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Side Impact Pressure Sensor Predictions with Computational Gas and Fluid Dynamic Methods.

INTRODUCTION

Acceleration-based (also called G-based) crash sensors have been used extensively in the automotive industry to detect crash severity and determine the restraint system deployment time in the event of a vehicle crash. The acceleration-based crash sensors record the deceleration pulses that are created by the deformation of vehicle components. Depending on the locations of the crash sensors and the structure designs, the acceleration (or deceleration) pulses recorded by the acceleration-based crash sensors are usually noisy; especially those installed in crush zones and/or obtained from body-on-frame vehicles. The prediction of acceleration crash pulses using computer simulations has been very challenging due to the high frequency and noisy responses obtained from the sensors. As a result, the sensor algorithm developments for acceleration-based sensors are primarily based on prototype testing.

A. Pressure Sensors

With the latest advancement in the crash sensor technology, side crash pressure sensors have emerged recently and been adopted increasingly in the automotive industry. The pressure sensors detect the dynamic air pressure change in a door system with cavities. When a door is deformed, the change in the door cavity volume creates pressure change which is recorded by the pressure sensors. Unlike the acceleration-based crash sensors, the data obtained from the pressure sensors exhibit lower frequency and less noisy responses. In addition, the pressure sensors also offer the potential of earlier deployment times, more robust response, and less sensitivity to test variations. The lower frequency and reduced fluctuation characteristics have been viewed by CAE community as more appropriate to be predicted by using computer simulations. This research evaluated the advantages and limitations of the three computational gas and fluid dynamic methods, CV/UP, CPM, and ALE, with respect to the prediction of pressure sensor responses in an effort to help reduce prototype testing and improve the robustness of sensor algorithm development. A brief literature review of the developments of the three computational gas and fluid dynamic methods and their applications are summarized as follows.

B. CV/UP method

To predict the time-dependent behavior of the interior pressure of an airbag, Nefske [1] and Wang and Nefske [2] developed a CV method in the late 1980s. The CV method was also called UP method in much literature due to these assumptions that the pressure and temperature were uniform within a system at any specific time. Assuming an ideal gas law, Equations (1), (2), and (3) below, and an adiabatic process (no heat transfer into the control volume), Equation (4) below, scalar thermodynamics equations can be derived easily, (see details in Wang and Nefske [2]).

PV = nRT (1)

Equation (1) is the common form of ideal gas law; where P, V n, and T denote the bag pressure [Pa], volume [[m.sup.3]], number of molecules [moles], and absolute temperature [K, the Kelvin scale is a shifted Celsius scale, e.g. 0.0 K = -273.15 [degrees]C, the lowest possible temperature], respectively, while R being the gas constant [J/kg K, e.g. universal gas constant [??] =8.3145 J/kg K].

PV = m/MRT (2)

Equation (2) is the molar form of ideal gas law; where m denotes total gas mass [kg] and M denotes molar mass [kg/mole].

P = [rho]R/MT (3)

where p = m/V is the density of the gas [kg/[m.sup.3]].

[PV.sup.[GAMMA]] = constant (4)

where gamma [GAMMA] = Cp/Cv = cp/cv being the heat capacity ratio of the gas (1< [GAMMA]< 5/3), Cp being the heat capacity at constant pressure [J/mole K], cp being the specific heat capacity (heat capacity per unit mass) at constant pressure [J/kgK], Cv being the heat capacity at constant volume [J/mole K], and cv being the specific heat capacity at constant volume [J/kgK].

Due to the above assumption, discretization of the gas (or fluid) field is not needed. Instead, two inflow factors including mass flow rate and temperature-time relationship are needed to model the gases. The two inflow factors can be obtained through tank tests. Based on the assumptions, the gas response is not location dependent. In the application to occupant protection, the method is usually used to simulate the interaction of a normally seated dummy or an occupant with a fully deployed airbag or called "in-position" test condition. This method was also a dominating method for a long time to simplify the tire and fuel tank models that are needed in crash safety applications. In the case where the dummy or occupant contacts the airbag in an earlier stage of the deployment process such as the case of OOP (out-of-position) test conditions, more accurate methods are deemed necessary to predict the airbag transient responses reasonably.

C. ALE Method

The continuum mechanics usually adopt two classical descriptions of motion: the Lagrangian description and the Eulerian description (see e.g., Malvern [3]). The Lagrangian approach, coordinate system moving with materials, is usually adopted to describe structural problems due to the relatively smaller movement of the materials. The Lagrangian description allows an easy tracking of free surfaces and interfaces between different materials. For fluid flow problems, where the materials (fluids or gases) exhibit relatively larger movements, the Eulerian system with coordinates fixed in space is needed to describe the materials' motions mathematically. Developed for structure-fluid interaction problems, the ALE formulation allows an arbitrary Lagrangian and Eulerian coordinate system to be used to describe the structural and fluid/gas materials. In order to express the conservation laws for mass, momentum, and energy in an ALE kinematical description, a relation between material time derivative, which is inherent in conservation laws, and referential time derivative is needed. Original developments were made, among others, by Noh [4], Franck and Lazarus [5], Trulio [6], and Hirt et al. [7]. The developments were subsequently adopted in the finite element methods and early applications can be found in the work of Donea [8], Belytschko et al. [9], Belytschko and Kennedy [10], and Hughes et al. [11].

The ALE method has been regarded as one of the most advanced CFD (Computational Fluid Dynamic) methods developed for structure-fluid interaction problems today. Hughes et al. [11] adopted the ALE description in the early 1980s to solve free surface flows for incompressible viscous fluids. The Lagrangian-Eulerian description and general kinematics theory adopted by Hughes et al. [11] have served as the foundation of the ALE method in finite element computation. In the ALE calculation, discretization of both the structures and the fluid (or gas) volumes is needed. Different from the CV/UP method, the local responses of the gases or fluids can be predicted in the ALE calculation. As a result, the ALE method has been considered to be one of the most accurate methods for applications involving local predictions of structure-fluid interactions. More detailed formulations of the ALE theory and computational schemes can be found in Hughes et al. [11], Benson [12], Olovsson [13], and Hirth et al. [14].

In the automotive industry, the ALE method has been used to predict the fuel sloshing in fuel tanks under high speed impact conditions. Ma and Usman [15] used the ALE formulation available in LSDYNA to design a baffle during the development of a fuel tank. Tang, Guha, Tyan, and Doong et al. [16] adopted the ALE formulation to investigate the sloshing of fuel and ballooning of deformable fuel tanks in high speed impact conditions. Recently Craig, Qu, Pan, and Tyan et al. [17] employed the ALE method to predict fuel sloshing and tank deformation. In the study, blow molding simulations were conducted to predict the thickness distribution of thermoplastic fuel tanks. In addition, fuel tank assembly process was included in the simulation to predict the pretension between the fuel tank and its straps. Reported in [17], the integration of fuel tank forming and assembly processes as well as the employment of the ALE method not only made it possible to predict the pre-tension of tank straps, but also has contributed to the accuracy of the fuel tank modeling for high speed impacts.

In the aerospace, manufacturing, and defense industries, the ALE method has also been adopted for various applications such as bird strike, bulk metal forming, air blast, gun launch, and so on. Souli and Olovsson [18, 19] developed a new Lagrangian-Eulerian coupling algorithm to enhance the application of the ALE method in the areas of bird strike and die forging. More application of the ALE method to the bird strike problems can also be found in McCallum and Constantinou [20 ] and Anghileri et al. [21]. Many bulk metal forming processes, including extrusion, cutting, and punching, were simulated by employing the ALE method as illustrated by Gadala and Wang [22] and Movahhedy et al. [23]. Slavik [24] implemented a coupling method in LS-DYNA to allow empirical explosive blast loads to be applied to air domains described with the ALE formulation. Lapoujade et al. [25] worked with LSTC (Livermore Software Technology Corporation) to implement a new mapping technique for the air blast problems that were simulated by using the ALE method. Tabiei and Chowdhury [26] illustrated the use of the ALE method to predict the dynamics behavior of a generic gun launch. With an improved search algorithm specifically designed for explicit geometry information, a new S-ALE (Structured ALE method) method was developed by LSTC recently to speed up the calculation time and reduce memory usage for ALE simulations. The S-ALE method was applied to under body mine blast simulations by Hsieh, Vunnam, Bhalsod and Chen [27].

ALE method has also been adopted in the automotive industry for airbag deployment simulations, especially the OOP applications where the local response of transient stage cannot be predicted by using the CV/UP method. Olovsson [13], Marklund [28], Markland and Nilsson [29], and Fokin et al. [30] demonstrated how to employ the ALE method to model the inflators and the airbag deployments. Subsequently, Haufe and Weimar [31], and Lian [32], all have tried the ALE calculation to simulate the transient deployments of airbags with a focus on the OOP test condition.

D. CPM Method

Based on the kinetic molecular theory (KMT), Equation (5) below, the corpuscular particle method (CPM) in LS-DYNA was developed by Olovsson [33] in 2006 to simulate inflator firing and to predict airbag deployments in a more realistic manner. In this method, the gases are modeled as rigid particles obeying Newton's laws of mechanics and the ideal gas law, Equations (1), (2), and (3). Each particle represents multiple molecules, depending on the number of particles provided in the system intended to simulate.

p = 2/3*wk/v = nM/3V^2([nu]rms)^2 5

Wk = 1/2 nM/m ([nu]rms)^2 6

where Wk is the total translational kinetic energy of all molecules, and Dims is the root mean square velocity of all molecule with mass m.

From Equations (1) and (6), Equation (7) can be obtained.

