System and method of controlling clearance between turbine engine blades and case based on engine components thermal growth model

A system for controlling clearance in a turbomachine between turbomachine component blades and a wall adjacent to and opposing tips of the blades, the system comprising:

• means for determining components and if necessary subcomponents of the turbomachine such that thermal growth of each component or subcomponent is governed by 1st order differential equation in terms of component material temperature;
• means for determining fluid streams that exchange heat with the components or subcomponents each characterized by distinct temperature and flow rate;
• means for determining from a measurement and/or synthesis the temperatures and flow rates of the fluid streams defined for each of the components or subcomponents;
• means for determining from a measurement and/or synthesis parameters appearing in performance parameter correlations including temperatures, pressures and shaft speeds;
• means for determining turbomachine component heat transfer performance parameters each as a function of measured and otherwise synthesized engine characteristics including shaft speeds, pressures and temperatures;
• means for determining steady state growth of the turbomachine components each as a weighted average of growths resulting from thermal exchange with fluid streams of varying temperatures, flow rates and thermo-physical properties where weighting factors include the heat transfer performance parameters;
• means for determining an inverse of an equivalent time constant of the turbomachine components each as a sum of the respective performance parameters;
• means for determining thermal growth of the turbomachine components each with a difference equation by applying a closed form solution to a governing first order differential equation over a predetermined time step for a specified change in a forcing function, the forcing function including the steady state growth of the respective turbomachine component, and the time constant including the equivalent time constant;
• means for populating the equations for steady state growth, equivalent time constant and thermal growth difference equations with the approximating coefficients that are determined from regression analysis that minimizes errors between the subject thermal growth model and higher fidelity model and/or test data;
• means for determining the turbomachine tip clearance as total sum of all the turbomachine component and subcomponent growths where thermal growth of the turbomachine components or subcomponents is obtained with the subject thermal growth model;
• and
• means for controlling the turbomachine tip clearance based on the difference between desired and actual clearance of turbomachine components as determined by the thermal growth of the turbomachine components.

A turbine engine system comprising:

• a turbine engine including case and blades rotatable within the case;
• means for determining components and if necessary subcomponents of the turbine engine such that thermal growth of each component or subcomponent is governed by 1st order differential equation in terms of component material temperature;
• means for determining fluid streams that exchange heat with the components or subcomponents each characterized by distinct temperature and flow rate;
• means for determining from a measurement and/or synthesis the temperatures and flow rates of the fluid streams defined for each of the components or subcomponents;
• means for determining from a measurement and/or synthesis parameters appearing in performance parameter correlations including temperatures, pressures and shaft speeds;
• means for determining turbine engine component heat transfer performance parameters each as a function of measured and otherwise synthesized engine characteristics including shaft speeds, pressures and temperatures;
• means for determining steady state growth of the turbine engine components each as a weighted average of growths resulting from thermal exchange with fluid streams of varying temperatures, flow rates and thermo-physical properties where weighting factors include the heat transfer performance parameters;
• means for determining an inverse of an equivalent time constant of the turbine engine components each as a sum of the respective performance parameters;
• means for determining thermal growth of the turbine engine components each with a difference equation by applying a closed form solution to a governing first order differential equation over a predetermined time step for a specified change in a forcing function, the forcing function including the steady state growth of the respective turbine engine component, and the time constant including the equivalent time constant;
• means for populating the equations for steady state growth, equivalent time constant and thermal growth difference equations with the approximating coefficients that are determined from regression analysis that minimizes errors between the subject thermal growth model and higher fidelity model and/or test data;
• means for determining the turbine engine tip clearance as total sum of all the turbine engine component and subcomponent growths where thermal growth of the turbine engine components or subcomponents is obtained with the subject thermal growth model;
• and
• means for adjusting an amount of air flow adjacent to the wall in response to the thermal growth.