Influences of Tip Cooling Injection on Tip Clearance Control at Design and Off-Design Incidences

Table 3

Empirical correlations of the tip clearance losses.

Prediction method	The tip clearance losses coefficient
Denton [22]	𝐶po,tip=2CD𝜏C𝐻𝑠cos𝛼2∫^10(𝑉s𝑉2)^3𝑉(1−^p𝑉s)𝑉(1−(^p𝑉s)^2)𝑑𝑧𝐶
Benner et al. [23, 24]	𝐶po,tip=𝐶po,total−𝐶po,profile−𝐶po,secondary
	𝐶po,profile=𝑃𝑜,mid,1−𝑃𝑜,mid,2𝑃𝑜,mid,2−𝑃mid,2(1−0.10(𝐹𝑡)^0.79√CR(𝐻/𝐶)^0.55𝛿−32.70(𝐻)^2)
	𝐶po,secondary=0.038+0.41tanh(1.20𝛿/𝐻)√cos𝛾(𝐶𝑅)(𝐻/𝐶)^0.55(𝐶cos𝛼2/𝐶ax)^0.55
Yaras & Sjolander [25]	𝐶po,tip=2𝐾E𝐶D(𝜏𝐻𝐶)(𝑠)𝐶L^1.5(cos^2𝛼2cos^3𝛼m)+𝜁𝐾G(𝐶𝑠𝐶)(𝐻)𝐶D𝐶L^0.5(1cos𝛼m)
Ainley & Mathieson [26]	𝐶po,tip𝜏=0.5(𝐻𝐶)(𝑠)^2𝐶L^2(cos^2𝛼2cos^3𝛼m)(Re2×10^5)^−0.2
Dunham & Came [27]	𝐶po,tip𝐶=0.47(𝐻𝜏)(𝐶)^0.78𝐶L^2(Cs)^2(cos^2𝛼2cos^3𝛼m)
Kacker & Okapuu [28]	▵𝜂𝜂𝜏=0𝜏=0.93(𝐻1)(cos𝛼2𝑅)(^tip𝑅mean)