([nu]rms) = [[square root of (term)]3RT/M] 7

The particles behave just like molecules that can store energy as they vibrate and spin. The total translational kinetic energy, Equation (6). of the particles is the same as that of the molecules. The theory also ensures the correct heat capacity ratio, [GAMMA]= Cp/Cv = cp/cv in Equation (4), as the gases get expanded or compressed. The same properties of the gases are assigned to the particles directly. As a result, the ideal gas law, Equations (1), (2), and (3), the kinetic molecular theory, Equation (5), and thermodynamics are coupled, as seemed in Equation (7), seamlessly to allow simulations of transient gas dynamics problems.

Uniform porous materials, treated in the CV/UP or ALE methods, can be handled the same way in the CPM method. In addition, the vent holes can be modeled physically and the particles can be allowed to leak through. This method enables more realistic behavior of a system to be predicted both locally and globally. Due to the small size of the spherical particle, the CPM method will allow gases to leak through tiny vent holes, which provides an advantage over the CV/UP and ALE methods. More importantly, this approach does not encounter numerical difficulties, such as hourglass mode, element distortion, complex contact, and small time step, usually experienced with the continuum based approach.

The original objective for the development of the CPM method was to enable the applications associated with the inflation of an airbag and its interaction with an occupant, especially the OOP test conditions. Following the initial development of the CPM method, Feng and Coleman [34] adopted both the ALE and CPM approaches to simulate the deployment of an airbag through interior trims in 2008. A similar study was conducted by Lian et al. [35] to compare the ALE and the CPM methods in the OOP applications. In Lian's study, five benchmark problems were investigated to understand the performance difference between the ALE and the CPM methods. The method was further improved by Teng, Wang, and Bhalsod [36] to handle systems with initial air and multiple chambers. Lin, Cheng, and Wang [37] evaluated the CPM method for side impact airbag deployments. In addition to static and linear impactor tests, effects of inflator variations were also investigated in the study.

The prediction of side crash pressure sensor responses involves the modeling of a door structure and the air inside the door cavity. Physically, it is very similar to the modeling of fuel tanks and/or airbags. Based on the literature review summarized above, the ALE method can be a good candidate for such applications. Machens and Wessels [38] made the first attempt in 2007 to investigate the pressure changes inside a door subjected to side impact conditions by adopting the ALE calculation. Lin and Jerinsky [39] adopted both the CV/UP and the ALE methods to predict the side door pressure sensor responses with a focus on full vehicle side impact conditions. It was reported that both the CV/UP and the ALE methods can be used to predict the pressure change from side impact sensor calibration point of view.

Recently, Tyan et al. [40] made the first attempt to predict the responses of pressure sensors by employing the CPM method. In the research, the CPM method was improved with additional capabilities developed and existing features enhanced to expand the applications of the CPM method to solve SFI problems with existing gases. Simultaneously, Tyan et al. [41] also adopted the ALE method to predict the responses of pressure sensors. In the research conducted [40, 41], fifteen benchmark tests were designed and performed to allow enhancements and assessments of the CPM and the ALE methods and to ensure the robustness of numerical predictions. Sensitivity of the pressure sensor responses to different variables including, gas type, structure design, hole size, hole location, sensor location, impactor type, and impact speed, were all investigated to better understand the responses of pressure sensors under different impact scenarios.

OBJECTIVES

In this study, the authors made another attempt to predict the pressure sensor responses for side crash pressure sensors by adopting the CV/UP method which was not included in the original research [40, 41, 42, and 43]. The predictions of the same benchmark tests including the structure deformation modes and pressure sensor responses are compared to those of the CPM and the ALE methods that were obtained and reported previously [40, 41]. The numerical performance of each method is compared based on the results obtained from the fifteen benchmark simulations. The prediction accuracy, computational efficiency, and user-friendliness of the three methods are compared and discussed in details in this paper. One of the main goals of this study is to understand the advantages and limitations of the three computational gas (CV/UP and CPM) and fluid dynamic (ALE) methods for such applications. Thus, the most appropriate methods can be identified and the corresponding modeling methodologies can be developed to assist pressure sensor algorithm development. Through the entire research, the authors and code developers worked jointly with an intention to further enhance and/or develop the three computational gas and fluid dynamic methods so that their applications to different SFI problems can be conducted as broadly, accurately, and effectively as possible.

BENCHMARK TESTS

To help understand the responses of pressure sensors and to obtain reliable data for model development, a total of fifteen benchmark tests were designed and conducted in the first phase of this research [40, 41]. The second phase of the research involved full vehicle simulations [42, 43] which were more complex due to the need to include seat systems, restraint systems, (seat belt, side air bag, and side air curtain,) dummies, and full vehicle models in the simulations. The fifteen benchmark tests have been reported in detail [40, 41] and are briefly repeated in this paper for understanding of the test rationale and the simulation scenarios. The fifteen benchmark tests were divided into three different groups.

The first group, with only one hypothetical test condition, was designed to check the accuracy and stability of the numerical methods. In this benchmark test, a simple rectangular container was designed to simulate a piston compression condition with which the theoretical solution could be derived. For modeling simplicity, the piston and the container were assumed to be rectangular and rigid. Two different gases, with gamma (heat capacity ratio: [GAMMA]= Cp/Cv = cp/cv) equal to 1.01 and 1.4 (air), were considered inside the container and simulated separately. No leakage between the piston and container was allowed in this case. For calculation simplicity, an isentropic process (a thermodynamic process that is adiabatic and in which the work transfers of the system are frictionless; there is no transfer of heat and the process is reversible) was assumed for the piston compression test. The compression speed was assumed to be constant so that the volume change of the rectangular container could be calculated and air pressure change relative to the piston displacement could be derived theoretically.

With eight different test conditions, the second group of benchmark tests involved a rectangular steel box that was slightly larger than the container designed for the piston compression test in the first group of benchmark tests. Different steel boxes, with and without a hole, were included in the second group of benchmark tests to understand the pressure change due to the existence of a hole. In the test matrix, a hole was created at two different locations of the box so that the pressure sensitivity to hole location could be obtained also. In addition, three pressure sensors were instrumented on different sides of the box. Two impactors, a deformable barrier and a rigid impactor, impacted the rectangular steel box at two different speeds. The deformable barrier was fabricated by using the center portion of a FMVSS (Federal Motor Vehicle Safety Standard) 214 MDB (moving deformable barrier) aluminum honeycomb face with 400 mm in width. The rigid impactor was designed with its dimension, 400mm wide, the same as that of the deformable barrier except it is made out of thick steel so that no plastic deformation would occur in the impactor during the tests. As a result, the second group of benchmark tests would allow the sensitivity of pressure response to hole size, hole location, sensor location, impactor type, and impact speed to be investigated in detail. These tests were conducted using a VIA sled dynamic test facility due to the mass of the impactors and the high impact speeds needed for the tests.

Side doors from a production vehicle were used in the third group of benchmark tests, with five different test conditions. The side doors with different openings were tested to simulate different door designs. A production door with its plastic trim and side mirror removed was chosen as the baseline door. In the baseline door, the air could escape through the gaps between the glass and weather seal as well as the side mirror opening. Additionally, the weather seal surrounding both sides of the glass along with some plastic fasteners on the door inner were removed completely to simulate a different door design with more openings. In this case, more air was allowed to escape due to the additional openings created on the door. The same rigid and deformable impactors used in the second group of benchmark tests were used in the third group of benchmark tests. Three different impact speeds were chosen in this group of benchmark tests. The third group of benchmark tests were also conducted using the VIA sled dynamic test facility, with which the side doors could be tested with higher impact loads to approximate full vehicle test conditions.

FULL VEHICLE TESTS

The research was advanced into its final stage, full vehicle tests, after the completion of the above benchmark study. The full vehicle study conducted in this research, with different vehicle architectures (body-on-frame and unitized), body styles, test conditions (oblique pole side impact, IIHS side MDB, and FMVSS 214 MDB), and simulation methods (CV/UP, CPM, ALE) was too extensive to be included in this paper. To demonstrate the capability to predict pressure sensor responses in full vehicle test environments only unitized vehicles with ALE method were presented and discussed in this paper. A total of four full vehicle tests include two body styles with different powertrains, drivetrains, test modes, and impact speeds. The first three tests were utilized in the development of simulation methodology and calibration of air leakage while the fourth test was adopted to predict the pressure sensor response and validate the developed simulation methodology for full vehicle tests.

SIMULATION RESULTS

Computer simulations for all fifteen benchmark tests were performed by employing the CV/UP method in this study. The results obtained from the CV/UP method were compared to those of the tests as well as to those of the CPM and the ALE methods obtained previously. The modeling details of the CPM and the ALE methods have been discussed previously [40, 41] and are not repeated in this paper. For consistency, the same legend, with theoretical solution or test shown in red, CV/UP method in green, CPM method in blue, and ALE method in cyan, is used in the comparison of pressure sensor responses throughout the entire paper.

A. Piston Comprssion Test

The piston compression tests were designed hypothetically so that the theoretical solution could be derived and no physical tests would be required. The container being compressed is illustrated in Figure 1, with dimensions of 1100X650X150 mm (A)3. The top side of the container (1100X650 mm^2) is compressed downward along the vertical axis to simulate a piston moving toward the bottom of the container. The volume of the container is reduced and the air pressure inside the container rises once the piston starts to move downward. An isentropic process is assumed so that no heat is added to the system and no energy transformations will occur during the piston compression process. Two different gases, with gamma ([GAMMA]= Cp/Cv = cp/cv, heat capacity ratio) equal to 1.01 and 1.4, were assumed inside the container. It should be noted that [GAMMA] = 1.4 represents dry air at 20 degrees Celsius while [GAMMA] = 1.01 represents a gas whose heat capacity at constant pressure is very close to its heat capacity at constant volume. Two cases were simulated with only one gas type considered inside the container in each simulation. Since no physical test is involved, this case allows the numerical accuracy and computational stability of each method to be evaluated and compared to the theoretical solution.

