Surface Distribution of Temperature

The present predicted surface distribution of T* for the varied Z/D and X/D are as shown in Figure 5.32 (b and c), Figure 5.33 and Figure 5.334. These plots are very similar in distribution to those for the distribution of Nu in Figure 5.17, Figure 5.18 and 5.19, respectively as expected. These shows the existence of significant thermal gradients, in spite of the internal heat conduction within the wall. The impingement target wall predictions of the surface T* contours for the range of Z/D are shown in Figure 5.32 (a and b). Figure 5.32 (a and b) shows major axial temperature gradients with high leading edge temperatures at low Z/D and high trailing edge temperatures at high Z/D. This is more clearly shown in Figure 5.35 (a and b) for the X2 surface average normalized temperature axial distribution. In both cases the temperature normalization are by Equations 2.6 and 2.7, respectively.

(a) Varied Z/D for G of 1.84 kg/sm2bar (b) Varied Z/D for G of 1.93 kg/sm2bar

(c) Varied X/D for G of 1.93 kg/sm2bar

Figure 5.33: Contours of T* for varied n Figure 5.34: Comparison of T* for varied n Figure 5.32 (c) shows the predicted T* for the range of X/D geometries shown in Table 5.2, this shows that as the X/D decreases with increased in jet hole size, the cold spot with axial distance downstream the impingement gap gradually disappears. Hence the X/D of 1.86 has the highest T* and the cold spot is shown to be almost absent, this further confirmed that this X/D has the lowest HTC as was shown above. However, the predicted temperature gradients are much lower than those for the local Nu gradients predicted in Figure 5.17 (ii). For example, for X/D = 11.04, the Nu variation between the impingement point and the mid- distance between the impingement points is a factor of 10/1, but the same T* gradient is only about 1.5. This is the reason why in Figure 5.36, the X/D is shown to have the highest X2 average T* and decreases as X/D was decreased. Figure 5.36 also shows that upstream the impingement gap and up to the central rows of holes, the X/D of 1.86 - 4.66 are in the range of similar X2 average T* and increases downstream, with only X/D of 1.86 decreasing. This indicates that the X/D of 4.66 (n = 4306 m-2) and based on the Nu predictions shown in Figure 5.17 (i and ii), balanced out between the cooling heat transfer and the wall thermal gradients. In Figure 5.18, for n = 1076 m-2 the min to max Nu was about a factor of 5, but in Figure 5.33 the min to max temperature is about a factor of 1.25.

(a) Imposed q" for G of 1.84 kg/sm2bar

(b) Imposed Tw for G of 1.93 kg/sm 2

bar

Figure 5.35: Predicted target surface average T* for varied Z/D at fixed X/D

Figure 5.37: Predicted hole-to-hole target surface average T* of varied n at fixed X/D and G

Figure 5.38: Predicted target X2 average T* for varied n and X/D of two G values

Figure 5.33 shows that as n is decreased and X/D is increased (as X is also increased), the region of the hottest spot on the target wall is increased, but for a fixed X/D with increased in jet hole size this hottest spot vanished gradually. By comparing between these two X/D geometries with changes in n, Figure 5.33 shows that the varied X/D indicates better cooling as it has higher cool spot. But Figure 5.37Figure 5.38Figure 5.39 shows that the X2 average T* contradict what have been shown in Figure 5.33, as Figure 5.37 and 5.39 shows that X2 average T* increases with increased n at fixed X/D, while Figure 5.38 and 5.39 shows that T* increases with decreased n for increased X/D. Figure 5.39 compares surface X2 average T* that was shown in Figure 5.33, this shows that for similar n but different X/D, the smaller X/D of 4.66 of all n indicates better surface temperature gradients even though they show the worse in Figure 5.33.

