SCALING HEAT-TRANSFER COEFFICIENTS MEASURED UNDER LABORATORY CONDITIONS TO ENGINE CONDITIONS

摘要

Almost all measurements of the heat-transfer coefficient (HTC) or Nusselt number (Nu) in gas-turbine cooling passages with heat-transfer enhancement features such as pin fins and ribs have been made under conditions, where the wall-to-bulk temperature, T_w/T_b, is near unity. Since T_w/T_b in gas-turbine cooling passages can be as high as 2.2 and vary appreciably along the passage, this study examines if it is necessary to match the rate of change in T_w/T_b when measuring Nu, whether Nu measured at T_w/T_b near unity needs to be scaled before used in design and analysis of turbine cooling, and could that scaling for ducts with heat-transfer enhancement features be obtained from scaling factors for smooth ducts because those scaling factors exist in the literature. In this study, a review of the data in the literature shows that it is unnecessary to match the rate of change in T_w/T_b for smooth ducts at least for the rates that occur in gas turbines. For ducts with heat-transfer enhancement features, it is still an open question. This study also shows Nu measured at T_w/T_b near unity needs to be scale to the correct T_w/T_b before it can be used for engine conditions. By using steady RANS analysis of the flow and heat transfer in a cooling channel with a staggered array of pin fins, the usefulness of the scaling factor, (T_w/T_b)~r, from the literature for smooth ducts was examined. Nu_(engine), computed under engine conditions, was compared with those computed under laboratory conditions, Nu_(lab), and scaled by (T_w/T_b)~r; i.e., Nu_(lab,scaled) = Nu_(lab) (T_w/T_b)~r. Results obtained show the error in Nu_(lab,scaled) relative to Nu_(engine) can be as high as 36.6% if r = -0.7 and T_w/T_b = 1.573 in the "fully" developed region. Thus, (T_w/T_b)~r based on smooth duct should not be used as a scaling factor for Nu in cooling passages with heat-transfer enhancement features. To address this inadequacy, a method is proposed for generating scaling factors, and a scaling factor was developed to scale the heat transfer from laboratory to engine conditions for a channel with pin fins.