SOLID PROPELLANT ROCKET MOTOR NOZZLE HEAT TRANSFER MODEL VERIFICATION

Size: px

Start display at page:

Download "SOLID PROPELLANT ROCKET MOTOR NOZZLE HEAT TRANSFER MODEL VERIFICATION"

Edwin Armstrong
6 years ago
Views:

SOLID PROPELLANT ROCKET MOTOR NOZZLE HEAT TRANSFER MODEL VERIFICATION SAŠA ŽIVKOVIĆ Military Technical Institute, Belgrade, sasavite@yahoo.

1 SOLID PROPELLANT ROCKET MOTOR NOZZLE HEAT TRANSFER MODEL VERIFICATION SAŠA ŽIVKOVIĆ Military Technical Institute, Belgrade, RADOSLAV SIROVATKA Military Technical Institute, Belgrade, NIKOLA GLIGORIJEVIĆ Military Technical Institute, Belgrade, SREDOJE SUBOTIĆ Military Technical Institute, Belgrade, STEVAN KOZOMARA Military Technical Institute, Belgrade, MOMČILO NIKOLIĆ Military Technical Institute, Belgrade, Abstract: Heat transfer is one of the most important and complex rocket motor design task. Physical process of heat transfer is unsteady and complex itself and solid propellant rocket motor constructive and technological specificity additionally complicate design. Active thermal protective materials with ablative reaction mechanism are frequently in use, and the motor parts are geometrically complex and made from diverse materials. All this factors are leading to calculation with numerical methods, and one of them is described in this paper. A simple measurement is conducted to improve calculation reliability and for results verification. Key words: heat transfer, rocket motor, cfd, experiment. 1. INTRODUCTION Heat transfer calculation is one of the most significant rocket motor design process. According to released heat, thermal loads are extremely large, and thermal insulation is frequently necessary in the motor combustion chambers and nozzles. In high temperature conditions, large thermal dilatations are present, and also the motor s parts mechanical characteristics decreases. These occurrences are very important in the motor design process, and they are directly dependent from them temperature field. This is the reason why precise heat transfer calculation is necessary. Solid propellant rocket motor examination is conducted for heat transfer calculation verification. It is applied the motors surface temperature measuring technique with thermal camera. Comparing measured and calculated temperatures is stated good agreement, and conclusion can be made that complete temperature field in the parts structure is properly calculated. 2. COMBUSTION PRODUCTS FLOW CALCULATION First of all, released propellant s heat amount depends on combustion products thermal and flow characteristics. The dominant characteristic is combustion temperature, which depends on the propellants energy potential. Temperature has strong influence on flow parameters, particularly on flow velocity. The products flow parameters, like velocity field, boundary layers and turbulence characteristics, can be reliable calculated, even in complex flow domains. This can be achieved by using some of computational fluid dynamic methods (CFD), like is described in [1]. Input parameters for this calculation are the products thermophysical characteristics, the motor internal ballistics parameters and geometry. The most important products thermo-physical characteristics are combustion temperature, molecular weight, viscosity, specific heat and thermal conductivity. Some of these characteristics dependence from flow 1

2 temperature can be obtained by thermo-chemical calculation, based on propellants chemical composition [2]. In this examination is used double-based propellant with combustion temperature T c = 2300 K, and molecular weight M = 23.5 kg/kmol. Specific heat, thermal conductivity and viscosity change versus temperature is shown in picture 1. Picture 1. Thermo-physics characteristics of combustion products specific heat, thermal conductivity and dynamic viscosity. Necessary internal ballistics parameters for this calculation can be defined with mass flow rate or total pressure on flow domain inlet surfaces. These parameters can be determined by internal ballistics calculation [3] or can be measured in experiments. Turbulence parameters are also important, and they can be obtained by semiempirical equation [4]. These parameters are imported in calculation like boundary conditions. Picture 2. Rocket motor used in experiment. The motor geometry is shown in picture 2. Flow parameters depend from domain geometry. Nozzle throat area defines combustion chamber pressure; nozzle geometry defines flow parameters on exit area and from space complexity depend flow losses, turbulence intensity and boundary layer characteristics. Totality of these input characteristics defines the products flow parameters in the flow domain: velocity, pressure, temperature, density, turbulence parameters etc. With obtained flow field, heat transfer calculation can be conducted for separated parts or for whole motor. 3. HEAT TRANSFER CALCULATION Rocket motor heat transfer has been object of extensive research in past century. To present time, it is accumulated enough knowledge so this process can be quality mathematically modeled, and obtained complete design methods. All three types of heat transfer are present in rocket motors: Conduction through the products and the motor parts, Convection from the products to inner motor walls, and from outer walls to surrounding air, Radiation from the products to inner motor walls and from outer walls to the atmosphere. Conduction is diffusion type process of heat transfer trough material, solid or fluid, which is conditioned by material properties thermal conductivity, specific heat capacity and density. Conduction calculation always comes to solving of energy conservation equation (first law of thermodynamics). In this equation conduction is diffusion term which contributes to energy change proportionally to temperature difference and thermal conductivity [1]. Convection is more complex process, which mainly depends from flow parameters. As mentioned, CFD methods enable precise flow and turbulence parameters calculation in boundary layers, which are necessary for convection coefficient calculation. The motor examination is conducted in static experiment. It is assumed that convection is natural from nozzles outer walls, and is adopted recommended convection coefficient α = 50 W. Convective heat fluxes though mk outer walls are proportional to wall and atmosphere temperature difference Δ T = Tz Tat : q = αδ T (1). A radiation model in rocket motors is also described in [1]. In the nozzle flow, radiation on inner surfaces can be neglected because of lower products temperature and smaller space. Radiation from the outer nozzle surface is more intense when they reach higher temperatures. In examined motor this is the case because exit area of nozzle is without thermal insulation and reaches more then 1100 K. Radiation heat flux from these surfaces can be calculated as: qz 4 T = εc z (2), where: ε and c o surface emissivity coefficient and black body coefficient [4]. 4. NOZZLE PARTS CHARACTERISTICS The parts conduction calculation precision depends on available material thermo-physics characteristic accuracy. These characteristics are thermal conductivity and 2