5.7 Conclusions

Experimental results for impingement cooling were presented for ranged of geometries, where Z/D, X/D, n (or N) and G were varied. The impingement jet and target metal walls were Nimonic-75 of 6.35 mm metal thickness. Square array impingement jets were investigated using CHT CFD for these range of geometries and mass flux. At a constant mass flux G typical of the total compressor exit regeneratively cool combustor wall: the geometries Z/D was varied by changing only Z, X/D was varied by changing the hole diameter D at constant pitch X and Z, X/D was also varied (where n or N were varied) for smaller fixed D and Z at varied X and finally n was varied at fixed X/D for varied X and D at fixed Z. The mass flux G was also varied for a fixed geometry of n = 4306 m-2 at X/D = 4.66 and Z/D = 3.06, a similar variable for varied Z/D. These conditions were appropriate for an application of impingement cooling to regenerative combustor wall cooling for low NOx combustor applications.

For all these impingement cooling geometries, the measured locally surfaced averaged heat transfer coefficient (HTC) h and the impingement flow relative pressure loss ∆P/P were predicted. These results were compared for geometries with the same G and geometries with varied G, which have been shown give excellent agreement with the experimental surface and X2 averaged HTCs and with the measured pressure loss, whereby only few expception could not agree and the reasons for this were given. The CHT CFD computations employed the standard k - ε turbulence model using standard wall function, this showed that the aerodynmics of the impingement cooling were correctly predicted by this model based on the agreement given.

The experimental results showed that there was a strong influence of n on the surface averaged heat transfer h. The greater number of jets in the cross-flow direction as n was

increased for fixed X/D resulted in a reduction of heat transfer with distance along the impingement wall. This reduced the surface average heat transfer, but as X/D was varied and increased it increases it. For smaller n the distribution of the heat transfer across the surface was poor and gave rise to the highest thermal gradients. There were hot spots between the jets that reduced the overall surface averaged heat transfer to below that for 4306 m-2.

For an X/D of 1.86 and G of 0.35 kg/sm2bar (X/D = 4.66 and n = 4306 m-2), the predictions were low for pressure loss and low for h, although the axial variation of h was predicted to be similar to that measured. The reason for this was considered to be due to the laminar flow in the impingement holes for the lower G and the under prediction of turbulence generated by these flows. Similarly for the smaller X/D laminar flow occurred in the first few rows of holes, which was not taken into account in the predictions.

The CFD predictions that were influenced by the cross-flow for range of geometries and for varied rows of holes, showed that for the first few holes with low cross-flow, there was interaction between the jets on the surface that produced a reverse jet on the centre-point of the square array. This reverse jet was shown to carry heated air from the surface to the impingement jet surface which was subsequently heated.

The action of the cross-flow was to deflect this reverse jet and to decrease its effectiveness. The cross-flow also convected the surface turbulence downstream of the impingement point and thus reduced the average turbulence on the surface. The net result was a reduction in the mean local surface average heat transfer with distance. The predictions of this heat transfer reduction were in good agreement with the experimental measurements.

The CHT CFD predictions enabled the heat transfer to the impingement jet wall to be predicted. On average this h was about 50% of that for the impingement target wall at all X/D and an average of 70% of the target wall HTC for varied n at fixed X/D, for Z/D with varied gap this was about 30% and shows insignificant change with reduced Z/D. This should be a significant feature of the overall impingement heat transfer process. However, there were significant variations in this ratio with X/D and between the first few holes and the last few holes.

The conjugate heat transfer CFD was able to predict the surface distribution of temperature and the temperature gradients through the thickness of the Nimonic-75 wall. The axial gradients in surface temperature were much lower than the impingement jet side gradients in heat transfer coefficient, due to the internal conduction of heat within the metal wall. These gradients increased as the HTC increased and were greatest at the highest X/D. Thermal gradients increased as n decreased but were considered acceptable for the optimum n of

4306m-2 for maximum h and unacceptable for the lower n of 1076m-2. The conjugate heat transfer CFD gave very good agreement with the metal temperatures measured experimentally in the Nimonic-75 wall and showed that thermal gradients were relatively low. This indicates that CHT CFD is adequate for the prediction of metal temperatures in gas turbine cooling systems such as impingement cooling and should be used in optimization studies for optimum cooling configurations.

Conjugate heat transfer CFD has been shown to give good predictions of impingement cooling and is a viable design tool for combustor and turbine blade cooling design.

CHAPTER SIX

FOUR SIDED EXIT FLOW IMPINGEMENT COOLING