A simple finite element model, depicted in Figure 1, was created to represent the rectangular container. The finite element model is composed of only 6 shell elements, with one shell element representing each side of the container. A "boundary prescribed motion" with uniform compression speed was defined to control the motion of the top piston. During the compression process, the top side moves downward while the bottom side is fixed which was defined by using "boundary SPC set". The four vertical sides could become shorter and shorter as the top side moves downward. Knowing the robustness of the CV/UP method, the simulation was conducted with 99% volume compression, the same as that of the CPM method [40].

The compression of the air inside the container is shown in Figure 2 and compared with those of the CPM and the ALE methods. As expected, both the CV/UP and the CPM methods can sustain extreme compression condition with 99% volume compression without any numerical instability in this benchmark test while the ALE method exhibits leakage during the compression process. The simulation of the ALE method was terminated at 80% volume compression due to accumulated numerical error.

The prediction of the pressure response for this benchmark test is compared to those of the theoretical solutions as well as the CPM and ALE methods as shown in Figure 3. It should be noted that the unit is 10,000 bar (or kN/mm^2) for all pressure sensor responses presented in this paper because the simulations used kg, mm, and ms as the base unit for mass, length, and time. The pressure sensor responses obtained from the simulations are presented without any filtering. As can be seen, the predictions obtained from the CV/UP and CPM methods almost overlap exactly with the theoretical solutions for both cases with gamma equal to 1.01 and 1.4. The predictions obtained from the ALE method for both gamma equal to 1.01 and 1.4 are lower than the corresponding theoretical solutions due to the gas leakage found in the animation of Eulerian mesh. As mentioned in [39], the conflicting requirements of the Lagrangian mesh for the box structure and the Eulerian mesh for the gas domain caused the gas leakage. The gas leakage can be reduced or eliminated but may require extensive computation time. Detailed discussion for the discrepancy of the ALE method can be found in [39] and is not repeated here.

The computational performance for the piston compression test obtained from the three computational gas and fluid dynamic methods are compared in Table 1. The CV/UP method not only provides very accurate results, but also consumes the least amount of computation time. The CPM method also provides very accurate results but requires more computation time (1210 times) than that of the CV/UP method. The ALE method is not able to predict accurate results without more effort and requires the highest amount of computation time (491104 times the CV/UP method or 406 times the CPM method) in this benchmark test.

Regarding the user-friendliness, the CV/UP method is also the best due to the fact that no discretization is needed for the gas inside the container. The CPM method requires an appropriate number of particles to be defined for the gas but the optimal particle number can be obtained through a simple sensitivity study. The ALE method requires the gas to be meshed and the coupling of the Lagrangian and the Eulerian calculations with associated features to be defined in the input deck. The ALE method is the least user-friendly when comparing to the CV/UP and the CPM methods.

B. Box Impact Tests

As displayed in Figure 4a, rectangular steel boxes with dimensions 1100X150X660 mm^3 were manufactured for the second group of benchmark tests. Mild steel available in the laboratory was chosen to make the boxes. The VIA sled dynamic test facility is shown in Figure 4. The two impactors, one rigid and one deformable, designed for this research are shown at the end of the sled track in Figures 4b and 4c, respectively. Three pressure sensors were instrumented on the front, top, and side of the steel box, as can be seen in Figure 5a (highlighted in green circles). The locations of the three pressure sensors were kept the same for all the box impact tests. The seal of the box was checked prior to each test to ensure there was no leakage. For boxes with a hole, the locations of the right or left hand side hole can be found in Figures 5b and 5c (highlighted in a green circle), respectively. The size of the hole, 2" X 4" [50mm X 100mm], was kept the same for all the box impact benchmark tests with a hole.

To simulate the box impact benchmark tests, finite element models created are shown in Figure 6 with the two different impactors, rigid (Figure 6a) and deformable (Figure 6b). The size of the elements adopted to mesh the steel box was around 10 mm with a total of 34,978 shell elements. The locations of the three pressure sensors were modeled according to the test, as can be seen from Figure 6c (black squares on the front, side, and top sides of the box). Figure 6c also illustrates the case of a box with a RHS hole (rectangular hole) and a deformable impactor.

I. Rigid Impactor

Four benchmark tests were conducted for the box impacted with a rigid impactor. To better understand the sensitivity of the pressure response to impact speed, the baseline boxes without any hole were used in the first two tests, the first one with a lower impact speed and the second one with a higher impact speed. The boxes with RHS and LHS holes were subsequently tested to investigate the sensitivity of the pressure sensor responses to the hole location. From the studies conducted previously [39, 40], the pressure is not sensitive to the sensor location for the box impact tests. Therefore, the pressure response will be compared only at the top sensor location in this paper. The results of the four rigid impactor tests are presented in the following sections.

1. Low Speed without a Hole

The target speed was 5 mph [2.24 mm/ms] while the actual impact speed reached for the low speed test was 4.92 mph [2.2 mm/ms]. To prevent the impactor from damaging the VIA sled dynamic test facility, honeycomb blocks were used to artificially slow down the impactor after 50 ms. Therefore, the comparison between the simulation and the test is made only for the first 50 ms. The comparison of the box deformation mode is shown in Figure 7. It should be noted that the test picture was taken after the test; the rebound of the impactor has been completed, while the predicted deformation modes were obtained at 50 ms simulation time. As can be seen from Figures 7, the crease lines created on the box were predicted reasonably well by all the three methods. Some indentations created on the front top and front bottom were also captured in the three simulations.

The pressure sensor responses obtained from the three methods are compared to that of the test and shown in Figure 8. A shock wave propagated from the front side of the box and reached back sides of the box at around 10 ms. Due to the compliance of the system, the box was allowed to expand slightly when the shock wave reached the back sides of the box. The expansion of the box on the back side caused the pressure increase to slow down slightly, as can be seen from Figure 8 at around 10 ms to 17 ms. The prediction of the pressure slope change at around 10 ms to 17 ms is not trivial. The three methods are able to accurately capture the entire pressure response, including the pressure slope change between 10 ms to 17 ms. It can be seen that the pressure sensor responses predicted by the three methods are very consistent in this benchmark test.

2. High Speed without a Hole

The actual speed for this test was 11.87 mph [5.31 mm/ms] while the target speed was 12 mph [5.36 mm/ms]. Due to the higher impact speed than the previous test, the rigid impactor was decelerated by the honeycomb blocks after 30 ms. Therefore, the comparison between the prediction and the test is made only for the first 30 ms. The comparison of the box deformation modes is shown in Figure 9. As expected, the box deformed more severely in this high speed impact condition compared to that of the low speed impact condition, displayed in Figure 7. In Figure 9, it should be noted again that the post-test picture was taken after the test when the rebound of the impactor has been completed while the simulation deformation modes are shown at 30 ms simulation time. Similar to the low speed impact case, it can be seen that the crease lines and indentations created on the box were predicted reasonably well by the three methods.

The predicted pressure sensor responses obtained from the three methods are compared to that of the test, as graphed in Figure 10. The three methods are able to predict the pressure response accurately for the entire simulation duration, including the pressure slope change between 8 ms and 15 ms. Again, the variation among the four curves is very small for this benchmark test.

The entire impact event of this case was simulated in this study so that the pressure sensor responses during the rebound stage could be investigated in details. To achieve such goal, the deceleration pulse obtained from an accelerometer installed in the sled was adopted and defined as the "boundary prescribed motion condition" in the three simulations. Figure 11 (11a to 11c) compares the progression of the box deformation for the three methods. As can be seen, the deformation modes obtained from the three methods are quite similar.

The comparison of the pressure sensor responses at the top sensor location with respect to time is shown in Figure 12. The predicted pressure sensor responses obtained from the three methods, including the loading and rebound stages; correlate very well with that of the test. However, the pressure sensor response obtained from the ALE method starts to fluctuate severely after around 95 ms.

3. High Speed with a Right Hand Side Hole

The actual impact speed for this test was 11.81 mph [5.28 mm/ms] while the target speed was 12 mph [5.36 mm/ms]. In this test condition, a hole was created on the right hand side of the box, close to the locations of the front and side pressure sensors. Again the comparison between the simulation and the test is made only for the first 20 ms before the rigid impactor is decelerated by the honeycomb blocks. Figure 13 compares the box deformation modes obtained from the test, Figure 13a, and the three simulations as shown in Figures 13b, 13d, and 13f. The air leakages through the RHS hole predicted by the CPM and ALE methods are presented in Figures 13c and 13e respectively. Similar to those of the above two cases, the predicted crease lines of the box seem to be reasonable. The box deformation patterns predicted at 20 ms from the three methods are found to be quite similar although some small differences can be identified on the indentations located on the center top of the box.

Even with a hole, the pressure distribution is independent of sensor location, as previously discussed [40, 41]. The predicted pressure sensor responses obtained from the CPM and ALE methods are reasonable compared to that of test, graphed in Figure 14. However, the pressure response predicted by the CV/UP method is lower than those of the others after 8 ms. The existence of a hole seems to differentiate the prediction of the CV/UP method from those of the other two methods, the CPM and ALE methods. Unlike the above two benchmark tests, the variation of the four curves is greater in this benchmark test.

4. High Speed with a Left Hand Side Hole

The hole was created on the left hand side (LHS) of the box in this test. Since the front and side pressure sensors are located on the right hand side of the box, the LHS hole is far away from the two pressure sensors. The purpose of this benchmark test is to investigate the sensitivity of the pressure response to the hole location, as compared to the previous test with a hole on the RHS of the box. The impact speed for this test was 11.89 mph [5.32 mm/ms], very close to than that of the previous test, 11.81 mph [5.28 mm/ms].