specific heat functions of temperature k(t) and c p (T). For many materials used in rocket industry these characteristics are published or available from manufacturers.

Nozzle parts material. Some nozzle parts have function of thermal insulation, like intake, which is made from composite material AG- 4V. This material has ablative property.

Part of the material is evaporating with temperature increase, using part of absorbed heat. In dependence of the products abrasive effect and heat load duration, compact carbonized layer is forming.

3 specific heat functions of temperature k(t) and c p (T). For many materials used in rocket industry these characteristics are published or available from manufacturers. The motors nozzle parts materials scheme is shown in picture 3. according to process dynamic. Used resolution is pixels. Examples of characteristic frames are given in picture 5. Picture 3. Nozzle parts material. Some nozzle parts have function of thermal insulation, like intake, which is made from composite material AG- 4V. This material has ablative property. Behavior of this material is very complex, and extensive research is required in order to model heat transfer in they presence. Part of the material is evaporating with temperature increase, using part of absorbed heat. In dependence of the products abrasive effect and heat load duration, compact carbonized layer is forming. Density and thermal conductivity is decreasing in that layer and its thickness is increasing during the motor work. For calculation in this example is used research [5], which give quantitative assessment of ablative process effect on thermo-physics characteristic (picture 4). Picture 5. Thermal camera frames before, on the end and after motor work. There was problem with the camera sensor saturation, in first examinations. The motors combustion products jets temperature is much higher then camera limit and sensor protection stops recording, until jets despairs. Recording continues after that. The cameras software enables plotting temperature diagrams for chosen control points. In figure 6 are shown position of those points. The software calculates change of temperature for chosen pixels in every frame, and generates diagrams. Sample of those diagrams are shown in picture 10, together with calculated values. Picture 4. AG-4V material effective specific heat and thermal conductivity change vs. temperature. 5. NOZZLE SURFACE TEMPERATURE MEASURING For the motor parts surface temperature measuring is used thermal camera FLIR. The camera can capture the frame of whole motor, and record all surfaces temperature change. Range of temperature is up to 550ºC. The camera speed is up to 30 frames per second, witch is enough Picture 6. Part of frame with control points position. 6. MEASUREMENTS AND CALCULATION RESULTS COMPARATION The control point s positions are identified according to nozzle geometry. They positions are defined in calculation geometry model, like is shown in figure 7. The geometry model is segregated from the motor in order to calculate only the nozzle heat transfer. In this 3

calculation is neglected conduction trough separation plane, what will be discussed later. The geometry model (fig. 7) corresponds to real geometry, but some simplifications were made.

During the motor work, because of thermal dilatations, the gaps mainly disappear, and this effect deteriorates. calculation, only the energy equation is necessary.

This is acceptable approximation, because interior of rocket motor have accumulated heat and high surface temperature long time after burn out.

