The numerical research of the gas flow in the exhaust duct of the gas turbine with a waste heat boiler

1. Introduction

Nowadays, gas turbines are widely used as primary engines for various units in the power range from 6 to 50 MW; for example, they are employed for electric power generation and gas turbine-powered compressor setups. The majority of modern day gas turbine engines, for the areas mentioned, are built on the base of converted aircraft engines. It defines the basic characteristics and parameters of the working process: a simple thermodynamic cycle, high pressure ratio in the cycle and the high initial temperature of the gas. The main disadvantage of such engines is large energy losses from the exhaust gases.

For such gas turbine engines, the recycling superstructures are actively developing, such as heat exchangers installed in the exhaust path of the engine, in which exhaust heat is used to heat water, air or oil, or for a steam generation [1], [2], [3], [4], [5].

As in the combination, and cogeneration engines, one of the most important elements that determines the efficiency of the recycling cycle is a heat exchanger – waste heat boiler. The installing of a waste heat boiler is possible even at the operating power or drive gas turbines, by a simple modification of the equipment – replacing regular muffler in the exhaust system to waste heat boiler.

Waste heat boiler, developed by the company JSC RPCE “Turbocon” [1], [2], allows to simplify the structure and reduce the weight and size of heat exchanger for gas turbine as compared with classic heat recovery boiler. This is achieved by installation of a compact gas turbine exhaust system of the heat exchanger, in which the gas transfers its heat to the high-pressure water, followed by its expansion and release of the steam for the steam turbine.

Waste heat boiler should have a compact and simple design and a high energy efficiency. If we consider a heat recovery heat exchanger as a part of the exhaust duct of the gas turbine setup, then, it is important to minimize the total pressure losses. Increase of these losses causes a pressure increase at the turbine outlet and, therefore, a decrease in the gas turbine unit power. The losses in the gas duct waste heat boiler consist of the pressure loss in the tube bundle and the losses in the inlet and outlet channels. To design an efficient combined setup we need to optimally arrange the waste heat boiler in the engine exhaust.

The current investigation focuses on the study of total pressure loses of engine exhaust, and optimization of the gas flow in the gas duct of the waste heat boiler.

2. Design analysis overview

A gas flow in the exhaust duct of the gas turbine setup GPA-C-16, produced on the basis of the gas turbine engine NK-16ST (JSC “KUZNETSOV”) (Fig. 1), has been investigated. The engine exhaust duct includes the volute with the exhaust axial-radial diffuser and the exhaust stack that represents a rectangular diffusor channel. At the outlet section, the diffuser silencer or the waste heat boiler is installed. For alignment of a flow in the outlet diffuser section, the honeycomb is mounted.

Waste heat boiler, developed by the company JSC RPCE “Turbocon”, consists of the two parallel sections of finned tubes installed in the heat exchanger. Fig. 2(a) shows a drawing of the heat-recovery module. The tube bundle has a staggered arrangement: 27 rows of tubes in the depth of the tube bundle and 42 rows of tubes across a gas flow. Fig. 2(b) shows the finning parameters.

Two modules of the heat exchanger are installed in the common casing. Its longitudinal dimension is determined by the length of the tube sections, and the transverse dimension - by the total width of the sections plus the width of the bypass channel. The height of the heat exchanger body is equal to the height of regular muffler exhaust tract. Basic geometric dimensions of the enclosure heat exchanger are presented in Fig. 3.

Two cases were investigated:

Case A: heat exchanger modules are located symmetrically in the middle of the heat exchanger casing; the side bypass channels are arranged on both the sides (Fig. 4a).
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Figure 4. Possible configurations of the two sections of the heat exchanger: (a) case A; (b) case B.
Case B: heat exchanger modules are located along the walls of the heat exchanger casing, and the bypass channel is located in the center (Fig. 4b).

The objective of our study was to obtain the total pressure losses in the exhaust duct for the cases specified. The calculations were done for the two operation regimes: for a gas flow through the heat exchange section with the closed bypass and a flow through only the bypass channels.

