Hybrid Prediction of Fan Tonal Noise

Hybrid Prediction of Fan Tonal Noise A hybrid method is used to simulate the downstream rotor-vane interaction tonal noise associated with the NASA Source Diagnostic Test (SDT) 22-in fan rig. A 3-D, unsteady, Reynolds-averaged Navier-Stokes (URANS) CFD simulation is used to predict the un-steady surface pressure on the exit guide vanes (EGVs). The resulting downstream duct acoustics are then computed using two methods. The first is an analytical Green’s function method approximation for an infinite, fixed duct geometry. The second is a finite element model for a realistic duct geometry. One case from the SDT matrix is the main focus of this paper: approach condition for 22 rotor blades and 54 vanes. The configuration was designed for cutoff at the first blade-passing frequency. Comparison of the exhaust power level results for the 22x54 case reveal that the nonuniformity of the duct does not significantly influence the overall power level but it does cut-off the fifth radial mode and redistributes the energy between the other modes. The current acoustic simulation which models only the vane-wake interaction predicts an exhaust power approximately 13 dB lower than the experimental exhaust power. Nomenclature √ β = 1 − M2 ω Φnm c I k = ωrt /c ± knm M m n p, pnm rh , rt , r u x compressibility parameter radial frequency of disturbance annulus’ eigenfunction mean speed of sound acoustic intensity nondimensional acoustic wave number axial wave number (± upstream/downstream) Mach number radial mode number circumferential mode number pressure, complex amplitude of pressure for mode (n,m) radial location of rotor hub, tip, radial coordinate acoustic velocity in the axial direction axial coordinate 1 of 12 I. Introduction One source of fan noise is the interaction of rotor wake flow with downstream exit guide vanes (EGV). Many previous studies of fan noise have coupled cascade models that provide the unsteady response of the exit guide vanes to an acoustic duct calculation. The cascade calculations have varied from semianalytical approaches valid for two-dimensional, unloaded, flat-plate cascades,1 to flat-plate cascades used in conjunction with a strip theory,2, 3 to computational and asymptotic solutions of the linearized Euler equations for two-dimensional cascades with a real blade section geometry.4–8 The acoustic calculations have been based on Green’s method4, 9–11 and other semi-analytical methods.12, 13 In these simulations, the wake flow has been canonically modeled (e.g., [4, 5, 8]), empirically derived (e.g., [9]), and predicted using CFD simulations (e.g., [7]). Some of these methods were used to study tonal noise (e.g., [4, 11]) and others broadband noise (e.g., [7, 10]). Recently, researchers have integrated computational fluids simulations more fully into turbofan noise prediction by calculating the exit guide vane and/or duct sources via CFD.14–18 The results from the studies that integrate CFD simulations in order to generate the wake flow or compute directly the exit guide vane or duct noise sources show great promise. In addition to the development of turbofan noise simulations, experiments have been constructed to both study fan noise directly and to provide validation data for simulations.19–25 Data from NASA’s Source Diagnostic Test21–25 are used to validate the current simulations. Others who have validated their method against the SDT data include Nallasamy and Envia7 who studied broadband noise created by vane-wake interaction. In many ways, their simulation was the catalyst for this work, albeit only tonal noise is addressed in this research. The current simulation method extends Nallasamy and Envia’s method in three ways. First, a 3-D, unsteady, Reynolds-averaged Navier-Stokes CFD code is used to predict the fully coupled turbomachinery flow field as compared to using the average passage computational method. Second, the unsteady EGV pressure computed via the CFD is used as input to a duct acoustic calculation. Both the classical Green’s function method and a finite element method that can account for geometry variation are used. This paper focuses mainly on the simulation of one case from the SDT matrix. The fan configuration has 22 rotor blades and 54 EGVs and it is run at the approach condition. At this speed, the blade passing frequency is cut off. A second, cut-on, configuration with 26 exit guide vanes (EGVs) is currently being analyzed and some preliminary CFD results are included in this paper. The first section of the paper will describe briefly the computational methods that combine to provide the acoustic predictions. Then acoustic results from the 22 × 54 case are presented. The sensitivity of the simulations to inclusion