4 calculation is neglected conduction trough separation plane, what will be discussed later. The geometry model (fig. 7) corresponds to real geometry, but some simplifications were made. Contacts between the parts surfaces are not ideal, and always exists gaps. These gaps can significantly change heat transfer effects. During the motor work, because of thermal dilatations, the gaps mainly disappear, and this effect deteriorates. calculation, only the energy equation is necessary. On the nozzles inner surfaces is set zero heat flux boundary condition. This is acceptable approximation, because interior of rocket motor have accumulated heat and high surface temperature long time after burn out. From that reason convection and radiation from nozzles inner surfaces are negligible. The nozzle parts temperature contours are shown in picture 9, at 100 s from calculations start. The highest temperature is in the throat and the exit cone, and slowly equals in all parts in same time deteriorates with laws defined by (1) and (2). Picture 7. Calculation geometry model with control points and the products velocity contours, at 0 second. More significant simplification is neglecting the gaps in threaded connection, between the nozzle body and top (picture 3). This gaps results with more intense heat flux reduction. It is possible to calculate even this effect, but size, position and shape of gaps in threads are random, so must be taken in consideration like statistics value. Effect of this simplification will be considered during the results analysis. Before heat transfer calculation it is conducted stationary calculation of the products flow, because process of establishing flow field is mach faster then heat transfer. When the flow field is established, unsteady calculation starts with initial condition for temperature of 300 K in all nozzle parts. Calculation was conducted with time step of 0.1 second and with variable total pressure at inlet, according to values measured in combustion chamber in experiment (picture 10). The products velocity contours in first moment are shown in picture 7. In picture 8 are shown temperature contours in 0.1 s. Picture 8. Temperature contours in flow field and the nozzle parts at 0.1 second. The motor stops after 4 seconds, and flow domain can be deactivated. For the nozzle parts thermal conductivity Picture 9. Temperature contours in the nozzle parts at 100th second. In picture 10 are given calculated and measured diagrams of temperature change in control points. In first 4 seconds, during the motors work the camera stops recording. Diagrams in that period are straight lines between values before and after pause. Also control points T1 and T2 reaches temperature higher then cameras limit, in first 30 seconds. Anyway from the rest of diagrams in these points, conclusions can be made about results matching. In points T1 and T2, in the first part of the process, calculation gives about 100 K higher temperatures. In the last part of the process calculation and measurement agrees perfectly. As mentioned, disagreement in the first part appears because of the threads gaps neglecting. The gaps influence decreases because of the thermal dilatation. The top of the nozzle worms up faster and during expansion fills up gaps. This is the case with all gaps, but it is the most influential in the threads areas. The calculation is more uncertain in points T3 to T6, because that parts of nozzle has ablative insulation (picture 3). Like is mentioned, thermo-physics characteristics of this material are not precisely determined, and this calculation shows some incorrectness in used functions. In the first part calculated temperatures are slightly lower then measured, and in the last part higher. Temperature of the motors aft closure is lower then the nozzle, as can be seen on picture 5. This means that exist heat transfer trough segregation plane, witch is neglected in calculation. Because of that reason, calculation gives little higher values of temperature in points T5 and T6. 4

5 Picture 10. Parallel diagrams of measurement (Sp) and calculation (T) temperature for control points in first 55 and 150 seconds; and pressure diagram (P c ). 7. CONCLUSION In this paper is described finite volumes method for heat transfer calculation in rocket motor. This method has advantage because of accurate combustion products flow calculation ability, and this is one of the most important preconditions for quality heat transfer calculation. Second important advantage is possibility for complex geometry heat transfer calculation, what is necessary in many practical cases. In order to verify calculation a simple measurement technique is conducted. Solid propellant rocket motor outer surface temperature was measured with thermal camera. This contactless measurements technique is very efficient, with short preparation period and whole visible objects surface measurement. Applied measurement technique is sensitive on rocket motor jets radiation, witch can temporary deactivate the camera. This can be overrun using camera with high temperature ability, or using deflectors against undesirable radiation. Measured and calculated temperatures have good agreement, despite several simplifications. Firstly, gaps in threaded connections between the motor elements have notable influence on heat transfer. Secondly, calculation domain can be reduced, but appropriate boundary condition must cover influences of omitted regions. Great importance has accuracy of thermo-physics characteristics for applied materials, primarily thermal conductivity. Behavior of ablative thermal insulation material isn t accurately defined, so are used effective functions for thermal conductivity and specific heat. These functions aren t universal, so they can be used only in similar conditions. For other geometry and work parameters they must be specially determined. References [1] Živković, S.: Prilog modeliranju prenosa toplote u raketnom motoru, Eaborat VTI , VTI, Beograd, [2] Filipović, M., Kilibarda, N.: The Calculation of Theoretical Energetic Performances of Composite Rocket Propellants, J. Serb. Chem. Soc., 2001, Vol.66 (2), [3] Živković, S.: Metode proračuna potiska u procesu optimizacije sistema upravljanja vektora potiska, Jugoslovenski komitet za eksplozivne materije, Bar, [4] Добровольски, М.: Жидкостные ракетные двигателеи, Москва, [5] Pavlović, P., Hrabar, J.: Ispitivanje ablacionih karakterist. kompozitnih termozaštitnih materijala na bazi fenolformaldehidnih smola, XIV simpozijum o eksplozivnim materijama, Čačak,

Departures from Ideal Performance for Conical Nozzles and Bell Nozzles, Straight-Cut Throats and Rounded Throats Charles E. Rogers

Departures from Ideal Performance for Conical Nozzles and Bell Nozzles, Straight-Cut Throats and Rounded Throats Charles E. Rogers This article covers departures from ideal performance for conical nozzles