3. Computational details

3.1. Governing equations

The computation algorithm is based on the equations of mass, momentum and energy conservation. These equations are formulated in the Cartesian coordinates as follows: $\frac{\partial}{\partial x_{i}} (ρ u_{i}) = 0$ $\frac{\partial}{\partial x_{j}} (ρ u_{i} u_{j}) + \frac{\partial p}{\partial x_{i}} = \frac{\partial}{\partial x_{j}} (τ_{ij} + τ_{ij}^{R}) + S_{i}$ $\frac{\partial ρ u_{i} h^{*}}{\partial x_{i}} = \frac{\partial}{\partial x_{i}} (u_{j} (τ_{ij} + τ_{ij}^{R})) - τ_{ij}^{R} \frac{\partial u_{i}}{\partial x_{i}} + ρ ε + S_{i} u_{i} + W$ where

$τ_{ij} = μ \frac{\partial u_{i}}{\partial x_{j}}$ – tangential stress;
$τ_{ij}^{R} = μ_{t} (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}) - \frac{2}{3} δ_{ij} ρ k$ – Reynolds stress tensor;

The turbulent viscosity μt is calculated as follows: $μ_{t} = C_{μ} ρ \frac{k^{2}}{ε}$ .

where k and ɛ are the turbulence kinetic energy and its dissipation raterespectively.

$h^{*} = h + \frac{u^{2}}{2}$ – total enthalpy;
Si – the force per unit volume introduced to simulate the pressure drop across the finned tubes bundle;
W – thermal power drawn from a fluid flow as a result of the heat recovery.

As a rule, in 3D modeling processes in heat exchangers with finned tubes it is impossible to use detailed predetermined geometrical features of the finned tube bundles for the entire heat exchanger as a whole. This is because the dimensions of the fin and the heat exchanger differ by 1000–10,000 times whereas for an accurate 3D flow modeling the calculated cell size should generally be less than 1/3–1/5 of the thickness of a rib. Therefore, an extremely large number of computational cells representing the heat exchanger are needed. For example, the heat exchanger of dimensions of 6500 × 1080 × 1080 mm with the waste heat boiler at 1 mm thickness of the edges of its heat transfer surfaces approximately requires a number of computational cells to be ∼6500 ∗ 1080 ∗ 1080 ∗ 3 ∗ 3 ∗ 3 = 2.05 ∗ 1011. Such computations cannot be carried out even on most powerful modern supercomputers. Therefore, the area occupied by finned tube bundles is substituted with “shallow” geometry volumetric filters characterized by desired anisotropic properties [6], [7].

For the considered waste heat boiler, installed in the gas turbine exhaust, the heat transfer surfaces were modeled as the volume filters with given anisotropic hydraulic properties. These filters were placed in the area occupied with the finned tube bundles (Fig. 5). The filters provide pre-defined hydraulic characteristics at each point of the heat exchange surface.

For all the investigated cases, the following assumptions were employed for the area of anisotropic filters:

1.
Heat removal represents cooling of a gas passing through the heat exchange surface. Heat removal is introduced to account for an effect of changes of gas properties (density, viscosity, etc.) on flow characteristics.
2.
The x and y velocity components are zero (see Fig. 5).
3.
The total pressure loses in the tube bundle are defined as $Δ p^{*} = f (G)$ , where G is a mass flow rate through the tube bundle.

The total pressure losses of the tube bundle (Fig. 6) were obtained by 3D modeling of flows in the waste heat boiler module. The methods of calculation of the total pressure loss characteristics in the tube bundle are described in [6].

3.2. Boundary conditions

On the computational grid, based on the 3D model of the gas turbine exhaust, the following boundary conditions were imposed (Fig. 7):

The following boundary conditions were applied to the 3D model of the gas turbine exhaust:

1.
The inlet boundary condition is applied to the axial flow from the gas turbine into the axial-radial diffuser of the volute. The mass flow rate: G = 70 kg/s, the gas temperature = 708 K. The gas chemical composition is: g[H2O] = 3.6%; g[O2] = 16%; g[N2] = 76%; g[CO2] = 4.4%.
2.
The walls are assumed to be adiabatic with no gas-solid surface slip. The shear stress between a fluid and the wall is computed based on local flow details.
3.
The outlet boundary condition sets the environmental parameters. These parameters are as follows: p = 101,300 Pa, T = 288 K.

4. Results and discussions

The total pressure value in the control planes (shown in Fig. 8) was calculated for determining the hydraulic losses through the flow path. The average of the parameters in the sections was conducted based on the mass flow rate.