of real duct effects are discussed. Finally, the preliminary results for the 22 × 26 case are presented. Here the focus is mainly on the comparison between the simulated vane unsteady surface pressure and the experimental data. II. CFD Method The flow field simulation has been performed using Phantom, a time-dependent, three-dimensional Reynolds-averaged Navier-Stokes solver for turbomachinery.26, 27 It uses an implicit, time-marching, finite difference scheme that is third-order accurate in space and second-order accurate in time. The inviscid fluxes are discretized using Roe’s scheme,28 and the viscous fluxes are calculated using standard central differences. Approximate-factorization is used along with dual time-stepping, which minimizes factorization errors. Large-scale unsteady phenomena such as tip vortices and wake interactions are resolved in the simulation, and small-scale turbulent structures are modeled using the Baldwin-Lomax algebraic turbulence model. One may think of this as decomposing the scales as shown in Eq. (1) φ = φ̃ + φ̂ + φ0 (1) where φ represents a time-varying quantity, φ̃ is it’s ensemble average at a fixed phase of the blade-passing frequency, φ̂ is deviation from φ̃ due to large-scale, non-random fluctuations such as vortex shedding, and φ0 is the random fluctuation. The solver uses O and H-type zonal grids to discretize the flow field and facilitate relative motion of the blades and vanes. The O-grids are body fitted to the surfaces of the blades and generated using an elliptic equation solution procedure. They give good resolution at the leading and trailing edges of the blades, and make it easy to apply the turbulence model. O-grids are also used in the tip-clearance region. Algebraically 2 of 12 generated H-grids are used to discretize the remainder of the flow field. Further details on the numerical procedure can be found in Ref. [26]. At the inlet, the total pressure, total temperature and the circumferential and radial flow angles are specified, and the upstream-running Riemann invariant is extrapolated from the interior of the computational domain. At the exit, the circumferential and radial velocity components, entropy, and the downstreamrunning Reimann invariant are extrapolated from the interior of the computational domain. The static pressure is specified at the mid-span of the exit of the domain, and the pressure values at all other radial locations are obtained by integrating the radial equilibrium equation. Periodicity is enforced along the outer boundaries of the H-grids in the circumferential direction. No-slip boundary conditions are enforced at the hub and tip end walls and along the airfoil surfaces. It is assumed that the normal derivative of the pressure is zero at the solid wall surfaces, and that the walls are adiabatic. The flow variables at zonal boundaries are explicitly updated after each time step by interpolating values from adjacent grids. Phantom has been extensively validated in the past on a wide variety of configurations.29–31 While prior comparisons of simulations using this turbomachinery code have all shown excellent agreement with experiment, this is the first time it is being used as part of an aeroacoustic simulation. III. Acoustic Method Two acoustic propagation methods are used and the results are compared. First, the duct is approximated as an infinite annular cylinder with uniform axial flow and the acoustic propagation is computed via Green’s method as described in Ref. [1]. The application of this semi-analytic method to the current simulation is described in more detail in Ref. [32]. This is referred to as the uniform duct case. Second, the variation in the duct cross-sectional area is modeled and the acoustic propagation is computed using an axisymmetric frequency domain finite element model (FEM).33 This is referred to as the nonuniform duct case. The input for the FEM simulation is obtained by using the semi-analytic method to propagate the vane surface pressure to duct modal amplitudes just downstream of the vane. Both methods are performed in the frequency domain and model the acoustic pressure at the source as an eigenfunction expansion such that p(x, r, θ, t) = ∞ X ∞ X ± pnm Φnm (r)e−i(kt−nθ−knm x) (2) n=−∞ m=−∞ The FEM models the non-uniform duct geometry and mean flow field and currently treats the termination as non-reflecting. The termination is described as non-reflecting because the duct is extended past the nominal termination as a uniform duct and the process of radiation to the far field and the resulting termination impedance is not modeled. Reflections that occur due to duct non-uniformities are included. An irrotational formulation is used in which mean flow and acoustic particle velocity