The box deformation modes and the pressure sensor responses are compared and shown in Figures 15 and 16, respectively. Examining the test and simulation results obtained for this case, it can be concluded that the box deformation modes, the pressure sensor responses, and the air leakage obtained from the LHS hole case are all very similar to those of the RHS hole case. Similar to the case discussed above with a RHS hole, the CV/UP method predicts lower pressure response after 8 ms due to the presence of the LHS hole on the box. Also similar to the benchmark test with a RHS hole, the variation of the four curves obtained from this test is greater than those two benchmark tests without a hole.

II. Deformable Impactor

The four box tests were repeated using a deformable impactor to investigate the sensitivity of pressure response to different impactors. In addition, the four benchmark tests with the deformable impactor will allow any potential error that might be induced from the MDB model to be identified. The deformable impactor has the same width, 400 mm, as that of the rigid impactor and was cut directly from a FMVSS 214 MDB aluminum honeycomb face. The same finite element models, including the box structure as well as the gas and fluid dynamic models, used in the simulations with the rigid impactor were used in the simulations with the deformable impactor. The deformation modes of the steel box and the progression of the air leakage obtained from the simulations with the deformable impactor are very similar to those with the rigid impactor. To avoid repetition, only the pressure sensor responses are presented for the four box tests with the deformable impactor.

1. Low Speed without a Hole

The recorded impact speed for this test was 4.90 mph [2.19 mm/ms] while the target speed was 5 mph [2.24 mm/ms]. The predicted pressure sensor responses are compared to that of the test, as depicted in Figure 17. Similar to Figures 8 and 10 with the rigid impactor, the pressure sensor responses predicted from the three methods are quite accurate when compared to test results. The four curves shown in Figure 17 are very consistent, with very limited variation. The pressure sensor responses obtained with the deformable impactor are lower than those of the rigid impactor, shown in Figure 8. This is because the deformable impactor was able to absorb some of the impact energy, thus reducing the impact severity on the box.

2. High Speed without a Hole

With a target speed of 12 mph [5.36 mm/ms], the actual impact speed reached for this test was 12.01 mph [5.368 mm/ms]. The comparison of predicted pressure sensor responses with that of the test is shown in Figure 18. The predicted pressure sensor responses obtained from the three methods are very close to that of the test for the entire 30 ms simulation duration. The pressure sensor responses obtained from the deformable impactor are lower than those of the rigid impactor, shown in Figure 10. Again, this is because some of the impact energy was absorbed by the deformable impactor which led to lower impact severity of the box.

3. The impact speed recorded for this test was 11.87 mph [5.31 mm/ms] while the target speed was 12 mph [5.36 mm/ms]. Figure 19 compares the predicted pressure sensor responses with that of the test. Due to the deformable impactor used in this case, the pressure sensor responses predicted from simulations or recorded from test are lower than those of the rigid impactor, shown in Figure 14. The predicted pressure sensor responses obtained from the CPM and ALE methods are very similar to that of the test. As can be noticed, the predicted pressure obtained from the CV/UP method starts to deviate from those of the others after around 13 ms.

4. High Speed with a Left Hand Side Hole

Similar to the test with a RHS hole, the impact speed recorded for this test (with a LHS hole) was 11.86 mph [5.30 mm/ms]. The comparison of pressure sensor responses obtained from simulations and the test is shown in Figure 20. The predicted pressure sensor responses from the three methods seem to show more variation in this benchmark test. However, the overall predictions obtained from the CPM and ALE methods are still quite reasonable. Similar to all other benchmark cases with a hole on the box, the CV/UP method predicts lower pressure compared to the others. As can be noticed from the results of the above eight box benchmark tests, the pressure sensor responses obtained from the three methods are very consistent for the cases without any holes. When a hole existed on the box, the variation of the numerical results became more visible and the CV/UP method predicted lower pressure sensor responses. As expected from the assumption of uniform pressure, the CV/UP method allows the gas leakage to occur earlier which leads to slightly lower pressure predictions toward the end of simulations.

The computational performance among the three methods is summarized in Table 2 for the eight box impact benchmark tests. It can be concluded from the discussions conducted above that all the three methods predict accurately when there is no hole on the box. With a hole added to the box, no matter RHS or LHS, the CPM and ALE methods are able to provide accurate predictions while the CV/UP method predicts slightly lower pressure response after certain simulation time. As discussed previously [39, 40], the pressure distribution of the box is still quite uniform (except for the small area surrounding the hole) even with the existence of a hole. The uniform pressure distribution is due to the fact that the air can flow without any blockage inside the box during the impact. Even with the situation that the pressure is close to uniform, the pressure sensor responses predicted by the CV/UP method still deviate from those of the tests after certain simulation time. It can be concluded that the accuracy of the CV/UP method is affected by the existence of holes. With a hole on the box, the CV/UP method allows the air to leak at an earlier stage and/or a higher rate than that of the test.

From a computational efficiency point of view, the CV/UP method outperforms both the CPM and ALE methods. For the box impact benchmark tests, the CPM method requires 6 times the computational time needed for the CV/UP method. The ALE method is the least efficient among the three methods. The ALE method requires 104 times the computational time needed for the CV/UP method and 17 times the computational time needed for the CPM method. Similar to the piston compression test, the CV/UP method is the most user-friendly while the ALE is the least user-friendly among the three computational gas and fluid dynamic methods investigated. The CV/UP method does not require discretization of the air domain. The CPM method requires a proper particle number to be defined for the air to provide an accurate prediction. The ALE method not only requires the discretization of the air domain, but also the prediction is very sensitive to the Eulerian mesh created to model the air domain.

C. Vehicle Side Door Impact Tests

Production vehicle side doors shown in Figure 21 were used for the third group of benchmark tests. Figures 21a and 21b illustrate the test fixture designed for the door benchmark tests. To understand the sensitivity to opening, the glass weather strips were removed and some small holes on the door inner were kept open (unplugged) from one of the side doors, as shown in Figure 21b. The same rigid and deformable impactors used in the box benchmark tests were also adopted in the side door benchmark tests. The pressure sensors instrumented to record the pressure change at different locations of the door are marked in Figure 21c for the tests with the rigid impactor (four sensors, highlighted in green circles) and in Figure 21d for the tests with the deformable impactor (three sensors, highlighted in green circles). The third group of benchmark tests were conducted using the VIA sled dynamic test facility, same as the second group of benchmark tests. The test speeds chosen in this group of benchmark tests ranged from 13 mph [5.81 mm/ms] to 32 mph [15.65 mm/ms] to simulate different impact severities.

The finite element models developed for the side door impact tests are illustrated in Figure 22a, with window weather strips, and Figure 22b, without window weather strips. Many internal and external components such as glass guides, door beams, beltline reinforcements, motor, lock mechanism, brackets, hinges, local reinforcements, etc., are included in the door model as shown in Figure 22c. To be used in the simulations with the rigid impactor, Figure 22d shows the door model with four pressure sensors (highlighted in green blocks). Similarly, Figure 22e shows the door model with three pressure sensors (highlighted in green blocks) that were instrumented in the door impact tests with the deformable impactor. As can be seen in Figures 22d and 22e, the door was mounted on a rigid test fixture (dark gray colors) on the inner side of the door. The size of the elements adopted to mesh the door inner and door outer is approximately 10 mm by10 mm. Smaller elements were used to model smaller components, with a total of 47,048 shell elements used for the door structure and the test fixture. Also can be observed in Figures 22d and 22e, the locations of the pressure sensors (green elements) were modeled according to those of the tests as depicted in Figures 21c and 21d.

Rigid Impactor

Two doors with different openings were tested with the rigid impactor. The first one was the side door with the door trim and side mirror removed, as shown in Figure 21a, which is the baseline door for this research. In the baseline door, the holes that the door trim fastened to the door inner were plugged after the door trim was removed so that no air can escape through the door inner. In addition to the door trim and the side mirror, the glass weather strips were removed and some additional holes on the door inner were unplugged in the second test to simulate a door design with more opening, as depicted in Figure 21b. The target impact speed for the two tests was 32 mph [14.304 mm/ms].

1. High Speed with Baseline Door

The actual impact speed reached for the baseline door test was 31.4 mph [14.04 mm/ms]. The predicted deformation modes of the door obtained at 9 ms simulation time are shown in Figures 23c, 23d and 23g to compare with that of the post-test door shown in Figures 23a and 23b. The air leakages predicted by the CPM and ALE methods are presented in Figures 23d, 23e, and 23f. In this benchmark test, the lower door hem was found to be opened in the front portion (highlighted with green circle in Figure 23b) during a post-test inspection. As can be seen in Figures 23d, 23e, and 23f, concentrated air represented by the particles (CPM) and Eulerian elements (ALE) are leaking through the lower door hem opening in additional to the side mirror opening and window gap. The opening of the door hem was due to the deformation caused by the rigid impactor and the presence of the glass weather strip that limited the air leakage. The deformation modes predicted by the three methods are very similar, although small differences can be detected when examining closely.

The comparison of the four pressure sensor responses obtained from the simulation and the test is made for the first 15 ms, as presented in Figure 24, before the deceleration induced by the honeycomb block. The predictions of the pressure sensor responses obtained from the CPM and ALE methods are very close to those of the tests as shown in Figure 24. Not only the initial slopes, but also the peak values and the overall shapes of the pressure sensor responses correlate reasonably well with those of the tests. However, the CV/UP method predicts much lower pressure sensor responses. The predicted pressure response obtained from the CV/UP method starts to deviate from those of the test after only 2 to 3 ms. The pressure sensor response of the door benchmark test is very sensitive to sensor locations. The overall shapes of the pressure sensor responses are different among the four sensor locations as can be seen from Figure 24. Due to the assumption of uniform pressure and some openings in the baseline door, the CV/UP method is not able to distinguish the pressure difference among the four sensor locations.

