Rocket Nozzle Plume Heating

Rocket Plume Heat Transfer

Thermal Desktop® is commonly used for thermal analyses of spacecraft and propulsion systems. Less frequently, these tools are used for calculating the temperatures in supersonic exhaust nozzles, such as those in rockets or thrusters.

The temperature of the nozzle wall is an important aspect of rocket design. The exhaust-gas temperature typically exceeds the maximum allowable temperature of the nozzle wall material. The ability to estimate the wall temperature allows the design of a cooling system.

Four types of cooling systems can be modeled in Thermal Desktop: heat sink; thermal radiation; even regenerative (using FloCAD®). A difficult part of modeling the cooling system is approximating the heat transfer from the plume to the nozzle wall. The convective film coefficient can be estimated through a number of methods (Bartz equation, TDK boundary layer technique, etc); the coefficient is highly dependent on the axial location within the nozzle.

Rocket nozzle segments

    C&R Thermal Desktop® Model of a Radiating Nozzle

 

The steady-state solution is presented below. Note the increased temperatures on the front right side of the nozzle caused by variation in the heat transfer coefficient, called streaking. The radiating section of the nozzle shows varying wall temperatures as a result of the changing heat transfer coefficient.

When compared to the actual system, the convective heat fluxes for the radiating portion of the nozzle are underestimated by about 20%. These are reasonable results based on simplification of the geometry (no structural reinforcements were included) and assumptions made within the fluid properties and equilibrium reactions. The correction factor mentioned above could be adjusted to remove this error or provide a safety factor: a key benefit of model parameterization.

Rocket nozzle temperature results with streaking

   Steady-State Results of Plume Convection in a Radiating Nozzle Using the Bartz Equation with Streaking

 

Expansions of the model could be:

  • Adding regenerative cooling in place of the fixed-temperature boundary condition
  • Adding surfaces representing the throat (a torus, perhaps) and the combustion chamber
  • Adding ablative properties to the inner wall of the nozzle or throat
  • Adding a second, concentric surface around the nozzle and mapping solid elements between the surfaces to form a heat sink nozzle
  • Mapping the results to a NASTRAN or ANSYS structural FE model

 

dispersed vs. coalesced front

Tuesday, June 26, 2018, 1-2pm PT, 4-5pm ET

This webinar describes flat-front modeling, including where it is useful and how it works. A flat-front assumption is a specialized two-phase flow method that is particularly useful in the priming (filling or re-filling with liquid) of gas-filled or evacuated lines. It also finds use in simulating the gas purging of liquid-filled lines, and in modeling vertical large-diameter piping.

Prerequisites: It is helpful to have a background in two-phase flow, and to have some previous experience with FloCAD Pipes.

Register here for this webinar

FloCAD model of a loop heat pipe

Since a significant portion of LHPs consists of simple tubing, they are more flexible and easier to integrate into thermal structures than their traditional linear cousins: constant conductance and variable conductance heat pipes (CCHPs, VCHPs). LHPs are also less constrained by orientation and able to transport more power. LHPs have been used successfully in many applications, and have become a proven tool for spacecraft thermal control systems.

However, LHPs are not simple, neither in the details of their evaporator and compensation chamber (CC) structures nor in their surprising range of behaviors. Furthermore, there are uncertainties in their performance that must be treated with safety factors and bracketing methods for design verification.

Fortunately, some of the authors of CRTech fluid analysis tools also happened to have been involved in the early days of LHP technology development, so it is no accident that Thermal Desktop ("TD") and FloCAD have the unique capabilities necessary to model LHPs. Some features are useful at a system level analysis (including preliminary design), and others are necessary to achieve a detailed level of simulation (transients, off-design, condenser gradients).

CRTech is offering a four-part webinar series on LHPs and approaches to modeling them. Each webinar is designed to be attended in the order they were presented. While the first webinar presumes little knowledge of LHPs or their analysis, for the last three webinars you are presumed to have a basic knowledge TD/FloCAD two-phase modeling.

Part 1 provides an overview of LHP operation and unique characteristics
Part 2 introduces system-level modeling of LHPs using TD/FloCAD.
Part 3 covers an important aspect of getting the right answers: back-conduction and core state variability.
Part 4 covers detailed modeling of LHPs in TD/FloCAD such that transient operations such as start-up, gravity assist, and thermostatic control can be simulated.