perturbations are represented by a mean flow potential and acoustic particle velocity potential. A separate FEM code generates the mean flow using a weak formulation. For the propagation code the mean flow field is compressible and an iterative process is used in which a succession of incompressible calculations converge to the compressible solution. The acoustic solution is based on a weak form of the method of weighted residuals in which the acoustic continuity equation is cast in a potential formulation. Acoustic pressure is obtained by postprocessing the acoustic potential solution using the acoustic momentum equation. In the present case the duct walls are acoustically hard so that only the natural boundary condition is required. The acoustic source is modeled at a nominally uniform section of duct in terms of duct modes. On the source plane the acoustic field is expanded in terms of a finite number of incident modes with specified amplitudes plus an equal number of reflected modes with amplitudes determined by the solution of the problem. The termination is represented by a like number of transmitted modes in a short uniform duct extension of the geometry. No reflected modes are present providing the reflection free boundary condition. IV. Results for the 22 × 54 case. The off-design operating point simulated for the 22 × 54 geometry matched the approach condition in the SDT. This will be called Case 1. The flow conditions were provided in the form of a solution file from a similar simulation performed by NASA Glenn using APNASA. A corrected fan speed of 7808 RPM was used with a corrected mass flow of 58.01 lbm/s. 3 of 12 420 400 400 380 380 380 360 340 320 300 axial velocity, ft/s 420 400 axial velocity, ft/s axial velocity, ft/s 420 360 340 320 300 experiment current simulation APNASA simulation 280 260 0 0.2 0.4 0.6 passage fraction 0.8 280 1 260 0 (a) 10% span 360 340 320 300 experiment current simulation APNASA simulation 0.2 experiment current simulation APNASA simulation 280 0.4 0.6 passage fraction 0.8 1 260 0 (b) 50 % span 0.2 0.4 0.6 passage fraction 0.8 1 (c) 90 % span Figure 1. Axial wake profile 1/2 rotor chord downstream of rotor trailing edge. To increase the computational speed, a 2 on 5 scaling was used as an approximation to the 22 rotor blades and 54 EGVs with the EGV geometry scaled by 54/55 to maintain the correct blockage. The actual tip clearance from the experiment was not available, so a value of 1% span was assumed. Details of the grid which consists of O- and H-grids for the rotor and EGVs and moving rotor grids are given in the appendix and also in Ref. [32]. The computations were first validated via comparison with available LDV velocity measurements. There are 101 grid points in the circumferential direction, resulting in approximately 14 grid points resolving the rotor wake mid-way between the rotor trailing edge and vane leading edge. The axial wake profiles 3.125 inches from the rotor trailing edge (1/5th the distance between the rotor trailing edge and vane leading edge) at 10%, 50%, and 90% span are shown in figure 1. The plots compare the current simulation with both the experimental data and the APNASA simulation. The two simulations tend to over-predict or under-predict the wake deficit in different locations and both seem quite reasonable. 1.12 0.05 BPF 0.045 1.1 0.04 0.035 1.08 2 BPF p/ps p/ps 0.03 1.06 0.025 0.02 1.04 0.015 0.01 1.02 0.005 1 0 0.002 0.004 0.006 time, s 0.008 0.01 0 0 0.012 (a) pressure vs. time 1000 2000 3000 4000 frequency, Hz 5000 6000 (b) pressure vs. frequency Figure 2. Nondimensional pressure at a point near the suction side leading edge of the EGV midspan. The surface pressure on one of the five EGVs has been recorded from the CFD solution. For the acoustic simulation, it is assumed that all of the EGVs have the same pressure adjusted by the inter-vane phase angle. Figure 2 shows the time trace over 30 blade passings of the surface pressure on the representative vane for a point located at mid-span on the suction surface near the leading edge. The pressure is normalized by the upstream static pressure, ps . The corresponding FFT is also shown in figure 2. For Case 1, the blade passing frequency of 2863 Hz is cut off in the duct and 2 BPF, 5726 Hz, is cut-on. The average Mach number of the flow downstream of the EGV calculated by the CFD simulation is 0.334. The acoustic simulation was set to match the experimental system and has 54 EGVs. The circumferential interaction mode of interest is thus n = −10. The real part of the nondimensional surface pressure at 4 of 12 the first and second blade passing frequencies is shown in figure 3. The real and imaginary parts of the nondimensional unsteady pressure along the midspan