2. High Speed with Additional Door Openings

The actual impact speed reached for this test was 31.5 mph [14.08 mm/ms], almost identical to that of the baseline door test. Figure 25 shows the door deformation modes obtained from the test (post-test) and simulations at 1) ms. The additional openings on the door in this benchmark test allowed more air to escape and the pressure to rise more slowly compared to those of the baseline case. This was proven through the CPM and ALE simulations conducted previously [39, 40]. As a result, the air leakage through the door hem was almost eliminated due to the fact that more air could escape more easily through the glass opening on the top of the window. The door deformation modes predicted by the three methods are very similar.

The comparison of pressure sensor responses for this benchmark test is shown in Figure 26 for the four sensor locations. Similar to the baseline simulation, the pressure sensor responses obtained from the CPM and ALE methods are close to those of the test. Due to the removal of the glass weather strips and with some additional holes on the door inner, the pressure sensor responses predicted from the simulations and recorded from the test are lower than those of the baseline. Again, the CV/UP method predicts much lower pressure sensor responses compared to those of the others. With more openings in this benchmark test, the pressure predictions of the CV/UP method at the four censor locations seem to be much lower than that of the baseline door with fewer openings.

Deformable Impactor

Three baseline doors were tested with the deformable impactor to study the sensitivity of pressure response to impactor type and impact speed. The three test speeds chosen were 32 mph [14.30 mm/ms], 24 mph [10.73 mm/ms] and 13 mph [5.81 mm/ms] and were designated as high, medium, and low speeds in this research. The door deformation mode and the air flow discussed previously in the two rigid impactor tests are not discussed repeatedly for the three deformable impactor tests. The discussion focuses on the pressure sensor responses and pressure distributions for the three door benchmark tests with deformable impactor.

1. High Speed with Baseline Door

The impact speed reached for this high speed test was 32.5 mph [14.53 mm/ms]. The pressure sensor responses recorded for the three pressure sensors are quite different in terms of the overall shape, as depicted in Figure 27 for the high speed impact test. The same phenomenon was also found in the two doors tested with the rigid impactor. As a result, it can be concluded that the sensitivity of the pressure response to the sensor location is more pronounced for the side door benchmark tests than for the box benchmark tests. The nonuniform pressure distribution can be understood by examining the predicted pressure contour obtained from the ALE method as shown in Figure 27d. The difference is due to the different structure designs between the vehicle door and the box. The vehicle door contains many internal components such as door beams, glass guides, motor, speaker, lock mechanism, brackets, local reinforcements, etc. On the contrary, the box is completely hollow inside. Therefore, the air inside the door cannot travel without obstruction as it can in the box. In addition, the different holes and geometry changes inside the door also affect the local air flow during impact. Inside the door in the areas where the surfaces are flat, the pressure responses seems to be lower than those of the areas where there are geometry changes such as indentations, protrusions, notches, and so on that the air can get trapped and produce higher pressure. These factors contribute to the different pressure sensor responses at different sensor locations of the door. As seen from Figure 27, the predicted pressure sensor responses obtained from the CPM and ALE methods correlate reasonably well with those of the test. The predicted pressure sensor responses obtained from the CV/UP method deviate from those of the test after 4 to 5 ms.

2. Medium Speed with Baseline Door

The pressure sensor responses obtained from the medium speed test and simulation are compared in Figures 28a, 28b, and 28c for the three sensor locations. The predicted pressure contour obtained from the ALE method is shown in Figure 28d to illustrate the pressure distribution in this impact condition. With the impact speed lowered to 24 mph [10.73 mm/ms] from 32 mph [14.30 mm/ms], the pressure sensor responses obtained from the medium speed test were expected to be lower when compared to those of the high speed impact. The phenomenon is predicted by the three methods when compared Figures 28a, 28b, and 28c to Figures 27a, 27b, and 28c respectively. The pressure contour shown in Figure 28d further confirms the phenomenon when compared to the pressure contour shown in Figure 27d. It is quite consistent to observe in Figure 27d again that the air can flow with higher velocity thus produces lower pressure in the areas where the surfaces are flat. On the contrary, the air can get trapped and produces higher pressure in the areas where there are geometry changes such as indentations, protrusions, notches, and so on. The phenomenon is due to conservation of energy and is also called "Bernoulli effect".

In this impact condition, the pressure peaks for all three sensor locations seem to be over predicted for the CPM and ALE methods and under predicted for the CV/UP method. It was suspected that test variation might have contributed to the discrepancy. However the pressure sensor responses prior to the peaks predicted by the CPM and ALE methods, critical from a sensor calibration point of view, match very well with those of the test. The pressure sensor responses obtained from the CV/UP method deviates from those of the tests after around 4 ms. Similar to other door benchmark tests, it is also noticed that the pressure sensor responses predicted by the ALE method fluctuate more significantly compared to those of the CPM and CV/UP methods.

3. Low Speed with Baseline Door

The impact speed was further reduced to 13 mph [5.81 mm/ms] in this low speed test condition. As expected, the pressure sensor responses were further reduced in the three sensor locations as well as the entire door, as shown in Figure 29. Again the overall shapes of the predicted pressure sensor responses obtained from the CPM and ALE methods for the three sensor locations look similar to those of the test. The slopes of the pressure sensor responses and the peak values, except for the front middle sensor location, reasonably match with those of the test for this low speed impact condition. Again, the pressure sensor responses predicted by the ALE fluctuate even more severely compared to those of the CPM and CV/UP methods. The CV/UP method predicts lower pressure sensor responses at all three sensor locations and the overall shapes, slopes, and peaks do not resemble those of the tests.

The computational performances for the three methods are compared in Table 3 for the door impact benchmark tests. Through the discussions conducted for the five door impact cases, the CPM and ALE methods reasonably predict the pressure sensor responses at different sensor locations. With openings on all door benchmark tests, the CV/UP method predicts lower pressure response for all cases. The pressure sensor responses predicted by the CV/UP method deviate from those of the tests after certain simulation time. With additional openings, the predictions of the CV/UP method deteriorate more significantly. Due to the door design with many internal components and holes and uneven surfaces on the door inner, the pressure sensor responses are location dependent. The CV/UP method cannot distinguish the different pressure sensor responses at different sensor locations even though the pressure sensor responses predicted by the CV/UP method have the least fluctuation. The pressure sensor responses predicted by the CPM method fluctuate very severely in the early stages of the research. After improvements made to the code to allow calculation of the pressure response with more particles, the fluctuations of the CPM prediction have been reduced significantly and seem to be better than those of the ALE method, as evident from the five door benchmark simulations.

From a computational efficiency point of view, the CV/UP method outperforms the CPM and ALE methods in every benchmark test. For the door impact benchmark tests, the ALE method requires 37 times the computation time needed for the CV/UP method. The CPM method is the least efficient among the three methods. The CPM method requires 211 times the computation time needed for the CV/UP method and 5.7 times the computation time needed for the ALE method. The high computation time needed for the CPM method is due to the initial air filling and more particles needed to capture the different pressure sensor responses at different sensor locations. If the total computation time for the CPM method could be reduced further, it would be more viable for the method to be adopted for full vehicle simulations.

Similar to all other benchmark simulations, the CV/UP method is the most user-friendly while the ALE is the least user-friendly. The CV/UP method does not require discretization of the air mesh for all benchmark cases. Although a very high particle number is needed for the CPM method in the door benchmark simulations, the particle number can be assigned or changed easily in the input deck without any discretization of the air domain. The ALE not only requires the discretization of the air domain, but also the prediction is very sensitive to the Eulerian mesh size. Fine meshes are required for the areas with narrow openings or small holes.

D. Full Vehicle Tests

The research was advanced into its final stage, full vehicle tests, after the positive results obtained from the above benchmark study. The full vehicle study included two major vehicle architectures, body-on-frame [42] and unitized [43] that are commonly used to design vehicles in the automotive industry. The entire full vehicle study, with different vehicle architectures, test conditions, and simulation methods (CV/UP, CPM, ALE) was too extensive to be included in this paper. The key challenges encountered in full vehicle study were far greater than those of the benchmark test study since they involved the accurate predictions of air leakage due to separations of various parts during the crash event as well as the involvement of more complex components, such as dummies, seat structures, seat foams, seat belts, side air bag, side air curtain, and so on.

Depending on the crash severity of the different side impact tests, the plastic water shield attached to the door inner, rubber weather strips surrounding the window glass, speak connected to the door inner, and door hem can separate differently and allow the air to leak as the crash progresses. The pressure sensor responses cannot be predicted accurately without the air leakage being captured accurately in the simulations. A method to capture the air leakage was of the most critical tasks during the full vehicle study and took quite an effort to develop, adjust, and validate. The enhancements of the computational gas and fluid methods made during the benchmark study were found to be insufficient for the full vehicle study. Additional improvements, such as speedup of initial air filling, pressure response measurement, reduction of pressure fluctuation, adjustment of air leakage, and so on, were made during the full vehicle study which took more than two years to complete, including a pilot phase to predict the pressure sensor responses of two vehicle programs prior to their prototype tests.

To demonstrate the capability to predict pressure sensor responses in full vehicle tests only unitized vehicles with ALE method were selected and presented in this paper. A total of four tests, including two body styles (vehicle A and vehicle B) with different powertrains, drivetrains, test modes, and impact speeds, were discussed in the following. The first three tests, including an oblique pole side impact, a IIHS side MDB, and a LINCAP test, were utilized in the development of simulation methodology for pressure sensor prediction in full vehicle tests while the fourth test, a FMVSS 214 test, was adopted to predict the pressure sensor response directly and validate the developed simulation methodology.

