Evaluation of potential flow models for unsteady separated flow with respect to experimental data

The wake characteristics and force production of an aspect-ratio-8 flat plate rectangular wing starting from rest at a high angle of attack ($\alpha ={45}^{\circ }$) were examined. The first portion of this paper presents experimental measurements that focus on circulation production at the leading edge of the wing. Circulation production is shown to be coupled to both the wing kinematics and the wake state. The second portion of the paper reviews the implementation of several pertinent potential flow models from the literature and compares the results of these models to the experimental results. Quasisteady and fixed-wake models were found to be poor predictors of both force and circulation. A similarity-solution-based model was found to make accurate predictions only at very short times. An unsteady strength two-vortex model predicted the circulation production during the acceleration portion of the kinematics, but did not predict the force. A multiple-discrete-vortex model was found to predict both the force and circulation production well, but had difficulty after the shedding of the first leading-edge vortex.

Figure 1

Vorticity fields for a wing rapidly started in translation at ${45}^{\circ }$ incidence, ensemble averaged over five runs. The wing is moving from left to right, so the relative flow is from right to left. Red represents counterclockwise rotation; blue represents clockwise rotation. (a) Time history of wing velocity, indicating the timing of the flow-field images below: (b) $t^{*}=1$, (c) $t^{*}=2$, (d) $t^{*}=3$, (e) $t^{*}=4$, (f) $t^{*}=5$, (g) $t^{*}=6$, (h) $t^{*}=7$, (i) $t^{*}=8$, (j) $t^{*}=9$, (k) $t^{*}=10$, (l) $t^{*}=11$, and (m) $t^{*}=12$.

Figure 2

Forces on an aspect-ratio 8 wing undergoing surge at $\alpha ={45}^{\circ }$. The shaded area corresponds to the acceleration portion of the velocity profile.

Figure 3

Vortex location measurements on a surging wing. Data from five independent trials are overlaid for both methods: (a) trajectory of the LEV in the wing frame, (b) $x$ location of the LEV in time, and (c) $y$ location of the LEV in time.

Figure 4

Circulation production from the leading edge of the wing. The lines show filtered values from five separate trials.

Figure 5

Positive circulation nominally in the LEV for five independent measurements.

Figure 6

Quasisteady thin airfoil theory model force prediction compared to experimental data.

Figure 7

Comparison of the circulation predicted by pure thin airfoil theory and the measured values. Note that technically the measured data are those of the LEV in the wake, while the model curves show bound circulation: (a) total circulation and (b) circulation production.

Figure 8

Quasisteady model augmented with empirical force coefficients and compared to experimental data.

Figure 9

Results of Wagner's fixed-wake model compared to experimental results.

Figure 10

Comparison of the circulation predicted by Wagner's model and the measured values. Note that technically the measured data are those of the LEV in the wake, while the model curves show bound circulation: (a) total circulation and (b) circulation production.

Figure 11

Similarity solution model compared to experimental data.

Figure 12

Comparison of the circulation predicted by the similarity solution model and the measured values: (a) total circulation and (b) circulation production.

Figure 13

Wang-Eldredge point vortex model.

Figure 14

Comparison of the circulation predicted by Wang and Eldredge's model and the measured values: (a) total circulation and (b) circulation production.

Figure 15

Comparison of the location predicted by Wang and Eldredge's model [21] and the measured values: (a) LEV $x/c$ and (b) LEV $y/c$.

Figure 16

Representative panel method mesh with $N=12$. The actual computations used a finer mesh where $N=64$.

Figure 17

Wake comparison at $t^{*}=10.0$: (a) multiple-vortex model and (b) vorticity field from PIV with the frozen-wake hypothesis.

Figure 18

Point vortex model compared to experimental data.

Figure 19

Comparison of the circulation predicted by the point vortex model and the measured values: (a) total circulation and (b) circulation production.

Figure 20

Normal force predictions from all models.

Figure 21

Velocity profile of the motion.

Figure 22

Results of applying the frozen-wake hypothesis. The extent of the actual PIV frame is shown to the right of the vertical black line.

Figure 23

Location of flux measurement marked by the black box around the leading edge.

Figure 24

Flux measurements for the two different fields of view. Note that each field of view is represented by five independent trials.