-mean absorption coefficient. Radiative emission, reabsorption and radiation reaching the walls are computed in a postprocessing mode for a heavy-duty compression-ignition engine at part-load and full-load operating conditions with different levels of EGR and soot. The results show that band b2 (~4.2 μm) is responsible for most of the reabsorption, and that the P1/StepwiseGray model captures that quite accurately. With higher soot (not shown), band b5 reabsorption becomes important, and the model continues to perform well. The results show that the P1/StepwiseGray model can compute reabsorption for different engine-relevant operating conditions with less than 10% error, while the error for the P1/Gray model is as high as 60%. The computational cost of the P1/StepwiseGray model is approximately 15 times lower than that of P1/FSK and 30 times lower than that of PMC/LBL. Hence the P1/StepwiseGray model has great potential to provide a computationally less expensive alternative to detailed radiation models for engine relevant conditions. While the focus here is diesel engines, it is expected that the model should be broadly applicable to other high-pressure hydrocarbon-air combustion systems, with or without soot. 5

6 Acknowledgements This research has been funded by the U.S. National Science Foundation through grants CBET and CBET This material also is based upon work supported by the Department of Energy, Office of Energy Efficiency and Renewable Energy (EERE) and the Department of Defense, Tank and Automotive Research, Development, and Engineering Center (TARDEC), under Award Number DE EE References Cited [1] M.F. Modest, D.C. Haworth, Radiation Heat Transfer in Turbulent Combustion Systems, Springer, [2] C. Paul, A. Sircar, S. Ferreyro Fernandez, A. Imren, D.C. Haworth, S. Roy, W. Ge, M.F. Modest, 10th U. S. National Combustion Meeting, College Park, Maryland, USA, [3] S. Ferreyro Fernandez, C. Paul, A. Sircar, A. Imren, D.C Haworth, S. Roy, M.F. Modest, Combust. Flame 190: (2018). [4] L. Rothman, I. Gordon, R. Barber, H. Dothe, R. Gamache, A. Goldman, V. Perevalov, S. Tashkun, J. Tennyson, J. Quant. Spectrosc. Rad. Trans. 111: (2010). [5] H. Chang, T. T. Charalampopoulos, Proc. Royal Soc. London A: Mathematical, Physical and Engineering Sciences 430: (1990). [6] M.F. Modest, Radiative Heat Transfer, Third ed.,academic Press, New York, [7] C. Paul, D.C. Haworth, M.F. Modest, Proc. Combust. Inst. (2018). Under review. [8] OpenFOAM (2016) [9] V. Raj Mohan, D.C. Haworth, Proc. Combust. Inst. 35: (2015). 6