The finite element model created for vehicle A has 2,802,411 nodes, 2,489,496 shells, 856,540 solids, and 99,900 beams. The vehicle B model contains 2,663,605 nodes, 2,399,069 shells, 857,738 solids, and 92,190 beams. Three side impact modes, oblique pole side impact, IIHS side MDB, and FMVSS 214 MDB, were investigated in this study. The finite element models of SID-IIs and ES-2re dummies, required in different side impact simulations, were included in the full vehicle models, as shown in Figures 30a and 30b. Illustrated in Figures 31a, 31b, and 31c, the oblique pole model (127 mm radius) has 24,080 nodes and 24,000 shells while the IIHS MDB model (mass 1500 kg, 379 mm above ground, 759 mm height, 1676 mm width, 90 degree) has 142,793 nodes, 38,501 shells, 94,048 solids, and 22 beams. The FMVSS 214 MDB (mass 1368 kg, 279 mm above ground, 559 mm height, 1676 mm width, 27 degree crab angle) was modeled with 238,130 nodes, 487,428 shells, 108,788 solids, and 20 beams. As depicted in Figures 31b and 31c, solid elements were used to model the honeycomb materials (bumper and main blocks) in the IIHS MDB while shell elements were used to model the FMVSS 214 MDB main honeycomb block.

1. Oblique Pole Side Impact--Vehicle A (10 MPH/4.47 mm/ms)

The vehicle chosen for the oblique pole side impact condition was vehicle A with FWD, a 2.0L EcoBoost engine, and a SID-IIs. The weight distribution of the vehicle was 2,383 lbs [1,082.73 kg] in the front axle and 1,730 lbs [786.36 kg] in the rear axle. It should be noticed that the impact speed for a regular oblique pole test is 20 mph [8.94 mm/ms]. In this test, the impact speed was 10 mph [4.47 mm/ms] in which the pressure sensor responses were used to develop restraint deployment algorithm.

The vehicle impacted the oblique pole on the passenger side in the physical test. Because the left and right front doors are symmetric; the simulation was conducted with the vehicle impacting the oblique pole on the driver side, as depicted in Figure 32a and 32b. Due to the lower impact speed at 10 mph [4.47 mm/ms], the deformation of the door at 15 ms is quite mild as observed in Figures 32a and 32c. As a result, the air leakage surrounding the door is also very limited as predicted in Figure 32d.

The pressure sensor response obtained from the simulation is compared to that of the test and shown in Figure 32e. The numerical fluctuations are visible throughout the entire simulation. The numerical fluctuations are more predominant in low speed impact simulations, due to the overall lower pressure magnitudes. The correlation of the pressure sensor responses between the simulation and the test is reasonable as can be seen from Figure 32e.

2. IIHS Side MDB--Vehicle B (31 MPH/13.86 mm/ms)

The second test selected was an IIHS side MDB test and the test vehicle was vehicle B with a 2.0L HEV powertrain and a CVT drivetrain. The front axle weight was 2,460 lbs [1,118.18 kg] and the rear axle weight was 1,863 lbs [846.82 kg] with SID-IIs dummies in the front row and the second row seats. The deformation of overall vehicle structure predicted from simulation at 10 ms is compared to that of the physical test as shown in Figures 33a and33b. The door deformation obtained from the simulation at 10 ms cannot be compared to the test but is presented in Figure 33c since it affects the pressure sensor responses. The comparison of pressure sensor responses between the simulation and test is made in Figure 33d for the first 10 ms simulation time which was needed for development of restraint deployment algorithm.

Comparing the pressure sensor responses between the simulation and test, the first peak was captured reasonably, as depicted in Figure 33 d. Due to higher impact speed at 31 mph [13.86 mm/ms], the first pressure peak, around 1.18 bar, obtained from this test is higher than that of the oblique pole test (about 1.1 bar) discussed previously. The MDB bumper block impacted the door outer and produced the first pressure peak before 10 ms. Due to the higher impact speed and more aggressive MDB design, representing a truck front end, the air leakage caused in this test condition is expected to be more severe than that of the pervious test. The progression of air leakage obtained from the simulation is illustrated in Figures 33e to 33l. As can be seen from the simulation, the majority of the air leakage seems to occur from the location of glass weather strips at beltline. Some air leakage also appears in the lower portion of the door due to the separation of plastic water shield attached to the door inner. Comparing the air leakage between this test (Figure 33h) and the previous test (Figure 32d) at 15 ms, it is confirmed that the air leakage is more severe in this test condition. It is also noticed from Figure 33f that the air leakage (red circle) starts at about 5 ms and gets more and more extensive as the crash advances. After 25 ms, the door outer and door inner contact each other at roughly the MDB bumper block left edge area where the air gets squeezed out (green circle) as can be seen in Figures 32j, 32k, and 321.

The progressions of air leakage along with door deformation for 10 ms, 17 ms, and 35 ms are presented in Figures 33m, 33n, and 33o, respectively. As can be seen that the door deformation is not only caused by the impact of MDB from outside of the door but also by resistances of the dummy, seat structures, seat foams, and side airbag from inside of the door. The finite elements models of the dummy, seat structures, seat foams, side airbag, and seatbelt are recommended to be included in the IIHS MDB side impact simulations since their contributions to the door deformation, pressure sensor responses and overall structural responses are quite significant.

3. FMVSS 214 MDB - Vehicle B (38.5 MPH/17.21 mm/ms)

The vehicle selected for the LINCAP test was vehicle B, which was a FWD vehicle and was equipped with a 3.7L V6 engine. With the two dummies, the front axle weight was 2,425 lbs [1,102.27 kg] and the rear axle weight was 1,815 lbs [825 kg]. Figure 34 compares the vehicle structural deformations and the pressure sensor responses between the simulation and test. The deformation of overall vehicle structure predicted from simulation at 10 ms is compared to that of the physical test as depicted in Figures 34a and 34b. Due to the high impact speed at 38.5 mph [17.21 mm/ms], deformations are more extensive and can be found on the door outer, inner, and interior door trims. The deformation of the front door at 10 ms, as presented in Figure 34c with wider deformation, is clearly more severe than that of the IIHS MDB side impact shown in Figure 33c.

Comparing the pressure sensor responses between the simulation and test, the correlation for the entire 30 ms duration is reasonable, as can be seen in Figure 34d. The prediction of the first 15 ms is more accurate than that of the second 15 ms which is affected by the air leakage. The impact of the MDB bumper block on the door created the first pressure peaks before 10 ms at around 1.2 bar which is the highest among the three full vehicle tests discussed so far. The second pressure peak (between 10 ms to 15 ms) was caused by the additional resistant forces from the dummy, seat structures, seat foams, and side airbag, as evidenced by examining the interior the vehicle, illustrated in Figure 34e. As mentioned previously, the finite elements models of the dummy, seat structures, seat foams, side airbag, and seatbelt are also recommended to be included in the LINCAP simulations due to their contributions to the door deformation, pressure sensor responses, and overall structural responses.

It is expected that significant air leakage would occur in this test condition due to the high velocity, the MDB impact location of the door, and the shape of the MDB. The progressions of air leakage obtained from the simulation are illustrated in Figures 34f to 34m. As can be observed from the simulation results, the air leakage occurs at the glass weather strip area between the door outer and inner at beltline as well as from the lower portion of the door. Post-test photos and film review, shown in Figures 34q and 34r, confirm that the glass weather strip did get pushed out and detached from the beltline due to the high door pressure produced in the crash event.

Comparing the air leakage (Figures 34f to 34m) obtained from this simulation with those of the oblique pole (Figure 32d) and IIHS side MDB (Figure 33e to 33l), it can be seen clearly that the air leakage for the LINCAP test is the most severe one among the three test conditions. The air leakage for the LINCAP test occurs not only earlier but also more extensively than the other two tests. Figure 34g suggests that the air leakage (red circle) occurs before 5 ms. Shown in Figures 34i at 15 ms, the door outer and door inner contact each other at the lower portion of the door due to the push of the MDB bumper block from outside of the vehicle and the resistances of the seat, side air bag and dummy from inside the vehicle. The forces exerting on both sides of the door result in the air in the area being squeezed out (green circle). The door outer and inner contact area grows larger and larger as can be observed in Figures 34j at 20 ms and Figure 34k at 25 ms respectively. Examining Figures 34l and 34m, it is found that a second contact area (yellow circle) is formed before 30 ms due to the additional impact of the MDB main block from outside of the vehicle and the continuous resistances of the seat, side air bag and dummy from inside of the vehicle.

Similar to the IIHS side MDB simulation, the results obtained from this simulation indicate that the air leakage cannot be ignored in the LINCAP simulations if the goal is to predict pressure sensor responses for restraint deployment analysis. The air leakage through the glass weather strip area is already very visible at 5 ms. Without considering air leakage in simulations, the predicted pressure sensor responses would be higher than those of the physical tests.

The progressions of the air leakage and door deformation are presented in Figures 34n, 34o, and 34p for 10 ms, 17 ms, and 35 ms, respectively. It can be seen that the door deformation patterns obtained for this test condition are more severe than those of the IIHS side MDB test shown in Figures 33m, 33n and 33o at the corresponding time frame. The more severe door deformation and more extensive air leakage explain why the pressure sensor response in the LINCAP test is higher than the IIHS side MDB test.

4. FMVSS 214 MDB - Vehicle A (23 MPH/10.28 mm/ms)

This test was not originally planned for inclusion in the full vehicle study, but was added at the end of study because it was a deployment-threshold development test and would offer an opportunity to replace test data with simulation results. The test vehicle was vehicle A with FWD and a 2.5L iVCT engine. The front axle weight was 2,168 lbs [985.45 kg] and the rear axle weight 1,657 lbs [753.18 kg] with two dummies included. This test also provided an opportunity to validate the vehicle simulation methodology developed in this study. Examining the vehicle configuration and the test condition, two FMVSS 214 full vehicle models that had been correlated to a 38.5 mph [17.21 mm/ms] and a 10 mph [4.47 mm/ms] tests were chosen to predict the 23 mph [10.28 mm/ms] test directly without any modification. The two full vehicle models are slightly different in terms of the total vehicle weight, mass distribution, and air leakage parameters due to the fact that they correlated to two different test conditions.