at 1BPF and 2BPF are shown in figure 4. The (a) 1 BPF (b) 2 BPF Figure 3. Real part of the nondimensional unsteady pressure on the EGV. −3 x 10 −3 5 Real:pres surf Imag:pres surf Real:suc surf Imag:suc surf 8 6 3 2 2 1 p/ps p/ps Real:pres surf Imag:pres surf Real:suc surf Imag:suc surf 4 4 0 0 −2 −1 −4 −2 −3 −6 −4 −8 0.68 x 10 0.7 0.72 0.74 x/a 0.76 0.78 −5 0.68 0.8 (a) 1 BPF 0.7 0.72 0.74 x/a 0.76 0.78 0.8 (b) 2 BPF Figure 4. Nondimensional unsteady pressure along the midspan of the EGV. surface pressures shown here differ from the results reported in Ref. [32] which were obtained using only 6 blade passings in the FFT from much earlier in the CFD simulation when transients waves were large. For the results reported in this paper 30 blade passing events have been used to obtain the pressure spectrum and the transient has greatly decayed. First the semianalytical Green’s method was employed to simulate the downstream acoustics produced by the vane-wake interaction. A uniform duct, as depicted in figure 5 with hub-to-tip radius of 0.4814 (matching the duct dimensions at the leading edge of the EGV) was used. For this cross-section geometry, the associated nondimensional acoustic wave number is k = 29.4. When the duct area is not changing, the power in each mode at every cross-section is identical. Table 2 shows the resulting power in each radial mode as well as the total power for the n = −10 circumferential mode. 5 of 12 1 When the FEM is used to compute the downstream acoustics, the input modal amplitudes are specified from the semianalytical method at the location in the duct just downstream of the trailing edge of the EGV where the hub-to-tip radius is 0.5274. The modal amplitudes are listed in Table 1 and are normalized such that the associated radial eigenfunction has a maximum of 1.0. At the input location for the FEM, the outer radius differs from that used in the semianalytic duct calculation. Therefore, the reduced frequency is renormalized to 29.049 for the FEM simulations. However, there is still a slight mismatch between the geometry used to compute the input modal amplitudes and the geometry Figure 5. Flowpath of the experimental rig at the FEM input location. Table 2 summarizes the acoustic power computed by the with uniform flowpath for the semianalytical method (dashed line) superposed. FEM for both the uniform (assuming a slightly smaller annulus than used in the semianalytic calculation) and the nonuniform ducts. For the nonuniform duct, power in the incident reflected, and transmitted modes are reported. The total power is also shown in each category. Visualizations of the acoustic field in the uniform and Table 1. Modal amplitudes for first 5 ranonuniform ducts are shown in figure 6. The plots depict dial modes at n = -10. The modal amcontours of equal SPL scaled so that the highest level on plitudes are unscaled and have dimensions 2 the source plane in terms of acoustic pressure magnitude consistent with pressure (lbf /ft ). is set at 100 dB. Levels on the figure are therefore only Mode Amplitude relative and not consistent with the acoustic power reported in Table 2. Due to constructive and destructive 1st mode 2.9461e-02 + 5.5917e-02 i interference of the five input modes, the acoustic pres2nd mode -4.5807e-03− 1.8956e-02 i sure field is not highly organized and in fact the highest 3rd mode 8.624e-03 − 1.6624e-02 i SPL levels are not on the source plane. 4th mode 1.2784e-02 − 8.4086e-03 i For the uniform duct, the acoustic results from the 5th mode 6.0003e-03 − 9.7450e-03 i semianalytical and FEM simulations are in good agreement with differences arising from the difference in duct geometry between the two simulations. When one compares the results for the uniform and nonuniform simulations, the most notable difference is that the 5th radial mode is almost completely reflected by the nonuniform duct. Power is also scattered into the 1st radial mode at the expense of the 2nd and 3rd modes. However, the net transmitted power at the termination is only slightly less than the power in the incident modes. It is also clear that the acoustic power at the source is affected very little by the duct. This indicates that it is not necessary to account for the interaction of reflections due to duct nonuniformity with the vanes in this case. 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 Table 2. Modal power for first 5 radial modes at n = -10. 