Instrumentation Development for Study of Reynolds Analogy in Reacting Flows

Introduction Boundary layer development in supersonic The intended application for this study is to further the understanding of the flow reacting flows is not well understood. A new capability has been developed which makes through the combustor of a scramjet (supermore extensive surface measurements practisonic combustion ramjet) engine. Experical, leading to an increased understanding of ments with supersonic combustors have, until these turbulent boundary layers. The new recently, focused mostly on the basic global technique provides measurements which alissues of thrust measurement, fuel injection low the formulation of a relation between the and mixing. Advances in instrumentation transfer of momentum and the transfer of technology have made it practical to measure heat for reacting flow, similar to the Reynolds more detailed aspects of the boundary layer Analogy for laminar flow. An instrument has of this flowfield, and efforts have been made been designed and built which simultaneously to include more surface measurements in exmeasures the surface heat transfer and shear perimental test programs. in the presence of combustion. These conA considerable step in understanding this current measurements made at the same lohigh enthalpy, high heat flux environment is cation, combined with local flow conditions, to formulate an analytic relation between the enable a quantitative analysis of the relation skin friction and heat transfer in the combetween the surface drag and wall heating, as busting flow, similar to the one that exists well as identifying possible ways of reducing for laminar flow. Schlichting [1] defines this both. relation, called Reynolds Analogy, as Nomenclature 1 x gu = _CIR_f(7,P_ ) (1) Cf skin friction coefficient Nu Nusselt Number where the Nusselt number Nu, the Reynolds P0 total pressure number R_, and the Prandtl number, P_, P_ Prandtl Number are related in terms of a Stanton number, P_,t Turbulent Prandtl Number St = R.PrN'-'-_, which includes the heat transfer q dynamic pressure coefficient in its definition. This relation is q_ heat flux valid for all laminar flow, and similar relaR_ Reynolds Number tions have been developed to apply to turbuS area of sensing head lent flow. However, as the flow becomes more "St Stanton Number complicated, classical Reynolds Analogy conTo total temperature cepts become less reliable. The mechanisms V free-stream velocity present for reacting flow are not well under,o p density stood because of its complicated turbulent, r_, shear stress combusting and three-dimensional character. The major emphasis for this project is there1800's. In its most simple form, fore to provide a means to extend the baseline of information available for predicting drag in C--A= StP_ (2) this reactive flowfield. 2 Due to the uncertainties invol-ed in predicting this boundary layer numerically, it is Reynolds Analogy will hold for laminar, inmost sensible to perform an experimental excompressible flowfields. It has been modiamination of the flow; even though this is not fled and extended to compressible and turn simple flowfield in which to make surface bulent flows in various analytical and commeasurements. Means are now available to putational forms. Mally investigations took directly measure skin friction and heat flux place in the 1950's, comparing experimental concurrently at the same location in this flowdata to existing or new theories. For example, field. Measurements taken of the two quantian early analysis done by Beckwith [2] apties first need to be combined with state variplies an integral method to extend the analables and information about local flow condiogy to compressible laminar flow. Ludwieg and Tillmann [3] examined turbulent flows tions and then a quantitative analysis enables with pressure gradients. Another analysis by a relationship to be established between the Hool [4], uses the yon Karman improvement two. to Reynolds Analogy for two-dimensional furNote that the instrumentation capability bulent fows. developed here can be utilized in a number of other relevant flows. The technique will Van Driest also derived his own variable give further experimental validation to corredensity, variable property Reynolds Analogy lations for hypersonic flows,supersonic flows, [5]. The law is determined from incompressand transition studies. The gauge is also ible yon Karman mixing-length theory with the momentum integral equation over a flat suited for jet engine or rocket nozzle tests and in experiments exploring engine/airframe plate written in terms of temperature and integration. Any boundary layer investigaflow variables. The van Driest analysis is tion where heat and momentum transfer are important in that it is valid for high speed turbulent flow over a flat plate and does inlinked can benefit from a simultaneous meaclude cases of heat transfer, but not combussurement at one location. In addition, the extion [6]. At about that same time, Eckert [7] periments create an expanded database that is vital to new code validation. The gauge deintroduced a semi-empirical method for twosign concept is simple and versatile, such that dimensional flow for a Mach number range modifications for new facilities can easily be up to 20. Using the recovery temperature, Eckert generates a solution for laminar and made. The criteria for geometry and mateturbulent flow, generally agreeing with experrials are based on tunnel logistics constraints imental flat plate measurements. and expected flow conditions. An analysis of available experimental data in 1970 [8] concluded that not enough useBackground ful data existed to allow for an empirical Reynolds Analogy definition for turbulent Reynolds Analogy has been a powerful anflows either below or above Mach 5. In addialytical tool since it first appeared in the late tion, the data needs to contain measurements