The vehicle structural deformations and the pressure sensor responses predicted from the simulations and obtained from the test are compared in Figure 35. The vehicle and door deformations (Figures 35a, 35b, and 35c) are compared at 10 ms since the pressure peak occurs at around 7 ms. The air leakage surrounding the door at 10 ms is shown in Figure 35d. Since the progression of air leakage has been presented and discussed in details for the IIHS side MDB and LINCAP tests at 31 mph [13.86 mm/ms] and 38.5 mph [17.21 mm/ms] respectively, it is not repeated again in this test condition. As expected, the door deformation (Figure 35c) in terms of volume change is less severe compared to those of the higher speed tests, IIHS side MDB (Figure 33c) and LINCAP (Figure 34c), but more severe than the one obtained from the low speed oblique pole side impact test (Figure 32c).

The pressure sensor responses obtained from the test and two predictions are compared in Figure 35e. The prediction obtained from the high speed model (38.5 mph/17.21 mmms) is shown in green while the low high speed model (10 mph/4.447 mm/ms) is shown in blue. As can be seen, the predictions obtained from the two models are very close to that of the test shown in red. The overall pressure response predicted for this test at 23 mph [10.28 mm/ms] is lower than that of the one discussed previously for LINCAP test at 38.5 mph [17.21 mm/ms]. The predicted pressure sensor responses were provided to the pressure sensor supplier for restraint deployment time analysis. It was confirmed that replacing the test data with the predicted results would result in the same restraint deployment algorithm. The prediction obtained for the test validated the vehicle simulation methodology developed in the full vehicle study.

Table 4 summarizes the finite element model size needed to represent the air and structures, numerical stability, prediction accuracy, and computational time required for the three full vehicle side impact modes, including the oblique pole, IIHS side MDB, and FMVSS 214. As can be seen in the table, about 2.1 million Eulerian elements are required to model the air inside and surrounding the front side door. The Lagrangian elements used to model a unitized vehicle in this research are around 3.4 to 3.9 million. The IIHS side and LINCAP models are slightly larger than the side pole model due to the IIHS and LINCAP MDB carts which require more solid, shell and beam elements to represent.

With 32 MPP processors, a typical side pole simulation would take eleven hours to finish while IIHS side and LINCAP side would take fifteen hours and nine hours respectively. The computational time depends on the model size, initial model quality, and the complexity of the restraint systems (such as seatbelts with pre-tensioners, folded side air bags and side air curtains) as well as the time step encountered in the simulation. For example, the side pole model may have smaller overall model size. However, the more severe and concentrated deformation induced by the side pole may trigger smaller time steps and require longer computation time in some cases. In this study, the IIHS side impact simulations took longer time to complete than those of the oblique pole and LINCAP simulations. The longest simulation time was attributed to not only the more concentrated vehicle deformation in the IIHS side impact simulations but also the severe interactions among the dummy, door trim, seatbelt, seat, side airbag, side air curtain, and the Eulerian elements. The LINCAP test caused the most severe door deformation and the highest door pressure peak among the three side impact test modes studied but the deformation was not as concentrated and localized as those of the oblique and IIHS side impact modes. As a result, the computational time required for the LINCAP simulation was the shortest.

It was experienced several times during the full vehicle study that the IIHS side impact simulations actually terminated around 10 to 15 ms after the numerical instability started. Luckily, the simulation results obtained before termination were still very useful since the main information required to develop the restraint deployment algorithm was the first 10 ms. Among the three side impact modes studied, it can be concluded that the LINCAP was the most stable one while the IIHS side being the least stable one from the numerical stability perspective. In terms of prediction accuracy, the predictions of the side pressure sensor responses obtained from the three side impact modes were all reasonable as presented previously.

CONCLUSIONS

A total of fifteen component benchmark tests and four full vehicle tests were simulated and presented in this paper to investigate the feasibility of adopting three computational gas and fluid dynamic methods for side crash pressure sensor applications. The fifteen benchmark tests included two tests with piston compression, eight tests with steel box impacts, and five impact tests using vehicle side doors. To understand the pressure sensor responses, different factors including gas type, structure design, sensor location, hole location, hole size, impact speed, and impactor type were considered in the benchmark tests. For the full vehicle tests, two vehicle body styles with different powertrains, drivetrains, test modes, and impact speeds, were chosen and simulated. From the fifteen benchmark tests and four full vehicle tests investigated, the following can be concluded.

A. Benchmark Tests

1. Sensor [c]tivity

The sensitivity of pressure response to the sensor location is minimal for the piston compression and the box impact benchmark tests. The small hole size, lack of internal components, and smooth box geometry made the pressure distribution rather uniform. However, the pressure sensor responses are very sensitive to the sensor locations for the side door benchmark tests. In addition to the peak value and the slope, the overall shape of the pressure response is different among the different sensor locations for all side door benchmark tests. The CPM and ALE methods are able to predict the pressure sensor responses that are location sensitive. The CV/UP method assuming uniform pressure is not able to distinguish the pressure sensor responses that are location dependent.

2. Hole Location and Size Sensitivity

Although the pressure response was found to be insensitive to the location of the hole in the box benchmark tests, the pressure sensor responses of the box benchmark tests were reduced when a hole was added. For the door tests, the pressure sensor responses are found to be very different between the two doors with different openings. The CPM and ALE methods are able to predict the pressure sensor responses with different hole locations and/or different openings. With openings or holes existing in a system, the predictions of pressure sensor responses obtained from the CV/UP method deviate from those of the tests after certain simulation time. The prediction of the UP method deteriorates when the opening in the system increases.

3. Speed Sensitivity

Different impact speeds were chosen in the box and side door benchmark tests. The pressure sensor response was found to be sensitive to the impact speeds for both the box and side door benchmark tests. Higher impact speeds result in higher pressure sensor responses. The three methods are able to predict the sensitivity of pressure response to impact speed. However, the fluctuation of the pressure sensor responses obtained for the CPM and ALE methods are magnified relatively for the low speed impact conditions due the overall smaller pressure magnitudes.

4. Impactor Type Sensitivity

With the same impact speed and structure design, the pressure response is higher for the test with the rigid impactor and lower with the MDB impactor. The MDB impactors absorbed some impact energy during the tests thus the pressure sensor responses were reduced. The CPM and ALE methods are able to predict the pressure sensor responses with different impactors. The CV/UP method can also predict the pressure sensor responses reasonably with different impactors when there is no large opening.

5. Particle Number and Eulerian Mesh Sensitivity

The number of particles plays a very important role in the simulations of CPM method while the ALE method is very sensitive to the Eulerian mesh as reported in [40, 41]. More particles and a more refined mesh provided better predictions for the CPM and ALE methods. However, the computation time is dependent on the particle number and the Eulerian mesh size. The numerical accuracy and the computational efficiency need to be optimized when considering the appropriate particle number or Eulerian mesh. The CV/UP method does not require discretization of the air mesh and is the most user-friendly and computational efficient method among the three computational gas and fluid dynamic methods investigated.

B. Full Vehicle Tests

1. Computational Time

The computational time depends on initial model quality, the model size, and the time step encountered in the simulation. Among the three side impact modes studied, the oblique pole and IIHS side impact modes create more concentrated and/or localized deformation on the vehicle door structures as well as more intensive interactions between the dummy and its restraint systems. Although the LINCAP test creates the most severe deformation on the door structure in terms of volume change but is usually more uniform and occurs at the lower portion of the door which has less impact on the dummy. In general, the IIHS side impact simulation takes the longest time to complete while the LINCAP simulation takes the shortest time among the three side impact modes investigated.

2. Numerical Stability

The numerical stability is influenced by several factors such as the deformation of shell elements used in the sheet metals and plastic components, seatbelt modeling with pre-tensioner, the deformation of solid elements used to represent the dummies and seat foam structures, the deformation of Eulerian elements adopted to model the air inside and outside the door structures as well as the initial mesh quality of the entire finite element model. Based on the results obtained from this study, the IIHS side impact simulation is the least stable and the LINCAP simulation is the most stable among the three side impact modes chosen. Even with early terminations in the oblique pole and IIHS simulations, the results obtained before termination are still sufficient for the development of restraint deployment algorithm.

3. Prediction Accuracy

The predictions of the side pressure sensor responses obtained from the three side impact test modes are all reasonable as presented by using the ALE method. The key point is that the air leakage needs to calibrated first based on some existing tests. As demonstrated in this paper that well calibrated models can be used to predict pressure sensor responses directly and reduce prototype vehicle testing. The inclusion of air inside the door structure not only is needed for pressure sensor response prediction but also helps to improve the overall side impact simulation quality. In addition to the inclusion of air in the door structure, the dummies, seat structures, seat foams door trims, side airbag, side air curtain as well as the seatbelts, also play very important roles in the prediction accuracy of the side impact simulations.

SUMMARY

The CV/UP method was investigated in this research and the predictions were compared to those of the CPM and ALE methods to understand the advantages and limitations of the three computational gas and fluid dynamic methods for the side crash pressure sensor predictions. The fifteen benchmark tests representing different side crash conditions, reported in [40, 41], were adopted in this study for the comparison of computational performances among the three computational gas and fluid dynamic methods.

For almost all fifteen benchmark cases, the pressure sensor responses predicted by the CPM and ALE methods correlate reasonably well with those of the tests. The CV/UP method accurately predicts the benchmark tests without large holes or opening. With existing of large holes or opening in a system, the pressure sensor responses predicted by the CV/UP method are lower and deviate from those of the tests. The prediction of the CV/UP method deteriorates when the hole or opening increases. From a computational efficiency perspective, the CV/UP method consumes the least amount of computation time for all benchmark tests. The CPM method outperforms the ALE method in the piston compression and box impact benchmark tests. However, the CPM method needs initial air filling and a large amount of particles in the door benchmark tests and is not as efficient as the ALE method. Regarding user-friendliness, the CV/UP method does not require discretization of the air domain and is the best among the three computational gas and fluid dynamic methods. The CPM method does not need discretization of the air domain but the number of the particles needs to be optimized through sensitivity studies. The ALE method requires discretization of the air domain thus is the least user-friendly among the three methods. The prediction of the ALE method is very sensitive to the Eulerian mesh. Refined mesh is needed for the areas with tiny component, narrow opening or small hole.