2 BPF. Mode 1st mode 2nd mode 3rd mode 4th mode 5th mode Total at exhaust Semianalytic 8.0816e-04 8.1885e-05 4.8143e-05 1.8121e-05 5.7432e-06 9.6205e-04 FEM uniform 8.0526e-04 8.3627e-05 3.8554e-05 1.7335e-05 2.8417e-06 9.4761e-04 Power (lbf ft/s) Input FEM Reflected FEM 8.0526e-04 -3.0685e-08 8.3627e-05 -1.9926e-08 3.8554e-05 -7.3669e-08 1.7335e-05 -1.5832e-07 2.8417e-06 -2.8289e-06 9.4761e-04 -4.1114e-06 Transmitted FEM 9.0033e-04 2.8532e-05 9.3533e-06 5.0751e-06 1.7793e-26 9.4329e-04 As part of the SDT, exhaust power levels were measured.25 A rotating rake gave an overall exhaust power level for the n = −10 mode of almost 115 dB (reference 10−12 Watts). The exhaust power level reconstructed from far-field measurements (that filtered out sound emanating from the inlet) was 105 dB.22 More faith is placed in the power levels obtained from the field measurements because of complexities in 6 of 12 (a) Uniform duct. (b) Nonuniform duct. Figure 6. Sound pressure level on cut through annular duct from source plane to exhaust plane. resolving modal information from the rakes which are affected by the mean flow velocity gradient in the annulus. The simulated exhaust power level varied from 90.6 to 93.4 dB when the simulation was run with variations in the inputparameters and input data. For instance, we analyzed the effect of variation in the unsteady surface pressure due to the number of blade passings used to obtain the values at 2BPF, of slight errors in Mach number and reduced frequency, of the geometry mismatch at the input source location, and of uniform and nonuniform duct geometry. The estimated power is lower than the experimental value which is expected because many noise sources have not been modeled here including rotor related noise and duct self noise. However, it is unclear which neglected physical phenomena are most important and if the simulation has done a good job of producing the interaction noise duct source term. A. CFD Duct results The hybrid method used in this research to simulate fan noise is similar to other methods16, 18 in that the acoustic propagation is computed using a linearized Euler solver. It is of interest, however, to determine the extent to which the CFD simulation itself resolves the acoustic pressure downstream of the EGV. At this point, only a preliminary analysis of the CFD data has been completed. Time correlation of the computed pressure at two axial locations in the duct does indicate correlation at a propagation speed of u + c where u is the mean axial speed and c is the speed of sound. Visualization of the nondimensional pressure at 1BPF and 2BPF in figure 7 on an axial cut through the duct annulus indicates that 1BPF contains only hydrodynamic information. In addition, while the remnants of the rotor wakes are clearly visible in a snapshot of pressure at 2BPF, radial variation of the type depicted in figure 6 can also be seen. Further modal decomposition will hopefully allow for better assessment of the CFD capabilities. 7 of 12 (a) 1 BPF from CFD (b) 2 BPF from CFD Figure 7. Nondimensional pressure at axial location 4.35 chord lengths downstream of the EGV V. Preliminary results for the 22 × 26 case. p/ps Preliminary results for a second SDT configuration are reported in this section. The 22 × 26 case (Case 2) differs from Case 1 in two important ways. First, the configuration gives rise to a propagating mode at 1 BPF. Second, experimental measurements of the unsteady vane surface pressure are available. For this simulation the exact blade count was used, with 11 rotor blades and 13 vanes. The grid size for 0.06 this case is shown in the Appendix. The CFD simulations were run at a corrected wheel speed of 7808 rpm. 0.04 Currently in the simulation, the mass flow rate is 55.75 lbm/s. 39 blade passings have been simulated thus far. 0.02 For performance calculations, and even for turbine clocking studies, often 1.5 rotor revolutions has been sufficient 0 to obtain good results.29 For this simulation, however, the transients are just beginning to die away at 1.5 rotor −0.02 revolutions. −0.04 In order to compare the experimentally measured vane pressure to the numerically simulated data, the −0.06 experimental data must be lowpass filtered in order to 0 2 4 6 8 10 12 14 16 blade passings eliminate the noise as shown in figure 9. Early in the CFD simulation, when transients are still present, highFigure 8. CFD generated pressure trace near suc- pass filtering the computational data, as shown in figure tion side leading edge at midspan. Dashed: ac8 aids the comparison. Some of the energy can be lost tual unsteady pressure trace for 15 blade passings. when the data are filtered, but the filter allows one to get Solid: highpass filtered result. an indication if the simulation models the experimental flow field well. The EGV pressure data were obtained experimentally using untaped and taped configurations.24 The untaped configuration measured ∆p across the blade and the taped configuration measured pressure on the pressure side of the vane. Comparison between the experimental and computational EGV pressure results for ∆p is shown in figure 10 for the 10%, 30%, 50% and 70% chord locations at 60% span. The figures show the CFD results from the last 15 blade passings computed. The agreement between the latest data from the CFD simulation and the experiment indicates that the computation, once settled, will predict the vane pressure very well. 8 of 12 0.015 0.01 p/ps 0.005 0 −0.005 −0.01 −0.015 0 5 10 blade passings 15 20 0.01 0.01 0.008 0.008 0.006 0.006 0.004 0.004 0.002 0.002 p/ps p/ps Figure 9. Experimental pressure trace on suction side at 10% chord and 60% span for 20 blade passings. Dotted: actual unsteady pressure trace. Solid: lowpass filtered result. 