UFR 4-16 Test Case

Flow in a 3D diffuser

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Test Case Study

Brief description of the test case studied

The diffuser shapes, dimensions and the coordinate system are shown in Fig. 3 and Fig. 4. Both diffuser configurations considered have the same fully‐developed flow at channel inlet but slightly different expansion geometries: the upper-wall expansion angle is reduced from 11.3° (Diffuser 1) to 9° (Diffuser 2) and the side-wall expansion angle is increased from 2.56° (Diffuser 1) to 4° (Diffuser2). The flow in the inlet duct (height h=1 cm, width B=3.33 cm) corresponds to fully-developed turbulent channel flow (enabled experimentally by a development channel being 62.9 channel heights long). The L=15h long diffuser section is followed by a straight outlet part (12.5h long). Downstream of this the flow goes through a 10h long contraction into a 1 inch diameter tube. The curvature radius at the walls transitioning between diffuser and the straight duct parts are 6 cm (Diffuser 1) and 2.8 cm (Diffuser 2). The bulk velocity in the inflow duct is ${U_{\textrm {bulk}}=U_{\textrm {inflow}}=1m/s}$ in the x-direction resulting in the Reynolds number based on the inlet channel height of 10000. The origin of the coordinates (y=0, z=0) coincides with the intersection of the two non-expanding walls at the beginning of the diffuser's expansion (x=0). The working fluid is water (ρ=1000 kg/m³ and μ=0.001 Pas).

Figure 3: Geometry of the 3-D diffuser 1 considered (not to scale), Cherry et al. (2008); see also Jakirlić et al. (2010a)

Figure 4: Geometry of the 3-D diffuser 2 considered (not to scale), Cherry et al. (2008).

Experimental investigation

Brief description of the experimental setup

The measurements were performed in a recirculating water channel using the method of magnetic resonance velocimetry (MRV), Fig. 5. MRV makes use of a technique very similar to that used in conventional medical magnetic resonance imaging (MRI), Fig. 6. Experiments were performed on a 1.5 Tesla magnet with resolution of 0.9 x 0.9 x 0.9 mm and a 7 Tesla magnet with resolution of 0.4 x 0.4 x 0.4 mm. Interested readers are referred to Cherry et al. (2008, 2009) for more details about the measurement technique.

Figure 5: Schematic of the experimental flow system (upper) and design of the 3D diffuser. Courtesy of J. Eaton (Stanford University)

Figure 6: 3D diffuser arrangement in a medical magnetic resonance imaging device. Courtesy of J. Eaton (Stanford University)

Mean velocity and Reynolds stress measurements

Cherry et al. provided a detailed reference database comprising the three- component mean velocity field and the streamwise Reynolds stress component field within the entire diffuser section. Both diffuser configurations considered are characterized by a three-dimensional boundary-layer separation, but the slightly different expansion geometries caused the size and shape of the separation bubble exhibiting a high degree of geometric sensitivity to the dimensions of the diffuser as illustrated in Figs. 7, 8 and 9

Figure 7: Streamwise velocity contours in a plane parallel to the top wall, from Cherry et al. (2008)

Figure 8: Measured streamwise velocity contours in the central plane (upper) of the Diffuser 1 and in the three selected cross-sectional slices positioned at different distances from the diffuser inlet (lower; their locations are denoted by thick white lines in the upper figure). Note that the black line indicates zero streamwise velocity and the purple and pink regions are reverse flow. The velocity values are normalized by the bulk inlet velocity being Vref=1 m/s. Courtesy of J. Eaton (Stanford University)

Pressure measurements

In addition Cherry et al. (2009) provided the pressure distribution along the bottom non-deflected wall of diffuser 1 at different Reynolds numbers. Complementary to the Reynolds number 10000 (for which the entire flow field was measured), two higher Reynolds numbers - 20000 and 30000 - were also considered, Fig. 11. The surface pressure distribution was evaluated to yield the coefficient [pic]; the reference pressure was taken at the position x/L=0.05. The pressure curve exhibits a development typical of flow in diverging ducts. The pressure decrease in the inflow duct is followed by a steep pressure increase already at the very end of the inflow duct and especially at the beginning of the diffuser section. The transition from the initial strong pressure rise to its moderate increase occurs at [pic], (x/h=4.5) corresponding to the position where about 5% of the entire cross-section is occupied by the flow reversal (see e.g., Fig. 19). The onset of separation causes a certain contraction of the flow cross- section, leading to a weakening of the deceleration intensity and, accordingly, to a slower pressure increase. The region characterized by a monotonic pressure rise was reached in the remainder of the diffuser section.

CFD Methods

Provide an overview of the methods used to analyze the test case. This should describe the codes employed together with the turbulence/physical models examined; the models need not be described in detail if good references are available but the treatment used at the walls should explained. Comment on how well the boundary conditions used replicate the conditions in the test rig, e.g. inflow conditions based on measured data at the rig measurement station or reconstructed based on well-defined estimates and assumptions.

Discuss the quality and accuracy of the CFD calculations. As before, it is recognized that the depth and extent of this discussion is dependent upon the amount and quality of information provided in the source documents. However the following points should be addressed:

• What numerical procedures were used (discretisation scheme and solver)?

• What grid resolution was used? Were grid sensitivity studies carried out?

• Did any of the analyses check or demonstrate numerical accuracy?

• Were sensitivity tests carried out to explore the effect of uncertainties in boundary conditions?

• If separate calculations of the assessment parameters using the same physical model have been performed and reported, do they agree with one another?

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Contributed by: Suad Jakirlić, Gisa John-Puthenveettil — Technische Universität Darmstadt

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