In general, the CV/UP method is the best method, among the three methods investigated, to predict the pressure sensor responses for systems without opening and the local pressure sensor responses were not location dependent (i.e. local response is similar to the global response). The ALE method is best suited for applications in which the pressure sensor responses are location sensitive and the openings are not too small. For applications with small holes existed in the systems, the CPM method is the best choice since the particles can leak through the small holes easily. If the initial air filling time can be shortened and the fluctuation of response can be reduced further without using large particle numbers, the CPM method will be the best method for all different applications.

For full vehicle simulations, only ALE method was presented in this paper. As discussed in details, the method can be used to predict the pressure sensor responses for all side impact modes, including the oblique pole, IIHS side MDB, and LINCAP. It was also demonstrated that once the air leakage is calibrated, the full vehicle model can be used to predict the pressure sensor responses and reduce prototype testing. It was also found that the inclusion of air in the door structure improved not only the prediction of door deformation but also the overall side impact simulation quality. Without the inclusion of air inside the door, the door structure would behave softer than the physical one during the impact event. In addition, the finite elements models of the dummies, seat structures, seat foams, door trims, side airbag, side air curtain as well as the seatbelts, are also recommended to be included in the side simulations due to their contributions to the door deformation, pressure sensor responses, and overall vehicle structural responses.

The main objective of this research was to identify the most appropriate methods to predict pressure sensor responses and to enable computer simulations for the development of restraint deployment algorithms associated with the side crash pressure sensors. In an effort to help reduce prototype testing and improve the robustness of sensor algorithm development, fifteen benchmark tests and four full vehicle tests were carefully designed and rigorously simulated. The advantages and limitations of the three computational gas and fluid dynamic methods, CV/UP, CPM, and ALE, with respect to the prediction of pressure sensor responses were presented and discussed in details in this paper. In addition to the main objective, extensive enhancements and further developments were also made jointly with the code developers throughout the computational investigations during the three year of research period. Especially, the CPM method initially developed for inflator modeling and air bag systems without initial gases can now be applied to a broader range of SFI problems accurately and effectively in the automotive and/or aerospace industries in which the simulated systems have initial gases and complex structures.

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CONTACT INFORMATION

Dr. Tau Tyan

Global Safety Engineering 20901 Oakwood Blvd Dearborn, MI, 48124 USA ttyan@ford.com

ACKNOWLEDGMENTS

The authors would like to acknowledge our colleagues, Steven Kelly and Matt Maltarich at Ford Safety Innovation Laboratory for conducting the VIA sled crash tests. In addition, the support and encouragement provided by Wayne Bahr, previously Ford Global Safety Chief, for this project is greatly appreciated. Without their help, support, and encouragement, this research would be impossible.

DEFINITIONS/ABBREVIATIONS

CPM - (Corpuscular Particle Method)

ALE - (Arbitrary Lagrangian Eulerian)

S-ALE - (Structured ALE method)

UP - (Uniform Pressure)

CV - (Control Volume)

CFD - (Computational Fluid Dynamic)

SFI - (Structure Fluid Interaction)

CAE - (Computer Aided Engineering)

LSTC - (Livermore Software Technology Corporation)

KMT - (Kinetic Molecular Theory)

FMVSS - (Federal Motor Vehicle Safety Standard)

LINCAP - (Lateral Impact New Car Assessment Program)

CAD - (Computer Aided Design)

OOP - (Out Of Position)

MDB - (Moving Deformable Barrier)

RHS - (Right Hand Side)

LHS - (Left Hand Side)

ATM - (standard atmosphere, 101.3 KPa, or 1.013 bar)

P - (System pressure [Pa])

V - (System volume [[m.sup.3]])

n - (Number of molecules [mol], 1 mole = 6.0221415E+23 molecules)

T - (Absolute temperature [K, the Kelvin scale is a shifted Celsius scale, e.g. 0.0 K = -273.15 [degrees]C, the lowest possible temperature])

R - (Gas constant [J/kg K], e.g. universal gas constant [??] =8.3145 J/kg K)

Gamma - (heat capacity ratio, [GAMMA]=Cp/Cv=cp/cv, also known as adiabatic index, ratio of specific heats, Poisson constant, or isentropic expansion factor, 1< [GAMMA]< 5/3)

Cp - (heat capacity at constant pressure, the energy required to raise the temperature 1K of a gas, per mole, while the pressure is kept constant, J/mol K, dp=0, isobaric process)

Cv - (heat capacity at constant volume, the energy required to raise the temperature 1K of a gas, per mole, while the volume is kept constant, J/mol K, dv=0, isochoric process)

cp - (specific heat capacity at constant pressure, the energy required to raise the temperature 1K of a gas, per unit mass kg, while the pressure is kept constant, J/kg K, cp = Cp/m)

cv - (specific heat capacity at constant volume, the energy required to raise the temperature 1K of a gas, per unit mass kg, while the volume is kept constant, J/kg K, cv = Cv/m)

kg - (kilogram, 1000 gram)

mm - (millimeter, 0.001 meter)

ms - (millisecond, 0.001 second)

bar - (100 kPa, 100,000 N/m^2, 0.0001 KN/mm^2, or 0.987 atm)

MPP - (Massively Parallel Processing

FWD - (Front Wheel Drive)

HEV - (Hybrid Electric Vehicle)

CVT - (Continuously Variable Transmission)

SID-IIs - (Small Side Impact Dummy)

ES-2re - (2nd Generation Euro Side Impact Dummy; a 50th percentile adult male without lower arms)

Tau Tyan, Leonard Shaner, Matt Niesluchowski, and Nand Kochhar

Ford Motor Company

Dilip Bhalsod and Jason Wang

Livermore Software Technology Corp.

doi:10.4271/2017-01-0379
Table 1. Comparison of computation performance for the piston
compression test.

Method              CV/UP          CPM            ALE

Simulation          99%            99%            80%
Time                Compression    Compression    Compression
Air                 n/a            200,000        1.716M
Element #                          Particles      Eulerian
                                                  Elements
Computation         12000          12000          89010
Cycle
CPU#                4              4              32
(MPP)
Prediction          Accurate       Accurate       No So
Accuracy                                          Accurate
Elapsed Time        2s             53 m 36 s      2 h 38 m 46 s
                                                  (6.4531E+06)
(CPU                (1.3140E+01)   (1.5896E+04)   [491104/UP]
Seconds)
[Ratio]             [1/UP]         [1210/UP]      [406/CPM]
User-Friendliness   Easiest        2nd Easiest    3rd Easiest

Table 2. Comparison of computation preformance for the box impact test.

Method                CV/UP           CPM            ALE

Simulation            51 ms           51 ms          51 ms
Time
Air                   n/a             200,000        1.824 M
Element #                             Particles      Eulerian
                                                     Elements
Computation Cycle     33333           32978          32972
CPU# (MPP)            16              16             16
Prediction Accuracy   Accurate for    Accurate       Accurate
                      boxes without
                      holes. Not so
                      accurate for
                      boxes with
                      holes.
Elapsed Time          3 m21 s         20 m 31 s      5 h 49 m 25 s
                                                     (3.3442E+05)
(CPU Seconds)         (3.2060E+03)    (1.9491E+04)   [104/UP]
[Ratio]               [1/UP]          [6/UP]         [17/CPM]
User-Friendliness     Easiest         2nd Easiest    3rd Easiest

Table 3. Comparison of computational performance for the door impact
test.

Method              CV/UP          CPM               ALE

Simulation Time     15 ms          30ms              20 ms
                                   (with 15 ms
                                   for initial air
                                   filling)
Air Element #       n/a            2.2 M Particles   892,800
                                                     Eulerian
                                                     elements
Computation         33334          66667             44445
Cycle
CPU# (MPP)          16             16                16
Prediction          Not so         Accurate          Accurate
Accuracy            accurate                         (2.2 M
                                                     particles
                                                     needed to
                                                     smooth out
                                                     pressure
                                                     fluctuation)
Elapsed Time        4 m 16 s       2 h 38 m 46 s     15h7m1 s
(CPU                (4.1036E+03)   (1.5230E+05)      (8.6704E+05)
Seconds)            [1/UP]         [37/UP]           [211/UP]
[Ratio]                                              [5.7/ALE]
User-Friendliness   Easiest        2nd Easiest       3rd Easiest

Table 4. Comparison of computational performance for the side impact
simulations.

Impact Mode           Oblique Pole    IIHS Side      LINCAP

Simulation Time       35 ms (ALE)     35ms (ALE)     35 ms (ALE)
(Method)
Eulereian             2,125,240       2,125,240      2,125,240
Element #
Lagrangian            3,355,803       3,488,374      3,854,129
Element #
Computation Cycle         55556           55556          55556
CPU# (MPP)                   32              32             32
Numerical Stability   Medium          Low            High
Prediction            Reasonable      Reasonable     Reasonable
Accuracy
Elapsed Time          11 h 0 m 20 s   15h 2m 10s     9h 12 m 23 s
(CPU Seconds)         (39620 s)       (54130 s)      (33143 s)
[Ratio]               [1]             [1.366/Pole]   [0.837/Pole]
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Author:Tyan, Tau; Shaner, Leonard; Niesluchowski, Matt; Kochhar, Nand; Bhalsod, Dilip; Wang, Jason
Publication:SAE International Journal of Engines
Date:Apr 1, 2017
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