CFD model

6.2.1 How it works

The second method of analyzing the recuperator was a computational fluid dynamics (CFD) model. The geometry was the one described in Figure 5.7 and Figure 6.3. A single 64-wafer sector was modeled. As before, each wafer is 1mm thick and comprises four layers: two solid walls, each .25 mm thick, with a .25 mm exhaust layer and a .25 mm air layer between them.

For the CFD model, a wedge-shaped box was drawn around the sector to constrain the flow at the air inlet and outlet. Its walls were thin (.25 mm) to avoid greatly increasing streamwise heat conduction area. All outer walls were adiabatic with respect to the environment. The box was made of CeSZ-mullite with the same properties used in the FVM: specific heat, 710 J/(kgK); thermal conductivity, 3.5 W/(mK); density, 3400 kg/m3_{. The properties were independent of}

temperature, a reasonable assumption because the thermal conductivity of mullite varies little with temperature from 300 to 1200C [193]. The model assumes that air enters through the top of the box at 382K and 202650 Pa, and leaves at the bottom at a defined mass flow rate, 1/36th

of the design value for the engine (.0566/36 = .001572 kg/s). Exhaust enters the port at 1416K, 108500 Pa, and leaves the twin exhaust ports at the same .001572 kg/s. The solver assumed laminar flow, which is safe due to the low Reynolds number (~100). The surface roughness was 10 microns, a conservative value.

Radiation heat transfer is neglected, because efforts to make SolidWorks Flow account for this in the model were not successful. Since the channels are thin compared with their length in the thermal gradient direction, the view factor of wall elements relative to directly opposite walls (which should be at nearly the same temperature) would be near 1.0, while the view factor vs. far away elements (which would be at significantly different temperatures) would be small. Thus, it was thought that radiation heat transfer should not make a big difference in the results.

The model calculates heat conduction through all solid walls of the model, gas flows, convection heat transfer coefficients, local gas and wall temperatures, and other variables of interest. The gases were modeled as pure air for convenience. This would slightly underestimate the specific heat of the exhaust stream, making the performance appear slightly worse than in reality.

6.2.2 Results

Table 6.4. Recuperator inlet and outlet flows and calculated performance from CFD Pressure (Pa) Temperature (K) Pressure loss (Pa) Air in 202,649 382

2,693 Turbine pressure ratio 1.85

Air out 199,956 1281 Combined pressure losses - Vick model (eq. 3.20) 14.5%

Exhaust in 108,103 1416

6,463 Combined pressure losses - Wilson model (eq. 3.19) 9.0%

Exhaust out 101,640 540 Effectiveness 86.9%

Recuperator Air Outlet (RAO)

[FloWorks] Iteration [ ] 196

Local parameters Integral parameters

Parameter Minimum Maximum Average Bulk

Average

Surface

Area [m^2] Parameter Value

Pressure [Pa] 199,918 199,991 199,956 199,956 6.37E-4 Mass Flow Rate [kg/s] -.00157

Density [kg/m^3] .520 .569 .544 .544 6.37E-4 Volume Flow Rate [m^3/s] -.00289

Velocity [m/s] 4.53 12.6 7.79 7.86 6.37E-4 Total Enthalpy Rate [W] -2,170

Temperature [K] 1,225 1,338 1,281 1,281 6.37E-4 Uniformity Index [ ] .628

Recuperator Exhaust Outlet (REO)

[FloWorks] Iteration [ ] 196

Local parameters Integral parameters

Parameter Minimum Maximum Average Bulk

Average

Surface

Area [m^2] Parameter Value

Pressure [Pa] 100,995 101,849 101,634 101,640 1.15E-4 Mass Flow Rate [kg/s] -.00157

Density [kg/m^3] .527 .789 .663 .661 1.15E-4 Volume Flow Rate [m^3/s] -.00240

Velocity [m/s] 19.5 29.5 24.2 24.2 1.15E-4 Total Enthalpy Rate [W] -864

Temperature [K] 449 667 538 540 1.15E-4 Uniformity Index [ ] .897

Recuperator Air Inlet (RAI) [FloWorks] Iteration [ ] 196

Local parameters Integral parameters

Parameter Minimum Maximum Average Bulk

Average

Surface

Area [m^2] Parameter Value

Pressure [Pa] 202,647 202,650 202,649 202,649 .00131 Mass Flow Rate [kg/s] .00157

Density [kg/m^3] 1.85 1.85 1.85 1.85 .00131 Volume Flow Rate [m^3/s] 8.51E-4

Velocity [m/s] .0246 1.73 .650 1.14 .00131 Total Enthalpy Rate [W] 609

Temperature [K] 382 382 382 382 .00131 Uniformity Index [ ] .614

Recuperator Exhaust Inlet (REI)

[FloWorks] Iteration [ ] 196

Local parameters Integral parameters

Parameter Minimum Maximum Average Bulk

Average

Surface

Area [m^2] Parameter Value

Pressure [Pa] 107,859 108,208 108,111 108,103 1.17E-4 Mass Flow Rate [kg/s] .00157

Density [kg/m^3] .267 .267 .267 .267 1.17E-4 Volume Flow Rate [m^3/s] .00591

Velocity [m/s] 46.8 69.4 53.8 54.3 1.17E-4 Total Enthalpy Rate [W] 2,429

6.2.3 Discussion

The engine model in section 4.3 budgeted for pressure losses of 5100 Pa for the recuperator air side and burner, and 7100 Pa for the exhaust side. The CFD model predicts pressure losses of 2693 and 6463 Pa, leaving an adequate allowance of 2407 Pa for combustor pressure losses, and 607 Pa of extra losses on the exhaust side. The calculated effectiveness is 86.9%, while the engine model budgeted for only 84%. This performance level is considered very good. Many other designs were subjected to CFD modeling and abandoned upon finding that the pressure losses were too high, the weight was too great, the effectiveness was too low, or the manufacturability was poor.

The streamline plots shown in Figure 6.8 and Figure 6.9 contain a wealth of information. For example, the fact that the exhaust flow is fairly evenly-distributed in this design can be deduced from the fact that the color bands in the pressure and temperature plots are aligned horizontal. Other designs had manifold tubes that were too small, resulting in high velocities and significant pressure variations across the channels. An example of a design with undersized outlet manifolds is shown below.

Figure 6.10. Exhaust flows in a recuperator sector designed with deliberately undersized exhaust outlet manifolds.

The air streamline plots show that the main pressure losses are in the core channels, which is the desirable outcome. Heightened pressure losses are created at the channel outlets due to the flow area constriction there. This is suggested by the tighter spacing of color countours there than in the core channels, and it means that the air exit area could perhaps benefit from slight

Exhaust inlet Exhaust outlet outlet

Explanation: angled contours (dashed line following the color bands) suggest flow is not well distributed. Note the low pressure area (dark blue) in the top exhaust manifolds. This suggests the velocity at the exhaust outlet is too high. Enlarging the tubes would solve this. In contrast, the inlet manifold is uniformly red, so the pressure varies less there. The inlet tube is probably not causing the maldistribution.

Angled pressure contour

enlargement. Conversely, the air inlet area is does not appear overly restricted because the colors are changing only gradually in that area.

Perhaps more deductions could be made from the CFD model output, and more plots could be generated. However, the above information is sufficient to conclude that according to the CFD model, the recuperator’s performance should be adequate.