0 0 −0.002 −0.002 −0.004 −0.004 −0.006 −0.006 −0.008 −0.008 −0.01 0 5 10 −0.01 0 15 5 blade passings (a) 10% chord 0.01 0.01 0.008 0.006 0.006 0.004 0.004 0.002 0.002 0 p/ps p/ps 15 (b) 30% chord 0.008 −0.002 0 −0.002 −0.004 −0.004 −0.006 −0.006 −0.008 −0.01 0 10 blade passings −0.008 5 10 −0.01 0 15 blade passings 5 10 15 blade passings (c) 50% chord (d) 70% chord Figure 10. Thin line: computational highpass filtered, Thick line: experimental lowpass filtered, unsteady pressure on EGV at 60% span for 15 blade passings. 9 of 12 VI. Conclusions and Future Work A 3-D, unsteady, Reynolds-averaged Navier-Stokes CFD code was used to predict the fully coupled turbomachinery flow field and vane surface pressures for two geometries consistent with the NASA 22 inch fan rig. The vane unsteady surface pressures were then used in conjunction with both a semi-analytical duct acoustic model and an finite element model to predict the tonal sound power level at the exhaust plane. The results show that for the 22x54 case, the changing cross-section in the duct area does not affect the overall power, however, the distribution of power between circumferential modes is modified as compared to the uniform duct case. The simulated power at the exhaust for the 22x54 case is much lower than that measured in the SDT. At least part of the difference is due to the lack of inclusion of all sources (rotor self-noise, duct noise, etc.) in the simulation, but the magnitude of these effects is not presently known. The computations for the 22x54 case will be continued so that a more detailed investigation can be performed into the dependence of the vane surface pressure on the number of blade passings included in the FFT. Our analyses have shown that using 10, 20, or 30 blade passings from our data set can affect the final power level by more than 2 dB. A better understanding of this effect will help guide future CFD simulations. The preliminary results for the 22x26 case for which there are experimental vane pressure data show that the simulation is capturing the vane pressures reasonably well. The simulation will be continued in order to eliminate the effect of transients. As the computed 22x26 data become available, futher comparisons with the vane measurements, both taped and untaped, will be completed. The duct propagation at 1 and 2 BPF will be simulated using both the semianalytical method and the FEM. In addition, the FEM will be used to compute the far field acoustics and these will be compared to the measurements. The simulation will take advantage of the ability of the FEM code to represent the non-uniform duct geometry, the interior mean flow field, the extended center body, and the exterior flow field including the shear layer between the fan exhaust jet and the exterior mean flow field.34 Appendix A total of 18 grids were used in the Case 1 simulation and 64 in the Case 2 simulation. For both cases, H-grids were used for the inlet duct, an O, H, and clearance grid were used for each rotor blade, and an O and an H grid were used for each EGV. Tables 3 and 4 show the grid densities for the two configurations described in this paper. The H-grid dimensions are given as axial, circumferential, and spanwise respectively, and the O-grid and clearance-grid dimensions are given as around-the-blade, normal-to-the-blade, and spanwise.The grid spacing at the airfoil surface normalized by chord is approximately 2.5 × 10−4 . Table 3. GRID DIMENSIONS, CASE 1 grid duct rotor rotor rotor EGV EGV total type h h o cl h o no. 2 2 2 2 5 5 dimensions 37x51x46 124x51x46 351x41x46 351x12x5 122x21x46 351x31x46 pts. per grid 69,782 290,904 661,986 21,060 117,852 500,526 total pts. 139,564 581,808 1,323,972 42,120 589,260 2,502,630 5,179,305 Table 4. GRID DIMENSIONS, CASE 2 grid duct rotor rotor rotor EGV EGV total type h h o cl h o no. 5 11 11 11 13 13 dimensions 37x53x46 124x53x46 351x31x46 351x12x5 122x45x46 351x31x46 pts. per grid 90,206 302,312 500,526 21,060 252,540 500,526 total pts. 451,030 3,325,432 5,505,786 231,660 3,283,020 5,505,786 18,302,784